Public-private sector pay differentials in a devolved Scotland

Public-PRIVATE Pay Differentials

standard practice.⁶ Maximum likelihood of the bivariate probit leads to four sample
selection correction terms
where P = P_uv. Again, φ and Φ are the univariate standard normal density and
distribution functions respectively, and F the bivariate standard normal distribution
function. Equations (5) to (8) collapse to the usual univariate Heckman expressions
for P_uv = 0.

Now, the wage equations (1) and (2) can be re-written as

''

^E(ln w1,i | ^Xi^,Pi ^{= 1,S}i ^{= 1) = X}1,i^β1 ⁺σ11P1u^λi, p1 ⁺σ11P1v^λi,s1              (9)

^E(ln w2,i | ^Xi ^,Pi ^{= 1,S}i ^{= 0) = X}2,i^β2 ⁺σ22P2u^λi, p2 ⁺σ22P2v^λi,s2         (10)
where the correction terms are according to (5) to (8).

⁶ Since the covariance of ε₁ and ε₂ is not identifiable in this model, the covariance matrix has
been split into two matrices (see Co et al. 1999 for details; see Koop and Poirier 1997 for a
discussion on these identification issues).

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