Monetary rules matter for the equilibrium rate of employment when the number of price-wage setters is small, even when assuming rational expectations, complete information, central bank precommitment, and absence of nominal rigidities. If the central bank is nonaccommodating, sufficiently large unions, bargaining independently, have an incentive to moderate sectoral money wages, and thereby expected real wages. The result is an increase in the real money supply, and hence higher demand and employment. This does not hold with accommodating monetary policy since unions' wage decisions cannot then affect the real money supply. A similar argument holds for large monopolistically competitive price setters.
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Soskice et al. (2000) studied this question.
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