5. [In continuation of PS 10] [Essential to pass] We are interested in the return to education and the gender gap. The table below summarizes regression results estimated using data on full-time workers, ages 30 through 64, from the Current Population Survey (CPS). All the four regressions use logarithm of hourly earnings as dependent variable and include Years of Education as the independent variable of interest. Then different combinations of variables (refer to the first column for variable names and what they measure) are used in each regression. Significance of each variable is indicated by * (significant at the 5% level) or **(significant at the 1% level). Dependent variable: logarithm of Hourly Earnings. Regressor Years of education Female Female x Years of education Potential experience Potential experience Midwest South West (1) (2) (3) (4) 0.1082** 0.1111** 0.1078** 0.1126** (0.0009) (0.0009) (0.0012) (0.0012) -0.251** -0.367** -0.392** (0.005) (0.026) (0.025) 0.0081** 0.0099** (0.0018) (0.0018) 0.0186** (0.0012) -0.000263** (0.000024) -0.080** (0.007) -0.083** (0.007) -0.018** (0.007) Intercept R 1.515** (0.013) 1.585** (0.013) 1.632** (0.016) 0.221 0.263 0.264 1.335** (0.024) 0.276 The data are from the March 2013 Current Population Survey (see Appendix 3.1). The sample size is n - 50,174 observa- tions for each regression. Female is an indicator variable that equals 1 for women and 0 for men. Midwest, South, and West are indicator variables denoting the region of the United States in which the worker lives: For example, Midwest equals 1 if the worker lives in the Midwest and equals 0 otherwise (the omitted region is Northeast). Standard errors are reported in parentheses below the estimated coefficients. Individual coefficients are statistically significant at the *5% or **1% sig- nificance level. (a) Consider (3). Is the return to education statistically different by gender? (b) Consider (4). Regression (4) also controls for the potential experience of the worker, as measured by years since completion of schooling. i. Write down the mathematical expression for the partial/marginal ef- fect of Potential experience on Hourly Earnings. ii. Consider a man with 16 years of education and 2 years of experience who is from a Western state. Use the regression result (4) to esti- mate the expected change in the logarithm of average hourly earnings associated with an additional year of experience. iii. Repeat (ii) assuming 10 years of experience (with the same years of education). iv. Explain why the answers to (ii) and (iii) are different. v. Test whether the return to experience is constant or not (that is, it is varying with the level of Potential experience). What are the null and alternative hypotheses?