the regression analysis but included when examining how nonprot employment is distributed across industries and occupations.
17
The econometric models also control for a quadratic in age and dummy variables for education high school dropout, high school graduate, some college, college grad-
uate, graduate degree, marital status currently married, previously married, never married, race white, black, other nonwhite, Hispanic origin, sex, metropolitan area
residence, and the survey year. Some specications add regressors for work hours and the industry and occupation of the ‘‘main’’ job.
As shown in Appendix Table B1, variable means are similar for the cross-sectional and panel samples. The main differences are that the second group earn more and
are older, more likely to be married, and to live in metropolitan areas. These dispari- ties probably reect patterns of mobility and employment stability.
V. Theoretical Framework
This section provides a model of nonprot wage differentials in a com- petitive labor market without turnover costs and then considers mobility between non-
prot and for-prot jobs. For simplicity, we abstract from many important consider- ations labor contracts, for example inuencing the adjustment to a new equilibrium.
Assume the utility U that individual i receives from working for employer j at time t depends on wages W, possibly some additional benet from holding a non-
prot position N , and other compensating differentials related to job characteristics or nonwage payments Z, according to the additive separable function:
1 U
ijt
5 W
ijt
1 cN
ijt
1 dZ
ijt
, where the wage coefcient has been normalized to one.
The wages enterprise j is willing to pay are characterized by: 2
W
ijt
5 G
it
1 gN
ijt
1 dZ
ijt
1 e
ijt
, where G represents individual determinants affecting earnings across all employers
such as general human capital; g is a market differential associated with nonprot status; d represents the effect of job characteristics or other compensating differen-
tials; and e is a random variable indicating person-enterprise-time specic determi- nants of wages such as specic-human capital, worker-rm job matches, idiosyn-
cratic employer payments, or macroeconomic shocks.
With competitive labor markets, no job will be systematically preferred to any other. This occurs if g 5 2c, d 5 2d, and Ee
ijt
5 0, as can be seen by substituting Equation 2 into Equation 1, with the parameter restrictions, to obtain:
1¢ U
ijt
5 G
it
1 e
ijt
, implying that that E[U
ijt
] 5 G
it
for all j, with E[.] the expectations operator.
18
17. Persons employed in government jobs in either Years 1 or 2 are excluded from the panel sample. In preliminary work, we estimated models that included government workers and directly controlled for public
sector employment. Doing so had little effect on the estimated nonpro t differentials. 18. This does not mean that individuals will be indifferent across jobs. For instance, specic-human capital
or match quality can vary, implying the position held last period will generally be preferred over others.
Denoting the best available for-prot and nonprot jobs with the subscripts p and n
, utility is maximized by choosing nonprot employment if 3
W
ipt
1 dZ
ipt
, W
int
1 c 1 dZ
int
or 3¢
W
ipt
2 W
int
, c 1 dZ
int
2 Z
ipt
, and by working in a for-prot company if the inequality is reversed.
Competition equalizes expected utility across the two types of jobs. Averaging across workers, this occurs when:
4 E
[W ¯
pt
2 W ¯
nt
] 5 c 1 dE[Z¯
nt
2 Z¯
pt
], where W
¯ and Z¯ represent economy-wide average values of wages or job characteris- tics.
19
Equation 4 demonstrates that nonprot enterprises will tend to pay less than prot-seeking rms if workers are willing to ‘‘donate’’ labor to them c . 0 or
they offer other positive compensating differentials Z¯
nt
2 Z¯
pt
. 0. Conversely, wage equalization suggests that there is no labor donation to nonprots and no difference in
average working conditions, or that the two effects exactly offset each other. Impor- tantly, identical predicted earnings, after controlling for Z
ijt
, suggests an absence of labor donations.
Next consider economically motivated switches from for-prot employment in period one to nonprot jobs at time two. If there are no turnover or contracting costs,
such moves occur if: 5
U
ip 1
2 U
in 1
. 0 . U
ip 2
2 U
in 2
, where U
ipt
and U
int
represent the utility to individual i of the best available for-prot and nonprot jobs at time t. Rearranging these relationships, this mobility takes place
if: 6
U
in 2
2 U
in 1
. U
in 2
2 U
ip 1
. U
ip 2
2 U
ip 1
.
20
One requirement for this is that the utility of nonprot employment must rise by a larger amount than the change in prot-seeking rms.
It is useful to distinguish two types of mobility. Utility-enhancing moves reect unusually good opportunities that pull the worker into the nonprot sector. In this
case, U
in 2
2 U
ip 1
. 0. Conversely, defensive transitions involve a loss of utility U
in 2
2 U
ip 1
, 0 but prevent a still larger reduction for instance due to loss of specic human capital or a good job match following an involuntary layoff that
would occur if the individual remained in for-prot employment.
21
One implication,
19. Implicitly Equation 4 also requires that the pure utility effect of nonpro t employment c is the same across individuals and time periods. This assumption can easily be relaxed.
20. The corresponding condition for nonpro t to for-prot mobility is: U
ip 2
2 U
ip 1
. U
ip 2
2 U
in 1
. U
in 2
2 U
in 1
. 21. The situation is analogous for moves from nonpro t to for-prot employment.
relevant in the econometric analysis below, is that e
in 2
2 e
ip 1
will be positive for the rst type of mobility and negative for the second.
22
VI. Empirical Methods
