Aid Policies and GrowthBurnside Dollar AER.2000

Replication part 1:Pooled OLS and 2-SLS with panel data:

Interaction terms and outlierswith a spurious pair of

highly correlated regressors weakly correlated with the dependent

variable

Plan

1. Data and Specification issues (5 general +3 for policy index): Pooled OLS and pooled 2SLS not adapted for panel data.

2. Endogeneity of Aid/GDP (2SLS versus OLS), subgroup of low income, government consumption.

3. Pbm1: Conflicting outcomes of Interaction terms4. Pbm2: Bostwana Outliers (simple interaction term).5. Pbm3: Gambia Outlier (two interaction terms).

Replication AssignmentBurnside and Dollar

Part 1: Identification of a spurious interaction term effect

Part 2: Panel data estimators

* (2) POOLED OLS REGRESSIONS and SPURIOUS INTERACTION TERM* 2A: REPLICATION OF BD (4) and CR (2) OLS REGRESSIONS* 2B: REPLICATION OF GRAPHS p-values from N=275 to N=269* 2C: DFBETA*LEVERAGE * 2D: SPURIOUS PAIR of regressors with interaction term* 2E: VIF PIF highly collinear pair* 2F: Contribution to R2 and power* 2G: Robust regressions Quantile regressions

1. BD specification issues and Results

• 3 sets of equations:Growth equationAid equation (as share of GDP)Government consumption equation (as share of GDP)

• Main Results:Aid might have more impact on growth in the developing world if allocated toward good policy environment.

However donors were not favoring good policy environments in their allocations.

Data sources

• The World Bank Debt Reporting System that contains all the official loans received by the developing countries from multilateral and bilateral sources.

• Data is converted into constant 1985 dollars using the unit value of imports price index from International Financial Statistics.

• Divide the aid by real GDP in constant 1985 prices from the Summers and Heston (1991).

• All : 56 countries, 275 observations.• Low income : 40 countries, 189 observations

2013 exercise on data sources

(1) Could you find on the internet the websites providing the updated values of each of the variables of Burnside and Dollar?

(2) Could you find issues on measurement errors for these variables (cf Penn World Tables versus World Development Indicators)

UNBALANCED PANEL DATA SET: 56 COUNTRIES, 6 PERIODS OF 4 YEARS AT MOST. Freq. Percent Cum. | Pattern -------------------------+------- 34 60.71 60.71 | 111111 3 5.36 66.07 | 11111. 2 3.57 69.64 | ...11. 2 3.57 73.21 | ...111 2 3.57 76.79 | .11... 2 3.57 80.36 | .11111 1 1.79 82.14 | .....1 1 1.79 83.93 | ....1. 1 1.79 85.71 | ..1... 8 14.29 100.00 | (other patterns) ---------------------------+------ 56 100.00

Econometric Model: growth of GDP/head averaged over 4 years

1. The country specific (time invariant) random term is missing in both regressions: panel data estimator should have been used: unbalanced panel of 56 countries times 5 periods (a few with a single period): endogeneity cov(x(it), alpha(i)) different from zero.

Four other specification issues

2. The distinction between time invariant and time varying variables should have been made (cf. panel data estimators).3. Other regressors than aid/gdp are potentially endogenous (e.g. policy).4. Missing regressors (education? Investment? malaria?)5. Endogenous sample selection driven by the availibility of regressors.

3 specification issues for the Policy index

1. Other policy variables than those ones may matter.

2. For example, corruption and institutions index are not included in their « policy ».

3. The weights are sensitive to the other regressors in equation (1), they are not « equal » for each of the three variables (those variables were not standardized).

Results: Statistically significant R2=35%

1. Trade openness index developed by Sachs and Warner (1995).

2. (negative) Inflation as a measure of monetary policy developed by Fischer (1993).

3. Fiscal variable suggested by Easterly and Rebelo (1993): budget surplus

4. Time invariant ICRGE indicator for quality of institutions (Knack Keefer).

5. (negative) Time invariant geographical Sub-saharan dummy

Not statistically significant

Aid/GDPLagged(M2/GDP) (Levine)Ethnic fractionalization (time invariant; Easterly and Levine).AssassinationsInteraction term EF*A (spurious statistically significance)

2. Endogeneity issue: Aid equation (1st stage of 2SLS)Statistically significant variables R2=61%

Lower income countries N=195 observations

• Negative effect: Log(population): size of the country: this instrument is a problem according to Bazzi and Clemens (AER2013), as used to instrument many variables (also used in the Rajan Subramanian paper).

• Negative effect: GDP/head beginning of period• Positive: Dummy for Egypt

Aid equation (1st stage of 2SLS)Not statistically significant

• Arms/exports• Strategic: franc zone dummy, latin america

dummy, sub-saharan dummy.• Policy• Remark: no reverse causality tested.

2 SLS versus OLS contrastHausman test (Statistics Chi2 dist.)

If the 2-SLS and OLS parameters are different (Hausman test), the endogeneity bias is large, 2SLS is to be prefered.

Else, endogeneity bias is negligible: OLS can be prefered : it is the case in BD paper.

Regression on sub-group

Lower income countries, N=189 observations.

Dependent variable is governement consumptioncorrelated with bilateral aid

3. Problem 1. Interpretation of the interaction terms:

Opposite effects for large value of AID/GDP ?

Development aid has an effect on the growth of a developing country conditional on “good” macroeconomic policy.

Real GDP growth

depends significantly on:

(Aid/GDP) * Policy

(Aid/GDP)² * Policy

Policy

Policy = 1.28 + 6.85 * government budget surplus - 1.40 * inflation rate+ 2.16 * (exports + imports/GDP)

Political implication: make the development aid conditional on macroeconomic policy criteria.

