lnYi=0+1Si+2Expi+3Whitei+4Malei+i Where lnYi is the natural logarithm of annual dollar earnings for the ith individual, Si is the number of years of schooling for the ith individual, Expi is the years of labor market experience for the ith individual, Whitei is a dummy variable equal to one if the ith individual is white and 0 [All coefficients are expected to be positive]. a) Based on the functional form, what relationship between the dependent variable and the independent variables do the coefficients capture? b) Researcher 1 estimates the model (partial Stata results reported below). Based on these results interpret the impact of the independent variables on the dependent variable. Are they statistically significant determinants of earnings at 5 percent level of significance? c) Researcher 1 finds that the constant is not statistically significant (based on results not reported above) and decides to leave it out and re-estimate the model. Do you agree with their decision? Why or why not? d) Researcher 2 extends the model by including dummy variables to capture the regions where the individual lives (and earns). The sample includes individuals from four regions, Northeast, South, Midwest, and West. Thus, the researcher includes three additional variables, NEi is a dummy variable equal to 1 if the ith individual lives in the Northeast, 0 otherwise; MWi is a dummy variable equal to 1 if the ith individual lives in the Midwest, 0 otherwise; Wi is a dummy variable equal to 1 if the ith individual lives in the West, 0 otherwise. Stata results (partial) are given below. Is there evidence to support this researcher's claim that there are regional differences in earnings? e) Researcher 3 believes that the model is mis-specified because the coefficient for Si is too small (in both cases). Explain the researcher's concern. Assuming this concern is correct, explain how this problem must be addressed. [Please note: the question is not asking you to solve the problem, but rather how you may solve the problem.] lnYi=0+1Si+2Expi+3Whitei+4Malei+i Where lnYi is the natural logarithm of annual dollar earnings for the ith individual, Si is the number of years of schooling for the ith individual, Expi is the years of labor market experience for the ith individual, Whitei is a dummy variable equal to one if the ith individual is white and 0 [All coefficients are expected to be positive]. a) Based on the functional form, what relationship between the dependent variable and the independent variables do the coefficients capture? b) Researcher 1 estimates the model (partial Stata results reported below). Based on these results interpret the impact of the independent variables on the dependent variable. Are they statistically significant determinants of earnings at 5 percent level of significance? c) Researcher 1 finds that the constant is not statistically significant (based on results not reported above) and decides to leave it out and re-estimate the model. Do you agree with their decision? Why or why not? d) Researcher 2 extends the model by including dummy variables to capture the regions where the individual lives (and earns). The sample includes individuals from four regions, Northeast, South, Midwest, and West. Thus, the researcher includes three additional variables, NEi is a dummy variable equal to 1 if the ith individual lives in the Northeast, 0 otherwise; MWi is a dummy variable equal to 1 if the ith individual lives in the Midwest, 0 otherwise; Wi is a dummy variable equal to 1 if the ith individual lives in the West, 0 otherwise. Stata results (partial) are given below. Is there evidence to support this researcher's claim that there are regional differences in earnings? e) Researcher 3 believes that the model is mis-specified because the coefficient for Si is too small (in both cases). Explain the researcher's concern. Assuming this concern is correct, explain how this problem must be addressed. [Please note: the question is not asking you to solve the problem, but rather how you may solve the problem.]
