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I study optimal monetary policy with an expectational AS curve and private agents who optimally choose their amount of information pertinent to predicting policy. Shocks with time-varying variance (ARCH) induce interesting information acquisition (IA) dynamics; optimal IA affects optimal policy and vice versa. Under discretion, IA dynamics cause time-varying effectiveness of policy because of the expectational AS curve; policy may be rendered completely ineffective. In policy game equilibrium, a fall in the shock’s variance typically induces less IA and raises welfare. In one exceptional case the opposite occurs, a result which does not require implausible unstable equilibria. An agent becoming informed increases the endogenous component of economic volatility; IA therefore has a negative externality. Under commitment policy’s effectiveness is again time-varying, but policy is never completely ineffective: commitment enables the central bank to credibly limit policy’s volatility; this limits private agents’ incentive to become informed, so limits expectation-induced policy neutrality.

This paper presents optimal monetary policy for a model in which private agents can choose whether to acquire information that helps them predict policy actions. Private sector (PS) information acquisition is important in the model because a monetary policy action has real effects only to the extent that it surprises the PS. This means that as the PS’s information acquisition changes over time, the effectiveness of monetary policy also changes, a phenomenon that would appear to an econometrician as an output-inflation tradeoff with a time-varying slope. This topic is important for monetary policy in empirical economies; to the extent that policy neutralization occurs in such economies when private agents become informed, their information acquisition affects the results of monetary policy.1 In the model, interesting dynamics of information acquisition are produced by output shocks that have time-varying variance—specifically autoregressive conditional heteroskedasticity, or ARCH. The monetary authority’s offsetting of ARCH shocks causes inflation to also exhibit ARCH; furthermore, inflation is the variable the PS might become informed about, but its ARCH behavior implies that becoming informed is worth the cost only in some periods. Recently, interest in the effects of the PS’s information on monetary policy has increased; in particular see Woodford, 2002, Ball et al., 2005 and Branch et al., 2006a. This paper advances the literature on this topic in several ways. One way is that PS agents are allowed to have different costs of acquiring information, which seems to be unique in the information strand of the monetary policy literature. Another way is the incorporation of ARCH shocks. The third and most important way is the inclusion of both private agents who optimally choose their information and a monetary authority (MA) that optimally conducts monetary policy. The only other paper with both optimal information acquisition (IA) and an optimizing MA is that of Branch et al. (2006a) (discussed below); the rest of the literature has only one of these features. There is of course a vast literature on optimal monetary policy under exogenous PS information sets. Ball et al. (2005) is part of this literature in that each private agent in their setting has an exogenous probability of information updating. Regarding optimal IA, Evans and Ramey (1992) study a model in which private agents endogenously (optimally in some cases) acquire information under ad hoc monetary policy. Hahm (1987) studies the PS’s optimal IA but does not describe optimal monetary policy response to output shocks. Neither does Hahm consider private agents with different costs of becoming informed, ARCH shocks, or the differences between discretionary and committed policy, which I do below. Branch et al. (2006a) study optimal monetary policy in a model with endogenous IA but assume all PS agents have the same cost function for IA. They also assume the shocks to which the MA responds are homoskedastic, so that the IA problem is not intrinsically time-varying. In this paper the following results emerge. First, under discretion, changing IA causes policy’s effectiveness to change over time. This provides a possible explanation for time-varying output-inflation tradeoffs, e.g., the weakening of the tradeoff in the US in the 1970s, when the economy became more volatile.2 Also, the effects of a change in the shock’s variance can be path-dependent in that a switch from the low-variance regime to the high-variance regime does not necessarily induce a mirror image result of a switch from the high-variance regime to the low-variance regime. Second, it is possible, although only in one exceptional case, that a decreased variance of the shock induces more private agents to become informed and lowers welfare, and though such comparative statics are the exception, they do not require equilibria which are implausible on stability grounds. Third, aside from responding to economic volatility, the fraction of agents who are informed also affects the volatility. The higher is the fraction of agents who are informed, the higher is inflation’s volatility; informed agents therefore impose a negative externality on uninformed ones. This result is novel. In previous work IA has positive external effects on the uninformed, because of the information-revealing behavior of the informed, cf. the free rider problem in financial markets. 