The Yale Journal of Economics

Spring 2014Volume 2, Issue 2

Staff

Editor-in-ChiefAntonia Woodford

Managing EditorMoss Weinstock

Associate EditorsDhruv AggarwalElijah GoldbergJimin He

Copy EditorsJun Hwan RyuJames Austin SchaeferYalun Zhang

Production and Design EditorMadeline McMahon

PublisherBrian P. Lei

Board of AdvisersJoseph G. AltonjiPinelopi K. GoldbergSamuel S. KortumAnthony A. Smith, Jr.

The Yale Journal of Economics

Spring 2014Volume 2, Issue 2New Haven, CTWebsite: http://econjournal.sites.yale.edu/

2

Table of Contents

Editors’ Note 4

Alex Dombrowski(University ofCalifornia, Berkeley)

Returns to Schooling: A CollegeAthlete’s Perspective

7

Stefano Giulietti(Yale)

Contagion in the Eurozone SovereignDebt Crisis

47

Disha Verma(Harvard)

The Socioeconomic Impact of PoliticalFragmentation in India: What theRise of Regional Politics Implies forEconomic Growth and Development

67

Dounia Saeme(University ofCalifornia, Berkeley)

Does the Implementation ofAffirmative Action in a CompetitiveSetting Incentivize UnderrepresentedPublic School Applicants’Performance? Evidence From SãoPaulo

93

Adin Lykken(Yale)

A Question of Intent: Explaining thePerformance of Governments inGlobal Development Projects

115

This journal is published by Yale College students and Yale University is notresponsible for its contents.

A full list of references for the papers in this issue is available on our website.

3

Editors’ Note

Another semester in the books. Now a little more than ayear old, the Yale Journal of Economics is still finding its footingin the academic community—a process that we knew wouldrequire time and, more importantly, effort. Without those, theJournal could never achieve its goal: showcasing original economicresearch performed by undergraduates. We are thankful for theenthusiasm for our project shown by students around the globe,who have continued to submit insightful and innovative papers;we are excited to publish their research here and in future issues.We are also thrilled to expand the Journal’s online presence via aredesigned website that allows undergraduates’ excellent work toreach an even wider audience.

This issue contains five essays written by students at HarvardUniversity, Yale University, and the University of California,Berkeley. In fact, this issue has a bit of a global flavor. To startthe issue, Alex Dombrowski examines a key U.S. institution: theNational Basketball Association. Specifically, he considers theoptimal time for college players to “go pro” by declaring forthe NBA draft. Stefano Giulietti turns his gaze towards Europeand its sovereign debt crisis, using credit default swap spreadsto measure contagion effects across countries. Disha Vermastudies the effects of political fragmentation in India and findsthat coalition governments grow faster, undertake more socialspending, and incur less debt than majority governments. DouniaSaeme investigates Brazil’s college entrance examination systemto see how the implementation of affirmative action incentivizespublic school students in São Paulo. Completing the issue, AdinLykken’s research spans the globe; he analyzes the performance ofgovernments that complete projects financed by the World Bank,and concludes that improving project supervision may be themost effective way to yield better project outcomes.

We also need to thank the generous donors whosecontributions make the Journal possible. In addition to theYale Department of Economics and the Yale UndergraduateOrganizations Committee, Stephen Freidheim ’86 and DavidSwensen GRD ’80 made substantial contributions that allow us

4

to continue to produce the Journal and distribute it free of charge.Thanks to their support, we have published the Journal two timesthis academic year, this spring and last fall. Finally, we would liketo thank the members of our advisory board for their guidanceduring the publishing process. Together, we hope to bring theJournal to new heights.

5

6

Returns To Schooling: A College Athlete’sPerspective

Alex Dombrowski, University of California, Berkeley1

Abstract. Two decades ago, 90% of the National BasketballAssociation (NBA) college draftees had completed their senioryear of college. Today that number is only 30%. College basketballplayers are making the jump to the NBA earlier on, after theirfreshman, sophomore, or junior seasons. This paper uses bothempirical and theoretical frameworks to study a player’s decisionof when to "go pro." I estimate returns to schooling by comparingthe earnings of two groups of NBA players: those who went proout of high school or immediately after freshman year of collegefrom 1989 to 2005 versus those who went pro immediately afterfreshman year from 2006 to 2012. A new rule was implementedin 2005 that forced players to wait at least one year after their highschool graduation before going pro. Thus, 2005 was the last yearwhen players could move directly from high school to the NBA,and the latter group contains players who were forced to completean additional year of school. I find no significant difference inearnings between the two groups.

Keywords: returns to schooling, optimal stopping, NBA

1Alex Dombrowski is a senior at the University of California, Berkeleymajoring in mathematics, statistics, and economics. He wrote this senior honorsthesis for Professor David Card. He would like to thank Professor Card for histime and support.

7

1 Introduction

In economics, returns to schooling are commonly thought of as theexpected change in earnings due to an additional year of school.So for example, an undergraduate considering whether or notto pursue graduate study may like to know the expected salarydifference from getting those additional years of education.

This paper approaches returns to schooling from theperspective of a college athlete. In particular, I consider collegebasketball players, but as a motivating example and illustration ofthe widespread nature of this phenomenon, consider the footballplayer Matt Barkley. Barkley, a member of the class of 2013,was a quarterback at the University of Southern California (USC)where he had a phenomenal junior season. Speculators thoughthe would forego his senior year at USC to go directly intothe National Football League (NFL). Instead, Barkley opted tostay at USC for his senior year, intending to go pro right after.Unfortunately, his senior year performance was not nearly ascompelling and he was drafted much lower. His contract wasestimated to be worth millions of dollars less than if he had gonepro after junior year. In Barkley’s case, his returns to schooling forthat year were negative.2

The composition of the NBA draft from 1989 to 2012 shownin Figure 1 illustrates how players have been going pro earlier. Ineach draft, the 30 teams each select two players, for a total of 60players moving from college into the NBA. Throughout the early1990s, around 90% of those drafted were seniors. This percentagehas fallen dramatically over the last two decades. In 2012 only35% of those drafted were seniors.

So why strategize about when to leave college and go pro? Ifa collegiate basketball player enters the NBA draft, he foregoeshis remaining college eligibility regardless of whether or not he isdrafted.3 For example, if a freshman enters the draft, he can no

2There are of course other benefits to finishing senior year (e.g. earningthe degree), but here I focus solely on maximizing the player’s earnings as aprofessional athlete.

3If the player does not sign with an agent, has never applied for a previousNBA draft, and withdraws his name from the draft by the deadline, then hecan retain his eligibility. However, the National Collegiate Athletic Association(NCAA) rules only allow players to enter the draft once without losing eligibility.

8

Figure 1: Draft Composition 1989-2012

longer play college basketball even if he is not drafted.The paper is laid out as follows: Section 2 gives a brief

literature review. Section 3 is an overview of the NBA. Section 4 isa study testing the effect of playing an additional year of collegebasketball on earnings. Sections 5, 6, and 7 contain the theoreticalframework. Section 8 concludes.4

2 Literature Review

There are a few notable papers that discuss contracts and earlyentry. Li and Rosen (1998) analyze when and why contractsare made early. Winfree and Molitor (2007) analyze returns toschooling for baseball players. In particular, they focus on a recenthigh school graduate’s decision of whether to go to college orgo directly into the Major League. Arel and Tomas (2012) viewdeclaring for the NBA draft as exercising an American-style "putoption" early.

4All figures throughout this paper are original.

9

3 Overview of the NBA

The NBA can be viewed as a labor market where each yearthe 30 teams (firms) hire 60 players (employees) from a poolof players, most of whom live in the United States. The NBAplayers have a labor union, called the National Basketball PlayersAssociation (NBPA), which negotiates rules with the League,which is comprised of the commissioner and team owners.Every few years, the League and NBPA form a new CollectiveBargaining Agreement (CBA), which lays the foundation for howthe NBA is governed. The CBA contains information abouthow the draft works, how basketball revenue is allocated amongthe players and the League, and the minimum and maximumamounts a team can pay its players. For example, the 1995 CBAintroduced the “rookie pay scale," which structured how incomingplayers would be paid. Players drafted in the first round areguaranteed a two-year contract, followed by two one-year teamoptions. Players drafted in the second round are not guaranteedcontracts. Also, being picked later in the draft results in lower pay.

The NBA draft is held annually at the end of June. Startingin 1989, the draft instituted a two-round system, in which eachteam selects one player in each round. This new drafting systemis the main reason I focus on draft data beginning in 1989. Iconstructed a dataset of 1,382 players who were drafted from 1989to 2012.5 Data were collected from www.basketball-reference.comand verified using basketball.realgm.com. During the 24 draftyears from 1989 to 2012, 53.11% of the 1,382 players drafted wereseniors, 14.40% were juniors, 14.26% were international, 9.62%were sophomores, 5.79% were freshmen, and 2.82% were highschool seniors.

4 Returns to Schooling: An Additional Year

The 2005 CBA made 2005 the last season in which a high schoolplayer could go directly into the NBA. Beginning in 2006, a playerhad to be one year removed from high school before going into

5Although there were 30 total teams in 2012, at the beginning of 1989 therewere only 27. Consequently, earlier drafts saw fewer than 60 players drafted.

10

the NBA.6 Figure 2 shows how the numbers of high school seniorsand college freshmen have evolved in drafts dating back to 1989.The dark line falls to zero in 2006 as a result of the new CBA. In2007, the light line spikes from two to eight. This spike representsthe 2006 high school class that was forced to play a year in college,along with a couple of 2006 high school graduates who wouldhave chosen to play their freshman year even without the newrule. Thus, the light line post-2005 can be thought of as a mergingof the pre-2006 dark line and the pre-2006 light line. In this study, Iexplore differences in earnings between the following two groupsof players: freshmen and high school seniors drafted in 1989-2005versus freshmen drafted in 2006-2012. The first group, which I

Figure 2: Number of High Schoolers and Freshmen Drafted

call the “pre-law” group, has 67 players. The second group, the“post-law” group, has 52 players. Of these 119 players, three neverplayed a game in the NBA and were removed from the data.7Table 1 provides a detailed comparison of these two groups.

From Table 1, we can informally compare the statistics of the

6The player doesn’t have to attend college for that year; however, attendingcollege for that year is standard.

7Ousmane Cisse (2001 draft), Ricky Sanchez (2005 draft), and Keith “Tiny”Gallon (2010 draft) never played in the NBA.

11

Tabl

e1:

Com

pari

son

ofPr

e-la

wan

dPo

st-la

wG

roup

Perf

orm

ance

1989

-200

520

06-2

012

Car

eer

Stat

istic

sM

ean

Med

ian

SDM

ean

Med

ian

SDG

ames

Play

ed54

8.9

560.

032

3.9

193.

417

0.5

129.

9M

inut

esPl

ayed

1574

014

250

1155

7.1

4883

3568

4176

.8To

talP

oint

s75

5657

0967

50.9

2201

.014

00.0

2281

.2To

talR

ebou

nds

3129

.025

16.0

2785

.288

4.0

601.

084

6.6

Tota

lAss

ists

1302

.084

0.0

1464

.442

5.9

156.

054

9.6

Fiel

dG

oalS

hoot

ing

Perc

enta

ge0.

4439

0.45

400.

092

0.44

540.

4455

0.08

833

Poin

tSho

otin

gPe

rcen

tage

0.26

260.

3130

0.15

410.

2471

0.29

850.

1458

Free

Thro

wSh

ootin

gPe

rcen

tage

0.70

070.

7410

0.15

571

0.68

580.

7330

0.15

06M

inut

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rG

ame

23.8

024

.90

9.98

2221

.95

21.4

59.

3834

Poin

tsPe

rG

ame

10.9

19.

906.

4508

9.42

58.

250

5.72

59R

ebou

nds

Per

Gam

e4.

679

4.20

02.

7339

94.

015

3.65

02.

5015

Ass

ists

Per

Gam

e1.

858

1.50

01.

5396

1.86

21.

200

1.82

57C

aree

rLe

ngth

(yea

rs)

9.26

99.

000

4.26

93.

481

3.00

01.

862

12

two groups. Since the pre-law group has players with longercareers than those in the post-law group, it may be more difficultto compare statistics like points and total rebounds. To comparethese, note that the median career length of the pre-law groupis three times that of the post-law group. Thus, multiplyingthe post-law group’s total points by three may give a reasonablenumber to compare to the pre-law group’s total points. For a finercomparison, use minutes played instead of career length. Themedian minutes played of the pre-law group is four times that ofthe post-law group. Thus, numbers could be scaled appropriatelyby a factor of three to four to make more accurate comparisons.

4.1 Analysis of Earnings

Salary data were collected from www.basketball-reference.comand checked againsthttp://www.eskimo.com/⇠pbender/.8 Salaries were put intoreal 2013 dollars using CPI numbers from the Federal ReserveBank of St. Louis. Figure 3 shows how earnings have evolvedthroughout this time period. All 116 players are plotted, with eachplayer represented by a line. The light lines are the pre-law playersand the dark lines are the post-law players. The figure is meant togive a general sense of how earnings progress as the players gainmore years of experience. Notable players Kevin Garnett (1995draft), Kobe Bryant (1996 draft), and Kevin Durant (2007 draft)are highlighted.

Figure 4 is a condensed version of Figure 3. Figure 4 illustratesthe difference in earnings between the pre-law and post-lawgroups. Average earnings in real 2013 dollars are plotted againstcareer year. So for example, the post-law group (dark line) forcareer year one corresponds to the average earnings of players inthat group during their rookie year.

In career year 1, the post-law group earned on average$580,000 more than the pre-law group. In career year 2, the post-law group earned on average $480,000 more than the pre-lawgroup. In career year 3, the post-law group earned on average$270,000 more than the pre-law group. In career years 4 and 5,

8For the NBA lockouts in 1998 and 2011, I used the full years’ earnings, notthe prorated salary.

13

Figure 3: Annual Earnings

the pre-law group out-earned the post-law group by $270,000 and$1,250,000 respectively.9

Draftees often hire agents to negotiate their rookie contracts.The rookie pay scale is not completely rigid: The team can paybetween 80% and 120% of the salary specified by the rookie payscale. However, nearly all contracts end up at 120%. Arel andTomas (2012) find that, of the players drafted in the first roundbetween 2006 and 2012, 98% had contracts for 120% of the amountspecified by the rookie pay scale. Therefore I did not control forthe quality of the agent in the analysis.

The following two subsections use a two sample z-test andMann-Whitney test to determine if the difference in earningsbetween the two groups is significant.

9I don’t analyze career years 6 and 7 in detail because there are less than 10players from the post-law group who played six or more years, and only twowho played all seven.

14

Figure 4: Average Earnings of Pre-law and Post-law Groups

4.1.1 Parametric Two Sample Z-Test

The test assumes X1, . . . , Xniid⇠, N(µX , s2), and Y1, . . . , Ym

iid⇠N(µY , s2) where s2 is estimated by a pooled variance:

s2p =

(n � 1)s2X + (m � 1)s2

Ym + n � 2

where s2X =

1n � 1

n

Âi=1

(Xi � X)2. (1)

In this case, the observations Xi, Yi are the annual earnings of eachplayer for some specified year. The observations are reasonablyindependent and identical. The histograms in Figure 5 showthe distribution of earnings for each group in the first two years.Though the data are not convincingly normal, the next section’sanalysis uses the nonparametric Mann-Whitney test and givesvery similar results to this two sample z-test.

Table 2 gives the results from this two sample z-test (two-sided) for career years 1 through 5. In each test, the nullhypothesis is:

H0 : µXj = µYj j = 1, 2, 3, 4, 5 (2)

where for example µXj is the mean of the distribution of earnings

15

Figure 5: Earnings in Years 1 and 2 for the Pre-law and Post-lawGroups

Pre-law group earnings in year 1 are on the top left, pre-law group earnings in year 2 areon the bottom left, post-law group earnings in year 1 are on the top right, and post-lawgroup earnings in year 2 are on the bottom right.

in career year j for the pre-law group.The difference in earnings between the two groups during

career year 1 is significant at the 5% level. The difference inearnings between the two groups during career year 2 is just shyof being significant at the 10% level. The other tests do not yieldsignificant results.

4.1.2 Nonparametric Mann-Whitney Test

The Mann-Whitney test is nonparametric, which means itmakes no assumptions about the underlying distribution of theobservations. The test instead ranks the observations fromsmallest to largest and compares the sum of ranks. The nullhypothesis is that the treatment has no effect, where in this casethe treatment is the additional year of school the post-law groupexperienced. Table 3 has the results, which are similar to those inTable 2. Again, the post-law group’s average earnings in careeryear 1 are significantly higher than the pre-law group’s averageearnings in career year 1.

16

Table 2: Results of Two Sample Z-Test

Career year t-statistic p-value1 2.12749991 0.033378572 1.6017363 0.10921393 0.8169752 0.41394264 -0.3234246 0.74637375 -0.9189319 0.3581312

Table 3: Results of Mann-Whitney Test

Career year t-statistic p-value1 -2.06083935 0.039318372 -1.6164613 0.10599463 -0.7660718 0.44363364 -0.7233642 0.46945615 -0.7660718 0.4436336

4.2 Linear Regression Model

The following model is the form for the regressions:

(3)ln Earningsi = b0 + b1Si + b2Abilityi+ b3Draft picki + b4Experiencei + ei

The dependent variable Earnings varies from regression toregression. S is an indicator variable taking on zero for the pre-law group and one for the post-law group. Ability is measuredby rookie year statistics: minutes played, points, assists, andrebounds. Experience is measured by a player’s total career points.Experience can be thought of as long term ability, controlling forwhatever the ability regressor doesn’t. Table 4 gives the results.

Table 4 has four regressions. The choice of regressionsis unconventional in the sense that all regressions use thesame set of regressors, but have different dependent variables.Instead of settling on one measure for earnings, it seemed moreappropriate to give several measures. The dependent variablesin regressions (1) and (2) are Career Average Yearly Earnings andYear 1 Earnings; dependent variables in regressions (3) and (4) areEarnings in First 2 Years and Earnings in First 3 Years.

17

For all regressions, the coefficient of Year of School Dummy isnot significant. Thus, in these tests, there is no evidence thatsupports that one group had significantly different earnings thanthe other group.

The results of regressions (2), (3), and (4) are very similar,mostly because of the rookie pay scale, which was introduced in1995.10 Under the new contract system, earnings in years 1 and 2are highly correlated.11

In each regression, Draft Pick is significant at 1%. This isnot surprising for regressions (2) and (3), because, as a playeris drafted later, his pay will decline according to the rookie payscale. It is not as obvious why Draft Pick is significant in regression(1) where Career Average Yearly Earnings is the dependent variable.The coefficient of Draft Pick in regression (1) is �0.024, which issmaller in absolute value than the corresponding coefficient inthe other three regressions. This is consistent with the rookiepay scale’s influence on average career yearly earnings becomingdiluted because of the expiration of the contract and room formore variability in earnings in later years.

The regressions highlight the importance of draft pick onaverage yearly earnings throughout a player’s career. Regression(1) estimates that being drafted one position later leads to a2.4% decrease in average career earnings, on average. Table 5summarizes how each group was drafted. A Mann-Whitney teston the draft number for the pre-law and post-law groups yieldeda p-value of 0.16. Thus, there is no evidence that suggests draftpositions are significantly different between the two groups.

5 Optimal Entry

A major concern for college players is when to go pro. Playersmay play all four years of college basketball or may opt to enterthe draft early. Once a player declares for the draft, he can neverplay college basketball again, regardless of whether he is drafted

10Although this data set of 116 players encompasses the time period 1989-2012,only 3 players were drafted before 1995: Shawn Kemp (1989), Shawn Bradley(1993), and Dontonio Wingfield (1994).

11Of the 116 players, 104 played at least 2 years. The correlation between theseplayers’ earnings in years 1 and 2 of their career is 0.996.

18

Tabl

e4:

The

Effe

ctof

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dditi

onal

Year

ofSc

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ing

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Dep

ende

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(1)

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0.09

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088

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7(0

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)(0

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)

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utes

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19

Table 5: Summary of Draft Pick Number

Group Min 1st Qu. Median Mean 3rd Qu. MaxPre-law 1.00 6.00 13.00 17.98 26.00 56.00Post-law 1.00 4.00 11.00 14.75 22.00 49.00

to an NBA team or not. A very talented underclassman maywant to enter the draft early for many reasons. He may havehad an outstanding season or his team may have won the nationalchampionship. He could have received a prestigious award like“Most Valuable Player" or may be concerned his performance willbe worse during his later years of college. He could also getinjured in a later season. There are many cases in which collegeathletes went pro at the “wrong time." Hence, we would like toanalyze optimal entry.

Consider a college player wanting to go pro. He wants to bedrafted high, not low (i.e. in the first round rather than the secondor third round).

Let:

PH := probability of being drafted high,PL := probability of being drafted low,

EH := high career earnings (when drafted high),EL := low career earnings (when drafted low),

where EH > EL > 0. Consider a player seeking to go pro andassume this player won’t go undrafted.12 That is, PH + PL = 1.Suppose that PH and PL depend only on that player’s skill level,S. Thus,

PH = PH(S) and PL = PL(S), (4)

where these two functions have the property

dPH

dS> 0 and

dPL

dS< 0, (5)

since a player’s chance of being drafted high should be

12Relaxing this assumption leads to the same conclusion. See Appendix forproof.

20

monotonically increasing in his skill level. Likewise, a player’schance of being drafted low should decline as the player’s skillincreases. A player’s skill level will vary over time as heprogresses through college. So letting y denote years of collegeexperience we have

S = S(y) y 2 [0, 4], (6)

where y = 2 ,for example, corresponds to 2 years of experience.Let the player have a utility function, u(e), where e is careerearnings as a professional with u0(e) > 0 and u00(e) < 0. Inother words, the player’s utility is increasing and concave inhis career earnings. Thus, to maximize utility, it is sufficient tomaximize expected career earnings, E(e). Therefore, we have theoptimization problem,

(7)maxy

E(e) = maxy

hPH(S) · EH + PL(S) · EL

i

From (4), (7) becomes

(8)maxy

PH(S(y))EH +

⇣1 � PH(S(y))

⌘EL

�

The solution to (8) involves making PH(S(y)) as large as possible,which occurs when S(y) is as large as possible. Let us verify thatthis is indeed the case. The first order condition says,

(9)

ddy

PH(S(y))EH +

⇣1 � PH(S(y))

⌘EL

�

= EHP0H(S(y))S0(y) � ELP0

H(S(y))S0(y)= (EH � EL)P0

H(S(y))S0(y)= 0

By assumption, EH > EL and so EH 6= EL. Also by assumption,PH(S) is monotonically increasing, and hence P0

H(S) 6= 0 for all S.Therefore,

(EH � EL)P0H(S(y))S0(y) = 0 () S0(y) = 0 (10)

Let y⇤ be such that S0(y⇤) = 0 and S00(y⇤) < 0. Then y⇤ denotes thenumber of years of college experience that maximizes skill level.

21

Claim:max

yLyyRE(e) = E(e)|y=y⇤ (11)

provided that y⇤ is the absolute maximum of S(y).

Proof : We already know S0(y⇤) = 0 which makes y⇤ a criticalpoint of E(e). So we must check

d2ydy2 [E(e)|y=y⇤ ] < 0 (12)

From (10),

(13)

ddy

(EH � EL)P0

H(S(y))S0(y)�

= (EH � EL)

P0H(S(y))S00(y)

+ S0(y)P00H(S(y))S0(y)

�

Letting y = y⇤,

(14)= (EH � EL)

P0H(S(y⇤))S00(y⇤) + (S0(y⇤))2P00

H(S(y⇤))�

Since by assumption S0(y⇤) = 0 this becomes

= (EH � EL)P0H(S(y⇤))S00(y⇤) (15)

By assumption, EH > EL and S00(y⇤) < 0. Also, P0H(S) > 0 for all

S. So in particular, P0H(S(y⇤)) > 0. Therefore,

(EH � EL)P0H(S(y⇤))S00(y⇤) < 0. (16)

From (16) we conclude

maxy

E(e) = E(e)|y=y⇤ for 0 < y < 4. (17)

Now evaluate expected earnings at the boundary and compare to

22

E(e)|y=y⇤ . Let yB generically denote either yL or yR. Then

(18)

E(e)|y =y⇤ > E(e)|y=yB

() PH(S(y⇤))EH +h1 � PH(S(y⇤))

iEL

> PH(S(yB))EH +h1 � PH(S(yB))

iEL

() PH(S(y⇤))EH � PH(S(y⇤))EL> PH(S(yB))EH � PH(S(yB))EL

() EL

PH(S(yB)) � PH(S(y⇤))

�

> EH

PH(S(yB)) � PH(S(y⇤))

�

Since EL < EH,

() PH(S(yB))� PH(S(y⇤)) < 0 (19)

Since P0H(S) > 0,

() S(y⇤) > S(yB) (20)

Therefore to maximize expected career earnings, and henceutility, a player should go pro when his college skills are best. Thisconclusion is simple. The complication is that a player does notknow when his skills will be best. He may have a great freshmanyear and expect to get better, but actually have worse years laterin college. Players don’t know when S(y) is at its maximum, justlike stock market agents don’t know when the price of a stock is atits maximum. This naturally leads to random walks and optimalstopping rules, which are considered next.

6 Stochastic Model

In the previous section, we concluded that a player can optimizeexpected career earnings by strategically entering the draft whenhis skill level is highest. Thus we should analyze how skill levelmoves from year to year and find when it’s likely to be highest.

