xtivreg and changing the first-stage model

[Tunga Kantarci]

I am using xtivreg. I have two endogenous variables. Both are dummy variables. This means that xtivreg is considering two first stage regressions. Both regressions imply a linear probability model since the endogenous variables are dummy variables. In one of the two first stage regressions, one of the regressors has a coefficient larger than one. This seems implausible since in a linear probability model the coefficients should be between zero and one (in particular, the coefficient of the first order 'age' term when I consider a continous cubic age function). This seems to suggest that I should change the first stage linear probability model, perhaps to a probit model. As far as I am aware, Stata does not allow me to do this. Or does it, and otherwise is there a way I could deal with the problem?

Meanwhile, I assume that I am right that xtivreg is estimating a lienar probability model in the first stage if the endogenous variable is a dummy variable. From Stata's xt manual, unfortunately, it is not so clear to me what model precisely is being estimated in the first stage, which also seems to depend on if the fe or re options are specified. Could you please provide some clues for the first stage model too?

[Tunga Kantarci]

Let me provide further details. My model is a FE-IV model (I carried out the Hausman test which rejected a random effects model, for the main, second stage model). Hence, in the first stage, xtivreg estimates a fixed effects model. The outcome variable of the first stage regression is a dummy variable. Therefore the first stage model implies a linear probability model with fixed effects. I consider a cubic age function, among several other independent variables (instruments), in the first stage. The coefficient to the linear age term takes a value greater than one. Hence it seems I cannot rely on the linear probability model estimation. Therefore I thought of changing the first stage lienar probability model to a logit fixed effects model. However, when I execute xtlogit with the fe option, more than half of the panel units are dropped (although I get an output). But I am not sure how I should proceed.

[Jeff Wooldridge]

You're not thinking of this correctly. Look at a reputable book that covers IV -- for any kind of data, including panel data -- and see if it ever states that the endogenous explanatory variables cannot be binary. It will not. In fact, in my own book, Econometric Analysis of Cross Section and Panel Data, MIT Press, 2010, I emphasize that the nature of the EEVs is unrestricted. IV can used anyway. That the reduced form for the EEV looks like a "linear probability model" is neither here nor there. In fact, it is just a linear projection, and that's always well defined for any kind of variable -- discrete, continuous, or mixed. So you should just use the usual xtivreg. You do not need to use a different first stage.

And it is not necessary for the coefficients in an LPM to be less than unity, anyway. For example, if x ranges between .4 and .6, I very well might expect a coefficient larger than unity on x, even if y is binary.

I hope this helps. The bottom line is, worry about having a convincing IV, and make the choice between FE and RE. And you should make that Hausman test robust. The Stata canned command does not do it.

JW

[Tunga Kantarci]

This indeed helps. I will be considering the robust version of the Hausman test too. Recieving a response from the author of the econometrics book that inspired me to do econometrics... What could one wish for more. Thanks.