3 Fourth, under commitment some private agents may acquire information in equilibrium, though the MA never chooses policy that would induce all private agents to be informed (as can happen under discretion). Finally, for both discretion (with one exception) and commitment (always), policy is less effective precisely when it would be most useful, when the shock’s variance is high. With discretion this is because the PS becomes informed when output volatility, which the MA would like to offset, is high; this IA behavior tends to neutralize policy in high-variance periods and in fact can completely neutralize it. With commitment it is because the MA is optimally less responsive to shocks in high-variance periods to limit the PS’s information acquisition, and preserve some policy effectiveness. Thus policy is of limited help in high-volatility periods, partly because the policy action has a weak effect on output and partly because the policy action itself is restrained. As explained more thoroughly in Section 3, the above results on discretion are consistent with the stylized fact that US inflation and GDP exhibit correlated regime shifts in their volatilities. Branch and Evans (2007) provide references to empirical work documenting this stylized fact and note, “[T]he volatility of GDP and inflation vary over time. In particular, each series appears to move in tandem and alternate between high and low variance regimes.” The main interest of Branch et al. (2006a) is conditions under which the usual policy tradeoff between output volatility and price level volatility disappears, so that both volatilities could be lowered simultaneously. Their focus differs from the present one in that they are mainly concerned with shifts between equilibria for static environments, i.e., they do not rely on ARCH shocks to motivate discussion of these volatility changes. However, for this very reason their model cannot account for such shifts since it requires going beyond them to explain why the PS and the MA would suddenly change from one Nash equilibrium to another. The present paper motivates such equilibrium switching as occurring when the shock’s variance changes. However, in a companion paper, Branch et al. (2006b) provide an analysis of a possible mechanism for a one-way shift, MA learning. While the motivation of this paper is theoretical, it can also be viewed as a contribution to the recent literature on the high macroeconomic volatility of the 1970s and the decline in volatility since 1983, the Great Moderation. One strand of this literature has sought to explain this episode in terms of the Federal Reserve System entertaining overly optimistic beliefs about what monetary policy could accomplish in the 1970s, leading to excessive policy activism, and then learning its way to more resigned beliefs that led to the Great Moderation. Examples of this literature include Sargent, 1999, Sargent et al., 2006 and Branch et al., 2006b. Another strand has emphasized the role of changing variances of exogenous shocks that have buffeted the economy; see, e.g., Sims and Zha (2006). This paper strengthens the second kind of argument because the endogenous IA is an amplification mechanism by which a small amount of exogenous ARCH can help explain a large amount of overall macro ARCH (overall in the sense of including both the exogenous and endogenous components of macro volatility). The endogenous IA’s other contribution is to help explain the policy neutralization that was associated with the higher volatility in the 1970s, which the exogenous ARCH by itself does not address. The “learning” strand of the literature is more optimistic because it can imply that a recurrence of the 1970s experience is unlikely, depending on what exactly the Fed has learned (but see the “Reservations” section in Sargent, 1999). The “shocks” argument, at least for discretionary policy, is pessimistic regarding macro volatility; it implies a 1970s recurrence is inevitable because the high-variance regime eventually will return.

This paper has presented results for optimal information acquisition in a setting in which information acquisition affects the effectiveness of monetary policy. Under discretionary policy, the endogenous IA causes a time-varying inflation-output tradeoff, and in fact it tends to weaken monetary policy exactly when monetary policy would be most useful, in high-volatility periods. Under commitment the MA can manage policy’s effectiveness by committing to low-variance policy rules that limit the PS’s incentive to become informed. That is, if the MA “doesn’t abuse it, then it won’t lose it.” However, the required restraint also limits the MA’s ability to stabilize the economy. The model also brings out a novel externality: informed agents, by increasing the MA’s optimal inflation variance, impose a negative externality on uninformed ones. The empirical episode of most interest in light of these theoretical results is the change in US macroeconomic volatility over the last few decades. The paper’s endogenous IA choice provides a mechanism by which regime changes in an exogenous shock’s variance can have amplified effects on overall macro volatility; thus it buttresses the “changes in shocks” explanation of the high-volatility of the 1970s and the subsequent Great Moderation.