23

Let Sn be skill level after n years of experience and let {Sn, n =1, 2, 3, 4} be a random walk defined by

Sn+1 = Sn + µ + e, (21)

where e ⇠ N(0, s2) and the jumps from year to year areindependent. e allows for variation in the amount of skillgained. µ represents a drift and is thought of as the baselineamount of skill gained from year to year. Typically µ > 0, sowe make this assumption in the algebraic solution, though thesimulations in section 6.2.3 allow for µ 0. Note that S(y) is morenaturally thought of as being continuous since a player’s skillevolves (perhaps continuously) throughout his career. However,we can consider our discrete time analysis as using only thevalues S(1), S(2), S(3), and S(4) of the continuous time S(y). Theprobability that skill increases over a year is given by

P(Sn+1 > Sn) = P(Sn + µ + e > Sn)= P(e > �µ)= 1 � F(�µ)= F(µ)

(22)

where(23)F(µ) =

Z µ

�•

1sp

2pe�

12 ( x

s )2dx.

The conditional expectation and variance are

E(Sn+1|Sn) = E(Sn + µ + e | Sn) = Sn + µ (24)

andVar(Sn+1|Sn) = Var(Sn + µ + e | Sn) = s2. (25)

Next, consider the maximum value of the random walk. Define“probability functions” Pi to be

Pi = P⇣

max{S1, S2, S3, S4} = Si

⌘, i = 1, 2, 3, 4. (26)

We would like to find expressions for Pi. For µ = 0, theexpressions are simple. However, for µ > 0, the expressions aremessier. The following solves for Pi when µ = 0, gives an outline

24

of the solution for Pi when µ > 0, and provides a simulation thatillustrates the estimated solution for Pi for all µ.

6.1 No Drift (µ = 0)

Let’s find expressions for Pi, i = 1, 2, 3, 4 when µ = 0. To simplifythe notation, let p = F(µ), the probability the random walk goesup. Since µ = 0, we could use p = F(µ) = F(0) = 1/2; however,the next subsection generalizes these expressions, so we do notexplicitly use 1/2 here. The following lemma illustrates the logicused in this section.

(Lemma 6.1) For the walk Sn+1 = Sn + e, P(max{S0, S1, S2} = S1) =p(1-p).

Verification:

P(max{S0, S1, S2} = S1) = P(S1 > S0, S1 > S2)= P(S1 > S2|S1 > S0)P(S1 > S0)= P(S1 > S1 + µ + e)F(µ)= P(e < �µ)F(µ)= (1 � F(µ))F(µ)= (1 � p)p

(27)

Now let’s find P1, the probability that S1 is the maximum(i.e. the player’s skill is highest after freshman year). S1 is themaximum in four cases: the walk goes

1. down down down

2. down down up, with the two down steps being larger thanthe up step

3. down up down, with the first down step being larger thanthe up step

4. down up up, with the down step being larger than the twoup steps

25

Thus,

(28)

P1 = (1 � p)3 + p(1 � p)2 · P⇣

N(0, 2s2)

> N(0, s2)⌘

+ p(1 � p)2 · P⇣

N(0, s2)

> N(0, s2)⌘

+ p2(1 � p) · P⇣

N(0, s2)

> N(0, 2s2)⌘

,

where we’ve used the fact that N(0, s2) + N(0, s2) d= N(0, 2s2).Also, by symmetry, if X ⇠ N(0, s2

X) and Y ⇠ N(0, s2Y), then

P(X < Y) = P(X > Y) = 1/2 8 sX , sY . (29)

From (28), using (29) and simplifying gives

(30)P1 = (1 � p)3 +

p2

(1 � p)2 +p2

(1 � p)2 +p2

2(1 � p)

! P1 = 1 � 2p +32

p2 � 12

p3

Continuing in this manner, let’s find P2, P3, P4. S2 is themaximum in two cases: the walk goes

1. up down up, with the down step begin larger than the lastup step

2. up down down

Thus,

(31)

P2 = p2(1 � p) · P⇣

N(0, s2)

> N(0, s2)⌘

+ p(1 � p)2

! P2 = p � 32

p2 +12

p3

S3 is the maximum in two cases: the walk goes

1. down up down, with the up step greater than the first downstep

2. up up down

26

Thus,

(32)

P3 = p(1 � p)2 · P⇣

N(0, s2)

> N(0, s2)⌘

+ p2(1 � p)

! P3 =12

p � 12

p3

S4 is the maximum in four cases: if the walk goes

1. up up up

2. down down up, with the up step larger than the sum of thetwo down steps

3. down up up, with the sum of the two up steps larger thanthe down step

4. up down up, with the last up step larger than the down step

So,

(33)

P4 = p3 + p(1 � p)2 · P⇣

N(0, s2)

> N(0, 2s2)⌘

+ p2(1 � p) · P⇣

N(0, 2s2)

> N(0, s2)⌘

+ p2(1 � p) · P⇣

N(0, s2)

> N(0, s2)⌘

! P4 =12

p +12

p3

As a sanity check, let us verify that

P1 + P2 + P3 + P4 = 1 (34)

Summing (30)–(33),⇣

1 � 2p +32

p2 � 12

p3⌘

+⇣

p � 32

p2 +12

p3⌘

+⇣1

2p � 1

2p3⌘

+⇣1

2p

+12

p3⌘

= 1+⇣�2+1+

12

+12

⌘p+

⇣32� 3

2

⌘p2 +

⇣� 1

2+

12

+�12

+12

⌘p3

= 1(35)

27

Equations (30)-(33) are only valid for p = 1/2, as assumed in thissection. Evaluating these four expressions when p = 1/2 gives

P1 = 5/16P2 = 3/16P3 = 3/16P4 = 5/16

(36)

Hence when a player has no drift in skill, the probability his skillwill be highest after freshman year is 5/16, after sophomore yearis 3/16, after junior year is 3/16, and after senior year is 5/16. Theassumption of no drift may hold for some players, but it is morerevealing to incorporate drift and build the full model.

6.2 Probability Functions with Positive Drift (µ > 0)

We want to find expressions similar to (30)-(33) which relaxthe assumption of zero drift. The process for constructing theanalogue to (30) is the same. That is, there are still the same fourways S1 could be the maximum. However, the second, third, andfourth ways will have a different form.

Three problems need to be solved: cases 2, 3, and 4 from (30).

1. The probability the walk goes down down up, with the twodown steps being larger than the up step.

2. The probability the walk goes down up down, with the firstdown step being larger than the up step.

3. The probability the walk goes down up up, with the downstep being larger than the two up steps.

After finding 1, 2, and 3, these values can be substituted in(30) to get the new P1. Similarly, substituting these values (ortheir complements) into the old expressions for the other Pi willgive the new probability functions. We begin with case 2.

6.2.1 Case 2

The task here is to find the probability of the walk going down,up, down, with the first down step being larger than the up step.

28

Keeping with the same notation, let the probability of an up jumpbe p = F(µ). Let A be the event the walk goes down, then up, thendown. Let B be the event that the down step is larger than the upstep. Then

P(AB) = P(A) · P(B|A) = p(1 � p)2P(B|A). (37)

So we must solve P(B|A), the probability that the down jump islarger than the up jump, given the walk went down then up onthose first two steps. Let

X = size of the up jumpY = size of the down jump.

(38)

Figure 6: Distribution of How Sampling is Done

First, make X and Y into densities by scaling the originalN(0, s2) by the appropriate factor. The density of X is given by

efX(x) =1

sp

2pe�

12s2 x2 1

F(µ), �µ x < •. (39)

The density of Y is given by

efY(y) =1

sp

2pe�

12s2 y2 1

1 � F(µ), µ y < •. (40)

29

Since we are concerned with |X�µ| and |Y�µ|, shift the densitiesso the support is [0, •). So the density of X becomes

fX(x) =1

sp

2pe�

12 ( x�µ

s )2 1F(µ)

, x � 0. (41)

The density of Y is now given by

fY(y) =1

sp

2pe�

12 ( y+µ

s )2 11 � F(µ)

, y � 0. (42)

Using (41) and (42), compute P(X < Y):

P(X < Y) =ZZ

RfX,Y(x, y) dA R = {(x, y) : x � 0, y > x}

=ZZ

RfX(x) fY(y) dA

=Z x!•

x=0

Z y!•

y=x

1sp

2pe�

12 ( x�µ

s )2 1F(µ)

· 1sp

2pe�

12 ( y+µ

s )2 11 � F(µ)

dy dx

=Z x!•

x=0

1sp

2pe�

12 ( x�µ

s )2 1F(µ)

Z y!•

y=x

1sp

2pe�

12 ( y+µ

s )2

· 11 � F(µ)

dy�

dx.

(43)

The inner integral involves a N(�µ, s2), which can be shifted andscaled to get a N(0, 1).Z x !•

x =0

1sp

2pe�

12 ( x�µ

s )2 1F(µ)

· 11 � F(µ)

h1 � F

⇣ x + µ

s

⌘idx

=1

F(µ)(1 � F(µ))

Z •

0

1sp

2pe�

12 ( x�µ

s )2 ·h1 � F

⇣ x + µ

s

⌘idx

=1

F(µ)(1 � F(µ))

Z •

0

1sp

2pe�

12 ( x�µ

s )2dx �

Z •

0

1sp

2pe�

12 ( x�µ

s )2

· F⇣ x + µ

s

⌘�.

(44)

30

The first integral can be shifted and scaled. The second we do notsolve explicitly:

(45)1

F(µ)(1 � F(µ))

F(µ/s)�

Z •

0

1sp

2pe�

12 ( x�µ

s )2 ·F⇣ x + µ

s

⌘�.

The expression in (45) can be substituted into (37) for P(B|A). Asa sanity check on (45), plug in µ = 0 and s = 1. Then (45) reducesto

(46)1

(1/2)(1 � 1/2)

F(0)�

Z •

0f(x)F(x) dx

�= 4(1/2�3/8) = 1/2

This is exactly what is expected if µ = 0 since the up jump anddown jump come from the same distribution.

6.2.2 Cases 1 and 3

I outline the solution for cases 1 and 3, but do not solveexplicitly for them. This is because the next section gives the fullapproximate probability functions through simulation, which aremuch more enlightening than the algebraic derivations. For case1, we want to solve P(Y + Y > X). First, use convolution to find thedensity of Y + Y, then set up an integral as in the previous case.For case 3, we want to solve P(Y > X + X). Again, use convolutionto find the density of X + X, then set up an integral.

6.2.3 Simulated Probability Functions

Figure 7 plots the probability functions P1, P2, P3, and P4 forvarious levels of s. All plots have µ along the x-axis.

Note that for each plot in Figure 7, when µ = 0, the probabilityfunctions coincide with the numbers from section 6.1: P1 = 5/16 =P4 and P2 = 3/16 = P3. The plots include values of negative drift,just to include players who may be best at the start of college,then steadily decline throughout their college career. The top leftplot is for a player with s = 0.5. This player has low variationabove and beyond his usual drift from season to season. The solidline in the top left plot shows that if this player has a µ > 1, itis very likely his skills will be highest after senior year. However,if the player’s drift is between 0 and 1/2, the solid line is much

31

Figure 7: Probability Functions

The solid line is P4, the dotted line is P3, the dashed line is P2, and the dotted-dashedline is P1. The top left plot is for s = 0.5. Top right is s = 1. Bottom left is s = 2. Bottomright is s = 3.

lower and so the probability his skill level is highest before senioryear is more substantial (sum of the heights of the three non-solidlines). The bottom right plot is for a player with high volatilityin his skills above and beyond the season to season drift (s = 3).The solid line is still monotonic, yet increases much slower. Theprobability a high volatility player is best after senior year is lessthan the probability a low volatility is best after senior year for allµ > 0.

6.3 The Stochastic Model as a Predictive Model

From Figure 7, we could give an estimate as to when the player ismost likely to have the highest skills, based on his s and µ. To useFigure 7 as a predictor, we would like to measure a player’s µ ands. I do not pursue this idea here; rather, I suggest it as potentialfuture work.

One way is to look at the player’s high school statistics orthe player’s game-by-game statistics in his first year of college.

32

For each year in high school, say, use statistics like the player’spoints, rebounds., etc. to construct a proxy for skill level that year.Then for each of the four years, we would have a number thatcorresponds to skill level. Plot these four skill levels versus years1, 2, 3, and 4. The best-fit line through these points could givean estimate for µ and s: The slope of the best-fit line would beµ and the sum of squared residuals would be s. For each player,we could construct a µ and s and compare across players. So, forexample a s in the first quartile of all players’ s’s would classifythat player as a low volatility player, whereas a s in the fourthquartile of all players’ s’s would classify that player as a highvolatility player. The same could be done for the drift values. Thiswould allow us to compare players and predict when a player’sskill level would most likely be highest, relative to other players.

6.4 Threshold Idea

Section 5 determined a player can maximize expected careerearnings by entering the draft when his skills are the best (i.e.by maximizing S(y)). Section 6.2 showed that if the player hasa positive drift, then he is most likely to be best after his senioryear, regardless of the actual value of the drift and regardless ofthe volatility in e. Thus, if a player has positive drift, which Isuspect almost all do, we should not expect players to enter thedraft before senior year. So why is this not the case?

To reconcile this, I suggest that players do indeed want tomaximize their success by strategically entering the draft whentheir skills are best; however, if a player is very talented he mayalready be good enough to go pro. That is, perhaps there is some“skill threshold” players want to reach before going pro. If theyattain this threshold before senior year, then they enter the draftbefore senior year. For example, after a player’s team wins thenational championship, or after the player receives a prestigiousaward, or after the player averages more than a certain numberof points in a season. A player coming off a big year receiveswidespread attention which puts him in the spotlight and maymake him more likely to go pro. The player may feel like hischances of being drafted are especially good, despite the factthat his skills may indeed improve if he stays in college for an

33

additional year.

7 The Optimal Stopping Problem

The decision to stop playing college basketball and go pro is astopping problem. Since a player wants to optimize earnings withthis decision, it is an optimal stopping problem. Figure 8 showshow, after completing each year in college, a player must choosewhether to stop (S) and try to go pro or continue (C) playing incollege. At each node a player must choose whether to continueplaying college basketball or stop and go pro. Stopping after yeari leads to career earnings of ei.

Figure 8: College Basketball Player’s Decision Tree

Figure 8 captures the player’s dilemma, but it simplifies theproblem because it doesn’t consider the probability a playeris drafted to the NBA. Not all early entrants are drafted andso this approach should incorporate the chance of being drafted.13

Consider the finite state Markov chain in Figure 9 with statespace

S = {0, 1, 2, 3, 4, d1, d2, d3, d4, NBA, ND},

where13Using my data set of 856 players from 1989 to 2012 who opted for early

entry, 35.5% went undrafted. Arel and Tomas (2012) find that, from 2006 to2010, 38% went undrafted.

34

(i) State 0 means the player has 0 years of college experience, 1means the player has 1 year of college experience, etc.

(ii) dj = declare for draft with j years of experience, j = 1, 2, 3, 4

(iii) NBA = player was drafted to the NBA. ND = player was notdrafted to the NBA (both absorbing).

Figure 9: NBA Player Markov Chain

The stochastic matrix is

P =

2

666666666666666664

0 1 0 0 0 0 0 0 0 0 00 0 p2 0 0 q2 0 0 0 0 00 0 0 p3 0 0 q3 0 0 0 00 0 0 0 p4 0 0 q4 0 0 00 0 0 0 0 0 0 0 1 0 00 0 0 0 0 0 0 0 0 p01 q010 0 0 0 0 0 0 0 0 p02 q020 0 0 0 0 0 0 0 0 p03 q030 0 0 0 0 0 0 0 0 p04 q040 0 0 0 0 0 0 0 0 1 00 0 0 0 0 0 0 0 0 0 1

3

777777777777777775

.

35

P has dimension 11 by 11, where the states run across thetop and down the side in the order 0, 1, 2, 3, 4, d1, d2, d3,d4, NBA, ND. So for example, the (1, 2) entry of P givesthe probability of moving from state 0 to state 1, which is1 in Figure 9 since a player must be at least a freshman todeclare for the draft. The kth step stochastic matrix (k � 6) is

36

Pk=

2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4

00

00

00

00

0q 2

p0 1+

p 2q 3

p0 2+

p 2p 3

q 4p0 3

+p 2

p 3p 4

p0 4q 2

q0 1+

p 2q 3

q0 2+

p 2p 3

q 4q0 3

+p 2

p 3p 4

q0 40

00

00

00

00

q 2p0 1

+p 2

q 3p0 2

+p 2

p 3q 4

p0 3+

p 2p 3

p 4p0 4

q 2q0 1

+p 2

q 3q0 2

+p 2

p 3q 4

q0 3+

p 2p 3

p 4q0 4

00

00

00

00

0q 3

p0 2+

p 3q 4

p0 3+

p 3p 4

p0 4q 3

q0 2+

p 3q 4

q0 3+

p 3p 4

q0 40

00

00

00

00

q 4p0 3

+p 4

p0 4q 4

q0 3+

p 4q0 4

00

00

00

00

0p0 4

q0 40

00

00

00

00

p0 1q0 1

00

00

00

00

0p0 2

q0 20

00

00

00

00

p0 3q0 3

00

00

00

00

0p0 4

q0 40

00

00

00

00

10

00

00

00

00

00

1

3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5

37

The entry of concern in this matrix is the (1, 10) entry, whichrepresents the probability of going from state 1 to state NBA:

Pk(1, NBA) = q2 p01 + p2q3 p02 + p2 p3q4 p03 + p2 p3 p4 p04, (k � 6). (47)

That is, (47) is the probability that a player who just finishedfreshman year will be in the NBA by the time he graduates.P6(1, NBA) is the probability he makes it to the NBA afterfreshman year (q2 p01) plus the probability that he makes it to theNBA after sophomore year (p2q3 p02) plus the probability that hemakes it after junior year (p2 p3q4 p03) plus the probability that hemakes it after senior year (p2 p3 p4 p04). Hence P6(1, NBA) is theprobability that he eventually makes it to the NBA. Clearly, aplayer would like this probability to be as high as possible. Sincepi + qi = 1 for i = 2, 3, 4, substitute qi = 1 � pi in (47) to get

P6(1, NBA) = (1� p2)p01 + p2(1� p3)p02 + p2 p3(1� p4)p03 + p2 p3 p4 p04.(48)

We can use data from the empirical section to estimate P6(1, NBA).Getting estimates for p0i is simple: Consider all players whoapplied to the NBA draft after i years of college and look athow may were drafted into the NBA.14 This is a good firstapproximation for p0i. The pi are more difficult to estimate. Thiswould involve looking at all players who finished i years of collegebasketball and seeing how many declared for the draft versus howmany stayed for another year. Trying to estimate all the collegeplayers who did not apply for the draft is challenging since thereare many colleges in the nation with many college players on eachteam.

To solve this issue, consider p2 as a function of p01. That is,p2 = p2(p01). Recall, p2 is the probability that a rising sophomoreremains in college for a second year and p01 is the probability thata rising sophomore makes it to the NBA after applying for thedraft. It is reasonable to assume

dp2

dp01< 0. (49)

14Using my data set of 856 domestic players from 1989-2012 who remainedearly entry, 78% of freshmen were drafted, 66% of sophomores were drafted,and 54% of juniors were drafted. Also, 81% of high school seniors who appliedwere drafted. p04 is difficult to estimate, but is likely to be well less than 50%.

38

That is, as the probability of being drafted increases, the playerwill be less and less likely to want to remain in college for asecond year. We can imagine that p2(0) ⇡ 1 since the playerhas no chance of being drafted and so it is likely he will remainin college. Also, p2(1) ⇡ 0 since the player will definitely bedrafted and so he forgoes his second year to apply for the draft.This reasoning makes the analysis of this optimal stopping sectionmore appropriate for an average college player. A very talentedplayer may still be reluctant to try for the draft just because hethinks he will be drafted. The talented player would probablystrive for a high draft position, whereas the average player wouldbe happy to be drafted at all.

The last thing to notice about p2(p01) is its second derivative:

risk neutral ) d2 p2

dp210

= 0

risk averse ) d2 p2

dp210

< 0

risk loving ) d2 p2

dp210

> 0.

These three properties are summarized by Figure 10.To work with explicit equations, I assume the following

functional form of p2(p01) :

p2(p01) = 1 � (p01)k, k > 0. (50)

If the player is risk loving, k < 1. If the player is risk neutral,k = 1. If the player is risk averse, k > 1. The argument above forreasoning that p2 is a function of p01 can be used to conclude thatp3 is a function of p02 and p4 is a function of p03. These other twofunctions behave exactly the same. Hence (48) becomes

f (k) =

1 � (1 � pk10)

�p10 + (1 � pk

10)

1 � (1 � pk

20)

�p02 + (1 � pk

10)(1

� pk20)

1 � (1 � pk

30)

�p03 + (1 � pk

10)(1 � pk20)(1 � pk

30)p04

(51)

39

Figure 10: Risk Preferences of a Player

which, after some algebra, simplifies to

f (k) = p04 + (p03 � p04)p0k3 + (p01 � p04)p0k1 + (p02 � p04)p0k2 + (p04 � p02)(p01 p02)k

+ (p04 � p03)(p02 p03)k + (p04 � p03)(p01 p03)k + (p03 � p04)(p01 p02 p03)k

(52)

f (k) in (52) can be thought of as the chance of making it tothe NBA eventually, where k is a measure of the player’s riskaverseness. Regardless of the values of p01, p02, p03, and p04, f (0) = p01and limk!• f (k) = p04. Data from the previous page in footnote 14showed p01 ⇡ 0.78 > p02 ⇡ 0.66 > p03 ⇡ 0.54 > p04. Using thesevalues in (52) and taking p04 = 0.3 (without loss of generality),Figure 11 depicts f (k).

Unlike the first optimal entry model where we assumed theplayer was talented (i.e. would be drafted if he were to applyto the draft), a not so talented player cannot be as picky aboutwhen he applies to the draft. The average player may have onlyone shot throughout his college career to make a feasible attemptto go pro. Therefore, if an average player wants to optimize hischances of making it to the NBA, he should be as risk loving aspossible. If he thinks he has any shot of making it to the NBA after

40

completing any year of college, then he should drastically reducethe probability he stays in college for another year and stronglyconsider applying for the NBA draft.

Figure 11: Chances of Making it to the NBA

7.1 Secretary Problem Approach

The classic Secretary Problem from optimal stopping theory canprovide another template for when a college basketball playershould go pro. The secretary problem is as follows: An employeris looking to hire a single secretary from an applicant poolof n applicants. The applicants can be ranked from best toworst (i.e. there is a best applicant, a second best, etc.). Theemployer does not know the talent of an applicant until thatapplicant is interviewed. The employer interviews applicants oneby one hoping to find the best applicant. After an interview,the employer can hire that applicant and never get to see theremaining applicants, or reject that applicant forever.

The optimal solution involves automatically rejecting the firstn/e applicants immediately after the interview, then hiring thefirst applicant who is better than all of those interviewed so far.If no such applicant exists, the employer hires the last applicant

41

interviewed. This strategy can be shown to be successful in hiringthe best applicant in the pool with probability 1/e, as n ! •.

This solution method can be applied to a college basketballplayer’s decision about when to make the jump to the NBA. Aplayer can opt to go pro after any one of four years. But afterelecting to go pro, he cannot try to go pro in later years becausehe has relinquished his college eligibility. At the end of each yearof college basketball the player assesses his “offer,” which can bethought of as his chance of going pro, his potential earnings, andprojected overall initial success in the NBA. This is analogous tointerviewing an applicant. The player does not necessarily knowif his skill level will be higher or lower the following year, or ifhis offer will be better or worse. The secretary problem solutionimplies the player should reject the first n/e offers automatically.In the case of the player, n/e = 4/e ⇡ 1.47 offers. Therefore, theplayer should not go pro after freshman year. Instead, he shouldgo pro in the subsequent year that gives him a better offer than theoffer he received his freshman year. In the case that his offers aftersophomore year and junior year are worse than after freshmanyear, the player should go pro after senior year.

Using this approach, it can be shown that the playersuccessfully accepts the best offer 46% of the time. To see why,rank the four offers as 1, 2, 3, and 4 where 1 corresponds to thebest offer and 4 is the worst. Since there are 24 permutations,all equally likely, directly count the number of cases for whichthis secretary solution successfully has the player select 1. Forexample consider the order 2, 3, 1, 4. This means that the playerwill receive the best offer following his junior year, second bestoffer after freshman year, third best offer after sophomore year,and worst offer after senior year. The solution says to reject theoffer after freshman year, then select the first offer that is betterthan the offer freshman year. Since the offer after sophomore yearis worse, it is rejected. Since the offer after junior year is betterthan the offer after freshman year, the player accepts this offer. Henever plays a senior year of basketball and never sees what hisoffer after senior year would have been. Therefore this methodwas successful in picking out the best offer. In the 24 cases, thebest offer is picked in 11 of them (⇡ 46%). In seven cases, thesecond-best offer is picked, in four cases the third-best offer is

42

picked, and in only 2 cases (1, 2, 3, 4 and 1, 3, 2, 4) the worst offeris picked.

The above example is encouraging since the player would havebeen rather unlucky if he remained for his senior year. The playerof course does not know if his offer after senior year will be betterthan after his junior year. Coming off a great junior year he mayhave been tempted to play senior year, thinking that he would getan even better offer after senior year. The method above results inthe player stopping at the optimal time.

7.1.1 Nondeterministic Secretary Problem

A final thought introduces more randomness into the player’sdecision about when to go pro. In the previous section it wasassumed that the number of applicants n was known. However,this does not have to be the case. Letting N be a random variabledenoting the number of applications received, the employerwould have to find a new optimal stopping rule to optimize theprobability of selecting the best applicant (see Presman & Sonin1973). Likewise for the player, n = 4 is not always the case.The player for example may suffer a long-term injury junior yearwhich ends his college career. Hence N took on the value 2, sincehe only saw two offers, both of which he rejected. Using N alsomakes sense in the following way: suppose in the previous sectionwe defined "offer" as the event in which the probability of beingdrafted once a player enters the draft is nonzero. Then the playermay not have offers every year. That is, there may be some yearswhere he simply may not be talented enough, in which case ifhe applied to the draft he would almost certainly not be drafted.Thus N would denote the number of years in which he has anonzero probability of being drafted.

