William Greene 549
- See, as well, Hsiao (2003) for a survey of dynamic panel data models and other applica-
tions by van Doorslaer and Nonneman (1987), Wagstaff (1993) and Vella and Verbeek
(1999).
- This is the formulation used by Contoyanniset al.(2004). Wooldridge (2006) suggested,
instead, that the projection be upon all of the data, (xi 1 ,xi 2 ,...). Two major practical
problems with this approach are that, in a model with a large number of regressors,
which is common when using large, elaborate panel data sets, the number of variables
in the resulting model will become excessive. Second, this approach breaks down if the
panel is unbalanced, as it was in the Contoyanniset al.study.
- Becket al.(2001) is a bit different from the others mentioned in that, in their study
of “state failure,” they observe a large sample of countries (147) observed over a fairly
large number of years, 40. As such, they are able to formulate their models in such a
way that makes the asymptotics with respect toTappropriate. They can analyze the
data essentially in a time series framework. Sepanski (2000) is another application which
combines state dependence and the random coefficient specification of Akin, Guilkey
and Sickles (1979).
- Wynand and van Praag (1981) used a two-step procedure similar to Heckman’s (1979)
procedure for the linear model. Applications since then have used the MLE.
- Since the coefficient vectors are assumed to be the same in every period, it is only nec-
essary to normalize one of the diagonal elements inRto 1.0. See Greene (2004a) for
discussion.
- For example, the parameters can be written in terms of a set of latent parameters so that
μ 1 =τ 12 ,μ 2 =τ 12 +τ 22 , etc. Typically, the explicit reparameterization is unnecessary.
- One could argue that this reformulation achieves identification purely “through func-
tional form,” rather than through the theoretical underpinnings of the model. Of course,
this assertion elevates the linear specification to a default position of prominence, which
seems unwarranted. Moreover, arguably the underlying theory (as, in fact, suggested in
passing by Pudney and Shields, 2000)isthat there are different effects of the regressors
on the thresholds and on the underlying utility.
- Cross-section versions of the ordered probit model with individual specific thresholds
appear in Terza (1985), Pudney and Shields (2000) and in Greene (2007a).
- No theory justifies the choice of the log-gamma density. It is essentially the same as a
conjugate prior in Bayesian analysis, chosen for its mathematical convenience.
- The use of the linear index form is a convenience. The random component,ε, could enter
the model in some other form, with no change in the general approach.
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Akin, J., D. Guilkey and R. Sickles (1979) A random coefficient probit model with an
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Albert, J. and S. Chib (1993) Bayesian analysis of binary and polytomous response data.
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