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Price and output stability under price-level targeting.

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] - ([sub.t][p.sub.t+1] - [p.sub.t])] + [[epsilon].sub.i,t]; [alpha] > 0. (1)

LM: [m.sub.t] - [p.sub.t] = [ky.sup.d.sub.t] - [beta][R.sub.t] + [[epsilon].sub.2,t]; [beta], k > 0. (2)

AS: [y.sup.s.sub.t] = c + [gamma]([p.sub.t] - [sub.t-1][p.sub.t]) + [[epsilon].sub.3,t]; [gamma] > 0. (3)

Time subscripts are denoted by t. The logarithms of output demanded and supplied are [y.sup.d.sub.t] and [y.sup.s.sub.t], respectively, [p.sub.t] is the logarithm of the price level, [m.sub.t] is the logarithm of the money stock, [R.sub.t] is the nominal rate of interest, and a and c are constants. The expected value of [p.sub.t], given information available during period t - 1, is denoted [sub.t-1][p.sub.t]. The [[epsilon].sub.i,t] are mutually and serially uncorrelated, mean zero shocks with variances equal to [[sigma].sup.2.sub.i].

Equation 1 is an IS curve that states that output demand decreases as the real interest rate increases. Equation 2 is a portfolio equilibrium condition or LM curve that states real money balances demanded increase as output demanded increases and as the nominal rate of interest decreases. Equation 3 is an expectations-augmented aggregate supply curve. As [gamma] in Equation 3 approaches zero, the aggregate supply curve becomes vertical, and the model approaches a real business cycle model. On the other hand, as [gamma] increases without bound, the aggregate supply curve becomes very flat, and the model approaches a Keynesian model in which unexpected fluctuations in aggregate demand affect output with practically no effect on the price level. (10)

The model is closed by assuming that monetary policy is implemented in a manner that minimizes the monetary authority's loss function. Here, the loss function is assumed to be (11)

Loss: [L.sub.t] = [OMEGA][([p.sub.t] - [p.sub.t-1] - [[bar.[phi]].sub.t]).sup.2] + (1 - [OMEGA]) ([y.sub.t] - [[bar.y.sub.t]); 0 < [OMEGA] < 1, (4)

where [bar.[[pi].sub.t] and [bar.[y.sub.t]], respectively, are the target values for the rate of inflation and level of output for period t.

Under inflation targeting, [bar.[[phi].sub.t] is fixed for all t values and always equals [bar.[phi]]. Under price-level targeting, the value of [bar.[[phi].sub.t] depends on the difference between [p.sub.t-1] and its target value, [[bar.p].sub.t-1], in a way that will be shown in section 4.2.

The output target at time t is given by

[[bar.y].sub.t] = c + [[epsilon].sub.3,t]. (5)

This target reflects the contemporaneous supply shock. To the extent that supply shocks reflect real productivity shocks, economic theory suggests that we should not attempt to stabilize against them. Thus, our specification for the output target would appear to be valid in a normative context. Whether it explains actual central bank objectives is less clear, but the positive implications of our model are robust to the alternative assumption that the output target is constant at c. The reason is that the central bank sets the interest-rate target before it views the current period supply shock. (12)

Because there is no output persistence in the model, the central bank's optimization problem is time separable in the following sense: Minimization of the loss function in Equation 4 each period is equivalent to the minimization of a loss function that is explicitly intertemporal. Since these approaches are equivalent for our model, we will use the simpler specification of the loss function in Equation 4. The timing of the model is as follows:

(i) At the beginning of time period t, the monetary authority chooses the nominal rate of interest, [R.sub.t], which minimizes the expected value of Equation 4. Once chosen, the rate of interest is not changed until the beginning of the next period.

(ii) The current period's shocks are realized.

(iii) The time t price level and output are determined, and agents form expectations of the time t + 1 price level.

Note that the expectation of the time t price level is set in period t - 1 and is taken as given at time t by the monetary authority. The graphical discussion in section 5 makes it clear that the results do not depend on the assumption that the monetary authority pegs the rate of interest rather than the money supply.

