Senior Seminar Assignment 4
Due April 2, 2007
Finding and detecting Heteroskedasticity
The purpose of this exercise is to reinforce our data manipulation skills, to run simple
regressions, and to learn to deal with heteroskedasticity. Be sure to include a constant
term in all regressions.
1. Load the data file Manufactures which I will send you and which contains data from
the U.S. Census Bureau’s American Survey of Manufactures on 455 Industries from 1994
on the following variables: shipments (value of output shipped), materials (value of
materials inputs used in production), newcap (expenditure on new capital by this
industry), inventory (value of inventories held), managers (number of supervisory
workers employed), and workers (number of production wokers employed). The first
four variables are measured in thousands of dollars.
A. Estimate the regression:
shipments = f(materials, newcap, inventory, managers, workers)
If a firm employs one more manager, how much do shipments rise? If a firm employs
one more production worker, how much do shipments rise? Does this match your
intuition about the salaries earned by managers and production workers?
B. Perform the White test, no cross terms, for heteroskedasticity of unknown
form. How many right-hand side variables does the test regression have? What is the
test statistic, and what is the critical value? Does this test find heteroskedasticity or not?
C. Now perform the White test with cross-terms. How many right hand side
variables does the regression have? What is the test statistic, and what is the critical
value? Does this test find heteroskedasticity or not? Does it match your answer in part
B?
D. Reestimate the equation, using the correction for heteroskedasticity-consistent
standard errors. How much do the standard errors change? How many variables change
their reported statistical significance as a result?
E. Let’s assume that the heteroskedasticity depends upon materials. What is the
median value of the materials variable? Estimate the regression using only the data
points where materials has a value less than 90% of the median value. How many
observations are used in the regression? What is the sum of squared residuals? Now
estimate the regression using only the data points where materials has a value greater
than 110% of the median value. How many observations are used and what is the sum of
squared residuals?
F. Calculate the Goldfeld-Quandt test statistic. What value do you get? What is
the critical value? Does this test detect heteroskedasticity or not?