Two sticky-wage models are introduced in this paper to examine the implications of having either households or firms as wage setting actors. The rate of wage inflation depends positively on the output gap if households set wages whereas such a relationship is of negative sign when firms set wages. Moreover, impulse–response functions and the statistical comparison with US data show different business cycle properties depending upon wage setting actors. Finally, optimal monetary policy is derived for each case, and compared with a Taylor-type monetary policy rule.
In a highly influential article, Erceg et al. (2000) show how sticky wages can be modeled by giving households a fixed probability à la Calvo (1983) to optimally reset wage contracts. 1 Households own some differentiated labor services and may decide the nominal wage associated with their labor supply. The optimal wage can be reset only when receiving a market signal that arrives with a constant probability. In turn, the dynamics of wage inflation can be formulated in a single forward-looking equation. Fluctuations of wage inflation are governed by the gap between the households' marginal rate of substitution and the real wage. This sticky-wage structure is becoming very popular among New Keynesian researchers in recent times ( Amato and Laubach, 2004, Smets and Wouters, 2003, Woodford, 2003, Giannoni and Woodford, 2004, Christiano et al., 2005, Levin et al., 2005 and Casares, 2007). 2
The analysis of this paper begins by describing a sticky-wage model where households set wages in an economy with perfect competition and flexible prices in the goods market. Alternatively, this paper switches the decision-making of the optimal wage from households to firms. As a result, wages may be set at the value that maximizes profit of a monopsonistically competitive firm.3 In both models, nominal rigidities can be readily introduced as Calvo-style contracts with either households or firms being the wage setting actors.
Following Woodford's (2003) book and many New Keynesian papers, the output gap is the difference between current output and the amount of output that would prevail in the economy if nominal rigidities were dropped. Assuming sticky wages in the labor market and perfect competition in the goods market, the output gap in this paper is one endogenous variable that emerges from wage rigidities. Moreover, it will be shown how a forward-looking dynamic equation relates changes in the rate of wage inflation to those on the output gap. With households acting as wage setters, the output gap affects positively the rate of wage inflation. By contrast, if firms are the wage setting actors, the output gap has a negative impact on the rate of wage inflation. This paper also argues that the assumption of having either households or firms as setting actors in a sticky-wage model is not trivial for the business cycle analysis; impulse–response functions and second-moment statistics are significantly influenced by one case or the other.
The consequences of nominal rigidities on the optimal design of monetary policy were first examined in sticky-price models (Rotemberg and Woodford, 1997 and Clarida et al., 1999). Such analysis was extended to the case of economies where both prices and wages were sticky by Erceg et al. (2000).4 This paper discusses the optimal monetary policy when the only source of nominal frictions is wage stickiness.5 In that respect, the monetary policy analysis will distinguish the implications of the two variants on wage setting actors, using welfare-theoretic targeting rules introduced by Woodford (2003, chapter 6). Furthermore, optimal policy will be compared with the case of having the central bank adjusting the nominal interest rate as prescribed by a Taylor (1993)-type simple rule.
The rest of the paper is organized as follows. The sticky-wage model where households set wages is described in Section 2. The case where firms are wage setting actors is introduced in Section 3 as another sticky-wage variant. Section 4 contains the model calibration and business cycle simulations based on impulse–response functions, and calculation of second-moment statistics to be compared with US data. The analysis of Section 5 is devoted to the theoretical monetary policy analysis. Finally, Section 6 reviews the main conclusions of the paper.
The assumption on who set wages is not trivial for an optimizing macroeconomic model with sticky wages. If households may decide on nominal wages, the optimal wage depends on the difference between the marginal rate of substitution and the real wage. By contrast, if firms can set wages, they determine its optimal value looking at the difference between the marginal product of labor and the real wage.
This paper has also shown that, in a sticky-wage economy with Calvo-type wage contracts and perfect competition in the goods market, the rate of wage inflation is forward-looking on the output gap with a sign defined by who the wage setting actors are. Hence, when households set wages the relationship is of positive sign whereas when firms set wages that relationship turns negative. This fact has significant consequences on the business cycle behavior of sticky-wage models.
Finally, optimal monetary policy must minimize, in both sticky-wage models, a weighted sum of variabilities of the rate of wage inflation and the output gap. The central bank optimal plan leads to a different targeting rule on each case: wage inflation must react either positively (firms set wages) or negatively (households set wages) to the first difference of the output gap. Optimal monetary policy in both cases achieves full stabilization of the two targeting variables in the presence of either technology or preference shocks. Nevertheless, the assumption on who act as wage setters is relevant for the optimal interest-rate responses to wage indexation shocks. Such nominal shocks also give rise to distinctive second-moment statistics.
