Palgrave Handbook of Econometrics: Applied Econometrics

William Greene 523

Table 11.6 Estimated marginal effects: pooled model

HSAT Age Income Kids Education Married Working

0 0.0006 −0.0061 −0.0020 −0.0012 −0.0009 −0.0046

1 0.0003 −0.0031 −0.0010 −0.0006 −0.0004 −0.0023

2 0.0008 −0.0072 −0.0024 −0.0014 −0.0010 −0.0053

3 0.0012 −0.0113 −0.0038 −0.0021 −0.0016 −0.0083

4 0.0012 −0.0111 −0.0037 −0.0021 −0.0016 −0.0080

5 0.0024 −0.0231 −0.0078 −0.0044 −0.0033 −0.0163

6 0.0008 −0.0073 −0.0025 −0.0014 −0.0010 −0.0050

7 0.0003 −0.0024 −0.0009 −0.0005 −0.0003 −0.0012

8 −0.0019 0.0184 0.0061 0.0035 0.0026 0.0136

9 −0.0021 0.0198 0.0066 0.0037 0.0028 0.0141

10 −0.0035 0.0336 0.0114 0.0063 0.0047 0.0233

a variety of complications in survey data. The latent regression underlying their
ordered probit model is:

h∗it=x′itβ+H′i,t− 1 γ+αi+εit,

wherexitincludes marital status, race, education, household size, age, income,
and the number of children in the household. The lagged value,Hi,t− 1 , is a set of
binary variables for the observed health status in the previous period. In this case,
the lagged values capture state dependence, as the assumption that the health
outcome is redrawn randomly in each period is inconsistent with evident runs
in the data. The initial formulation of the regression is a fixed effects model. To
control for the possible correlation between the effects,αi, and the regressors, and
the initial conditions problem that helps to explain the state dependence, they use
a hybrid of Mundlak’s (1978) correction and a suggestion by Wooldridge (2002b)
for modeling the initial conditions:

αi=α 0 +x′α 1 +H′i,1δ+ui,

whereuiis exogenous. Inserting the second equation into the first produces a
random effects model that can be fitted using Butler and Moffitt’s (1982) quadrature
method.

11.6 Models for counts

A model that is often used for interarrival times at such facilities as a telephone
switch, an ATM machine, or at the service window of a bank or gasoline station, is
theexponential model:

f(t)=θexp(−θt), t≥0,θ>0,

where the continuous variable,t, is the time between arrivals. The expected inter-
arrival time in this distribution isE[t]=1/θ. Consider the number of arrivals,y,