Elsevier

European Economic Review

Volume 106, July 2018, Pages 1-20
European Economic Review

Some implications of learning for price stability

https://doi.org/10.1016/j.euroecorev.2018.03.002Get rights and content

Abstract

Survey data on expectations of a range of macroeconomic variables exhibit low-frequency drift. In a New Keynesian model consistent with these empirical properties, optimal policy in general delivers a positive inflation rate in the long run. Two special cases deliver classic outcomes under rational expectations: as the degree of low-frequency variation in beliefs goes to zero, the long-run inflation rate coincides with the inflation bias under optimal discretion; for non-zero low-frequency drift in beliefs, as households become highly patient valuing utility in any period equally, the optimal long-run inflation rate coincides with optimal commitment – price stability is optimal. The optimal state-contingent response to cost-push disturbances similarly reflects properties of optimal discretion and optimal commitment, depending on the degree of low-frequency variation in beliefs. When beliefs exhibit substantial variation in response to short-run forecast errors, optimal policy is closer to commitment.

Introduction

If expectations themselves are a source of low-frequency drift in macroeconomic data, then important questions arise about the validity of standard monetary policy advice. While a large literature has emerged evaluating the robustness of rational expectations policy advice to learning dynamics, relatively little attention has been paid to the question of optimal policy design conditional on such belief structures. Important exceptions are Gaspar, Smets, Vestin, 2006, Gaspar, Smets, Vestin, 2010, Eusepi et al. (2015), and Mele et al. (2015), which explore ways in which optimal policy under learning differs from that under rational expectations. While these papers provide insights on the constraints non-rational belief structures place on monetary policy, they all have in common the implicit assumption that, absent disturbances to the economy, price stability is optimal in the long-run.1 Stated differently, conditional expectations of inflation in these analyses converge to price stability as the forecast horizon extends to the indefinite future.

This paper explores whether price stability should be expected to arise as an implication of optimal policy. Building on Molnar and Santoro (2013), a New Keynesian model is adapted to be consistent with low-frequency drift in beliefs identified in macroeconomic data.2 The analysis is distinguished from this earlier work by solving for optimal decisions, conditional on the belief structure. We also employ the welfare-theoretic loss function (to a second-order approximation) implied by the microfoundations, which accounts for a distorted steady state arising from monopolistic competition and tax policy. In this environment price stability is, in general, not optimal in the long run, even when a central bank has an inflation target of zero as part of its objectives, and even when fully informed about the nature of agents’ expectations formation. Drifting beliefs represent a fundamental constraint on what can be achieved by monetary policy, and optimal policy exhibits an inflation bias of the kind observed under optimal discretion when compared to optimal commitment under rational expectations. In contrast to the inflation bias under discretion, the positive inflation rate under learning is the best a central bank can do – because beliefs are state variables, there is no distinction between commitment and discretion.3 However, under some special cases, long-run price stability will emerge as an optimal outcome under imperfect knowledge.

The mechanism generating a positive optimal inflation rate reflects two competing tensions. As identified by Kydland and Prescott (1977), for given inflation expectations higher household discount factors lead to a deterioration in the short-run output-gap-inflation trade-off. Exploitation of given expectations generates higher equilibrium inflation rates. However, while learning dynamics imply beliefs are slow-moving state variables, they do adjust over time – indeed, they are consistent with policy in the long run. As beliefs are revised in response to a positive surprise in inflation, permanently higher inflation expectations raise present discounted losses. The central bank internalizes the effects of its policy actions on expectations. For a given sensitivity of beliefs to new information, and, therefore, a given rise in beliefs about long-run inflation, as the discount factor rises, welfare declines – it becomes optimal to lower the inflation rate in the long run. At the same time, the less sensitive are beliefs to new information, the more can beliefs be exploited, because surprise inflation induces smaller adverse shifts in the short-run inflation-output trade-off. This raises the equilibrium long-run inflation rate.

Two special cases are observed when this tension is resolved in favor of one or the other effect, which bounds the optimal rate of inflation, and makes tight connection to rational expectations policy advice. When the size of low-frequency variation in beliefs goes to zero, so that beliefs are almost never revised, the optimal inflation rate coincides with optimal discretion; alternatively, with low-frequency variation in beliefs and when households are highly patient, valuing utility in any period almost equally, then price stability obtains giving the optimal commitment solution. As such, a principle contribution of this work is to make perspicuous connections across optimal policy outcomes under alternative belief structures in the canonical New Keynesian model.

These insights continue to apply to the optimal state-contingent response to disturbances under learning. We study optimal policy in response to cost-push shocks, which deliver a policy trade-off even in the simple New Keynesian framework. Similarly to the steady-state analysis, when low-frequency drift in beliefs is negligible, the stabilization bias in response to shocks coincides with the predictions of optimal discretion. Indeed, the optimal policy problem is formally equivalent to optimal discretion in the limiting case of a zero gain coefficient. Conversely, when long-run inflation expectations exhibit greater sensitivity to short-run forecast errors (i.e. a larger constant gain), and are therefore ‘poorly anchored’, it becomes optimal to induce some overshooting in the response of inflation to cost-push shocks. This property mimics the history-dependence featured by the optimal policy under commitment, which stabilizes the price level to a greater degree than under optimal discretion.

A further contribution concerns recent proposals to raise the Federal Reserve’s inflation target from 2%, to some higher rate. Blanchard et al. (2010), Ball (2013) and Krugman (2014) all argue a higher inflation target would lower the potential output costs arising from the zero bound on nominal interest rates. However, Ascari et al. (2015) and Coibion et al. (2012) demonstrate in structural New Keynesian models, that the optimal rate of inflation is not much greater than zero. A range of frictions, such as staggered pricing and wage-contracting, deliver significant welfare costs for non-zero rates of inflation, that more than offset the gains from being constrained by the zero lower bound on interest rates less frequently. The current paper suggests beliefs themselves may be a constraint on policy, under which a positive rate of inflation is optimal. The baseline calibration of our model indicates that relative to rational expectations, drifting beliefs might warrant up to a 2% annual inflation target.

Section snippets

The model

This section recapitulates a simple New Keynesian model presented in Eusepi and Preston (2018a), which is valid for arbitrary beliefs. A range of assumptions, which are without loss of generality, are made for expositional simplicity, and give focus to long-run outcomes. Further details on the microfoundations can be found in Woodford (2003).

A continuum of households i on the unit interval maximize utility E^tiT=tC¯TβTt[lncT(i)χnT(i)],where 0 < β < 1 and χ > 0, by choice of sequences for

The policy problem

The central bank seeks to minimize the expected discounted quadratic loss E0t=0βt[πt2+λx(xtx*)2]where λx ≥ 0 determines the relative weight placed on inflation stabilization versus output gap stabilization, and x* is the optimal output gap.9 The period loss function is derived as a

Discussion

This final section provides brief commentary on various aspects of the optimal policy problem.

Conclusion

This paper demonstrates that optimal policy generally delivers a positive inflation rate in the long run when agents have beliefs that exhibit low-frequency drift. The optimal long-run inflation rate depends on all model parameters, though it is bounded by the optimal long-run inflation rates observed under discretion and commitment when agents have rational expectations. Interestingly, these rational expectations outcomes are delivered as special cases of the optimal policy model under

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    The authors thank Chris Gibbs, James Hansen and Michael Woodford for useful discussions. The usual caveat applies. The views expressed in the paper are those of the authors and are not necessarily reflective of views at the Federal Reserve Bank of New York, Federal Reserve Bank of Dallas or the Federal Reserve System. Preston acknowledges research support from the Australian Research Council, under the grant FT130101599.

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