Interaction terms in Hausman-Taylor estimator or Mundlak/Chamberlain estimator

[Sofia Svensson]

Hi everyone,

I want to estimate the effect of giving informal care to a parent on labor supply (hours worked and employment probability). I'm also interested if the effect has changed over the time in my sample (I have panel data with N=6556 and T=4). Since i suspect the care variable (which is binary) to be correlated with the individual fixed effects I cannot use the RE estimator. The fixed effects estimator however drops most of my observations in the linear regression and does not run at all in the logit regression (STATA says "not concave").

So, following previous research I decided to proceed with the Mundlak/Chamberlain approach to be able to use the RE estimator but allow for correlation with the individual fixed effects. However, STATA does not accept that I ad the interaction variable 1.care#c.year. I have the same issue when I want to use the Hausman-Taylor estimator.

Is this simply not statistically computable or is there a way around it? And if not, is there Another way I can estimate these effects?

The regressions I want to run are:

mundlak lnhours care woman married highed age year badhealth 1.care#c.year
mundlak employed care woman married highed age year badhealth 1.care#c.year

xthtaylor lnhours care woman married highed age year badhealth 1.care#c.year , endog(care highed)
xthtaylor employed care woman married highed age year badhealth 1.care#c.year , endog(care highed)

Also, does the mundlak estimator automatically use an estimator for binary models for the employment regression?

Thanks in advance,

Sofia

[daniel klein]

Sofia,

I can only provide a few hints.

First note that the two proposed models are actually different from each other. The Correlated-random-effects (Mundlak) model is not primarily motivated by instrumenting endogenous predictors, as is the Hausman-Taylor estimator implemented in xthtaylor. Which model is better suited, I cannot tell.

Note also that the former basically relies on decomposing the variances of a given predictor into a within-unit and between-unit specific part. The within estimates resemble the fixed-effects estimates. However, the between-estimates are not consistent if the predictors are correlated with the (unobserved) unit fixed-effects. So if you cannot obtain estimates in a fixed-effects framework (and you did not provide enough information on why this is the case), you are unlikely to get (consistent) estimates from the Mundlak model.

Third, introducing interaction terms in a model as the one discussed above is not as trivial as it seems (although it is not very hard, either). Please see Schunck (2013) for a discussion of how to do so.

Technically, note that mundlak is a user-written command (from SSC) and requires Stata version 8 - long before factor variable notation was introduced. It seems that xthtaylor does not allow factor variable notation, either.

It is further important to note that neither mundlak nor xthtaylor will somehow switch to a logit (or more general non-linear) model internally. Both estimate linear models.

For related discussions see this thread.

Best
Daniel


Schunck, Reinhard. (2013). Within and between estimates in random-effects models: Advantages and drawbacks of correlated random effects and hybrid models.The Stata Journal, 13(1):65-76.

[Sofia Svensson]

Thanks for the pointers Daniel,

I'm gonna try to work it out from here.

Sofia