PRICE LEVEL STABILITY: SOME ISSUES.

Gaspar, Vitor ; Smets, Frank

Frank Smets [*]

This article challenges the conventional wisdom that price level targeting necessarily increases the volatility of inflation and economic activity. It shows that the optimal policy under commitment for a society that cares only about the variability of output and inflation involves only a limited degree of base drift. The result crucially depends on the importance of forward-looking behaviour and on the credibility of the commitments. The case for price level targeting is strengthened when the possibility of a binding lower bound on nominal interest rates is considered. This may be increasingly relevant in a low inflation environment. This justifies renewed interest on price level targets in the context of thinking through how to prevent and respond to deflationary risks

Introduction

There is a spur of interest in the choice between targeting the inflation rate and targeting the price level. For example, this issue has recently been raised by Blinder (1999b), King (1999), Svensson (1999b) and Parkin (2000). This is particularly remarkable given that, just a few years ago, there seemed to be a strong professional consensus on the superiority of inflation targeting over price level targeting.

The question may be raised as follows: faced with an unexpected change in prices, should a central bank attempt to return the price level to a well-defined, possibly increasing, path, or should it allow base drift and aim at stabilising the inflation rate? In the first case, the central bank is expected to bring down inflation below its medium-term price stability objective in order to achieve price level stability following a positive shock to inflation. In the second case, bygones are bygones, shocks to the price level are accommodated and it suffices to stabilise the inflation rate.

Until recently there was a quite widely shared consensus that pursuing price level stability would not be a good idea. This consensus is, for example, expressed in Stanley Fisher's piece on Modern Central Banking, which he presented on the occasion of the tercentenary celebration of the Bank of England in 1993. [1] Fisher concluded: "Price level targeting is thus a bad idea, one that would add unnecessary short-term fluctuations to the economy. It is also true... that there is more variability and uncertainty about short-term inflation rates with a price level target than with a target inflation rate." [2] The intuition behind this view is that under price level targeting, higher-than-average inflation must be followed by lower-than-average inflation to meet the price level objective. This reduction in inflation, while reducing variability in the price level, leads to higher variability in inflation. Moreover, in the presence of nominal rigidities, the central bank may have to induce a slowdown in economic ac tivity to achieve the necessary reduction in inflation. A greater variability in inflation therefore also translates in higher output variability.

In part, the dominant view that price level objectives would be costly in terms of inflation and output variability was a result of the disinflation experience of the 1980s. Therefore disinflating the economy in response to a one-time level shock to prices did not appear to be a great idea. This view was backed up by early simulation studies (for example, Lebow, Roberts and Stockton, 1992, and Haldane and Salmon, 1995). These studies showed that, in models dominated by backward-looking expectations, there is a trade-off between low-frequency variability in the price level and high-frequency variability in inflation and output.

More recently, however, the tide has turned gradually in favour of avoiding base drift. The renewed interest in price level as opposed to inflation rate objectives has various sources. First, the stochastic properties of the inflation process cannot be taken as given when considering alternative monetary policy regimes. Focusing on the postwar period it would seem that persistence in inflation has changed significantly when comparing the period up to 1965, where inflation seems to be roughly stationary, with the subsequent period up to 1990, where it exhibits a unit root. In the 1990s, after low inflation became enshrined, both the degree of persistence and the variability of inflation seem to have been reduced. [3] The endogeneity of the inflation process makes it interesting to explore the costs and benefits of price level targeting in the context of models with forward looking agents. In such a setting Svensson (1999a) has shown that once the effect of price level targeting on the formation of inflation ex pectations is taken into account, such a regime does not necessarily lead to increased inflation and output variability and may even reduce it.

A second source for this renewed interest in price level objectives lay in concerns about the effects of a zero lower bound on nominal interest rates in a low inflation regime. The recent Japanese experience with the zero nominal interest rate policy provides real world illustration. [4] With inflation close to zero, credible price level objectives may alleviate the constraint on monetary policy from the zero lower bound on nominal interest rates. They appear superior to inflation objectives because an incipient decline in prices triggers expectations of a future increase in prices, i.e. inflation expectations, which reduces the ex ante real interest rate and therefore operates as an automatic stabiliser.