Aid has an effect on growth conditional to good macro-policies

Growth of GDP/head (i,t) =Beta1. Aid/GDP (i,t)+Beta2. Policy (i,t)+Beta3. Aid/GDP * Policy+Beta4. (Aid/GDP)2 * Policy+….=(Beta1+Beta3*policy)*Aid/GDP + …=(Beta2+Beta3*Aid/GDP+Beta4*(Aid/GDP)2)*Policy+….

Interaction terms: endogenous marginal effect

Beta1 + Beta2*Policy could be >0, <0, not statistically different from zero.

The sensitivity of a variable on the dependent variable cannot be isolated independently of the other variables (no ceteris paribus interpretation).

An interaction term is different from endogeneity such as: Aid/GDP=function of regressors.

Marginal effect of policyAs a function of Aid/GPD

Marginal effect of Aid as a function of policy

With Bostwana or without (linear)With Gambia86 (red) or without (quadratic)

With Bostwana (red)or without Bostwana (green). No interaction

H0: X=0 outside the 95% confidence interval: reject the null hypothesis

When a segment of the line y=0 is within the confidence interval:

NO EFFECT (cf. during crisis below):

0 outside of 95% confidence interval for policy<-4 and policy>4 including Botswana

0 outside of 95% confidence interval for Aid/GDP> « 5 » including Botswana

Marginal effect of policyAs a function of Aid/GPD

Marginal effect of Aid as a function of policy

With Bostwana or without (linear)With Gambia86 (red) or without (quadratic)

With Bostwana (red)or without Bostwana (green). No interaction

1 is included in 95% confidence interval even including Gambia

Missing in table 6

The marginal effect of policy on growth as a quadratic function of aid policy is only evaluated at Aid/GDP=1.6: in this area, the linear and quadratic interaction terms marginal effects are similar.

But at Aid/GDP=5.5 the gap of marginal effects is 0.8 (2 versus 1.2, +66% from 1.2, -40% from 2).

At Aid/GDP=12.5 maximal value, the gap of marginal effects is 2.7 (3 versus 0.3, -90% from 3)

4. How to find influential outliers driving the statistical significance of parameters in multiple regression?

And how to obtain « outliers robust » statistical significance of

parameters?

Benchmark Reference (1980, 2004)

« Influence statistics » for each observation used in a regression have been programmed since mid 1980s closely following BKW.proc reg / influence (SAS) reg , influence (stata) procedures.

Follow up literature: Rousseeuw (2003).

Proc robustreg (SAS)Robustreg (stata)

Regressions which do not minimize the sum of square of errors, which underweight outliers in regressions.

Outliers in Burnside and Dollar

4.1. Regressions only with Aid/GDP * Policy:DFBETAS * LEVERAGE graphs helps to identify Botswana and Mali as outliers.

4.2. Regressions with Aid/GDP*Policy and(Aid/GDP)2*Policy:Analysis of variance of (Aid/GDP)2*Policy helps to identify Gambia as outlier.

4.1. Regressions with only Aid/GDP * Policy

The result is obtained by keeping 3 or 4 outliers (Botswana, Mali) and omitting 5 others.BD decided to remove 5 outliers within a set of 16 outliers with large « leverage »(observations which are the farthest in absolute value from the mean of the variable) for the variable Aid/GDP*Policy.

Outliers influence statistics:DF-beta*leverage graphs

• Df-beta (difference of slope when one removes or not only one observations, divided by a standard error).

• Leverage: distance from the mean of a regressor (normalized in the so called « hat » matrix): increasing function of the distance to the mean of the regressors.

The 68–95–99.7 rule, also known as the three-sigma rule states that nearly all (less than 3/1000) values lie within 3 standard deviations of the mean in a normal distribution.

Range Population in range Expected frequency outside range

Approx. frequency for daily event

μ ± 1σ 0.682689492137 1 in 3 Twice a week

μ ± 1.5σ 0.866385597462 1 in 7 Weekly

μ ± 2σ 0.954499736103 1 in 22 Every three weeks

μ ± 2.5σ 0.987580669348 1 in 81 Quarterly

μ ± 3σ 0.997300203936 1 in 370 Yearly

μ ± 3.5σ 0.999534741841 1 in 2149 Every six years

μ ± 4σ 0.999936657516 1 in 15,787 Every 43 years

Three thresholds for high leverage observations of a single regressor

1) Leverage index h (Belsley Kuh and Welsh) threshold: > 2(k+1)/n. h(ii) is not very intuitive.2) Observations farther than +/- 2 or 3 standard errors from the mean of the distribution. Easy to remember with normal law properties but not outlier robust. 3) Observations outside: Median (Q2) +/- 1.5 (Q3 – Q1)Q3=p75, Q1=p25Better than (2) because median and interquartile interval are not sensitive to outliers whereas mean and standard errors are sensitive to outliers.

What is df-beta influence statistics?

Measure of how much an observation has effected the estimate of a regression coefficient (there is one DFBETA for each regression coefficient, including the intercept).

Values larger than threshold in absolute value are considered highly influential on a given parameter estimate.

INFLUENCE: DFBetas (for each observation i and each parameter beta of a given multiple regression):

Value of a parameter beta in the regression (including observation (i) minus the value of this parameter

excluding only one observation (i); divided by their standard error.

Cutoff: > +/- 2/SQRT(N), N number of observations.

DFBetas > 0 means that single observation (i) contributes to increase the estimated value of this particular

parameter.

DFBetas < 0 means that single observation (i) contributes to decrease the estimated value of this particular

parameter.