4. The Model's Solution

Solution under Inflation Targeting

Under inflation targeting, as long as [OMEGA] > 0, it can be shown that [sub.t] [p.sub.t+1] = [p.sub.t] + [bar.[phi]]. We begin by defining expected inflation for the next period and current inflation as [sub.t] [[phi].sub.t+1] = [sub.t][p.sub.t+1] - [p.sub.t] and [[phi].sub.t] = [p.sub.t] - [p.sub.t-1], respectively. Therefore, we can write ([p.sub.t] - [p.sub.t-1] - [bar.[phi]]) = ([[phi].sub.t] - [bar.[phi]]).

To come up with an expression for [sub.t][p.sub.t+1], we must analyze how economic actors during period t evaluate policy during period t + 1. The loss function during period t + 1 is

[L.sub.t+1] = [OMEGA][([p.sub.t+1] - [p.sub.t] - [bar.[phi]]).sup.2] + (1 - [OMEGA]) [([y.sub.t+1] - [[bar.y].sub.t+1])).sup.2].

If we define [[bar.y].sub.t] to be c + [[epsilon].sub.3,t], then, using Equation 3, the loss function becomes

[L.sub.t+1] = [OMEGA][([p.sub.t+1] - [p.sub.t] - [[bar.[phi]]).sup.2] + (1 - [OMEGA])([gamma][([p.sub.t+1] - [sub.t] [p.sub.t+1])).sup.2]. (6)

Applying the expectations operator to Equation 6, conditional on information available during period t, yields

[E.sub.t][L.sub.t+1] = [E.sub.t] {[OMEGA][([p.sub.t+1] - [p.sub.t] - [bar.[pi]]).sup.2] + (1 - [OMEGA])[([gamma]([p.sub.t+1] - [sub.t][p.sub.t+1])).sup.2]}. (7)

While noting the dependence of [p.sub.t+1] on [R.sub.t+1], take the first derivative of Equation 7 with respect to [R.sub.t+1] and set the result equal to zero to yield (13)

[sub.t][p.sub.t+1] - [p.sub.t] = [bar.[pi]].

Now, replace [sub.t][p.sub.t+1] - [p.sub.t] in the IS equation with [bar.[pi]] to obtain

[y.sup.d.sub.t] = a - [alpha][[R.sub.t] - [bar.[pi]]] + [[epsilon].sub.1,t]. (1')

Because the solution for [sub.t][p.sub.t+1] also implies that [sub.t-1][p.sub.t] = [p.sub.t-1] + [bar.[pi]], we can use Equations 1' and 3 to solve for the price level and level of output as a function of the interest rate. Inserting these solutions into Equation 4 and simplifying yields

[E.sub.t-1][L.sub.t] = {[[OMEGA] + (1 - [OMEGA])[[gamma].sup.2]]/[[gamma].sup.2]}[E.sub.t-1] [[a - c - [alpha]([R.sub.t] - [bar.[pi]]) + [[epsilon].sub.1,t] - [[epsilon].sub.3,t].sup.2]

Taking the derivative of this expected loss function with respect to [R.sub.t] and setting the result equal to 0 yields

[R.sub.t] = [(a - c)/[alpha]] + [bar.[pi]]. (8)

Insert Equation 8 into Equation 1 to obtain

[y.sub.t] = c + [[epsilon].sub.1,t]. (9)

At the beginning of period t, the monetary authority will choose the rate of interest that causes expected output, [E.sub.t]-[sub.1][y.sub.t], to equal c. Note that output depends on the IS shock but not on the LM or aggregate supply shock. This reflects the fact that interest-rate targeting by the central bank causes the aggregate demand curve to be vertical. (14) Inserting Equation 9 into Equation 3 and solving for the price level yields

[p.sub.t] = [p.sub.t-1] + [bar.[pi]] + (1/[gamma])([[epsilon].sub.1,t] - [[epsilon].sub.3,t]). (10)

The IS shock raises the current period price level, while an AS shock lowers the current period price level.

