beta regression for panel data

[Marcelo Resende]

The betareg command handles beta regression estimations for cross-sections. Is there any Stata code for beta regression in the context of panel data?

Any suggestion would be welcome

Thanks, Marcelo Resende

[Jared Greathouse]

betareg y x i.unit i.time

[Marcelo Resende]

Thanks, but I´m not sure that manuallly creating fixed effects will have good properties for the estimators. Apparently no xtbetareg command exists or perhaps some random effects alternative. Thanks any way, I willll think more about possibilties

[Jeff Wooldridge]

betareg y x i.unit i.time

This causes an incidental parameters problem and the inference that comes out is very unreliable. And clustering won't help, either.

But Marcelo: What exact do you want to do? Control for heterogeneity correlated with the explanatory variables? You can easily use a correlated random effects approach. But I'd recommend the fractional response probit or logit because it's more robust; doesn't require any particular distribution.

But if you

want to use beta regression with z1 ... zJ not changing over time:

egen x1bar = mean(x1), by(id)
egen x1bar = mean(x1), by(id)
...
egen xKbar = mean(xK), by(id)
beta y x1 ... xK x1bar ... xKbar z1 ... zJ i.year, vce(cluster id)

You can then use margins with respect to the xj. You can compare this with linear fixed effects estimation.

[Jared Greathouse]

I should really know the answer to this, but the reason it creates an incidental parameters problem is because unlike OLS, nonlinear models are consistent, but not unbiased? Jeff Wooldridge

In other words, unlike OLS where the beta converges to the true value as N increases, GLMS are consistent... where the ratio of predictors to observations affects the standard errors, making the coefficients unreliable? I hope I'm saying this correctly.

[Jeff Wooldridge]

If it were only a lack of unbiasedness we could accept that. The problem is the parameter estimators, and resulting average partial effects, are inconsistent as N increases with T fixed. OLS is consistent in this case. Poisson regression is, too. But there aren't any other cases that I know about. Not probit, not logit, not fractional versions of these. And not beta regression, either. If T is "large" then the bias can be small. But even then, calculating valid standard errors is quite difficult.