Palgrave Handbook of Econometrics: Applied Econometrics

David T. Jacho-Chávez and Pravin K. Trivedi 791

0.0

0.2

0.4

0.6

Density

30–32 years old

19–26 years old

67891011

log (Average Annual Earnings)

Figure 15.1 Marginal probability density functions

Algorithm 15.4.1.2.1 implements the necessary steps.

Algorithm 15.4.1.2.1 Conditional density estimation – implementation

1. Select functionsk(·)andl(·)in (15.11) and (15.12), and vectors of smooth-
   ing parametershandλby cross-validation maximum likelihood, i.e., select
   [h 1 ,...,hq 1 ,λ 1 ,...,λq 2 ]to minimize:

L[h,λ]=

∑n

j= 1 loĝf−i(x

c

i|x

d

i),

wherêf−i(·)equals (15.14) after replacing

∑n

j= 1 by

∑n

j=1;j=i.

2. Usinghandλfound in the previous step, calculatêf(xci|xdi)in (15.14) for each
   i=1,...,n.


3. Plot (if feasible) or present summary statistics.

Using 453 observations of individual transportation mode choices in Croissant
(2006) (datasetMode), we estimate the conditional joint density of preferred trans-

portation mode’s cost,x 1 , and time,x 2 , given observed choices: car (xd =1),

carpool (xd = 2), bus (xd =3), and rail (xd = 4). The results are shown in
Figure 15.2. The estimated joint p.d.f.s are multi-modal. This might indicate that
other characteristics besides cost influence transportation mode choices.