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When and How Much Does a Peg Increase Trade The Role of Trade Costs and Import Demand Elasticity under Monetary Uncertainty

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When and How Much Does a Peg Increase Trade? The Role of Trade Costs and Import Demand Elasticity under Monetary Uncertainty Alexander Mihailov? University of Essex April 2004 Abstract This paper extends recent research in stochastic new open-economy macroeconomics (NOEM) to study the e?ects of the exchange-rate regime on international trade in a more realistic, yet rigorous, analytical set-up. We essentially embed trade in similar and di?erent output mixes within a common framework and focus on the implications of impediments to cross-border transactions under alternative invoicing, namely producer's currency pricing (PCP) versus consumer's currency pricing (CCP). Given separable utility and symmetry in structure and in the distributions of national money shocks, the only source of uncertainty in the model, our principal contribution is to show that with (some degree of) PCP — al- though not (full) CCP — a peg slightly reduces expected trade, measured in terms of GDP, relative to a float under elastic import demand. Inelastic import demand, possible under the same taste for diversity but dissimilar outputs arising from di?erences in endowments, reverses this conclusion. JEL Classification: F10, F33, F41. Keywords: international trade costs, import demand elasticity, al- ternative price setting, exchange-rate regimes, stochastic NOEM models. ?I am grateful to Philippe Bacchetta, Hans Genberg, Aude Pommeret and — particularly — Cédric Tille for comments on earlier versions as well as to Giancarlo Corsetti and Philip Lane for discussing related research.

