Consumption and Real Exchange Rates With Goods and Asset Markets Frictions 1

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1 Consumption and Real Exchange Rates With Goods and Asset Markets Frictions 1 Giancarlo Corsetti University of Rome III, Yale University and CEPR Luca Dedola Bank of Italy and University of Pennsylvania Sylvain Leduc Federal Reserve Bank of Philadelphia October 22 1 We thank Fabrizio Perri, Paolo Pesenti, Morten Ravn, Martin Uribe and seminar participants at the 22 AEA meetings, the Bank of Italy, the Ente Einaudi, New York University, the University of Rochester, the Wharton Macro Lunch group, and the 22 SED meetings for helpful comments. Corsetti s work on this paper is part of a research network on The Analysis of International Capital Markets: Understanding Europe s Role in the Global Economy, funded by the European Commission under the Research Training Network Programme (Contract No. HPRN-CT ). The views expressed here are those of the authors, and do not necessarily reflect the positions of the Bank of Italy, the Federal Reserve Bank of Philadelphia, the Federal Reserve System, or any other institution with which the authors are affiliated.

2 Abstract Standard open economy models postulate high degrees of international risk sharing. This, in turn, should imply a strong, positive link between real exchange rates and cross-country relative consumption levels, when large purchasing power parity deviations prevail. Yet, this prediction is overwhelmingly rejected empirically. What has now been termed the Backus-Smith puzzle plagues a wide range of models including economies with incomplete asset markets, nontraded goods, or sticky prices. This paper revisits the puzzle by allowing for distributive trade in an otherwise standard open economy framework with incomplete markets. We find that the interaction of frictions in the goods and assets market in our model significantly improves the match between the model and the data in several dimensions. For a plausible parameterization, the correlation between the real exchange rate and relative consumption can be rather low and even negative, as it is in the data. The reason for this result is of interest on its own, as it is rooted in the international transmission of sectoral shocks through relative price and terms of trade movements JEL classification: F3, F4 Keywords: goods markets segmentation, distribution services, incomplete asset markets, consumption-real exchange rate anomaly.

3 1 Introduction The standard textbook approach to open-economy macroeconomics envisions a world of highly open economies with frictionless goods and capital markets subject to the forces of international competition. However, as argued by Obstfeld and Rogoff [21], goods markets are not frictionless, and this may be a key reason why, some 2 years further on in the process of postwar globalization, the world s large industrial economies remain strikingly fragmented and insular. Indeed, economic models allowing for frictions reducing the tradeability of some categories of goods have met some degree of success in accounting for notable aspects of insularity, such as home bias in portfolio formation, the high correlation between savings and investment, the low cross-country correlation between consumption growth rates (see, e.g., Obstfeld and Rogoff [21], Tesar [1993] and Stockman and Tesar [1995]). Nonetheless, there is one aspect of insularity the literature has not made much progress on. As first pointed out by Backus and Smith [1993], in the data there is virtually no correlation between relative consumption levels and real exchange rates. 1 Clearly, this empirical regularity cannot be explained by models allowing for trade frictions but relying on complete asset markets: in such a setup, efficient risk-sharing would imply higher consumption levels for countries that experience a fall in the real price of consumption. Relative consumption levels across countries would then be perfectly correlated with the real exchange rate. 2 What is less obvious is that the Backus-Smith anomaly would not be explained by simply combining nontradability with incomplete markets frictions. Important examples are provided by Obstfeld and Rogoff [2] and Chari, Kehoe and McGrattan [21]. According to the numerical results in the latter s contribution, limiting international asset trade to bonds only does not seem to matter for the correlation between relative consumption and the real exchange rate that remains high 1 Backus and Smith [1993] document this empirical regularity in a fairly simple and direct way calculating bilateral correlations for the G7 countries. Kollman [1995], using a sample of industrialized countries, convincingly shows that real exchange rates and relative consumption levels are neither cointegrated, nor there is any discernible short-run relationship. 2 Although Backus and Smith [1993] stress this point using a specification in which some goods are exogenously assumed not to be traded internationally,their result holds for more general specifications of the frictions in the goods or labor markets, including sticky prices or wages, shipping and trade costs, and so on. 1

