Public-private sector pay differentials in a devolved Scotland

Journal of Applied Economics

IV. Decomposition

Once wages are consistently estimated, differences in public and private sector
pay can be decomposed into several components. In the following a modified
decomposition methodology is applied suggested by Neuman and Oaxaca (2002).
According to this the wage gap is split into three terms such that

__ __ ʌ __ ʌ ʌ

^ln wι / ^w 2 = (X1 ^- X 2) ^β1 + X 2( ^{β -} β2) +

[ʤ( ^p1 u^λi, p 1 ^{+ p}1 v^λi, s 1)  ^c^22( ^p2 u^λi, p 2 ^{+ p}2 v^λi, s 2)],

where ln w is the predicted mean log wage, X the mean vector of characteristics,
β the estimated vector of coefficients, and λ the estimated mean correction term.
Yet, λ is a non-linear function in Zγand B_iμ and the central tendency is estimated
N_j

as λ= ∑ λ_i / N_j , where λ_i is the estimated correction term from the first step
i =1                             ⁱ

in equation (3) and (4) and Nj refers to the respective set of observations in each
sector (Even and Macpherson 1990).

Similar to the simple Oaxaca decomposition (Oaxaca 1973) the term ( X₁ - X ₂) β^1
is the explained and X2(β₁ -β₂) the unexplained part of the predicted mean
wage gap. However, it is a priori unclear how to tread the selection terms in equation
(11). One way of dealing with them is by subtracting the terms from the left hand
side which leaves one with the familiar Oaxaca decomposition where the left hand
side is now the selectivity corrected wage differential as opposed to the observed
differential (e.g. Reimers 1983).⁷

V. Estimation results

A. Identification and variable choice

Estimating the above two step model requires some identification assumptions
on the coefficients and the covariance parameters (Tunali 1986). First, as already
stated, σ_v² and σ_u² are normalised to 1. Depending on whether the selection

⁷ Equation (11) can be decomposed differently by using the private sector wage structure β^2 as
weight rather than the public wage structure β1^. Since results may vary, both methods are
reported.

<<   7   8   9   10   11   12   13   >>

More intriguing information