Endogeneity in Multinomial Logit model

[Martin Dombrowki]

Hello,
I am trying to estimate Durational Multinomial Logit model and it feels like one of the explanatory variables is endogenous. Therefore, I would like to ask:
1. Is there any way to test it?
2. How to address this issue? (I have an instrument with questionable validity)

Any help will be appreciated
Thanks!

[Jeff Wooldridge]

Martin: Testing is actually pretty easy. What is the nature of the EEV? Continuous? Binary? Something else? Let me know and I think I can suggest something. JW

[Martin Dombrowki]

Dear Pr. Wooldridge

The idea is that I have a model of employment duration where I use distance (continuous) as an explanatory variable. This distance might be affected by unobserved ability. In principle, I was thinking to instrument it by the shortest distance between individual place of residence and organization of the same sectoral profile i.e. calculate predicted values for distance on the first step using OLS and plug predicted values into Multinomial Logit. But it feels like it would not allow me to eliminate the problem of endogeneity. Pr.Angelo Guevara proposes to apply Control Function or Multiple Indicator Solution but I guess there is no relevant routine in Stata. My data represents individual records over 10 years.

[Jeff Wooldridge]

So you will use something like log(distance), which can be treated as continuous. I second the idea of using a control function approach. You just have to insert the residuals from the first stage into the second stage problem. This always works as a test. In a recent Journal of Econometrics paper (2014, "Quasi-Maximum Likelihood Estimation and Testing for Nonlinear Models with Endogenous Explanatory Variables," Journal of Econometrics 182, 226-234) I argue that it can be used generally as an approximation, or an exact solution if one simply assumes the model holds conditional on the control function. There is precedent cited in my paper. Also, I've been pushing this in NBER Lecture notes with Guido Imbens, that are available on various sites. I hope this helps.

The two-step procedure is easy to implement in Stata. A similar approach is illustrated here:

http://www.stata.com/meeting/chicago...wooldridge.pdf

[Martin Dombrowki]

Thank you, your answer is very helpful. In the same time, I have another question. Application of CF would anyway require a possession of the strong and valid instrument. So is there any way to test the exogeneity and weakness of the instrument in particular setting?
Thanks,
Martin

[Jeff Wooldridge]

Martin: You can use the usual diagnostics in the first-stage regression. With one IV, you are looking for a first-stage t stat of around sqrt(10) or larger. (First-stage F >= 10.) I don't think anyone has systematically discussed weak instruments in the kinds of nonlinear models you are interested in, but it's a start. With one IV, you cannot test whether it is exogenous. You'd need to collect another, and then you can only test the overid restriction.

[Benjamin Hammer]

Dear all,

I have a follow-up to this conversation. My problem is similar to the one outlined by Martin except that I consider using a competing risks survival framework rather than a multinomial logit (in order to account for censored observations in the sample). I was wondering whether the control function approach is still the best thing to do? What do you think?

I would highly appreciate any thoughts on this issue! Many thanks in advance!

Best,

Benjamin

[Corine Ngomi]

Hello,

Please I urgently need help.
I estimated a logistic regression where my dependent variable is dichotomous. But one of my independent variables (Income) I suspect is endegenous. how can i solve this endogeneity problem without completely changing my analysis? I know IV is one of the best remedies for this. but given that i carried out primary survey and could not possibly find valid instruments, what can i do? please help me. my econometrics knowledge is very limited.

Thank you

[Raymond Frempong]

Martin: You can use the usual diagnostics in the first-stage regression. With one IV, you are looking for a first-stage t stat of around sqrt(10) or larger. (First-stage F >= 10.) I don't think anyone has systematically discussed weak instruments in the kinds of nonlinear models you are interested in, but it's a start. With one IV, you cannot test whether it is exogenous. You'd need to collect another, and then you can only test the overid restriction.

Thank you for the suggestion. Please, in implementing the two-step procedure, does one need to use the built in Stata routines for mlogit (second stage) .and probit/reg(first stage), or we need to write a new Q-MLE command. if the latter could you show where I can get help.

Thank you

[Ikechukwu Nwaka]

Jeff Wooldridge is there a way of estimating an IV model such as having an outcome variable that is binary and an endogenous variable that in 4 levels. Example, I am estimating the probability of being Self-employed (versus non) using several covariates where the endogenous variable captures levels of cultural diversity ie fractionalization index of four levels.