Palgrave Handbook of Econometrics: Applied Econometrics

David T. Jacho-Chávez and Pravin K. Trivedi 805

2.00

4.00

6.00

8.00

10.00

12.00

Intercept

0 .2 .4 .6 .8 1

Quantile

–0.20

0.00

0.20

0.40

0.60

=1 if has supplementary private insurance^0 .2 .4 .6 .8^1

Quantile

–0.02

0.00

0.02

0.04

Age

0 .2 .4 .6 .8 1

Quantile

–0.40

–0.20

0.00

0.20

0.40

=1 if female

0 .2 .4 .6 .8 1

Quantile

0.30

0.40

0.50

0.60

0.70

Total number of chronic problems

0 .2 .4 .6 .8 1

Quantile

–0.20

–0.10

0.00

0.10

0.20

0.30

log(income)

0 .2 .4 .6 .8 1

Quantile

Figure 15.4 Coefficients of regressors at various quantiles

15.5.2 Example: finite mixture model

Fully parametric models are popular in microeconometrics even though a para-
metric distributional assumption is an important simplification. There are many
ways of replacing or relaxing this assumption, which may lead to additional com-
putation. Replacing the assumption of a given parametric distribution by the
assumption that the data distribution is a discrete mixture, also called a finite mix-
ture (FM), of two or more distributions, not necessarily from the same family, can
provide additional flexibility (Frühwirth-Schnatter, 2006). The FM representation
is an intuitively attractive representation of heterogeneity in terms of a number of
latent classes, each of which may be regarded as a “type” or a “group.” It has found
numerous applications in health and labor economics and in models of discrete
choice. The FM model is related to latent class analysis (Aitken and Rubin, 1985;
McLachlan and Peel, 2000).
In an FM model a random variable is a draw from an additive mixture ofCdistinct
populations in proportionsπ 1 ,...,πC, where

∑C
j= 1 πj=1,πj^0 (j=1,...,C),
denoted as:

f(yi|)=

C∑− 1

j= 1

πjfj(yi|θj)+πCfC(yi|θC), (15.33)