Public-PRIVATE Pay Differentials
317
Eventually, given the predicted wages, a structural switching regression
_ * _ . ʌ . ʌ ’ ⅛ , - _ .
S = δ(lnwι,i - In w⅛,i ) + Biμ + vi (12)
can be estimated, where v* = δ(ε1i - ε2,i ) - vi and ln w1,i and ln w2,i are the
predicted wages for the public and private sector respectively (Maddala 1983, van
der Gaag and Vijverberg 1988 and Hartog and Oesterbeek 1993). For public sector
workers the private sector wage is a counterfactual and vice versa for private
sector employees.
Table 6 reports the marginal effects of both the reduced form (4) and the
structural switching regression (12) which takes expected earnings differences in
the sector choice explicitly into consideration. The vector of regressors is identical
to equation (4) except that the difference in expected predicted wages in the public
and private sector for an employee have been included as an instrumental variable.
Again, predicted wages are based on the single selection correction specification
for sector choice and simple OLS for males and females respectively.17
This specification requires some remarks. Equation (12) contains two estimated
regressors. Lee (1979) showed that the resulting coefficients δ and μ are consistent.
However, the standard errors are incorrect and need to be adjusted (Maddala
1983). Rather than recovering the corrected variance-covariance matrix,
bootstrapping is applied once more as described above.
Furthermore, recall that the set of characteristics for wage equation and sector
choice are identical except for the two variables on union membership and union
perception. Hence, the potential wage differential is already implicitly included in
the reduced form probit estimations. Yet, explicitly including the estimated
wage gap will have two effects. First, since the earnings difference is a non-
linear construct it will substitute for higher order terms. However, since all but
one regressor are dummy variables and the only continuous variable is tenure
which is included in both as a first and second order term, this should be of
lesser concern. Secondly, it will net-out the earnings effect from the coefficients
and the remaining effect can be seen as everything that impacts on the sector
choice except earnings.
17 Note, however, that the main results are not sensitive against the model specification used to
predict the expected wages. For example, the double sample selection specification for males
yields almost exactly the same results as the single sample selection one.