RDP 2009-01: Currency Misalignments and Optimal Monetary Policy: A Re-examination 1. Introduction

Exchange rates among the large economies have fluctuated dramatically over the past 30 years. The euro/US dollar exchange rate has experienced swings of greater than 60 per cent, and even the Canadian dollar/US dollar has risen and fallen by more than 35 per cent in the past decade, but inflation rates in these economies have differed by only a few percentage points per year. Should these exchange rate movements be a concern for policy-makers? Would it not be better for policy-makers to focus on output and inflation and ignore a freely floating exchange rate that settles at a market-determined level?

It is widely understood that purchasing power parity does not hold in the short run. Empirical evidence points to the possibility of ‘local-currency pricing’ (LCP) or ‘pricing to market’.^[1] That is, exporting firms may price discriminate among markets and/or set prices in the buyers' currencies. A currency could be overvalued if the consumer price level is higher at home than abroad when compared in a common currency, or undervalued if the relative price level is lower at home. Currency misalignments can be very large even in advanced economies.

There is frequent public discussion of the importance of controlling currency misalignments. For example, on 3 November 2008, Robert Rubin (former US Secretary of the Treasury) and Jared Bernstein (of the Economic Policy Institute) co-authored an op-ed piece in the New York Times that argued, ‘Public policy … has been seriously deficient [because of] false choices, grounded in ideology’ (Rubin and Bernstein 2008). One of the principles they argue that all should agree upon is ‘we need to work with other countries toward equilibrium exchange rates’. Yet there is little support in the modern New Keynesian literature on monetary policy for the notion that central banks should target exchange rates. Specifically, if policy-makers are already optimally responding to inflation and the output gap, is there any reason to pay attention to exchange rate misalignments?

The answer is yes. In a simple, familiar framework, this paper draws out the implications for monetary policy when currency misalignments are possible. Currency misalignments lead to inefficient allocations for reasons that are analogous to the problems with inflation in a world of staggered price setting. When there are currency misalignments, households in the home and foreign countries may pay different prices for an identical good. A basic tenet of economics is that violations of the law of one price are inefficient – if the good's marginal cost is the same irrespective of where the good is sold, it is not efficient to sell the good at different prices. The key finding of this paper is that currency misalignments lead to a reduction in world welfare and that optimal monetary policy trades off this currency misalignment with inflation and output goals.

These currency misalignments arise even when foreign exchange markets are efficient. That is, the currency misalignment distortion that is a concern to policy-makers arises in the goods market – from price setting – and not in the foreign exchange market. In the model of this paper, the foreign exchange rate is determined in an efficient currency market as a function of fundamental economic variables.

The literature has indeed previously considered models with LCP. Some of these models are much richer than the model considered here. To understand the contribution of this paper, it is helpful to place it relative to four sets of papers:

1. Clarida et al (2002, hereafter referred to as CGG) develop what is probably the canonical model for open-economy monetary policy analysis in the New Keynesian framework. Their paper assumes that firms set prices in the producer's currency (PCP, for ‘producer-currency pricing’). Their two-country model also assumes that home and foreign households have identical preferences. These two assumptions lead to the conclusion that purchasing power parity (PPP) holds at all times – the consumption real exchange rate is constant.^[2]
   
   

   This paper introduces LCP into CGG's model. Simple rules for monetary policy are derived that are similar to CGG's. While the model is not rich relative to sophisticated models in the literature (models that introduce capital, working capital, capacity utilisation, habits in preferences, etc), the simple model is helpful for developing intuition because the model can be solved analytically, an explicit second-order approximation to the policy-maker's loss function can be derived, as can explicit ‘target criteria’ for policy and explicit interest rate reaction functions. As I shall quickly explain, a lot can be learned from these relationships in the simple model.

   The paper also allows home and foreign households to have different preferences. They can exhibit a home bias in preferences – a larger weight on goods produced in a household's country of residence.^[3] This generalisation does not change the optimal target criteria at all in the CGG framework, but as I now explain, is helpful in developing a realistic LCP model.

2. Devereux and Engel (2003) explicitly examine optimal monetary policy in a two-country framework with LCP. Corsetti and Pesenti (2005) extend the analysis in several directions. However, neither of these studies is suited toward answering the question posed above: is currency misalignment a separate concern of monetary policy, or will the optimal exchange rate behaviour be achieved through a policy that considers inflation and the output gap?
   
   

   These models have a couple of crucial assumptions that make them unsuited to answering this question. First, like CGG, they assume identical preferences in both countries. This assumption (as shown below) leads to the outcome that currency misalignments are the only source of CPI inflation differences between the two countries in the LCP framework. Eliminating inflation differences eliminates currency misalignments and vice versa.^[4]

   Second, price stickiness is the only distortion in the economy in these papers. In contrast, CGG introduce ‘cost-push shocks’, so that policy-makers face a trade-off between the goals for inflation and the output gap. In Devereux and Engel, the optimal monetary policy under LCP sets inflation to zero in each country, thus eliminating any currency misalignment.

