econometrics

1. [Specification] You are interested in returns to college education. You decide to use log (wage) as the dependent variable, and the main variable of interest is college education (a dummy variable, taking value 1 if an individual is college graduate, and 0, otherwise). (a) Suppose education and experience are important determinants of wage and you decide to add them in the regression. Propose a population regression equation to examine the return to college education. Name variables as you wish. Be careful with notation in your answer; that is, be clear with whether you use the population regession function or the sample regression function (or fitted line). (b) Suppose you want to test whether graduates from top 10 universities fare better in the labor market. Propose a population regression equation that allows a wage gap between top-10 University graduates (Group 1) and non- top-10 University graduates (Group 2). Define relevant variable(s). Write down the null and alternative hypotheses to test whether the means log wages differ between the two groups. (c) Propose a population regression equation that allows the return to college education to vary with experience. Write down the null and alternative hypotheses to test whether the returns to college education vary with ex- perience. 1 (d) Propose a population regression that allows the return to experience to vary with the level of experience. Write down the null and alternative hypotheses to test whether the returns to experience vary with the level of experience. (e) Propose a population regression equation that allows the return to col- lege education to vary with which university you graduate from (that is, whether one belongs to Group 1 or Group 2). Write down the null and al- ternative hypotheses to test whether the return to college education differ between the two groups. 1. [Specification] You are interested in returns to college education. You decide to use log (wage) as the dependent variable, and the main variable of interest is college education (a dummy variable, taking value 1 if an individual is college graduate, and 0, otherwise). (a) Suppose education and experience are important determinants of wage and you decide to add them in the regression. Propose a population regression equation to examine the return to college education. Name variables as you wish. Be careful with notation in your answer; that is, be clear with whether you use the population regession function or the sample regression function (or fitted line). (b) Suppose you want to test whether graduates from top 10 universities fare better in the labor market. Propose a population regression equation that allows a wage gap between top-10 University graduates (Group 1) and non- top-10 University graduates (Group 2). Define relevant variable(s). Write down the null and alternative hypotheses to test whether the means log wages differ between the two groups. (c) Propose a population regression equation that allows the return to college education to vary with experience. Write down the null and alternative hypotheses to test whether the returns to college education vary with ex- perience. 1 (d) Propose a population regression that allows the return to experience to vary with the level of experience. Write down the null and alternative hypotheses to test whether the returns to experience vary with the level of experience. (e) Propose a population regression equation that allows the return to col- lege education to vary with which university you graduate from (that is, whether one belongs to Group 1 or Group 2). Write down the null and al- ternative hypotheses to test whether the return to college education differ between the two groups