Applied Econometrics - Lecture 5 - Nathaniel Higgins · Wrapup of basic IV Applied Econometrics...

ReviewOther IV papers

B & C (1994), A & K (1991)Homework ReviewWrapup of basic IV

Applied EconometricsLecture 5

Nathaniel Higgins

ERS and JHU

4 October 2010

Nathaniel Higgins Notes on Butcher and Case (1994) and Angrist and Krueger (1991)



Outline

Some key questions that came up from HWWhere we left off last time (Levitt 1997)Review other IV papers

WalmartTrade & EnvironmentVietnam draftOthers?

Review IV papers you readButcher and Case (1994)Angrist and Krueger (1991)

Next topic — which is . . .

panel data (part I)




Outline

Some key questions that came up from HWWhere we left off last time (Levitt 1997)Review other IV papers

WalmartTrade & EnvironmentVietnam draftOthers?

Review IV papers you readButcher and Case (1994)Angrist and Krueger (1991)

Next topic — which is . . . panel data (part I)




Key questions from homework

What the heck is going on in question # 5?

Write down the structural equations:

y = β0 + β1x1 + β2x2 + ε

x2 = α0 + α1 + α2z1 + η

Substitute the first stage into the second stage to get thereduced form relationships:

y =β0 + β1x1 + β2(α0 + α1 + α2z1 + η) + ε

y =(β0 + β2α0) + (β1 + β2α1)x1 + (β2α2)z2 + (β2η + ε)





What the heck is going on in question # 5?Write down the structural equations:

y = β0 + β1x1 + β2x2 + ε

x2 = α0 + α1 + α2z1 + η

Substitute the first stage into the second stage to get thereduced form relationships:

y =β0 + β1x1 + β2(α0 + α1 + α2z1 + η) + ε

y =(β0 + β2α0) + (β1 + β2α1)x1 + (β2α2)z2 + (β2η + ε)





Rewrite the second stage in terms of coefficients we would getif we regressed the dependent variable on the independentvariables:

y =(β0 + β2α0) + (β1 + β2α1)x1 + (β2α2)z2 + (β2η + ε)

y =π0 + π1x1 + π2z1 + u

where:

π0 = β0 + β2α0

π1 = β1 + β2α1

π2 = β2α2

u = β2η + ε





So now we have the reduced form regression:

y =π0 + π1x1 + π2z1 + u

and the first stage regression:

x2 =α0 + α1 + α2z1 + η

If we run both of these regressions, we obtain estimates of allthe coefficients:

π̂0, π̂1, π̂2, α̂0, α̂1, α̂2





Question #5 asked you to examine the ratio π̂2α̂2

:

π̂2

α̂2=β̂2α̂2

α̂2

= β̂2

The procedure simply gives us another way to obtain β̂IV2 in the

simple case when we have one endogenous variable and oneinstrument. Using this procedure to obtain the IV estimate formore than one endogenous regressor is not feasible.






:

π̂2

α̂2=β̂2α̂2

α̂2

= β̂2


simple case when we have one endogenous variable and oneinstrument.

Using this procedure to obtain the IV estimate formore than one endogenous regressor is not feasible.






:

π̂2

α̂2=β̂2α̂2

α̂2

= β̂2


simple case when we have one endogenous variable and oneinstrument. Using this procedure to obtain the IV estimate formore than one endogenous regressor is not feasible.





Why do we get the incorrect standard error if we run the firststage regression, then substitute the “clean” endogenousregressor into the second stage equation?

Intuition: because the “clean” endogenous regressor in thesecond stage is really a combination of estimates. When welearned how to calculate the standard errors of our regressionestimates (based on the var-cov matrix), we learned how thestandard errors of our estimates were based on the sum ofsquared errors and the diagonal values of (x ′x)−1x ′y . Usingthat same technique to calculate the standard errors from thesecond stage regression does not reflect the fact that there arevariables in the first stage regression that influence thestandard error of the IV estimate.





Why do we get the incorrect standard error if we run the firststage regression, then substitute the “clean” endogenousregressor into the second stage equation?Intuition: because the “clean” endogenous regressor in thesecond stage is really a combination of estimates. When welearned how to calculate the standard errors of our regressionestimates (based on the var-cov matrix), we learned how thestandard errors of our estimates were based on the sum ofsquared errors and the diagonal values of (x ′x)−1x ′y . Usingthat same technique to calculate the standard errors from thesecond stage regression does not reflect the fact that there arevariables in the first stage regression that influence thestandard error of the IV estimate.




Basker 2005

are estimated to have been created in the year beforeWal-Mart entry. Though this increase is small in absolutemagnitude, it is statistically significant and disconcertinglylarge relative to the estimated postentry effect.16

The IV results are shown in figure 4. The effect of entryis estimated much more cleanly at approximately 100 jobs.In the years immediately following entry, there is a loss of40–60 jobs. The net effect at the 5-year horizon, however, ispositive and significant (p-value 0.0003).

Recall that the typical Wal-Mart store employs 150–350workers. These results suggest that employment increasesby less than the full amount of Wal-Mart’s hiring, evenbefore allowing other firms time to fully adjust to Wal-Mart’s entry. Part of this discrepancy can be explained bybuyouts of existing chain stores by Wal-Mart Corporation,and prompt exit and cutbacks by other retailers. Another(albeit unlikely) possibility is that Wal-Mart replaces exist-ing part-time jobs with full-time jobs. CBP employmentfigures do not control for hours worked, so full-time andpart-time employees are weighted equally.

