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Re: st: heteroskedasticity in ordered probit model


From   Richard Williams <richardwilliams.ndu@gmail.com>
To   statalist@hsphsun2.harvard.edu, <statalist@hsphsun2.harvard.edu>
Subject   Re: st: heteroskedasticity in ordered probit model
Date   Sun, 23 Dec 2012 09:19:26 -0500

At 06:25 AM 12/23/2012, John Stymans wrote:
Dear Statalist Users,
I have a problem with heteroskedasticity in an oprobit model.
I am using Stata 12.
I am new to econometrics and Stata, however I would like to estimate an equation with following set-up (number of observations are around 200) ; Dependent variable (y) is ordered (0-no, 1- sometimes, 2- a lot) over 2 countries, so I use a country dummy as independent variable. Other independent variables are: size, budget, service, R&D.
Given the dependent I used an ordered probit model.
Setup in Stata is the following: oprobit y size budget service R&D country dummy Yet literature (e.g. Cameron and Trivedi (2009) Microeconometrics Using Stata, chapter 14 page 455) says the above model has a weakness: heteroskedasticity. So I decided to test this and I compared the model with one including a heteroskedasticity term. This term included budget. A Likelihood ratio test confirmed the presence of heteroskedasticy as did a Wald test. Setup in Stata: oglm y size budget service R&D country dummy, link(probit) het(budget) When comparing results, I noticed that 2 terms which are not significant in the first equation without heteroskedasticity term are actually significant in the equation with heteroskedasticity term. Is this possible: can heteroskedasticity affect the significance of variables, or is something else going on?

See section 4.4 of http://www.stata-journal.com/article.html?article=st0208. The first paragraph of that section states

"In many types of analyses, it often makes little difference whether z tests or Wald tests or likelihood-ratio chi-squared tests are used to test hypotheses about individual coefficients. It is important to realize that this is often not the case with heterogeneous choice models. In particular, seemingly trivial changes in the coding of variables used in the variance equation can change the hypotheses that z tests or Wald tests of coefficients in the choice equation address. In brief, z tests of individual coefficients in the choice equation are conditional on the coding of the variables in the variance equation, while likelihood-ratio tests are not."

If you don't have access to the Stata Journal, an earlier working paper version is available at

http://www.nd.edu/~rwilliam/oglm/oglm_Stata.pdf

In short, you should use LR tests, not Wald tests, to test the coefficients in the choice equation.

Consider too if there are ways to make the hetero go away. The next section of that piece shows how adding a squared term to the model made a variance equation unnecessary. In your case, it might make sense to add budget^2. Life is much simpler if you don't have to add a variance equation to the model.

In a second step I would like to run a Mont Carlo simulation (I will have to figure this out, any advice on how to run such a thing is greatly appreciated) with a similar setup and check the above. Is this possible, can I use a Monte Carlo simulation to check if heteroskedasticity influences the significance of variables? There is a lot of literature on the effect of heteroskedasticity on size of determinants (which often uses Monte Carlo simulations), yet I did not find any using Monte Carlo to check the significance (can however be my fault).
Many thanks in advance and best regards,
JOhn
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Richard Williams, Notre Dame Dept of Sociology
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