Public-private sector pay differentials in a devolved Scotland

Public-PRIVATE Pay Differentials

equations are independent, further identification assumptions are necessary. In
case ρ_uv = 0, the matrices Z _i^' and B_i^' are required to contain at least one element
that is not part of X_i^'_,j (j=1,2). In the second case, where ρ_uv ≠ 0, an additional
identification is necessary in order to estimate σ_vu. Hence, at least one element in
Z_i^' must not be contained in B_i^' and vice versa. Additionally, these variables must
not be part of X _i^'_, j .

In the case of the participation equation, identification has often been achieved
by controlling for the number of children. Hence, data on the number of children in
two age groups, 0-11 and 12-18 are included in the participation equation and not
in either the sector choice or wage equations.

More difficult, however, is the identification of the sector choice equation (4).
It has been argued that social background characteristics do not impact on the
wage but on the sector decision. Various variables such as father’s and mother’s
education and occupation and the number of siblings have been used for
identification (see, e.g., Bender 2003 and Hartog and Oosterbeek 1993).

Even though the BHPS contains questions on, for example, the occupation of
the respondent’s father, the number of observations is very small and does not
allow the use of these variables. Yet, there is evidence to suggest that public
sector employees are far more likely to be unionised compared to private sector
workers (see e.g. Gregory and Borland 1999). Hence, one alternative identification
measure is union status. On the other hand, union status is usually controlled for
in the wage equation as well and using it in the sector choice equation as an
identification variable would render this unfeasible. The BHPS, however, asks
individuals about their perception and the importance of unions.⁸ Since union
status and union perception are positively correlated but well below unity, which
makes it possible to treat them as two distinct variables, union perception has
been used as identification in the sector choice equation. Unfortunately, this
question is only included in wave 10 and not in the latest wave.

Besides the identification variables, Z_i^' and B_i^' contain information on personal
characteristics such as age, marital status and education. In addition, the sector
choice equation also controls for occupation, firm size and job tenure. The wage
equations contain the same set of regressors except for the identification variables.
Additionally, appropriate sample correction terms are included depending on the
model estimated.

⁸ In particular, individuals are asked whether strong trade unions are needed to protect the
working conditions and wages of employees. Four possible answers can be given which range
from strong agreement to disagreement.

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