Solution under Price-Level Targeting

Price-level targeting is assumed to take the following form:

[[bar.p].sub.t] = [[bar.p].sub.t-1] + [bar.[pi]] (11)

Subtracting [p.sub.t-1] from both sides of Equation 11 yields

[[bar.p].sub.t] - [p.sub.t-1] = [[bar.p].sub.t-1] - [p.sub.t-1] + [bar.[pi]]. [bar.[pi]].sub.t] = [bar.[pi]] - ([p.sub.t-1] - [[bar.p].sub.t-1] (12)

According to Equation 11, there is a predetermined path of prices that the monetary authority is targeting. If [bar.[pi]] > 0, this implies that the price-level target is trending upward over time. Thus, price-level targeting is consistent with a positive average rate of inflation. As shown by Equation 12, if the price level is below its target during period t - 1, the target rate of inflation during period t is above [bar.[pi]]. Similarly, if the price level is above its target during period t - 1, the target rate of inflation during period t is below [bar.[pi]].

Substituting Equations 3, 5, and 12 into the loss function, Equation 4, yields

[L.sub.t] = [OMEGA][([p.sub.t] - [[bar.p].sub.t-1] - [bar.[pi]]).sup.2] + (1 - [OMEGA]) [([gamma]([p.sub.t] - [sub.t-1][p.sub.t])).sup.2]. (4")

Rewriting Equation 4" for period t + 1 and taking the expected value yields

[E.sub.t][L.sub.t+1] = [E.sub.t]{[OMEGA][([p.sub.t+1] - [[bar.p].sub.t] - [bar.[pi]]).sup.2] + (1 - [OMEGA])[([gamma]([p.sub.t+1] - [sub.t][p.sub.t+1])).sup.2]}. (13)

While noting the dependence of [p.sub.t+1] on [R.sub.t+1], taking the first derivative of Equation 13 with respect to [R.sub.t+1] and setting the result equal to zero yields [sub.t][[p.sub.t+1] = [[bar.p].sub.t] + [bar.[pi]]. This allows the equation for the IS curve to be written as

[y.sup.d.sub.t] = a - [alpha][[R.sub.t] - [bar.[pi]] - ([[bar.p].sub.t] - [p.sub.t])] + [[epsilon].sub.1,t] (1")

Since [sub.t-1][p.sub.t] = [[bar.p].sub.t-1] + [bar.[pi]], Equations 1" and 3 can be used to write the expected loss function for the current period as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].

Minimizing the expected loss with respect to [R.sub.t] yields

[R.sub.t] = [(a - c)/[alpha]] + [bar.[pi]]. (14)

Inserting Equation 14 into Equation 1" yields the expression for output demanded.

[y.sup.d.sub.t] = c - [alpha] ([p.sub.t] - [sub.t-1][p.sub.t]) + [[epsilon].sub.1,t]. (15)

Solving Equations 15 and 3 jointly for equilibrium output and the price level yields the results for price-level targeting.

[y.sub.t] = c + ([gamma[[epsilon].sub.1,t] + [alpha][[epsilon].sub.3,t])/ ([alpha] + [gamma]); (16)

[p.sub.t] = [[bar.p].sub.t] + ([[epsilon].sub.1,t] - [[epsilon].sub.3,t])/ ([alpha] + [gamma]). (17)

From Equation 16, we see that output is increasing in both the aggregate demand and aggregate supply shocks. The interest-rate peg makes the aggregate demand curve vertical, so how does a supply shock affect output? A positive supply shock in the current period lowers the current price level below its target value, as shown in Equation 17. Under price-level targeting, this implies a higher rate of inflation in the next period. Since the interest rate is pegged, the real rate of interest falls, leading to a higher level of aggregate demand. This mechanism is not at work under inflation targeting, which is why output is independent of the supply shock under that regime (see Eqn. 9).

Comparison of Price-Level and Inflation Targeting

Under inflation targeting, the time t price-level target is implicitly

[[bar.p].sub.t] = [p.sub.t-1] + [bar.[pi]].

This equation plus Equations 5, 9-11, 16, and 17 can be used to find the deviations of output, the price level, and inflation from their target values under both inflation and price-level targeting. The results for inflation targeting are given in Equation 18a-c.

[y.sub.t] - [[bar.y].sub.t] = [[epsilon].sub.1,t] - [[epsilon].sub.3,t]. (18a)

[p.sub.t] - [[bar.p].sub.t] = 1/[gamma]([[epsilon].sub.1,t] - [[epsilon].sub.3,t]). (18b)

[[pi].sub.t] - [bar.[pi]] = 1/[gamma]([[epsilon].sub.1,t] - [[epsilon].sub.3,t]). (18c)

The results for price-level targeting are given in Equation 19a-c.