Very little is known about employment conditions atWal-Mart, including the prevalence of part-time work. Areasonable prior is that Wal-Mart employees work fewerhours than other retail workers [using French data, Bertrandand Kramarz (2002) find that entry of large retailers isincreases part-time employment relative to all retail em-ployment]. Wal-Mart claims that 70% of its employeeswork 28 hours a week or more (Wal-Mart, 2001a). Thisfigure is within the norm for workers in the discount retailindustry (Peled, 2001), and also in keeping with the rest ofthe retail industry: the 30th percentile of hours worked byretail employees, computed from the March Current Popu-lation Survey (CPS) for 1978–1999, is 28 hours acrossemployer size, state, and year.

As noted in section IV C, if the timing of entry wereendogenous, we would expect to see an increase in thecounty’s retail employment prior to entry. No such effect is

evident in the leading coefficients, although, as footnote 14makes clear, this is not conclusive evidence in support of theidentifying assumption.

B. Retail Establishments

To capture the effect of Wal-Mart on the number of retailestablishments, I estimate IV regressions replacing the left-side variable retailjt /popjt by estabjt /popjt, where estabjt isthe number of retail establishments in county j at year t ineach of three size categories.

To confirm that Wal-Mart’s creation can be detected inthe data, I estimate the regressions using the number of largeretail establishments (with 100 or more employees). IVresults are shown in figure 5; the estimated coefficientsmirror those on retail employment shown in figure 4. Theincrease in the number of large retail establishments, ap-proximately 0.7, suggests that Wal-Mart’s entry often coin-cides with exit or contraction of other large retailers. Insome cases, Wal-Mart acquired a large number of storesfrom a competitor; in other cases, incumbent establishments

16 Reduced-form estimates using WMplanjt are extremely similar.

FIGURE 4.—EVOLUTION OF RETAIL EMPLOYMENT (IV)

FIGURE 5.—EVOLUTION OF NUMBER OF LARGE

RETAIL ESTABLISHMENTS (IV)

FIGURE 3.—EVOLUTION OF RETAIL EMPLOYMENT (OLS)

JOB CREATION OR DESTRUCTION? LABOR MARKET EFFECTS OF WAL-MART EXPANSION 179




Frankel and Rose 2005of trade and income is the main new contribution of thispaper.

II. Methodology

We turn directly to the empirics.

A. Equation to Be Estimated

We estimate the following cross-country equation:

EnvDami � �0 � �1 ln�y/pop�90,i � �2�ln�y/pop�90,i�2

� ��X � M�/Y�90,i � �3�Polity�90,i

� �4 ln�LandArea/pop�90,i � ei,

where:

● EnvDami is one of three measures of environmentaldamage for country i,

● {�i} is a set of control coefficients,● ln( y/pop)90,i is the natural logarithm of 1990 real

GDP per capita for country i,● [X � M]/Y represents the ratio of nominal exports and

imports to GDP (“openness”),● Polity is a measure of how democratic (versus auto-

cratic) is the structure of the government,● LandArea/pop is a measure of per capita land area,

and● e is a residual representing other causes of environ-

mental damage.

The coefficient of interest to us is �, the partial effect ofopenness on environmental degradation.

Income plays a strong role in determining environmentaloutcomes. We incorporate into our analysis—without rely-ing on—the environmental Kuznets curve (EKC). This is arough U-shaped relationship between income per capita andcertain types of pollution, brought to public attention by theWorld Bank (1992) and Grossman and Krueger (1993,1995). Growth increases air and water pollution at the initialstages of industrialization, but later on can reduce pollutiongiven the right institutions, as countries become rich enoughto pay to clean up their environments. The EKC hypothesispredicts that the coefficient on the squared income term isnegative, so that the pollution curve eventually turnsdown.10

The market does not address externalities left to itself.Higher income is unlikely to result in an improved environ-mental regulation absent appropriate political institutions.

Thus it is important to control also for the latter, which wedo by including polity in our equation.11

B. Addressing Endogeneity

The endogeneity of trade is a familiar problem from theempirical literature on openness and growth.12 What isneeded is a good instrumental variable, which is exogenousyet highly correlated with trade. The gravity model ofbilateral trade offers a solution. It states that trade betweena pair of countries is determined, positively, by country size(GDP, population, and land area) and, negatively, by dis-tance between the countries in question (physical distanceas well as cultural distance in the form of, e.g., differentlanguages). Geographical variables are plausibly exoge-nous. Yet when aggregated across all bilateral trading part-ners, these variables are highly correlated with a country’soverall trade, and thus make good instrumental variables, asfirst noted by Frankel and Romer (1999). Thus we constructan instrumental variable for openness by aggregating upacross a country’s partners the prediction of a gravityequation that explains trade with distance, population, lan-guage, land border, land area, and landlocked status.

We use a cross-country approach, thus choosing not tofollow Grossman and Krueger (1993) and Antweiler et al.(2001) in using panel data. We realize that a pure cross-section approach means that we cannot control for unob-servable heterogeneity. But our key instrument is driven bycross-country geographical variation, which does notchange over time, so there seems little advantage for us ina panel study.

Income per capita too is endogenous. Both trade andenvironmental regulation may affect income.13 We thus usea second set of instrumental variables for income, takenfrom the growth literature. These include lagged income(thus we incorporate the conditional convergence hypothe-sis), population size, and rates of investment and humancapital formation (the factor accumulation variables familiarfrom neoclassical growth equations).

C. Data

We focus on results for three 1990 measures of airpollution, all measured as concentrations in micrograms percubic meter (simply averaged across a country’s measuringstations and cities, in cases where more than one observa-tion was available):

10 A number of studies have confirmed the EKC, especially for SO2 andparticulate matter, but the results are not always favorable; for example,Bradford, Schlieckert, and Shore (2000) get mixed answers. Many moreEKC references are available there, in Frankel (2003), and in the workingpaper version of the present study.