4 and positive as in their complete market specification. Yet the relationship between real exchange rates and relative consumption is central to all equilibrium open economy models: the stylized fact pointed out by Backus and Smith cannot be ignored when modelling international interdependence. In this paper we show that the stylized fact stressed by the Backus-Smith anomaly can be replicated by using a realistic model of trade frictions in the form of distributive trade using intensively local inputs. The model is a version of the two-country open economy model developed by Corsetti and Dedola [21]. For standard parameter values, and calibrating the share of distribution in consumer prices so as to match the US data, the model predicts that the correlation between the real exchange rate and relative consumption be close to zero or negative, similar to the data. The reason for this result is of interest on its own, as it sheds light on the interaction between sectoral shocks, relative prices and terms of trade movements. In our model, we assume that differentiated traded goods must be combined with distribution services, intensive in local nontradeables, before they can reach consumer markets much in the same fashion as Burstein, Neves and Rebelo [2]. Different from previous literature, however, the distinctive element of our framework is optimal pricing by producers with monopoly power. As shown by Corsetti and Dedola [21], mark-up pricing in the presence of distributive trade plays a key role in bringing theory closer to the main stylized facts of the international economy. Not only does the need for distribution services drive a wedge between consumer prices of traded goods across countries: it can also make the elasticity of demand for tradeables country-specific. Therefore, monopolistic manufacturers of traded goods will find it optimal to charge different producer prices in the domestic and foreign markets, causing deviations from the law of one price that are larger than differences in distribution costs in line with the well established evidence on the pervasiveness of international price discrepancies due to price discrimination (e.g. Goldberg and Knetter [1997]). To account for the Backus-Smith anomaly, we obviously need to severe the tight ex-post link between real exchange rates and marginal utilities of consumption implied by complete markets. Our main results can be specifically attributed to the interaction between imperfect risk sharing and deviations from the law of one price that are implied by our model with distribution. 3 3 We should note here that it takes more than introducing simultaneous frictions in 2

5 In our model, the sign of the comovements between the real exchange rate and relative consumption depends on which sector experiences productivity shocks. Consider first productivity shocks in the non-traded goods sector. As productivity in this sector is unexpectedly higher, the price of nontraded goods falls and the real exchange rate depreciates consistent with Balassa- Samuelson s hypothesis. The increase in the consumption of Home nontraded goods then raises domestic aggregate consumption both in absolute terms and relative to consumption abroad. Hence the correlation between relative consumption and real exchange rate is positive. Conversely, a supply shock to the tradeable sector moves the real exchange rate and relative consumption in opposite directions. As in the standard models of international real business cycle with product specialization, a positive technology shock to the home production of exports causes the home country s terms of trade to worsen. In the presence of (endogenous) international price discrimination, however, the domestic relative price of the home to foreign tradeables falls by less than its foreign counterpart. But this in turn implies that aggregate consumption rise by less at home than abroad. As the real exchange rate closely mimics the terms of trade, the correlation between relative consumption and the real exchange rate is therefore negative in the case of a supply shock to tradeables. For a higher share of distribution costs in consumer prices, the unconditional correlation between the real exchange rate and relative consumption is dominated by the influence of supply shocks to the export sector. For realistic parameter configurations with distributive margins accounting for roughly 5 percent of the goods consumer price correlation is close to zero or even negative. The paper is organized as follows. The following section briefly discusses the extent of the puzzle while Section 3 presents a theoretical economy with goods markets segmentation and incomplete asset markets. Section 4 explores the implication of the model for the correlation between consumption ratios and real exchange rates in some numerical examples. Finally, Section different markets to account for the Backus Smith anomaly. Previous contributions pursuing this route have often ended up adding a further wrinkle to the riddle. An important example is provided by recent work by Chari, Kehoe and McGrattan [21]. In their model, the combination of frictions in the asset and the goods market does not seem to matter for the Backus-Smith anomaly, that remains as severe in their incompletemarkets specification as in their benchmark complete-markets specification. 3