In this article we critically review some of the recent literature on the choice between price level versus inflation rate objectives. After reviewing briefly why society may care about price level uncertainty per se in the next section, the main focus of the article is on the impact of price level targeting on inflation and output variability. [5] We use a standard loss function in output and inflation variability and a simple backward/forward looking model to assess whether price level targeting may be useful even if society does not care about price level stability per se. [6] For the simulations, an estimated version of the model for the euro area as discussed in Smets (2000) is used. Using this set-up, we show in the third section that the optimal policy under commitment results in a partial reversal of shocks to the price level. As shown by Clarida, Gali and Gertler (1999) this reversal is complete when inflation is completely forward-looking as is the case with Calvo-pricing.

In the fourth section we go on to analyse the optimal policies under discretion and examine whether assigning price level objectives to a discretionary central bank can reduce inflation and output variability in the presence of nominal price rigidities. Important factors determining whether this is true are how forward-looking inflation expectations are, the horizon over which the price stability objectives are pursued and the credibility of the price level objectives.

In the fifth section we focus on interest rate volatility. This concern may be important for the issue of the zero lower bound on interest rates as lower interest rate volatility reduces the probability of hitting the lower bound. Several papers have shown that credible price level objectives have a favourable effect on nominal interest rate variability because the price level itself starts to play an intertemporal role. Whenever prices are low, they will be expected to rise. These positive inflation expectations reduce the ex ante real rate and have a positive impact on spending. As a result the need to lower nominal interest rates in this case is reduced. We discuss the mechanism behind this result.

The sixth section concludes with some final remarks.

Why should society care about price level stability?

The case for price level stability is a very old one. In history it has been made often in connection with the role of money as the 'unit of account'. In very general terms, if one assumes that economic calculation is costly then the savings associated with a stable standard of value may be considerable. To the best of our knowledge there has been no attempt to apply this framework to the estimation of the costs from price (in)stability. This may be an interesting topic for further research.

A very popular quote dates back to the 17th century: "if there is something in the world which ought to be stable it is money, the measure of everything which enters the channels of trade. What confusion would there not be in a state where weights and measures frequently changed? On what basis and with what assurance would a person deal with another and which nations would come to deal with people who lived in such disorder?" [7] Somewhat later, in 1742, David Hume stated: "... money is nothing but the representation of labour and commodities, and serves only as a method of rating and estimating them. Where coin is in greater plenty; as a greater quantity of it is required to represent the same quantity of goods; it can have no effect, good or bad, taking a nation within itself; any more than it would make an alteration on a merchant's books, if, instead of the arabian method of notation, which requires few characters, he should make use of the roman, which requires a great many. Nay, the greater the quantity of money, like roman characters, is rather inconvenient, and requires greater trouble both to keep and transport it".

Probably nobody presented a stronger case than Irving Fisher(1920): "Once the yard was defined, in a rough and ready way, as the girth of the chieftain of the tribe and was called a gird.... Except the dollar, none of the old rough and ready units are any longer considered good enough for modem business. The dollar is the only survival of these primitive crudities....And yet...the dollar is used in all contracts in which the yardstick of length is used and in all others besides! Consequently the evils our unstabilized dollar works - evils of confusion, uncertainty, social injustice, discontent, and disorder - are as vast as would be the evils experienced in all other units of commerce - the yardstick, the bushel basket, the hour of work, etc - should vary concertedly to the same extent."

It is this widespread use of money as the numeraire for contracts that is behind the arguments that have been put forward in favour of reducing price level variability. Recently, a number of papers have formalised this idea in connection with price setting by firms. For example, King and Wolman (1999) analyse the optimal policy implications of introducing Taylor-style staggered price setting in a dynamic general equilibrium model with monopolistic competition. Using a public finance approach, they conclude that optimal central bank policy is to target a zero inflation rate and stabilise the price level in response to productivity shocks. [8] More recently, Kahn et al. (2000) have generalised these results in an economy with more generalised price setting, a variety of productivity and demand shocks and an additional friction arising from the interest rate tax on holding money. Again they find that the optimal inflation rate is close to zero and that optimal policy should stabilise the price level in response to the various shocks. The intuition for these results is that stabilising the price level minimises the distortions (i.e. the misallocation of resources across industries due to relative price changes) that are due to the fact that some firms can adjust their prices while others can not.

