Introductory Econometrics Problem set 2
Transcription
Introductory Econometrics Problem set 2
Introductory Econometrics Problem set 2 Jan Zouhar Department of Econometrics, University of Economics, Prague, [email protected] Due date: 24 April Problem 2.1. Use the data in wage2.gdt for both this problem and the remaining problems below. a ) Estimate the equation log.wage/ D ˇ0 C ˇ1 exper C ˇ2 exper2 C ˇ3 educ C ˇ4 female C ˇ5 nonwhite C u: (1) and report the results using the usual format. b ) Based on your results from part a, find the 99% confidence intervals for ˇ5 . Is the (partial) effect of race statistically significant at the 1% level in your equation? c ) Use White’s test and the Breusch-Pagan test (Tests ! Heteroskedasticity ! White’s test / BreuschPagan) to show whether Assumption MLR.5 holds. What do you conclude? (Report the value of the test statistics and the resulting p-value along with your conclusions.) What does the test tell you about the results you obtained from the regression? d ) Using the approximation %wage 100.ˇ1 C 2ˇ2 exper/exper; find the approximate return to the fifth year of experience. What is the approximate return to the twentieth year of experience? e ) At what value of exper does additional experience actually begin to lower predicted log.wage/? (Or, what is the turning point in the effect of experience?) How many people have more experience in this sample? (Hint: Sorting the data using Data ! Sort data ! exper might help you out with the last question.) Problem 2.2. Based on (1), you want predict the salary of a white male person with 5 years of work experience and 18 years of education. This prediction is made difficult by the presence of logarithms; read Wooldridge’s section ‘Predicting y when log.y/ is the dependent variable’. a ) Find the prediction, assuming that u is normally distributed (conditional on all independent variables), i.e. that assumptions MLR.1 through MLR.6 hold. b ) Save the residuals from (1) to a new variable uhat, and test for normality (Variable ! Normality test), the null is that uhat is normally distributed). What do you conclude? c ) Find the prediction once again, this time using Duan’s (1983) smearing estimate, described in the same section of Wooldridge’s book. (Hint: you will need to create a new variable, calculated as exp.uhat/, and find its mean, e.g. by displaying summary statistics.) Problem 2.3. a ) Estimate a modified version of (1) with the level, rather than log, of wage as the dependent variable: wage D ˇ0 C ˇ1 exper C ˇ2 exper2 C ˇ3 educ C ˇ4 female C ˇ5 nonwhite C u: (2) b ) Save the residuals (u) O from (2) and find the sample correlation coefficients between uO and all the explanatory variables (i.e., 5 correlation coefficients). Explain the results. c ) Save the fitted values wage from (2) and find the sample correlation coefficient between wage and wage. Is there any relationship between this correlation coefficient and the R2 from the regression model? (Hint: See Wooldridge, look for the origin of the term ‘R-squared’.) 1 1 1 1 d ) Based on (1), calculate the predicted wage for all people in the sample (wage2), using Duan’s estimate as in Problem 2.2. Find the squared correlation between wage and wage2, and use the result to compare the goodness of fit of (1) and (2). (See Wooldridge, same section as in Problem 2.2, for a comparison of goodness of fit for models that combine dependent variables in the level and the log form.) 1