Heckman's solution to the initial conditions, calculating average partial effects with -redprob-

[Andrew Black]

Hello statalist,

I am estimating a dynamic, random effects probit model and using -redprob-, a module developed by Mark Stewart to do so. I'm wondering if anyone who has used it could tell me how they have calculated the average partial effect? . The model was

reprob belnmw lbelnmw $variables ($instruments), quadrat(10) i(pid) t(n)

where pid is the panel variable and n the time variable. This is all in accordance with the syntax for redprob as detailed here:
http://www2.warwick.ac.uk/fac/soc/ec...edprobnote.pdf

I attempted to use the

 margins, predict(pu0) at(lbelnmw=0) atmeans

command, where lbelnmw is the lagged dependent variable of interest, but I got the following message:

option pu0 not allowed

I assume it is possible to calculate the average partial effects (Mark Stewart does in another paper) as the coefficients don't mean much without them. All I can get is linear predictions, which are not what I want.
Thanks for any help

[Andrew Black]

Sorry, reference for the Mark Stewart paper which uses it: "Stewart, M. B. (2007) The interrelated dynamics of unemployment and low pay. J. Appl. Econometr., 22, 511–531"

[Simon Ihan]

Hi Statalist users,
I've the same problem that Andrew Black has pointed in this post. The code "margins, predict(pu0) atmeans" does not work after the code "redprob". Is there a written STATA code to calculate the average partial effects after "redprob"?
Hi Andrew, did you manage to solve your problem, or has anybody responded to your post?
I'd really appreciate for any help!

[Jeff Wooldridge]

I would suggest a couple of different things. First, the paper by Arulampalam and Stewart (2009), "Simplified Implementation of the Heckman Estimator of the Dynamic Probit Model and a Comparison with Alternative Estimators," Oxford Bulletin of Economics and Statistics, seems to supersede the work by Stewart. They show how the -gllamm- command can be used to estimate Heckman's model.

Second, you can try the approach I proposed in Wooldridge (2005), “Simple Solutions to the Initial Conditions Problem for Dynamic, Nonlinear Panel Data Models with Unobserved Heterogeneity,” Journal of Applied Econometrics 20, 39-54. Computationally, this is much easier than Heckman's approach, and, if done properly it seems to gives similar estimates. This is shown via simulations in Arulampalam and Stewart (2009). Plus, in the Heckman approach one can easily forget to include the entire history of the covariates when modeling the heterogeneity, which can cause severe bias. See the application in Arulampalam and Stewart (2009).

Rabe-Hesketh and Skrondal (2012), "Avoiding biased versions of Wooldridge’s simple solution to the initial conditions problem," Economics Letters 120, 346-349, shows that the biases that can arise from my approach occur because of inappropriate restrictions that are sometimes imposed. If you implement it the way I originally proposed the biases are small. The nice thing is that my approach can be implemented using -xtprobit-, a built-in Stata command, which is of course well supported. Finally, the margins command can be used after xtprobit to obtain the average marginal effects.

[Stephen Jenkins]

Simon: In addition to Jeff's sage advice, I recommend that you get in the habit of searching past Statalist posts (use the Search box above or Google) before you post. See also the Forum FAQ on this..

Closely related issues to your question have been discussed multiple times here; virtually all of which suggest using the "Wooldridge (2005)" approach. For one example, see http://www.statalist.org/forums/foru...ridge-approach.

In addition to the references cited by Jeff, see also A Skrondal & S Rabe-Hesketh, "Handling initial conditions and endogenous covariates in dynamic/transition models for binary data with unobserved heterogeneity", Journal of the Royal Statistical Society, Series C (Applied Statistics), 2014, 63, Part 2, pp. 211–237. A common theme in the papers is that differences between the various estimators of the dynamic random effects probit model are more likely to arise if the panel dataset you have is relatively short. With long panels, the estimates from the various approach (such as Heckman, Wooldridge, or Orme methods for handing the 'initial conditions' problem) tend to be very similar and, also, in my experience having a unbalanced panel rather than balanced panel is not particularly important if the panel is long. (See references in the post I cite, and others referred to there.)

Jeff refers to using xtprobit for fitting the model. Examples are shown in previous posts (as I say above). I would add that there are some advantages to using meprobit instead or as well. E.g. potential to have clustered standard errors, and random slopes as well as a random intercept.