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We present a dynamic stochastic general equilibrium (DSGE) New Keynesian model with indivisible labor and a dual labor market: a Walrasian one where wages are fully flexible and a unionized one characterized by real wage rigidity. We show that the negative effect of a productivity shock on inflation and the positive effect of a cost-push shock are crucially determined by the proportion of firms that belong to the unionized sector. The larger this number, the larger are these effects. Consequently, the larger the union coverage, the larger should be the optimal response of the nominal interest rate to exogenous productivity and cost-push shocks. The optimal inflation and output gap volatility increases as the number of the unionized firms in the economy increases.

One of the most striking differences among modern industrialized economies is the role trade unions play in determining wages and employment conditions. While in the US only about 15% of workers are covered by collective contract agreements, in the UK this percentage is about 36% and in countries such as France, Italy or Sweden is much higher, rising above 84%.1 Given the importance of labor markets in determining output, inflation and the response of the economy to aggregate shocks, a very natural question is whether and how central banks, in formulating monetary policy, should take into account the structure of industrial relationships. In this paper we address this issue by studying optimal monetary policy in a dynamic stochastic general equilibrium New Keynesian (DSGE-NK henceforth) model2 with a dual labor market. Firms may belong to two different final-goods-producing sectors: one where wages and employment are determined under perfect competition, and the other where wages and employment are the result of a contractual process between unions and firms. As in Hansen (1985) and Rogerson and Wright (1988), labor supply is indivisible and workers face a positive probability to remain unemployed. Wages in the unionized sector are set according to the popular monopoly-union model developed by Dunlop (1944) and Oswald (1982) which has been recently introduced in a real business cycle (RBC) model by Maffezzoli (2001) and in a DSGE-NK model by Zanetti (2007). By doing this we depart from the recent literature, that has recently analyzed search and matching frictions à la Mortensen and Pissarides (1994)3 in DSGE-NK models and we concentrate on the consequences of collective bargaining between unions and firms. Unions, in this model, do not simply maximize the utility of their members, but are institutions that also have “political” objectives in the sense that their objective function takes into account the preferences of workers, the preferences of leaders and market constraints. In this respect we take side on the old and never settled debate initiated by Dunlop (1944) and Ross (1948) over the appropriate maximand for the unions’ utility function, and we assume that the unions’ objective function is a Stone-Geary utility function as in Dertouzos and Pencavel (1980), Pencavel (1984) and, more recently, in De la Croix et al. (1996), Raurich and Sorolla (2003) and in Chang et al. (2007). This function is extremely flexible and, depending on parameter values, allows for different distribution of power, inside the union, between members and leaders who may have diverging objectives. The divergence between the union's objective and households’ utility creates a distortion in the economy and gives rise to real wage rigidity. Interestingly, wage rigidity does not apply only to new hirings, as in the model with search and matching frictions (see for example Thomas, 2008) but also to ongoing relationships. The presence of a unionized sector has very important consequences for monetary policy. What Blanchard and Galì (2007), define as the “divine coincidence” does not generally hold: for a central bank stabilizing output around the level that would prevail under flexible prices (natural output) is not equivalent to pursuing the efficient level of output and a trade-off arises between output stabilization and inflation stabilization. A first major result of our model is that the trade-off between inflation stabilization and the level of output (and unemployment) depends on the relative weight of the unionized and competitive sectors: the larger is the fraction of firms that are able to set wages in a unionized labor market, the larger is the trade-off they face in response to productivity shocks. This has significant consequences for optimal monetary policy that we derive, as in Woodford (2003), from the maximization by the central bank of a second-order approximation of agents’ utility function. We find that, differently from the standard New Keynesian model where monetary policy must not respond to technology shocks, in our model monetary policy must be procyclical in response to such shocks. Moreover, and this is the second major result of this paper, monetary policy must be progressively more accommodating as the size of the unionized sector increases; in an economy where labor markets are mainly competitive, the nominal interest rate must decrease much less in response to a productivity shock than in an