Exclude: Gam86+Gam90+Nic90: difbeta<0, Guyana90, Nic86: difbeta>0

Include: Botswana: difbeta>0

+/- 2/sqrt(N=275)=0.12: threshold dfbeta+/-2 standard errors from mean of edapolicy:

5% extremes if normal distribution, N=275 β=0.013

GMB6

GMB7

NIC7 ECU2

JAM3PHL5GAB2EGY3 GMB5SYR3BRA7KOR6SLV4URY5CHL6CHL2CHL7GHA3CHL4TZA5TTO4CHL3GAB3CMR7SEN5SYR4KOR5JAM4EGY7PHL7THA6TUR7MDG7SYR6GAB5TZA6CIV4URY2CRI4MDG3TGO4NER4PER5NIC4DOM7IDN6PER6IDN5TTO3MAR5COL6GTM2PAK3GUY6KEN7VEN7COL7SLE3ARG4LKA2IND2IND4CMR4KEN6LKA4THA7NIC2MDG2HTI2CMR3CMR5ZMB6GMB3MEX5HTI6BRA4PHL2MWI5IDN4KOR7LKA5IND3ETH6PAK2ZAR4LKA7NGA3 HND7COL3ETH5ZWE7HTI5VEN4HTI3ECU6SOM3DZA2IND7KEN3TTO5EGY6SLV5MAR2GTM3ZAR3IDN2KOR3CRI3URY7PRY5IDN7GUY2PER3HND2MEX2HND3MEX3SEN3DOM5SLV2TUN7HND6DOM3MYS4SYR2HND4SLE5GAB7PRY2ZWE5SLE7IND5THA5ZAR2DZA3SLE2SLV6PER2KEN5SLE6IDN3GHA5MDG6GMB2GUY4BOL3MAR4ZAR6LKA3JAM5DOM4KOR2GHA2ZWE6TGO3CRI5 TGO6ARG2SLV3ZMB2ZAR5HND5LKA6KEN4MYS7KOR4 BOL6PHL6MYS5PRY6CRI2PRY3COL2TUN6THA4BRA3 GHA7NGA2PER7GHA4COL5 MWI7GHA6PHL3NIC5ECU5CRI7VEN6GTM4DOM6KEN2ZMB3VEN3NIC3 TGO5TTO2MYS2GAB6MWI4GTM6URY3TUN5 BOL7NGA5MYS6COL4TTO6SLE4SEN2GTM5ZMB4GUY3HTI4SEN4BOL4BRA2ECU7CMR6THA2MYS3VEN2ARG7PER4VEN5GUY5 IND6MAR6MEX4 CRI6PAK6DOM2MAR3URY4GTM7THA3PAK5PRY4SOM4NGA4PHL4ZMB5PAK7ARG6PAK4GMB4MWI6NER3NGA6ARG5URY6BRA5EGY4PRY7 SLV7MAR7ECU4MEX7SYR7ECU3ZMB7MEX6BOL2EGY5ARG3 MLI6GAB4 BWA6NGA7 BWA5CHL5BOL5

NIC6 GUY7BWA4BRA6

-.6

-.4

-.2

0.2

Dfb

eta

ed

apo

licy

-5 0 5 10Standardized values of (edapolicy)

N=270, β=0.18 for (Aid/GDP)*Policy BD prefered regression

BOL5

GUY5

NIC5

ZMB6

GUY4

ZMB7

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EGY3

SLE6SLE5ARG5

CHL2

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BRA7

BRA6

ARG6

ARG3

BRA5

ARG4MEX5ARG7

MEX6

BRA4MEX3ARG2JAM4

VEN6MEX7

MEX4VEN4VEN3MEX2BRA3VEN5NGA5

NGA7

URY3TTO5

NGA6

URY5

VEN2

JAM3

COL5URY4TTO6BRA2URY2

URY6COL4

TTO4TTO3

NGA4

TTO2GHA4IND6IND7

KOR6

CHL3COL6

NGA3COL3

CHL6

PER4

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KOR7PER3

COL7IND4PER7

KOR5

PHL4PER2ECU6MAR3GTM4CRI3PHL3CRI4

PAK7

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COL2IND2

GUY3SLV3NIC2IND3GTM3GTM2KOR4

CHL5

GAB3

DOM3CIV4MYS4GTM5ECU5NIC3PHL2SLE3SLE7

CHL4

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DOM7PAK6SLV2NGA2SLE4MAR4JAM5URY7LKA2CRI2MYS3PAK3MYS7

CHL7

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PAK4

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THA3PAK2

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LKA6KOR3EGY6TUN5

SLV4

ZAR3MYS6DOM2PRY5ZMB4THA7DZA3PRY3MYS2DZA2HND2ZMB3

TUR7

THA2LKA3IDN5THA4IDN6

ECU3NIC4

THA5PRY2GUY2IDN4THA6GHA2DOM5IDN7ZWE5MAR2ZWE6SYR2ZAR6ECU7

ECU2

PRY6HND3ZMB2ZAR4PHL6KEN3CMR5LKA5TUN6ZAR5TGO4

SOM4

IDN3HTI4CMR6ZWE7HND4MWI4HTI3

TZA5

GAB4

SLE2

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CRI5KEN5KEN4MAR6GAB6MAR5KEN2GHA5GTM6MDG3BOL4

SYR3

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PHL7MWI5GAB5

GTM7ETH5KEN6KOR2

CMR4

GMB2IDN2BOL3CMR3SYR4GAB7

PRY7

SLV5

SEN5

BOL2

EGY7

GMB3MDG6TUN7LKA7HND6LKA4CRI7SEN3TZA6MDG7MAR7

CMR7

HTI6

MWI6

SOM3SEN2KEN7ETH6

GMB4

NER4SEN4GMB5

CRI6NER3SLV6TGO6TGO5MWI7

BOL6

SLV7

HND7

GHA7BOL7GHA6

MLI6

BWA4

BWA5

BWA6

-.2

0.2

.4

Dfb

eta

ed

apo

licy

-5 0 5 10Standardized values of (edapolicy)

N=266, β=-0.025

EGY3

ECU2CMR7

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-5 0 5 10Standardized values of (edapolicy)

N=259, β=-0.019

CMR7EGY3

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-5 0 5 10Standardized values of (edapolicy)

STATA code for figure: dfbeta(x1) and thresholds as a function of std(x1)

egen stdedapolicy = std(edapolicy)reg gdpg edapolicy …predict dfbedapolicy, dfbeta(edapolicy)quietly twoway (scatter dfbedapolicy stdedapolicy, msize(small) msymbol(o) mlabel(countryyear) yline(0) yline(0.1206) yline(-0.1206) xline(2) xline(-2) xline(3) xline(4) xline(5) )

Bostwana data: high dfbeta and high leverage

1. BD did not plotted the Belsley Kuh and Welsh proposed threshold value for dfbeta(edapolicy) which signalled that dfbeta(policy) of observations Botswana4 and Bostwana5 were over this threshold (0.12).