[y.sub.t] - [[bar.y].sub.t] = [gamma]([[epsilon].sub.1,t] - [[epsilon].sub.3,t])/[alpha] + [gamma] (19a)

[p.sub.t] - [[bar.p].sub.t] = ([[epsilon].sub.1,t] - [[epsilon].sub.3,t])/ ([alpha] + [gamma])

[[pi].sub.t] - [bar.[pi]] = ([[epsilon].sub.1,t] - [[epsilon].sub.3,t]) - ([[epsilon].sub.1,t-1] - [[epsilon].sub.3,t-1])/([alpha] + [gamma]) (19c)

Note that in Equation 19c, we write [[pi].sub.t] - [bar.[pi]] rather than [[pi].sub.t] - [[bar.[pi]].sub.t]. As pointed out by Svensson (1999), the interesting issue is whether price-level targeting performs better than inflation targeting, even when society's preferences correspond to inflation targeting. Thus, in Equation 19c, we examine the deviation from a fixed inflation target.

Table 1 provides a summary of the variances of these variables around their target values. As can be seen from the table, the variance of output (about its full-information value) as well as the variance of the price level (about its target value) are always lower under price-level targeting than under inflation targeting. This contrasts with Svensson's (1999) results, in which under both forms of targeting, the variance of output is the same. It also contrasts with the conventional wisdom that price-level targeting increases the variance of output. The reason for this superiority of price-level targeting is as stated in the introduction: Whenever there is a shock that changes the price level, under price-level targeting, there is a change in expected inflation in the opposite direction, which in turn (through its effect on the real rate of interest) causes aggregate demand to change in a way that stabilizes the economy. This can be seen from Table 1 by noting that as [alpha] approaches zero, the variances of output and the price level under price-level targeting approach those under inflation targeting. If the real rate of interest does not affect aggregate demand (i.e., [alpha] = 0), then the stabilization effect we have identified is not present in the model. Further intuition for this result is provided in the next section of this paper.

As pointed out in the introduction, the emerging conventional wisdom is that price-level targeting results in a higher variance in inflation than does inflation targeting. But as can be seen from the last column of Table 1, the comparison of inflation variance under the two regimes is ambiguous. It can easily be seen from the entries in the table that if [alpha] is large enough relative to [gamma], then the variance of inflation is lower under price-level targeting.

To obtain some intuition for this result, note that (-1/[alpha]) is the slope of the IS curve, while (1/[gamma]) is the slope of the AS curve. When the IS curve is relatively flat ([alpha] is relatively large), spending is highly responsive to changes in the real rate of interest. On the other hand, if the AS curve is relatively steep ([gamma] is relatively small), changes in demand have a relatively large effect on the price level and therefore induce a relatively large change in expected inflation under price-level targeting. Hence, as [alpha] increases relative to [gamma], the change in demand induced by price-level targeting and the resulting degree of built-in stability both increase. If the built-in stability induced by price-level targeting is sufficiently large, then price-level targeting also stabilizes the rate of inflation more than does inflation targeting.

5. A Graphical Explanation

Figure 1 presents a graphical description of what happens in the above model when there is an aggregate demand shock. At the beginning of the period, the monetary authority sets the rate of interest at [R.sub.0], causing the LM curve to be horizontal at [R.sub.0]. When the interest rate equals [R.sub.0], the quantity of output demanded is [Y.sub.0]. Since interest-rate targeting causes the aggregate demand curve to be vertical, output demanded equals output supplied at the point [P.sub.0], [Y.sub.0] on the lower graph in Figure 1. Let us assume that if there are no shocks during the current period, [Y.sub.0] is the optimal level of output, and [P.sub.0] is the target for the price level. (15)

[FIGURE 1 OMITTED]

If there is a demand shock that shifts the IS curve to IS', then under inflation targeting, the new level of output is [Y.sub.[pi]]. That is, under a fixed rate of interest and inflation targeting, output increases by the full amount of any demand shock. (16) Since an unexpected increase in the price level is necessary for output to increase, the price level also must increase all the way to [P.sub.[pi]]. But if the monetary authority is targeting the price level, as the price level increases in response to the demand shock, expected inflation decreases. An overshooting of the price-level target in the current period leads to a reduced target level for inflation in the subsequent period. For a given nominal rate of interest, a decrease in expected inflation raises the real rate of interest. This causes the IS curve to shift back to the left to IS", so that output and the price level increase only to [P.sub.p], [Y.sub.p]. Hence, price-level targeting causes an automatic decrease in demand that partially offsets any unexpected increase in demand. That is, price-level targeting provides built-in stability for demand shocks.

