Public-PRIVATE Pay Differentials
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(2)
'
ln w2,i = X2,i β2 +ε2,i
where Xi is a matrix of explanatory variables, β the vector of corresponding
coefficients to be estimated and ε the error term. Henceforth, the index j = 1,2
refers to public and private sector, respectively.
In general, simple OLS of equations (1) and (2) may lead to inconsistent
estimates. First, OLS estimates are prone to suffer from sample selection bias due
to the exclusion of non-participants in the labour force. If the participation decision
is systematic the pool of employees is non-random. This problem is commonly
addressed by including an additional regressor which corrects for the bias in the
participation decision (Heckman 1979). Second, given the participation decision,
individuals have to decide in which sector to work. Again, if the assignment to
public or private employment is non-random, OLS estimates are biased and a
further correction term for this type of self-selection is required (Maddala 1983,
Maddala and Nelson 1975). The recent literature on public-private sector earning
differentials has mainly accounted for the latter and widely ignored the former.3
However, controlling for one type of selection in earnings equations only and
ignoring non-labour force participants may still lead to biased estimates.
Hence, this section will closely follow an approach by Co et al. (1999) used to
study self-employment decisions, adjusting for multiple selection types. In order
to test, and potentially account for, both types of selection, a double sample
selection model can be fitted (Tunali 1986). Let the reduced form participation and
sector choice equations be determined by
Pi* = Zi'γ + ui
(3)
(4)
*
Si = Bμ+vi
where P* and S* are latent variables, Z and B the vectors of characteristics, γ and
μ the coefficients to be estimated and μiand νi the error terms for participation and
sector respectively.
An individual will participate in the labour market if the utility of participation
exceeds the gain of non-participation. Similarly, individuals will choose the public
sector if the expected earnings differential is positive and/or personal preferences
for public sector employment are strong. These preferences may be correlated
3 The only exception the author is aware of is Stillman (2000) in a study on the Russian labour
market.