However, these results in favour of a complete stabilisation of the price level are obtained in models where there are no cost-push shocks and the central bank has perfect control over the price level. Rotemberg and Woodford (1997) and Woodford (1999b) show in a model with Calvo price-setting that the deadweight loss associated with relative price variability can be approximated by a quadratic loss function in the inflation rate, nor the price level. This implies that cost-push shocks to the price level or other short-term changes to the price level over which the central bank has no control will not necessarily be completely reversed. The intuition is as follows. Once a fraction of firms has already adjusted to the new price level, the central bank has a reduced incentive to undo the effects of such shocks on the price level. Because those firms are already committed to the new price level, even an expected decline in prices will create a deadweight loss. On the other hand, the firms that are able to adjust following the central bank's action do nor care about updating their prices to the new price level as they can do so costlessly. What fraction of the initial shock to the price level is optimal to reverse will depend on the contracting structure. Using a standard Taylor four-quarter contracting specification with equal weights, Goodfriend and King (1997) calculate that the optimal policy would imply a 0.4 percentage point reversal of a 1 per cent price shock. In general, one would expect that the longer the average age of the contract, the greater the incentive to the central bank to undo the effects of price shocks. In the limit, when contracts last very long, it will be optimal to avoid all base drift. [9]

As briefly discussed above, there is a long and old Literature on why society and central banks may care about price level stability per se. One of the new insights of the recent theoretical literature is that giving a price level stability mandate to a central bank may alleviate the time-inconsistency problem in monetary policy. This provides a rationale for price level targeting even if price level stability per se does not enter society's loss function. For example, Svensson (1999b) first pointed out that in a simple model with a Lucas-supply function giving a price level target to a discretionary central bank which has an over-ambitious target for output may avoid the appearance of an average inflation bias. Although the over-ambitious output target does result in a price level bias, Svensson (1999b) shows that when there is enough persistence in output, giving such a mandate involves a free lunch which comprises identical output variability and lower inflation variability. [11]

The potentially distorting effects of price level instability may be even more important for financial contracts. Such contracts are normally agreed in nominal terms and specify an obligation (right) to pay (receive) a given sum at some future date. Some of these contracts have very long duration. The redistribution between creditor and debtor associated with an unexpected departure from the expected price level path may be very significant. The subsequent impact on the economy will depend on the strength of the 'financial accelerator' as a propagation mechanism. The debt-deflation spiral has been one of the mechanisms mentioned to try to explain the 'Great Depression' episode (see, for example, Fisher, 1933). It was perceived as a relevant policy problem at the time. This may be illustrated by quoting a speech by President Roosevelt, on 7 May, 1933: "The Administration has the definite objective of raising commodity prices to such an extent that those who have borrowed money will, on the average, be able to repay that money in the kind of the dollar which they borrowed. We do not seek to let them get such a cheap dollar that they will be able to pay back a great deal less than what they borrowed; in other words we seek to correct a wrong and not to create another wrong in the opposite direction." The President elaborated further on 3 July. He said: "The United States of America seeks the kind of dollar which a generation hence will have the same purchasing power and debt paying power as the dollar we hope to attain in the near future." The following day J.M. Keynes is quoted as having stated: "The President is magnificently right." [10]

Price level drift and the optimal commitment solution to stabilising inflation

More recently, Clarida, Gali and Gertler (1999) and Svensson and Woodford (1999) have pointed out that in a simple New-Keynesian model with inflation targeting the optimal policy under commitment results in a stationary price level process. Intuitively, the reason is that the commitment of the central bank to limit or even avoid price level drift has strong stabilising effects on inflation expectations, which in turn results in a more stable economy. A given shock to inflation has much smaller effects on inflation expectations and thus actual inflation when agents in the economy realise its effects on the price level will be reversed.

In this section we illustrate the latter result in a simple stylised model of the economy which features both backward- and forward-looking components in the formation of inflation expectations. In particular, we compare the outcome of inflation targeting under commitment and discretion and show that, following a shock to prices, the optimal policy under commitment results in considerably less price level drift. In the next section we will discuss how under the assumption that central banks act in a discretionary manner mandating central banks to pursue a price level objective may improve on the discretionary outcome under inflation targeting.