2. Bostwana4, Bostwana5 and Bostwana6 are more than 3 standard errors from the mean of Edapolicy (3.2; 3.45; 3.79)

Omitting outliers shifting the parameter downwards to zero

4 of the 5 omitted outliers by BD were shifting downwards the parameter of Aid/GDP*Policy (dfbeta<0). The 4 next outliers kept by BD (Bostwana for three periods and Mali) are all shifting upwards the parameter of Aid/GDP*Policy (Dfbeta>0)

Observations abs(x-mean)/sigma Aid*Policy Parameter p-value

SLV7 1,47023 - 0,109 < 0 0,39HND7 1,48981 - 0,104 < 0 0,37GHA7 1,52173 - 0,087 < 0 0,41GUY5 1,58642 - 0,044 < 0 0,67BOL5 1,66400 - 0,061 < 0 0,55BOL7 1,82182 - 0,044 < 0 0,65GHA6 1,99605 - 0,025 < 0 0,77

MLI6 dfb>0 2,72407 0,051 0,60BWA4 dfb>0 3,23028 0,140 0,15BWA5 dfb>0 3,45475 0,176 0,03*BWA6 dfb>0 3,79632 0.186 (MAX) 0,007*NIC6 dfb>0 (-) 4,07443 0,183 0,002*GUY7 dfb>0 5,65247 0,154 0,004*NIC7 dfb<0 (-) 5,79056 0,104 0,03*

GMB7 dfb<0 6,31273 0,048 0,39GMB6 dfb<0 7,87388 0,013 0,79

The number of outliers removed (5) maximized the Aid*Policy estimated parameter value (0.186).

Statistical significance obtained when removing 2 to 7 outliers, ordered by their distance to the mean of Aid*Policy, in multiples of its standard error (>3).

1 2 3 4 5 6 7 8 9

-0.2

0

0.2

0.4

0.6

0.8

1

0.390.370.41

0.67

0.55

0.65

0.77

0.6

0.15

0 0 0 00

0.39

0.79

-0.109-0.104-0.087-0.044-0.061-0.044-0.025

0.051

0.140.1760.1860.183

0.1540.104

0.0480.013

Aid*Policy Parameter p-value

« The reason that the results are so robust can be seen in table 7…»

Outliers explain that « the results are so robust».

« For these 13 observations, the correlation between unexplained aid/GDPxPolicy and unexplained growth (partial correlation) is 0.40… Countries with large value of aid/GDPxPolicy are reformers… Their observations largely explain our finding. They include a wide range of country (follows a list of 6 countries including Bostwana and Mali). »

BD « robust » doubletalk

A « robust » result is usually in statistics « robust to omitting outliers », cf. « robust regressions ».

Here, the « outliers » which are kept in the regression are presented in table 7 to demonstrate that the results are « robust ».

4.2. Regressions with (Aid/GDP)2*Policy: Two highly correlated interaction terms

and Gambia outlier

A near-multicollinearity problem with quadratic and interaction terms

Often interaction term or quadratic term are highly correlated with at least one of their component or the term in level. Then, their variance may sometimes differ only due to a few observations with high leverage [outliers].

This correlation can be decreased when computing the quadratic term on demeaned observations (x-mean(x)).2 and if the level is also demeaned.

A problem related to near-multicollinearity and outliers

Sometimes, quadratic and interaction terms captures outliers

instead of the intended smooth quadratic or interaction pattern a over a sufficiently large set of observations.

This is revealed by visualizing a pattern within residuals, NOT by the usual summary statistics of regressions.

Outliers – Graphs for detecting patterns in residuals (heteroskedasticity). Anscombe quartet, all summary statistics

identical including t-stats.

Property Value

Mean of x in each case 9 (exact)

Variance of x in each case 11 (exact)

Mean of y in each case

7.50 (to 2 decimal places)

Variance of y in each case

4.122 or 4.127 (to 3 decimal places)

Correlation between x and y in each case

0.816 (to 3 decimal places)

Linear regression line in each case

y = 3.00 + 0.500x (to 2 and 3 decimal places, respectively)

A quadratic model may be fitted instead of model with dummy for outliers

A quadratic model may fit case 3 (line 2 column 1), whereas a model with a dummy for the outlier is the best fit.One tries model for case 2 (line 1 column 2) for the model for case 3.

Two conflicting specifications:Interaction term versus dummy for outlier

Growth GDP/head= Beta0+Beta1 * Policy+Beta2 * Aid/GDP+Beta3 * (Aid/GDP * Policy) +Beta4 *(Aid/GDP)2 * Policy+control variables

Growth GDP/head= Beta0+Beta1 * Policy+Beta2 * Aid/GDP+Beta3 * (Aid/GDP * Policy) +Beta5 *Dummy for Gambia86-89+control variables

Regression with a highly correlated pair of regressors

Keeping Aid/GDP * Policy in the regression:When including (Aid/GDP)2 * Policy in the regression

The parameter of Aid/GDP*Policy is multiplied by 15.5=0.202/0.013.