11 Notice in figure 1 that the low-democracy countries tend to havehigher SO2 pollution. Barrett and Graddy (2000) also find that an increasein civil and political freedoms significantly reduces some measures ofpollution.

12 Rodrik (1995) and Rodriguez and Rodrik (2001) are among thosecritical of previous studies on the grounds of simultaneity.

13 The usual presumption is that environmental regulation, by raisingbusiness costs, slows economic growth. But we should also consider thePorter hypothesis, in which a tightening of environmental regulation issaid to stimulate technological innovation and thereby raise productivity,(e.g., Porter and van der Linde, 1995).

IS TRADE GOOD OR BAD FOR THE ENVIRONMENT? 87




Frankel and Rose 2005

● SO2: mean sulfur dioxide,● NO2: mean nitrogen dioxide, and● PM: mean total suspended particulate matter.

We have also looked at four other measures of environmen-tal quality:

● CO2: industrial carbon dioxide emissions per capita, inmetric tons,

● deforestation: average annual percentage change,1990–1995,

● energy depletion: “genuine savings” as a percentage ofGDP,14, and

● rural clean water access: as percentage of rural popu-lation, 1990–1996.

Of these seven, the three measures of local air pollution—SO2, NO2, and particulates—are the most relevant. CO2 is apurely global externality, and unlikely to be addressed byregulation at the national level. Deforestation and energydepletion are not measures of pollution, and measuring theminvolves some serious problems of composition and datareliability, as does water access. Still, it seems worthwhile tolook as well at these broader measures of environmentalquality.

Per capita income is defined as 1990 GDP per capita(measured in real PPP-adjusted dollars), taken from thePenn World Table 5.6. The Penn World Table also suppliesour measure of openness. Polity ranges from �10 (stronglyautocratic) to �10 (strongly democratic), and is taken fromthe Polity IV project. Land area is taken from the CIA’s Website and is intended to allow for the likelihood that higher

population density leads to environmental degradation (for agiven level of per capita income). Descriptive statistics areincluded in appendix table A1 of this article, and simplescatterplots are portrayed in appendix figure A1.

III. Results

Table 1 reports our key estimation results, where thedependent variable is represented in turn by the threemeasures of air pollution. The three columns at the left ofthe table are the OLS estimates; the IV estimates are on theright.

The estimated effect of the polity variable on pollution isalways negative, suggesting that improved governance has abeneficial effect. It is generally significant statistically. Thesame is true of land area per capita, evidence that populationdensity has an adverse effect on concentration of pollutants.

Of greater interest is the relationship with per capitaincome. The estimated coefficient on the quadratic term isnegative for all three measures of air pollution, confirmingthe EKC hypothesis: after a certain point (recorded at thebottom of the table as “income peak”), growth reduces theseenvironmental indicators. Statistically, it is highly signifi-cant in the case of SO2 and NO2, and moderately so in thecase of PM.

Our central interest is �, the coefficient on openness. TheOLS estimate is negative for all three kinds of air pollu-tion—insignificantly so for PM, moderately significantly forNO2, and highly significantly for SO2. Apparently anyadverse race-to-the-bottom effect on air pollution is out-weighed by a positive gains-from-trade effect.

The main contribution of this paper is to address whetherthese apparent effects may be the spurious results of simul-taneity. The right part of the table reports instrumentalvariables estimates, where the gravity-derived prediction ofopenness is the instrument for trade, and the factor accu-mulation variables are the instruments for income. The IVresults are generally similar to the OLS results, though with

14 Energy depletion is a measure computed for the World Bank’s WorldDevelopment Indicators. It is equal to the product of unit resource rentsand the physical quantities of fossil fuel energy extracted (including coal,crude oil, and natural gas). Table 3.15, available at http://www.worldbank.org/data/wdi2001/pdfs/tab3_15.pdf, explains the data compu-tations.

TABLE 1.—DETERMINANTS OF AIR POLLUTION CONCENTRATIONS

Determinant

OLS IV

NO2 SO2 PM NO2 SO2 PM

Trade/GDP �0.29 �0.31 �0.37 �0.33 �0.23 �0.31(0.17) (0.08) (0.34) (0.19) (0.10) (0.41)

log(real GDP per capita) 409 287 567 461 296 681(122) (119) (336) (199) (140) (412)

[log(real GDP per capita)]2 �22.8 �16.6 �35.6 �25.6 �17.1 �42.0(6.9) (6.8) (19.1) (10.9) (7.7) (23.2)

Polity �3.20 �6.58 �6.70 �3.77 �6.41 �7.78(1.47) (2.05) (3.42) (1.37) (2.27) (4.07)

log(area per capita) �5.94 �2.92 �13.0 �6.14 �1.54 �12.6(5.93) (1.39) (6.29) (6.43) (1.96) (6.84)

Observations 36 41 38 35 40 37R2 0.16 0.68 0.62 0.18 0.67 0.63Income peak ($) 7,665 5,770 2,882 8,015 5,637 3,353

Cross-country estimation across countries in 1990. (Robust standard errors in parentheses.) Regressands are averages per cubic meter. Intercept included but not reported. Instrument for trade constructed byaggregating predicted bilateral gravity equation of trade on distance, population, area, and dummies for language, land border, and landlocked status. Instruments for income (and square) constructed from regressionof income on lagged income, population, openness, investment, population growth, and primary and secondary school enrollments.

THE REVIEW OF ECONOMICS AND STATISTICS88




Frankel and Rose 2005

somewhat diminished significance levels in some cases. TheEKC is still there for all three pollutants, and the coefficienton openness is negative for all three pollution measures. Asin the OLS results, the statistical significance is high forSO2, moderate for NO2, and lacking for particulates.

