Statistical significance for sigma_u and rho from Stata’s xtprobit command

[Alina Hackl]

Dear all,

I'm estimating a dynamic random effects probit model assuming a first order Markov process accounting for the initial condition bias with Wooldridge (2005) method.
Based on xtprobit outcome lag.outcome controls initialcondition.controls, re I get the following coefficient for lnsig2u, sigma_u, and rho and their standard errors, respectively:

	Coef.	Std. Err.
/lnsig2u	-.0139146	.3804387
sigma_u	.9930669	.1889005
rho	.4965214	.0951051

LR test of rho=0: chibar2(01) = 20.42 Prob >= chibar2 = 0.000


I was wondering how to make statements about the statistical significance of lnsig2u, sigma_u, and rho and would really appreciate any comments on that.

Thanks!


Wooldridge, J. M. (2005). Simple solutions to the initial conditions problem in dynamic, nonlinear panel data models with unobserved heterogeneity. Journal of Applied Econometrics, 20(1), 39–54. https://doi.org/10.1002/jae.770

[Jeff Wooldridge]

Alina: All of the estimates and test statistics are consistent. Your estimate of sigma_u is about one, which means the estimate of sigma2_u (the square) is also close to one. That means ln(sigma2_u) should be close to zero and slightly negative -- and that's what you see. So the estimates and standard errors for the first two lines confirm that sigma_u is not statistically different from one. But it is very different from zero. rho is just a transformation of sigma2_u: rho =sigma2_u/(1 + sigma2_u). In your case, rho should be close to 0.5 and that's what you find. So there is strong evidence of a heterogeneity term and its variance is estimated to be very close to one. The LR test is a test of sigma2_u = 0, and of course it strongly rejects.

[Alina Hackl]

Hi Jeff,
thank you very much for your answer! I'm happy that we both agree that the results look consistent. Besides the interpretation of the coefficients, my question targeted more at the statistical significance. Sorry, if that was not quite clear. As xtprobit only provides the standard errors and CI, how can I calculate the t-statistics?

On another note: One of my explanatory variables describes the state-level development of the nominal wage index nwindex. As the information (typically) is time-variant, I include all future values, nwindex2 for t=2, nwindex3 for t=3 and so on, as controls. My notation starts with the initial period in t=1 and xtprobit is based on two periods t=2 and t=3. Unfortunately, my observation period covers the year to which the index is normalised (for all observations nwindex3=100). Hence, Stata excludes nwindex3 due to collinearity. Nwindex2 is still part of the analysis. Until now, I kept the wage index as an time-varying control. Would you suggest to treat the nominal wage index as time-invariant, for example like gender or migration background?
I would really appreciate your opinion!

[Jeff Wooldridge]

The t statistics are just the ratio of the coefficients over the standard errors, and those are both given in the table.

It sounds like treating the nominal wage index as time invariant is a good idea.

[Alina Hackl]

Thanks for your helpful comments, Jeff!

[Pinaki Banerjee]

Hii Prof. Wooldridge,
I am also trying to estimate the same model with a large panel and sigma_u in my case is statistically different is 1.18 (0.021) which is statistically different from 1. Are the estimates ok ?