THIS IS AN INSANE INFLATION OF THE PARAMETER DUE TO NEAR-MULTICOLINEARITY.

Regression includes an outlier driven highly correlated pair of regressors

When the observation of Gambia86-89 is omitted, the parameter of aid/gdp*policy falls from 0.202 to 0.159: its DFBETA is now positive (+3) when including the variable (Aid/GDP)2 * Policy in a regression

Whereas its DFBETA=-6 in a regression excluding the variable (Aid/GDP)2 * Policy .

N=275, β=0.013, excluding (Aid/GDP)2 *PolicyGMB6 lowers the estimated parameter of Aid*Policy

GMB6

GMB7

NIC7 ECU2

JAM3PHL5GAB2EGY3 GMB5SYR3BRA7KOR6SLV4URY5CHL6CHL2CHL7GHA3CHL4TZA5TTO4CHL3GAB3CMR7SEN5SYR4KOR5JAM4EGY7PHL7THA6TUR7MDG7SYR6GAB5TZA6CIV4URY2CRI4MDG3TGO4NER4PER5NIC4DOM7IDN6PER6IDN5TTO3MAR5COL6GTM2PAK3GUY6KEN7VEN7COL7SLE3ARG4LKA2IND2IND4CMR4KEN6LKA4THA7NIC2MDG2HTI2CMR3CMR5ZMB6GMB3MEX5HTI6BRA4PHL2MWI5IDN4KOR7LKA5IND3ETH6PAK2ZAR4LKA7NGA3 HND7COL3ETH5ZWE7HTI5VEN4HTI3ECU6SOM3DZA2IND7KEN3TTO5EGY6SLV5MAR2GTM3ZAR3IDN2KOR3CRI3URY7PRY5IDN7GUY2PER3HND2MEX2HND3MEX3SEN3DOM5SLV2TUN7HND6DOM3MYS4SYR2HND4SLE5GAB7PRY2ZWE5SLE7IND5THA5ZAR2DZA3SLE2SLV6PER2KEN5SLE6IDN3GHA5MDG6GMB2GUY4BOL3MAR4ZAR6LKA3JAM5DOM4KOR2GHA2ZWE6TGO3CRI5 TGO6ARG2SLV3ZMB2ZAR5HND5LKA6KEN4MYS7KOR4 BOL6PHL6MYS5PRY6CRI2PRY3COL2TUN6THA4BRA3 GHA7NGA2PER7GHA4COL5 MWI7GHA6PHL3NIC5ECU5CRI7VEN6GTM4DOM6KEN2ZMB3VEN3NIC3 TGO5TTO2MYS2GAB6MWI4GTM6URY3TUN5 BOL7NGA5MYS6COL4TTO6SLE4SEN2GTM5ZMB4GUY3HTI4SEN4BOL4BRA2ECU7CMR6THA2MYS3VEN2ARG7PER4VEN5GUY5 IND6MAR6MEX4 CRI6PAK6DOM2MAR3URY4GTM7THA3PAK5PRY4SOM4NGA4PHL4ZMB5PAK7ARG6PAK4GMB4MWI6NER3NGA6ARG5URY6BRA5EGY4PRY7 SLV7MAR7ECU4MEX7SYR7ECU3ZMB7MEX6BOL2EGY5ARG3 MLI6GAB4 BWA6NGA7 BWA5CHL5BOL5

NIC6 GUY7BWA4BRA6

-.6

-.4

-.2

0.2

Dfb

eta

ed

apo

licy

-5 0 5 10Standardized values of (edapolicy)

N=275, β=0.202 including (Aid/GDP)2 *Policy GMB6 increases the estimated parameter of

Aid/GDP*Policy

ECU2 GMB7NGA2GUY7BOL6

CMR7KOR6PHL5CHL6CHL7JAM3CHL4NGA3EGY7KOR5NIC4BRA7COL7 HND7SEN4COL6TUR7CHL2 CRI6NIC7 ARG7HTI6PHL7CHL3VEN7KEN7NGA6 NER3SLV6SYR6CRI5GUY6TTO6TTO5JAM4IDN5URY5NGA5CMR5GAB3KOR7IDN6SEN2IDN7IDN4PRY4TTO4DOM2BRA2ZAR5GTM2PAK3NGA7PER6ZWE5TZA5THA6MAR2DOM6URY2MDG7GMB2TGO5GMB5ARG4PHL2IDN2CRI4SLE4TTO3LKA2ZWE6DZA2IND2MAR7PER5JAM5THA7GUY2URY7MWI5TGO4MEX5COL4PAK2TUN6ZMB6HTI5MYS5KOR3MYS6GTM3EGY6 GHA7GAB5SLV3IND5SLE6 TGO6IND4GHA2COL5IND3MYS2PRY3GHA4MEX2MYS3HND5 BOL7ECU6 MWI7BRA4IND7NIC3TGO3COL2MYS4SYR2MEX4ZWE7PER3DZA3HTI3ZAR2BRA3CRI7MAR4 GHA6HND3BOL4HND4DOM4TZA6BOL3DOM7SLE7GTM4TUN7THA5TTO2CRI3GMB4PRY2SLE2SEN3KEN5GUY4HND6MEX3IDN3KEN3PER2ARG2HND2ZMB2LKA3DOM3DOM5ZAR6THA4MDG6PHL3CIV4PER7SEN5CRI2KOR2KEN4MAR5GAB6PRY6NIC2PHL6URY4COL3SLV2GTM6HTI4KEN2NIC5MWI4ZMB3LKA4LKA6ZMB4SLV4BOL5 URY3TUN5VEN4SLE5ECU5SOM3THA2KEN6MYS7PER4GHA5GAB7PAK5VEN3KOR4MWI6MDG2CMR3PRY5IND6ZAR4ETH6GMB3MAR6PAK6SLV5EGY3HTI2GAB2ECU7NER4VEN2GTM7PAK7VEN6SLE3GUY3ZMB5ZMB7PHL4LKA5CMR6ARG6THA3MDG3MAR3SOM4PAK4ARG5SYR7LKA7BRA5GTM5CMR4URY6GHA3ZAR3BOL2VEN5PRY7ETH5ECU4EGY4ECU3GUY5 MEX7GAB4ARG3EGY5MEX6SYR4

