Price and output stability under price-level targeting.

• Author: Cover, James Peery

1. Introduction

   Most central banks operate under the twin goals of price and output stability, with price stability defined as a low and stable inflation rate somewhere between 2 and 3% per year. (1) There are two ways, however, to achieve an average inflation rate of 3%. Under what is called inflation targeting, even if the target rate is missed during the current period, the target remains at 3% for all future periods. Under what is called price-level targeting, the long-run path of the expected price level is predetermined. (2) Thus, if inflation is 4% during the current period, the inflation target during the next period is reduced to a level below 3% until the path of the price level returns to its original target growth path. In contrast, under inflation targeting, anytime the realized price level differs from its expected value, there is a new long-run path for the expected price level. (3)

   This paper shows that this difference between price-level targeting and inflation targeting is sufficient to cause price-level targeting to be superior to inflation targeting under a reasonable set of assumptions. These include rational expectations and an inverse relationship between the real interest rate and aggregate demand. The reason for this result is straightforward. Suppose the monetary authority pegs the nominal rate of interest for the duration of the period in question. Under price-level targeting, whenever the realized price level is above its expected value in the current period, expected future inflation declines, raising the real rate of interest. This reduces aggregate demand, thereby reducing the size of the unexpected change in the price level. As a result, the variation of output around its full-information value and the variation of the price level around its target value are both reduced. That is, price-level targeting provides the economy with a form of built-in stability not provided by inflation targeting. (4)

   The argument of this paper is important because it is widely believed that the only advantage of price-level targeting over inflation targeting is the former's ability to provide a greater degree of price-level stability in the long run. According to Svensson (1999), the emerging conventional wisdom is that this advantage comes "at the cost of increased short-term variability of inflation and output." (5) Although writers in addition to Svensson have recently questioned this conventional wisdom and presented models in which price-level targeting is superior to inflation targeting, Mishkin (2000) argues that these results are model-specific and that they therefore do not make a convincing case for the superiority of price-level targeting. By identifying a new mechanism through which price-level targeting may stabilize the economy, this paper strengthens the case for price-level targeting. The mechanism we identify operates under a different set of assumptions from those made by Svensson. Taken together, this suggests a wider set of conditions under which price-level targeting will be beneficial.

   The remainder of this paper is organized as follows. Section 2 discusses some of the recent literature on the choice between price-level and inflation targeting. Section 3 presents the model, while section 4 presents solutions to the model, first under inflation targeting and then under price-level targeting. A comparison of the solutions shows that price-level targeting provides greater output and price stability. Section 5 presents a graphical explanation of the results that is straightforward enough to use in an intermediate-level macroeconomics classroom. Finally, section 6 offers a summary and some conclusions.

2. Previous Literature

   It is widely accepted that price-level targeting leads to a lower long-run variance of the price level than does inflation targeting. Thus, for advocates of inflation/price-level targeting, the interesting comparison between the two is within the context of short-run stabilization policy. Hence, if one agrees with McCallum (1990) that the gain in long-run price-level predictability obtained from price-level targeting is relatively small, then an acceptance of the conventional wisdom that price-level targeting results in more short-run variability in both output and inflation is enough to make inflation targeting preferable to price-level targeting. Svensson (1999), however, presents a model in which this conventional wisdom does not hold. Rather, in his model, the variance of output is the same under price-level targeting as it is under inflation targeting. Further, he finds that the variability of inflation can be lower under price-level targeting than under inflation targeting. That is, price-level targeting might provide the monetary authority with a "free lunch."

   In Svensson's model, aggregate supply is described by [g.sub.t] = [rho][g.sub.t-1] + [alpha]([[pi].sub.t -- t-1][[pi].sub.t]) + [[epsilon].sub.t], where [g.sub.t] is the output gap (or the natural log of output relative to its target value), [rho] is the autoregressive coefficient, [[epsilon].sub.t] is a supply shock, and [sub.t-1][[pi].sub.t] is the expectation of time t inflation conditional on time t - 1 information. The policymaker observes the supply shock and then chooses the price level (making the aggregate demand curve a horizontal line at the chosen price level). If the policymaker cannot commit to an optimal policy and if p > 1/2, then the variance of inflation is lower under price-level targeting than it is under inflation targeting. (6)

   But do Svensson's results apply to any real-world economies? Parkin (2000), citing several simulation studies (7) and asserting that the output correlation coefficient is likely to be very high, argues that they do. But, as Howitt (2000) and Mishkin (2000) point out, it is not obvious that the specific assumptions necessary for a free lunch within Svensson's framework hold in practice. Because the mechanism we identify operates under a set of assumptions that differ in important ways from Svensson's model, it suggests that there is a broader set of circumstances under which price-level targeting can lead to superior stabilization properties when compared to inflation targeting. Thus, the model presented in this paper considerably strengthens the case for price-level targeting.

   A key assumption in Svensson's model is the existence of output persistence. Because the mechanism identified below does not depend on the existence of output persistence, it is not included in the model. Rather, the model employed below emphasizes the effect of the interest rate on aggregate demand and assumes that the central bank uses an interest-rate instrument. The model shows that if aggregate demand depends on the rate of interest, then the contemporaneous response of economic actors to shocks is different under price-level and inflation targeting. This difference in responses, which has been neglected in the previous literature, causes price-level targeting to provide the economy with built-in stability.

   Svensson's results will not hold if the central bank has the ability to commit to an optimal policy. Our result is not sensitive to whether or not the central bank can commit to an optimal policy. (8) One other important difference between our model and Svensson's concerns the timing of aggregate shocks. Svensson assumes that monetary policy is set after shocks have been realized, and we assume that policy is set before these shocks are realized. The role of this assumption is discussed further in the conclusion.

   In the model presented below, the one-step-ahead variances of output and the price level are lower under price-level targeting than under inflation targeting. In Svensson's model, these variances are identical. To our knowledge, the possibility of lower output variance under price-level targeting has not been previously identified in the theoretical literature. Further, in the case of zero-output persistence, Svensson finds that inflation variance is always lower under inflation targeting, whereas the present model yields an ambiguous comparison. Thus, if the mechanism in this paper is considered in addition to Svensson's, the case that inflation variance can be lower under price-level targeting is strengthened considerably.

3. The Model

   The model developed below assumes rational expectations and uses a Lucas (1972) aggregate supply curve under which aggregate supply is positively related to innovations in the price level. The aggregate demand relationship is derived from the goods market cleating (IS) and money market (LM) clearing conditions. In a recent paper, McCallum and Nelson (1999) defended the use of the IS-LM model and argued that it could be made consistent with microfoundations. Although their approach results in an IS curve that includes the expected future value of output, since here the expected future value of output is constant, such a term is subsumed into the intercept, a, in Equation 1 below (see also McCallum 1989, pp. 102-7).

   Although the model employed here is simple, it is reasonable. The simplicity of the model allows the derivation of analytical solutions that have a meaningful economic interpretation. Furthermore, the crucial feature of aggregate demand in our model is that it is decreasing in the real interest rate. This is a reasonable property that survives in more complex settings. (9)

   The basic model consists of the following three equations:

   IS: [y.sup.d.sub.t] = a - [alpha][[R.sub.t] -...