8 Conclusion

This paper analyzes when a player should go pro through bothempirical and theoretical frameworks. The empirical sectionestimates returns to schooling by comparing two groups ofplayers: high school seniors and freshmen drafted from 1989 to2005 versus freshmen drafted from 2006 to 2012. A new law made

43

2005 the last year that players could go directly into the NBAout of high school, so the latter group contains individuals whowere forced to complete an additional year of school. Comparingthe earnings of the two groups shows that the “post-law” groupearned $580,000 more during their first year in the NBA. However,the regressions, which controlled for ability, experience, and draftposition, found no evidence to support a significant difference inearnings.

The theoretical section showed that players can optimize theircareer earnings by going pro when their skills are highest. Playerswho are especially talented should go pro as soon as they attainsome minimum skill threshold, despite the possibility that theirskills may be higher in later years. Players who are average shouldgo pro if they receive any positive signals that indicate they havea chance of being drafted. That is, they should have risk lovingpreferences.

44

Appendix

Here I generalize Section 5 to include the probability of the playergoing undrafted. This is mainly to show the robustness of theanalysis in Sections 5-7 and also to allow for “average players” tobe defined more broadly.

Let PH , PL be defined as they were previously and let PU be theprobability that the player is undrafted. If the player is undrafted,his earnings are zero: EH > EL > 0 = EU . Assume dPU/dS < 0and that PH + PL + PU = 1. The optimization problem is

maxy

E(e) = maxy

hEHPH(S(y)) + ELPL(S(y))

i, (53)

which becomes

maxy

hEHPH(S(y)) + EL

⇣1 � PH(S(y))� PU(S(y))

⌘i. (54)

Differentiating with respect to y gives

dE(e)dy

= EHP0H(S(y))S0(y) � ELP0

H(S(y))S0(y) � ELP0U(S(y))S0(y)

= 0) S0(y)

hEHP0

H(S(y)) � EL

⇣P0

H(S(y)) + P0U(S(y))

⌘i

= 0,(55)

which holds when S0(y) = 0. To see why the term in the bracketcannot be zero, rearrange to get

(56)

EH

EL=

P0H(S(y)) + P0

U(S(y))P0

H(S(y))

= 1 +P0

U(S(y))P0

H(S(y)).

Since EH > EL, EH/EL > 1. But the term on the right in (56) is lessthan one since P0

U(S) < 0 and P0H(S) > 0. Therefore, the maximum

of S(y) is the only candidate to optimize earnings. Letting y⇤ besuch that S0(y⇤) = 0 and S00(y⇤) < 0, let’s verify that this is indeed

45

the maximizer. Differentiating (55),

(57)d2E(e)

dy2

���y =y⇤

= S0(y⇤)h

EHP00H(S(y⇤))S0(y⇤) � EL

⇣P00

H(S(y⇤))S0(y⇤)

+ P00U(S(y⇤))S0(y⇤)

⌘i+ S00(y⇤)

hEHP0

H(S(y⇤))

� EL

⇣P0

H(S(y⇤)) + P0U(S(y⇤))

⌘i

= S00(y⇤)h(EH � EL)P0

H(S(y⇤)) � ELP0U(S(y⇤))

i< 0

since S00(y⇤) < 0 and the term in brackets is positive.Lastly, check the boundary:

(58)E(e)|y =y⇤ > E(e)|y =yB() EHPH(S(y⇤))

+ EL

⇣1 � PH(S(y⇤)) � PU(S(y⇤))

⌘> EHPH(S(yB))

+ EL

⇣1 � PH(S(yB)) � PU(S(yB))

⌘

() EL

hPH(S(yB)) � PH(S(y⇤)) + PU(S(yB)) � PU(S(y⇤))

i

> EH

hPH(S(yB)) � PH(S(y⇤))

i

For (58) to hold, each term in brackets must be negative.To make the term in the right bracket negative, it’s necessary

that S(y⇤) > S(yB).The term in the left bracket of (58) is PH(S(yB))� PH(S(y⇤)) < 0and PU(S(yB)) � PU(S(y⇤)) > 0. To see how the first differencedominates, recall

(59)

PH + PL + PU = 1

=) dPH

dS+

dPL

dS+

dPU

dS= 0

=) dPH

dS>

����dPU

dS

����

since we assumed the derivative of PL is nonzero. Therefore S(y⇤)optimizes expected earnings. The player should go pro when hisskills are highest.

46

Contagion in the Eurozone Sovereign DebtCrisis

Stefano Giulietti, Yale University1

Abstract. Since the end of 2009, the Eurozone has faced a severesovereign debt crisis, which had its roots in Greece and graduallyspread to other countries. This paper estimates an autoregressiveconditional heteroskedasticity (ARCH) model of credit defaultswap (CDS) spreads in order to analyze whether contagioneffects are identifiable during the crisis—equivalently, whetherthe financing difficulties faced by several European countrieswere due to investor panic, herding, or speculation, or actualfundamental problems. The analysis shows the presence of Greekcontagion effects on Spain, Italy, Belgium, France, and Portugal,both through CDS markets and credit rating downgrades. Furthercontagion is documented among Portugal, Spain, Italy, and Francein later stages of the crisis.

Keywords: sovereign debt crisis, credit default swaps, Eurozone,ARCH model

1Stefano Giulietti graduated from Yale University in 2013. He wrote thissenior essay in economics for Professor Costas Arkolakis. The author wouldlike to thank Professor Arkolakis for his continuous guidance and helpful andstimulating discussions. He would also like to thank Professor Yuichi Kitamurafor helping him with the more complex econometric issues he encountered.

47

1 Introduction

Since the end of 2009, the Eurozone has faced a severe sovereigndebt crisis. EU and IMF interventions neither reversed the crisisnor contained it to Greece. On the contrary, the problem spreadto several other countries, such as Portugal and Ireland. Eventhe sovereign debt markets of large economies like Spain’s andItaly’s, and to a much lesser extent France’s, came under pressure.Sovereign debt woes may have spread to other countries whenfinancial markets recognized an effective increase in credit risk,but it may also be the case that Greece infected other debt marketsby negatively impacting the market’s assessment of countrieswhose conditions were not as critical.

This paper investigates whether the financing problems facedby some Eurozone countries are disproportionate comparedto their fundamentals; that is, whether there have beenany contagion effects across countries during the debt crisis.Contagion due to market panic, investor herding, and otherfactors is identified whenever the correlation coefficients acrosstwo countries’ credit default swap markets increase temporarily,together with their volatilities.

An ARCH regression model is estimated in order to analyzethe size and volatility of cross-market correlations. Credit defaultswap spreads are used as an indicator of countries’ perceiveddefault risk, as explained in Section 2. The sample includesthe credit default swap spreads of seven Eurozone countriesover the German benchmark: France, Italy, Austria, Portugal,Spain, Belgium, and the Netherlands. The model investigatescontagion caused by spillovers in credit default swap markets andby the effects of credit ratings. The analysis shows evidence thatcontagion stemming from Greece affected Portugal, Spain, Italy,France, and Belgium during the crisis. The only two countriesthat were immune to contagion were Austria and the Netherlands.Additionally, further instances of contagion are identified fromSpain to Italy, from Portugal to Spain and vice versa, and fromItaly to France and vice versa.

The study generally confirms the findings of Missio andWatzka (2011), who showed that the Portuguese, Spanish, Italian,and Belgian bond markets were affected by spillovers of the

48

Greek crisis, while Austria and the Netherlands were immune tocontagion. However, this paper not only expands on previousresearch by including France in the sample of analyzed countries,but also uses credit default swaps instead of bond yields as a moreaccurate measure of perceived credit risk.

2 Bonds vs. Credit Default Swaps

Government bond yields and prices of credit default swaps ongovernment bonds are both measures of a country’s credit riskas perceived by financial markets. The following section explainswhy this paper chooses to rely on credit default swap spreadsrather than bond yields as an indicator of sovereign credit risk.

A bond buyer is exposed to an interest rate risk and a fundingrisk, given by the initial outlay of the principal. The need to hedgeor speculate on credit risk has given rise to a large market forcredit default swaps (CDS), a type of derivative that protects thelender in case of default of a sovereign or corporate bond. A CDSgives a bondholder insurance against pure credit risk: the buyerof the CDS agrees to make periodic payments to the seller, and inreturn receives a payoff if the underlying security experiences acredit event such as a default. In the case of such a credit event,the CDS buyer is entitled to a payment equal to:

Payment = B(1 � R) (1)

where B is the net notional value of the bond and R is the recoveryrate.

CDS are traded over-the-counter, which makes them highlyliquid, unlike fixed income instruments. Moreover, the fact thatthe position taken through the bond has to be funded by collateral,while the position taken through the CDS is unfunded, impliesthat derivatives have higher built-in leverage, which can meanthat a CDS may be a cheaper instrument than a bond for acquiringexposure to the same credit risk. For these reasons, credit defaultswaps are used not only for hedging risk, but also for speculation.Liquidity and cheapness make CDS ideal for placing bets on debtinstruments.

CDS buyers are often speculative investors such as hedge

49

funds, while bond buyers tend to have a longer-term investmentperspective; this difference implies that CDS prices are moreresponsive to changing economic conditions than bond spreads.Hence, CDS markets have emerged as a highly visible indicator ofa country’s perceived credit risk.

Research on European sovereign debt markets has indeedshown that when explosive trends appeared during the sovereigncrisis, the CDS market appeared to have been a driver in mostcases. In other words, due to their high liquidity, CDS had a pricediscovery effect: changes in CDS prices anticipated correspondingchanges in bond prices. The price discovery effect was furtheraccentuated by the flight to liquidity that characterized thecrisis. Therefore, in order to investigate contagion effects acrossEurozone sovereign debt markets, this paper uses CDS prices as aproxy for European countries’ perceived default risk.

3 Identifying Contagion

As defined by Corsetti et al. in Financial Contagion: The ViralThreat to the Wealth of Nations, the term “contagion” (generallyused in contrast to “interdependence”) conveys the idea thatduring financial crises there might be breaks or anomaliesin the transmission mechanism among markets, reflectingswitches across multiple equilibria, market panics unrelated tofundamentals, investor herding, and so on. Pericoli and Sbracia(2003) give an overview of the most commonly used definitions ofcontagion. According to the existing literature, contagion can beidentified if:

(i) the probability of a crisis in one country increasesconditional on the probability of a crisis occurring in anothercountry;

(ii) volatility of asset prices spills over from a crisis country toother countries;

(iii) cross-country co-movements of asset prices cannot beexplained by fundamentals alone;

(iv) co-movements of prices and quantities across markets

50

increase conditional on the probability of a crisis occurringin a market or group of markets; and

(v) the transmission channel intensifies or changes after a shockin one market.

All these definitions of contagion take into account thecorrelations and volatilities of markets and financial assets andclarify the importance of volatility measures in the study ofcontagion. Earlier models defined contagion as an increase incross-market correlations of stock market returns during a crisis.Forbes and Rigobon (1999) argue that this approach is biased,because standard estimates of cross-market correlations will bebiased upward when stock market volatility increases, such asduring a time of financial turmoil. Indeed, an adverse shockin one country could propagate to other countries by directlyaffecting their fundamentals through a series of real linkages.

For example, one country being hit by a crisis could leadto a decline in asset prices in other countries due to trade orpolicy coordination. In such cases, the propagation of the crisiswould be due not to investor panic, but to an actual increase ininterdependence. Only when the propagation mechanism cannotbe explained by interdependence does contagion come into play;in such a case, we expect to observe increases and volatility (asmeasured by the standard error of the correlations), which thenrevert to normal after the shock. The importance of accounting forvolatility can be explained by a simple model of correlation, wherex and y represent returns in two different stock markets and # isan idiosyncratic shock, independent of any aggregate shocks:

y = a + bx + # (2)

where E[#] = 0, E[x#] = 0 and |b|< 1. We can divide thehypothetical dataset into two periods: one of relative marketstability, where sx will be low (sl), and one of financial turmoil,where sx will be high ( sh). In a standard OLS regression, theestimator b is by definition equal to:

b =Â xiyi � 1

n  xi  yi

 x2i �

1n (Â xi)2

=Cov[x, y]

Var[x]=

sxy

sx(3)

51

Notwithstanding changes in variances, bl = bh, becauseE[x#] = 0. We can rewrite the equality as:

bl = bh =sl

xy

slx

=sh

xy

shx

(4)

which implies that shxy > sl

xy, because shx > sl

x. The variance of yis given by:

sy = b2sx + s# (5)

Since the variance of # is constant and |b|< 1, any increase inthe variance of y is less than proportional to the increase in thevariance of x. Correlation r is defined as:

r =sxy

sxsy(6)

which implies that rh > rl . This inequality shows that thecorrelation between stock market returns is conditional on thevariance of the stock market returns; in other words, an increasein the variance of x and y would cause an apparent increase inthe correlation coefficient even if the volatility-adjusted coefficienthad not actually risen.

The above example shows the importance of taking volatilityinto account when performing a contagion analysis. AsForbes and Rigobon (1999) point out, a permanent and stableincrease in cross-market correlations indicates stronger economicinterdependence rather than contagion. Indeed, economicintegration is a long-term process and does not revert back inshort periods of time. Therefore, contagion is identified whencorrelation coefficients and their standard errors increase duringa period of financial turmoil and subsequently return to pre-crisislevels.

The main model developed in this paper analyzes how theGreek CDS market and credit ratings affected the CDS marketsof other Eurozone countries. In this specific case, contagionis identified whenever the correlation coefficient of Greece withanother country increases from one year to the next, coupled withan increase in the standard error (the volatility) of that coefficientover the same time period.

52

4 Data

For the analysis of contagion in European sovereign debt markets,this paper uses CDS data from seven countries: France, Italy,Portugal, Spain, the Netherlands, Austria, and Belgium. Thesample thus includes both countries whose sovereign debtmarkets underwent severe pressure and countries relativelyunaffected by the crisis. The dataset includes daily closingprices of US dollar-denominated credit default swaps on 10-year government bonds, as calculated by Bloomberg. The pricesquoted are for five-day weeks, in order to exclude non-tradingdays from the analysis, over a period ranging from January 1,2008 to September 16, 2011.

The time period was specifically chosen in order to allow for acomparison of the pre-Euro crisis period (2008 to mid-2009) witha period of high financial distress. The analysis does not includeCDS prices after Friday, September 16, 2011, because shortlythereafter Greek Finance Minister Evangelos Venizelos announcedthe possibility of a 50% debt haircut during a speech to rulingSocialist party lawmakers.

European policymakers repeatedly stressed the fact that thehaircut would be borne by private-sector creditors but would haveto be strictly voluntary, meaning that the write-down would nottrigger the $3.7 billion worth of CDS contracts held by Greekbanks. The International Swaps and Derivatives Association(ISPDA), which regulates the CDS market, stated that a voluntarybond exchange into new debt would not trigger CDS payments,even if there may have been some degree of coercion.

Eventually, the ISDA declared in March 2012 that the termsof the 2012 Greek debt restructuring did trigger CDS payouts, butuntil then it had stated that a voluntary agreement would not havebeen officially catalogued as a credit event. The ISDA’s originalstance could have thus hindered the value of CDS prices as thebest indicators of credit risk; if an effective default on the part ofGreece does not trigger debt-insurance payments, CDS prices nolonger represent the best indicator of Greece’s perceived sovereignrisk.

53

5 Methodology

German CDS prices are used as a risk-free benchmark in orderto obtain an indication of the risk premia of the other countries.CDS prices on 10-year US dollar-denominated bunds are thussubtracted from the CDS prices of the other countries in thesample. The use of CDS spreads over the benchmark, ratherthan pure CDS prices, allows us to remove parallel economicdevelopments of the Eurozone from the contagion study and toanalyze the country-specific risk premium.

It is also important to include the German benchmark in thestudy because of the sheer size of the German economy, the largestwithin the Eurozone. The exclusion of such an important countrymay lead to a model that is potentially misspecified and couldyield misleading outcomes.

CDS spreads are a non-stationary time series and exhibitclustering of volatilities, meaning that the size of price volatilitytends to cluster in periods of low volatility and periods of highvolatility. Volatility throughout the sample is particularly high,but it does tend to group in periods of relative calm and periodsof turmoil. Due to the nature of the data, an autoregressiveconditional heteroskedasticity model (ARCH) should be specified,since it can describe the time evolution of the average size of thesquared errors; i.e. the evolution in the magnitude of uncertainty.

ARCH captures the time dependent nature of the variance byusing a short rolling window for estimates; in fact, the varianceis forecast as a moving average of past error terms. In a simpleARCH specification, the dependent variable return rt is given bythe mean value mt plus an error term:

rt = mt + #t (7)

The error term will have the form:

#t = ztp

ht (8)

where zt is an independent, standard normal variable and ht is the

54

variance as a function of the moving averages of past error terms:

ht = w +p

Âi=1

ai#2t�i (9)

with w and ai being positive constants and #t�i being the errorterm in the previous periods, with lags of t � i.

Running an ARCH regression with CDS spreads, however,generates a potentially misspecified outcome: the Durbin-Watsonstatistic and Ljung-Box test for randomness reveal that theresiduals for such a model are non-random, meaning that the dataare not independently distributed. Correlations identified in thesample could thus be caused by autocorrelation in the data ratherthan by effective contagion effects.

An autoregressive integrated moving average (ARIMA)filtration of the data is thus necessary. ARIMA removesautocorrelation by stationarizing the time series; lags of theseries are added to the prediction equation in order to removeautocorrelation from the forecast errors. An ARIMA(p) modelis applied to the CDS spread of each country, where (p) isthe number of autoregressive lags. The optimal value of (p) isdifferent for each country, and is obtained with the Schwarz-Bayesian information criterion. The Schwarz-Bayesian criterionpredicts that the optimal number of lags is 1 for the French series,3 for Italy, 3 for Portugal, 3 for Spain, 1 for the Netherlands,1 for Austria, 1 for Belgium, and 4 for Greece. These lags arethen used in the ARIMA filtration, which specifies the followingautoregressive equation:

Xt = c +p

Âi=1

jiXt�i + #t (10)

where c is a constant, ji are the parameters or coefficients of thelags, and #t is white noise. For example, the ARIMA(1) processfor France is:

Xt = c + jXt�1 + #t (11)

where Xt is the French CDS spread on day t. Xt�1 is the CDSspread on the previous day.

The residuals of each ARIMA regression are then extracted

55

and used as variables in the ARCH regression. The modelcan now be correctly specified, since residuals are random,as confirmed by the Ljung-Box test. Ljung-Box tests the nullhypothesis that the data are random against the alternativehypothesis that the data are not random. Since the test gives p-values < 0.05 for all series, the residuals pass the test and can beused as ARCH inputs. To capture any contagion effects of Greeceon other CDS markets, the dataset is divided by year (2008-2011)and then each country’s residuals are regressed ARCH(1) year-by-year against the Greek residuals.

Rating changes should also be accounted for, given the weightthat they have in forming market perceptions of credit risk. Forthis reason, credit ratings from Standard & Poor’s (which areavailable on the agency’s website) are included in the analysis.Greek ratings may be related to other countries’ ratings, in thesense that a rating cut in Greece may make a rating cut in anothercountry more likely. For example, it may be rational for investorsto expect a Portuguese downgrade after a Greek downgrade ifthere is interdependence between the two countries. The modelthus considers changes in relative credit rating, as defined by adummy variable indicating the rating spread between the countrybeing analyzed and Greece. The S&P rating scale ranges betweenC and AAA, which were respectively assigned numerical valuesof 0 and 20. Every country’s rating thus corresponds to a numberbetween 0 and 20, with AA+ being 19, AA being 18, AA- being17, and so on. The Greek rating is then subtracted from such anumber to obtain a rating spread; because Greece’s rating was thelowest for the whole period being analyzed, all the rating spreadsare positive.

In sum, the original data are modified through a series ofstatistical procedures in order to obtain the residuals used in theARCH model:

(i) German CDS prices are subtracted from each country’s CDSprices in order to obtain a CDS spread;

(ii) An ARIMA regression is performed on the CDS spreads,with a number of lags specified by the Schwarz-Bayesianinformation criterion;

(iii) The residuals of each ARIMA regression are extracted and

56

Figure 1: CDS Spreads and Greece S&P Downgrades0

001000

1000

1000200020

0020003000

3000

3000400040

0040005000

5000

500001 Jan 08

01 Jan 08

01 Jan 0801 Jan 09

01 Jan 09

01 Jan 0901 Jan 10

01 Jan 10

01 Jan 1001 Jan 11

01 Jan 11

01 Jan 1101 Jan 12

01 Jan 12

01 Jan 12Greece

Greece

GreeceFrance

France

FranceItaly

Italy

ItalyPortugal

Portugal

PortugalBelgium

Belgium

BelgiumNetherlands

Netherlands

NetherlandsAustria

Austria

AustriaSpain

Spain

SpainData: Bloomberg, Standard&Poor's

Data: Bloomberg, Standard&Poor's

Data: Bloomberg, Standard&Poor'sCDS Spreads and Greece S&P Downgrades

used in the ARCH(1) model.

Thus our final model specification is:

pt = at + b1G + b2R + #t (12)

where pt represents the CDS residuals of a country after theARIMA filtration, at is a constant, G are the Greek residuals andR is the rating spread. The error term is described by equation (8)with:

ht = w + a#2t�1 (13)

In the cases in which the rating spread is dropped because ofcollinearity, the term is eliminated and the equation becomes:

pt = at + b1G + #t (14)

The regressions that produce a probability > c2 less than0.05 indicate a statistically significant effect of the independentvariables on a country’s residuals, with a 95% confidence level. As

57

previously explained, contagion is identified where the correlationcoefficients in the ARCH regression, as well as their standarderrors, increase from one year to the next. The analysis showscontagion effects in France, Italy, Portugal, Spain, and Belgium;Austria and the Netherlands, on the other hand, are immunefrom contagion. This finding does not mean that Greece alonecaused the financing difficulties faced by the “infected” countries,but rather that the problems in Greece worsened the potentiallyexisting fundamental problems in other countries. Quantifyingthe proportion of CDS price increases due to contagion as opposedto fundamentals is, however, beyond the scope of this analysis.

6 Results and Discussion

The model identifies contagion effects stemming from Greecein Portugal, Spain, Italy, Belgium, and France, caused both byturmoil in the Greek CDS market and by Greek downgrades.Spillage of the debt crisis from country to country is drivenin most cases partly by fundamentals and partly by contagion.Economic interlinkages often accentuate fundamental problemsby acting as transmission channels for economic turmoil. The onlytwo countries in the sample that appear to have been immunefrom contagion throughout the whole period are Austria and theNetherlands, since both have enjoyed top credit ratings and stablepolitical systems. In other words, the countries that were alreadyunder investor scrutiny suffered from spillover effects. The ARCHmodel also finds evidence for contagion effects of Portugal onSpain, Spain on Italy and vice versa, and Italy on France and viceversa.

The volatility of Portugal-Greece correlations—together withtheir standard error—more than doubled from 2008 to 2009,indicating mounting worries about Portugal’s solvency risk thatcannot be explained by fundamentals alone. As of 2010, the traderelations between Portugal and Greece were negligible—exportsto Greece constituted only 0.1% of Portuguese GDP.

However, Portuguese banks and other financial firms hadextended loans to Greece worth 4.2% of Portuguese GDP(Global Trade Information Services). Such large exposure toGreece unsettled the Portuguese financial system, worsening the

58

Table 1: ARCH Model of Contagion Effects From Greece to OtherEurozone Countries

2008 2009 2010 2011France Prob.>X2 0.0000*** 0.0000*** 0.0006*** 0.8158

CDS coefficient 0.0297239 0.1455889 0.0186672 0.0039692Std. error 0.0050456 0.0199051 0.0048311 0.0082143Rating coefficient collinear 0.4753365 -0.1154252 0.0833719Std. Error – 0.636 0.6210384 0.2259387

Italy Prob.>X2 0.0009*** 0.5935 0.0016** 0.3306CDS coefficient 0.0751675 -0.0263292 0.0008332 0.0219262Std. error 0.0226569 0.0306993 0.0181181 0.0202039Rating coefficient collinear 0.4595032 2.8750550 0.4660443Std. Error – 0.8139468 0.8219466 0.5564207

Portugal Prob.>X2 0.0000*** 0.0000*** 0.0025** 0.8626CDS coefficient 0.1473455 0.1366586 0.0601887 0.0008259Std. error 0.0129079 0.0288803 0.0183478 0.0064993Rating coefficient collinear 2.3796360 1.6276110 0.4088153Std. error – 0.9277528 1.9108080 0.8305202

Spain Prob.>X2 0.0000*** 0.0000*** 0.0000*** 0.3346CDS coefficient 0.068791 0.0368748 -0.0470753 -0.0026164Std. error 0.0054091 0.0270421 0.0045154 0.0105459Rating coefficient collinear 2.4643810 10.4030700 0.378626Std. error – 1.0932330 0.0721375 0.256944

Netherlands Prob.>X2 0.7611 0.5279 0.8822 0.6111CDS coefficient -0.0202776 0.0075679 -0.000664 -0.01885Std. error 0.0667035 0.0208615 0.0057261 0.0370737Rating coefficient collinear -0.3608043 -0.2928234 collinearStd. error – 0.3390125 0.597633 –

Austria Prob.>X2 0.8387 0.0791* 0.1355 –CDS coefficient 0.0148756 -0.0017699 -0.0079454 –Std. error 0.0730833 0.0204286 0.0039799 –Rating coefficient collinear 1.680653 -0.0291779 –Std. error – 0.7464425 0.5229457 –

Belgium Prob.>X2 0.3302 0.0002*** 0.9171 0.7305CDS coefficient -0.0532767 0.0293775 0.0030445 -0.0195063Std. error 0.0547142 0.012252 0.0096197 0.0404967Rating coefficient collinear 1.192503 0.1935683 0.3814195Std. error 0.3677701 0.7009665 0.7009665 0.7651257

Portugal on Spain Prob.>X2 0.0000*** 0.0000*** 0.0104 0.0025**CDS coefficient 0.4448857 0.2026737 -0.0766774 0.0855804Std. error 0.0084142 0.0388562 0.0299338 0.0282931

Italy on France Prob.>X2 0.0000*** 0.0038** 0.1247 0.0000***CDS coefficient 0.3811751 0.097476 0.0412572 0.3039836Std. error 0.0207702 0.0336625 0.0268688 0.0269942

Spain on Italy Prob.>X2 0.0000*** 0.2116 0.1107 0.0000***CDS coefficient 0.9434361 0.0660258 0.0648574 0.4389144Std. error 0.0144626 0.052855 0.0406627 0.045918

France on Italy Prob.>X2 0.0000*** 0.0494** 0.0000*** 0.0000***CDS coefficient 1.029702 0.1829117 0.4946055 0.9933403Std. error 0.0412852 0.0930866 0.0975066 0.0621817

Spain on Portugal Prob.>X2 0.0000*** 0.0000*** 0.1872 0.0000***CDS coefficient 1.030083 0.290055 -0.041686 0.9224701Std. error 0.033918 0.0401719 0.0316087 0.1414841

*, **, *** indicates statistical significance at the 10%, 5%, and 1% level, respectively.