   By introducing home bias in preferences, the tight link between relative inflation rates and currency misalignments is broken. A more realistic model for inflation results when relative CPI inflation rates depend not only on currency misalignments, but also on the internal relative price of imported to domestically produced goods. Moreover, we follow CGG in allowing for cost-push shocks.^[5]

   This paper also derives optimal policy in a framework that is consonant with the bulk of New Keynesian models of monetary policy analysis. Devereux and Engel (2003) and Corsetti and Pesenti (2005) assume price setting is synchronised, with prices set one period in advance.^[6] Here the standard Calvo price-setting technology is adopted, which allows for asynchronised price setting. This change is important, because it emphasises the point that the cost of inflation under sticky prices is misaligned relative prices. Also, the previous papers assumed that the money supply was the instrument of monetary policy. This paper follows CGG and most of the modern literature in assuming that the policy-makers directly control the nominal interest rate in each country.^[7]

3. Monacelli (2005) has considered optimal monetary policy under LCP in a simple small country model.^[8] But a small country model is not capable of addressing the global misallocation of resources arising from violations of the law of one price. In such a model, import prices are exogenous for the home country, and the welfare of the rest of the world is ignored. Hence, such a framework is not designed to consider the problems of currency misalignments.
4. There are many papers that numerically solve very rich open economy models and examine optimal policy. Some of these papers allow for LCP. Many of those papers are in the framework of a small open economy, and so do not specifically account for the global misallocation of resources that occurs with currency misalignments.^[9] Moreover, many use ad hoc welfare criteria for the policy-maker or approximations that are not strictly derived from household welfare.^[10]
   
   

   Some papers have considered whether it is beneficial to augment the interest rate reaction function of central banks with an exchange rate variable.^[11] They ask the question: if the Taylor rule has the interest rate reacting to inflation and the output gap, is there any gain from adding the exchange rate?
   Typically these studies find little or no evidence of welfare gains from adding the exchange rate to the Taylor rule.

The question posed this way is misleading. To understand this point, it is helpful first to return to the optimal policy analysis in CGG. That paper finds (under their assumption of PCP) that optimal monetary policy can be characterised by a pair of ‘target criteria’ or ‘targeting rules’: and . In these equations, refers to the output gap of the home country – the percentage difference between the actual output level and its efficient level. π_Ht is producer price inflation in the home country. Analogously, is the foreign output gap and is foreign producer price inflation.^[12] These equations describe the optimal trade-off between the output gap and inflation for the policy-maker. It will be desirable to allow inflation to be positive if the output gap is negative, for example. CGG then derive optimal interest rate rules that will deliver these optimal policy trade-offs. They find that the optimal interest rate reaction functions (assuming discretionary policy) are: and is the home nominal interest rate, and rr_t is the ‘Wicksellian’ or efficient real interest rate. The response of the interest rate to inflation, b, is a function of model parameters.^[13]

The key point to be made here is that CGG's model shows that optimal policy must trade off the inflation and output goals of the central bank. But the optimal interest rate reaction function does not necessarily include the output gap. That is, adding the output gap to the interest rate rule that already includes inflation will not improve welfare. Focusing on the ‘instrument rule’ does not reveal the role of the output gap that is apparent in the ‘targeting rule’ in the terminology of Svensson (1999, 2002).

An analogous situation arises in the LCP model concerning currency misalignments. We can characterise the ‘target criteria’ in this model with two rules, as in the CGG model. The first is . This rule, at first glance, appears to be simply the sum of the two ‘target criteria’ in the CGG model. It is, except that the inflation rates that appear in this trade-off (π_t and ) are based on the CPI, rather than the producer price index (PPI) as in CGG's model.

The second target criterion is , where q_t is the real exchange rate (defined as foreign prices relative to home prices expressed in a common currency) and is the deviation of the real exchange rate from its efficient level. (The parameters in this equation are defined below.) The important point is that the trade-off described here relates real exchange rates and relative CPI inflation rates. For example, even if inflation is low in the home country relative to the foreign country, optimal policy may, under some circumstances, still call for a tightening of the monetary policy stance in the home country if the home currency is sufficiently undervalued.

Like CGG, the optimal interest rate rules that support these targeting rules can be derived. These interest rate reaction functions are and . They are identical to the ones derived in CGG (the parameter b is the same), except they target CPI inflation rather than PPI inflation as in CGG. The conclusion is that while the target criteria include currency misalignments, the currency misalignment is not in the optimal interest rate reaction function. If we focus on only the latter, we miss this trade-off the policy-maker faces.

Previous studies have found little welfare gain from adding an exchange rate variable to the Taylor rule. Properly speaking, these studies examine the effects of simple targeting rules under commitment. My results describe the welfare function, the target criteria and the optimal interest rate reaction functions under discretionary policy-making. But the results here suggest that even if there is no role for the currency misalignment in a simple targeting rule, exchange rate concerns may still be important in terms of welfare. This point is brought out in the context of a relatively simple model that can be solved analytically (with approximations), but is obscured in larger models that are solved numerically.^[14]

The paper proceeds in two steps. After setting out the objectives of households and firms, the production functions, and the market structure, a global loss function for cooperative monetary policy-makers is derived. The period loss function can be derived without making any assumptions about how goods prices or wages are set.^[15] I find that in addition to squares and cross-products of home and foreign output gaps, and the cross-sectional dispersion of goods prices within each country, the loss also depends on the squared currency misalignment. This loss function evaluates the welfare costs arising because firms set different prices in the home and foreign countries (assuming that the costs of selling the good in both countries are identical), and does not depend on whether the price differences arise from local-currency price stickiness, from price discrimination, or for some other reason.

The paper then follows CGG and assumes a Calvo mechanism for price setting. However, allowance is made for the possibility of LCP. As in CGG, optimal policy under discretion is derived. Both targeting rules and instrument rules are obtained. Only optimal cooperative policy is considered. The goal is to quantify the global loss from currency misalignments, which can be seen by deriving the loss function for a policy-maker that aims to maximise the sum of utilities of home and foreign households. Practically speaking, international agreements that prohibit currency manipulation may mean that the currency misalignment can only be addressed in a cooperative environment.^[16] That is, it seems likely that if central banks are going to move toward policies that explicitly target exchange rates, they will do so cooperatively.