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. 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 5% level) or ** (significant at the 1% level).

a) Consider (1) and (2). Comment on whether the omission of gender in regression (1) causes substantial omitted variable bias (OVB). Discuss why or why not.

b) Discuss whether the returns to education are economically and statistically different for men and women.

c) Regression (4) controls for the region of the country in which the individual lives, thereby addressing potential omitted variable bias that might arise if years of education differ systematically by region. Comment on to what extent adding regional dummies is justified based on the regression results.

Dependent variable: logarithm of Hourly Earnings. Regressor Years of education Female Female x Years of education Potential experience Potential experience Midwest South West Intercept R2 (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) 1.515** (0.013) 1.585** 1.632** 1.335** (0.013) (0.016) (0.024) 0.221 0.263 0.264 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.