Consider the following standard quadratic loss function in the deviation of inflation from an inflation objective and the output gap:

[E.sub.t] [[[sigma].sup.[infinity]].sub.j=0] [[beta].sup.j][[[[pi].sup.2].sub.t+j] + [[[omega]y.sup.2].sub.t+j]] (1)

where [[pi].sub.t] is the annual inflation rate, that is, [[pi].sub.t] = [p.sub.t] - [p.sub.t-1], [y.sub.t] is the output gap, [beta] is the central bank's discount factor and [omega] is the weight on output gap stabilisation. The target inflation rate is assumed to be constant at zero.

Next, assume that the economy can be described by an aggregate supply equation of the following form:

[[pi].sub.t] = [alpha][[pi].sub.t-1] + (1 - [alpha])[E.sub.t][[pi].sub.t+1] + [kappa][y.sub.t] + [[epsilon].sub.t] (2)

where [alpha] denotes the weight on the backward-looking component of inflation expectations, [kappa] represents the slope of the Phillips curve and [E.sub.t] captures so-called cost-push shocks and is assumed to be serially uncorrelated. Equation (2) captures a variety of possible supply functions. For [alpha] =0, it corresponds to the case of Calvo-pricing as, for example, analysed in Clarida, Gali and Gertler (1999). In that case, although prices are sticky, inflation is completely forward-looking. For [alpha] = 1 equation (2) becomes an accelerationist Phillips curve, with inflation only responding to past inflation. Finally, on empirical grounds, Fuhrer and Moore (1995) have argued that an intermediate weight for [alpha] is appropriate. The presence of lagged inflation can be justified on the basis of a model in which agents care about relative wages (e.g. Garcia and Ascari, 1999) or in which a fraction of the price setters use a simple rule of thumb based on past inflation (e.g. Gali and Gertler, 2000).

The central bank is assumed to minimise loss function (1) subject to the dynamics of the economy described in equation (2). A characterisation of the optimal solution under discretion and commitment is discussed in McCallum and Nelson (2000). One can show that the first-order conditions under discretion yield the following optimality condition: [12]

[y.sub.t] =-[kappa]/[omega](1-(1-[alpha])[delta]) [E.sub.t]

[[[sigma].sup.[infinity]].sub.j=0][([alpha]/1-(1-[alpha])[delta]).sup .j][[pi].sub.t+j] (3)

where [delta] is a function of the parameters of the model and is less than one. [13] Under discretion, the optimal policy requires output to fall in response to expected and future inflation being above the central bank's target. In a fully-fledged model this will be achieved by rise in the real interest rate. How much output has to move depends on the slope of the Phillips curve and the preferences of the central bank for output stabilisation. Equation (3) is a generalisation of the condition discussed in Clarida, Gali and Gertler (1999) for the case of [alpha] = 0. In this case the optimality condition becomes [y.sub.t] = -[kappa]/y[[pi].sub.t].

To derive the solution under commitment we use the 'timeless perspective' notion. In this case, the optimality condition is given by:

[y.sub.t] - [y.sub.t-1] = - [kappa]/[omega](1-[alpha]) [E.sub.t] [[sigma].sup.[infinity]].sub.j=0] [([alpha]/1 - [alpha]).sup.j] [[pi].sub.t+j] (4)

A comparison of equations (3) and (4) makes clear that under commitment changes in the output gap rather than the level of the output gap respond negatively to expected and future inflation. Under commitment the central bank promises to keep reducing the output gap as long as inflation is above its target. The credible threat to continue to contract output in the future has the immediate effect of dampening current inflation given the dependence of current inflation on future output. The benefit of commitment lies in the fact that as a result cost-push shocks have a smaller impact on current inflation and the need for policy action is reduced.

When [alpha] = 0, equation (4) can be simplified to [y.sub.t] = - [kappa]/[gamma] [p.sub.t]. As mentioned before and discussed in Clarida, Gali and Gertler (1999), in this case the optimal policy under commitment results in a trend-stationary price level. For the more general case (0 [less than] [alpha] [less than] 1) there will also be some price level drift in the commitment case. However, as suggested by comparing equations (3) and (4), the policy under commitment results in considerably less price level drift than the one under discretion.

