Title: Fixed Effects in Non-Linear Panel Data Models - Reducing the Bias

Author: Nathan J. Carroll

Affiliation: Department of Economics, University of Regensburg

Abstract:
Ordered discrete dependent variable models such as ordered probit and
ordered logit are frequently used across the social sciences to study out-
comes such as health status, happiness, wealth and educational attain-
ment. When panel data are available we are able to ask questions con-
cerning whether previous experience of an event (e.g. bad health status)
affects the future likelihood of that same event. In panel data settings
the question of how to deal with unobserved individual heterogeneity is
an important one, however this is of even greater concern in non-linear
models such as ordered probit as, unlike in linear models, fixed effects can-
not be differenced away so that they must be estimated. Given a finite
number of periods of the panel estimation of fixed effects will typically
induce bias in estimation of the parameters of interest (this is the inci-
dental parameters problem identified by Neyman and Scott [1948]) and
the bias is particularly problematic when estimating a dynamic model.
Two main routes around this issue have been used in the literature; ap-
plying a random effects approach which requires at least some structure
to be imposed on the individual heterogeneity or continuing to estimate
the fixed effects but making a correction for the bias. Here the focus is on
the second approach. Carro [2007] introduced of the modified maximum
likelihood estimator (MMLE) to reduce the bias for a binary dependent
variable and a single fixed effect per individual Carro and Traferri [2014]
extended the use of the estimator to ordered discrete variables with two
fixed effects per individual. This paper introduces the oglmxFE package
for the R programming language which makes the MMLE estimator func-
tional for a wider class of models by allowing a model for the variance of
the error term to be included and permitting an individual fixed effect to
be included in variance equation. Simulations of the efficacy of the MMLE
approach are included together with an application to the estimation of
hot hand effects in golf tournaments. Furthermore, the package permits
time savings when estimating the MLE with fixed effects when compared
to inclusion of a factor variable in the currently available methods for es-
timation of ordered probit in the R language, this results from use of the
concentrated likelihood in the optimization process.