As an alternative to our quadratic functional form for theEKC, we have also tried a three-segment spline, with knotsat the 33rd and 66th percentiles of the logarithm of percapita income. The results are comparable, and are reportedin the NBER working paper.15

A. Results for Other Environmental Measures

Air pollution is only one kind of measure of environmen-tal quality. We also produced analogous estimates for othermeasures of environmental degradation. Table 2 reports ourOLS and IV estimates of � for carbon dioxide, deforesta-tion, energy depletion, and access to clean water.16

Beneficial OLS effects of openness show up only forenergy depletion and clean water access (an increase inclean water access indicates a beneficial environmentaleffect, the reverse of the other six indicators), and are ofborderline statistical significance. The case that would givean environmentalist the greatest concern is CO2. The coef-ficient on openness is positive and of moderate signifi-cance.17 This result could be viewed as one piece of evi-dence supporting the idea that the free-rider problem andfears of lost competitiveness inhibit individual countriesfrom curbing emissions of greenhouse gases on their own.CO2 is a purely global externality, so there is no reason toexpect individual countries to address it without somemechanism of international cooperation.

When instrumental variables are used, the detrimentaleffect of openness on carbon dioxide emissions loses allsignificance, while the apparently beneficial effect on en-ergy depletion becomes significant at the 10% level. On theother hand, the beneficial OLS effect on water accessdisappears. Evidently the use of instrumental variables tocorrect for simultaneity can make an important difference tosome results.

To summarize: The results are generally supportive of theenvironmental Kuznets curve, and of the positive effect ofdemocracy on environmental quality. More importantly,there is some evidence that openness reduces air pollutionand little evidence that openness causes significant environ-mental degradation, other things equal. The most importantexception is carbon dioxide.

B. Do Some Countries Have a “Comparative Advantage”in Pollution?

We also test the pollution haven hypothesis, according towhich economic integration results in some open countriesexporting pollution to others, even if there is no systematiceffect on the world environment in the aggregate.

One version of the hypothesis is that open countries thathave a particularly high demand for environmental qual-ity—rich countries—specialize in products that can be pro-duced cleanly, letting poor open countries produce and sellthe products that require pollution. This hypothesis can bereadily tested by adding the interaction of openness andincome per capita to our equation. If rich countries takeadvantage of trade by transferring the location of pollution-creating activities to poor countries, the interaction betweenopenness and income should have a negative effect onpollution. When we tried this, the coefficient on the inter-active term was insignificant for most of the seven environ-mental measures. The exceptions are particulates and SO2.With either OLS or IV estimation, openness interacted withincome has a positive effect on these two types of pollution,opposite of that predicted by the standard pollution havenhypothesis.18

A second version of the pollution haven hypothesis is thatcountries endowed with a large supply of environmentalquality (e.g., those with large land area per capita) becomepollution havens, exporting dirty goods to more denselypopulated countries. We tested this by adding the product ofopenness and land area per capita. Again, signs were di-vided between negative and positive, and the coefficientswere usually insignificant. The only two cases with signif-icant interaction coefficients (IV for particulates, and OLS

15 That is, it is estimated that increases in income in the low-incomecountries increase pollution, and in the high-income countries reduce it.The coefficient on openness is again negative for all three measures of airpollution.

16 In most cases, the effects of polity, area, and quadratic income—notreported here, to save space—go in the same direction as with the airpollution indicators. The EKC shows up highly significant for deforesta-tion, energy depletion, and rural water access.

17 Further, the coefficient on quadratic income is positive and highlysignificant, whereas in the spline version income has a positive effectthrough all three segments in this case. This confirms others’ findings ofno environmental Kuznets curve for CO2.

18 The significance level for SO2 is 5% under OLS and 10% under IV(and for PM is more marginal). This is consistent with the finding ofAntweiler et al. (2001) that trade has a significantly less favorable effecton SO2 emissions in rich countries than in poor countries. Their explana-tion is that, because rich countries have higher capital/labor ratios, thefactor-based pollution haven effect—the third hypothesis, consideredbelow—tends to outweigh the income-based pollution haven effect.

TABLE 2.—EFFECT OF OPENNESS ON OTHER TYPES OF ENVIRONMENTAL

DEGRADATION

OLS IV

CO2 .016 .000(.008) (.010)

Deforestation .002 .001(.003) (.004)

Energy depletion �.014 �.034(.009) (.020)

Rural clean water access .111 �.067(.078) (.266)

Estimation across countries in 1990. (Robust standard errors in parentheses.) Income, income squared,polity score, log area per capita, and intercept were included in the regression, but are not reported here,to save space.

IS TRADE GOOD OR BAD FOR THE ENVIRONMENT? 89




Butcher and Case 1994

Relationship of interest is between education and earnings

earni = β0 + educiβ1 + Xα+ ε

Education is an endogenous variableAbility is an omitted variableOmitted variable gets absorbed into ε and causescorrelation between education and the error term, causingendogeneity

Paper is all about the instrument




Butcher and Case 1994Preview of Results

Impact of education on the earnings of women isunderestimated in other studies.IV approach is used to show that the returns to educationfor women are higher than previously estimated.




Butcher and Case 1994Introduction

Educational attainment in math/science is higher amongmales than females (in 1994, anyway).Why?Explanations:

Self-selectionWomen do not obtain specialized education because theyplan to have childrenWomen with children need to take significant time out of thelabor force, and usually at a crucial time, career-wise

Persistent ”statistical discrimination”If the returns to education are higher for men (for whateverreason), then it is rational for women to invest less ineducation than menThis can be a self-fulfilling prophesyIf families have finite resources to invest in their children,they might invest more in boys




Butcher and Case 1994Introduction

Explanations (cont.):”Sex-typing”Cohort effects in the household




Butcher and Case 1994Household composition

Instrument is the sibship compositionSibship?

