[Alex Mai]

Dear Stephen,

Thank you very much once more for your comments and the suggestion of literature! Btw, is it appropriate to use the dynamic probit commpand you provided to the case of dynamic logit model?

 
 xtprobit outcome_t  lagged_outcome $predictors $avge_tvar outcome_t_1 if wave > wavefirst, i(pid)

You have mentioned in another post that dynamic probit is more commonly used than dynamic logit model, and Wooldridge argued that it is easier to interpret dynamic probit than dynamic logit.

However, I find that Wooldridge mentioned in his paper in 2005 that

When specialized to the binary response model, the approach here is more flexible, and computationally much simpler: the response probability can have the probit or logit form, strictly exogenous explanatory variables are easily incorporated along with a lagged dependent variable, and standard random effects software can be used to estimate the parameters and averaged effects.

So I am not sure about the use of his dynamic probit to the case of dynamic logit.

[Stephen Jenkins]

Wooldridge is the expert here. I think the approach to handling initial conditions he sets out in his 2005 paper could also be applied to logit models -- as he says in the quotation you report. But why would you want to do so? I don't see any particular gain to using logit over probit. It doesn't particularly help with interpretation of parameter estimates since, as the papers I cite illustrate (as well of course as Wooldridge's paper), interpretation is often not a matter of simply reading off the coefficients. (The lagged depvar complicates things somewhat.) And unless the outcome probability is near one or zero, a logit model is likely to give very similar results to probit. In addition, with probit, one has a closer link with Heckman's approach to handling initial conditions (with a separate model for the first outcome, and errors correlated between that equation and the equation for other year's outcomes -- normality is used to do this.)

[Alex Mai]

Wooldridge is the expert here. I think the approach to handling initial conditions he sets out in his 2005 paper could also be applied to logit models -- as he says in the quotation you report. But why would you want to do so? I don't see any particular gain to using logit over probit. It doesn't particularly help with interpretation of parameter estimates since, as the papers I cite illustrate (as well of course as Wooldridge's paper), interpretation is often not a matter of simply reading off the coefficients. (The lagged depvar complicates things somewhat.) And unless the outcome probability is near one or zero, a logit model is likely to give very similar results to probit. In addition, with probit, one has a closer link with Heckman's approach to handling initial conditions (with a separate model for the first outcome, and errors correlated between that equation and the equation for other year's outcomes -- normality is used to do this.)

Thank you for the comments! Actually, since I have always used static panel logit model in previous regressions of the same research (some of them are fixed-effects logit model), I think it would be better to keep using logit, rather than shifting to probit, in the dynamic setting. Another reason is that I have always chosen to report odds ratios, instead of the original coefficients, but it seems that probit model does not allow to directly report odds ratios as what people do with logit model (simply adding -or- at the end of the command).

May I ask if it is appropriate to interpret the results of dynamic logit model in the same way as interpreting standard static logit model? And why dynamic logit model leads to computationally more difficult estimators than dynamic probit (as suggested by Wooldridge)?

Many thanks once more!

[Stephen Jenkins]

Sorry, but I think I've contributed enough, and am going to bow out now. Please please read the relevant literature in details and digest it. Simply reporting odds ratios is inadequate here, I believe (and not simply for the reasons that are often rehearsed regarding odds ratios). To derive informative interpretations of the model parameters estimates, one has to take account of the presence of the lagged dependent variable. Put differently, you need to think carefully about what you're conditioning on when you think about the 'effect' of any particular covariate.

[Alex Mai]

Dear Stephen,

Thank you very much again for the suggestions! And sorry for taking your time.

[Alex Mai]

Sorry for bothering you again. May I ask a question about deeper lags in dynamic probit model? I have read papers on dynamic probit model, but I think they only discuss the case of introducing the first lag of the dependent variable as a regressor. Do you think if any modifications should be made for the following command when the second lag of the dependent variable is used together with the first lag (besides the addition of second_lagged_outcome)?

   
 xtprobit outcome_t lagged_outcome $predictors $avge_tvar outcome_t_1 if wave > wavefirst, i(pid)

Many thanks!