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What inflation rate should the central bank target? We address determinacy issues related to this question in a two-sector model in which prices can differ in equilibrium. We assume that the degree of nominal price stickiness can vary across the sectors and that labor is immobile. The contribution of this paper is to demonstrate that a modified Taylor Principle holds in this environment. If the central bank elects to target sector one, and if it responds with a coefficient greater than unity to price movements in this sector, then this policy rule will ensure determinacy across all sectors. The results of this paper have at least two implications. First, the equilibrium-determinacy criterion does not imply a preference to any particular measure of inflation. Second, since the Taylor Principle applies at the sectoral level, there is no need for a Taylor Principle at the aggregate level.

Since at least Taylor [18] it has been commonplace to think of monetary policy in terms of directives for the nominal interest rate. The “Taylor Rule” posits that the central bank moves its interest rate instrument in reaction to movements in inflation and output. The recent literature on Taylor rules is voluminous. See [8] for a survey. One branch of this literature is concerned with the issue of local equilibrium determinacy: what Taylor Rule coefficients ensure local uniqueness of the equilibrium? The problem is that following a rule in which the central bank responds to endogenous variables may introduce real indeterminacy and sunspot equilibria into an otherwise determinate economy. 1 These sunspot fluctuations might be welfare-reducing and can potentially be quite large. The policy conclusion of this literature is that a benevolent central banker should only use a Taylor Rule that ensures determinacy of equilibrium. 2 A familiar result is that a necessary and sufficient condition to ensure determinacy is that the central bank’s response to inflation must exceed unity, i.e., a one percentage point increase in the inflation rate should lead to a greater than one percentage point increase in the nominal interest rate. This has been called the “Taylor Principle.” 3 There are numerous operational issues that arise when implementing theTaylor Principle. One such issue is what inflation rate should be targeted. The entire consumer price index (CPI)? The CPI stripped of food and energy prices? The median CPI? For example, in a two-sector model in which prices are flexible in one sector and sticky in the other, Aoki [1] argues that it is appropriate to stabilize “core” inflation, which he argues is the inflation rate in the sticky-price sector. The fundamental contribution of this paper is to demonstrate that a modified Taylor Principle holds. If the central bank elects to target a subset of goods in the economy, and if it responds with a coefficient greater than unity to current price movements of these goods, then this policy rule will ensure price level determinacy across all sectors. 4 This paper thus confirms and refines an idea that dates back to at least Patinkin [13]: “In brief, a necessary condition for the determinacy of the absolute price level. . . is that the central bank concern itself with some money value. . .” (Chapter 12, Section 6). What is important for determinacy is that the central bank cares enough about, in the sense of being willing to respond forcefully enough to, movements in some nominal anchor. Exactly which nominal price or money value it cares about does not really matter. What matters is that it cares about some nominal price. This price may be anything, from the price of gold to core-CPI. 5 There are at least two implications of the results of this paper. First, the equilibriumdeterminacy criterion does not imply a preference to any particular measure of inflation. The choice of which inflation rate to target can be made on other grounds. 6 Second, since the Taylor Principle applies at the sectoral level, there is no need for a Taylor Principle at the aggregate level. For example, suppose that the central bank targets inflation in specific sector(s) of the economy (say, core inflation) with a Taylor coefficient
> 1, but that the econometrician estimates a Taylor rule using the total CPI. Depending upon the variances and covariances of shocks across the sectors, the estimated Taylor coefficient could be much less than unity. From this we cannot conclude that the Taylor Principle is violated by simply looking at aggregate CPI numbers if in fact the central bank is reacting to something less general. Acorollary of the first implication above is that, in a currency union such as the euro-zone, the European Central Bank (ECB) will be able to ensure determinacy of the economy even by reacting to inflation in only a subset of countries. For example, Benigno [2] considers inflation targeting policies in which the central bank of a currency area stabilizes a weighted average of the inflation rates of two different countries. He demonstrates that it is optimal to attach more weight to inflation in countries with higher degrees of nominal rigidity. Benigno