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country’s already weak fundamentals. A poor educational systemand a rigid labor market had long hindered growth in Portugal,while low-cost labor in Eastern Europe had diverted foreigndirect investment away from the country. The combination oflow growth prospects and a budget deficit amounting to 10.1%of GDP in 2009 made Portugal particularly vulnerable to bondmarket turbulence, until yields reached unsustainable levels andthe EU/IMF granted the country a e78 billion emergency loan tooverhaul its economy. Hence, the financial interlinkages betweenGreece and Portugal and Portugal’s large budget deficit paved theway for a contagion effect in 2009.

The 2009 contagion effect between Greece and France wasdue to the French banking sector’s exposure to Greece, ratherthan by weakness in French fundamentals. In 2009, thecorrelation coefficient between French residuals and Greekresiduals increased by a factor of 4.9, while volatility increased3.98 times, even though it remained at relatively low levels. TheFrench banking sector’s direct exposure to Greece totaled 2.5%of French GDP as of 2010. Conservative UBS estimates showthat net sovereign exposure to Greece amounted to 14% of equityfor BPCE, 8% for BNP Paribas, and 6% for Société Générale, thecountry’s largest banking groups (UBS Equity Research 2011).Société Générale’s business was also negatively affected throughits Greek subsidiary Geniki Bank.

By contrast, Unicredit and Banco Popolare, Italy’s mostexposed banks, had net exposure to Greece totaling 1% of equity.Nonetheless, French fundamentals were unanimously consideredvery solid—even though the country was running a relativelylarge budget deficit in 2009, at 7.6% of GDP, there was nouncertainty regarding its solvency. Therefore, the contagionidentified by our model must stem from the systemic risk ofthe French banking system, which held ample exposure to Greeksovereign debt and the Greek economy.

Since the beginning of the Eurozone crisis, Frenchand international banks have recognized the importance ofperipherals’ credit risk and have sought to reduce their exposureto Greece by selling off assets at a loss, thus further contributingto the worsening of Greece’s solvency problems.

The last country to suffer from contagion in 2009 was Belgium.

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Figure 2: Greece-France CDS Spreads0

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Indeed, 2009 is the only year of the dataset in which GreekCDS residuals appear to have a significant effect on Belgian CDSresiduals; in 2010 and 2011 the model reverts back to statisticalinsignificance. Belgium’s small open economy was hit in earnestby the global recession and the decline in world trade, leading todeterioration of the interbank market and lending to firms andhouseholds. Its government deficit increased from 1.3% of GDPin 2008 to 5.9% in 2009 (Organization for Economic Cooperationand Development).

Investors in Belgian public debt also became preoccupied withthe country’s long-running political instability; Belgium had beeneffectively devoid of a government since 2007, and would remainhighly unstable until Elio Di Rupo’s election as Prime Ministerin December 2011. These worries materialized in 2009, the onlyyear in which the ARCH model produces a statistically significantoutput, to then revert back to values of probability > c2 greaterthan 0.05 in 2010 and 2011. In 2009, the Greek downgrade alsohad a statistically significant effect on the residuals of Belgian CDSspreads, with a coefficient of 1.1925, indicating some mild degreeof contagion both across CDS markets and credit ratings.

In 2010, contagion spread to Italy and Spain. The correlationcoefficient for Italy increased in 2010, but, most importantly, bothItaly and Spain underwent financing pressures due to the effectof a Greek rating cut. The downgrade in 2010 had a sizableand statistically significant effect, with a coefficient of 2.8751 forItaly and 10.4031 for Spain. Spain was vulnerable due to itshigh budget deficit (9.3% of GDP) and ailing economy, which hadcontracted 3.7% in the previous year. Public debt had risen from47.4% of GDP in 2008 to 66.1% in 2010, while unemployment roseabove 20% in 2010 (OECD).

The state of the Spanish economy had been severely worsenedby the real estate bubble that began to explode in 2007-2008.The loss of value of residential properties, coupled with soaringhousehold mortgage debt, had negative repercussions on thebanking system. Notwithstanding Spain’s problematic economicfundamentals, it appears that the Greek downgrade still didhave a contagion effect on the prices of CDS on bonds. Infact, the interdependence of the Spanish and Greek economies isnegligible—Spanish exports to Greece amount to a mere 0.2% of

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Spain’s GDP, and lending to Greece to 0.1%.Contagion can also be identified in 2010 from Greece to Italy,

because the rating coefficient increased even though the twoeconomies are not significantly interconnected: loans to Greeceaccount for only 0.3% of Italy’s GDP, and exports to Greece for0.4%. In fact, Italian fundamentals in 2010 were significantlystronger than those of the peripherals, yet the Eurozone’s thirdlargest economy was not spared from financing difficulties. Italyhad a history of successfully servicing a high public debt load,which stood at 119% of GDP in 2010, and had a budget deficit of4.5% of GDP, roughly in line with Germany’s 4.3% (InternationalMonetary Fund). The economy had not been affected by anyproperty bubble, and the banking system was among the safest inthe continent, given its relatively conservative business practices,strong Tier I capital ratios, and low exposure to peripheral debt.The combination of low private debt and high consumer savingsmade the Italian economy “substantially robust,” according torating agency Moody’s.

The solidity of the Italian economy is highlighted by a cross-country comparison of external debt, meaning the sum of publicand private debt payable in a foreign currency. According to thismetric, Italy’s external debt-to-GDP ratio in 2010 stood at 108%,compared to 142% for Germany, 182% for France, 154% for Spain,217% for Portugal, and 1,103% for Ireland (Moody’s 2010).

Nonetheless, the relatively stronger fundamentals and thesheer size of the Italian economy appear to have been insufficientto stave off contagion stemming from Greece. Worries about thesize of the Italian public debt began mounting, further increasedby the lack of policy responses on the part of the government, andCDS on Italian Treasury Bonds suffered from the Greek malaise.

The only two countries in the sample that appear to havebeen completely immune from contagion are Austria and theNetherlands, which both enjoyed top credit ratings and politicalstability during the crisis. The model is in fact statisticallyinsignificant for both Austria and the Netherlands in every yearof the series (2008-2011 for the Netherlands, and 2008-2010 forAustria because of insufficient CDS price data in 2011), havingprobability > c2 greater than 0.05. Austria and the Netherlandshad a public debt-to-GDP ratio equal to 65.8% and 51.8%,

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Figure 4: Greece-Italy CDS Spreads0

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respectively, in 2010, with deficits of 4.4% and 5%.Interestingly, the CDS coefficients for Austria were negative in

2009 and 2010, and those for the Netherlands were negative in2008, 2010, and 2011, highlighting the flight to safety that tookplace in European debt markets.

Therefore, while turmoil in Greece did influence investorsentiment about the financial stance of economically problematicor politically unstable countries, contagious tendencies did notseem to hit countries that were perfectly stable both economicallyand politically. Yet if a country was already under close investorscrutiny for any reason, the sudden downturn of financingconditions in one country generated spillover effects.

The contagion dynamics do not apply to Greece alone.As the Eurozone crisis progressed and turmoil spread toseveral other sovereign debt markets, more instances of cross-country contagion can be observed. Economic interdependencesaccentuated fundamental problems when, in 2011, pressure onSpanish CDS spilled over to Italy, which exports 1.5% of itsGDP to its southern European neighbor. In the same year,

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Figure 5: Greece-Austria CDS Spreads0

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contagion effects spread from Portugal to Spain and vice versa,and from Italy to France. Exports to Spain are equivalent to5.3% of Portugal’s GDP, while exports to France constitute 3% ofItaly’s GDP. Even more importantly, France has extended loansworth 18.2% of its GDP to Italy through its banking system.In 2010, a small contagion effect of French CDS markets onItaly can also be observed. Hence it appears that, for thelarger European economies, economic interdependences act astransmission channels through which sovereign debt turmoilmoves from one country to another, worsening the actualfundamental problems.

7 Conclusion

This paper estimates an ARCH model in order to analyzecontagion dynamics across Eurozone CDS markets, which are aproxy for investors’ perceptions of sovereign risk. The resultsdo indicate the presence of contagion effects stemming from

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Greece in Portugal, Spain, Belgium, Italy, and France, and furthercontagion among countries as the crisis progresses. The policyimplications that can be drawn from this analysis are ambiguous;however, contagion could be staved off by signaling a country’sstrength to international investors. Possible reactions thus includebailouts, such as those implemented for Greece, Portugal, andIreland, as well as measures aimed at consolidating a country’sfiscal stance and competitiveness. For example, Spain hassignificantly consolidated and strengthened its banking sector,while Italy has embarked on a series of austerity measures andtax increases in order to balance its budget. However, sincecontagion cannot be explained by economic fundamentals, itremains particularly difficult to forecast and quantify, so thetiming and correct measure of successful policy interventionscontinue to be challenging.

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The Socioeconomic Impact of PoliticalFragmentation in IndiaWhat the Rise of Regional Politics Implies for

Economic Growth and Development

Disha Verma, Harvard University1

Abstract. This paper uses a regression discontinuity approachbased on panel data from the 28 states of India and the unionterritories of Delhi and Puducherry during the period 1994-2012to study the association between political fragmentation in theState Legislatures and growth, debt, and social spending. Politicalfragmentation is judged along three different measures. The firstis the re-election of the incumbent, the second is the marginof victory, and the third is Herfindahl’s index.2 This studydemonstrates that the effects of the incumbent winning and themargin of victory are different between coalition and majoritygovernments. On the whole, coalition governments grow faster,undertake more social spending, and incur less debt. Results areconsidered across several different margins of victory to betterestimate the relationships under consideration.

Keywords: India, political fragmentation, regressiondiscontinuity

1Disha Verma is a junior at Harvard University. She wrote this paper forProfessor Dale Jorgenson’s seminar “The Rise of Asia and the World Economy"in Fall 2013. The author would like to thank Professor Jorgenson for hisinvaluable support and guidance in formulating this topic and understandingthe Indian growth story. She would also like to thank Wentao Xiong and DanaBeuschel for their help in navigating the technical aspects of this paper. Lastly,she is grateful for the input of Professor Torben Iversen and Professor JeffreyFrieden on the political economy theories discussed in this paper.

2Herfindahl’s Index is used in this paper as a measure of politicalcompetition. See Appendix (online) for an explanation of the calculation.

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1 Introduction

India is a remarkable example of a democratic nation among thedeveloping countries in the world. It gained its independencefrom the British in 1947 as a very poor country that had yet toindustrialize.3 Despite global skepticism, India proved that a poor,illiterate country is capable of maintaining democratic principles.India stands out even among the BRICS (Brazil, Russia, India,China, and South Africa) for its history of robust democracy.Democracy involves having multiple voices in government,however, and the question arises of how the resulting politicalfragmentation affects social and economic growth in India. Thequestion that arises is how resulting political fragmentation affectssocial and economic growth in India.

Democratic politics brings individual rights and freedom, butarguably at the cost of efficiency and political sustainability.Political economy models have repeatedly linked fragmentedgovernments to poorer fiscal performance in the form of higherspending and deficits. Volkerink and Haan (2001) find that morefragmented governments, as measured by the number of politicalparties in a coalition or the number of spending ministers, havehigher deficits. They also find some evidence that decreasing thenumber of seats in parliament is linked to lower deficits.

The issue of political fragmentation has become increasinglyprevalent in India since the 1990s. The Indian National Congress(referred to in this paper as the Congress or the INC) led India’sfreedom struggle, and, while other parties did exist and flourishafter independence, the Congress dominated for several decades.4Starting in the 1980s and 1990s, however, regional parties andother national parties such as the Bharatiya Janata Party (BJP)started to increase significantly in popularity. The Congressslowly but surely began to lose its predominance in Indian

3As late as 1973, more than 20 years after independence, more than 40% ofthe urban population and more than 50% of the rural population lived in poverty(Panagariya 2008).

4India did in fact from the time of independence have a well-developedpolitical spectrum on both the right and the left. The Communist Party of Indiawas well established as a leftist national party. On the opposite end of thespectrum, the Jan Sangh, from which the BJP originated, is just one example of aright-wing national party formed in the early decades following independence.

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politics, although it remains the largest national party today.The expansion of political parties has affected political

outcomes in a number of ways: it has increased options forvoters, amplified variance and diversity in who holds seats inparliament, and diluted the concentration of power in the handsof the major parties. Politics has become more uncertain andabsolute majorities harder to achieve. Coalition politics has rearedits head and the importance of alliances has risen drastically. Thenature of politics in India has fundamentally changed.

More uncertainty and tougher competition can change partypreferences, making parties more willing to incur liabilities ifthe future burden is likely to rest on someone else’s shoulders.Social expenditure might become more attractive as a wayto garner support among voters. The short-run could risein importance compared to the long-run when the future ismore uncertain. As a result of these changes, growth, debt,and spending patterns would probably all be impacted. Indiaexperienced almost double-digit growth for the last decade beforewitnessing a growth slowdown starting in 2011. The slowdownhas been attributed to factors such as the global macroeconomicenvironment, falling investor confidence, and deteriorating fiscalindicators. The International Monetary Fund (IMF) estimates thatif India does not return to pre-2008 growth levels, an additional35 million people will live in poverty (IMF India 2013, Article IVConsultation). But the effect of the changing nature of Indianpolitics on growth has not been adequately considered.

This paper aims to assess the effect of political fragmentationin India on socioeconomic outcomes. The rise of regionalpolitics in India is exogenous, in that it took place without anyinstitutional changes, making it an ideal variable to study. Theregression discontinuity approach used in this paper highlightsthe differences between coalition and majority governmentsto identify the effects of political fragmentation. It takesadvantage of the detailed data collected on state-wide electionsand socioeconomic indicators in India from 1994 to 2012. 1994 ischosen as the initial year due to data availability and because itpredates by exactly one political term (five years) the first non-Congress government at the Center to last an entire term. Itthus allows the establishment of the background against which

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the Congress started to lose its dominance.The term “political fragmentation" is defined rather

comprehensively. Rather than narrowing it to one particularmeasure, it is used to describe a full range of changes. Threedifferent aspects of fragmentation are explored: re-election ofincumbents, margins of victory, and the Herfindahl index. Thesethree factors are considered for both coalition and majoritygovernments. The socioeconomic outcomes considered aregrowth rates, social sector expenditures, and total outstandingliabilities of the government.

The paper is organized as follows. Section 2 establishes theinstitutional context of Indian politics and theoretically considersthe political economy of increased fragmentation theoretically.Section 3 analyzes the data and variables used in the study,Section 4 explains the empirical strategy and methodology, andSection 5 presents the results and their implications. Section 6concludes the paper and considers avenues for future research.

2 Background

2.1 Institutional Context

India consists of 28 states and seven union territories. Everystate has a Legislative Assembly that carries out the government’sadministration and is directly elected by the people everyfive years. Since India is a federal republic, the constitutiongrants considerable autonomy to the states and union territories.National issues such as defense and foreign policy are reservedfor the national government; other issues, such as education, areshared between the national and state governments; and a thirdset of issues, such as agriculture and land rights, fall entirelyunder the purview of state governments. These LegislativeAssemblies can make laws, amend central government laws,allocate expenditures, and oversee local governments (Panchayats).State government expenditures account for more than half of totalgovernment expenditures in India. States oversee 60% of medicaland health expenditures, 60% of expenditures on economicservices, and 85% of educational expenditures (Rao & Singh1998). On the whole, state governments have more influence over

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issues such as education, social security, and transportation (Clots-Figueras 2011). For these reasons, the relation between politicalfragmentation and socioeconomic outcomes is assessed in thisstudy through State Assemblies rather than the Parliament (i.e.the central government).

The size of Legislative Assemblies is based on population.Each elector has one vote based on universal suffrage. Any Indiancitizen who is over 18 and is registered as a voter can cast his orher vote. The length of a term served by members of an Assemblyis five years. Any Indian citizen over 25 who is registered to votecan run for election. Elections in a constituency are first-past-the-post, so that the candidate with the most votes wins. A partythat gains a majority of seats in the Assembly (>50%) comes topower and elects the state’s Chief Minister. If no single partywins a majority, a coalition must be formed. As a consequenceof coalitions, although elections are scheduled to take place everyfive years, in some cases shifting political alignments and hungparliaments can lead to elections before the end of a five-yearterm.

2.2 The Political Economy of Increased Fragmentation

The change in the nature of politics has increased uncertaintyand fostered competition. The rise in the number of politicalparties means there is greater competition; the potential winnersof elections become more uncertain. These changes have ledto three main results. First, seats are more divided betweenparties, leading to the prevalence of coalition governments at boththe State and Center. Second, the balance of power has shiftedaway from national parties towards regional parties, so there aremore political actors with power. Third, political frontiers haveshortened because the incumbent party can switch repeatedlyover subsequent elections and even within one term, as is the casein states such as Tamil Nadu, Rajasthan, and Uttar Pradesh.

These changes can be expected to change equilibriumpreferences for political actors and affect socioeconomic outcomes.Fragmentation, especially in multi-party coalition governments,creates what can be termed a “common pool problem," in whichparties spend on their own constituencies and discount the

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adverse effects on the economy as a whole. Olson introduces theidea of "distributive coalitions" that increase in number over timeand are concerned not with expanding the size of the economicpie but the way it is split (Olson 1965). Since the benefits ofthese policies are concentrated among a select few groups andthe costs are diffused among the population, these coalitionswill prosper by the logic of collective action. Economic growthwill suffer because, by the exclusive nature of their membership,distributional coalitions tend to favor protectionist and anti-technology policies that benefit only their members (Olson 1965).

Another reason to be concerned about political fragmentationis that rapid government turnover and instability make politiciansmyopic. An inability to commit to the future, or "timeinconsistency," is perpetuated (Kydland & Prescott 1977).Governments that expect to stay in power for a short period willdiscount the future and try to grab what they can in the present,harming investment and long-term growth. This effect will bereinforced if parties become less concerned about their reputationbecause of rapid turnover. Populist policies may become moretempting as political parties try to gain voter support. Socialexpenditures may rise at the cost of fiscal responsibility. Thecurrent Congress government has been widely criticized for therecent Food Security Act of 2013 for exactly this reason. Criticsallege the act is nothing but a ploy to get more votes withoutconcern for the impact of the additional expenditures, assessed at1.5% of GDP at the bare minimum (“The massive hidden costs ofIndia’s food security act" 2013).

Finally, the burgeoning of coalition politics increases thenumber of "veto" players. There are more parties or groupswho must all agree to a policy before it can be implemented.Uncertainty about who will suffer more if no agreement is reachedmay lead to a “war of attrition" (Alesina & Drazen 1991). Thistranslates to a “battle of the sexes" game and can be understoodthrough the example of fiscal consolidation, where all partiesagree that it is necessary to cut the deficit but disagree as to howthe burden should be distributed. If the parties do not know whowill bear the greater burden when no agreement is reached (i.e.there is high uncertainty), all parties may hold out for a betterdeal, even though this will leave everyone worse off.

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3 Data

3.1 Electoral Data

The electoral data used were collected from elections in the periodfrom 1994 to 2012 for every state in India and the union territoriesof Delhi and Puducherry. The data were obtained from theelectoral reports published by the Election Commission of India.They include the year of election, the number of seats won byeach of the three largest parties, the total number of seats inthe Assembly, whether or not the incumbent won, how manyparties competed, and how many parties ultimately won seats.This information is used to calculate the margin of victory andHerfindahl’s index, which is a measure of political competition.

Rather than assessing just the relationship between theoutcomes and the incumbent winning through a dummy variable,this paper also calculates the connection between the incumbentwinning conditional on the margin of victory. This processis repeated for successively smaller margins, allowing for theformulation of clearer causal effects. A positive margin of victorymeans that the winning party had a majority. A negative marginof victory means that the party with the most seats did not havean absolute majority and needed to form a coalition.

The margin of victory is measured this way because it allowsus to easily investigate the relationship between coalitions vs.single-party (majority) governments and development outcomes.In cases where the largest party (the one with the most seats)needed to form a coalition, the margin of victory does not indicateit was successful in doing so. The margin of victory simplyindicates that no party managed to get absolute power and hencea coalition government was needed. There are examples of states,such as Nagaland in 2002, where the party with the most seats, inthis case Congress, did not have enough seats to form a majorityon its own and ended up not coming to power because partieswith fewer seats formed a coalition. In this paper, Herfindahl’sindex applies to political competitiveness (or fragmentation). Itsvalues range between zero and one. The closer to zero a state’sscore is, the more politically competitive it is, which means ithas more parties with a significant number of seats and is morefragmented.

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3.2 Outcome Variables

The rise of regional politics in India is a relatively newphenomenon, and its effect on developmental outcomes hasnot yet been well documented. As already discussed, highturnover, distributional coalitions, and an increase in veto playerscan increase government deficits, change expenditure patterns,and focus energy on the distribution rather than growth of theeconomic pie. With this in mind, this paper considers threeoutcomes at the state level that would be affected by politicalfragmentation: growth rates, total outstanding liabilities of stategovernments, and social sector expenditures. Social servicesare primarily the responsibility of state governments, whichincur more than 80% of combined government expenditures inthese areas (Reserve Bank of India, “State Finances: A Study ofBudgets"). The ratio of social expenditures to total expenditurescan thus be considered a good indicator of the extent to whichthe expansion of the social safety net is a priority comparedto economic services such as energy, transportation, and debtservicing. The total outstanding liabilities of the state government,as well as social sector expenditures, together indicate how fiscallyresponsible a state government is.

Rather than assessing the effect of fragmentation on theseoutcomes in a given year, this paper calculates the average of theoutcome under consideration for the duration of a party’s termin office. This allows for better assessment of a government’sperformance, and also avoids the tricky question of which yearis most appropriate to use for assessment. Descriptive statisticsfor the outcome variables as well as the electoral variables arepresented in Table 1.

3.3 Controls

A number of controls are included and are indicative of thenormal condition of affairs in the state. They help ascertain thatthe results were due to the factors tested in the experiment and notto a natural or random occurrence. Equivalently, they reduce thecorrelation of the X variables with the error term. All the controlsmay be correlated with the measures of fragmentation, but noneare perfectly multicollinear. Literacy rate is included to factor out

74

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619.

153

12.4

8

75

the effect of education on the outcome variables. It is calculatedbased on the population aged seven or above. Also included is thepercentage of people below the poverty line (BPL), determined bythe Planning Commission of India. This is a good indicator ofhow developed a state is; poorer states will have more peoplebelow the poverty line. If development is a process, then a state’slocation in that process might determine its expenditure prioritiesor debt liabilities. Hence percent BPL is included to control, atleast to some degree, for the effect of poverty and developmenton the outcomes being investigated.5

The third control is an average of the rural and urban Ginicoefficients. States that have lower inequality might be theones spending more on social services, and might consequentlyincur more debt to provide these services. The fourth controlis sex ratio. There is an extensive sophisticated literature thatdocuments how women’s political preferences are different frommen’s (Clots-Figueras 2011). Political fragmentation might varyacross these preferences; thus, the sex ratio is included to controlfor the effect of differential preferences of men and women.The last two controls are the number of parties competing andthe number of parties that ultimately win seats, to account fordifferent political backdrops.

In any given regression, out of the three dependent variablesbeing studied, the other two are included as controls. Debt toGDP, social sector expenditures, and growth rates are likely tobe correlated, and adding them to the regression separates theirintercausality from that of political fragmentation. When addedas controls, their value in the year in which the government gotelected is included. The base year is selected in this mannerbecause the election might impact the concerned variables,leading to an endogeneity problem.

5Percent BPL ultimately had to be dropped as a control because it did nothave enough observations and was complicating the test results.

76

4 Causal Effects of Fragmentation

4.1 Graphical Analysis

The data used in this paper are examined in a way that candistinguish between pure selection and the proposed causaleffect of type of government and incumbency. Despite the factthat coalition and majority governments are likely systematicallydifferent, it is highly plausible that majority governments formedby a very slim margin are ex ante comparable to coalitiongovernments formed by just falling short of the majority. Whenwe focus on the set of states with close elections, it becomesmore plausible that idiosyncratic factors, and not systemic statecharacteristics, affect the outcomes of interest. Thus, under certainconditions, states where the party with the most seats barelyformed a majority can serve as a reasonable counterfactual forstates where they barely lost out on the majority. Thistlethwaiteand Campbell (1960) originally provided the idea of exploitingcases where a treatment variable is a deterministic function of anobserved variable. In this case, the nature of an election providesthe deterministic function, and the observed variable is the marginof victory.

