Hsiao Li Racine test for correct specification of parametric regression models

[George Kollias]

Hello, I am searching but have no luck in finding the stata code for the Hsiao Li Racine test that checks if a parametric regression is correctly specified.

Does anyone know if this test can be done in stata and has the code available for it?

Thank you in advance!

[Rich Goldstein]

first, note that the -hsearch- command is helpful in situations such as this; see

help hsearch

second, please provide more information including a full citations (see the FAQ) and maybe it is known by someone by some other name

third, it would be helpful to define what you mean by "correctly specified" here as I find the phrase ambiguous (at best)

[George Kollias]

Thank you for your reply! It is a kernel based specification test for when there are both continuous and categorical variables. This is the link to the paper:

https://pdfs.semanticscholar.org/230...549.1562505343

This is the reference:

Hsiao, C., Q. Li, and J. S. Racine (2007), ‘A consistent model specification test with mixed categorical and continuous data’. Journal of Econometrics 140, 802–826.

R appears to have the code (as it is written by one of the authors of the paper: Jeffrey S. Racine) so I would assume that Stata would as well since it would be relatively easy for someone to have coded it in Stata. This is the link with the R code:

http://www.stat.cmu.edu/~cshalizi/35...p.cmstest.html

[Jeff Wooldridge]

George: I worked on a similar test in the early 1990s with the same feature that it is generally consistent against nonparametric alternatives. The HLR paper is a very nice theoretical contribution to this literature. But in most cases, applying any of these tests is likely to be overkill. They are pure functional form tests of the conditional mean and it seems like important nonlinearities would be picked up by a standard RESET test. Anything not picked up is unlikely to be practically important, at least for the smooth kinds of mean functions we expect. A statistical rejection, especially with a large sample size, does not mean the linear (in parameters) mean function is missing a lot.

In my 1992 Econometric Theory paper, the test I proposed is to add fitted values from a sieve regression -- something like Fourier series -- to the linear regression and perform a t-test on the fitted values. It's a Davidson-MacKinnon test against nonparametric alternatives, so the sieve you choose cannot nest the linear regression equation. In any case, I don't really expect it to pick up much that a careful RESET test would not. No doubt one can come up with situations where the nonparametric test works better, but how much would it practically matter?

Both RESET and the Davidson-MacKinnon approach are easily coded in Stata.

JW

[George Kollias]

Thank you so much for the detail in your answer Mr. Wooldridge it is greatly appreciated!