Question

Considering the following economic model of wages and education: wage-b0+b1educ+u, where wage is the individuals hourly wage, educ is the individual's years of schooling, u is the error and b0 and b1 are population parameters Do you expect b1 to be positive or negative. Explain your answer. [2 points] Explain intuitively how an OLS regression fits the relationship between wage and education. [3 points) ii. Showing all of your working, derive the OLS estimators of b0 and b1. [6 points]

Answer 1

(i) Given linear regression in two variable, the slope coefficient shows the impact of education on an average hourly wage of an individual. The expected sign of b1 is positive as the years of schooling increases of an individual, the person will be more skilled and productive implies average hourly wage would rise.

(ii)

(i) Given linear regression in two variable, the slope coefficient shows the impact of education on an average hourly wage of an individual. The expected sign of b1 is positive as the years of schooling increases of an individual, the person will be more skilled and productive implies average hourly wage would rise. (ii) Given population regression function wage = b_0 + b_1 educ + u let us define sample regression function Yi = b_0 + b_1 X_i + u_i where Y_i = wage Xi = educ using OLS max sigma u^2_i = sigma (Yi minus b_0 minus b_1 Xi) Differentiating in terms of b_0 and b_1 gives following, results dEu^2_i/db_0 = 0, dEu^2_i/db_1 = 0 b_0 = Yi minus b_1 x_1 b_1 = sigma (x_i minus x) (y_i minus y)/sigma (x_i minus x)^2