Now consider Figure 2. Once again, assume that if there are no shocks during the current period, [Y.sub.0] is the optimal level of output, and [P.sub.0] is the target level for the price level. If there is a shock to aggregate supply that shifts the short-run aggregate supply curve to SRAS', the full-information level of output increases to [Y.sub.optimal]. Under inflation targeting, output demanded remains at Y0, and the price level declines to [P.sub.[pi]], while under price-level targeting, as the price level declines toward [P.sub.[pi]], expected inflation increases. For a given nominal rate, an increase in expected inflation reduces the real rate of interest, so there is an increase in output demanded. Thus, the IS curve shifts to the right to IS'. This increase in output demanded prevents the price level from declining as much as otherwise and allows output to increase in response to the temporary increase in aggregate supply. As a result, under price-level targeting, both output and the price level stay closer to their optimal levels in response to both supply and demand shocks.

[FIGURE 2 OMITTED]

The superior performance of price-level targeting when there is an aggregate supply shock depends in part on our assumption that the output target should reflect the current period supply shock. Suppose that this is true but that, for some reason, the preferences of the monetary authority do not incorporate the contemporaneous supply shock. The result discussed in Figure 2 continues to hold because the interest rate is set prior to observance of the supply shock. As a result, the monetary authority optimally chooses the same interest-rate target, regardless of whether or not the output target in its loss function is adjusted to reflect the contemporaneous aggregate supply shock.

The above discussion of Figures 1 and 2 can easily be modified for the case in which the rate of interest is not pegged. In this case, there would be an upward-sloping LM curve and a downward sloping aggregate demand curve. The results, as shown by Figures A1 and A2 in the Appendix, are the same. Price-level targeting reduces the variation of the price level about its target value and the variation of output about its full-information value.

[FIGURES 1A-2A OMITTED]

6. Conclusion

This paper employs a standard macroeconomic model to contrast the economy's contemporaneous response to shocks under inflation targeting and price-level targeting. Output and the price level show less variance around their target values under price-level targeting. When a shock hits the economy under price-level targeting, this changes expected inflation for next period, which in turn causes changes in the real interest rate that act to stabilize the economy against both aggregate demand and aggregate supply shocks. This mechanism by which price-level targeting stabilizes output and the price level has not, to our knowledge, been previously identified in the literature.

Our model uses a neoclassical Phillips curve, but our results are not sensitive to this assumption. As the graphical presentation in section 5 makes clear, our results do not depend on the reason why the short-run aggregate supply curve is upward sloping. In particular, the results of the model hold not only if the Phillips curve is neoclassical, but also if it is New Keynesian. (17)

The mechanism through which price-level targeting leads output to be more stable under price-level targeting than under inflation targeting does depends on a key informational assumption of the model. We assume that the central bank sets the interest rate before observing the contemporaneous shocks. If the central bank can fully observe all shocks before setting the interest rate, the mechanism we identify will not apply. Svensson (1999) assumes that the central bank can fully observe the contemporaneous shock, and this assumption is crucial for his result. Thus, if we make this informational assumption, we are essentially returning to the framework of his model, and his insights will apply. (18)

Although the central bank probably has some ability to forecast contemporaneous shocks, it clearly cannot do so perfectly. Nevertheless, the insights of our analysis apply to the components of the current shocks, which the central bank is unable to forecast correctly. If these forecasting errors are significant, then the insight provided by our model is important in evaluating the choice between inflation and price-level targeting. Combined with Svensson's work, our model suggests potential gains from price-level targeting, regardless of the timing of aggregate shocks.