To illustrate these results, chart 1 compares the optimal policy response to a price shock under commitment and discretion for an estimated version of the model. Smets (2000) estimates the parameters of equation (2) using annual synthetic euro area data over the period 1975-98. This estimation yields the following parameters: [alpha] = 0.48, [kappa] = 0.18 and [[sigma].sup.2].sub.[epsilon]] = 0.53. In addition, the lower panel of chart 1 also shows the results for [alpha] = 0.10. For these simulations we assume an equal weight on output and inflation stabilisation in the central bank's loss function ([omega] = 1.0) and a discount factor equal to 0.96.

In both cases optimal policy under commitment results in a partial reversal of the price level following a price level shock. In the pure Calvo-pricing model the reversal is complete and the price level is a stationary process. In the estimated model, the ultimate level of base drift is somewhat larger than the initial effect of the shock. In contrast, when the central bank acts under discretion, i.e. it reoptimises every period, the level of base drift in prices is considerably larger.

Can the pursuit of price level stability reduce inflation and output variability?

The analysis in the previous section suggests that under the assumption that central banks act in a discretionary manner, mandating central banks to pursue a price level objective may reduce output and inflation variability compared to the discretionary outcome under inflation targeting. This suggestion is in sharp contrast to the traditional view discussed in the introduction that the pursuit of a price level objective is likely to increase inflation and output gap variability when prices are sticky. In this section we examine this issue empirically by analysing how the efficiency frontiers for inflation and output variability change when the central bank's loss function contains a small weight on price level stability. [14]

More concretely, we extend the loss function (2) with an additional price level stability term as follows:

[E.sub.t] [[sigma].sub.[infinity]].sub.j=0] [[beta].sup.i][(1 - [[omega].sub.2])([omega].sub.1][[[pi].sup.2].sub.t+j] + (1 - [[omega].sup.1])[[y.sup.2].sub.t+j]) + [[omega].sub.2][[p.sup.2].sub.t+j] (5)

where [[omega].sub.2] is the relative weight on price stability versus the two more standard objectives. We then analyse the outcome for inflation and output variability when [[omega].sub.2] increases from zero. Charts 2a, 2b and 2c plot the efficiency frontiers for three cases corresponding to three values of [alpha] (the estimated model ([alpha] = 0.48), the accelerationist model ([alpha] = 0.99) and the Calvo-pricing model ([alpha] = 0.0)). In each of these charts the solid line depicts the efficiency frontier when there is no weight on price level stability, whereas the broken line corresponds to a small weight on price level stability ([[omega].sub.2] = 0.05).

Three results deserve to be highlighted. First of all, an important factor in determining the effect of price level targeting on inflation and output variability is the degree of inflation stickiness and in particular to what extent the policy regime is allowed to affect the formation of inflation expectations. When the Phillips curve is accelerationist, such positive expectational effects are non-existent. As a result the efficiency frontier deteriorates as more weight is put on price level stability (chart 2a).

In contrast, when inflation is completely forward-looking the efficiency frontier moves inward when [[omega].sub.2] is increased from zero. In this case the pursuit of price level stability is complementary to the goal of stabilising inflation and the output gap (chart 2c). Similarly, also with the estimated persistence in inflation (chart 2b), there is some gain in terms of the overall output--inflation efficiency frontier, as the efficiency frontier shifts inward. [15]

To a large extent these results can explain the different results obtained in the literature. For example, Fuhrer (2000b) finds that including a positive response to a price level term in the central bank's reaction function shifts the inflation--output efficiency frontier upward in a variety of models of the US economy (mainly his own Fuhrer-Moore model and a version of the model by Rudebusch and Svensson, 1999). In contrast, using the Federal Reserve's FRB model, Williams (1999) finds that including a price level term is beneficial in reducing the volatility of both output and inflation. As discussed in Levin et al. (1999), the persistence of inflation in the FRB model is much lower than that in the Fuhrer-Moore model. This is even more the case for the Rudebusch-Svensson (1999) model, which has an accelerationist Phillips curve. In analogy with the analysis above, the difference in results can thus be explained by differences in how sticky inflation is assumed to be.

