Average Partial Effects (APE) after Dynamic Probit Model ala (Wooldridge, 2005)

[Soumyadeb Chatterjee]

I am trying to calculate the average partial effects of the state dependence and some other covariates after running a dynamic probit model. I am mainly following Wooldridge (2005), Contoyannis et al (2004), Capellari and Jenkins (2009), and Skrodal et al (2013). Assuming my model to be similar to the above papers, I am running

global var varlist           /*Covariate list*/
global var_mean varlist           /*Longitudinal Mean of $var */
global var_0 varlist           /*Initial observed values of $var */

meprobit y i.year y_0 $var_mean $var_0 $var y_lag z_lag || id: , intpoints(12)

z_lag is treatment whose effect I want to extract from the state dependence y_lag. Now I want to study the average partial effects of z_lag & y_lag on the predicted values of y. Following Wooldridge (2005), Contoyannis writes;

In this case the partial effects are averaged over the population distribution of heterogeneity and computed using the population averaged parameters ... Wooldridge shows that computing the partial effect at the observed values of the regressors for each observation and averaging the estimates over the observations provides a consistent estimate of the APE

From my understanding, this what is done by the "margins, dydx()" command after the meprobit. I want to confirm that I am correct in assuming that the following code will calculate the APE of y_lage and z_lag on the outcome, as calculated by Wooldridge and Contoyannis

margins, dydx(y_lag z_lag) nose

Thanks
Soumya

[Alfonso Sánchez-Peñalver]

Couple of comments. First, if you cite something you have to provide the references because just citing doesn't mean we know what you're referring to. Second, your estimation does a random effects probit estimation, not a random parameters probit estimation. This means that you're estimating a random intercept not a random slope, which means that all the slopes you're estimating are fixed, and thus an APE or a partial effect at the mean are the only thing you can estimate on those variables.

[Stephen Jenkins]

#1: (1) you cannot use margins in this case. For an explanation of how Cappellari and Jenkins derived their "marginal effects", see pages 603-604 of their article (Modeling low income transitions, Journal of Applied Econometrics 19: 593–610, 2004) Having a lagged dependent variable adds additional complications.
(2) please read the Forum FAQ and note well the injunction to provide full bibliographic references. (How can you expect readers of this multidisciplinary list to know the articles you are citing; how can they help you if they don't know what you're referring to?

[Soumyadeb Chatterjee]

I sincerely apologize for not adding the bibliographic references or links to the articles I cite, Wooldridge (2005), Contoyannis (2004), Capellari and Jenkins (2009), and Skrondal (2013). Thank you both for your comments and suggestions.

Stephen Jenkins Professor, I have a follow-up inquiry. I need some help understanding why margins will not work after the meprobit for this case. I understand the issues that a lagged dependent variable might create but in Dr. Wooldridge's paper (linked above), pages 47-48, he explains how one might calculate the APE for the dynamic model. From my understanding of his procedure, I think this is what he suggests (for a simplified panel probit regression)

meprobit y ylag x xbar y0 x0 || id:      /*xbar is the within mean, y0 and x0 are initial observed values*/
predict xbhat, xb
gen xbhata=xbhat/sqrt(1+e(sigma_u)^2)
gen scale=normalden(xbhata)
gen b1=_b[x]/sqrt(1+e(sigma_u)^2)
gen pe1=b1*scale
summarize pe1
return scalar apex=r(mean)

This is what I wanted to ask,
1) Do you think the above code does what Dr. Wooldridge suggests in his paper for calculating the APE?
2) If it is correct, can the margins command be somehow tweaked to do this? I want to do this with margins is to get the standard errors. Otherwise, I think I will have to bootstrap the above code to produce the s.e.

Thank you so much for putting in the time to helping me out.
Soumya

[Stephen Jenkins]

Sorry, but I do not have the time to look at this because of my other commitments.

[Soumyadeb Chatterjee]

Thank you, Dr. Jenkins.

[Nick Cox]

Cross-posted at https://stackoverflow.com/questions/...idge-2005-in-s

Please note our policy on cross-posting -- explicit at https://www.statalist.org/forums/help#crossposting -- which is that you tell us about it.

[Soumyadeb Chatterjee]

I am embarrassed to have missed so many Statalist policies.