Figure 1 illustrates the regression discontinuity with respectto the type of government. A government’s mean socialexpenditures, mean total outstanding liabilities, and mean growthrecord over its term in office are expressed as functions of itsmargin of victory. To assess purely causal effects, the observationsconsidered are only those of close elections, in which the marginof victory falls between ±5% of the threshold needed to form amajority, and hence the outcome can reasonably be said to havebeen determined by chance.6 Points on the line to the rightrepresent outcomes for majority governments (margin of victory> 0). Points on the line to the left represent outcomes for coalitiongovernments (margin of victory < 0).

Comparing the graphed functions of the outcome variablesbetween the right- and left-hand sides of the threshold reveals thedifference that arises between majority and coalition governments.

6These figures were calculated using triangular kernels. The bandwidthdefined was 15.

77

Figure 1: Effect of Margin of Victory Within a ±5% Interval of theThresholda

Mean Growth Mean Social Expenditures Mean Outstanding Liabilities

aIn reality, a party needs more than 50% of seats to obtain a majority. In thispaper however, the margin of victory is calculated in a way that takes this intoaccount and makes zero the effective threshold for ease of analysis. See dataappendix for exact details on calculation.

Although not too large, it indicates that coalition governmentsare associated with lower outstanding liabilities, higher socialexpenditures, and higher growth than majority governments. Theresults stay the same if the interval considered for the margin ofvictory is extended to ±10% (see Figure 2).

Figure 2: Effect of Margin of Victory Within a ±10% Interval ofthe Threshold

Mean Growth Mean Social Expenditures Mean Outstanding Liabilities

78

4.2 Validity

Identification requires that all relevant factors besides treatmentvary smoothly at the threshold between a coalition andmajority government. Formally, letting y1 and y0 denotepotential outcomes under a coalition and majority, identificationrequires that E[y1|margin] and E[y0|margin] are continuous atthe majority-coalition threshold of 50%. All observable andunobservable pre-determined characteristics that could influencethe outcome variables must not be systemically different betweenmajority and coalition governments. For instance, if majoritygovernments are formed with more adept political candidatesthan are present in coalitions, outcomes may vary not because ofthe type of government but because of the people who form them.Causality would be incorrectly attributed and the internal validityof the discontinuity jump as a causal effect could be questioned.Thus, the baseline characteristics of the treatment group shouldnot in any observable way be ex ante systemically different fromthe control group.

To test this, the mean and standard deviation for controlvariables on both sides of the margin of victory threshold arecomputed, including demographic factors, economic indicators,and electoral factors. Also included are the base year values ofthe outcome variables. As Table 2 indicates, the results appearfairly equal on both sides of the threshold. The only statisticallysignificant difference was in the average Gini coefficient, lendingcredibility to the identification strategy employed in this paper.

4.3 Methodology

The regression discontinuity approach used in this paper toestimate the association between type of government and growth,liabilities, and social sector expenditures at the state level exploitsthe fact that the type of government (coalition vs. majority)changes discontinuously at the threshold of 50% of seats. Theformal empirical specification for the right side of the threshold(i.e. majority governments) is:

Yit = a0 + a1 Iit + a2Mit + a3 Iit Mit + a4Hit + dXit + ai + bt + uit, (1)

79

Tabl

e2:

Base

line

Cha

ract

eris

tics

Maj

ority

Gov

ernm

ents

Coa

litio

nG

over

nmen

tsN

umbe

rof

Obs

erva

tions

Mea

nSt

anda

rdD

evia

tion

Num

ber

ofO

bser

vatio

nsM

ean

Stan

dard

Dev

iatio

n

Con

trol

sLi

tera

cyR

ate

6065

.062

12.6

6749

66.9

8313

.457

Sex

Rat

io61

925.

541

44.6

0249

950.

122

48.1

42To

talP

artie

sTh

atW

onSe

ats

615.

852

2.99

949

8.02

03.

430

Tota

lPar

ties

Con

test

ing

6131

.049

32.6

7549

32.4

4820

.957

Soci

alSe

ctor

Expe

nditu

re61

34.6

497.

029

4735

.114

6.22

5G

row

thR

ate

577.

729

5.83

348

8.05

45.

034

Tota

lOut

stan

ding

Liab

ilitie

s61

39.4

7820

.404

4736

.382

11.7

78A

vera

geG

ini

49.2

84.0

3739

.299

.048

80

where Yit is the outcome of interest in state i in year t, ai and bt arestate and year fixed effects, I is a dummy variable for whether theincumbent won with a positive margin, M measures the margin ofvictory, and H is Herfindahl’s index. Iit Mit is the interaction termfor the margin conditional on the incumbent winning and themargin being positive. Xit represents other control variables anduit is a measure of the error term. The inclusion of time effects andfixed effects improves the precision of the estimates by allowingus to account for state-specific factors and time trends. Thisspecification has a counterpart for the left side of the threshold, inwhich case the dummy variable indicates whether the incumbentwon with a negative margin, and the interaction term is for themargin of victory conditional on the incumbent winning and themargin being negative.

As outcome variables, the mean social expenditures (asa percentage of Aggregate State Expenditure), mean totaloutstanding liabilities (as a percentage of Gross State DomesticProduct), and mean growth rates (as a percentage of StateGross Domestic Product) over a government’s term in office areused, allowing for comprehensive evaluation of a government’sperformance. All the control variables, such as sex ratio andliteracy rate, are for the year of the election itself to avoidendogeneity. To check for robustness, results are reported withand without the outcome variables as regressors. When includedin this manner as controls, it is not the mean but the base yearvalue of the outcome variables that is considered.

Close elections are more likely to have had outcomesdetermined by chance rather than systemic characteristics andhence be more indicative of causality. Therefore, regressions arecarried out first for the whole set of elections and then for electionswith a margin of victory above and below 10% and 15% of thethreshold. Due to the limited dataset, it was not possible to lookat elections within the 5% margin with the expanded empiricalspecifications. The graphical analysis, by contrast, consideredonly the margin of victory and thus the 5% margin could beincluded.

To identify the causal effects of incumbent governments, astrong assumption has to hold: an incumbent win and incumbentloss should be similar in all observable and unobservable

81

Tabl

e3:

Des

crip

tive

Stat

istic

sBa

sed

onIn

cum

benc

y

Incu

mbe

ntW

inIn

cum

bent

Loss

Num

ber

ofO

bser

vatio

nsM

ean

Stan

dard

Dev

iatio

nN

umbe

rof

Obs

erva

tions

Mea

nSt

anda

rdD

evia

tion

Con

trol

sLi

tera

cyR

ate

5365

.281

12.8

4359

67.2

3513

.342

Sex

Rat

io54

927.

055

42.3

3859

948.

186

51.2

90To

talP

artie

sTh

atW

onSe

ats

546.

259

3.24

559

7.20

33.

40To

talP

artie

sC

onte

stin

g54

28.6

8521

.119

5933

.644

32.5

7So

cial

Sect

orEx

pend

iture

5334

.845

6.30

858

34.9

367.

072

Gro

wth

Rat

e50

7.82

45.

323

577.

875

5.59

7To

talO

utst

andi

ngLi

abili

ties

5340

.011

18.5

858

37.0

7915

.985

Ave

rage

Gin

i43

.281

.044

48.2

99.0

43

82

characteristics that might determine the outcome variables.Candidate and constituency characteristics should be similar. Thetest conducted to check this is similar to that in Section 3.2 tocompare similarity of controls on both sides of the threshold. Inthis case, the “threshold" is whether or not the incumbent won.The outcome variables for the base year are also included. Theresults display no statistically significant difference between caseswhere the incumbent won and did not win except for the averageGini coefficient. They are displayed in Table 3.

However, this test does not consider the traits of the partiesand candidates themselves. Close elections would have been anideal condition under which to study the effect of incumbency,but the dataset is too limited. The results must be interpreted assimply indicating a link between incumbency and the outcomevariables rather than displaying a causal effect.

5 Results and Interpretation

5.1 Mean Growth Rate

While the results are in general not statistically significant, it isstill possible to draw inferences about their meaning. Table 4includes results for the association between mean growth rateand political fragmentation first without controls, with controls,and finally with the other two outcome variables (social sectorexpenditures and total outstanding liabilities) as controls aswell. When an incumbent wins with enough seats to forma majority government, the results clearly show that growthsuffers. The results are also statistically significant in theregression excluding controls, especially when one considers thatthe standard deviation for the average of the mean growth ratein majority governments across states is 2.6 and the mean is 7.0,while our regression coefficients are all below �4, which is morethan three standard deviations away. Lack of accountability couldbe a possible reason for this negative effect, as could complacencyon being re-elected. The incumbent winning when the consequentgovernment is a coalition does not seem to have much of an effecton growth, with the coefficient being less than 0.3, albeit positive,in all cases.

83

Tabl

e4:

Dep

ende

ntVa

riab

le:M

ean

Gro

wth

Rat

e

Inde

pend

entV

aria

bles

All

Obs

erva

tions

Coa

litio

nM

ajor

ityC

oalit

ion

Maj

ority

Coa

litio

nM

ajor

ity

Incu

mbe

ntW

in.1

44�

4.08

9***

.248

�4.

694

.284

�4.

734

(3.1

23)

(1.8

03)

(4.0

72)

(2.6

32)

(2.3

44)

(3.2

01)

Her

finda

hl’s

Inde

x-3

9.03

6.94

4�

50.7

803.

677

�46

.560

�11

.369

(26.

821)

(17.

543)

(32.

357)

(21.

025)

(15.

142)

(26.

905)

Mar

gin

ofV

icto

ry.2

67�

.232

.338

�.2

27.2

76�

.059

(.240

)(.1

84)

(.305

)(.2

16)

(.988

)(.2

87)

Incu

mbe

ntW

ingi

ven

Mar

gin

.166

.227

***

.186

.237

-.086

.258

(.188

)(.1

03)

(.257

)(.1

32)

(.151

)(.1

45)

Lite

racy

Rat

e-

�.0

47�

.050

.035

�.0

08(.4

77)

(.253

)(.2

35)

(.312

)To

talP

artie

sth

atW

onSe

ats

-1.

175

�.1

95.9

24�

.224

(.832

)(.4

18)

(.508

)(.4

39)

Sex

Rat

io-

.028

�.0

32.0

60�

.030

(.123

)(.0

93)

(.127

)(.1

23)

Tota

lPar

ties

Con

test

ing

-.0

01�

.030

�.2

55�

.000

(.266

)(.1

78)

(.161

)(.1

90)

Gro

wth

Rat

e-

.327

.192

(.210

)(.2

11)

Soci

alSe

ctor

Expe

nditu

re-

.196

.012

(.257

)(.0

86)

N48

6048

5946

59

*,**

,***

indi

cate

sst

atis

tical

sign

ifica

nce

atth

e10

%,5

%,a

nd1%

leve

l,re

spec

tivel

y.

84

Herfindahl’s index represents the extent of politicalcompetition or division. Since it only varies between 0 and1, the coefficient from the regressions does not have much value.However, the signs of the coefficients clearly show that, whenthere is a coalition government, greater power division amongdifferent parties is bad for growth. This is evidence for theargument that more veto players can harm growth by causingdelays and inefficiencies.

The coefficient on margin of victory represents the change ingrowth due to a 1% change in the number of seats held by thelargest party. Interestingly, the coefficient is consistently negativefor majority governments and positive for coalition governments.It would seem that, when a party has a majority, larger marginsof victory are worse for growth. Accountability and complacencycould again be the reasons for this. On the other hand, whenthe winning party must form a coalition because it does not haveenough seats to come to power independently, coming closer tothe 50% threshold is correlated with slightly higher growth. Thiscould be because while accountability is beneficial to an extent,too much division of power could cause inefficiencies, and henceit is better to have power more concentrated within one party in acoalition.

However, when the incumbent wins, our findings about theeffect of the margin of victory change somewhat, such thata higher margin generally appears good for growth in bothcoalition and majority governments. Perhaps re-election, byallowing continued momentum on the same path, impacts growthpositively, and the higher the margin, the more freedom theincumbent has to continue its chosen policies. This does not refuteour earlier conclusion that incumbents winning with a majorityare bad for growth; it simply states that, when an incumbent wins,a higher margin of victory could be better for growth. None ofthe coefficients on the controls are statistically significant, and theresults were mixed, making it hard to draw a clear picture of theirconnection to growth.

85

Tabl

e5:

Dep

ende

ntVa

riab

le:M

ean

Soci

alSe

ctor

Expe

nditu

res

Inde

pend

entV

aria

bles

All

Obs

erva

tions

Coa

litio

nM

ajor

ityC

oalit

ion

Maj

ority

Coa

litio

nM

ajor

ity

Incu

mbe

ntW

in5.

963

1.00

15.

976

�.9

111.

772

5.28

8(3

.974

)(2

.727

)(5

.418

)(3

.859

)(5

.139

)(3

.257

)H

erfin

dahl

’sIn

dex

2.96

613

.978

10.7

6110

.584

�46

.560

***

�2.

512

(33.

998)

(26.

101)

(43.

058)

(30.

557)

(15.

142)

(19.

965)

Mar

gin

ofV

icto

ry�

.068

�.1

98�

.054

�.2

19.3

45.1

70(.3

05)

(.274

)(.4

07)

(.315

)(.4

22)

(.226

)In

cum

bent

Win

give

nM

argi

n.3

98.1

29.3

89.2

05.4

02�

.011

(.252

)(.1

57)

(.379

)(.1

94)

(.438

)(.1

44)

Lite

racy

Rat

e-

.076

-.332

�.2

06�

.268

(.645

)(.3

69)

(.540

)(.2

50)

Tota

lPar

ties

that

Won

Seat

s-

-.768

.101

�.4

96.4

04(1

.207

)(.6

03)

(.941

)(.4

02)

Sex

Rat

io-

�.2

20-.0

13.2

59�

.006

(.165

)(.1

35)

(.259

)(.1

14)

Tota

lPar

ties

Con

test

ing

-.0

58�

.024

.262

.196

(.359

)(.2

6)(.2

74)

(.154

)G

row

thR

ate

-�

.807

.438

***

(.628

)(.0

93)

Tota

lOut

stan

ding

Liab

ilitie

s-

�.6

61*

�.0

48(.3

68)

(.071

)N

4861

4860

4656

*,**

,***

indi

cate

sst

atis

tical

sign

ifica

nce

atth

e10

%,5

%,a

nd1%

leve

l,re

spec

tivel

y.

86

5.2 Mean Social Sector Expenditures

Table 5 displays the results pertaining to mean social sectorexpenditures. Social sector expenditures are calculated as aratio to aggregate expenditure, and the mean is calculatedover a government’s term in office. The findings indicate thatsocial sector expenditures rise by more if the incumbent winsand has to form a coalition than if the incumbent wins amajority. Considering that the standard deviation for mean socialexpenditures is 5.354 for coalitions, the coefficients on incumbentswinning in coalitions seem more significant (5.96, 5.97, and1.77). Coalition governments by definition represent a broaderset of interests, which may lead to higher social spending than agovernment representing a narrower group.

The coefficients on Herfindahl’s index do not hold upconsistently under the different regressions and are thusinconclusive. The margin of victory has mixed results anddoes not seem to have a significant impact either way in bothgovernment types. However, if an incumbent wins, an increase inthe margin seems to be associated with a slight increase in socialspending, especially for coalition governments.

5.3 Mean Total Outstanding Liabilities

Table 6 displays the results for the link between fragmentationand average outstanding liabilities of a state government overits term in office. The standard deviation for the average of themean liabilities across states is 11.149 for coalitions and 17.06 formajorities. None of the coefficients from the results fall outsidethese margins, except the coefficients on Herfindah’s index, whichas mentioned before cannot be interpreted in the same way as theother coefficients because the index only ranges between zero andone.

The incumbent winning and forming a coalition governmentis consistently associated with lower outstanding liabilities, orreduced debt. The incumbent winning and forming a majorityis associated with increased debt. The issue of accountabilitywould seem to again rise to the fore. In a coalition, the incumbentmust justify its debt to its allies. However, an incumbent winningin a coalition is simultaneously related to a bigger increase in

87

Tabl

e6:

Dep

ende

ntVa

riab

le:M

ean

Tota

lOut

stan

ding

Liab

ilitie

s

Inde

pend

entV

aria

bles

All

Obs

erva

tions

Coa

litio

nM

ajor

ityC

oalit

ion

Maj

ority

Coa

litio

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ajor

ityC

onst

ant

27.7

2641

.264

***

�24

1.94

0�

417.

456*

�47

.050

�53

6.76

7(1

6.91

3)(1

9.23

)(2

19.5

02)

(246

.489

)(3

21.5

97)

(345

.897

)In

cum

bent

Win

�.6

933.

870

�6.

283

4.86

5�

1.21

05.

760

(5.1

59)

(5.6

6)(7

.086

)(7

.336

)(8

.042

)(1

2.27

4)H

erfin

dahl

’sIn

dex

14.4

41�

15.2

99�

2.47

023

.187

�66

.128

7.52

1(4

4.13

6)(5

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(90.

475)

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gin

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ry�

.072

�.0

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99)

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00)

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)In

cum

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give

nM

argi

n�

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�.1

60�

.5�

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.213

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(.326

)(.4

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(.369

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(.576

)Li

tera

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ate

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107

�.1

32.4

20�

.440

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lPar

ties

that

Won

Seat

s-

�.7

68�

.952

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399

.902

(1.2

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(1.5

78)

(2.2

08)

(1.6

38)

Sex

Rat

io-

�.2

2.2

30.1

10.6

08*

(.165

)(.2

15)

(.295

)(.3

61)

Tota

lPar

ties

Con

test

ing

-.0

58.0

27.4

29.6

10(.3

59)

(.469

)(.6

17)

(.62)

Gro

wth

Rat

e-

�1.

288

�.2

71(1

.435

)(.4

59)

Soci

alSe

ctor

Expe

nditu

re-

�.3

90.5

35(.6

89)

(.925

)N

4861

4860

4656

*,**

,***

indi

cate

sst

atis

tical

sign

ifica

nce

atth

e10

%,5

%,a

nd1%

leve

l,re

spec

tivel

y.

88

social spending than in a majority. One possible explanation isthat the leading party has more pressure to satisfy voters whenit is in a coalition, hence the increase in social expenditure.At the same time, it is also held more accountable for thespending it undertakes. The increase in social spending and thedecrease in debt in coalitions could perhaps reflect a realignmentof priorities towards social spending, and also more fiscallyprudent and efficient spending. The higher debt incurred byincumbents gaining majorities goes hand in hand with lowergrowth, pointing to unaccountability and inefficiency, perhapsrelated to complacency, as culprits.

This conclusion is opposed, however, by the consistentlynegative coefficient on an incumbent winning a majority asits margin of victory rises. While the coefficients are small,there nonetheless seems to be an inverse relationship betweenthe margin of victory and total debt if an incumbent wins amajority. The answer might lie in the democracy-efficiencytradeoff. As power becomes more concentrated, policies becomemore streamlined, and improved governance could result in lowerdebt as well as higher growth, which were indeed indicated by thefindings. Moreover, as a majority incumbent party strengthens itshold, it could be said that it in fact becomes more accountableto the people, since it is clearer where the power is concentrated.This too could result in lower debt and higher growth. This doesnot negate that an incumbent winning a majority takes on moredebt than an incumbent winning but needing a coalition. It simplymeans that, if the margin of victory by which an incumbent winsan absolute majority rises, the debt it takes on reduces.

The findings are inconclusive for the effect of Herfindahl’sindex on debt, as they are for the margin of victory. However,we can infer by the small coefficients in relation to the standarddeviation from the descriptive statistics that the margin of victorydoes not have a significant impact.

6 Conclusion

A question that remains is the external validity of this study. Inthe case of India in particular, the applicability of this model tothe national government rather than the state governments has

89

not been investigated. However, it is reasonable to assume thatthere is some correlation between a voter’s decisions in state andnational elections, and that a government’s performance at theCenter affects to at least some degree a voter’s preferences at thestate level and vice versa. If this holds true, we can draw someinferences about the performance of India as a whole over the lastfew years.

The last general (national) elections in India were held in2009. The Indian National Congress remained in power througha coalition by winning 61 more seats, and all the oppositioncoalitions witnessed declines in the number of seats they held.The result, a huge win for the Congress, meant more powerconcentration in the Congress at the cost of all opposing parties.As per the findings in this paper, this should have been associatedwith slightly higher growth, which was indeed the case untilabout two years into the INC’s second term, when a slowdownstarted. The results provide no plausible explanation for thisslowdown; economic factors outside the realm of institutionalarrangements are likely to be the culprit. The findings from thispaper further show that the incumbent winning and forming acoalition is associated with an increase in social spending, asis a rise in the incumbent’s margin of victory. This is indeedwhat India has witnessed through the Food Security Act and thecontinuance of the National Rural Employment Guarantee Act.The results for mean liabilities are conflicted with respect to theoutcome of the 2009 elections, and no strong conclusion can bedrawn.

On the positive side and from a long-term perspective,the results in this paper do seem to indicate that coalitiongovernments can be better for growth than majority governments,and that re-election of the incumbent through majoritygovernments is bad for growth. It is only in the last 20 yearsthat the Congress has had to depend on coalitions, and regionalparties have risen at the state level. India’s faster growth afterthe crisis of 1991 might then in part be associated with the rise ofcoalitions and regional politics.

However, there is still reason to be apprehensive that therise of regional politics may negatively impact growth in India.Coalitions in which there is one major party and several smaller

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parties might be good for growth, but more equal power divisionbetween several different parties is conclusively bad for growth,whether at the state or national level. If the next general electionsusher in a greater split of power at the Center, between not justnational but also regional parties, the outlook for India is notpromising. The growth slowdown that India is witnessing couldtake a turn for the worse, with more veto players, greater chanceof deadlock, and a rise in distributional coalitions.

The findings in this paper are unclear about the relationbetween fiscal prudence and political fragmentation. Theyindicate on one hand that the rise of regional parties andopposition parties such as the BJP should be associated with arise in social spending, and on the other that they should berelated to a reduction in debt, both of which have indeed beenthe case over the past decade (World Bank, Data Indicators).A rise in social spending could also be harmful in ways otherthan fiscal imprudence; it could indicate increased financialallocation away from economic services, such as transportationand communication, which foster growth. Greater focus ondistributing the pie at the cost of increasing its size can beinjurious if it affects long-term growth prospects, especiallyconsidering the extent of poverty in India.

A reduction in outstanding liabilities associated withcoalitions could also be detrimental to India’s growth prospects.Although tempting, a decline in debt cannot be taken as a positivedevelopment at face value. It is the composition of the debt thatmatters. If the decrease in liabilities is because of a reductionin ’good debt,’ meaning debt that fosters long-term growth andinvestment, then that is yet another factor India has to worryabout.

There is very likely some interplay or reverse causalitybetween liabilities, social spending, and growth that has not beenadequately explored. More research is needed to establish therelationship between these factors in the case of India. One reasonthat the predicted associations with liabilities and social spendingcan already be seen may be that the latter two are more directlyand quickly impacted by government decisions. Growth, bycontrast, depends on numerous other factors, which could be whya longer timeframe is needed to observe the results suggested in

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this paper. A continuation of the ideas presented in this study overa longer timeframe could be beneficial in more clearly establishingrelationships.

Future research also needs to experiment with differenttime periods in which a government’s performance is studied.This study takes data on state governments and then drawsinferences for central governments; future work could lookat the relationship between voters’ preferences in state andgeneral elections or undertake similar studies targeted at thecentral government. A more nuanced understanding of thesocioeconomic changes ushered in by political fragmentation willnot just aid voters and their political representatives in makingmore informed decisions, but might also shed light on thevariance in national and state development outcomes.

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Does the Implementation of Affirmative Actionin a Competitive Setting IncentivizeUnderrepresented Public School Applicants’Performance?Evidence from São Paulo

Dounia Saeme, University of California, Berkeley1

Abstract. In 2011, the Federal University of São Carlos(UFSCar) in São Paulo, the most populous state in Brazil,created a 40% quota for black and public school applicants.This study investigates whether the introduction of affirmativeaction at the university level creates an incentive for thetargeted underrepresented applicants to perform better on theirqualifying exams in a state where public universities admitone out of 25 students on average. Using data providedby the standard Brazilian entrance exam (ENEM) and itsmandatory socioeconomic survey from 2010 and 2011, I employa difference-in-differences (DID) methodology in order to exploitthe characteristics of this quasi-experiment. I use the favoredgroup’s counterparts from comparable states in Brazil that had notintroduced any type of affirmative action during those years as acomparison group. I find that, on average, black students frompublic schools in São Paulo scored 1.54% higher on the ENEM asa result of the introduction of quotas in UFSCar admissions, andthe scores of public school students (unconditional on race) in SãoPaulo were 1.16% higher on average. I find no change amongprivate school test-takers.

Keywords: affirmative action, Brazil, difference-in-differences

1Dounia Saeme is a senior double-majoring in applied mathematics andeconomics at the University of California, Berkeley. She wrote this honors seniorthesis for Professor David Card. The author is very grateful for Professor Card’shelpful comments and useful discussion throughout her research. She wouldalso like to thank Mikkel Sølvsten for his advice on her analysis.

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1 Introduction

In August 2012, the Brazilian government enacted one of theWestern hemisphere’s most sweeping affirmative action laws,requiring public universities to reserve half of their admissionspots for public school students, who primarily come from lowerincome groups. This vastly increased the number of students ofAfrican descent in universities across the country.

