1. Estimate the regression hourswmi=0+1kidcounti+2agemi+3blacki+4hispani+i by OLS and obtain the heteroskedasticity-robust standard errors using White's Heteroskedasticity consistent standard errors. Interpret the coefficient on kidcount and discuss the statistical significance. 2. Angrist and Evans propose an instrumental variable, samesex, a binary variable equal to one if the first two children are the same biological sex. What do you think is the argument for why it is a relevant instrument for kidcount? 3. Estimate the regression kidcounti=0+1samesexi+2agemi+3blacki+4hispani+i and see if the reasoning from problem (2) holds. Interpret the coefficient on samesex and comment on statistical significance. Does this appear to be a relevant instrument? 4. Do you think the instrument is exogenous? In other words, can you think of any reason why samesex might be correlated with in problem (1)? (Note that biological sex can be reasonably assumed to be randomly determined. However, would you expect a family's finances to be affected based on whether they have two children of the same sex or two children of the opposite sex?) 5. Can we test for the exogeneity of samesex by adding it to the regression in problem (1) and testing its significance? Explain. 6. Use samesex as an instrumental variable for kidcount Obtain the IV estimates for the regression in problem (1). Note: To estimate using IV, you will need the AER package and you can use the following R code: ivreg(YX+W+VZ+W+V,) Endogenous variables (X) can only appear before the vertical line; instruments (Z) can only appear after the vertrical line; exogenous regressors that are not instruments ( W and V ) must appear both before and after the vertical line. How does the coefficient on kidcount compare with the initial OLS estimate? Is the IV estimate of coefficient more or less precise than the OLS estimate? 7. Add multi2nd as a second instrument. Obtain the F-statistic from the first stage regression and determine whether samesex and multi2nd are sufficiently strong. Note: Estimate the regression from problem (3), but include multi2nd as well. Conduct an F-test for the joint significance of the two instruments. 8. Using samesex and multi2nd as instruments for kidcount, how does the 2SLS estimate compare with the OLS (problem (1)) and IV (problem (6)) estimates? 1. Estimate the regression hourswmi=0+1kidcounti+2agemi+3blacki+4hispani+i by OLS and obtain the heteroskedasticity-robust standard errors using White's Heteroskedasticity consistent standard errors. Interpret the coefficient on kidcount and discuss the statistical significance. 2. Angrist and Evans propose an instrumental variable, samesex, a binary variable equal to one if the first two children are the same biological sex. What do you think is the argument for why it is a relevant instrument for kidcount? 3. Estimate the regression kidcounti=0+1samesexi+2agemi+3blacki+4hispani+i and see if the reasoning from problem (2) holds. Interpret the coefficient on samesex and comment on statistical significance. Does this appear to be a relevant instrument? 4. Do you think the instrument is exogenous? In other words, can you think of any reason why samesex might be correlated with in problem (1)? (Note that biological sex can be reasonably assumed to be randomly determined. However, would you expect a family's finances to be affected based on whether they have two children of the same sex or two children of the opposite sex?) 5. Can we test for the exogeneity of samesex by adding it to the regression in problem (1) and testing its significance? Explain. 6. Use samesex as an instrumental variable for kidcount Obtain the IV estimates for the regression in problem (1). Note: To estimate using IV, you will need the AER package and you can use the following R code: ivreg(YX+W+VZ+W+V,) Endogenous variables (X) can only appear before the vertical line; instruments (Z) can only appear after the vertrical line; exogenous regressors that are not instruments ( W and V ) must appear both before and after the vertical line. How does the coefficient on kidcount compare with the initial OLS estimate? Is the IV estimate of coefficient more or less precise than the OLS estimate? 7. Add multi2nd as a second instrument. Obtain the F-statistic from the first stage regression and determine whether samesex and multi2nd are sufficiently strong. Note: Estimate the regression from problem (3), but include multi2nd as well. Conduct an F-test for the joint significance of the two instruments. 8. Using samesex and multi2nd as instruments for kidcount, how does the 2SLS estimate compare with the OLS (problem (1)) and IV (problem (6)) estimates
