ARE 212: Problem Set 3

Posted 2021-02-13 abacd

ARE 212: Problem Set 3
Spring 2019
Wage Regressions - Blackburn and Neumark (QJE 1992)
The goal of this problem set is to explore some tests for heteroscedasticity and explore the fixes discussed
in class. The paper is available on Jstor. The data can be downloaded from BCourses. The problem
set is due on Monday 18, 2019 at 10am.
1. Read the data into R. Plot the series and make sure your data are read in correctly.
2. Let us explore the issue of heteroskedasticity a bit. We would like to estimate the model:
log(wage) =β0 + exper · β1 + tenure · β2 + married · β3 + south · β4+
urban · β5 + black · β6 + educ · β7 + 
(a) Estimate the model above via least squares.
(b) Choose one of the three following heteroskedastic error detection tests to conduct. Comment
on whether the assumption of spherical errors might be misguided:
a White - test for heteroskedastic errors. Use levels, interactions and second order terms
only.
a Goldfeld - Quandt Test for heteroscedastic errors. (Use the tenure variable, leaving out
the 235 observations in the middle.)
a Breusch Pagan Test for heteroscedastic errors. (Use all the covariates as a simple linear
combination).

ARE 212作业代做
(c) Calculate the White robust standard errors. Comment on how they compare to the traditional
OLS standard errors. Is this the right way to go about fixing the potential problem?
(d) Estimate the model using the two step FGLS estimation procedure outlined in class. (Again
in the regression to calculate the weights, use all of the covariates). Talk about the standard
errors obtained from your method. And how they compare to the White standard errors.
3. Now let us explore the wonders of the delta method a bit. When β3 is small, 100 · β3 is the
approximate c.p. percentage change in wages between married and unmarried men. When β3 is
large, one would prefer the exact percentage difference in E[wage|other variables]. We will call this
θ1. Questions (a) and (b) are optional.
(a) Show that if  i is independent of all covariates, then θ1 = 100·[exp(β3)?1], where β3 is the OLS
coefficient from the OLS equation above. A consistent estimator of θ1 is θb1 = 100·[exp(βb3)?1],
where βb3 is the estimated OLS coefficient.
(b) Use the delta method to show that the asymptotic standard error of θb1 is 100·[exp(βb3)]·se(βb3)
(c) Using the estimation results and the facts derived from (a) and (b), calculate θb1 and its
standard error.

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