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*Econ930 Spring 2020
*Problem Set 2 Soltions
*Problem 4
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cd "C:\Users\vkbostwick\Dropbox\Teaching_Grad_Metrics930\Homeworks"

clear
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log using "HW2_Problem4.log", replace



use "wagepan.dta", clear

***(a) Estimate this equation by pooled OLS and report the results. 
reg lwage i.year educ black hisp c.exper##c.exper married union

***Are the usual OLS standard errors reliable? Explain. 
*Answer: No. Even if ci is uncorrelated with xit for all t, the usual OLS standard errors do not account for the serial correlation in vit = ci + uit. You can see below that the fully robust standard errors (which account for correlation between all vit within the same person) are substantially larger than the usual ones because of this serial correlation.

***Compute more appropriate standard errors.
reg lwage i.year educ black hisp c.exper##c.exper married union, cluster(nr)




***(b) Estimate the equation by Random Effects.
xtset nr year
xtreg lwage i.year educ black hisp c.exper##c.exper married union, re cluster(nr)

***Compare your estimates with the pooled OLS estimates.
*Answer: The random effects estimates on the time-constant variables are similar to the pooled OLS estimates. The coefficients on the quadratic in experience for RE show an initially stronger effect of experience, but with the slope diminishing more rapidly. There are important differences in the variables that change across individual and time; they are notably lower for random effects. The random effects marriage premium is about 6.4%, while the pooled OLS estimate is about 10.8%. For union status, the random effects estimate is 10.6% compared with a pooled OLS estimate of 18.2%. Note that the RE standard errors for the coefficients on the time-constant explanatory variables are similar to the fully robust POLS standard errors. However, the RE standard errors for married and union are substantially smaller than the robust POLS standard errors, suggestive of the relative efficiency of RE. 





***(c) Now estimate the equation by Fixed Effects. 
xtreg lwage i.year educ black hisp c.exper##c.exper married union, fe cluster(nr)


***Why is experit redundant in the model even though it changes over time? 
*Answer: The variable experit is redundant because everyone in the sample works every year, so experi,t+1 = experit + 1, t = 1,…,7, for all i. The effects of the initial levels of experience, experi1, cannot be distinguished from ci because we are allowing experi1 to be correlated with ci. Then, because each experience variable follows the same linear time trend, the effects cannot be separated from the aggregate time effects (year dummies).

***What happens to the marriage and union premiums as compared with the RE estimates?
*Answer: The marriage and union premiums are even smaller that in the RE analysis (4.7% and 8% respectively). However, both premia are still statistically significant and economically relevant.





***(d) Add the interaction terms: blacki*unionit and hispi*unionit. Do the union wage premiums differ by race? Obtain the usual FE statistics and those fully robust to heteroskedasticity and serial correlation.

*Answer: With usual (non-robust) standard errors and statistics:
xtreg lwage i.year educ c.exper##c.exper married i.black##union i.hisp##union , fe
lincom 1.union + 1.black#1.union
lincom 1.union + 1.hisp#1.union

*Answer: With fully robust standard errors and statistics:
xtreg lwage i.year educ c.exper##c.exper married i.black##union i.hisp##union , fe cluster(nr)
lincom 1.union + 1.black#1.union
lincom 1.union + 1.hisp#1.union

*The union premium is 9.6% for non-black, non-hispanic workers. For black workers the union premium is 7.1 percentage points higher (16.7%) but this difference is not statistically significant. For hispanic workers, the union premium is 13pp lower and this difference between the non-black, non-hispanic premium and the hispanic union premium is statistically significant. This makes the total union premium for hispanic workers negative (-0.35%) but this is not statistically different from zero.

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