In identifying a new mechanism by which price-level targeting may stabilize output and the price level, the results of this paper are strongly complementary to those of Svensson (1999), and they significantly strengthen the case for price-level targeting.

Appendix

This appendix employs graphs to demonstrate that the paper's main results continue to hold if the monetary authority uses a money-stock rather than an interest-rate instrument. We first consider the case of a demand shock and then the case of a supply shock.

Consider Figure A1. Suppose the monetary authority sets the money stock at [M.sub.0]. Assume that, if there are no shocks, this causes the equilibrium interest rate to be [R.sub.0], the equilibrium output to be [Y.sub.0], and the equilibrium price level to be [P.sub.0]. Assume that [Y.sub.0] and [P.sub.0] are also the target values of output and the price level. A shock to aggregate demand shifts the IS curve to IS' and the aggregate demand curve to AD'. Under inflation targeting, as the price level increases toward its new equilibrium value, the quantity of real money balances declines, causing the LM curve to shift upward until it intersects with IS' at the same level of output at which AD' intersects the short-run aggregate supply curve, SRAS. Hence, the price level increases to [P.sub.[pi]], and output increases to [Y.sub.[pi]]. Under price-level targeting, however, as the current price level increases toward [P.sub.[pi]], expected inflation decreases, causing an increase in the real rate of interest (for any given nominal rate of interest). This shifts the IS curve back to the left to IS", causing AD to shift back to the left to AD". Since the price level does not increase by as much, the LM curve shifts only to LM([P.sub.p]). The new equilibrium price level is [P.sub.p], and the new equilibrium level of output is [Y.sub.p]. Hence, under price-level targeting, a given shock to aggregate demand causes smaller changes in both output and the price level than it does under inflation targeting.

Now consider Figure A2. Once again, suppose that the monetary authority sets the money stock at [M.sub.0]. Assume that if there are no shocks, this causes the equilibrium interest rate to be [R.sub.0], the equilibrium level of output to be [Y.sub.0], and the equilibrium price level to be [P.sub.0]. Assume that [Y.sub.0] and [P.sub.0] are also the original target values of output and the price level. Now, suppose that a shock to aggregate supply shifts the SRAS curve to SRAS'. This increases optimal output to [Y.sub.optimal]. Under inflation targeting, there is no change in expected inflation, so the new equilibrium is at [Y.sub.[pi]] and [P.sub.[pi]], the point at which SRAS' intersects the original aggregate demand curve, AD. The lower price level shifts LM to LM([P.sub.[pi]]), which intersects IS at [Y.sub.[pi]] and [R.sub.[pi]]. But under price-level targeting, as the current price level decreases toward [P.sub.[pi]], expected inflation increases, causing a decrease in the real rate of interest (for any given nominal rate of interest). This lower real rate of interest shifts the IS curve to the right to IS'. This in turn shifts the AD curve to the right to AD'. The equilibrium under price level targeting therefore is at [P.sub.p] and [Y.sub.p]. The price level, therefore, does not decrease by as much under price-level targeting as under inflation targeting. Furthermore, under price-level targeting, the level of output is closer to [Y.sub.optimal] than it is under inflation targeting. Therefore, the variances of both these variables about their target values resulting from supply shocks are lower under price-level targeting.
Table 1. Variances of Output, the Price Level, and Inflation
under Inflation and Price-Level Targeting

 Variance of Variance of
 Output about Price Level
 Full-Information about its
 Value Target Value

Inflation [[sigma].sup.2.sub.1] + ([[sigma].sup.2.sub.1] +
targeting [[sigma].sup.2.sub.3] [[sigma].sup.2.sub.3])/
 [[gamma].sup.2]

Price-level [[gamma].sup.2] ([[sigma].sup.2.sub.1] +
targeting ([[sigma].sup.2.sub.1] + [[sigma].sup.2.sub.3])/
 [[sigma].sup.2.sub.1])/ ([alpha] + [gamma]).sup.2]
 ([alpha] + [gamma]).sup.2]


The authors wish to thank two anonymous referees and Dek Terrell for many helpful comments.

Received September 2003; accepted November 2004.

(1) The target range in Canada, for example, has been 1-3% since 1991 (Freedman 2001).

