st: Does the fixed-effect fractional response model require BALANCED panel?

[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 fractional
logit/probit model developed by Papke and Wooldrigde (1996). As I have
panel data, I further want to account for fixed effects using the
panel fractional response method proposed by Papke and Wooldridge
(2008). This approach has been applied in papers such as Wagner (2008)
and Eickelpasch and Vogel (2009), and is also recommended in a related
thread by Prof. Jenkins at
http://www.stata.com/statalist/archive/2009-04/msg00114.html.

However, I have questions on the applicability of panel fractional
response model. While Wagner (2008) and Eickelpasch and Vogel (2009)
adopt this approach, they emphasize that "The data need not cover the
whole population, but they must form a balanced panel data set with
complete information on all variables in each year for each firm."
(Wagner 2008, pp. 3, see Eickelpasch and Vogel, 2009, pp. 10 for
similar statement.) My understanding on Papke and Wooldridge (2008)'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.

I have carefully checked the paper Papke and Wooldridge (2008) but
didn't find any explicit description on data requirement, except that
"The nonlinear models we apply are difficult to extend to unbalanced
panel data – a topic for future research." on section 5, pp. 127. But
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.

In sum, my questions are:
1. Is the fixed effects fractional probit only applicable on balanced
panel? Why?

2. 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:
Eickelpasch, A. and Vogel, A. (2009). Determinants of Export Behaviour
of German Business Services Companies. DIW
    Berlin Discussion Paper No. 876.

Papke, L. E. and Wooldridge, J. M. (1996). Econometric Methods for
Fractional Response Variables with an Application to
    401 (k) Plan Participation Rates. Journal of Applied Econometrics,
11(6): 619–632.
—— (2008). Panel Data Methods for Fractional Response Variables with
an Application to Test Pass Rates. Journal of
    Econometrics, 145(1-2): 121–133.

Wagner, J. (2008). Exports and Firm Characteristics õ First Evidence
from Fractional Probit Panel Estimates. Working
    Paper Series in Economics, Leuphana University of Ljneburg, 97.

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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