Readers of this blog will know I'm a proponent of more specification testing in the context of Logit, Probit, and related models. For, instance, see this recent post, and the links within it.
I received an email from Paul Johnson, Chair of the Department of Economics at Vassar College, today. He wrote:
"I thought that, given your interest in specification tests in probit etc. models, you might find the attached paper of mine (written some years ago) to be useful as it expounds the straightforward generalization of the Bera, et al. (1984) test to the ordered probit case."
Paul's paper is, indeed, very interesting and I hadn't seen it before. It's titled, "A Test of the Normality Assumption in the Ordered Probit Model", and it appeared in the statistics journal, Metron (1996, LIV, 213-221).
Here's the abstract:
"This paper presents an easily implemented test of the assumption of a normally distributed error term for the ordered probit model, As this assumption is the central maintained hypothesis in all estimation and testing based on this model, the test ought to serve as a key specification test in applied research. A small Monte Carlo experiment suggests that the test has good size and power properties."
A year later, a closely related paper by P. Glewwe appeared in Econometric Reviews. That author doesn't mention Paul's paper, but these things happen. Glewwe's paper does take things a little further than Paul does, by allowing for censoring of the data.