economy where wages are largely set by collective bargaining between unions and firms. The procyclicality of optimal monetary policy and its dependence on union coverage represent a significant departure from the most recent contributions such as Faia (2008) where optimal monetary policy is procyclical only for some parameters of the matching technology and Blanchard and Galì (2008) where the main friction characterizing labor markets are hiring costs.4 In our model, if we consider two countries hit by the same shocks and where the central bank behaves optimally, we observe that in the country where the number of “Walrasian” firms is larger, the interest rate will vary much less than in the other country. This, however, is not the consequence of differences in the reaction functions of the two central banks to a unit change in expected inflation; rather it is caused by the fact that the economy where the labor market is more competitive experiences smaller inflationary tensions. Our model provides also a convenient framework to address important normative issues such as, for example, the optimal behavior of central banks in periods characterized by labor market turmoil and exogenous wage shocks. In the framework we propose here a policy trade-off for the central bank arises also in response to exogenous changes in the unions’ reservation wage, that we interpret as cost-push shocks. If the unions’ reservation wage is subject to exogenous changes, and these changes tend to be persistent over time, then a welfare maximizing central bank must again face the problem of whether to accommodate these shocks with a easier monetary policy. As in the case of technology shocks, also in this case optimal monetary policy requires only partial accommodation, and the response of the central bank is crucially determined by the fraction of firms that, in the economy, set wages competitively. We finally calibrate the model and we analyze the differences between an economy where the central bank follows a standard Taylor rule, as the one estimated by Smets and Wouters (2003) for Europe, and an economy where the central bank follows the optimal rule. The calibration of the model under the Taylor rule estimated by Smets and Wouters (2003) for Europe shows that our model is able to qualitatively replicate the dynamics of the main economic variables and that a unionized economy tends to have larger responses to productivity shocks than an economy where competitive labor markets prevail. The difference in the impulse response functions (IRFs) between these two types of economies becomes much larger, however, under an optimal monetary policy. Optimality implies also that monetary policy be much more accommodating when wages are the result of bargaining between unions and firms. The paper is organized as follows. In Section 2 we develop a DSGE-NK model with indivisible labor and two-sector labor market while in Section 3 we study optimal monetary policy and the optimal volatility of inflation and output gap. In Section 4 we discuss the calibration of the model under the optimal policy with different degrees of the union coverage. Section 5 concludes.

In this paper we consider a DSGE-NK model where labor is indivisible and there are two types of labor markets that coexist: a Walrasian one and a unionized one where wages are the result of the bargaining between firms and monopoly unions. We found that, with respect to the standard DSGE-NK framework, we are able to account for the existence of significant trade-offs between stabilizing inflation and stabilizing unemployment, in response to technology and exogenous wage shocks. Because of real wage rigidity, which is induced by the presence of unions, an optimizing central bank must respond to positive technology shocks by increasing the interest rate and, similarly, must respond with an interest rate increase to exogenous increases in unions’ reservation wage. The effect of these shocks on inflation and the necessary interest rate movements set by an optimizing central bank depend on the size of the Walrasian sector relative to the unionized sector. If a large part of wages are set in a competitive market, technology and cost-push shocks will have little effect on inflation and will induce small interest rate movements, while an economy where large part of wages are set in unionized markets will experience larger inflation and interest rate movements. If we consider, however, an optimal instrument rule where the central bank reacts to expected inflation, the response of the nominal interest rate to an increase in expected inflation is not influenced by the dualistic structure of the labor market. Even though, for the sake of simplicity, we concentrate on a rigid dualistic structure of the labor market and we abstract from other market imperfections like search and matching and hiring–firing costs we are able to single out, with this model, some of the challenges provided to monetary policy by different institutional settings in the labor market. The model, in particular, captures an important difference between Anglo-Saxon economies and continental Europe providing, therefore, a useful benchmark to evaluate and compare the monetary policies enacted by the Fed, the Bank of England and the ECB.