Similar results are obtained for other countries. For example, Batini and Yates (1999) find that price level targeting increases the variability of both inflation and output in a model for the UK economy that features Fuhrer-Moore style contracts. However, they also show that a specification with Taylor-Calvo contracts, which implies much less persistence in inflation, leads to lower inflation variability under price level targeting, although output variability is still higher. Finally, using a somewhat different methodology, Smets (2000) finds that for a given policy horizon inflation variability is always lower with price level objectives while output variability is higher. He also shows that increasing the weight on the forward looking component of inflation expectations improves the trade-off and works in favour of price level targets rather than inflation targets. [16] Second, most of the benefits of pursuing price level stability arise for a small weight on the price stability objective (See also Batini and Yates, 1999, and Maclean and Pioro, 2000). The reason is that even a small weight on price stability will make the price level stationary and the variability of the price level bounded and thus have stabilising effects on inflation expectations. As shown in chart 3, increasing the weight on price level stability dramatically (to 0.9 in the chart) is very effective in stabilising inflation, but becomes very costly in terms of output variability. This rise in output variability is so large, that a Pareto improvement is no longer possible. In addition, Batini and Yates (1999) note that most of the reduction in price level uncertainty is obtained for small weights on the price level stability objective.

Finally, chart 2 suggests that for a given [[omega].sub.1] adding a price stability objective will generally reduce inflation variability, while increasing output variability. When inflation is sufficiently forward-looking, it is nevertheless possible to reduce both inflation and output gap variability by implicitly increasing the weight ([[omega].sub.1]) on output gap stabilisation in the mandate of the central bank. [17] This result was highlighted by Vestin (1999), who shows that in a model with a forward-looking Calvo-Taylor Phillips curve, price level targeting under discretion outperforms inflation targeting if one allows the relative weight on output variability to vary appropriately. Another way of phrasing the same result is that in order to avoid an increase in output variability price level targeting requires a longer policy horizon. As shown in Svensson (1997), the weight on output variability in the central bank's loss function is related to the policy horizon over which the price stability objec tive is achieved. [18] Smets (2000) shows that the optimal policy horizon for a price level target is always longer than that for an inflation target. While for short horizons inflation targets dominate price level targets, the reverse is true for longer horizons. Smets (2000) also shows that once the horizon is chosen optimally, price level targeting may dominate inflation targeting.

Overall, the results presented here and the related literature suggest that pursuing price level stability can be complementary to both inflation and output gap stabilisation if inflation expectations are sufficiently forward-looking and an appropriate policy horizon is chosen. Obviously this analysis assumes that the policy regime is credible. The issue of credibility in the context of price level objectives is explicitly analysed in Maclean and Pioro (2000). As such credibility cannot be taken for granted, an important policy question is how costly the transition to a credible price level targeting regime would be.

Price level stability and the zero lower bound on interest rates

The recent Japanese experience of near-zero short-term nominal interest rates has led to a vivid debate about how to avoid liquidity traps and the deflationary spirals that may arise from them. One of the first authors in the recent literature to emphasise that credible price level targets may help in alleviating the zero lower bound problem is Coulombe (1997). He emphasises that credible price level objectives are superior to inflation objectives because an incipient decline in prices triggers expectations of a future increase in prices, i.e. inflation expectations, which reduces the ex ante real interest rate and has an automatic equilibrating impact on the economy. Coulombe (1997) argues that in a price level targeting regime, the price level itself plays an intertemporal role. When prices are high, consumers will postpone consumption as they expect prices to fall. Conversely, when prices are low, consumers will increase consumption expecting prices to rise again. This reduces the need to change nominal in terest rates and thus the probability that the nominal interest rate would hit the zero lower bound.

To show this more formally, it is instructive to consider a linearised version of a standard consumption Euler equation, which in the current literature is frequently used to derive a forward-looking IS curve. [19]

[c.sub.t] = [E.sub.t][c.sub.t+1] - [sigma][[R.sub.t] - [E.sub.t][[pi].sub.t+1]] (6)

Solving forward, the following expression for consumption can be derived:

[c.sub.t] = -[sigma][E.sub.t] [[[sigma].sup.[infinity]].sub.j=0] [[R.sub.t+j]]+[sigma][E.sub.t] [[[sigma].sup.[infinity]].sub.j=0] [[pi].sub.t+1+j] (7)

The first term can be written as a nominal long-term term interest rate ([RL.sub.t]), which can be influenced by monetary policy through current and expected changes in the short-term rate. Now consider a negative shock to inflation, which is likely to have a persistent effect on inflation. Under an inflation targeting regime, such a shock will reduce inflation expectations, raise the ex ante real rate and have a negative impact on current consumption. In order to offset this negative impact, the central bank needs to lower nominal interest rates. When rates are already low, the central bank's freedom of action may be constrained by the lower bound on interest rates. The resulting negative impact on demand may then put further downward pressure on prices and inflation, thereby further increasing real rates and depressing demand. The economy risks getting trapped in a deflationary spiral.