Composition of brothers and sisters

Composition of brothers and sisters influences education(under certain plausible assumptions) and does notinfluence earnings (or so the author claims)




Butcher and Case 1994Household composition

Models of household decision-making can explain sibshipeffects if credit markets are not perfect

Constrained borrowing means that the marginal conditionwill not be metConstrained borrowing can mean that differential costs ofraising girls and boys can result in a more- or less-relaxedbudget constraint

MimicryYou have to believe in biological differences for this story tomake much senseThis is OK, as long as you’re not the president of Harvard

Comparative standardsAre girls held to the same standards as boys?




Butcher and Case 1994Data

What data is used?Panel Study of Income Dynamics (PSID)National Longitudinal Survey of Women (NLSW)Current Population Survey (CPS)

What would the ideal data tell us?




Butcher and Case 1994Data

Data suggest that men have a higher average educationalattainment than women in each cohort except the youngestMore women graduate high school than menConditional on graduating HS, more men go to collegethan womenAlso conditional on graduating HS, more men than womencomplete college than women




Butcher and Case 1994The instrument

The first thing to notice: how complex the facts ofeducational attainment areEducational attainment for men and women differconditional on reaching certain levels of educationUnconditionally, women actually get more schooling inolder cohortsConditional on HS graduation, more men go to collegeAuthors deal with this by looking at the influence of sibshipsex composition in parts

Don’t assume the effect is constant -> allow the effect to belumpyInvestigate the difference in sibling effect by gender





THE EFFECT OF SIBLING SEX COMPOSITION 541

TABLE II FRACTION OF WOMEN AND MEN AT EACH LEVEL OF EDUCATION CONDITIONAL ON

COMPLETING THE PREVIOUS LEVEL BY AGE COHORT

PSID 1985

White White White White

women men women men

Level of education 45-65 45-65 24-44 24-44

Finish high school .721 .632 .856 .828 (standard deviation) (.449) (.483) (.351) (.378)

Number of observations 760 662 1267 1167 Start college .437 .583 .602 .699

(.496) (.494) (.490) (.459) 528 406 1058 943

Finish college .493 .574 .552 .589 (.501) (.495) (.498) (.492) 231 261 651 685

For both men and women there has been throughout the century an inverse relationship between sibship size and educational attainment [Blake 1989; Duncan 1974], often attributed to a reduction in the availability of family resources per child. We find in the CPS (see Figure II) that mean education increases from one-child families to two-child families but decreases thereafter. The relationship between number of siblings and educational attainment is robust across men and women. Although the average education of women and men increases as one moves from the oldest to the youngest cohorts, the pattern between number of siblings and education remains firm across age cohorts.'7

The number of siblings in a family is highly correlated with other measures of family background that affect educational attainment. We run regressions of completed education on number of siblings, parents' education, socioeconomic status, birth order, and religion (see Table III) to understand each variable's indepen- dent effect. An additional sibling is associated with a reduction in education of roughly a fifth of a year for both younger and older women, evaluated at mean family sizes. The effect for men has changed significantly over time: an additional sibling reduces educational attainment of older men by roughly a half year and younger men by a third of a year. If sibship size were the only variable that changed through time, the levels of both men's and

17. Similar results are found in the PSID and the NLSW.





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Butcher and Case 1994First stage

THE EFFECT OF SIBLING SEX COMPOSITION 555

TABLE VIII ORDINARY AND Two-STAGE-LEAST-SQUARES ESTIMATES OF RETURNS TO EDUCATION

WHITE WOMEN, PSID 1985 DEPENDENT VARIABLE: LOG HOURLY EARNINGSb

(STANDARD ERRORS IN PARENTHESES)

TSLSd (anysis,

Explanatory Reduced TSLSC numsib, variables:a OLS form (anysis) numsib2)

Years of education 0.091 0.184 0.182 (0.007) (0.113) (0.055)

Any sisters -0.033 -0.066 -

(0.037) (0.040) Number of siblings -0.025 -0.039 -0.009 -

(0.020) (0.021) (0.032) Number of siblings2 0.002 0.003 0.001 -

(0.002) (0.002) (0.002) Number of observations 1061 1061 1061 1061 R2 0.2366 0.1168

a. Also included in the regression: intercept, age, age2, age3, indicators for Catholic, oldest child, poor household, and parental education variables Mother HS degree, Mother college degree, Father HS degree, Father college degree. Sample includes white women between the ages of 24 and 65 with a positive number of years of education and at least one sibling, but fewer than 15 siblings. All regressions weighted using sampling weights.

b. The dependent variable is hourly earnings on the worker's "main job." It is hourly wages for those who report being paid hourly, and the salary converted to an hourly figure for those who report receiving an annual salary. People were excluded if they reported working but reported no earnings, or reported no work but did report earnings. People who reported earning a dollar an hour or less were also excluded.

c. Indicator variable for "any sisters" is used as an instrument for years of education. d. Indicator variable for "any sisters," number of siblings, and number of siblings2 are used as instruments.

on the noninstrumented estimate of returns to education, and thus it is an empirical matter whether the ordinary least squares estimate in this case is too large or too small.

Table VIII presents the results of log earnings regressions, with and without instrumenting for years of completed education. The dependent variable is log hourly earnings on the respondent's current job, for both hourly wage employees and salaried employees. A full description of this variable is given in the Data Appendix.

The first column presents an estimate of the return to education for women in the PSID from an OLS regression. This estimate of 9 percent is similar to those found by other researchers using U. S. data.25 An indicator that the respondent had a sister is

25. The results of eight studies reported in Griliches all find returns to education in this range, as does more recent work by Ashenfelter and Krueger [ 1992] and Card [ 1993].




