جستجو و تطابق اختلاف و سیاست پولی بهینه

A recent literature has merged the New Keynesian and the search and matching frameworks, which has allowed the former to analyze the joint dynamics of unemployment and inflation. This paper analyzes optimal monetary policy in this kind of hybrid framework. I show that zero inflation is optimal when all wages are Nash bargained in every period and the economy's steady state is efficient. In the more realistic case in which nominal wage bargaining is staggered, a case against price stability arises: in response to real shocks, the central bank should use price inflation so as to avoid excessive unemployment volatility and excessive dispersion in hiring rates. For a plausible calibration, the welfare loss under the zero inflation policy is about three times as large as under the optimal policy.

The search and matching paradigm has become a powerful tool for the analysis of unemployment and the labor market.1 It is able to accommodate a wide range of labor market policies and analyze their long-run effect on unemployment and wages. When incorporated into otherwise standard real business cycle (RBC) models, it has been shown to improve significantly their empirical performance.2 More importantly, it allows to analyze the cyclical behavior of unemployment, vacancies and job flows, important phenomena which general equilibrium models based on Walrasian labor markets are not designed to address. Parallel to this literature, the New Keynesian model has emerged as the standard model of the monetary transmission mechanism. In its simplest version, the New Keynesian model incorporates monopolistic competition and staggered price setting into the standard RBC model. Because it is based on optimizing behavior, it allows for rigorous welfare analysis of alternative monetary policy rules. This, together with its simplicity, has allowed the model to become the workhorse for the analysis of optimal monetary policy.3 However, its assumption of Walrasian labor markets (inherited from the RBC model) means that it is unable to say anything about unemployment. This is somewhat surprising, given that central banks have traditionally been concerned with the joint dynamics of unemployment and inflation, i.e. the Phillips curve. The last few years have witnessed the integration of both frameworks.4 This literature, however, has focused on the positive implications of this integration, i.e. how search and matching frictions affect the empirical performance of the New Keynesian model. In this paper, I address a different but equally important question within this hybrid framework: the analysis of optimal monetary policy. With this aim, I construct a model economy where the presence of search frictions in the labor market prevents some unemployed workers from finding jobs and some vacancies from being filled. The flow of meetings between job-seekers and vacancies is given by the so-called matching function. Aggregate hiring by firms determines the dynamics of unemployment. Inside each firm, the management and the workers bargain over wages and hours per worker. Finally, prices are set in a staggered fashion. First I analyze the benchmark case in which all wages in the economy are Nash-bargained in every period. I refer to this as the flexible-wage equilibrium. In this case, and provided the economy's steady state is efficient, the central bank can implement the efficient equilibrium by keeping the price level constant. This way, it can eliminate the distortionary effects of price staggering, because those firms that cannot reset prices would not want to change them anyway. This result can be thought of as a ‘case for price stability’, in the sense that it requires price level constancy even in response to real shocks.5 Perfect wage flexibility, however, is not a realistic assumption. In most industrialized economies, nominal wages typically remain fixed for several periods and adjust in a staggered fashion.6 Therefore, I also analyze the more relevant case of staggered nominal wage bargaining, i.e. in each period only a fraction of firms renegotiate nominal wages with their employees.7 In response to real shocks, the failure of some nominal wages to adjust creates two kinds of distortions. First, the resulting rigidity in average real wages translates into inefficient job creation and therefore inefficient unemployment fluctuations. Second, the ensuing wage dispersion across firms leads to inefficient dispersion in hiring rates. The zero inflation policy is no longer optimal for the following reason. By controlling the inflation rate, the central bank has leverage over the real value of nominal wages. Under the optimal policy commitment, the central bank uses price inflation so as to bring real wages closer to their flexible-wage levels. This reduces the two distortions arising from nominal wage staggering. First, the greater flexibility in real wages reduces the distortion in the unemployment path. Second, since actual wages are closer to their flexible-wage targets, nominal wages in renegotiating firms adjust by less, which reduces wage dispersion. For a plausible calibration of the model, the welfare loss under the zero inflation policy is approximately three times as large as under the optimal commitment. This result suggests the existence of a case against strict price stability as the only goal of monetary policy. Previous research in the New Keynesian tradition emphasized the existence of a similar case against price stability in the presence of both price and wage staggering (see Erceg et al., 2000). Relative to this line of research, the current framework offers an important theoretical advantage. As is well known, (New) Keynesian models of wage stickiness are subject to the following criticism due to Barro (1977). Given the ongoing nature of most employment relationships, we would expect employers and employees to neutralize any distortionary effects of wage stickiness. Therefore, the case against price stability motivated by wage stickiness would be based on the imposition of arbitrary inefficiencies on existing jobs. By introducing search frictions, I can analyze the distortionary effects of nominal wage staggering in a way that respects the private efficiency of employment relationships. On the one hand, search frictions create a bargaining set between employer and employee; even if the nominal wage is sticky, as long as it remains inside this bargaining set it does not affect the continuity of the match.8 On the other hand, hours per employee are determined efficiently, i.e. by maximizing the joint surplus of the match, which is itself independent of the wage. Therefore, while nominal wage staggering distorts the rate at which employment relationships are formed, it does not distort existing relationships. In other words, the case against price stability presented here is immune to Barro's critique. Search frictions and the efficiency of employment relationships also have important policy implications that differ from the standard New Keynesian analysis. In the Erceg et al. (2000) model of monopolistic competition in both labor and goods markets, closing the output gap (i.e. the gap between actual output and its flexible-price-and-wage level) is nearly optimal for any degree of price and wage staggering.9 This result stems from the symmetry between labor and goods markets, and the existence of similar inefficiencies in both markets. Search frictions introduce an explicit distinction between employment and hours per employee. The same frictions imply that in the short run firms adjust output by adjusting hours per employee; therefore, conditional on the employment stock, closing the output gap is equivalent to stabilizing hours per worker. Under bilateral efficiency, hours per worker may be distorted by price staggering but not by wage staggering. As a result, the policy that eliminates the distortionary effects of price staggering (zero inflation) is the same as the policy that stabilizes output. Therefore, conditional on the employment stock, closing the output gap is just as suboptimal as the zero inflation policy. In independent work, other authors have analyzed optimal monetary policy in New Keynesian models with search and matching frictions. A closely related paper is Blanchard and Gali (2006). They present a simple integration of both frameworks that allows for analytical solutions. They find that real-wage rigidity creates a case against price stability. An important difference between our papers is how we deviate from the flexible-wage benchmark. Instead of considering staggered nominal wage bargaining, Blanchard and Gali assume that real wages follow a weighted average of the Nash real wage and a constant real wage. The latter is an example of a real wage norm, in Hall's (2005) terminology. An advantage of assuming staggered nominal wage contracts is that the fraction of unchanged wages can be calibrated to match the average duration of nominal wage contracts, whereas a partial adjustment coefficient in a wage equation must be calibrated indirectly at best. 10 More importantly, the real-wage-norm specification may lead to very different policy implications. Once I introduce the latter specification in my model (replacing staggered nominal wages), zero inflation becomes nearly optimal for any degree of real-wage rigidity. The reason is that, when real wages are a weighted average of the Nash real wage and a constant real wage (or last period's real wage), the central bank loses most of its leverage over real wages and thus its ability to close the gap between actual and Nash real wages. It then finds it optimal to focus on stabilizing inflation. Faia (2006) analyzes how the size of the steady-state distortions (monopolistic competition and search externalities) affects the optimal variability of the inflation rate in response to shocks, in a model where price stickiness is introduced by assuming quadratic costs of price adjustment. Her analysis complements the one presented here, which is constrained to the case of an efficient steady state. She finds that optimal inflation volatility is an increasing function of workers’ bargaining power. Finally, Faia (2008) analyzes optimal Taylor rules in a similar kind of model, finding that a rule that responds both to unemployment and inflation performs best. The remainder of the paper is organized as follows. Section 2 presents the model. Section 3 obtains the efficient equilibrium in this economy. Section 4 proves that zero inflation is optimal when wages are flexible and the steady state is efficient. Section 5 introduces staggered bargaining of nominal wages. Section 6 casts the monetary policy problem in a linear-quadratic (LQ) representation, which facilitates the understanding of the central bank's stabilization goals and trade-offs. The model is then calibrated and simulated both under the zero inflation policy and the optimal commitment. The implications of targeting the output gap, as well as replacing staggered nominal wages with a real-wage norm, are discussed in section 7. Section 8 concludes.