This drastic measure, aimed at restoring equal opportunity forall Brazilian children, has provoked heated debates in academic,political, and public spheres. Some claim that these aggressivequotas will generate adverse incentives for the accumulation ofhuman capital by benefiting a lower-performing, poorer segmentof the population. Others believe that, with this large reduction inthe marginal cost of education, low-income and minority studentswill finally have the opportunity to succeed in Brazilian societyand will perform just as well as their private school counterparts.

Since the 1960s, numerous countries have adopted affirmativeaction policies as a way to improve skill acquisition andhuman capital accumulation among minority groups (Sowell2004). The importance of Proposition 209 in the United States,which after 1996 prohibited the University of California fromusing affirmative action in admissions decisions, demonstratesthe pervasive and controversial nature of affirmative action.2Consequently, there is a vast literature on affirmative actionthat delivers insightful findings and theories on the importantcharacteristics of the affected minority population (Milgrom &Oster 1987, Card 2001, Lang 1993). Analyzing how targeted andnon-targeted groups are both affected by affirmative action iskey to understanding the impact of the Brazilian policy. Fryerand Loury (2005) argue that “confident a priori assertions abouthow affirmative action affects incentives are unfounded. Indeed,economic theory provides little guidance on what is ultimately asubtle and context-dependent empirical question."

In light of the Brazilian debate, I will examine the introduction

2Proposition 209, approved in November 1996, is an amendment to theCalifornia state constitution that prohibits state government institutions fromdiscriminating on the basis of race, sex, or ethnicity when making decisionsabout public employment, public contracting, or public education.

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of a quota system that benefits black and public school studentsin the admission procedure of the Federal University of SãoCarlos (UFSCar) in São Paulo, evaluating its incentive effecton applicants’ performance on the national Brazilian entranceexam. Affirmative action was first introduced in Brazilian federaluniversities in 2002, but São Carlos was the only university thatintroduced quotas in 2011.

I will investigate whether affirmative action enhances orundercuts incentives to perform well on the entrance exam. Idocument the impact of this quota system on test performancethrough Exame Nacional do Ensino Médio (ENEM), or NationalHigh School Exam, survey data from 2009 and 2010. Iemploy a difference-in-differences (DID) methodology, exploitingthe characteristics of this quasi-experiment to compare theperformance of the students favored by the policy in the state ofSão Paulo to the performance of similar students in comparablestates that did not introduce any type of affirmative action in thoseyears. Because the number of students who leave their homestates to attend an undergraduate program in Brazil is very low,this study assumes that students in other Brazilian states are notaffected by quotas implemented in São Paulo.

I find that, in São Paulo, the test scores of black students andpublic school students were 1.4% and 1.16% higher, respectively,as a consequence of the introduction of these quotas. Withan (unconditional) ENEM test score gap of approximately 15%between public school students and private school students inSão Paulo, a 1.16% increase in the performance of public schoolstudents indicates approximately an 8% closing of this gap.

The group most affected was black applicants, and thispattern is reflected within public school applicants. Conditionalon having been schooled in public establishments, the ENEMscore of white test-takers increased by 0.83%, the ENEM scoreof pardo (brown-skinned) test-takers increased by 1.27%, andthe ENEM score of black test-takers increased by 1.54%. Thispattern reflects the effect desired by the University of São Carlos:incentivizing and providing higher education to social groups thatare underrepresented in the state’s federal universities.

These results must be interpreted carefully. São Paulo isdifferent from the rest of Brazil on many levels. First, only 2.8%

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of its more than 10 million blacks have a university diploma(Pnad/Instituto Brasiliero de Geografia e Estatística (IBGE) 2001).In addition, public universities are extremely competitive; theyreceive 25 applications per available seat. Second, UFSCar is oneof the only two universities in the state that uses the ENEM, asSão Paulo universities resist adhering to the system, while otherstates embraced this unified exam in early 2000.

I also consider the limitations of attributing these resultsto UFSCar’s quota implementation. I discuss how I wouldverify whether my main results are robust to a series ofpotential problems, including some of the usual concerns in DIDmodels. First, I consider preexistent differential trends priorto the introduction of the quotas. I suggest the limitations ofincorporation data from previous and following years in myanalysis. Second, I address the size of the treatment consideredand potential omitted variables and confounding effects frompossible changes in state-level variables that might be correlatedwith the implementation of quota systems. I show that therewere no effects for private school students who should have beenequally affected by the state-level variables but less affected bythe quotas. Third, I consider another potential pitfall due to myreliance on self-reported racial information. Although Francis andTannuri-Pianto (2012) suggest that students might change theirself-description under the quota system, it is highly unlikely inthe context of this study, as students applying to universitiescould benefit from the quota only when their identity was verifiedupon admission. Finally, I consider the possibility that my DIDstandard errors are underestimated given the potential intra-stateand serial correlation of the residuals. If this were the case,my statistical inferences would be invalidated. As suggested byBertrand, Duflo, and Mulainathan (2004), I consider the possibilityof relying on robust standard errors clustered at the school level aswell as an alternative statistical inference procedure for our mainresults that would be robust to intra-state correlation in residuals.

This paper is organized as follows: Section 2 presentsbackground information on the Brazilian educational system andaffirmative action, followed by an introduction to admissions andaffirmative action at the Federal University of São Carlos. Section3 provides a literature review that explores the potential outcomes

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of such policy and ends with relevant findings about Brazil.Section 4 describes the data and provides summary statistics andexplains the choice of the comparison group. Section 5 reportsmy methodology. Section 6 presents the main empirical results.Section 7 considers further specification tests that I would like tocarry out in order to verify the robustness of my findings andbroaden the scope of this research project.

2 Background Information

While Brazil is known for its racial diversity, as the countryreceived the greatest number of slaves during the Trans-AtlanticSlave trade (Eltis 2001), it is also notorious for racial inequality.Today, about half of the population is white, 44.2% is pardo, and6.9% is black (IBGE 2010). In addition, the majority of blackBrazilians are impoverished and attend public schools. Althoughpardos and blacks represent 50% of the Brazilian population,they account for almost 75% of underperforming poor students(Stahlberg 2010). Inequality in education translates into incomeinequality: Blacks and pardos represent 73% of the poor, and only12% of the rich.3

2.1 Educational System in Brazil

The Brazilian educational system is split into two levels: basiceducation and higher education. Basic education has three stages:infantile education, from 0 to 6 years old; fundamental education,which is mandatory, free, and lasts at least 8 years; and middleschool, which lasts from 3 to 4 years.

The defeat of the Brazilian socialist movement in 1964 markedthe beginning of the stagnation of the public higher educationsystem, and, not coincidentally, the growth of private institutionsthroughout basic and higher levels.4 Brazil was ruled by a military

3A 2007 study by the Brazilian Institute of Geography and Statistics (IBGE)found that white workers received an average monthly income almost twice thatof blacks and pardos. Blacks and pardos earned on average 1.8 times the minimumwage, while whites had a yield of 3.4 times the minimum wage.

4The growth pattern of the private education sector and the recession of thepublic universities are analyzed by Cunha (1986). On the other hand, Barros,

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regime for two decades after 1964, and successive administrationscontinually disregarded the educational system so that by 1990,the federal government provided higher education for a mere19% of students, whereas in 1984 it had provided for 40% (Brasil1999).5 Meanwhile the private sector, which already providedservices to 59% of students in 1985, continued to expand in orderto satisfy the needs of 62% of students in 1998 (Brasil 1999).However, while the expansion of private education sustainedthe provision of high quality fundamental and middle schooleducation, the same could not be said about private universities.Private universities are often unable to match the quality offeredby federal universities because of the high fixed cost of highereducation.

The growth of the private school sector caused free publicschools in Brazil to decrease in quality. The competitiveness ofthe public university entrance exam and the lack of expansion ofthe public university system motivated upper and middle classfamilies to demand high-quality schools in order to prepare theirstudents for the exam.

Because the college admission process in Brazil considersonly test scores and leaves personal information and backgroundunknown, there is little chance that admission officialsdiscriminate based on race. But the process leads todiscrimination based on economic status. As poorer studentscannot afford the higher quality of education provided at privateschools, they tend to not perform as well on the college admissionexams as students with access to private education. Even asearly as the mid-1970s, some portion of Brazilian society, mainlycomprised of middle-class black students, was feeling the effectof these movements. As Santos (1985) writes, in order to obtaina higher education, young black students have to turn to theprivate institutions that offer diplomas with less value in the jobmarket. The Brazilian education literature blames the high costof acquiring qualified academic faculty and financing scientific

Henriques, and Mendonca (2001) analyze international data and come to theconclusion that “between the 60s and 80s, the Brazilian educational systemexpanded at a much slower rate than the corresponding international mean."

5Mainly the administrations led by José Soarney, Fernando Collor de Mello,Itamar Franco, and Fernando Henrique Cardoso.

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research for the failure of private higher education institutionsto produce high-quality education. But this alternative merelyaccentuates the restrictions placed upon these populations byBrazil’s education system.

2.2 Affirmative Action and Racism in Brazil

Throughout the 1990s, the public university acceptance rate ofpublic school applicants remained stable at approximately 33.8%of the entering class (Peixoto 2000). The Ministry of Educationreports that, of the 54.9 million students enrolled in public basiceducation system at the time, 87.6% attended public universities.

While the concept of affirmative action was introduced at thestart of the 1980s, it was not until 2000 that Brazilian publicuniversities began to use racial quotas to influence their admissionpolicies. The first law treating affirmative action specifically wasapproved by the state of Rio de Janeiro, which established that50% of state university admissions would be reserved for publicschool applicants starting in 2003. The following year, in the samestate, the law changed to guarantee 40% of its seats for pardosand black students. That same year, the state of Bahia matchedthis guarantee for the two groups in its public universities. Sincethen, many schools in other states have adopted some form ofaffirmative action. In 2004, the total number of spots reserved forminorities was only 3.1% in 9 states, while in 2008 this numberwent up to 11.2% in 21 states.

2.3 Admissions and Affirmative Action at UFSCar

My analysis focuses on the Federal University of São Carlos, apublic research university located in São Carlos in the state ofSão Paulo. UFSCar is located in a rural area, with four campusesspread across the state’s countryside. It has approximately 14,000students and 1,000 professors and researchers. Its researchers areBrazil’s fourth most productive in terms of the quantity of articlespublished in indexed international journals of science.

In 1994, bucking the national trend, almost half of UFSCar’sadmitted students came from public schools. This number,however, decreased over time. In 2005, 80% of admitted studentscame from private schools. Similarly, while 35% of the population

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of Brazil’s southeast region (IBGE 2001) is black or pardo, UFSCar’s2005 entering class had less than 14% of students who are blackor pardo.

UFSCar took action to adjust this disproportion bymaintaining a 20% quota for students from public schools.UFSCar has accepted 2,577 students every year since 2009. Therewere 40,547 applicants in 2010 (pre-quota) and 71,439 applicantsin 2011 (post-quota). In 2011, the university implemented amore drastic measure by reserving 40% of its seats for studentswho were educated exclusively in public institutions. Of thatpercentage, 35% were reserved for black students. This last quotawill be the main focus of my analysis.

3 The Effects of the Introduction of Quotas onStudent Performance

3.1 Theoretical Channel

There are many mechanisms through which quotas canaffect students’ performance on the public university entranceexam. First, market imperfections can affect access touniversities. Specifically, liquidity constraints may prevent accessto universities for minorities, who are usually overrepresented inthe poorest part of the population. Andrade (2004), for example,builds a theoretical model in order to study how quotas affectthe economic efficiency of Brazilian society from the perspectiveof total expenditure (government and households), consideringthe coexistence of public and private universities. Starting fromthe assumption that basic education is available and equallyenjoyed by all, he shows that, depending on the difference inquality between public and private institutions and the size ofthe liquidity constraint faced by beneficiaries of the quotas, therecan be an increase in the efficiency of total (public and private)investment.

These findings are relevant in the Brazilian context given thelower level of public basic education relative to private education.If public school students were already giving their best effort,meaning that the gap between the scores of public and privateschools would be purely due to the difference in quality of

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education, no increase in performance should be visible. On theother hand, with the implementation of 40% quotas at UFSCar,qualified public school students who previously would not haveapplied—because in the past they did not have the means topay or considered public universities too competitive—might nowfind it worthwhile to apply, increasing the mean score of the poolof public school applicants.

A second possible factor that may discourage these otherwisepotentially higher-performing students is their anticipation offuture discrimination in the job market, in which case minoritystudents might be less motivated to accumulate human capitalduring their academic career (Lundberg & Startz 1983, Milgrom& Oster 1987, Lundberg & Startz 1998). In this case, quotascan alter minorities’ beliefs and affect their investment decisions.Models of race-based cultural norms (Ogbu & Forham 1986, Ogbu2003) assert that black children have lower norms of achievementthan otherwise similar white children. This discrepancy couldbe due to a lack of opportunities given and then expected byblack students over time. In either case, quotas could increaseopportunity, and this opportunity could trigger a shift in realisticnorms of achievement for minority students.

Finally, since the Brazilian selection process is based solely ona seemingly objective exam grade, perhaps quotas can improvethe selection efficiency of the exam. An efficient selection processwould select qualified students from diverse backgrounds sincetest scores provide no information about an applicant’s qualitativecharacteristics. This could have a mixed effect on entrance examperformance. There might also be a mixed effect on effort.According to Coate and Loury (1993), the effort level may decreasein the presence of quotas and thus diminish the incentives forinvestment in human capital. Specifically addressing the issueof the cost of the effort, a 1987 study by Bull et al. observes thebehavior of individuals in tournaments where the cost of the effortto achieve a certain goal is different. The results show that thebehavior of individuals is dependent on the size of the asymmetryof cost and effort. In general, individuals who face higher costsdemonstrate less effort than others. Given the high competitionat UFSCar, it is interesting to consider whether the quota changedapplicants’ beliefs regarding their cost of effort.

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3.2 Previous Evidence on the Introduction of Quotas inBrazil

Although the total number of spots reserved for minorities was11.2% in 21 states by 2008, only the most prominent cases—thoseof Rio de Janeiro in 2000, Bahia in 2003, and Brasilia in 2004—havereceived serious empirical analysis. These cases seem to showthat students who receive special treatment, such as preferredadmission, may perform worse than before the policy wasimplemented (D’Souza 1991, Murray 1994). Francis and Tannuri-Pianto (2009) show that this difference may be small. Studying theUniversity of Brasilia (UNB) applicants accepted under the quotasystem, the authors estimate that the differential performanceof the favored students compared to the unfavored students isonly 20% of the standard deviation of their standardized scores.On the other hand, Ferman and Asuncion (2006) say the dataprovided by the national evaluation exam show that the adoptionof racial and socioeconomic quotas in the state universities of Riode Janeiro and Bahia actually reduced incentives for high schoolstudents. However, Francis and Tannuri-Pianto (2009) argue thatthe conclusions of this study are unreliable since it is not possibleto identify those who actually paid for the public universityentrance exam.

In this paper I will focus on ENEM exam scores used byUFSCar. In 2009, the ENEM was already used by 42 of 55 federaluniversities in the country. This unique and rich dataset will shedlight on the controversial empirical results presented above.

4 Data

4.1 The ENEM

To be admitted to a public university in Brazil, a student mustpass an admission test called vestibular. Each university offersits own vestibular. Until 2009, some universities also consideredthe ENEM as part their selection process, but these were isolatedcases.

My empirical analysis relies on the ENEM micro-dataset.ENEM data provide complete test information for over fourmillion test-takers for the years of 2009-2010, as well as a

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mandatory socioeconomic survey providing family backgroundcharacteristics and high school identifiers for students applyingto public universities. The 40% quota at UFSCar was introducedin 2011, and in order to account for the one-year lag, it used the2010 ENEM results in the selection of the entering class, similar tohow it used the 2009 exam to select the entering class of 2010. Allobservations made in 2009 refer to the 2010 application process(pre-quota) and all 2010 observations refer to the 2011 applicationprocess (post-quota).

In 2009 the ENEM was methodologically reformulatedin order to standardize the admissions process for federaluniversities. In 2009, according to the Ministry of Education,541 of the 2,252 higher education institutions in Brazil used theENEM score, either as a unique or partial selection criterion.Of these, 42 were public universities. Universities can use theENEM in several ways: to allocate a percentage of the vacanciesto ENEM test-takers, as a unique selection process, as the firstphase of admission, to supplement applicant data, or as part ofthe entrance exam score.

It is important to note that the ENEM is open to anyone whowants to take it. For example, some students use it to applyfor a ProUni scholarship to attend a private institute of highereducation, while others use it as an evaluation of their capabilitieswhen applying for jobs. The dataset does not specify whichstudents applied to which university. In order to remedy this lackof specification, my analysis relies on the students who reportedtheir reason for taking the ENEM was in order to apply to auniversity and those who obtained a score greater than 0 (schoolswill not accept a score of 0 in one of the subjects). In addition,the different rates of growth of ProUni scholarships in differentregions presents an omitted variable bias that must be accountedfor. I attempt to examine the validity of my findings given thisconstraint in Section 7.

The ENEM evaluates students in natural science, humansciences, Portuguese, mathematics, critical thinking, and essayWriting. The proficiency measure is presumably comparable overtime, as it is calibrated using “item response theory" methodology.Unlike simpler alternatives for creating scales, this methodologydoes not assume that each item is equally difficult and treats the

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difficulty of each item as information to be incorporated in scalingitems. My analysis is based on the cumulative score of these sixsections. The 2009 survey contains a wide variety of informationon student and school characteristics that are, unfortunately,only partially replicated in 2010. Taking this into consideration,the control variables used are gender, age, household size, anindicator for rural schools, and parent schooling.

4.2 Summary Statistics

In selecting the comparison group for São Paulo, two constraintshad to be taken into consideration. First, the states beingcompared needed to have universities that used the ENEMconsistently in both the 2010 and 2011 selection processes.The number of seats offered varies slightly in the compareduniversities, but as there is no significant change, my resultsshould not be skewed (Brazilian Ministry of Education).

Second, the demographics of the comparison group had tobe comparable to São Paulo’s. São Paulo is the economic capitalof Brazil, and as a consequence it is wealthier and has a largerwhite population than the rest of the country. It follows thatschooling levels are also higher. Two other states in the southeastsubdivision of Brazil, Minas Gerais and Rio de Janeiro, arecomparable to São Paulo in wealth and education level despitethe lower percentage of whites and larger percentage of pardos. Ialso include Rio Grande du Sul, the southernmost state of Brazil,which is wealthy and has a large white population but has lower-quality education in my comparison group. As can be seen inTable 1, treatment and comparison groups are very comparableat baseline, with the exception that São Paulo is 80% white and12% pardo while the control group is 70% white and 22% pardo. Iconsider this constraint in Section 7 but will assume until then thatthis characteristic does not play a key role. In addition, accordingto Telles (2004) and Magnoli (2008), self-reporting of pardos is notentirely reliable as it depends on whether or not people considerthemselves as such.

At first glance, I note from columns A and C of Table 1 that,at the baseline, the score gap between private schools and publicschools in our treatment group (São Paulo) is 404.78 points, while

104

Tabl

e1:

Sum

mar

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atis

tics

Pre-

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taPo

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(B)

(C)

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ate

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cant

sN

3637

346

376

4782

861

515

Frac

tion

Fem

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0.56

0.50

0.58

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0.56

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tion

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800.

400.

700.

460.

820.

380.

710.

45Fr

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0.12

0.32

0.22

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150.

050.

230.

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150.

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ean

Age

18.5

2.79

18.6

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17.7

3.18

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580.

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3.49

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1.21

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1.14

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hold

Size

3.87

0.95

3.73

1.01

––

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ENEM

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80.9

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2950

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2529

81.2

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4.22

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15.0

346

0.24

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476.

53Pu

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3086

8041

6022

4593

5769

7697

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tion

Fem

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0.59

0.49

0.62

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0.58

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0.60

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580.

490.

500.

500.

620.

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520.

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0.34

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290.

120.

330.

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280.

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23.4

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3123

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7.26

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7.70

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8.02

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2.22

1.23

2.22

1.26

2.25

1.20

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061.

281.

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252.

081.

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891.

233.

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6.70

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1925

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851

4.92

2570

.36

515.

97Bl

ack

2461

.40

522.

9125

15.3

050

1.41

2480

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511.

5325

20.3

951

7.28

Not

e:U

nfor

tuna

tely

the

hous

ehol

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zem

easu

reis

diff

eren

ton

the

2010

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.Bro

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just

men

tsw

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mad

eso

that

itco

uld

bead

ded

asa

cont

rol

inth

ere

gres

sion

,but

itis

nota

sin

form

ativ

e.

105

the control group has a substantially smaller gap of 349.37 points.We would expect the implementation of a quota in São Pauloto lead to an improvement in public school performance relativeto the control group.6 This result can be seen in the post-quotascore gap, found using columns E and G. The score gap after theimplementation of the quota becomes 383.45 points for São Pauloand 370.58 points for the control group. Therefore, the score gapin São Paulo narrowed, while the score gap in the control groupwidened.

5 Methodology

To identify the impact of quota systems on the performance offavored applicants on the ENEM, I use a difference-in-differences(DID) framework to compare the difference in performancebetween the treatment and comparison groups after the quotaswere implemented (in 2011) with the same difference before thequotas were implemented (in 2010).

The basic DID estimate of the quota’s effect on theperformance of favored students is obtained from the followingleast squares regression:

ln (yi) = c + a · d2011i + b · dTreat

i + g · d2011i · dTreat

i + s0Xi + ei

where i indexes the students in the sample, which is pooled forthe exam years 2009 and 2010; yi refers to the proficiency variable;d2011

i indicates whether student i took the exam in 2009 or 2010;dTreat

i indicates whether student i belongs to the treatment group;Xi is a vector of student characteristics that are broadly dividedinto demographic characteristics, parental education and schoolmunicipality; and ei reflects unobserved variables that affectstudents’ proficiency. Different pairs of treatment and comparisongroups are considered in the next section. The coefficient ofinterest is related to the interaction between d2011

i and dTreati , g,

6According to the Brazilian annual household survey (PNAD), 15% of theundergraduate students in Brasilia are originally from another state. Thecorresponding figures are only 5% in São Paulo. Therefore, it is reasonableto assume that favored students in Brasilia faced stronger competition for thereserved spots than black students in Rio de Janeiro.

106

which can be interpreted as the average impact of the treatmenton the treated: the percentage variation in the performance offavored students due to the introduction of the quota system.

6 Results

I first present my DID estimates for the most affected groups:black students and students who were exclusively educated inpublic schools. While UFSCar’s quota was limited to publicschool applicants who had only attended public schools, therewas no restriction on black students; any black student waseligible. Therefore I begin by estimating the quota effect on allblack test-takers, followed by the effect on all test-takers whowere schooled in public institutions. I then estimate the DID fordifferent races within the pool of public school applicants whoattended public school only. Finally, I look at the DID estimatefor São Paulo’s private school applicants who might have beennegatively impacted by the implementation of this quota system.

The models in columns E through F of Table 2 presentestimates of the DID equation using black test-takers as thetreatment group and their counterparts in comparison states asthe control. In column E, no demographic, parental education,or school municipality control variables were included. Theestimated effect of being favored by the system of quotas is a1.11% increase in test score (significant at the 1% level). Theseresults reflect the difference between the mean test score of thetreatment and comparison groups after quotas were implemented,compared to the same difference before these quotas wereimplemented. These results must be analyzed carefully becausethey may reflect changes in the composition of the groups orchanges in factors other than the quota incentive.

Column F of Table 2 presents the same regression but includesa vector of student characteristics (age, gender, household size,rural/urban indicator). Controlling for student characteristicsdoes not significantly change the estimated effect of being favoredby the quota. The estimated effect is a score improved by 1.13%(significant at the 1% level). In column G, I add parental educationlevel to the control vector, which does not change the size or thesignificance of the estimate. In column H, I account for the school

107

Tabl

e2:

Effe

ctof

Quo

taSy

stem

onPu

blic

Scho

olan

dBl

ack

App

lican

ts

Dep

ende

ntVa

riab

leis

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ests

core

)Tr

eatm

entG

roup

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lican

tsfr

omTr

eatm

entG

roup

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ulo’

sPu

blic

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ols

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kA

pplic

ants

Com

pari

son

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from

Com

pari

son

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up:B

lack

RS/

RJ/

MG

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blic

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ols

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lican

tsin

RS/

RJ/

MG

(A)

(B)

(C)

(D)

(E)

(F)

(G)

(H)

d2011

i·d

Trea

ti

1.09

***

0.96

***

0.93

***

1.16

***

1.11

***

1.13

***

1.13

***

1.4*

**(0

.08)

(0.0

8)(0

.08)

(0.1

2)(0

.23)

(0.2

3)(0

.23)

(0.3

7)d20

11i

0.39

***

0.64

***

0.78

***

1.48

***

0.5*

**0.

73**

*0.

78**

*1.

45**

*(0

.05)

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5)(0

.05)

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8)(0

.13)

(0.1

4)(0

.14)

(0.2

2)dTr

eat

i-1

.97*

**-1

.65*

**-2

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*-3

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**-2

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**-2

.49*

**-2

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**3.

56**

*(0

.06)

(0.0

6)(0

.08)

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9)(0

.18)

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8)C

ontr

olVa

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les

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og.C

hara

ct.

NY

YY

NY

YY

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ntal

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atio

nN

NY

YN

NY

YSc

hool

Mun

icip

ality

NN

NY

NN

NY

N18

7412

618

6952

418

6312

570

7205

2477

6324

6788

2457

3681

884

Adj

uste

dR

20.

023

0.03

10.

107

0.11

50.

015

0.55

0.10

20.

