For any given year, each individual chooses their sector by utility

maximization where the utility of individual i in sector j is represented as follows:

Uij

¼ bj Z

i

þ W

ij

þ v

ij

where Zi is a Lz

��1 vector of observable, exogenous variables for person i in all three

sectors, bj is a 1

��Lz utility parameter vector on the exogenous variables in sector j, Wij is

the log wage of person i in sector j, vij is an independent (across individuals, sectors, years)

and identically normally distributed stochastic component of utility for person i in sector j,

with a mean of zero and a variance equal to rv

j

2

.

The log wage for individual i in sector j is modeled by the following:

Wij

¼ d

j Xj

þ r

j fi

þ u

ij

where Xi is a Lx

��1 vector of observable, exogenous variables for person i that enters all

three sectors, dj is a 1

��Lx vector of parameters on the exogenous variables, fi is a scalar

random factor distributed with a three-point discrete distribution between zero and one

(the variance of fi is represented byrf2), rj is a scalar sector-specific factor loading, uij is an

independent (across individuals, sectors, years, and from fi and vij) and identically

normally distributed stochastic component of utility in sector j for person i, with a mean

of zero and a variance equal to r

2

.