MLI6NIC6 SLV7NGA4SYR3

CHL5BRA6

BWA6

BWA5

BWA4 GMB6

-.2

-.1

0.1

.2.3

Dfb

eta

ed

apo

licy

-5 0 5 10Standardized values of (edapolicy)

N=274, β=0.159, excluding obs. GMB6 including variable (Aid/GDP)2 *Policy:

dfbeta(edapolicy) of GMB7 changes sign

CRI5

GAB2SLE2KEN5KEN4

GAB4

TZA5MAR6GAB6MAR5KEN2GHA5HTI3GTM6MWI4HND4MDG3ZWE7CMR6HTI4IDN3SOM4TGO4BOL4ZAR5TUN6LKA5

SYR3

HND5CMR5ZAR2KEN3PHL6HTI5MDG2ZAR4ZMB2HND3PRY6

ECU2

ECU7

PHL7

ZAR6SYR2MWI5ZWE6MAR2GAB5GTM7

ZWE5IDN7

ETH5DOM5KEN6GHA2THA6IDN4

KOR2

CMR4

GUY2PRY2THA5

NIC4

ECU3

IDN6THA4

GMB2IDN5LKA3THA2

TUR7

IDN2ZMB3BOL3HND2DZA2MYS2CMR3

SYR4

PRY3GAB7

DZA3PRY7

THA7ZMB4SLV5PRY5

DOM2SEN5MYS6

ZAR3SLV4TUN5EGY6KOR3LKA6

EGY4BOL2ZMB5

ECU4SYR7

PAK2THA3

DOM6MYS5SYR6

EGY7

GMB3PAK4DOM4PRY4

HTI2PAK5

CHL7

MYS7PAK3

MDG6MYS3CRI2LKA2URY7JAM5TUN7MAR4SLE4

NGA2

SLV2PAK6DOM7

EGY5

CHL4

SLE7SLE3PHL2NIC3ECU5GTM5MYS4CIV4DOM3

GAB3

CHL5

KOR4GTM2GTM3IND3NIC2SLV3GUY3IND2COL2

PHL5

PAK7CRI4PHL3CRI3

LKA7GTM4MAR3ECU6PER2PHL4

HND6

KOR5

PER7IND4

COL7

PER3LKA4KOR7IND5GHA3PER4

CHL6

COL3

NGA3COL6

CRI7CHL3

KOR6

IND7IND6GHA4TTO2

NGA4

SEN3TTO3TTO4COL4URY6URY2BRA2

TZA6TTO6URY4COL5MDG7

JAM3

VEN2

URY5NGA6TTO5URY3NGA7NGA5

VEN5BRA3MEX2VEN3VEN4MEX4

MEX7VEN6

JAM4ARG2MEX3BRA4

MEX6

ARG7MEX5ARG4BRA5

ARG3

ARG6

BRA6

BRA7VEN7PER5CHL2

ARG5

MAR7

SLE5

CMR7

HTI6SLE6

MWI6EGY3SOM3PER6SEN2

KEN7GUY6

ETH6GMB4NER4

SEN4

TGO3ZMB7GUY4

GMB5ZMB6NIC5

CRI6NER3SLV6TGO6TGO5

MWI7

BOL6

SLV7

HND7

GHA7

GUY5

BOL5BOL7GHA6MLI6

BWA4BWA5

BWA6

NIC6

GUY7

NIC7

GMB7

-.4

-.2

0.2

.4

Dfb

eta

ed

apo

licy

-5 0 5 10Standardized values of (edapolicy)

-40

-20

020

40ed

apo

licy

-7.564619-.0583638-.0096292.0091213.0109737.0146439.0381823.0669819.1242624.1262204.1545346.179565.2074886.2508489.3692497.412823.4941833.5683056.5948087.6384138.7247269.7387802.775421.7759466.776252.787003.89940361.0856391.1564761.2244481.2524241.3279761.4156451.5388751.5837811.6475681.7812841.8825962.0814652.1925182.3647112.431222.5345592.85823.0666253.1079283.279863.3817613.4894083.6536793.7310283.8731874.94910814.4406714.8756118.62207

Boxplots (per country) of aid*policy and Aid2*Policy ordered by

aid*policy(i.): the same few countries depart from « small » values: high

correlation 0.92

-200

020

040

060

0ed

a2p

olic

y

-51.18398-2.79541-.0002516.000174.0004187.0008187.0043965.0145151.0209916.0258429.0322472.0337574.0616103.1186159.1926836.2457322.2581988.3121285.3177678.3845654.3896744.397981.4410459.5594041.5744781.5931172.6132871.78449431.3197951.4484061.755161.9522572.7751342.7838692.9021643.2499533.3897483.951664.4271595.2107387.0500618.3241839.2244719.88985410.9641512.0066112.1251512.6576313.983821.7781125.2001826.9940654.1966994.54123113.7891149.2819

Analysis of variance of an interaction term

(Aid/GDP)2 * Policy [variance: 100%=]

= beta0 + beta1* (Aid/GDP)*Policy [R2=84.6%]

+ beta2 * (dummyGambia86-89) [+∆R2=4.9%]

+ residuals [excluding Gambia86-89] [+10.5%]

Analysis of variance: residuals are orthogonal to the regressors subspace.Var(y)=Var(prediction)+Var(residuals)

Analysis of variance of interaction term: variance of (Aid/GDP)2 * Policy

= 84.6% [=R2 of the auxiliary regression] the variance of (Aid/GDP) * Policy, explanatory variable included in regression+ 15.4% « specific » variance [of the residuals of the auxiliary regression] divided into:= 4.9% [R2=0.32% regression on dummy gambia] variance of the outlier observation Gambia86-89 (largest residual of the auxiliary regression)+ 10.1% variance for the other observations.

