Expectation Traps and Monetary Policy

Questions & answers

Q1. What gap in the existing time-inconsistency literature does the paper set out to fill?

That static Kydland-Prescott/Barro-Gordon models have a unique equilibrium (so persistent swings in inflation would require corresponding swings in fundamentals, which are often hard to identify), while infinite-horizon versions using trigger strategies can rationalize almost any inflation path – “such models have embarrassingly many equilibria. It is hard to know what observations would be ruled out by such trigger strategy equilibria” (Introduction, p. 1). The paper’s stated contribution is to embed the same economic forces “into a standard general equilibrium model” and show that persistent high- and low-inflation regimes can both arise “even though we explicitly rule out trigger strategies” (Introduction, p. 1).

Q2. How does the general equilibrium model reproduce the Kydland-Prescott/Barro-Gordon trade-off between the benefits of surprise inflation and the costs of realized inflation?

Unexpected inflation raises output because some prices are preset (sticky) and firms have monopoly power, so a monetary expansion that raises output “reduces the monopoly distortion,” benefiting households; realized inflation is costly because “households must use previously accumulated cash to purchase some goods, called cash goods,” and inflation forces substitution toward credit goods, which “tends to lower welfare” (Introduction, p. 1-2). By design, this general equilibrium structure captures “the trade-offs between the benefits of unexpected inflation and the costs of realized inflation in the Kydland-Prescott and Barro-Gordon framework” (p. 2).

Q3. What are the two “defensive actions” that generate multiple equilibria, and how does each work?

First, sticky-price firms: “if sticky price firms expect inflation to be high, they take appropriate defensive actions and set their prices correspondingly high. If the monetary authority fails to validate the expectations of firms, output will be low. A benevolent monetary authority may find it optimal to validate firms’ expectations” (Introduction, p. 2). Second, households choosing their cash/credit mix before the money growth rate is set: “if households expect high inflation and have chosen to purchase few goods with cash, the marginal cost of unanticipated inflation is small. The monetary authority has a strong incentive to inflate. If households expect low inflation, however, they choose to purchase most goods with cash and the marginal costs of unexpected inflation are high. The monetary authority then does not have a strong incentive to inflate” (Introduction, p. 2-3). Both mechanisms make private expectations partly self-validating through the monetary authority’s own optimizing response.

Q4. Why do the authors think this multiplicity is likely to be a robust feature of general equilibrium monetary models, not a knife-edge special case?

Because “the best response functions in general equilibrium models are inherently non-linear and… multiplicity occurs naturally,” in contrast to the linear best-response functions assumed (often implicitly) in the original static Kydland-Prescott/Barro-Gordon setup, which is what delivers their unique equilibrium (Introduction, p. 3). The paper’s formal existence result (Proposition 2) makes this precise: “there is a critical value of z… such that for z < ẑ there are no Markov equilibria, for z = ẑ there is at least one Markov equilibrium, and for z > ẑ there [are] at least two Markov equilibria” – the model does not admit a unique intermediate case (Section on interest rate policy correspondence).

Q5. How does this paper’s notion of “expectation trap” differ from the concept introduced in Chari, Christiano, and Eichenbaum (1998)?

The earlier paper showed expectation traps could arise in conventional general equilibrium monetary models but relied on trigger strategies – repeated-game punishments – to support the multiple outcomes, which the authors criticize because “for folk-theorem-like reasons, virtually any inflation outcome can be rationalized as an equilibrium” under trigger strategies (Introduction, p. 3). This paper instead “restrict[s] attention to Markov equilibria that rule out trigger strategies,” and its “key finding is that expectation traps occur even in the absence of trigger strategies” (Introduction, p. 3) – a substantially stronger and more disciplined result, since Markov equilibria are pinned down by current payoff-relevant states rather than histories of play.

Q6. What distinct empirical prediction does the model make about interest rates across the two equilibria, and is it confirmed?

“The interest rate response to a shock switches sign between the high and low inflation equilibria. For example, the interest rate is increasing in the technology shock in the low inflation equilibrium and decreasing in this shock in the high inflation equilibrium,” while “output is increasing in this shock in both equilibria” (Introduction, p. 3-4). This implies the output-interest-rate correlation should be more negative under high inflation, which the paper confirms in International Financial Statistics data: within high-inflation countries, the correlation “is 0.08 in low inflation episodes and −0.45 in high inflation episodes” (Table 1); across countries, it averages −0.20 for low-inflation countries and −0.33 for high-inflation countries (Table 2) – “with one exception, the correlation between output and interest rates is higher in the low inflation episodes than in the high inflation episodes” (Section IV).

Q7. Does the model also match the data on relative volatility, and how well quantitatively?

Qualitatively yes, though not to full quantitative scale: in the data, “the standard deviation of the interest rate is 3.57” in low-inflation episodes versus “350190” in high-inflation episodes (within-country), and 1.84 versus 283324 across low- versus high-inflation countries (Section IV) – a pattern the simulated model reproduces in direction (interest-rate volatility an “order of magnitude” higher in the high-inflation equilibrium) even though “the model obviously fails to match the level of volatility in these variables in the data” (Section IV). The model’s simulated output-interest-rate correlations (0.013 in the low-inflation equilibrium, −0.019 in the high-inflation equilibrium) are “qualitatively similar to the corresponding statistics in the data” (Section IV).

Q8. What is the paper’s main policy lesson?

That “the costs of discretionary monetary policy include not just high average inflation, but volatile and persistent inflation as well,” because “defensive actions taken by the public to protect itself from high inflation reduce the costs of inflation for a benevolent monetary authority and induce the authority to supply high inflation” – a force the authors argue “is likely to be present in a large class of monetary models” (Conclusion). They conclude “the gains to setting up institutions which increase commitment to future monetary policies are likely to be high” (Conclusion) – strengthening the traditional time-inconsistency case for commitment devices by showing the costs of discretion extend beyond a constant inflationary bias to include self-fulfilling volatility and persistence in inflation itself.