Output effects of disinflation with staggered price setting.

• Author: Carlson, John A.

1. Introduction

   Monetary authorities who choose to reduce their country's rate of inflation, that is, to disinflate, are usually faced with subsequent recessions. A pattern of slower growth in the money supply, followed by a lower inflation rate and lower output, can be seen in historical statistics, such as those examined by Friedman and Schwartz (1963).

   When there was thought to be a permanent Phillips curve trade-off between inflation and unemployment, an important policy question was what combination of inflation and unemployment was most desirable. As economists came to accept the idea of a short-run but not a long-run trade-off between inflation and unemployment, the stage was set to ask about how much output is lost as a result of a disinflation. Okun (1978), using results from several econometric models, estimated that an extra 1% unemployment rate for one year would reduce inflation between one-sixth and one-half of 1%. To reduce inflation by 1%, these figures suggested that the unemployment rate needed to be higher by 2 to 6% of the labor force. If one uses an "Okun's law" of 2.5% of gross national product (GNP) lost for an unemployment rate higher by 1%, then the output lost to reduce inflation by 1% would be between 5 and 15% of GNP.

   The term "sacrifice ratio" is now widely understood to mean the ratio of the cumulated percentage loss of output (at an annual rate) to the reduction in the trend rate of inflation. (1) For the disinflation in the early 1980s in the United States, Fischer (1986) figures the sacrifice ratio was about five. Other empirical studies, such as those in Ball (1994b) and Jordan (1997), find a range of estimates around an average sacrifice ratio of about two. (2)

   The pattern of slower rates of growth in the money supply being followed by recessions has posed a challenge to theorists to develop plausible models that help us understand this phenomenon. The existence of staggered price setting is one candidate explanation, and Taylor (1979, 1980) deserves credit for introducing formal analyses of how overlapping wage contracts can lead to a persistence in wages and deviations in output from its natural rate during disinflations.

   Sargent (1983), in discussing conditions for a successful disinflation without much output loss, characterizes the Taylor model as follows: "In this class of models, in terms of unemployment it is costly to end inflation because firms and workers are now locked into long-term wage contracts that were negotiated on the basis of wage and price expectations that prevailed in the past. ... In addition, the wage contracting mechanism contributes some momentum of its own to the process, so that the resulting sluggishness in inflation cannot be completely eliminated or overcome by appropriate changes in monetary and fiscal policies" (p. 55). Similarly, Vegh (1992), explaining why ending hyperinflations appears to involve less output loss than ending moderate inflations, writes, "The fact that in hyperinflations backward-looking contracts (so prevalent in industrial and chronic-inflation countries) disappears is probably at the heart of the difference in output costs" (p. 656).

   In a widely used textbook, Romer (1996, p. 273) writes that "the Taylor model exhibits price level inertia: the price level adjusts fully to a monetary shock only after a sustained departure of output from its normal level. As a result, it is often claimed that the Taylor model accounts for inflation inertia." Romer then adds the provocative sentence: "Ball (1994a) demonstrates, however, that this claim is incorrect." The link between the discrete-time model presented by Romer and the contention attributed to Ball is not immediately evident and needs to be clarified.

   Beginning with an environment of steady growth in money and prices, Ball (1994a) assumes that a new regime suddenly announces a fully credible continuous linear decline in the growth rate of money. He also assumes that each firm sets price for one year and that the timing of the changes is spread out evenly over a year. Instead of deriving the path for prices and comparing it with the path of money, Ball uses an indirect approach in which he shows that prices will be below the level necessary to keep output constant if the decline in the money supply does not proceed too rapidly. He reports that the borderline case for no change in output occurs when money growth reaches zero at 0.68 of a year, or after about eight months. Any fully-anticipated steady reduction in the future growth rate of money that will reach zero in more than 0.68 of a year generates increases in output. On the basis of this result, in a bit of an overstatement, Ball concludes, "With credible policy and a realistic specification of stagger ing, quick disinflations cause booms" (p. 289).

   In what follows, I will show that the discrete-time model can be readily used to analyze an array of disinflation scenarios, including Ball's, with explicit solutions for the paths of prices and output. This makes it possible to sort out how the degree of credibility may or may not overcome the negative output effects of price inertia imparted by the nonsychronization of price setters and helps build intuition about these tricky issues. The model is essentially the one used by Taylor (1979) in which two groups of workers have their wages fixed for two overlapping periods. The primary difference is that the model will be formulated in terms of price setters rather than wage setters. The basic structure for this analysis can be found in Romer (1996, pp. 265-73).

   Section 2 sets out the model, and section 3 characterizes the steady-state solution. Section 4 analyzes the impact of a cold-turkey disinflation. Sections 5 and 6 study policies of gradual disinflation under different assumptions about policy credibility. Section 7 looks at the effect of a credibly anticipated deflation, and section 8 concludes.

2. The Model

   The first assumption is that output is determined by the real money supply. A frequently used and simplest form of this hypothesis is the following equation:

   y = m - p, (1)

   where y is the log of output, m is the log of the money supply, and p is an average of the log of prices set by all firms. We can treat y = 0 as the natural rate of output so that in long-run equilibrium p = m.

   The next assumption is that a firm's desired price is an average of m and p:

   [p.sup.*] = [Phi]m + (1 - [Phi])p 0 < [Phi] < 1 (2)

   ...