Economics 561: Economics of Labour (Industrial Relations) Empirical Assignment #2 Due Date: March 7th

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1 Page 1 of 5 2/16/2017 The University of British Columbia Vancouver School of Economics Economics 561: Economics of Labour (Industrial Relations) Professor Nicole M. Fortin Winter 2017 Professor Thomas Lemieux Tue, Thu 11:00-12:30 Iona 533 Empirical Assignment #2 Due Date: March 7th The purpose of this assignment is to estimate the rate of return to education using IV and family fixed effect methods by replicating the results of classic papers on the topic. Feel free to work cooperatively. Groups of a maximum of 2 students can hand in a single assignment for the group. You are encouraged to use Stata which has some procedures already programmed and to gather your commands in a *.do file. Stata is available on the computers on the Iona Graduate Student Computer Lab 003 on the lower level. If you can find equivalent pre-programmed procedures within alternative software, it is fine to use it. Paste in parts of your log files into your assignment to show your results. The data for the assignment are available on the course web site in assign561_2.zip. 1. In this exercise, you are asked to reproduce some of the results of the paper Oreopoulos, P. "Estimating Average and Local Average Treatment Effects of Education when Compulsory School Laws Really Matter " American Economic Review, 96(1): In this paper, Oreopoulos uses the changes in the minimum school leaving age in Britain from age 14 to 15 in 1947 and from 14 to 15 in Northern Ireland in 1957 to estimate returns to schooling. In this assignment, you are first asked to reproduce some of Oreopoulos results (essentially Tables 1 and 2). There was a second change in school leaving age laws in Britain from age 15 to 16 in You are then asked to study whether this second change can be used to identify the treatment effect of education on earnings. Refer to the article for an explanation of the variables. To reproduce Oreopoulos results, you will only need to download the file ghhs_cell_means_05.dta. To extend his analysis to the second law change, you will need the file uk_ghhs_cell_means.dta which includes data until 1985 for Britain only. [Note: Phil Oreopoulos noted difficulties in reproducing the numbers in his orginal study. He provides a new version of ghhs_cell_means_08.dta in a Corrigendum. For the purpose of replication of the original results, please use the original data set ghhs_cell_means_05.dta data set] a) First we want to examine how the instrument is related to the variable of interest. Like Figure 1 and 2 in the paper, we will graph the fraction of adults aged 25 to 60 who said they finished schooling at age 14 by birth cohort, for the year that birth cohort was 14. The first step is to collapse the data by yearat14 and region (Britain: nireland=0 and Northern Ireland: nireland=1) use ghhs_cell_means_05.dta replace yearat14 = yearat

2 Page 2 of 5 2/16/2017 collapse (sum) wght (mean) learn linc lrearn yobirth drop14 drop15 drop16 /* */ educb14 educb15 agelfted [w=wght], by(yearat14 nireland) save ghhscol, replace /*save the file so that it can be used later*/ Second, use the following commands to reproduce Figure 1 * Figure 1 label var educb14 "By Age 14" label var educb15 "By Age 15" label var yearat14 "Year Aged 14" twoway (connected educb14 yearat14 if nireland==0 & yearat14>=1935 & /* */ yearat14<=1965, msize(medlarge) mcolor(black) clcolor(black) clwidth(thick) /* */ xline(1947)) (connected educb15 yearat14 if nireland==0 & yearat14>=1935 & /* */ yearat14<=1965, msize(vsmall) mcolor(black) clcolor(black) clpat(solid) /* */ clwidth(medthick)), ytitle("fraction Leaving Full-Time Education", /* */ margin(small)) ylabel( ) xlabel( /* */ ) scheme(s2mono)saving(figure1,replace) Then make the necessary changes to the code to reproduce Figure 2. Does it appear that the laws make students get even more education than the amount required? After the dropout age changed from 14 to 15 in Britain, did the trend in the fraction of students still in school at age 15 compared to that of Northern Ireland? Can you combine some curves from Figure 1 and Figure 2 to investigate this issue? b) Now investigate whether the 1972 change in the law provides another case of a sizeable effect of compulsory schooling laws on educational attainment. Redo Figure 1 in a) using the file uk_ghhs_cell_means.dta, extending the time period to 1985 and drawing the xline in Does this change look promising? c) Evaluate the reduced form of the effect of school age leavings laws on log earnings using the xi: reg command. First reproduce the results of row 3 (column 4-6) of Table 1 using the following commands, explore the additional regression that includes cohort dummies. use ghhs_cell_means_05.dta gen age2 = age^2 gen age3 = age^3 gen age4 = age^4 gen yearat14_2 = yearat14^2 gen yearat14_3 = yearat14^3 gen yearat14_4 = yearat14^4 egen clust = group(yearat14 nireland) xi: reg lrearn drop15 nireland yearat14 yearat14_2 yearat14_3 yearat14_4 /* xi: reg lrearn drop15 nireland yearat14 yearat14_2 yearat14_3 yearat14_4 age /* */ age2 age3 age4 [w=wght], cluster(clust) xi: reg lrearn drop15 nireland yearat14 yearat14_2 yearat14_3 yearat14_4 /* */ i.age [w=wght], cluster(clust) xi: reg lrearn drop15 nireland i.yearat14 i.age [w=wght], cluster(clust) Do your results match those of Oreopoulos? Try again using log nominal earnings learn instead of log real earnings lrearn. What is the interpretation of the coefficient of drop15? Now modify the above commands to reproduce row 1 and 2 (column 4-6). What is the problem in these cases with the last regression that includes age and cohort dummies?

