Public-private sector pay differentials in a devolved Scotland

Journal of Applied Economics

with individual characteristics and captured in B.⁴ Note that the expected earnings
difference is not observable prior to the estimation of the wage equations (1) and
(2). Hence, we will first estimate the reduced sector choice equation to gain
consistent wage estimates and only then the structural switching regression.

Since neither latent variable is observable, two index functions are defined. In
the case of participation this is P_i = 1 if P^* > 0 and P_i = 0 if P^* ≤ 0, where P_i = 1 and
P_i = 0 indicate labour market participation and non-participation respectively.
Similarly, for the reduced sector choice equation S_i = 1 if S^* > 0 and S_i = 0 if S^* ≤ 0,
where S_i = 1 and S_i = 0 indicate public or private sector employment, respectively.
Clearly, S_i = 1 and S_i = 0 are only observed for P_i = 1.

Given the above structure, consistent estimates can be achieved by Maximum
Likelihood Estimation (MLE) (Co et al. 1999). Yet, the number of parameters to be
estimated is rather large. Alternatively, a simple two-step Heckman (1979) approach
with extended correction terms may be adopted (see, e.g., Lee 1979, Ham 1982,
Fishe et al. 1981 and Tunali 1986). In the first, step equations (3) and (4) are estimated
and sample selection correction terms are constructed. In the second step, equations
(1) and (2) are estimated via simple OLS including the correction terms as additional
regressors.

Two cases can be distinguished, ρ_uv = 0 and ρ_uv ≠ 0 where ρ is the error correlation
term between equation (3) and (4) and the former is a special case of the latter.⁵ For
ρ_uv ≠ 0 the approach is to estimate (3) and (4) using a bivariate probit (Ham 1982,
Tunali 1986). In that case (ε_j, u, v) are jointly normally distributed with mean zero
and covariance matrix
where σ_v² and σ_u² are normalised to unity for identification purposes following

⁴ For a more rigorous theoretical derivation see, e.g., van der Gaag and Vijverberg (1988).

⁵ In the extreme case where the participation and sector choice depend solely on the difference
between reservation wage and either public or private sector wage the decision to participate
and the sector choice are indeed simultaneous. Yet, the two decisions are likely to depend on the
expected utility which is impacted on by more than simply wage differences. The bivariate
probit is a way to check whether the decisions are correlated or not.

<<   <   5   6   7   8   9   10   11   >   >>