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# ps3_sol - Department of Economics Columbia University...

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Department of Economics W3412 Columbia University Spring 2010 SOLUTIONS TO Problem Set 3 Introduction to Econometrics Prof. Marcelo J. Moreira and Seyhan E Arkonac, PhD for all sections Spring 2010 1. The following question is a continuation of problem set 2. The data set for this problem, growth.dta , is described at the end of this problem. Using STATA, compute the sample mean and standard deviation of growth and tradeshr. a) Estimate a regression of growth on tradeshr, using the “robust” option. Graph the data points and the estimated regression line, does the regression error appear to be homoskedastic or heteroskedastic? It is unfortunately rather hard to tell. One could argue that the spread is greater for moderate values of tradeshr than for low or high values, but there is no clear pattern. On the other hand one would not want to conclude that the residuals are homoskedastic. b) Run the regression again without the “robust” option. Compare the results to what you obtained with the “robust” option. What is different? . reg growth tradeshr; Source | SS df MS Number of obs = 65 -------------+------------------------------ F( 1, 63) = 8.89 Model | 28.4885066 1 28.4885066 Prob > F = 0.0041 Residual | 201.851551 63 3.20399287 R-squared = 0.1237 -------------+------------------------------ Adj R-squared = 0.1098 Total | 230.340057 64 3.5990634 Root MSE = 1.79 ------------------------------------------------------------------------------ growth | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- tradeshr | 2.306434 .773485 2.98 0.004 .7607473 3.85212 _cons | .6402653 .4899767 1.31 0.196 -.3388749 1.619405 ------------------------------------------------------------------------------ The standard errors, t -statistics, p -values, and confidence intervals are different, but the OLS estimates, R 2 , and RMSE are not. The heteroskedasticity-robust standard error of .66 is substantially smaller than the homoskedasticity-only standard errors of .77, so with this large a difference one should rely on the heteroskedasticity-robust standard errors.

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c) You should see an outlier in the data set. Rerun the regression (with the “robust” option), dropping the outlier. Does dropping the outlier make a qualitative difference to your results? Explain. . reg growth tradeshr if tradeshr<1.5, r; Linear regression Number of obs = 64 F( 1, 62) = 3.77 Prob > F = 0.0567 R-squared = 0.0447 Root MSE = 1.7894 ------------------------------------------------------------------------------ | Robust growth | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- tradeshr | 1.680905 .8656171 1.94 0.057 -.0494392 3.411249 _cons | .9574107 .5360579 1.79 0.079 -.1141537 2.028975 ------------------------------------------------------------------------------ Dropping the outlier makes a big difference! The slope falls considerably, and the coefficient is no longer significant at the 5% level! 2. For the following questions, use data set CPS04.dta. Each month the Bureau of Labor Statistics in the U.S. Department of Labor conducts the “Current Population Survey” (CPS), which provides data on labor force characteristics of the population, including the level of employment, unemployment, and earnings. Approximately 65,000 randomly selected U.S. households are surveyed each month. The sample is chosen by randomly selecting addresses from a database comprised of addresses from the most recent decennial census augmented with data on new housing units constructed after the last census. The exact random sampling scheme is rather complicated (first small geographical areas are randomly selected, then housing units within these areas randomly selected); details can be found in the Handbook of Labor Statistics and is described on the Bureau of Labor Statistics website (www.bls.gov ). The survey conducted each March is more detailed than in other months and
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