Forum: help

RE: Bivariate probit model with sample selection and panel structure [ Reply ]
By: Manuel Berkmann on 2018-04-23 14:22

Hi Arne,

many thanks for your reply (and sorry for the late response!). I appreciate your comments.

a) With regard to the description, I believe you are right. I have two equations, each with a binary DV. The first equation would be the sample selection equation and the second one the outcome equation. Unlike in many sample selection applications, however, the effects in the first stage are of interest as well - and not just a means to test for sample selection.

b) That is indeed still an underresearched issue in the literature. According to Greene, there are ways to estimate such a model. However, I have not found any package that has this feature implemented.

c) That is a valuable hint. As I understand it, the Heckmann approach with the inverse Mills ratio is the traditional approach compared to a simultaneous estimation. But maybe it can be a first step towards the solution.

Thanks again,
Manuel

RE: Bivariate probit model with sample selection and panel structure [ Reply ]
By: Arne Henningsen on 2017-12-31 06:19

[forum:45531]

Hi Manuel

Interesting question! I don't know the answer but I have a few comments that you may find helpful:

a) The description "bivariate probit model with sample selection" may be misleading, because it suggests that you have a sample-selection process in the first stage and a bivariate probit model in the second stage. The sampleSelection package cannot estimate this model specification. However, it seems to me that you want to estimate a sample.selection model, where the dependent variable of the outcome equation is binary, right? The sampleSelection package can estimate this model specification. Is this correctly understood?

b) The sampleSelection package does not implement any specifications for panel data. As the number of time periods T is quite small in most data sets, fixed-effects specifications would usually give inconsistent estimates (as consistency requires that T approaches infinity). As the unobserved individual effects are usually correlated with the explanatory variables, random-effects specifications, would usually also give inconsistent estimates. I suggest that you screen the scientific literature and check whether there exist any estimators for panel-data sample-selection models (with binary dependent outcome variable).

c) I am not sure whether a two-step estimation of (two) linear probability models with fixed effects (e.g., using the "plm" package), where the inverse Mills ratio derived from the first stage is used as an additional explanatory variable in the second stage, would give consistent estimates of the parameters. (You would need to correct the standard errors of the estimates.) I suggest that you consult the scientific literature and/or a statistician regarding this.

Best wishes,
Arne

Bivariate probit model with sample selection and panel structure [ Reply ]
By: Manuel Berkmann on 2017-11-16 10:01

[forum:45463]

Dear all,

The model I would like to estimate is a bivariate probit model with sample selection and panel structure.

To give a bit more background:

- I have panel data set of sales reps' customer visits over time
- There are two dependent variables: 1) Did the sales rep generate a lead during the visit? and 2) Given a lead was generated, was it successful or not?
- Given the non-linear nature of my two outcomes, I require a probit or logit specification.
- The panel structure (multiple observations per sales rep over time) requires the specification of a random (or fixed) effect.
- The errors of the two DVs are likely to be correlated, so I believe I need a sample selection approach (e.g. Tobit II) to control for this.

So far, I have tried the following:
1) Run two separate panel data models with random effects (clustering at sales rep ID) using the "glmmML" package.
2) Run a Tobit type II sample selection model using the "sampleSelection" package.

Both model work well. Yet, I was not able to combine the two. Can anyone recommend a way to estimate such a model? Does "sampleSelection" offer the option to include random effects?

Thanks for your answers.
Best, Manuel