This paper has analyzed optimal monetary policy in a New Keynesian model with search and matching frictions in the labor market. It therefore represents one of the first normative studies in the context of a macroeconomic framework that allows to study the joint dynamics of unemployment and inflation, i.e. the Phillips curve. I have shown that, when wages are Nash bargained in every period and the economy's steady state is efficient, the central bank can replicate the first-best equilibrium by keeping the price level constant. I have also analyzed the empirically relevant case in which only a fraction of firms renegotiate nominal wages in each period. Staggered bargaining of nominal wages creates two distortions as the economy is hit by real shocks. First, the failure of some nominal wages to adjust leads to wage dispersion, which in turn creates inefficient dispersion in hiring rates. Second, the resulting rigidity in real wages distorts job creation and therefore the path of unemployment. It becomes optimal for the central bank to deviate from full price stability. By using price inflation, the central bank can accelerate the convergence of actual real wages towards their flexible-wage levels. This reduces the inefficiency in unemployment fluctuations. It also reduces wage dispersion, by bringing actual wages closer to their targets and thus reducing the size of wage adjustments in renegotiating firms. For a reasonable calibration of the model, the zero inflation policy generates welfare losses that are about three times as large as under the optimal policy. The analysis presented here provides both important theoretical advantages and different policy implications relative to earlier monetary policy analysis in the New Keynesian tradition. On the one hand, the adoption of a search and matching labor-market structure allows to analyze the distortionary effects of nominal wage stickiness in a way that does not impose any arbitrary inefficiencies on employment relationships. On the other hand, and related to the latter, the convenience of output-gap targeting emphasized in earlier research becomes questionable in a search and matching framework in which employment relationships are assumed to be privately efficient.