Md Moshi Ul Alam
Md Moshi Ul Alam
Assistant Professor of Economics
Clark University
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Econometrics PS 2

Author

Prof Alam

Note

Follow the instructions of completing your problem set detailed in the syllabus.

Question 1

Adapted from wooldridge

Explore the lawsch85 dataset from the wooldridge package after loading it in R. This dataset contains information on the number of law school admissions and various characteristics of law schools in 1985.

  1. Estimate the following regression models using OLS. Report the estimates side by side (using the stargazer package or modelsummary package). Interpret the coefficients in each of the models. How does the inclusion of age and clsize affect the coefficients of GPA and rank?

model 1: lsalary on GPA and rank

model 2: lsalary on GPA, rank, and age

model 3: lsalary on GPA, rank, and clsize

  1. Examine the R-squared values of the models. How does the inclusion of age affect the R-squared and why does it not follow the usual pattern of always increasing with the addition of more variables ?

Question 2

Different states have different minimum wages. For example:

  • Alabama, Georgia, Mississippi: $7.25/hour (federal minimum)
  • Florida: $12.00/hour
  • New York: $15.00/hour
  • California: $15.50/hour

You want to estimate the effect of minimum wage on employment rates using data from different counties in the US indexed by c. You consider two regression specifications:

\text{employment rate}_c = \beta_0 + \beta_1 \text{min\_wage}_c + u_c \quad (1)

\text{employment rate}_c = \beta_0 + \beta_1 \text{min\_wage}_c + \beta_2 \text{avg\_wage}_c + u_c \quad (2)

where avg_wage is the average wage in the county and min_wage is the minimum wage in the county (which is the same as the state minimum wage for all counties in that state).

Which model correctly estimates the effect of minimum wage on employment and why?

Question 3

Load the wooldridge library and using the wage1 dataset, youa re interested in documenting the gender wage gap.

  1. Start with running the following regression: log(wage_i) = \beta_0 + \beta_1 \, female_i + u_i where female is a binary variable that takes the value 1 if the worker is female and 0 otherwise. Interpret the coefficient on female.
  2. In estimating the average gender wage gap, why did we not include a dummy variable for male in the regression above?
  3. Now include educ (years of education), exper (years of experience), and tenure (years with current employer) in your analysis. How and why does the inclusion of these variables affect the coefficient on female? (Report the estimates side by side using the stargazer or modelsummary package).
  4. Now suppose someone asks you does an additional year of education effects wages differently for male and female workers. How would you modify your regression to answer this question? Run the regression and interpret the relevant coefficients.
  5. Do you think adding any other variables non-linearly will be helpful? If so, which ones and do your best to show data patterns to support your argument? (You do not need to run any regressions for this part).

Question 4

  1. Problem C6 Wooldridge Chapter 3.
  2. How is this different from the partialling out analysis we did in class? Explain briefly.

Question 5

  1. Problem C13 Wooldridge Chapter 3.