Andrew M. Jones 597households who never purchase tobacco. To deal with the remaining zeros, they
compare specifications based on infrequency of purchase and on censoring. GMM
and systems-GMM are used to deal with errors-in-variables and unobservable
heterogeneity (Arellano and Bond, 1991; Bover and Arellano, 1997). Within-groups
two-step, within-groups three-step GMM and MD methods are used to allow for
censoring. To reduce the influence of distributional assumptions they adopt a
semiparametric approach to estimate each of theTcross-section equations using
Powell (1986) symmetrically censored least squares (SCLS). There is evidence that
the rational addiction specification is sensitive to unobservable heterogeneity and
censoring and the results suggest that failure to account for heterogeneity may lead
to overestimates of the impact of addiction. The panel data estimators imply that
behavior is more forward-looking than suggested by the results that fail to correct
for heterogeneity.
12.5.2.3 Finite mixture models
Deb (2001) applies a random effects probit model in which the distribution of the
individual effect is approximated by a discrete density. This is an example of a
finite mixture model and it relaxes the normality assumption for the distribution
of the random effects. Deb uses Monte Carlo experiments to assess the small sample
properties of the estimator. These show that only 3–4 points of support are required
for the discrete density to mimic normal and chi-square densities and to provide
approximately unbiased estimates of the structural parameters and the variance
of the individual effects. Deb applies the model to a cross-section of individuals
clustered in families, where the random effect represents unobserved family effects.
It is assumed therefore that all individuals in each family belong to the same latent
class. This approach aims to approximate the distribution of the random (family)
intercepts, whereas the responses to the explanatory variables are not allowed to
vary across latent classes. Clarket al.(2005) develop a latent class ordered probit
model for reported well-being, in which individual time invariant heterogeneity is
allowed both in the intercept and in the income effect.
12.5.3 Applications with count data
12.5.3.1 Poisson/log-normal mixtures
Winkelmann (2004a) proposes an alternative two-part, or hurdle, model based on a
Poisson/log-normal mixture rather than the usual negative binomial (Negbin) vari-
ants. Hurdle, or two-part, models make a distinction between the decision to seek
care, modeled as a binary choice, and the conditional number of visits, modeled
as a truncated count data regression. They are the most widely used specification
in the recent applied literature (see, e.g., Alvarez and Delgado, 2002; Chang and
Trivedi, 2003; Sarma and Simpson, 2006; Yenet al.,2001), although Santos Silva
and Windmeijer (2001) have pointed out that they may be problematic in appli-
cations where it cannot be assumed that there is a single spell of illness for each
period of observation in the data. Winkelmann’s (2004a) model leads to a probit
equation for the first hurdle and a truncated Poisson/log-normal model for the
second. Unlike the Negbin model, the latter does not have a closed form and is