3 Page 3 of 5 2/16/2017 d) Replace drop15 by agelfted in c) to obtain the OLS estimates of the returns to schooling. Can you reproduce the results of columns 1-3 of Table 2? (Sometimes, the answer is no.) Are these estimates likely to be biased, if yes in which direction? e) Now estimate the first stage of the regression, that is the one that predicts schooling using dropout laws. Here we will focus only on Britain and Northern Ireland together, but with a fixed effect for Northern Ireland. First reproduce the results of row 3 (column 1-3) of Table 1 and obtain a prediction of the education level (by the age left schooling) using the following commands: xi: reg agelfted drop15 nireland yearat14 yearat14_2 yearat14_3 yearat14_4 /* predict pageled1 xi: reg agelfted drop15 nireland yearat14 yearat14_2 yearat14_3 yearat14_4 age /* */ age2 age3 age4 [w=wght], cluster(clust) predict pageled2 xi: reg agelfted drop15 nireland yearat14 yearat14_2 yearat14_3 yearat14_4 i.age /* predict pageled3 Test whether the coefficient of drop15 is significant? Do we have a weak instrument? What is the interpretation of this coefficient? Compare the goodness of fit with and without the drop15 variable? How important is this variable in predicting schooling? f) Use the education prediction in e) to estimate the second stage, i.e. the effect of schooling on earnings. Simply substitute pageled1 for drop15 in the first command in c), pageled2 for drop15 in the second command in c), and so on. What is your interpretation of the coefficient of pageled*? Explain intuitively and briefly how you are estimating this coefficient, what is the source of identification? g) Use Stata s ivregress command to perform the first and second stage of the estimation simultaneously. What other changes do you have to make to reproduce the results of row 1 and row 3 (column 4-6) of Table 2? Compare the coefficients and standard errors for agelfted with those of f)? Which is the correct one? h) Now going back to our extended data set uk_ghhs_cell_means.dta, redo g) using drop16 as instrument. Are the results different? Can you explain what is going on? [Hint: you will find out the answer after doing i) for this sample.] i) Evaluate the potential for a RD design by using the command twoway qfitci which fits a quadratic to the data (Oreopoulos used a quartic) using the collapsed data use ghhscol gen lreabrb=lrearn if nireland==0 & yearat14<=1947 gen lreabra=lrearn if nireland==0 & yearat14>=1947 twoway (qfitci lreabrb yearat14 if nireland==0, sort xline(1947)) /* */ (qfitci lreabra yearat14 if nireland==0, sort xline(1947)) /* */ (scatter lrearn yearat14 if nireland==0, sort ), /* */ scheme(s2mono) xlabel( ) /* */ title("log of Annual Earnings (1998 UK Pounds)", margin(small)) /* */ saving(figure5,replace)

