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Econometrics (NA3011) Reza Mortazavi 2014 Stata Lecture 3
Explaining labor demand • use http://users.du.se/~rem/labour2.dta • browse • Do we have any reason to suspect heteroskedasticity? • regrlabor wage output capital • predict resid,residual
Testing for heteroskedasticiy • twoway (scatter resid output) • rvfplot • (Note: gives a plot of residuals against fitted values) • gen residsq=resid^2 • regrresidsq wage output capital • ereturn list • display e(N)*e(r2) • display 1- chi2(e(df_m),(e(N)*e(r2))) • (Note: chi2(df,x) is the cumulative chi-squared distribution with df degrees of freedom which gives the probability of drawing from the chi-squared distribution with df degrees of freedom and observing a value less than or equal to x.)
Testing for heteroskedasticiy • We don’t need to go through these steps every time we run a regression and want to test for heteroskedasticity: • regr labor wage output capital • estathettest capital output wage, iid • For our course it suffices to use: • estathettest
Logarithmic transformation • Let us use a log-log model: • gen lnlabor=ln(labor) • gen lnwage=ln(wage) • gen lnoutput=ln(output) • gen lncapital=ln(capital) • regrlnlaborlnwagelnoutputlncapital • How do we interpret the estimated coefficients? • Heteroskedasticity? • estat hettest • Still evidence of heteroskedastic errors
Robust standard errors • Regression with heteroskedasticity robust or White’s standard errors: • regress lnlaborlnwagelnoutputlncapital, vce(robust) • Compare with the previous regression. What is different? • It is recommendable that when working with cross sectional data you report these standard errors.
GLS • regrlnlaborlnwagelnoutputlncapital • predict ehat,residual • gen lnehatsq=ln(ehat^2) • regrlnehatsqlnwagelnoutputlncapital • Heteroskasticity? Look at the t-values for log of output and log of capital • generate hi=(exp(_b[lnwage]*lnwage+_b[lnoutput]*lnoutput+_b[lncapital]*lncapital))^0.5 • regress lnlaborlnwagelnoutputlncapital [aweight = 1/(hi^2)] • Point: given multiplicative heteroskedasticity,GLS is more efficient.