An explanation using the analysis of variance of interaction terms

Variance Interaction term xz =Variance of beta1.x+beta2.z(the information already brought in by the levels which may be highly correlated with xz) from a simple regression+ variance of residuals=the original contribution to the variance of the interaction terms: variances separated again between (1) the variance of a few large residuals (dummy for these outliers) and (2) the remaining residuals;

DZA2DZA3ARG2ARG3ARG4ARG5ARG6ARG7BOL2BOL3BOL4BOL5BOL6BOL7

BWA4BWA5BWA6

BRA2BRA3BRA4BRA5BRA6BRA7CMR3CMR4CMR5CMR6CMR7CHL2CHL3CHL4CHL5CHL6CHL7COL2COL3COL4COL5COL6COL7CRI2CRI3CRI4CRI5CRI6CRI7CIV4DOM2DOM3DOM4DOM5DOM6DOM7ECU2ECU3ECU4ECU5ECU6ECU7EGY3EGY4EGY5EGY6EGY7SLV2SLV3SLV4SLV5SLV6SLV7ETH5ETH6GAB2GAB3GAB4GAB5GAB6GAB7GMB2GMB3GMB4GMB5

GMB6

GMB7

GHA2GHA3GHA4GHA5GHA6GHA7

GTM2GTM3GTM4GTM5GTM6GTM7GUY2GUY3GUY4GUY5GUY6

GUY7

HTI2HTI3HTI4HTI5HTI6HND2HND3HND4HND5HND6HND7

IND2IND3IND4IND5IND6IND7IDN2IDN3IDN4IDN5IDN6IDN7JAM3JAM4JAM5KEN2KEN3KEN4KEN5KEN6KEN7KOR2KOR3KOR4KOR5KOR6KOR7MDG2MDG3MDG6MDG7MWI4MWI5MWI6MWI7

MYS2MYS3MYS4MYS5MYS6MYS7

MLI6

MEX2MEX3MEX4MEX5MEX6MEX7MAR2MAR3MAR4MAR5MAR6MAR7NIC2NIC3NIC4NIC5

NIC6

NIC7

NER3NER4NGA2NGA3NGA4NGA5NGA6NGA7PAK2PAK3PAK4PAK5PAK6PAK7PRY2PRY3PRY4PRY5PRY6PRY7PER2PER3PER4PER5PER6PER7PHL2PHL3PHL4PHL5PHL6PHL7SEN2SEN3SEN4SEN5SLE2SLE3SLE4SLE5SLE6SLE7SOM3SOM4LKA2LKA3LKA4LKA5LKA6LKA7SYR2SYR3SYR4SYR6SYR7TZA5TZA6THA2THA3THA4THA5THA6THA7TGO3TGO4

TGO5TGO6TTO2TTO3TTO4TTO5TTO6TUN5TUN6TUN7TUR7URY2URY3URY4URY5URY6URY7VEN2VEN3VEN4VEN5VEN6VEN7ZAR2ZAR3ZAR4ZAR5ZAR6ZMB2ZMB3ZMB4ZMB5ZMB6ZMB7ZWE5ZWE6ZWE7

-200

020

040

060

0

(Aid

/GD

P)2

*Polic

y

-40 -20 0 20 40

(Aid/GDP)*Policy

Actual Data

Linear fit

(Aid/GDP)2*Policy versus Aid/GDP*Policy

Residuals = Contribution of (Aid/GDP)2 * Policyorthogonal to (Aid/GDP)*Policy

Roodman graph: analysis of variance with residuals

Residuals are:E= X1 - a X1*X2 + bClose to dummies for Jordan Egypt and Syria(Highly correlated variables except Jordan, Egypt, Syria).It reveals another interpretation: three neighbours of Israël receiving strategic US Aid, instead of « non-tropical area ».

DZA2DZA3ARG2ARG3ARG4ARG5ARG6ARG7

BOL2BOL3BOL4

BOL5

BOL6BOL7BWA4

BWA5BWA6

BRA2BRA3BRA4BRA5BRA6BRA7CMR3CMR4CMR5CMR6CMR7

CHL2CHL3CHL4CHL5CHL6CHL7COL2COL3COL4COL5COL6COL7CRI2CRI3CRI4CRI5

CRI6CRI7

CIV4DOM2DOM3DOM4DOM5DOM6DOM7ECU2ECU3ECU4ECU5ECU6ECU7EGY3EGY4EGY5EGY6EGY7SLV2SLV3SLV4SLV5SLV6

SLV7

ETH5ETH6GAB2GAB3GAB4GAB5GAB6GAB7GMB2GMB3GMB4GMB5

GMB6

GMB7

GHA2GHA3GHA4GHA5

GHA6GHA7

GTM2GTM3GTM4GTM5GTM6GTM7GUY2GUY3GUY4

GUY5

GUY6

GUY7

HTI2HTI3HTI4HTI5HTI6HND2HND3HND4HND5HND6

HND7

IND2IND3IND4IND5IND6IND7

IDN2IDN3IDN4IDN5IDN6IDN7JAM3JAM4JAM5KEN2KEN3KEN4KEN5KEN6KEN7KOR2KOR3KOR4KOR5KOR6KOR7MDG2MDG3MDG6MDG7MWI4MWI5MWI6MWI7MYS2MYS3MYS4MYS5MYS6MYS7MLI6MEX2MEX3MEX4MEX5MEX6MEX7MAR2MAR3MAR4MAR5MAR6MAR7