does not address how such a policy could be operationalized, and the issue of how to implement optimal policy is also left open in [1]. To the extent that this is achieved through a Taylor-type interest rate rule, our results can be used to analyze whether the optimal policy is determinate. This is important since Aoki and Benigno do not address this question. In analyzing determinacy, we adopt a framework that shares important features with Benigno’s [2] two-country, currency area model. First, we consider two different sectors and allow for the prices in these sectors to differ in equilibrium.We assume that the degree of nominal price stickiness can vary across the sectors. Second, we consider the case where labor is immobile across the two sectors. If labor is mobile across sectors, it is straightforward to demonstrate that
> 1 is necessary and sufficient for determinacy. Hence we consider the opposite extreme of complete immobility, making it more difficult to generate determinacy as labor flows are not available to mitigate price differences. In short, we set up the model so that it is difficult to generate determinacy under a rule in which the central bank targets inflation in only one sector. This is important given the international implications of our results. The key assumption driving our results is that households purchase goods made in all sectors so that households, and thus all sectors’ firms, care about relative prices.With sticky prices, since households purchase goods in all sectors, there is a link between relative prices, and thus marginal costs, in each sector. For example, a high price in sector 1 implies a low demand for sector 1’s good. This in turn leads to: a low demand for sector 1 labor; a low wage in sector 1; and thus a low marginal cost in sector 1. For the case of equal nominal rigidity across sectors, this negative cross-sector link is opposite the positive link between prices and marginal cost implied by the Phillips curve. This incompatibility eliminates the possibility of self-fulfilling behavior in relative prices and thus generates determinacy of relative prices regardless of any aspect of monetary policy. A key result of the paper is that, even when nominal rigidity differs across sectors, a more than proportional reaction to any measure of inflation is necessary and sufficient to pin down all relative and general prices. The underlying logic of this relative-price-marginal-cost linkage is quite general and suggests that the results here may extend to a wider class of sectoral models. The paper proceeds as follows. Section 2 develops the model. Section 3 lays out the basic determinacy results, and Section 4 concludes.

A well-known result in the recent work on central bank interest rate policies is the Taylor Principle: to ensure equilibrium determinacy, the central bank must respond aggressively (
> 1) tomovements in inflation. This result comes from an aggregative sticky-price model. The contribution of this paper is to demonstrate that a modified Taylor Principle holds in a multi-sector economy in which the sectors differ by the degree of price stickiness irrespective of whether labor is mobile between the two sectors. In particular, it does not matter what price index the central bank targets—the median CPI, core CPI, or the entire CPI—an aggressive response to any one of these price indexes is sufficient for local determinacy. Another interesting question on which this paper may help shed light is whether it matters in an open-economy setup if central banks target tradable goods, non-tradable goods, or the entire CPI inflation. Benigno and Benigno [3] show that the Taylor Principle holds in a model with flexible exchange rates, purchasing power parity, and Taylor-type policy rules where the central banks react to the inflation rate of domestic products only. This paper suggests that it does not matter for determinacy which price level the central bank of an open-economy targets. Relative price adjustments should ensure determinacy given a properly aggressive reaction to any of the inflation rates above even if labor is completely immobile between countries. 15 Work in progress is presently trying to verify this hunch. We conclude with an example that will illustrate the empirical relevance of our theoretical result. Kozicki [11] provides estimates of backward-looking Taylor rules over the period 1983–97. 16 Using CPI inflation as the measure of inflation she estimates
= .88. This is a violation of the Taylor Principle at the aggregate level suggesting that the economy over that period could be subject to sunspots. However, Kozicki [11] also estimates a Taylor rule for this same period, where the central bank responds to core CPI inflation instead—a narrower measure of inflation. This estimate is
= 1.28, indicating that sunspots would not be a problem over this time period. In general, her results suggest that the US central bank responds to core CPI inflation and not total CPI. This may have important implications for papers such as that by Clarida et al. [7], who estimate whether sunspots are a potential problem for certain sub-periods in US history.