116

p-va

lue,

d2011

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Trea

ti

=0

0.00

0.00

0.00

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indi

cate

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atis

tical

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ifica

nce

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e10

%,5

%,a

nd1%

leve

l,re

spec

tivel

y.

108

Tabl

e3:

Effe

ctof

Quo

taSy

stem

onPu

blic

Scho

olA

pplic

ants

byR

ace

Dep

ende

ntVa

riab

leis

ln(t

ests

core

)Tr

eatm

entG

roup

:App

lican

tsw

how

ere

scho

oled

inSã

oPa

ulo’

sPu

blic

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ols

Com

pari

son

Gro

up:A

pplic

ants

who

wer

esc

hool

edin

RS/

RJ/

MG

Publ

icSc

hool

sW

hite

Pard

osBl

ack

(A)

(B)

(C)

d2011

i·d

Trea

ti

0.83

***

1.27

***

1.54

***

(0.1

6)(0

.22)

(0.4

)d20

11i

1.54

***

1.46

***

0.97

***

(0.1

1)(0

.14)

(0.2

4)dTr

eat

i-0

.33*

**-3

.97*

**-3

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**(0

.12)

(0.1

6)(0

.3)

Con

trol

Vari

able

sD

emog

raph

icC

hara

cter

istic

sY

YY

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ntal

Educ

atio

nY

YY

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olM

unic

ipal

ityY

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N38

3101

2303

4569

761

Adj

uste

dR

20.

137

0.13

80.

137

p-va

lue,

d2011

i·d

Trea

ti

=0

0.00

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0.00

*,**

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dica

tes

stat

istic

alsi

gnifi

canc

eat

the

10%

,5%

,an

d1%

leve

l,re

spec

tivel

y.

109

Tabl

e4:

Effe

ctof

Quo

taSy

stem

onPr

ivat

eSc

hool

App

lican

tsby

Rac

e

Dep

ende

ntVa

riab

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)Tr

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rand

eSu

l,R

iode

Jane

iro,

Min

ais

Ger

ais

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ate

Scho

ols

(A)

(B)

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i·d

Trea

ti

0.28

00.

180.

169

d2011

i3.

31**

*2.

79**

*0.

120.

12dTr

eat

i-0

.085

-0.6

7***

0.12

0.12

Con

trol

Vari

able

sD

emog

raph

icC

hara

cter

istic

sN

YPa

rent

alEd

ucat

ion

NY

Scho

olM

unic

ipal

ityN

YN

2571

4824

2048

Adj

uste

dR

20.

023

0.10

9p-

valu

e,d20

11i

·dTr

eat

i=

00.

110.

00

*,**

,**

*in

dica

tes

stat

istic

alsi

gnifi

canc

eat

the

10%

,5%

,an

d1%

leve

l,re

spec

tivel

y.

110

municipality, which results in the higher estimated effect of a1.4% increase in test scores (significant at the 1% level). However,this last estimate reduced the number of observations used from245,736 to 81,884. Perhaps the subpopulation differs from theaggregate black test-takers. One could interpret reporting of thenon-mandatory high school code on the ENEM as an indicatorof “overachievement" or wanting to perform well, which couldincrease the likelihood of students wanting to perform better onthe ENEM in order to benefit from UFSCar’s quota system.

The models in columns A through D of Table 2 containestimates of the DID equation using public school test-takersas the treatment group and their counterparts in comparablestates. In column A, no demographic control variables (parentaleducation or school municipality) were included. For studentsfavored by the quota system, the estimated effect is a 1.09%increase in test score (significant at the 1% level). When addingcontrols in columns B and C, the effect estimated is still significantbut reduced to slightly less than a 1% increase in test score. Again,we can use our “overachiever" subgroup to note a slightly largerestimate of a 1.16% increase in test score, which is 0.24% lowerthan the increase estimated for black test-takers in column H ofTable 2.

It seems that black students were slightly more affected bythe quota policy. This hypothesis is further supported by theestimates presented in Table 3. In Table 3, I estimate thedifference-in-differences equation for white public school test-takers (column A), pardo public school test-takers (column B), andblack public school test-takers (column C). All three estimateswere done using full specification, even though these results aresignificant without specifications. We find in column A that whitepublic school students are least incentivized by the UFSCar quota,with an estimated 0.83% increase in test scores, followed by, incolumn B, an estimated 1.27% increase in test scores for pardopublic school students. Finally for black public school students,the most affected group, the estimated impact is a 1.54% increasein test scores. All of these figures are significant at the 99% level.

Table 4 presents results for no control (column A) andcomplete specifications, including all control variables (column B)for private school test-takers. Neither estimate exhibits an effect

111

from quotas that is significantly different from zero. We note thatthe number of observations is only 6% less than in the modelwithout controls in the complete specification estimate, whereasthe numbers of observations for the black test-takers and publicschool test-taker models decrease by 67% and 62%, respectively(Table 2). This could support the hypothesis that reporting schoolmunicipality is associated with higher scores and could be a signof overachievement, given that private school students are moresuccessful.

Despite the significance of all the results, it is important tonote that the effect of the quota estimated by the DID modelis small. Black and public school students’ scores increased byapproximately 1%, which could be due to factors completelyunrelated to the quota implementation. In the next section, Iaddress some of the issues already mentioned and additionalpotential concerns such as time trends, selection bias, omittedvariables, serial correlation, and within-state correlation in theresiduals, as well as the comparability of São Paulo with the restof the country and the size of the treatment.

7 Specification Consideration

In this section, I consider the potential concerns in attributing theestimated 1% increase in black and public school test scores to theimplementation of 40% quotas at UFSCar.

The first issue we should consider is whether the increase inproficiency among the favored students occurred strictly after theimplementation of these quota systems, or if there was alreadya positive trend occurring in student performance before theimplementation of the quota system. Despite the comparabilityestablished by the summary statistics in Table 1, the baseline scoredifference is disconcerting. It could be the case that, relative tothe 2010 comparison group, São Paulo’s gap between public andprivate school average test scores was much larger. Therefore wecannot dismiss the possibility that São Paulo, Brazil’s economiccenter, has a different time trend than the rest of the country.

In order to address this problem, we could estimate a DIDmodel with data from previous ENEM years. There are twocomplications involved with such a procedure. First, the ENEM

112

became most widely used in 2009. Second, in previous yearsdifferent states implemented forms of affirmative action. Suchestimates could still provide trend evidence if São Paulo’s patternwas strikingly different from the rest of the country. In addition,considering ENEM data from the post-treatment years couldfurther cement a distinctive trend if one were to be found.

A second concern is the size of the treatment. UFSCar offersadmission to only 2,577 students every year, and there were 40,547applicants in 2010 (pre-quota) and 71,439 applicants in 2011 (post-quota). While the number of applicants per admissions spotnearly doubled from 15.73 to 27.72, it is unlikely that all 507,185ENEM test-takers in the state of São Paulo intended to apply toUFSCar when they decided to take the test initially. This leadsus to consider the potential for omitted variable bias. Also, weshould consider the fact that the ENEM became prominent in2009. Perhaps the growing popularity of the exam combined withProUni scholarship opportunities is what drove the results, butthis remains difficult to analyze because of the lack of ProUni data.

Another possible confounding effect is that the system ofquotas in UFSCar may have been implemented in conjunctionwith other statewide changes in educational policy, which wouldbias the estimators. Table 4 revealed non-significant effects forprivate school students who should be equally affected by state-level policies, but there is no evidence suggesting that they areless affected by the quotas. Nonetheless, even if there are no state-level omitted variables that correlate with the implementationof quotas, serial correlation and within-state correlation in theresiduals of DID models could lead to underestimated standarderrors and, therefore, incorrect statistical inferences, as suggestedby Bertrand, Duflo, and Mullainathan (2004).

But we still must evaluate whether this potential downwardbias in standard error is leading us incorrectly to reject the nullhypothesis: that the quota system had no effect on studentperformance of black and public school students in São Paulo.The strategy I would like to adopt is one that uses the same datastructure of the main regression to estimate placebo regressionsfor states that had not implemented quota systems during thisperiod as the treatment group. Otherwise, an alternative wouldbe to rely on robust standard errors clustered by municipality,

113

since the school-level data remains incomplete because studentsdo not consistently report this information.

My last concern is that the composition of the treatmentgroup may have changed due to the implementation of thequota system. First, a system of quotas that benefit blackstudents would likely change the way in which students describethemselves. However, this is unlikely because upon admissionthe candidate has to submit a transcript demonstrating that heor she attended public school and documentation proving his orher ethnicity. In an attempt to measure the quantitative relevanceof potential selection bias, we could use DID models in whicheach of the students’ observable characteristics are dependentvariables. If the system of quotas truly changed the compositionof the treatment group, this would have likely changed theobservable characteristics of this group. A more relevant problemof composition is the difference in the percentage of white test-takers in São Paulo relative to the comparison group, for which Iwould have to construct an adequate test to verify if this aspect isdriving my findings.

8 Conclusion

I provide empirical evidence justifying the claim that theimplementation of affirmative action policies in a competitivesetting can have positive effects on the performance of studentsapplying to universities. My estimate shows that, on average,the ENEM test score of black students from public schools inSão Paulo was 1.54% higher after the introduction of quotas inuniversity admission policies. The estimate, on average, for publicschool students (unconditional on race) was a 1.16% increase intest scores after the implementation of the UFSCar quota. Privateschool students were not affected, which implies that the quotasystem is encouraging public school applicants to perform betteras their odds of entering university are increased. The robustnessof these results is a project I hope to undertake in the future.

114

A Question of Intent: Explaining thePerformance of Governments in GlobalDevelopment Projects

Adin Lykken, Yale University1

Abstract. This paper seeks to explain the performance ofgovernments who complete externally financed developmentprojects. Previous research on the effectiveness of developmentefforts has analyzed macro-level indicators and overall projectoutcomes. Less research has explored the dynamics of howwell recipient governments implement specific projects. Iconstruct a principal-agent framework that explains governmentperformance in terms of the execution skills of governments andtheir alignment to the objectives of financing organizations. Toisolate the primary drivers of performance, I analyze project-level assessment data from the World Bank and country-levelindicators of political risk from the Political Risk Services Group.Across both linear and probit specifications, results suggest theoverwhelming importance of project supervision in improvinggovernment performance. I examine projects indicative of theseresults and discuss policy options to further improve governmentperformance.

Keywords: development projects, government performance,World Bank, principal-agent

1Adin Lykken is a senior majoring in economics at Yale University. He wrotethis paper for Professor Ioannis Kessides’ "Economics of Infrastructure Policy"seminar in Fall 2013. The author would like to thank his adviser, ProfessorKessides, for his invaluable guidance on this project. He would also like tothank Maximiliano Appendino and Alex Cohen, graduate students in the YaleEconomics Department, for their helpful feedback. This project was supportedby a Mellon Undergraduate Research Award from Yale University.

115

1 Introduction

Although global poverty rates have fallen in recent decades,22% of the developing world still lives on less than $1.25 a day(The World Bank 2012). Mass poverty remains a tremendouschallenge for the international community, one that has spurredincreased research into improving the outcomes of developmentassistance. Recent scholarship has produced mixed results on theeffectiveness of current development efforts in reducing poverty.Some studies find that development aid has led to unconditionaleconomic growth and poverty reduction (Lensink & Morrissey1999, Clemens et al. 2004), while others have indicated that effortsover the last few decades have been largely ineffective (Easterlyet al. 2003, Doucouliagos & Paldam 2007). Another strain ofresearch on development effectiveness yields results conditionalon country-specific characteristics, most notably geography andinstitutional quality (Dollar & Levin 2005).

A smaller subset of research has eschewed measuring macro-indicators like growth and poverty rates in favor of project-level outcomes. Several studies, most notably Kaufmann andWang (1995), have attempted to explain the success and failureof specific projects based on a country’s economic productivityand trade policy. Diallo and Thuillier (2005) have analyzedproject outcomes based on levels of open communication betweenproject stakeholders, while Chauvet, Collier, and Fuster (2006)have explored the impact of supervision of borrowers bylending institutions. Less research has attempted to explainthe behavior of national governments that actually implementdevelopment projects. As the performance of aided governmentscan significantly impact the effectiveness and sustainability ofdevelopment projects, there is a need for more research into theincentives facing borrowers. There is a demonstrated need toexamine such inputs into overall project performance, as 39%of all World Bank projects were rated as unsuccessful in 2010(Chauvet, Collier, & Duponchel 2010).

This paper seeks to explain the behavior of governmentsin developing nations that complete externally financeddevelopment projects. Building upon the work of Kilby (2000),I use a principal-agent model to examine the incentives that

116

underlie the behavior of governments that complete developmentprojects financed by the World Bank. In particular, I analyze theextent to which an adversarial or cooperative theory of behaviorbetter explains the performance of borrowing nations. I specifyan empirical approach using project-level data with both a linearand probit model. From the results, I suggest methods fordevelopment institutions to improve borrower performance andareas for future research.

2 Literature Review

There exists an emerging consensus on the importance ofexamining country-specific features in explaining the outcomesof development projects. To explore how differences indeveloping nations might explain development project outcomes,some studies have turned to measuring indicators of “goodgovernance.” The good governance agenda has been acentral concept in the field of international development sincethe mid-1990s (Earle & Scott 2010). This term is broadand can encompass improvements to “virtually all aspectsof the public sector” (Grindle 2004). In the context ofinternational development, measures of good governance caninclude the rule of law, budgetary and financial management,transparency, accountability, corruption, and public participation(Punyaratabandhu 2004). While development institutions likethe World Bank used to define good governance in termsof technocratic competence, there has recently emerged awider emphasis on the importance of institutional quality fordevelopment interventions to be sustainable (Hout 2009).

Despite the recent emphasis on governance quality, mostprevious research has tried to explain its effects in terms ofaggregate metrics rather than project-level outcomes. Acrossdeveloped nations, there is some evidence that weak governancereinforces poverty (Campos & Nugent 1999) and that goodgovernance leads to higher foreign direct investment (Busse &Hefeker 2005) and labor productivity (Hall & Jones 1999). Rodrik,Subramanian, and Trebbi (2004) have linked stronger publicinstitutions to higher per capita income levels and lower povertyrates. Research conducted by the World Bank has also found that

117

good governance in developing nations is linked to higher percapita incomes and literacy rates as well as lower infant mortality(Kaufmann & Wang 1995).

One framework to incorporate good governance as adeterminant of project-specific outcomes is the concept in agencytheory known as the principal-agent problem (PAP). Popularizedby George Akerlof’s 1970 paper “The Market for Lemons: QualityUncertainty and the Market Mechanism,” the PAP involves aprincipal and agent(s) who engage in cooperative behavior buthave differing goals and limited vision into the actions of theother party. In most principal-agent models, a principal pays anagent with specialized knowledge to complete a task but can neverperfectly monitor the agent’s behavior (Arrow 1963). The agentmay use his information advantage to take an action unobservedby the principal (moral hazard) or conceal the true cost orvaluation of his work (adverse selection) (Laffont & Martimort2002, Aerni 2006). In many cases, principals must considerthe tradeoff between increased costs of monitoring agents withthe agency costs associated with an agent’s deviant behavior(Bebchuk & Fried 2004). Since its conception, researchers haveundertaken experiments to test the applicability of agency theoryto fields as varied as marketing, compensation, diversificationstrategies, board relationships, vertical integration, and innovation(Eisenhardt 1989).

International development assistance represents a market inwhich participants respond to specific incentives, one in whichthe PAP also arises in numerous ways. Vaubel (2005) and Nielson(2003) have posited the existence of the PAP between internalmanagers who seek to expand the authority of developmentorganizations and the citizens of the member states who maybe rationally ignorant of most of the organization’s activities.Easterly (2006) has pointed out that in the context of relationsbetween donors and development organizations, the latter canbecome risk-averse and learn to shield donors from being exposedto negative project outcomes. Most salient for this analysis,Chauvet et al. (2006) consider situations in which a donoragency finances development projects that are implemented byrecipient governments, finding that donor supervision of projectsis more impactful on project performance where interests are

118

more divergent. A final PAP could also exist between governmentleadership that receives financing for a project and the staff whoactually conduct implementation.

According to the precepts of Stiglitz (1974), developmentprojects can be seen as principal-agent contracts if:

(1) The principal and agent have different objectives;

(2) The principal’s information about the agent’s actions isimperfect; and

(3) Contracts are imperfect.

With respect to (1), Chauvet et al. (2006) have posited an inherentlack of congruency between the interests of borrowing nations andlending institutions. Kilby (2000) has hypothesized that such alack of congruency likely stems from differences in time horizons.While development institutions have far-sighted perspectiveson reducing poverty in developing nations, even benevolentgovernments are inclined to direct projects with a shorter-termfocus. Chauvet et al. (2006) have also noted the existence of (2) inthe context of donor-borrower relationships because of the limitedobservability of the borrowing government’s effort. For instance,Aerni (2006) has described how implementing governments indeveloping countries may engage in “adverse selection” of whatinformation they report to lenders about the status of projects. Tocorrect for this information asymmetry, donor agencies may tryto monitor projects in borrowing nations, an effort Kilby (2000)has shown to be correlated with improved project outcomes. (3) isa natural consequence of the structure of modern developmentprojects, during which lending institutions do not implementprojects themselves, instead providing borrowers with decision-making capacity outside of formal contracts.

In the context of agency theory, Kilby (2000) proposestwo potential explanatory models: an “adversarial” modelthat explains project outcomes as a result of the PAP and a“cooperative” model that assumes congruent interests betweenborrowing nations and lending institutions. While this dichotomyis a useful framework for applying agency theory to developmentprojects, Kilby does not consider the effects of country-specificfactors like governance quality (outside of macroeconomic

119

controls). Furthermore, neither his study nor others examinethe impact of the PAP purely on the performance of borrowingnations rather than on overall project outcomes. In light ofthis underspecification, my analysis seeks to incorporate country-specific variables into an agency theory model to explain thebehavior of governments who borrow from the World Bank.While I adopt Kilby’s dichotomy between adversarial andcooperative models, I reconstruct them with country-specificfeatures, including indicators of good governance. I then definean econometric specification to test which of the two principal-agent models better explains variations in borrower performance.Finally, I discuss policy recommendations to improve theoutcomes of borrower performance and the implications of theresults for future research.

3 Theoretical Model

This section presents a theoretical model for the empiricalinvestigation of the determinants of borrower performance inprojects financed by the World Bank. Building off of Kilby’s twoagency models, one adversarial and one cooperative, I proposefurther specification based on country-specific factors, as Mubila’s(2000) results suggest that they are at least as important as project-specific characteristics for overall project success. The proceedingtheoretical model is adapted from Chauvet et al. (2006), whichis adapted from Baker, Gibbons, and Murphy (1991). Themodel focuses on the non-monetary utility function of a risk-neutral agent (the government of the borrowing country, C) ofa development project financed by a risk-neutral principal (thelending institution, L). Only non-monetary utility is consideredbecause the borrowing country C guarantees loan repayment toL. This reflects how, if a country fails to make a payment on aloan from the World Bank, the Bank will suspend preparationsfor any new loans and freeze all payments under existing loans(The World Bank 2013a).

Consider that L and C agree to a lending contract to financea project in the borrowing country. Borrower performance p is ameasure of the extent to which borrowers succeeded in achievingthe objectives of a given project. p is a function of two factors: the

120

alignment A of the borrower to the stated objectives of the projectand the technical execution E of the project. Thus, borrowerperformance is defined as the function

p = p(A,E) (1)

Alignment A reflects the alignment of the borrowing nation’sgovernment with the lending institution’s objectives for a givenproject. The model assumes a large degree of inherent alignmentacross projects because borrowing nations choose to partnerwith lending institutions voluntarily. However, there can stillbe misalignment of interests. As noted by Hall and Jones(1999), while governments are potentially the most efficientproviders of social infrastructure that protect against diversion ofresources, they are also a primary agent of behaviors against thegeneral public’s interest like expropriation, confiscatory taxation,and corrupt behavior. Kilby (2000) has hypothesized that thedeviant behavior of borrowers likely stems from their shortertime horizons relative to those of lending institutions. Analternate explanation is based on the existence of the principal-agent problem within the borrowing government. Even thoughborrower leadership may be aligned with project objectives,implementing staff may deviate from desired behavior.

Assuming that the people of developing countries similarlyshare a preference for long-term utility maximization, alignmentA can also be considered as the alignment of the borrowingcountry’s government with the objectives of its own people. Anydeviations from the public’s objectives by its government can thusbe measured in terms of overall governance quality g. Whilegovernance quality g, broadly defined as “good governance,”reflects the voluntary alignment of the developing nation tothe objectives of a project, lending institutions can supervisethe behavior of borrowers to potentially expose or halt abusivepractices. Therefore, the quality of supervision s by lendinginstitutions on the governments of developing countries is anothercritical determinant of project alignment. In sum, measures ofproject alignment A reflect an adversarial relationship between Cand L.

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Alignment A is thus defined as the function

A = A(g,s) (2)

By contrast, execution E reflects the ability of the borrowingnation to execute its objectives in relation to a developmentproject. E measures the technical execution of the projectwithout reference to the alignment of objectives, and thereforeassumes a cooperative relationship between C and L. The primarydeterminant of E is therefore the technical expertise t of theborrowing nation. To account for variations in difficulty ofexecution across projects, E also contains a measure of thecomplexity of the project c, which includes both the technical andmanagerial challenges posed by projects.

Execution E is thus defined as the function

E = E(t,c) (3)

While this model is relatively straightforward, it presents aframework with which to conduct an empirical analysis of thequantitative importance of the drivers of borrower performance.In addition to explaining the behaviors of governments, ifborrower performance is a driver of overall project outcomes,then this model would also be highly relevant to policymakersseeking to plan more effective overall projects. Furthermore,both A and E contain components segregated between the controlof the borrowing country C and the lending institution L. Thisdichotomy is critical in determining whether the principal oragents are more influential on agent behavior. Finally, thesegregation of project performance p into two mutually exclusivehypotheses between A and E allows for an empirical specificationof whether an adversarial or cooperative theory of behavior bettercharacterizes the principal-agent relationship.

4 Data

The World Bank is one of the most prominent development aidinstitutions, providing loans and grants to developing nationsfor a variety of development programs. Since 1947, the WorldBank has financed almost 12,000 poverty-reduction projects in

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172 countries (The World Bank 2013c). As part of the Bank’sattempt to improve its effectiveness, a unit called the IndependentEvaluation Group (IEG) evaluates the outcomes of Bank projectsto provide an objective assessment of the results and cultivatebest practices. The Director-General of the IEG reports directlyto the World Bank Group’s Board of Executive Directors and notto Bank Group Management (The World Bank 2014a). As partof the evaluation process, the IEG evaluator ranks the Bank andthe borrower across a variety of metrics including the quality ofthe Bank’s supervision efforts (Appendix A) and overall borrowerperformance (Appendix B) (The World Bank 2014b). I assumethe IEG’s reported evaluations to be accurate and unbiased forthe purposes of my analysis. In late 2011, the IEG releasedits entire project evaluation database comprised of some 9,855projects approved since Bank operations began (Sud & Olmstead-Rumsey 2012), allowing for an unprecedented analysis of thedeterminants of borrower performance.

The following analysis uses cross-sectional data on 3,592development projects across 101 countries that were started andcompleted between 1984 and 2013 (The World Bank 2013b).Projects spanned 19 sectors and took anywhere from two days to16 years to complete. This analysis excludes any projects that didnot require a monetary loan or had missing IEG reviews for Banksupervision, borrower performance, or overall project outcome.

The dependent variable for this analysis is defined as:

• BORRPERF (overall borrower performance) measures theperformance of the borrowing country’s government asrated by the IEG.

To generate project-level data, IEG officers review theassessments of project staff, with a fraction of reviews givena thorough audit. Performance of the Bank, borrowers, andthe projects overall are compared against stated objectives andstandards. To carry out these reviews, IEG staff have unrestrictedaccess to Bank staff, project sites, and borrower representatives(The World Bank 2014c). Borrower performance is a measureof the extent to which the borrower ensured quality preparation,implementation, and compliance with agreements in the contextof each country. Overall project quality is a measure of the extent

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to which the project achieved its major objectives in an efficientmanner. The correlation coefficient between overall borrowerperformance and overall project quality is 0.768, providingevidence that borrower performance is a probable determinant ofoverall project success.

IEG variables relevant to the adversarial model are defined as:

• QVISION (quality of Bank supervision) measures thequality of the Bank’s supervision effort during the course ofthe project as rated by the IEG as a proxy for s in equation(2) for alignment A.

IEG variables relevant to the cooperative model are defined as:

• LENGTH (length of the project) takes the natural log of thenumber of days between the listed start and closing date ofa project. I consider length because longer projects are likelyto be more complex.

• COST (project cost) takes the natural log of the total cost ofthe loan to the borrowing country in U.S. dollars with theassumption that more complex projects are more expensive.

• EXPER (experience with projects) measures the number ofpreviously completed World Bank projects in a borrowingcountry. I postulate that past project experience leads togreater technical expertise.

Bank supervision efforts are rated for proactive identificationof opportunities to further project goals as well as resolution ofpotential threats. LENGTH and COST should both be correlatedwith the increased managerial and technical complexity capturedin c, while EXPER is relevant for technical expertise t in equation(3) for execution E.

In order to fully identify the adversarial and cooperativeprincipal-agent models, my analysis also includes data obtainedfrom the Political Risk Services (PRS) Group, a commercialprovider of political and country risk forecasts based in EastSyracuse, New York. Since 1984, the PRS Group’s InternationalCountry Risk Guide has provided annual aggregates of severalpolitical risk and institutional quality indicators (PRS Group2013). PRS Group staff collect political, financial, and economic

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data and make each political index on the basis of subjectiveanalysis of the available information. Each indicator is assessed ona scale from 0 to 12, with 12 being the highest score.2 For example,a score of 12 on the index for corruption would indicate extremelylow corruption in a country. Numerous previous studies haveused data from the PRS Group to investigate, among othertopics, cross-country technology diffusion (Caselli & Coleman2001), foreign direct investment (Busse 2005), and agriculturalproductivity (Cervantes-Godoy & Dewbre 2010). These richindicators allow for a detailed examination of each recipientgovernment. Any explanatory model of overall project outcomeswould require further data on each project as well as furtherinsight into the interaction between Bank and borrower actions,which is why I focus purely on borrower performance.