NIC2NIC3NIC4

NIC5

NIC6

NIC7

NER3NER4NGA2NGA3NGA4NGA5NGA6NGA7PAK2PAK3PAK4PAK5PAK6PAK7PRY2PRY3PRY4PRY5PRY6PRY7

PER2PER3PER4PER5PER6PER7PHL2PHL3PHL4PHL5PHL6PHL7SEN2SEN3SEN4SEN5SLE2SLE3SLE4SLE5SLE6SLE7SOM3SOM4LKA2LKA3LKA4LKA5LKA6

LKA7SYR2SYR3SYR4SYR6SYR7TZA5TZA6THA2THA3THA4THA5THA6THA7TGO3TGO4TGO5TGO6TTO2TTO3TTO4TTO5TTO6TUN5TUN6TUN7TUR7URY2URY3URY4URY5URY6URY7VEN2VEN3VEN4VEN5VEN6VEN7ZAR2ZAR3ZAR4ZAR5ZAR6ZMB2ZMB3ZMB4ZMB5ZMB6ZMB7ZWE5ZWE6ZWE7

-100

010

020

0(A

id/G

DP

)2*P

olic

y-b

eta*

Aid

/GD

P*P

olic

y

0 .2 .4 .6 .8 1

Gambia6

Actual Data

Linear fit

(Aid/GDP)2*Policy-beta*Aid/GDP*Policy versus Gambia6

Residuals=a+b.dummy(Gambia6)+ε R2=r2=32.5% r=0.57

Finding outliers driving (or not) the statistical significance of interaction terms

The largest residuals of a regression of the interaction term on its level components allows to identify potential outliers driving the statistical significance of the interaction term.If one runs again the first regression with xz as explanatory variable excluding « the observations of largest residuals of the above auxiliary regression » and if there is still « statistical significance » of the interaction term: the interaction term is robust to outliers and should be kept in the final regression.

32.5% (one third) of the specific variance of the regressor:(Aid/GDP)2*Policy is the dummy (Gambia 6).

The dummy equal to one for the observation Gambia6 and else equal to zero may be a good substitute to the regressor (Aid/GDP)2*Policy.

Two conflicting specifications:Interaction term versus dummy for outlier

Growth GDP/head= Beta0+Beta1 * Policy+Beta2 * Aid/GDP+Beta3 * (Aid/GDP * Policy) +Beta4 *(Aid/GDP)2 * Policy+control variables

Growth GDP/head= Beta0+Beta1 * Policy+Beta2 * Aid/GDP+Beta3 * (Aid/GDP * Policy) +Beta5 *Dummy for Gambia86-89+control variables

BD1: Gambia86 (1 observation)

Gambia.86-89 (GMB6) dummy explains 33% of the variance of the regressor orthogonal to Aid/GDP.Policy (correlation coefficient close to 0.6):

(Aid/GDP)2.Policy –beta. Aid/GDP.Policy

Corr( aid/GDP*policy; (aid/GDP)2*policy ) = 0.92Corr(growth,x) BD1 (275 obs) CR1 (274 obs)

Less GambiaBD2 (270 obs) CR2 (267 obs)

Less Bostwana

Aid/GDP-0.173 (N=275)-0.224 (N=267)

0.049 (0.12)PIF=-0.2

0.054 (0.13)PIF=-0.2

-0.021 (0.16)PIF=0.1

0.026 (0.16)PIF=-0.1

Aid/GDP*Policy0.128 (N=275)0.037 (N=267)

0.20* (0.09)PIF = 2.1

0.16 (0.11)PIF = 1.2

0.186* (0.07)PIF=1

0.05 (0.1)PIF=0.8

(Aid/GDP)2*Policy0.058 (N=275)-0.014 (N=267)

-0.019* (0.008)PIF = -4.2

-0.013 (0.013)PIF = -1.2

- -

Policy0.452 (N=275)0.420 (N=267)

0.78 (0.20)PIF=0.6

0.81 (0.20)PIF=0.6

0.71 (0.19)PIF=0.5

0.80 (0.19)PIF=0.6

Addition fragility of the results: A minimal contribution to R2 of

(Aid/GDP)2 * Policy although its estimated parameter is « White » statistically significant

R2 (including) – R2 (excluding (Aid/GDP)2 * Policy)0.3981 – 0.3918 = 0.0063

In sample power: 30% < 80% (PROC POWER, SAS)

But statistical significance p-value < 5% (with White standard errors). White robust Standard error not adequate with one large outlier.

Pifometrics: Parameter Inflation Factor > 2besides Variance Inflation Factor

232

323212

1332

232

321312

1212

2

112

2

112

12

1212

1

1;1

1

1

2

rVIFVIF

r

rr

r

rrr

rPIF

rr

PIF

S

S

Another INFLUENCE statistics: Studentized residuals over 1.96

in absolute value (not used by Burnside and Dollar)

96

What to do with outliers? Robust estimates decreasing their weights

97

Over fitting, large R2, too many estimated parameters in order to capture outliers, out of

(learning) sample large predictions errors

Burnside and Dollar Conclusion

1. Aid has had a little impact on growth globally.2. Aid had a more positive impact on growth in good

policy environment.3. No significant tendency for total aid or bilateral

trade to favor good policy.4. Aid managed multilaterally (one third of the total)

is allocated in favor of good policy.5. Bilateral aid is stronly positively correlated with

government consumption: it is not « efficient » aid.

Our conclusion is different with respect to their conclusion 2

1. Botswana had a high growth rate of GDP/head for 3 periods of four years (cf. data set). It received a lot of aid/gdp. It had a top level « policy index » as defined in the paper.

2. For the other countries of the sample, there is no statistical evidence of that aid has an effect on growth of GDP/head conditional to good policies (as defined in the paper).

3. Do a monograph on the history of Botswana economic policy and its use of received aid to get insights for policies in other developing countries.