Under a credible price level targeting regime instead, equation (7) can be written as follows.

[c.sub.t] = -[sigma]R[L.sub.t] - [sigma][p.sub.t] (8)

where the target price level is normalised at zero. Equation (8) shows that in this regime a negative shock to prices will have a positive impact on consumption. The risk of getting trapped in a deflationary spiral following a negative shock to prices is therefore greatly reduced. As emphasised by Coulombe (1997), the price level very much plays the same intertemporal role as the nominal long-term interest rate. As a result the need for central banks to adjust nominal interest rates is much reduced.

To illustrate the impact of price level targeting on interest rate volatility, it is useful to augment the model described by equation (2) with an IS equation:

[y.sub.t] = [delta][y.sub.t-1] + (1-[delta])[E.sub.t][y.sub.t+1] + [sigma]([r.sub.t] - [E.sub.t][[pi].sub.t+1]) + [u.sub.t] (9)

Equation (9) is a generalisation of a standard forward-looking IS curve which allows for persistence in output. The presence of lagged output can be justified on the basis of a micro-based model in which agents' utility functions exhibit habit persistence (Fuhrer, 2000a). We again follow Smets (2000) to calibrate the parameters as follows: [delta] = 0.44, [sigma] = -0.06 and [[sigma].sub.u] = 0.65. In addition we assume that the central bank puts a small weight [[omega].sub.3] = 0.1) on interest rate variability. Chart 4 shows the standard deviation of the nominal interest rate as a function of the weight on price level objectives. Price level targeting has two opposing effects on interest rate variability. A greater weight on price level stability implies that the central bank has to move ex ante real rates and output more in order to revert the price level. This increases the variability of interest rates. The expectational channel, discussed above, implies, however, that inflation expectations take a part of the adjustment, so that nominal interest rates need to rise less. As can be seen from the chart, when the central bank cares about interest rate volatility, the second effect dominates the first for small weights on price level objectives.

These results are confirmed in the analysis of Wolman (1998) and Reifschneider and Williams (1999). In quite different models, both papers show that, when the central bank credibly responds to deviations of the price level from a deterministic target, problems associated with the lower zero bound on interest rates and possible risks of deflationary spirals become much less important even at zero inflation rates. These results are also echoed in Smets (2000), who finds that a greater concern with interest rate volatility in society's objectives, for example because of the lower zero bound, favours price level targets over inflation targets. One important condition for these results to hold is that real longer-term interest rates are important determinants of aggregate demand. This is the case in the models of Wolman (1998) and Smets (2000) which feature a forward-looking IS curve as discussed above. Smets (2000) shows that as aggregate demand becomes more backward-looking and its response to the real long-term interest rate falls, the benefits of a price level objective relative to that of inflation objectives fall. It also holds true in the Federal Reserve Board's FRB model where long-term interest rates determine important demand components like investment.

As in the previous section another condition for achieving the beneficial effects of pursuing price level stability is that the price level target is credible. This is particularly important in this case as it has been argued that the inability of central banks to actually inflate the economy when nominal interest rates hit the lower bound makes the price level target less credible. On the other hand, as argued by Goodfriend (1999), McCallum (1999), Svensson (2000) and many others there may be other channels through which monetary policy may have effects on the economy when interest rates are bounded at zero. [20]

Conclusions

This article challenges the conventional wisdom that price level targeting necessarily increases the volatility of inflation and economic activity. It shows that the optimal policy under commitment for a society that cares only about the variability of output and inflation involves only a limited degree of base drift.

The intuition behind the conventional wisdom only holds true in general for models with backward-looking expectations. In these models there is a trade-off between the low frequency unpredictability of the price level and high frequency volatility in inflation and output. In such a setting, justifying price level targeting would require significant benefits from price level stability, more than compensating the costs. In the literature arguments for price level stability are presented by analogy with the standardisation of units of measurement (the meter, the gram, the centigrade, etc.). Assuming that economic calculation is costly could provide a basis to build models in which this claim can be explored in a rigorous way. To the best of our knowledge such models are not available in the literature.

