University of Illinois Department of Economics
Fall 2005 Econ 508 Roger Koenker
Problem Set 3
Simultaneity, Causality, Cointegration, and Unit-Roots
This problem set combines two topics, the first part of the problem set is based on
the celebrated paper by Thurman and Fisher (1988) which resolved the longstanding
scientific dispute over āwhich came first: the chicken or the egg?ā The second part
deals with classical simultaneous equation models.
As a prelude to doing the problem set please use either the R or Stata versions
of the Granger-Newbold simulation code to generate 100 realizations and record the
proportion of them that give a significant t-statistic at the conventional 5 percent
level.
The data for the first part of the problem set was kindly provided by Thurman,
consists of annual time series 1930-1983 for U.S. egg production in millions of dozens
and the December 1 USDA estimate of the US chicken population, (excluding broil-
ers). Unfortunately, as provided, the data seems to be slightly different than that
analyzed by Thurman and Fisher. As a result your results based on the problem
set data can be expected to vary somewhat from those reported in the Thurman
and Fisher paper. The data is provided on the class web page as eggs.txt. Also
provided are two Rfunctions granger() and adf() to help analyze the data. We
also provide a johansen() function as well.
1. Using granger() try to reproduce the results of Thurman and Fisherās Table
1. Try to suggest some graphical technique that might help to explain the
nature of the rather striking results. Make sure that you take a close look at
the granger() function and understand how it works.
2. Test each series for I(1) behavior using the augmented Dickey-Fuller test. You
may use the adf() function for this purpose, but again look closely to see how
it works. Note that your results here may depend on the length of the lag you
specify in the ADF test. How do your results here influence your interpretation
of the findings in question 1?
3. Test for cointegration of the chicken-egg process, using both the Engle-Granger
and Johansen approaches. Contrast your results and reconsider findings in
question 1.
The second half of this problem set deals with two simple cobweb models of
supply and demand. Data for Questions 1-4 appears as system1 on the course
webpage. and data for Questions 5-6, appears as system2,