Butcher and Case 1994Criticism

Think of yourself as a reviewerDo you find anything particularly unconvincing?What would you ask the authors to do, if you could?




Angrist and Krueger 1991Preview of results

OLS and IV estimates are really similarIn opposition to the Butcher and Case resultsAny idea why?




Angrist and Krueger 1991

13.2

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Years of Education and Season of Birth 1980 Census

Note. Quarter of birth is listed below each observation.

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Note. Quarter of birth is listed below each observation. Nathaniel Higgins Notes on Butcher and Case (1994) and Angrist and Krueger (1991)



Angrist and Krueger 1991984 QUARTERLY JOURNAL OF ECONOMICS

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year of birth, based on the sample of men in the 1980 Census, 5 percent Public Use Sample. (The data set used in the figures is described in greater detail in Appendix 1.) The graphs show a generally increasing trend in average education for cohorts born in the 1930s and 1940s. For men born in the late 1950s, average education is trending down, in part because by 1980 the younger men in the cohort had not completed all of their schooling, and in part because college attendance fell in the aftermath of the Vietnam War.

A close examination of the plots indicates that there is a small but persistent pattern in the average number of years of completed education by quarter of birth. Average education is generally higher for individuals born near the end of the year than for individuals born early in the year. Furthermore, men born in the fourth quarter of the year tend to have even more education than men born in the beginning of the following year. The third quarter births also often have a higher average number of years of education than the following year's first quarter births. Moreover,




Angrist and Krueger 1991986 QUARTERLY JOURNAL OF ECONOMICS

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Season of Birth and Years of Schooling Deviations from MA (+ 2,- 2)





986 QUARTERLY JOURNAL OF ECONOMICS

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Angrist and Krueger 1991First stage THE EFFECTS OF COMPULSORY SCHOOL ATTENDANCE 987

TABLE I THE EFFECT OF QUARTER OF BIRTH ON VARIOUS EDUCATIONAL

OUTCOME VARIABLES

Quarter-of-birth effeCta Birth F-testb

Outcome variable cohort Mean I II III [P-value]

Total years of 1930-1939 12.79 -0.124 -0.086 -0.015 24.9 education (0.017) (0.017) (0.016) [0.0001]

1940-1949 13.56 -0.085 -0.035 -0.017 18.6 (0.012) (0.012) (0.011) [0.0001]

High school graduate 1930-1939 0.77 -0.019 -0.020 -0.004 46.4 (0.002) (0.002) (0.002) [0.0001]

1940-1949 0.86 -0.015 -0.012 -0.002 54.4 (0.001) (0.001) (0.001) [0.0001]

Years of educ. for high 1930-1939 13.99 -0.004 0.051 0.012 5.9 school graduates (0.014) (0.014) (0.014) [0.0006]

1940-1949 14.28 0.005 0.043 -0.003 7.8 (0.011) (0.011) (0.010) [0.0017]

College graduate 1930-1939 0.24 -0.005 0.003 0.002 5.0 (0.002) (0.002) (0.002) [0.0021]

1940-1949 0.30 -0.003 0.004 0.000 5.0 (0.002) (0.002) (0.002) [0.00181

Completed master's 1930-1939 0.09 -0.001 0.002 -0.001 1.7 degree (0.001) (0.001) (0.001) [0.1599]

1940-1949 0.11 0.000 0.004 0.001 3.9 (0.001) (0.001) (0.001) [0.0091]

Completed doctoral 1930-1939 0.03 0.002 0.003 0.000 2.9 degree (0.001) (0.001) (0.001) [0.0332]

1940-1949 0.04 -0.002 0.001 -0.001 4.3 (0.001) (0.001) (0.001) [0.0050]

a. Standard errors are in parentheses. An MA(+2, -2) trend term was subtracted from each dependent variable. The data set contains men from the 1980 Census, 5 percent Public Use Sample. Sample size is 312,718 for 1930-1939 cohort and is 457,181 for 1940-1949 cohort.

b. F-statistic is for a test of the hypothesis that the quarter-of-birth dummies jointly have no effect.

variable indicating whether person i was born in the jth quarter of the year. Because the dependent variable in these regressions is purged of MA(+2,-2) effects, it is necessary to delete observations born in the first two quarters and last two quarters of the sample.

Table I reports estimates of each quarter of birth (main) effect %) relative to the fourth quarter, for men in the 1980 Census who were born in the 1930s and 1940s.6 The F-tests reported in the last

6. We focus on men born in the 1930s and 1940s because many individuals in the 1950s birth cohorts had not yet completed their education by 1980.




Angrist and Krueger 1991Effect of instrument on the “treated”


TABLE II PERCENTAGE OF AGE GROUP ENROLLED IN SCHOOL BY BIRTHDAY AND LEGAL

DROPOUT AGEa

Type of state lawb

School-leaving School-leaving age: 16 age: 17 or 18 Column

Date of birth (1) (2) (1) - (2)