PRS variables that estimate governance quality g in equation(2) are defined as:3

• GOVST (government stability) measures the government’sability to carry out its policies and stay in office.

• CORR (corruption) assesses corruption in the politicalsystem, including demands for bribes, patronage, nepotism,job reservations, and close ties between politics andbusiness.

• LAW (law and order) measures the strength and impartialityof the legal system and popular observance of the law.

• DEMOC (democratic accountability) measures theresponsiveness of government.

• MILIT (military involvement in politics) measures theinfluence of the military in the political process.

• RELIG (religious tensions) measures the influence ofreligious sects that seek to replace civil law with religiouslaw and exclude other religions from the political process.

2In the original PRS Group data set, some indicators are scaled from 0-6 or 0-4. For easier interpretation of the results, all PRS indicators have been re-scaledto 0-12.

3Naming conventions adapted from Busse (2005).

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Many of the governance quality indicators are highlycorrelated. This is expected, as they all assess political risk andinstitutional quality. To specify the model, I calculate the meanof the annual governance indicators for each project as the sumof the indicators over the time period of each project divided bythe length of the project in years.4 Weighting all years equally isadmittedly an imperfect measure, as an anomalous year (perhapsfrom a temporary regime change) could artificially inflate ordepress the mean. To try and account for these differences in thevariance of governance quality throughout the course of projects,I also calculate the annual change of each governance indicator asthe difference in start and end year values divided by the lengthof the project in years (e.g. GSS).

In addition to EXPER, I further specify t in equation (3) withthe PRS variable:

• BUR (bureaucratic quality) measures the technical expertiseand professionalism of the bureaucracy.

To control for unobserved differences across nations atdifferent levels of development, I also include the PRS variableSOCIO (socioeconomic conditions) that measures unemployment,consumer confidence, and poverty levels rated on a scale of 0-12. I also define a set of six regional dummy variables to controlfor unobservable differences across regions. Variable names anddata sources are available in Appendix C (found online), anddescriptive statistics for all variables are displayed in AppendixD (found online). A quick review of the descriptive statisticsindicates that most governance indicators are centered aroundmid-range values on their 12-point scales, although their standarddeviations differ. As would be expected, the variables measuringchange in governance quality have both positive and negativevalues depending on the project. The mean project cost wasapproximately $71 million and took an average of 4.7 years tocomplete.

It should be noted that if lender supervision s also mitigatedtechnical challenges that arose during project implementation,the adversarial and cooperative theories of behavior would not

4Projects less than a year long are matched with the governance indicator forthat single year.

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be entirely orthogonal. However, although supervision by theWorld Bank does include technical assistance and managementadvising, the act of monitoring, both by staff at Bank headquartersand during trips to borrowing countries, is the central activitycaptured by IEG reviews of Bank supervision (Kilby 2000).This is reflected in the IEG criteria for rating Bank supervision(summarized in Appendix A), which emphasizes the “fiduciary”duty of the borrower (i.e. alignment of the borrower’simplementation to project objectives).

5 Methodology

I first use an ordinary least squares (OLS) model to test if anadversarial model based on alignment A or a cooperative modelbased on execution E better explains borrower performance. Thetest of which model is of greater importance will be based purelyon a segregation of the explanatory variables into either theadversarial or cooperative model. The OLS model is estimatedusing the standard multivariable regression relationship

Yi = b1 + b2X2i + ... + bkXki + ui (4)

In order to specify the model, I first conduct two stepwiseregressions. The first is of the means of the governance indicatorson BORRPERF and the second is of variables that measure changein governance quality over the course of the project (with Ssuffixes) on BORRPERF. The stepwise regression procedure usesforward selection to test the addition of each variable only if itimproves the model’s explanatory power (tested at the 15% level).The stepwise regression for means finds that GOVST, CORR,LAW, and RELIG are significant, and the stepwise regression forthe change variables finds that MS, or the change in militaryinvolvement in politics over the course of the project, is significant.

The full model includes the quality of bank supervision(QVISION), four variables measuring governance quality(GOVST, CORR, LAW, and RELIG), one variable measuringchange in governance quality (MS), the length of the project(LENGTH), the cost of the project (COST), experience withprojects (EXPER), bureaucratic quality (BUR), socioeconomic

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conditions (SOCIO), and five regional dummy variables (R1, R2,R3, R4, R5).

BORRPERFi = b1 + b2QVISIONi + b3GOVSTi + b4CORRi

+ b5LAWi + b6RELIGi + b7MSi + b8LENGTHi

+ b9COSTi + b10EXPERi + b11BURi + b12SOCIOi

+ b13R1i + b14R2i + b15R3i + b16R4i + b17R5i + ui (5)

In addition to the linear model, I use a probit modelwith the dependent variable, borrower performance, definedas a binary outcome of either 0 or 1. An evaluation of thebimodal distribution of borrower performance scores (Figure 1)supports such a specification. I define BORRPERF greater than7 as “satisfactory” (BORRPERF = 1) and any less than 7 as“unsatisfactory” (BORRPERF = 0), descriptions that mirror theprimary adjectives in the IEG’s methodology in Appendix B.

The probit regression model uses the cumulative standardizednormal distribution (CDF) to model a sigmoid relationship of alinear variable Z such that

Z = b1 + b2X2i + ... + bkXki (6)

The probability of the event occurring is defined as

pi = CDF(Zi) (7)

With the standard normal density function defined as

CDF(Z) =1p2p

e�z2

2 (8)

Thus, the probit specification with each governance indicatoris

CDF(BORRPERF)i = b1 + b2QVISIONi + b3GOVSTi

+ b4CORRi + b5LAWi + b6RELIGi

+ b7MSi + b8LENGTHi + b9COSTi

+ b10EXPERi + b11BURi + b12SOCIOi

+ b13R1i + b14R2i + b15R3i + b16R4i

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+ b17R5i + ui (9)

6 Results

Results of the determinants of borrower performance as specifiedin the linear equation (5) are reported in Table 1. As many ofthe variables, including BORRPERF, are measured on indexedscales rather than in absolute units, it is difficult to interpret thequantitative importance of some of the coefficients without anytransformation. To ease interpretation, I consider the percentagethat BORRPERF is increased from its 10th percentile value to its90th percentile value if an explanatory variable increases fromits 10th to its 90th percentile value. This impact on borrowerperformance ILinear is defined as

ILinear =(x90thpctile

ki � x10thpctileki )

(y90thpctilei � y10thpctile

i )bbk (10)

The overall model presents a reasonable goodness of fit withoverall borrower performance, with an adjusted R-squared of0.3513. Seven of the variables in the model are statisticallysignificant at the 5% level. The quality of the Bank’s supervisionhas the most impactful coefficient, with a 1-point increase leadingto an increase in overall borrower performance of 0.5923 points.This impact is shown to be quantitatively important, as animprovement in the quality of Bank supervision from its 10th to90th percentile value would result in a proportional improvementof 59.2% of the range separating the 10th percentile from the90th percentile in borrower performance. Of the five governancevariables included, four are statistically significant. The variablefor corruption has the most quantitative significance, as itscoefficient indicates that an improvement in corruption from its10th to 90th percentile value would result in a proportional increasein borrower performance of 7.5%. Indicators for governmentstability and law and order returned effects of similar magnitudes,with that of a change in military involvement in politics muchsmaller. However, as there does remain some multicollinearitybetween the first three governance indicators, their coefficients

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Figure 1: Histogram of Borrower Performance (BORRPERF)

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Table 1: Coefficient Transformation for Linear Regression

Variable Coefficient 90th percentile - I_Linear Impact %(t-stat) 10th percentile

QVISION 0.5923448*** 6 59.23449 59.2%(37.47)

GOVST 0.0975966*** 4.1111 6.687167 6.7%(3.17)

CORR 0.1206906*** 3.7182 7.479305 7.5%(4.05)

LAW 0.0619899*** 5.6388 5.825902 5.8%(2.63)

RELIG 0.0090508 - - -(0.46)

M_S 0.4068133*** 0.41666 2.825047 2.8%(2.76)

LENGTH -0.1371872*** 1.5578 -3.561937 -3.6%(-4.00)

COST -0.0292852 - - -(-1.02)

EXPER 0.0002513 - - -(0.21)

BUR 0.0207193 - - -(1.02)

SOCIO 0.1052104*** 3.4768 6.09668 6.1%(3.24)

Constant 2.110533*** - - -(3.14)

N = 3296R2 = 0.3513F(16,3279) =112.55

***significant at 1% level; **significant at 5% level; *significant at 10% level.Non-significant regional dummies omitted.

should not be considered perfectly precise.In terms of variables in the cooperative model, only the length

of projects was statistically significant, with an increase in projectlength by 1% leading to a decrease in borrower performance of0.137 points. Put another way, moving project length from its10th to 90th percentile value would result in a 3.6% decrease ofborrower performance from its 90th to 10th percentile. The finalstatistically significant variable was the measure of socioeconomicconditions, which found that an improvement from the 10th to90th percentile resulted in about a 6.1% corresponding increase inborrower performance.

To interpret the results from the probit regression, I willspecify a similar transformation as that for the linear model.However, unlike in linear regression, an interpretation of the

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coefficients in probit regression must account for the positionsof the other variables in the model. This is because theincrease in probability of a satisfactory borrower performanceattributable to a one-unit increase in a given explanatory variableis also dependent on the values of the other predictors. Totransform the coefficients, I will consider the marginal increase inprobability that borrower performance will be satisfactory versusunsatisfactory when an explanatory variable increases from its10th to its 90th percentile value. The use of the difference infitted probabilities for each given explanatory variable from its10th to 90th percentile values within a probit model is creditedto Malmendier and Nagel (2011) and Raman, Shivakumar, andTamayo (2013).

I define a new variable IProbit to measure the impact on theprobability of a “satisfactory” borrower performance as

IProbit = CDF(bb1 + x90thpctilei

bbi + Skj=1xjbb j)

� CDF(bb1 + x10thpctilei

bbi + Skj=1xjbb j) (11)

This formula assumes that all other explanatory variables notunder consideration are all at their mean values.5 IProbit canthus be interpreted as the contribution in probability towarda satisfactory borrower performance from a change in a givenexplanatory variable from its 10th to 90th percentile value.

The results of regression equation (11) and the transformedcoefficients are displayed in Table 2. The relative significanceof the explanatory variables are similar to those in the linearmodel. Again, the quality of the Bank’s supervision wasthe most quantitatively important explanatory variable, withan increase from its 10th to 90th percentile value leading toa 61.2% increase in the probability of satisfactory borrowerperformance. The same four governance indicators are againstatistically significant with similar magnitudes, although nowlaw and order was the most significant, with a 10th to 90th

percentile improvement contributing 7.6% toward the probabilityof satisfactory borrower performance. As in the linear model,

5This is not to say that alternate specifications are without interest. One couldalter the mean values of variables to match the conditions in a specific country.

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Table 2: Coefficient Transformation for Probit Regression

Variable Coefficient CDF CDF I_Probit Impact%

(z-value) 90thpercentile

10thpercentile

QVISION 0.2926934*** 0.854101117 0.241690702 0.612410414 61.2%(25.35)

GOVST 0.0563743** 0.802008121 0.731400805 0.070607316 7.1%(2.48)

CORR 0.0522062** 0.796799677 0.737653644 0.059146033 6.0%(2.30)

LAW 0.0450639** 0.807897204 0.731073587 0.076823616 7.7%(2.57)

RELIG 0.0101633 - - - -(0.70)

M_S 0.2327563** 0.78144241 0.754678352 0.02946589 2.9%(1.98)

LENGTH -0.106488*** 0.74803895 0.797922611 -0.040904072 -5.0%(-3.74)

COST -0.0379666* 0.748778262 0.789682334 -0.040904072 -4.1%(-1.76)

EXPER 0.002760*** 0.812823786 0.741567884 0.071255902 7.1%(2.90)

BUR 0.009905 - - - -(0.65)

SOCIO 0.075530*** 0.80435599 0.723970148 0.080385842 8.0%(3.07)

R2 0.2365606* - - - -(1.92)

Constant -2.04553*** - - - -(-3.95)

N = 3296Pseudo R2 = 0.2578LR chi2(16) = 966.67

***significant at 1% level; **significant at 5% level; *significant at 10% level.Non-significant regional dummies omitted.

project length and socioeconomic conditions are both significantwith similar economic impacts. Interestingly, the numberof previously completed projects and project cost are nowstatistically significant. In addition, both of their contributionstoward a satisfactory borrower performance are similar inmagnitude to the other variables in the cooperative model. Theaddition of dummy variables for each project sector to accountfor potential unobserved differences between projects did notmaterially change the results.

These models do not control for potential endogeneitybetween Bank supervision and borrower performance. As canbe seen from Table 3, the quality of Bank supervision is highly

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Table 3: Correlation between BORRPERF and QVISION

BORRPERF QVISIONBORRPERF 1.0000QVISION 0.5695 1.0000

correlated with Borrower performance. There is a materialconcern for reverse causality, as one could conceive that superiorborrower performance enables easier and more effective Banksupervision efforts. If endogeneity exists, the most likelyexplanation is that borrowers with more efficient bureaucraciesfacilitate Bank supervision while also improving their ownperformance. However, none of my four specifications foundthat bureaucratic quality (BUR) influenced borrower performancewith any statistical significance. An alternative explanation forendogeneity is that Bank officials may be more easily able tomonitor projects in countries with developed transportation andcommunication infrastructures. To test these hypotheses, I run aregression of QVISION on BORRPERF first with dummy variablesfor socioeconomic conditions and then with dummy variables foreach country. The results, presented in Appendix E (availableonline), indicate that the relationship between QVISION andBORRPERF remains robust, with coefficients and t-values verysimilar to those of the linear specifications.

In addition to my tests, I also review the findings of Chauvetet al. (2006), who consider the effects of project supervisionon development project outcomes. As part of their analysis,Chauvet et al. test for the potential for endogeneity betweenproject supervision and project outcomes. While I consider overallborrower performance, not overall project outcomes, the two arehighly correlated. Thus, the results of Chauvet et al.’s endogeneitytests are directly applicable to the potential reverse causality inmy models. In this process, Chauvet et al. use a recursivemultivariate probit model that transforms borrower supervisioninto a binary variable. The direct effect of supervision remainssignificant at the 1% level, implying a robust relationship. Whilenot conclusive in the context of my analysis, these results suggesta causal relationship between Bank supervision and borrower

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performance.

7 Discussion

The analysis found that the adversarial model explained borrowerperformance better than the technical model, although largelybecause of the impact of project supervision. In the linearmodel, the variables measuring the technical competence ofa borrowing country’s government show the least quantitativeimportance. However, the resulting statistical significance ofexperience with past projects in the probit model does suggestthat specific experience is important, and certainly more so thangeneral bureaucratic competence. Variables for the cost andlength of projects were slightly more robust, indicating that projectcomplexity also plays a role in borrower performance. However,project length may be subject to issues of reverse causality, as poorborrower performance could conceivably delay the completion ofprojects. Interestingly, the absolute values for the sum of theimpact of the statistically significant technical t and complexityc variables in the probit model were about equal, suggestingthat the oppositional factors defining execution E are in relativebalance.

Variables for governance quality were somewhat morequantitatively significant than technical variables, sometimes upto twice the extent as measured in the linear model. However,their impacts were also of limited overall significance. The relativesignificance of governance indicators inverted across models, withlaw and order becoming the most impactful variable in the probitmodel. In sum, the results do not provide clear evidence that thereis a single aspect of governance quality that is most important,and therefore there is no clear metric that the Bank should seekto improve over others. The lack of quantitative importance forimprovement in military involvement in politics also suggeststhat short-term changes in governance quality will do little toensure borrower performance, perhaps reflecting how governancequality can become entrenched in institutions. Rather, the Bankshould focus on improving the overall level of governance qualityover the long run. Considering again the theoretical model,the results indicate that the impact of technical expertise t,

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project complexity c, and governance quality g are all of similar(marginal) magnitudes.

Socioeconomic conditions were statistically significant andconsistently one of the most impactful explanatory variables.That improved conditions led to better borrower performance isnot surprising, although the marginal size of the impact mightbe an encouraging sign that governments in poor countries canstill perform admirably. Finally, dummy variables for regionhad limited significance, although the positive coefficient on thedummy for East Asia and the Pacific (R2) makes sense giventhe generally more developed nature of this region in contrastto regions such as Sub-Saharan Africa.

The most impactful variable in the analysis was the qualityof the Bank’s supervision efforts, which maintained considerablequantitative importance across models. That the other adversarialvariables would have a small impact appears reasonable, as theratings given by the PRS group apply to a whole country overan entire year. Even if the ratings are accurate, the indicatorsare an aggregate from a wide variety of potential agents andprojects, which decreases their precision. Traits like corruptionand government stability are diffuse and may not be obviouslyapplicable to any given project. For example, some projects maynaturally have less scope for corrupt activities or provide limitedelectoral benefits to an embattled regime. Thus, we may not haveexpected an enormous impact of governance indicators.

By contrast, IEG reports on completed projects indicate thatincreasing the quality of Bank supervision has been shown tomake a material impact on borrower behavior. For example, in arural finance project for Tunisia, Bank supervision was “somewhatsuperficial for the first few years of project implementation”(The World Bank 2001). But when Bank efforts to improvethe quality of the Tunisian National Agriculture Bank’s loanportfolio appeared to stagnate, supervision become “more activeand interventionist,” forcing the borrower to define indicators tomeasure portfolio quality and establish “new and realistic” returntargets. During the course of a series of agricultural credit loansto Morocco’s Caisse Nationale de Crédit Agricole (CNCA), projectsupervision was “unsatisfactory for a long period,” a result of toolittle attention paid to the allocation of Bank credit and CNCA’s

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credit process (The World Bank 1998). After an audit by KPMGrevealed gross procedural and management errors in CNCA,the Bank appointed new teams and “supervision dramaticallyimproved.” After supervision improved, the Bank refused to“endorse the vague rescue measures that were proposed byCNCA” and specified which “reforms would be necessary beforeformalizing further Bank support.” My findings on the outsizedimpact of Bank supervision also coincide with the results ofKilby (2000) and Ika, Diallo, and Thuillier (2012), who foundsupervision to be highly influential on overall project outcomes.

While many of the technical variables had at leastsome statistical significance, bureaucratic competence had nomeaningful impact on the performance of borrowers. Thisis surprising, as bureaucratic quality varies significantly acrosscountries. This result implies that bureaucratic efficiency is nomatch for experience with projects whose complexities createmeaningful challenges for borrowers. One possible explanationfor the small quantitative importance of technical variables as awhole is that project supervision may help mitigate poor borrowerperformance that would otherwise be significantly affected by alack of technical competency or project complexity. If true, thiswould imply a revision to my original model, which consideredBank supervision as a check against only low governance qualityg. More broadly, the regression coefficients of this analysis mayhave been underestimated because Bank projects were excludedif they had any missing IEG review data. If cancelled or failedprojects are less likely to be given comprehensive ratings by theIEG, as one might expect, then my sample would be biased towardprojects that may have succeeded in spite of meaningful absencesin governance quality.

Given the importance of Bank supervision, I now considermethods to improve supervision efforts. Several IEG reports ofprojects with the lowest reviews of Bank supervision highlightedhigh project leadership turnover as crippling to supervisionefforts because of difficulties in transferring knowledge andmaintaining communication (The World Bank 2005). A projectfor urban revitalization in Mozambique also cited a breakdownin communications as anathema to supervision, one that occurredbecause of a build up of tensions between the borrower and Bank

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staff (The World Bank 2002). Thus, the Bank should work tomaintain continuity among supervision teams and consistency ofcommunication at all times. Other common challenges to high-quality supervision included deficient documentation and a lackof use of standard monitoring and evaluation (M&E) tools (TheWorld Bank 2004). One approach to mitigate this failure is theeOperations platform built by the Asian Development Bank in2010 (The Asian Development Bank 2011). eOperations is anintegrated information technology solution with the ability tomonitor projects, streamline administrative procedures, provideuniform project related documentation, and prepare standardizedcustomizable reports.

IEG reviews also highlight how Bank officials could becomecomplacent about supervision. During a project to redesignTanzania’s roadways, Bank supervisors accepted the reassurancesof resident engineers even when their assessments were wildlymore optimistic than those of Bank headquarters. Supervisorsfailed to investigate emerging problems in sufficient detail, whichultimately led to eroding borrower performance and corruptactivities (The World Bank 2000). Similarly, IEG reviews ofprojects across Jordan, Egypt, and Yemen for higher educationreforms found that supervision missions tended to rate fulfillmentof all project objectives as satisfactory, thus failing to alertmanagement that parts of the reform agenda were not progressingwell (The World Bank 2011). Ultimately then, no matter theproject team and the technologies at their disposal, qualitysupervision depends on the willingness of Bank officials toquestion underlying assumptions and engage in potentiallyuncomfortable dialogue.

Despite the imperative to improve Bank supervision, thereremain potential structural challenges to doing so. As noted byChauvet et al. (2006), the long lag between the decision to proposea project and the eventual performance of the project mean thatincentives for Bank staff to abort projects are weak. The Bank’sincentive scheme instead encourages a culture of disbursementrather than ensuring project success, which in part dependson high-quality supervision. Furthermore, supervision alonewill likely not be enough to maximize borrower performance.While this analysis explained a reasonable amount of variance in

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borrower performance, there may remain some other reforms thatcould substantially affect the behavior of borrowers. Aerni (2006)has proposed changing the underlying principal-agent dynamicby shifting the role of the principal from lending organizationsto the middle classes of developing countries. He suggests thatdeveloping nations pay the annual interest on their debt to anindependent funding pool designed to improve the infrastructurefor domestic entrepreneurs. In the long run, this could helpdevelop a politically active middle class that could do a betterjob of selecting and monitoring development projects than stafffrom a global lending institution like the World Bank.

8 Conclusion

Despite billions of dollars spent in development aid, poorliving conditions still afflict billions of people globally. Recentresearch has sought to improve the effectiveness of internationaldevelopment efforts by measuring aggregate indicators andproject-level outcomes. This paper analyzed the behavior ofgovernments engaged in development contracts with the WorldBank within a principal-agent framework. The results indicatethat the most significant predictor of borrower performance ishow well the Bank supervises projects. By comparison, thetechnical competence and governance quality of borrowers, aswell as the complexity of projects, has only a marginal impact onborrower performance. In some sense it should be encouraging topolicymakers that supervision can dramatically improve projectperformance, as this variable is most fully within the control ofthe Bank. Whereas supervision may have once been considereda procedural requirement, it is now more than ever clearlya potent tool to direct borrowers toward high performance.Further research is necessary to examine how to maximize projectsupervision as well as other determinants of borrower behaviorunaccounted for in this model. As the behavior of borrowerscan impact overall project outcomes, developing a more completeunderstanding of the decisions made by development projectspartners will be crucial in the fight against global poverty.

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Appendix A: Quality of Bank Supervision Criteria

CriteriaBank performance is rated against the following criteria, asapplicable to a particular operation. The evaluator should takeaccount of the operational, sector, and country context in weighingthe relative importance of each criterion of quality of supervisionas it affected outcomes.

• Focus on Development Impact

• Supervision of Fiduciary and Safeguard Aspects (whenapplicable)

• Adequacy of Supervision Inputs and Processes

• Candor and Quality of Performance Reporting

• Role in Ensuring Adequate Transition Arrangements (forregular operation of supported activities after Loan/Creditclosing)

Rating ScaleWith respect to relevant criteria that would enhance developmentoutcomes and the Bank’s fiduciary role, rate Quality ofSupervision using the following scale:

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Highly Satisfactory There were no shortcomings in theproactive identification of opportunitiesand resolution of threats.

Satisfactory There were minor shortcomings in theproactive identification of opportunitiesand resolution of threats.

Moderately Satisfactory There were moderate shortcomingsin the proactive identification ofopportunities and resolution of threats.

Moderately Unsatisfactory There were significant shortcomingsin the proactive identification ofopportunities and resolution of threats.

Unsatisfactory There were major shortcomings in theproactive identification of opportunitiesand resolution of threats.

Highly Unsatisfactory There were severe shortcomings in theproactive identification of opportunitiesand resolution of threats.

Appendix B: Borrower Performance Criteria

Definition: Borrower performance is the extent to which theborrower (including the government and implementing agencyor agencies) ensured quality of preparation and implementation,and complied with covenants and agreements, towards theachievement of development outcomes.

Government PerformanceGovernment performance is rated against the following criteria,as applicable to a particular operation. The evaluator shouldtake account of the operational, sector, and country context inweighing the relative importance of each criterion of governmentperformance as it affected outcomes.

CriteriaGovernment ownership and commitment to achievingdevelopment objectives. Enabling environment includingsupportive macro, sectoral, and institutional policies (legislation,regulatory and pricing reforms, etc.)

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• Adequacy of beneficiary/stakeholder consultations andinvolvement

• Readiness for implementation, implementationarrangements and capacity, and appointment of keystaff

• Timely resolution of implementation issues

• Fiduciary (financial management, governance, provisionof counterpart funding, procurement, reimbursements,compliance with covenants)

• Adequacy of monitoring and evaluation arrangements,including the utilization of M&E data in decision-makingand resource allocation

• Relationships and coordination with donors/partners/stakeholders

• Adequacy of transition arrangements

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