سیاست پولی بهینه با دانش مشترک ناقص

This paper determines optimal nominal demand policy in a flexible price economy in which firms pay limited attention to aggregate variables. Firms’ inattentiveness gives rise to idiosyncratic information errors and imperfect common knowledge about the shocks hitting the economy. This is shown to have strong implications for optimal nominal demand policy. In particular, if firms’ prices are strategic complements and economic shocks display little persistence, monetary policy has strong real effects, making it optimal to stabilize the output gap. Weak complementarities or sufficient shock persistence, however, cause price level stabilization to become increasingly optimal. With persistent shocks, optimal monetary policy shifts from output gap stabilization in initial periods following the shock to price level stabilization in later periods, potentially rationalizing the medium-term approach to price stability adopted by some central banks.

The decentralized nature of economic activity suggests that not all economic decision-makers base their decisions on the same information set. Friedrich A. Hayek referred to information dispersion between decision-makers as the defining feature of economic policy problems: The peculiar character of the problem of rational economic order is determined precisely by the fact that the knowledge of the circumstances of which we must make use never exists in concentrated or integrated form but solely as the dispersed bits of incomplete and frequently contradictory knowledge which all the separate individuals possess. Hayek (1945). Most economic models, however, derive policy recommendations on the assumption that private agents share a common information set. In the realm of monetary policy, for example, information asymmetries between private agents have not yet received much attention, and the literature has mainly focused on asymmetries between the private sector and the policy-maker.1 This paper determines optimal monetary policy when there is information dispersion between firms. Analyzing information dispersion between firms seems particularly important when studying monetary policy because the real effects of nominal demand policy ultimately depend on firms’ pricing decisions. Moreover, it seems plausible to assume that firms do not pay attention to all aggregate developments, e.g., because of the limited number of managerial staff collecting and processing information and taking the corresponding decisions; see Radner (1992). Following earlier work by Sims (2003), limited attention is modeled by assuming that firms have limited capacity to process information. Such processing limitations imply that firms cannot pay attention to all aggregate developments and have to choose what information to process and what information to neglect. Since each firm processes information in a slightly different way, information processing leads to idiosyncratic processing errors, whose size is inversely related to the firm's processing capacity. Using a simple model with imperfectly competitive firms, flexible prices, and a policy-maker maximizing the welfare of the representative agent, it is shown that the presence of information processing constraints and differential information has stark consequences for the conduct of optimal nominal demand policy. In particular, if firms’ prices are strategic complements and aggregate disturbances display little persistence, it tends to be optimal for monetary policy to stabilize the output gap. In the presence of either weak complementarities or sufficient shock persistence, however, monetary policy should increasingly emphasize price level stabilization.2 Intuitively, private information renders coordination among firms difficult because firms are uncertain about the decisions of other firms that base their price decisions on (slightly) different information sets. Strategic complementarities increase the relevance of other firms’ pricing decisions, thereby increasing strategic uncertainty among firms, which causes each firm's price to react only weakly to own information. This amplifies the real effects of monetary policy and makes it optimal to stabilize the output gap. However, when shocks display sufficient persistence, firms are able to observe shocks better over time, which leads to less information dispersion and weaker real effects of monetary policy. This makes it optimal to stabilize the price level. Optimal monetary policy thus shifts its emphasis from output stabilization during initial periods following the shock to price stabilization in later phases, potentially rationalizing the medium-term orientation to price stability adopted by a number of monetary authorities in industrialized economies. Independent of whether monetary policy should stabilize the price level or the output gap, it is always optimal to nominally accommodate supply shocks, i.e., shocks that move the efficient output level. Firms then choose not to process any information about supply shocks. As a result, firms’ prices do not react to these shocks and appropriate nominal demand adjustments then induce real output movements that cause output to follow its efficient level. Supply shocks, therefore, do not generate a trade-off between price and output gap stabilization. The situation is different for real demand shocks, i.e., shocks to firms’ desired mark-up. These shocks generate a trade-off between price and output gap stabilization because nominal accommodation of such shocks stabilizes the output gap but makes the price level more variable. Whether such shocks should be nominally accommodated or not thus depends on whether it is optimal to stabilize prices or the output gap. As pointed out by Keynes (1936) and Phelps (1983), disparate information sets coupled with the assumption that agents hold rational expectations generates substantial technical difficulties: optimal decision-making requires that agents formulate ‘higher order beliefs’, i.e., beliefs about the beliefs of others and beliefs about what others believe about others, and so on ad infinitum.3 This is the case because a firm's optimal price depends on the prices set by other firms, and thus on other firms’ beliefs.4 Despite these difficulties, a number of recent papers successfully pioneer methods for determining rational expectations equilibria in imperfect common knowledge (ICK) environments, most notably Townsend, 1983a and Townsend, 1983b, Pearlman (1986), Sargent (1991), Binder and Pesaran (1998), Kasa (2000), Woodford (2002), Sargent and Pearlman (2004), and the recent literature on global games, see Morris and Shin (2003a). While the present setup in many respects is simpler than in these earlier contributions, it adds to the literature by solving an optimal policy problem for a private sector rational expectations equilibrium (REE) with ICK. Moreover, the paper endogenizes information imperfections by assuming limited information processing capacities. Limited processing capacity causes the information structure to be endogenous because firms choose what information to process, implying that the information structure reacts to the policy pursued by the central bank. In related papers Morris and Shin (2003b) and Amato and Shin, 2003 and Amato and Shin, 2006 derive normative implications for ICK settings, but focus on the welfare effects of disclosing public information. Hellwig (2002) derives impulse responses to a large range of shocks for an economy with monopolistic competition and ICK. Nimark (2005) solves a forward-looking pricing model with nominal rigidities and ICK.5 Ball et al. (2005) analyze optimal monetary policy with disparate information by assuming that some agents set prices based on lagged information. While there are many similarities to the present paper, the assumed information lags do not generate ICK. Moreover, by contrast with the setting studied by Ball et al., price level targeting fails to be optimal in the current setup because the trade-off between price and output gap stabilization shifts over time when shocks are persistent. The rest of this paper is organized as follows. Section 2 outlines a simple static economy with monopolistically competitive firms. As a benchmark, Section 3 derives optimal policy when there is common knowledge among firms. ICK and information processing constraints are introduced in Section 4, which builds on results from information theory. Section 5 determines the REE with ICK, and Section 6 characterizes optimal monetary policy. Results are extended to a dynamic setup in Section 7. A conclusion summarizes the main findings, and technical details are contained in an Appendix.

It has been shown by Phelps (1970) and Lucas (1973) that monetary policy has real effects when firms are only imperfectly informed about the shocks hitting the economy. Considering firms that can process information only at a finite rate, this paper shows that information dispersion, i.e., ICK about shocks, may significantly enhance the real effects of nominal demand policy in a flexible price economy. When firms’ prices are strategic complements, prices respond rather sluggishly to shocks and policy decisions. This gives rise to substantial real effects of monetary policy and makes it optimal to stabilize the output gap. However, when mark-up shocks are persistent, the ability to affect the output gap is reduced over time and optimal policy is again increasingly characterized by price level stabilization. Whether it is optimal to stabilize the output gap or the price level thus depends on the importance of strategic complementarities, on the degree of information frictions, and on the persistence of the shocks that hit the economy. Empirical work seeking to quantify the relative importance of these three determinants of optimal monetary policy would thus be of interest.