recursive mixed model (cmp)

[Inma Martinez]

I am trying to estimate a model for a cross-section of firms (pooled cross-section dataset) based on three sequential decisions: 1) To export or not, 2) to export directly or through an intermediary, 3) how much to export indirectly.

I have tried a Heckman, but the main problem is that I have 2 sequential decisions 1) and 2) and I can only include 1 of them in the first step heckman, for exampe 1):

heckman indirectshare2 lemp llabpro foreign transport crime legalfair eu cefta voleuro, select(xd = lemp llabpro foreign eu cefta transport customs crime permit legalfair voleuro ) vce(robust)


Then, I thougt about using cmp with three equations two probits and 1 continouos model, something like:

cmp setup
cmp (xd = lemp llabpro foreign eu cefta transport customs crime permit legalfair voleuro )(indirect = lemp llabpro expintens foreign transport customs crime legalfair eu cefta ) (indirectshare2 =lemp llabpro foreign exint transport customs crime legalfair eu cefta ), indicators($cmp_probit $cmp_probit $cmp_cont) quietly


my question is: is this equivalent to a Heckman with two initial steps or rather to a treatment effect model with (endogenous treatmenet) sequetial decisions? I will be grateful for suggestions whether this is appropriate or there is any other way(s) to model this,
many thanks
Inma

[Alfonso Sánchez-Peñalver]

Hola Inma,

from what you explain you have a heckprob model with your two probits, and then conditional on this, you have the share of indirect exports. Your code for cmp is a bit off in the indicators. Consider

cmp (xd = lemp llabpro foreign eu cefta transport customs crime permit legalfair voleuro)        ///
(indirect = lemp llabpro expintens foreign transport customs crime legalfair eu cefta)    ///
(indirectshare2 =lemp llabpro foreign exint transport customs crime legalfair eu cefta), ///
indicators($cmp_probit xd*$cmp_probit xd*indirect*$cmp_cont) quietly

The products in the indicator fields are to show that the explained variables on those models are conditional on the values of the binary variables. The double product in the last one is because they are conditional on only those that are indirectly exported. If I understood correctly it should be the same as indirect*$cmp_cont because you can only export indirectly if you've decided to export, but just in case. I believe that this will be a difficult model to estimate, so be patient and you may have to tinker with the maximum likelihood options to have it converge.

Suerte Inma!

[Inma Martinez]

Dear Alfonso,
many thanks for your answer. I tried your suggestion but when I use the interactions the model does not converge... I do not get se for most variables. I suppose that if I do not use the conditions I am just assuming that the error terms of the three models are correlated, it is like a SUR?
saludos
Inma

[Alfonso Sánchez-Peñalver]

Yes, without the products in the indicators it's a SUR with three equations. I had a suspicion that it would be difficult to converge. A quick thought. You could do sort of a two step heckman estimation. The first step would be a heckman selection probit, which you can estimate with either heckprobit or cmp. This would estimate the probability of exporting indirectly, which is equal to the probability of exporting and exporting indirectly given that you export. After that you calculate the mills ratio and include it in the estimation of the share. So basically the heckman probit is your selection process.

Another thing, I'm not convinced that a linear model would be the most appropriate to estimate indirectshare2. Is this variable, like its name indicates, a share? As such its fitted value should be bounded between 0 and 100, or 0 and 1 depending on the scale you use. Another thing is that it is hard to assume constant effects of the explanatory variables. The beauty of the two-step procedure is that it allows the estimation of the value equation to be with any type of estimator, not necessarily the maximum likelihood normal estimator. If indirectshare2 is a share, then it's basically a fractional response variable, so I suggest that you read Papke and Wooldridge (1996) to see how to best estimate that variable, if you haven't done so already.

Suerte!!!

Alfonso

Reference
Papke, L.E. and J.M. Wooldridge. 1996. "Econometrics Methods for Fractional Response Models with an Application to 401(K) Pension Plans". Journal of Applied Econometrics, 11(6), pp. 619-632.

[Inma Martinez]

many thanks again for your suggestions. Indeed, I started by estimating a heckman selection model in a first step and a fractional probit (fracreg) in the second step incorporating the inverse mills ratio, as you suggested. However, one referee wrote that he does not think that this is the right methodology and suggested to use a "recursive mixed model", then it when I found the cmp command....

Then, since the cmp does not include fracreg I was trying with a continuous distribution, I also thought about transforming the ratio variable as indicated in Papke and Wooldridge (1996) to make it continuous, but still didn't try.

At first, I thought that the advantage is that the three equations were estimated together with no need to bootstrap the se in the second step.

I think I will try to replicat the heckprobit results with cmp and for the second step I will continue to use fracreg,

muchos saludos y gracias de nuevo,
Inma

[Alfonso Sánchez-Peñalver]

Hola Inma,

I'm not an expert on recursive models, but how I understand them is that they are a system of equations that can be solved recursively. This means that one equation is self determined, i.e. doesn't have any endogenous variables other than the one that needs to be explained, and then using that equation you can determine another one, and with the use of those two equations you can determine the third, and so forth. I guess that your second and third equations are conditional on the other two, and that may make the system recursive in a sense, but I had never thought about it that way. Again, I'm not an expert so I could have been seeing it wrong.

Having said that, I believe that asymptotically there shouldn't be any difference between what you were trying to do with cmp and what we suggested if you were able to estimate a fractional response model with cmp and normality of the errors is a correct assumption. So if the cmp is a recursive estimation, so is this one. However, I really don't want you to go astray in your area of the literature because this is only my humble opinion, and the referee may have had something specific in mind that I'm unaware of.

Now, you mention using fracreg, but i don't know of a Stata command called that way. I'm using Stata 13, is that new in Stata 14? In Stata 13 you can estimate Papke and Wooldridge (1996)'s models with the glm command. Oberhofer and Pfaffermayr (2012) (available http://papers.ssrn.com/sol3/papers.c...act_id=2179865) discuss how. If you want to try and replicate their effort you can find the original data at http://qed.econ.queensu.ca/jae/1996-...ke-wooldridge/ . I know you're super busy, but this could be a good idea, to know if you're using the commands in an appropriate way.

Un saludo igual,

Alfonso

References
Papke, L.E. and J.M. Wooldridge. 1996. "Econometrics Methods for Fractional Response Models with an Application to 401(K) Pension Plans". Journal of Applied Econometrics, 11(6), pp. 619-632.

Oberhofer, H. and M. Pfaffermayr. 2012. "Fractional Response Models - A Replication Exercise of Papke and Wooldridge (1996)". Contemporary Economics, 6(3), pp. 56-64.