In models in which agents are sufficiently forward-looking, a small weight on price level stability allows, under discretion, for reductions in the variability of both inflation and output (the efficiency frontier shifts inward). That holds true for the parameters estimated for the Euro Area. The intuition here is that some weight (even small) on the price level is sufficient to avoid base drift. This is well understood by rational forward-looking agents. Therefore the response to price shocks is dampened. In this model the monetary policy regime affects the propagation mechanism of shocks in a fundamental way. The result crucially depends on the credibility of the commitment to the price level target.

The case for price level targeting is strengthened when the possibility of a binding lower bound on nominal interest rates is considered. This may be increasingly relevant in a low inflation environment. The recent Japanese experience with a zero interest rate policy provides real world illustration. Now under price level targeting a deflationary shock leads to inflationary expectations, in conformity with a return of the price level to its original path. This, in turn, leads to a decline in real interest rates for unchanged nominal rates. For small weights on the price level this effect is dominant and leads to lower interest rate volatility. That makes the lower bound on nominal interest rates less likely to be binding. This justifies renewed interest on price level targets in the context of thinking through how to prevent and respond to deflationary risks.

(*.) European Central Bank. The views expressed in this article are the authors' own and do not necessarily reflect those of the ECB.

NOTES

(1.) Fischer (I 994), 'Modern central banking', in Capie et al., The Future of Central Banking. One exception is Hall (1984) who argues in favour of an elastic price level standard.

(2.) See also, for example, Clarida, Gali and Gertler (1999), who in a recent survey conclude that, "This policy (price level targeting), which may be thought of as a more extreme version of inflation targeting, has not received much support among policy makers and applied economists."

(3.) This is of course nothing other than a manifestation of the celebrated Lucas critique.

(4.) There is a voluminous literature on the Japanese case. See, for example, Bernanke (1999), Blinder (l999a), Bryant (1999), Goodfriend (1999), Hetzel (l999), McKinnon (1999) and Svensson (2000).

(5.) A very interesting general discussion of the costs and benefits of price level targets can be found in Duguay (1994).

(6.) The model is popular in the literature on optimal monetary policy rules. See, for example, McCallum and Nelson (2000) for a recent application.

(7.) Quote from LeBlanc (1690). This quote has also been used in Eunaudi (1953), Konieczny (l994), Svensson (1999a) and Angeloni, Gaspar, Issing and Tristani (forthcoming).

(8.) See also Goodfriend and King (1997).

(9.) The introduction of explicit menu costs could also tilt the balance in favour of avoiding any base drift.

(10.) All quotes are from Irving Fisher (l934).

(11.) See also Dittmar et al. (1999).

(12.) For analytical simplicity we assume the discount rate to be equal to one. In the numerical simulations below the general case with a discount factor different from unity will be considered.

(13.) See McCallum and Nelson (2000) for details.

(14.) See Vestin (1999) for a similar analysis in the pure Calvo-pricing model.

(15.) Obviously these results may also depend on the slope of the Phillips curve. If prices respond quickly to changes in the output gap, then price level targeting is likely to be less costly in terms of output variability. In contrast, if price changes respond only slowly to changes in capacity utilisation, then output will have to move a lot in order to achieve the reversal of the price shock.

(16.) Papers focusing on the Canadian economy are Black et al. (1998) and Fillion and Tetlow (1994). Using the Bank of Canada's QPM model MacLean and Pioro (2000) show that adding a price level target in an otherwise standard Taylor rule always increases output and interest rate variability, when inflation expectations are backward-looking. When inflation expectations are model consistent, then both output and inflation variability fall when a small weight on a price level gap is added.

(17.) One model in which output variability does not increase with price level targeting is discussed in Svensson (1999a). Kiley (1998) shows that this result depends on the form of the supply curve. With a new-Keynesian Phillips curve in which current inflation depends on expected future inflation, output variability will always be higher under price level targeting for a given weight on the output gap in the CB's objective function.

(18.) King (1999) emphasises that the policy horizon may be important in determining the output cost of a price level targeting strategy.

(19.) See, for example, Rotemberg and Woodford (1997) or Clarida, Gali and Gertler (1999).

(20.) Berg and Jonung (1998) discuss the Swedish experience with price level targeting in the 1930s.

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