The ultimate determinants of central bank independence

where lower-case letters refer to logarithmic deviations from steady state values. Thus, y is
the log of output, 6 the log of employment, and μ_t a measure of productivity. β is the
exponent of labour and is less than unity.

Having described the level of output, it remains to be specified how productivity evolves
over time. For simplicity we assume that shocks to productivity are normally distributed
with zero mean and finite variance

μ_t = v^μt                       v^μt ~ N (0, σ²_μ)                                                (2.2)

Firms determine employment by equalizing the marginal product of labour to the real
wage w_t —p_t. This yields the following employment function

^ι' = - ɪɪp (wt - Pt - μt)                                                              ^(2.3)

where w is the log of the nominal wage and p the log of the price level.

The nominal wage is set at the beginning of each period and remains fixed for one
period. The objective of wage-setters is to stabilize real wages and employment around
their target levels. Thus wages in each period are set to minimize

W_t = E . [1 ({-Γ)2]                                                             (2.4)

t        t— ι 2

where E_t—1 is the operator of rational expectations, conditional on information at the end
of period t — 1. t is the employment target of the union. We assume that {* ≡ C,^s where
C_l^s is the number of insiders. Denoting the log of the labour force by {^s, we assume C,^s <
F. Thus we employ a variant of the insider—outsider approach to the labour market
[Blanchard and Summers (1986), Lindbeck and Snower (1986)]. The minimization of (2.4)
is subject to the labour demand function (2.3).

From the first-order conditions for a minimum of (2.4) subject to (2.3), the nominal
wage is given by

^wt = E_t-ιp_t - ⁽¹ -^β)r                                                                  (2.5)

Substituting (2.5) in the labour demand function (2.3), we get the following relation
between employment and unanticipated shocks

^{t = ^{r +} ʌ- (pt - Et-Λ ⁺ μt)                                               (2.6)

An unanticipated rise in prices p_t — E_t—1p_t reduces the real wage, and causes firms to
employ more labour. Thus, aggregate employment exhibits a transitory deviation from its

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