Percent enrolled April 1, 1960

1. Jan 1-Mar 31, 1944 87.6 91.0 -3.4 (age 16) (0.6) (0.9) (1.1)

2. Apr 1-Dec31, 1944 92.1 91.6 0.5 (age 15) (0.3) (0.5) (0.6)

3. Within-state diff. -4.5 -0.6 -4.0 (row 1 - row 2) (0.7) (1.0) (1.2)


4. Jan 1-Mar 31, 1954 94.2 95.8 -1.6 (age 16) (0.3) (0.5) (0.6)

5. Apr 1-Dec31, 1954 96.1 95.7 0.4 (age 15) (0.1) (0.3) (0-3)

6. Within-state diff. -1.9 0.1 -2.0 (row 1 - row 2) (0.3) (0.6) (0.6)


7. Jan 1-Mar 31, 1964 95.0 96.2 -1.2 (age 16) (0.1) (0.2) (0.2)

8. Apr 1-Dec 31, 1964 97.0 97.7 -0.7 (age 15) (0.1) (0.1) (0.1)

9. Within-state diff. -2.0 -1.5 0.5 (row 1 - row 2) (0.1) (0.2) (0.3)

a. Standard errors are in parentheses. b. Data set used to compute rows 1-3 is the 1960 Census, 1 percent Public Use Sample; data set used to

compute rows 4-6 is 1970 Census, 1 percent State Public Use Sample (15 percent form); data set used to compute rows 7-9 is the 1980 Census, 5 percent Public Use Sample. Each sample contains both boys and girls. Sample sizes are 4,153 for row 1; 12,512 for row 2; 7,758 for row 4; 24,636 for row 5; 42,740 for row 7; and 131,020 for row 8.

attend school until their seventeenth or eighteenth birthday.9 A summary of the compulsory schooling requirement in effect in each state in 1960, 1970, and 1980 is provided in Appendix 2.

The first three rows of Table II focus on individuals who were

9. There are three exceptions: Mississippi and South Carolina eliminated their compulsory schooling laws in response to Brown v. Board of Education in 1954. South Carolina reenacted compulsory schooling in 1967, and Mississippi in 1983. In 1960 Maine had an age fifteen compulsory schooling law. Ehrenberg and Marcus [1982] and Edwards [1978] also provide evidence on the impact of compulsory schooling legislation on school enrollment.




Angrist and Krueger 1991Reduced form


states]. Such factors should be borne in mind when utilizing school leaver data" [Department of Employment, Education, and Train- ing, 1987].

II. ESTIMATING THE RETURN TO EDUCATION

Do the small differences in education for men born in different months of the year translate into differences in earnings? This question is first addressed in Figure V, which presents a graph of the mean log weekly wage of men age 30-49 (born 1930-1949), by quarter of birth. The data used to create the figure are drawn from the 1980 Census, and are described in detail in Appendix 1.

Two important features of the data can be observed in Figure V. First, men born in the first quarter of the year-who, on average, have lower education-also tend to earn slightly less per week than men born in surrounding months. Second, the age- earnings profile is positively sloped for men between ages 30 and 39 (born 1940-1949), but fairly flat for men between ages 40 and 49

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Angrist and Krueger 1991The instrument

Instrument has an effect in a single, narrow caseThe instrument moves the variable of interest, but by howmuch?A person born early in the year and desiring to drop out willhave a few months of extra schooling compared to a personborn early in the year and desiring to drop outA person born early in the year and not desiring to drop outwill end up with the exact same amount of schooling as anequivalent person born late in the year

What are the implications for interpreting the coefficient inthe main regression?




Angrist and Krueger 1991The instrument

AK spend time defending their instrument, showing howgood it is by demonstrating that the impact of season ofbirth on schooling happens entirely through themechanism of high school dropouts

This argument strengthens the validity of the instrumentThis is not the same thing as saying that the instrument ispowerful, i.e. that it is a powerful explainer of earnings




Homework reviewQ1

Q1: What is sigmamore doing? The Hausman test only allowsus to reject the null with this option included.A1: The sigmamore thing just tells stata how to calculate thevariance of the estimators. In this case, what you are tellingstata is that you want to use a single estimate of the variance ofthe error term (rather than a separate one for both IV and OLS).You do this because the error term has the same interpretationin both models. You will see a situation later in the semester inwhich the interpretation of the error term will differ between thetwo models, implying that you will want to estimate the varianceof the error term twice, once for each estimator. For the use weare putting the Hausman test to right now, sigmamore is theway to go.




Homework reviewQ2

Q2: What does the following mean in Stata’s Hausman test?(Printed to the screen after running the test)"Note: the rank of the differenced variance matrix (1) does notequal the number of coefficients being tested (3); be sure this iswhat you expect, or there may be problems computing the test.Examine the output of your estimators for anything unexpectedand possibly consider scaling your variables so that thecoefficients are on a similar scale."




Homework reviewQ2

A2: The rank of the differenced variance matrix is the numberof unique differences between the columns of the var-covmatrix of the coefficients. If you have two separate estimators,you usually have two separate var-cov matrices. When youtake the difference between the two matrices, i.e. V1-V2, youget a new matrix V3=V1-V2. The "rank" (roughly speaking) isthe number of "unique" columns. Since you are calculating thevariance of the estimator using a single estimate of sigma(because you used sigmamore), you expect to get columns ofzeros for all coefficients except the column associated with theendogenous regressor. And by "expect" I simply mean that thisis not an error — I do not expect it to be obvious to people.




Homework reviewQ2

Try this as a little experiment after problem 4 in the homeworkto show yourself what’s going on:

1 First, just type: hausman iv ols (assuming you named yourestimates "iv" and "ols")- You will not get a warning message

2 Next, type: hausman iv ols, sigmamore- You will get a warning message about the rank of thedifferenced matrix being 1 and the number of coefficientsbeing tested as 2 because you are testing two coefficientsin the model (the coefficients on x1 and x2)

3 Finally, type: hausman iv ols, constant sigmamore




Homework reviewQ2

- You will get a warning message aobut the rank of thedifferenced matrix being 1 and the number of coefficients beingtested as 3 because you are testing three coefficients in themodel (the coefficients on the constant, x1, and x2)




Homework reviewQ2

Basically, you are testing the two models against each other,where the two models consist of three coefficients each.Because you are using a single estimate of the variance, statais asking if you are aware of this. The warning has more importin the situations I alluded to in 1 above, i.e. those situations inwhich you are testing restrictions across models, and so youmight want to have separate estimates of the error term(because, e.g. the error term has a different interpretation ineach model).




