Linear regression model for log wages on education

1. Estimate a linear regression model for log wages on education, experience, and experience squared. Report regression coefficients and standard errors. Also report the R2
   and the estimate of the standard deviation of the random error.
2. Predict the effect on average log earnings of increasing everybody’s education level by
   one year.
   Hint: If the regression model is
   log(wage)i = β0 + β1 × educi + β2 × experi + β3 × exper2
   i + εi
   .
   then the effect of increasing education level of individual i by one year is
   θi = β1 − β2 − β3 · (2 · experi − 1)
   because one year additional education implies one year less work experience. The average affect is the average of this.
   After you defined this, compare the task to that in lecture 5 where we consider the
   partial effect in a quadratic model. This is not necessary to solve this problem, but
   just a reminder to re-check the answer after you have studied lecture 5.
3. Can you obtain the above effect by running a regression with a redefined set of covariates? How? Hint: redefined means that the new covariates are functions of the
   regressors in the regression model of the first part of this assignment.
4. Assume that the error term in the regression has a normal distribution. Predict the
   effect on the average level of earnings of the following policy: increase the level of
   education for those who currently have education below 12 years of education to 12,
   and leave the level of education for others unchanged. Hint: Use the formula for the
   mean of the lognormal distribution.

Sample Solution