  • international trade

  • ultimate equilibrium

  • rate regime

  • exchange rate

  • equilibrium trade

  • often been

  • noem

  • when does

  • pricing


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When and How Much Does a Peg Increase Trade? The Role of Trade Costs and Import Demand Elasticity under Monetary Uncertainty
Alexander MihailovUniversity of Essex
April 2004
Abstract
This paper extends recent research in stochastic new open-economy macroeconomics (NOEM) to study the eects of the exchange-rate regime on international trade in a more realistic, yet rigorous, analytical set-up. We essentially embed trade in similar and dierent output mixes within a common framework and focus on the implications of impediments to cross-border transactions under alternative invoicing, namely producers currency pricing (PCP) versus consumers currency pricing (CCP). Given separable utility and symmetry in structure and in the distributions of national money shocks, the only source of uncertainty in the model, our principal contribution is to show that with (some degree of) PCP  al-though not (full) CCP  a peg slightly reduces expected trade, measured in terms of GDP, relative to a Inelasticoat under elastic import demand. import demand, possible under the same taste for diversity but dissimilar outputs arising from dierences in endowments, reverses this conclusion. JEL Classication:F10, F33, F41. Keywords:international trade costs, import demand elasticity, al-ternative price setting, exchange-rate regimes, stochastic NOEM models.
I am grateful to Philippe Bacchetta, Hans Genberg, Aude Pommeret and  particularly  Cédric Tille for comments on earlier versions as well as to Giancarlo Corsetti and Philip Lane for discussing related research. Feedback from the 2nd Annual Conference of the European Economics and Finance Society in Bologna (May 2003) and the 5th Annual Conference of the European Trade Study Group in Madrid (September 2003) is also acknowledged. The usual disclaimer applies. Department of Economics, University of Essex, Wivenhoe Park, Colchester CO4 3SQ; +44 (0)1206 87 3351 (phone); +44 (0)1206 87 2724 (fax); mihailov@essex.ac.uk; http://www.essex.ac.uk/economics/people/stam/hiialov.shtm.
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Contents
1 Introduction
2 The Extended Model 2.1 Our Baseline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Incorporating Iceberg Costs . . . . . . . . . . . . . . . . . . . . . 2.3 Distinguishing Brand from Type Substitutability . . . . . . . . .
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Costly Trade under CCP vs. PCP 3.1 Optimization and Equilibrium . . . . . . . . . . . . . . . . . . . . 3.2 Equilibrium Nominal Exchange Rate . . . . . . . . . . . . . . . . 3.3 Equilibrium Relative Prices . . . . . . . . . . . . . . . . . . . . . 3.4 Equilibrium Consumption and Leisure across Countries . . . . . 3.5 Equilibrium Trade Flows . . . . . . . . . . . . . . . . . . . . . . .
Does the Exchange-Rate Regime Matter for Trade? 4.1 When Does a Peg Increase Trade-to-Output? . . . . . . . . . . . 4.2 How Much Does a Peg Increase Trade-to-Output? . . . . . . . .
The Role of Trade Costs and Import Demand Elasticity 5.1 Trade Frictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Cross-Country Substitutability . . . . . . . . . . . . . . . . . . .
Concluding Comments
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5 5 8 9
11 11 14 16 17 18
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26 27 28
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A Derivation of Equilibrium Results 31 A.1 De 31nition of Equilibrium . . . . . . . . . . . . . . . . . . . . . . A.2 Equilibrium Nominal Exchange Rate . . . . . . . . . . . . . . . . 32 A.3 Equilibrium Trade Shares . . . . . . . . . . . . . . . . . . . . . . 35
B Proofs of Propositions 39 B.1 Proof of Proposition 1 (Equilibrium World Trade-to-Output) . . 39 B.2 Proof of Proposition 2 (Expected Trade-to-Output under PCP) . 39
List of Figures
1 Peg Trade Share Surface across Iceberg Costs and Substitutabilities 21 2 Peg Trade Share Curves across Iceberg Costs . . . . . . . . . . . 27 3 Peg Trade Share Curves across Substitutabilities . . . . . . . . . 29
List of Tables
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Gains from Peg/Float for World Trade: Simulation Summary . . 25
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Introduction
The literature that has directly or indirectly addressed the question whether the exchange-rate regime matters for trade has not arrived yet at a satisfactory answer. Axed exchange rate has often been claimed to substantially increase trade, mostly on empirical grounds and notably in Rose (1999), as far as recent research is concerned. But in theoretical work focusing on monetary uncer-tainty under high substitutability of cross-country output and no trade costs, Bacchetta and van Wincoop (2000 a) have warned that this is not necessarily the case. In related analysis in Mihailov (2003), still under frictionless trade, we have furthermore shown that alternative modelling of the currency of price set-ting in open economies with nominal rigidity implies certain distinction among the trade e main point was that under Ourects of the exchange-rate regime. (complete) consumers currency pricing (CCP),1as assumed in the quoted pa-per by Bacchetta and van Wincoop, a peg versusoat does not matter for trade prices and, hence,ows because the pass-through and expenditure-switching channel of the international transmission of money shocks is closed. However under (some degree of) producers currency pricing (PCP),2when pass-through and expenditure switching are operating, a peg can stabilize trade-to-output variability. Nevertheless it cannot, neither can aoat, increase theexpected trade share in GDP, irrespective of the assumed currency of price stickiness. The objective of the present paper is thus to examine further the eects of the exchange-rate regime on trade prices andows in a more careful manner, by also looking into some of their keynon-monetarydeterminants. Wishing to achieve analytical clarity in uncovering the mechanisms of such eects as well as direct comparability with earlier results, we build on a baseline stochastic new open-economy macroeconomics (NOEM)3set-up, such as that in Mihailov (2003). But a major import of the present paper is that it embeds trade in similar vs. dierent output mixes within acommontheoretical framework, at the same time taking an explicit account of the implications of impediments to cross-border transactions under alternative invoicing,4 PCP;namely CCP vs. whereas the previous literature, classic as well as NOEM, has usually modelled in separation either trade of dierentiated brands belonging to the same homo-geneous product5or trade arising from complete specialization in the production
1Also termed pricing-to-market (PTM) or local currency pricing (LCP) and possible under market segmentation. 2The standard assumption of open-economy models, both theoretical and empirical, in the Mundell-Fleming-Dornbusch tradition. 3NOEM is dened as a line of research and classied across diering assumptions in the recent survey by Lane (2001). A narrower and more technical summary of the basic NOEM methodology is also provided in Sarno (2001). 4Friberg (1998) points out to the fact that the currency ofprice setting, the currency of invoicingand the currency ofpayment, although theoretically corresponding to three distinct stages of a typical international trade transaction and hence potentially dierent, practically coincide with few known exceptions. Therefore in what follows we use invoicing and price setting interchangeably (without talking at all about the currency of payment). 5As in Obstfeld-Rogo(1995, 1998, 2000, 2001) models, to quote just the earliest NOEM examples.
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of just one national good-type.6Our unied approach becomes feasible, it is true, at the cost of a highly stylized environment, by essentially attributing the primary cause of the international exchange of goods to identical tastes for diver-sity and not to Ricardian comparative advantage in productivity. Nevertheless, our microfounded general-equilibrium parallel of consumers to producers cur-rency pricing under monetary uncertainty and costs of cross-border transactions has provided valuable insights into trade determination, in particular about the role of nominal and real factors in it. In essence, it has permitted us to derive and interpret conditions when a peg would dominate aoat in generating more expected trade-to-output and when aoat would do that instead. Our focus on trade, and not on welfare, is justied in the following two, com-plementary aspects. First, most NOEM comparisons of exchange-rate regimes have been centered around welfare issues, whereas international trade has been covered only marginally. Yet it is important to also look at trade for a purely theoreticalreason, namely because the underlying relative prices and the sub-sequentows of goods predetermine  through microfounded consumption and leisure choices  the ultimate equilibrium allocations of these welfare ingredients, themselves sensitive to the specication of utility. Moreover, and as a conse-quence of not undertaking welfare analysis, we are able to allow for a rather general utility function, although separable in consumption and leisure. Sec-ond, and now from apolicy-orientedperspective, much has been debated on the trade implications of a monetary union, i.e. axed exchange-rate regime at its extreme, within the context of a united Europe. In an attempt to extend NOEM research in a direction that throws more light on the theory that should under-pin such important but perhaps thus far somewhat misleading public discussion, we consider it worthwhile to address analytically the present topic. It turns out from our study that the eects of the exchange-rate regime on both expected trade shares and their variability ultimately depend on whether import demand is elastic or inelastic, once an international trade friction and distinct cross-country substitutability have been explicitly incorporated, like we do here, into the baseline NOEM set-up. In a preview of our principalnd-ings, we could say that,rst, with production ofsimilarbrands national trade shares in GDP drastically fall relative to the case of costless exchange. The reason is that obstacles to trade such as distance or taris induce a home bias in consumption, much stronger under CCP than under PCP, in the optimal behavior of agents with identical tastes. A major contribution is to show that this home bias is, however, considerably mitigated to more empirically relevant levels by each of two additional features of our model: (i) allowing for produc-tion ofdierent for inelastic import demand, under (evenoutput mixes, i.e. full) CCP; (ii) allowing for (even partial) PCP, which introduces expenditure switching to the cheaper nationally-specic good, determined by the particular realization of the nominal exchange rate underoat and to the extent this is feasible given cross-country output substitutability. But the most important 6As in Corsetti-Pesenti (1997, 2001 a, b, 2002) extensions, under unit substitutability across national good-types, of the original Obstfeld-Rogomeraf.krow
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