Homework reviewQ3

Q3: There was some confusion in the TA session about theoveridentified case. How do you explain the meaning of "valid"outside of saying an instrument meets the 2 basic criteria?What about the effect of adding extra instruments and the gmmtest? As one student said, "I thought that when the model isoveridentified, only one of the instruments had to effect thedependent variable through the endogenous variable, but theother one could also have a direct effect."




Homework reviewQ3

A3: The model is only overidentified if you have moreEXCLUDED instruments than endogenous regressors. That’sthe answer to the student’s question. If you run a first stageregression and you include a particular regressor in both thefirst stage and the second stage (this is OK), you are notincreasing the total number of instruments that obey theexclusion restriction.




Homework reviewQ4

Q4: How do we know IV is consistent and OLS efficient?A4: We know IV is consistent because it gets rid of the biasintroduced by endogeneity (introduced by correlation of aregressor and the error term) in large samples. There is amathematical proof for this, but we just focused on the intuition.By "cleaning" the endogenous regressor, the IV estimator getsrid of the bias. However, IV "throws out" information because inorder to "clean" the endogenous regressor, it must get rid ofsome of the variation in the endogenous regressor. So the IVestimator throws away information. Period. Because it doesthat, it is not an efficient estimator IF the regressor is notendogenous.




Homework reviewQ4

The null hypothesis of the Hausman test is exogeneity of theregressor (slide 22). Under the null, OLS is efficient. Againunder the null, IV is still consistent in large samples. That is,using only a small bit of the variation of a regressor will still getyou the correct coefficient in large samples, it’s just not optimalif the null is true. It’s not optimal because throwing awayinformation for no good reason is pointless.




Homework reviewQ5

Q5: Why do we include all of the explanatory variables in thefirst stage regression even when one or more of them areexogenous? In the context of part 5 of the homework, say thestructural model is y = x1 + x2, with x2 endogenous. Is the firststage model x2 = x1 + z1? Or is it just x2 = z1?A5: EITHER ONE could be fine. "The structural model" meansthe whole model, i.e. an explicit first and second stage. Thesecond stage could be y = x1 + x2 with x2 endogenous, andthe first stage could be either x2 = z1, or x2 = z1 + x1. They areequivalent! Try it. They are exactly the same thing.




Homework reviewQ5

If you include x1 in the first stage, then your "clean" x2 is equalto the variation in x2 that is explained by x1 and z1. If you theninclude x1 in the second stage, the co-variation of the clean x2and x1 is "tossed out" of the regression (remember theballantine).Instead, suppose that you did not include x1 in the first stage,but that you included it in the second stage. Then anycovariation between the "clean" x2 in the second stage and x1would be tossed out. So it doesn’t matter when you include x1— the exact same result will obtain.




Homework reviewQ5

Any covariation of x1 and x2 is tossed out of the regression,regardless of whether or not you clean x2 first. That’s exactlywhy z1 is the key instrument — because it is excluded from thesecond stage. The instrument that is excluded from the secondstage does the important cleaning in the first stage.




Homework reviewQ6a

Q6a: What is the difference between testing whether a secondinstrument is valid (given that the first instrument is valid) usinga Hausman test as in part 8 of the homework versus using:ivregress gmm y (x = z1 z2) estat overidto test the validity of the overidentifying restrictions asdescribed on slide 25 of lecture 4?A6a: Just different tests. The Hausman test is very general.You can use it for lots of things, but it doesn’t necessarily haveall the best properties in the world for every specific thing you’dlike to test.




Homework reviewQ6a

You can type estat overid after running an ivregress (2sls orgmm or liml) and you get back a host of test statisticsappropriate for testing overidentifying restrictions that areappropriate to the model you used. Hausman test is verygeneral.




Homework reviewQ6b

Q6b: What is the general pattern when using the Hausman testfor something other than endogeneity? Is it basically justwhether the difference between two inputs is statisticallysignificant from zero? Is the theory still to compare a consistentwith a more efficient estimator?




Homework reviewQ6b

A6b: That’s exactly what Hausman ALWAYS is. It turns out thatthe simple concept of comparing a consistent to an efficientestimator can be used for lots of things. Still, in many casesmore specialized tests exist as well. So Hausman is thegeneral test, basically comparing the two estimates of the samecoefficient (in this case, an IV estimate with one instrument vs.an IV estimate with two instruments), whereas theoveridentification tests (you can look up the names for it instata’s help as there are several reported by estat overid) aremore direct tests of the assumption E[z epsilon] = 0.




Homework reviewTypo alert

Typo alert: An alert student in Scott’s TA session noticed thatthe coefficient ratio on slide 14 included a typo. It has beencorrected. Luckily, the ratio was explained correctly in thehomework.




Where do good instruments come from

Mostly institutional knowledgeCreativitySometimes happy accidentOnly a few examples of generalized instruments that mightbe worth tryingSometimes mathematical tricks can help you, but usuallyintuition is the source of a good instrument

Rank-order trick (in measurement error context especially)Lagged endogenous variables (might have to play withlags, or might be able to argue based on theory)

Lagged X can be a good instrument for X , if the problem hasonly to do with contemporaneous correlation


Applied Econometrics - Lecture 5 - Nathaniel Higgins · Wrapup of basic IV Applied Econometrics...

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Transcript of Applied Econometrics - Lecture 5 - Nathaniel Higgins · Wrapup of basic IV Applied Econometrics...