4 Page 4 of 5 2/16/2017 Do the same graph for Northern Ireland? In which jurisdiction is there a stronger potential for a RD design? j) Find the IV-RD estimates of the returns to schooling in Britain and Northern Ireland. Begin by constructing the variables for the polynomial controls and the before and after variables, and then use the latter as instrument for schooling use ghhscol gen yearat14_1 = yearat gen yearat14_2 = yearat14_1^2 gen yearat14_3 = yearat14_1^3 gen yearat14_4 = yearat14_1^4 gen braf=0 if nireland==0 replace braf=1 if nireland==0 & yearat14>=1947 gen niaf=0 if nireland==1 replace niaf=1 if nireland==1 & yearat14>=1957 xi: ivreg lrearn (agelfted=braf) yearat14 yearat14_2 yearat14_3 yearat14_4 /* */ if nireland==0 [w=wght], robust xi: ivreg lrearn (agelfted=niaf) yearat14 yearat14_2 yearat14_3 yearat14_4 /* */ if nireland==1 [w=wght], robust Can you reproduce the result of row 8 (column 2) of Table 4? Show that these estimates for Britain and Northern Ireland correspond to the ones computed from the Wald estimate + + β RD = Y Y D D where the numerator is found by applying the procedures in c) and the denominator by applying the procedures in e) to Britain and Northern Ireland separately. k) Conclude by comparing your OLS estimates from d) with the IV estimates of g) and the RD estimates of j)? Regroup your results in a table (like Table 2, plus an additional column for RD results). Are they similar and what does this indicate? What are the limitations of the RD design in this case? What have you learned about whether compulsory schooling laws provide an adequate research design to estimate the returns to schooling? 2. In this exercise, you are asked to reproduce some of the results of the paper Ashenfelter, O. and A. Krueger, Estimates of the Economic Return to Schooling from a New Sample of Twins, American Economic Review, Vol. 84 (Dec., 1994): The data used by Ashenfelter and Krueger can be downloaded from the course web site under: twins.dta. Refer to the article for explanations of the variables. This study was trying to answer what seems a simple question: By how much will another year of schooling most likely raise one's income? A difficulty in trying to estimate the causal effect of education on earnings from the effect that other variables related to education have on income. Workers natural ability, family background and innate intelligence are all possible confounding factors that should be controlled for to estimate the effect of education on income accurately. Because monozygotic twins are genetically identical and have similar family backgrounds, they are thought to provide an excellent way of controlling for confounding variables. Use the following commands to expand the data set and obtain one observation per twin. expand 2 sort famid by famid: gen t=_n gen lwage=lwage1 if t==1

5 Page 5 of 5 2/16/2017 replace lwage=lwage2 if t==2 gen educ=educ1 if t==1 replace educ=educ2 if t==2 gen educ=educ1 if t==1 replace educ=educ2 if t==2 gen male=male1 if t==1 replace male=male2 if t==2 gen white=white1 if t==1 replace white=white2 if t==2 a) Run an OLS regression of log wages on a constant, schooling, age, age-squared, gender and a racial indicator ( white dummy). What do the coefficients on age and age-squared imply about the life-cycle profile of earnings? Do your estimates match those in column (1) of Table 3 in Ashenfelter and Krueger? What kinds of biases is the OLS coefficient on educ likely to incorporate? b) Use the cluster(famid)option and the robust option in the regress command to adjust the standard errors. Does the significance of the coefficients change? c) Now create dummy variables for each level of schooling, using tab educ, gen (educdd) and run the above OLS regression with those education dummies, omitting the one for high school (educdd=4) instead of the educ variable. Do the estimated coefficients indicate that the effect of education of log wages is linear? d) Compare your OLS estimates with those that incorporates a family fixed effect using the command xi:regress lwage educ age age2 white male i.famid An alternative to fixed effect estimation is to run a model on first differences. Write out the equation in first differences, estimate that differenced equation and compare the results to column (v) in table 3. Should the coefficient of educ in the family fixed effect and the first-differenced model be the same? Are they the same? Note: family fixed effects (dummy for each pair of twins) are directly included in the regression model shown above. As in Brown (1980), a numerically equivalent approach consists of running the regression on differences from means obtained by subtracting the mean family values of the y and x variables from the individual observations of y and x. Stata does this automatically for you using the xtreg command with the fixed effect option fe. In the example used here the Stata command would be: xtreg lwage educ age age2 white male, i(famid) fe e) Use Zellner s seemingly unrelated equations systems to estimate sureg (lwage1 educ1 educ2 age age2 white1 male1) (lwage2 educ2 /* */ educ1 age age2 white2 male2) if t==1 Under the assumptions of a pure family effects model, the difference between the own education coefficient and the estimated sibling education coefficient provides an unbiased estimate of the average marginal return to schooling. When these assumptions fail, we at least get an upper bound on the true returns to education. Are the coefficients previously a)-d) within those bounds?

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