(2) For a discussion of the advantages of price-level or inflation targeting, see Bernanke et al. (1999) and Svensson (1999). The latter also provides useful summaries of the experiences of inflation-targeting countries. See Berg and Jonung (1999) for a discussion of Sweden's experience under price-level targeting.

(3) Our terminology follows that of Svensson (1999). What Svensson calls inflation targeting, Balke and Emery (1994) call weak price stability. What Svensson calls price-level targeting, Balke and Emery call strong price stability.

(4) Even if expectations are not fully rational, as long as expected inflation changes in the direction implied by rational expectations, the advantage of price-level targeting identified in this paper still holds. See the graphical discussion presented in section 5.

(5) See also, for example, Lebow, Roberts, and Stockton (1992), Fillon and Tetlow (1994), Fischer (1994), and Haldane and Salmon (1995).

(6) The source of this "free lunch" from price-level targeting is the persistence of the output gap. If the output gap [g.sub.t] is positive during the current period, then in the absence of time t + 1 supply shocks the output gap during the period t + 1 is [g.sub.t+1] = [rho][g.sub.t]. Even though the central bank cannot cause [g.sub.t+1] to be any different from [rho][g.sub.t] (because of rational expectations), its goal remains at [g.sub.t+1] = 0. It is the attempt of the central bank to achieve an output gap of 0 when output persistence and rational expectations dictate otherwise that drives Svensson's results on inflation variance in the two regimes.

(7) Parkin emphasizes the work of Williams (1999), Black, Macklem, and Rose (2000), Dittmar and Gavin (2000), and Vestin (2000), as well as the Swedish price-level targeting experience.

(8) In our model, the outcomes under discretion and commitment are the same.

(9) Because the demand for output in the McCallum-Nelson model declines as the real rate of interest increases, our results hold in their model.

(10) Under interest-rate targeting, the model breaks down if we allow [gamma] to reach zero. When [gamma] = 0, the aggregate supply curve is vertical. Under interest-rate targeting, the aggregate demand curve is also vertical. As a result, there is either no intersection of supply and demand, or the curves coincide, in which case there is price-level indeterminacy.

(11) This is the loss function used by Taylor (1979) and Floden (2000), among many others.

(12) Also, because the monetary authority targets the full employment level of output, the credibility issues raised by the Barro-Gordon (1983) model do not arise in our paper. Thus, our results do not depend on whether or not the central bank can commit to an optimal policy.

(13) It can be verified by updating Equations 1 and 3 one period that [differential][p.sub.t+1]/[differential][R.sub.t+1] [not equal to] 0.

(14) When the money supply is pegged, a higher price level lowers the real money supply and raises the real interest rate. This in turn lowers output. Thus, aggregate demand is decreasing in the price level. When the nominal interest rate is pegged, an increase in the price level is met with an increase in the money supply in order to maintain the interest-rate peg. Thus, the real interest rate does not rise, and the aggregate demand is unaffected. As a result, the aggregate demand is vertical when plotted against the price level.

(15) That is, [Y.sub.0] = c and [P.sub.0] = [[bar.p].sub.t].

(16) Equation 9 shows that if there is a fixed rate of interest, then output increases by the full amount of any demand shock under inflation targeting.

(17) According to Kiley (1998), a neoclassical Phillips curve is one in which an unexpected increase in the price level (or inflation) causes an increase in output. Hence, Equation 3, which we call a Lucas aggregate supply curve, is a neoclassical Phillips curve. Kiley defines a New Keynesian Phillips curve to be one in which increases in output are caused by current inflation being higher than expected future inflation. These are the definitions used by Dittmar and Gavin (2000) as well. For a thorough discussion of the New Keynesian model, see the survey by Clarida, Gali, and Gertler (1999).

(18) To fully recover Svensson's results, we would need to add output persistence back into the model.

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James Peery Cover * and Paul Pecorino ([dagger])

* Department of Economics, Finance, and Legal Studies, University of Alabama, P.O. Box 870224, Tuscaloosa, AL 35487-0224, USA; E-mail jcover@cba.ua.edu; corresponding author.

([dagger]) Department of Economics, Finance, and Legal Studies, University of Alabama, P.O. Box 870224, Tuscaloosa, AL 35487-0224, USA; E-mail ppecorin@cba.ua.edu.
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