Germán Rodríguez
Generalized Linear Models Princeton University

## Problem Set 2: Determinants of Hourly WagesDue Wednesday, October 12, 2016

We will analyze an extract of 534 observations from the 1985 Current Population Survey (CPS) to explore, among other things, how hourly wages differ among men and women with similar observed characteristics.

The dataset is available here as a Stata file `http://data.princeton.edu/wws509/datasets/wages.dta`, and includes information for each worker on years of education, an indicator for southern states, indicator for females, years of work experience, indicator of union membership, the hourly wage in dollars, age, ethnicity (coded 1=other, 2=hispanic, 3=white), occupation (coded 1=management, 2=sales, 3=clerical, 4=service, 5=professional, 6=other), sector (coded 0=other, 1=manufacturing, 2=construction), and an indicator for married respondents.

## [1] Working with Wages

(a) Fit a linear model to explore how hourly wages depend on education, work experience, union membership, region, occupation and sex. (For simplicity we leave out the other predictors throughout this problem set.)

(b) Describe the net effects of education, work experience, and union membership on wages.

(c) Describe the gender gap after adjusting for the effects of the other variables in the model, and test its significance.

(d) Calculate and plot the jack-knifed residuals versus the fitted values. What does the plot indicate? Any outliers?

(e) Compute robust standard errors and comment on whether the gender gap is still significant. (R users should make sure to use the "HC1" method.)

## [2]Working with Log-Wages

(a) Fit the model of part 1.a working with the natural logarithm of hourly wages.

(b) Describe the coefficients of education, work experience and union membership in terms of the effects of these variables on wages (not on log wages).

(c) Describe the gender gap as estimated in this model and test its significance.

(d) Check whether the returns to work experience are the same for males and females.

(e) How does the result of part (d) affect the conclusions of part (c)? Do we still have a gender gap?

## [3] Regression Diagnostics

(a) Calculate and plot the jack-knifed residuals versus fitted values for the final model using log wages. What does the plot tell us? Any outliers?

(b) Run a quick Q-Q plot to check the normality of the residuals. How does the graph look? (No formal test required.)

(c) Calculate the leverages. Do we have any observation with high leverage? Identify the observation with the highest leverage. Can you tell why it has potential influence?

(d) Calculate the Cook's distances. Do we have any observations that stand out? What do you think would happen to the gender gap if we refit the model omitting the observation with the highest actual influence? (No need to do the fit.)

(e) Did we need to transform the data? Was the natural logarithm a good transformation? Explore these questions in a Box-Cox framework by plotting the profile log-likelihood for parameters in the range (-2,2) and formally testing for the identity and log transformations.

Posted Monday, October 3, 2016