Palgrave Handbook of Econometrics: Applied Econometrics

William Greene 547

It is difficult to obtain a precise interpretation of the coefficients in the utility
functions. The elasticities of the probabilities of specific outcomes with respect to
changes in the attributes of those and other outcomes are more informative. We
write these:

δ(m)j,l=

∂logPj

∂logxm,l

,

wheremindicates themth attribute,jis the choice probability affected andlis
the choice utility function in whichxm,lchanges. These are given in Table 11.12.
(specific forms of these appear in Greene, 2008a; Hensheret al., 2005). The values
given are averaged over the observations. Note that for the MNL form,δ(m)j,lis
the same for alll. This is the force of the IIA assumptions made at the outset. This
is a motivation for the more elaborate functions considered.

Table 11.12 Estimated elasticities with respect to changes in GC

Effect CG changes in choices:

is on

choice of: Air Train Bus Car

MNL –.0994 MNL .0455 MNL .0210 MNL .0346

Air MNP –.5230 MNP .3060 MNP .1179 MNP .1006

NL(2) .595 NL(2) –.0310 NL(2) –.0200 NL(2) –.0430

HEV –.9158 HEV .3771 HEV .2339 HEV .2144

RPL –.4808 RPL .2361 RPL .1440 RPL .0663

MNL .0435 MNL –.1357 MNL .0210 MNL .0346

Train MNP .3889 MNP –3.4650 MNP 1.1148 MNP .9416

NL(2) –.2440 NL(2) –.2160 NL(2) –.127 NL(2) .5420

HEV .3443 HEV –1.7389 HEV .4105 HEV .4621

RPL .3167 RPL –1.4151 RPL .5715 RPL .2360

MNL .0435 MNL .0455 MNL –.1394 MNL .0346

Bus MNP .2859 MNP 2.454 MNP –4.4750 MNP 1.2686

NL(2) –.2440 NL(2) –.2160 NL(2) .6100 NL(2) –.2900

HEV .4744 HEV 1.2723 HEV –3.1008 HEV .8358

RPL .7109 RPL 1.8434 RPL –2.9242 RPL .3246

MNL .0435 MNL .0455 MNL .0210 MNL –.0982

Car MNP .1113 MNP .8592 MNP .5587 MNP –1.4023

NL(2) –.2440 NL(2) .3940 NL(2) –.1270 NL(2) –.2900

HEV .4133 HEV .8108 HEV .6190 HEV –1.7829

RPL .2489 RPL .6300 RPL .2973 RPL –1.0332

11.8 Summary and conclusions

This chapter has outlined the basic modeling frameworks that are used in analyzing
microeconomic data when the response variable corresponds to a discrete choice.
The essential binary choice model is the foundation for a vast array of applications
and theoretical developments. The full set of results for the fully parametric models
based on the normal distribution, as well as many non- and semiparametric models,