st: Fractional response model for unbalanced panel data

[Jixiang Hu <jixhu.gsm@gmail.com>]

Hi All,

I'm considering to model my outcome variable, which is bounded between
zero and one and with large amount of zeros, using the panel
fractional response model developed by Papke and Wooldrigde (2008)
(P&W hereafter).  But I have questions on the applicability of this
approach on UNBALANCED panel data.

The data used in P&W is balanced and they mentioned that "The
nonlinear models we apply are difficult to extend to unbalanced panel
data – a topic for future research." (on section 5, pp. 127.)  I'm not
sure whether "the nonlinear models" refer to the case with endogenous
RHS variable, or also include the case of strictly exogenous
regressors.

My understanding on P&W's approach, is essentially adding the time
averages for all explanatory variables to the pooled fraction probit
approach, in order to control unobserved fixed effects. This does not
necessarily require balanced panel, as it only uses the time averages
of explanatory variables, instead of the full history on all periods.

As my data is highly unbalanced, I want to know is the fixed effects
fractional probit only applicable on balanced panel? Why?

Further,  if yes, is there any method to extend it to unbalanced
panel? How about the Correlated Random Effect Probit suggested by
Wooldridge (2009)? If I understand correctly, Wooldridge suggests
adding the time averages (Xi_bar) of the covariates, include that of
time dummies to get a FE estimator, and additionally add the number of
available periods for each unit (T_i), and the interactions of T_i and
Xi_bar to get a RE estimator.

References:

Papke, L. E. and Wooldridge, J. M. (2008). Panel Data Methods for
Fractional Response Variables with an Application to Test Pass Rates.
Journal of Econometrics, 145(1-2): 121–133.
Wooldridge, J. M. (2009). Correlated Random Effects Models with
Unbalanced Panels. Manuscript (version July 2009) Michigan State
University.

Thanks very much for any help!

Jixiang Hu

PhD Candidate
Dept. of Applied Economics
Guanghua School of Management, Peking University

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