Bootstrapping multinomial logit model with endogenous predictor using control function approach

[Max Schaub]

Dear Statalist,

I want to estimate a multinomial logit model where one of the predictors is likely endogenous. I thought of pursuing a control function approach instrumenting the endogenous predictor in a first step using OLS, and then including the residuals in the second-step, multinomial response model (as described in Petrin and Train 2010, cp. Wooldrigde 2010).

I wonder, however, how to best estimate the standard errors. The recommended way of doing so seems to be to use bootstrapping, but I am not sure whether the procedure below is correct.

As a – heavily constructed – MWE, imagine that in the auto data set, repair record (rep78, recoded as y) is a nominal response variable, weight (recoded as x) is our endogenous predictor, length (recoded as z) is the instrument, and headroom is an additional exogenous predictor. What I have in mind is to do the following:

sysuse auto, clear
rename rep78  y
rename weight  x
rename length  z
 
* Control function approach:
reg x z headroom                        // first stage
predict x_res, residuals               // cf
mlogit y x headroom x_res          //second stage

* Now, to correct for the uncertainty introduced by estimating the first stage, I thought of doing:
 
program bsses
            reg x z headroom                                    
            predict x_res, residuals                      
            mlogit y x headroom x_res                      
            drop x_res
end program
 
bootstrap, reps(1000): bsses

My question is: will this procedure (i.e. bootstrapping the whole program) lead to a reasonable estimate of the standard errors for the multinomial logit model?

Any help would be much appreciated,

Max

Refs:
Petrin, Amil, and Kenneth Train. 2010. ‘A Control Function Approach to Endogeneity in Consumer Choice Models’. Journal of Marketing Research 47 (1): 3–13.
Wooldridge, Jeffrey M. 2010. Econometric Analysis of Cross Section and Panel Data. Cambridge; London: The MIT Press.

[Jeff Wooldridge]

Yes, this will work.

JW

[Steph Ki]

Dear Statalist,

I estimate a logit model where the dependent variable is a dummy (0, 1) and the predictor also is a binary variable that is likely endogenous (simultaneity problem). I attempt to perform IV estimation, that is first regress my endogenous varaible (binary) on one excluded instrument (that takes values 1, 2, 3, 4 and 5) and control variables (age, age square, living location-rural or urban-, gender...) using logit. And second, regress the dummy dependent variable on the fitted probabilities that replace the endogenous regressor, using again logit.

However, it seems that, that is not the correct way to perform IV estimation with a dummy dependent variable and binary endogenous regressor.

I wonder whether I can use the two-step estimator, that is first regress the binary endogenous regressor on the excluded instrument and control variables using logit or probit. And then regress the dummy dependent variable on the fitted probabilities as excuded instrument adding control variables through two-satge least squares.

Or, can I just use ivreg2 command of stata to perform the IV estimation?

Many thanks in advance

Steph

[Carlo Lazzaro]

Steph:
for the future, please start a new thread, as yours has little to do with title of te original post. Thanks.
As an aside, please read the FAQ about how to post effectively (you're seemingly asking for help about Stata codes and results nobody can see). Thanks.

[Steph Ki]

Dear Lazzaro,
Thank you very much for your suggestion.

King regards,
Steph

[Max Schaub]

Dear Jeffrey, thank you very much for your reply!
(And sorry for my late response.)
Kind regards,
Max

[Maria Ferreyra]

Hi,

I would like to ask a follow-up question to Prof. Wooldridge's answer.

I have a problem similar to the one posed by Max Schaub (multinomial logit model with EEV), except that my EEV is binary.

Is the control function approach still appropriate?

Thank you very much,

Maria

[Mehwish Ali]

Hi steph aarsman

Im wondering if you found a solution to your problem and if you share the link incase you shared the problem in a seperate post?