6 5 summarizes and qualifies the paper s result, offering some suggestions for further research. 2 Exploring the puzzle In this section, we revisit the predictions of open-economy models for the correlation between real exchange rates and the ratio of consumption across countries. We start by looking at a world economy under complete asset markets and then move on to simple environments in which the number of assets that agents can trade is restricted. We show that a promising avenue to follow is one combining two fundamental features: incomplete asset markets and a low elasticity of substitution between domestic and foreign traded goods. The low elasticity of substitution between domestic and foreign traded goods highlights the importance of properties of the goods market that raise the volatility of exchange rates in standard open economy models. Our strategy will then be to build on these insights to show that a model with incomplete asset markets and a distribution sector can account for the apparent lack of risk sharing and the high volatility of real exchange rates and terms of trade. 2.1 International risk sharing under complete asset markets Assume that agents have intertemporal preferences represented by a timeseparable utility function of the form E n P o t= β t C1 σ 1 σ. Given these preferences, Backus and Smith [1993] showed that a key implication of complete risk sharing, in a world with PPP deviations, is the high and positive correlation between consumption levels across countries and the real exchange rate: RER t E tpt = C σ t, (1) P t Ct σ where we define the real exchange rate as the ratio of foreign to domestic price level, when expressed in domestic currency units via the nominal exchange rate, E, and where domestic and foreign consumption are represented by C t and Ct, respectively. However, empirical tests of this risk sharing condition 4

7 that have not implicitly assumed PPP have found this correlation to be low and even negative (see, for instance, Backus & Smith [1993], Kollman [1995] and Ravn [21]). To give a quick overview of the extent of the puzzle, Table 1 shows the correlation between real exchange rates and relative consumption for pairs of OECD countries and for each country relative to an aggregate of the OECD countries. Overall, relative consumption and real exchange rates do not appear to be strongly positively correlated. The highest correlation in the table is only.41 (Italy vis-a-vis the rest of the OECD countries), and most correlations are in fact negative. Indeed, the average of the table s entries is -.2. Therefore, the strong predictions of open-economy models with complete asset markets regarding the extent of risk sharing is not consistent with the data. To account for the apparent lack of risk sharing described in Table 1, a natural first step would be to depart from the assumption of complete asset markets. 2.2 Solving the puzzle with financial frictions? Although introducing incomplete asset markets is a promising first step towards accounting for the data in Table 1, it is by no means a sufficient one. In fact, Cole and Obstfeld [1991] present examples of economies in autarky in which complete risk sharing can nonetheless occur, because movements in the terms of trade make financial markets redundant. They show that one condition for this result is Cobb-Douglas preferences over domestic and foreign consumption bundles. In this section, we show that departing from the assumption of Cobb-Douglas preferences when the economies are in autarky has important consequences for the correlation between the real exchange rate and relative consumption. To see this, imagine a two-country world in which aggregate consumption in the domestic country is given by the following CES function: C t = h a 1 ρ H C ρ H,t +(1 a H ) 1 ρ C ρ i 1 ρ F,t, (2) where C H,t (C F,t ) is the domestic consumption of Home (Foreign) good and a H is the share of the domestically produced good in the consumption aggregator. 4 4 Foreign counterparts will be denoted with a superscript asterix. 5

8 The price index associated with C t can be derived as: ρ ρ ρ 1 ρ ρ 1 ρ 1 P t = a H P +(1 a H ) P, (3) H,t where P H,t (P F,t ) is the price of the Home (Foreign) good. Defining the terms of trade, TOT t, as the price of the imported good, P F,t, relative to the price of Home exports, P H,t, and using the balance trade condition, we get: F,t TOT t C F,t = C H,t. (4) Since the economies are in autarky, the value of the home country s imports must equal the value of what that country exports. Following some simple substitutions (see Appendix A), we can derive a log-linearized relationship between the real exchange rate and relative consumption: RER t = 2a H 1 ³ C b C 2a H ϕ 1 c, (5) where ϕ = 1 is the elasticity of substitution across the two goods. Therefore, for a given share of the domestically produced good in the consumption 1 ρ aggregator, the real exchange rate can in fact be negatively correlated with relative consumption if the elasticity of substitution, ϕ, is low enough. For instance, assuming that countries have preferences characterized by a home bias in consumption, namely that a H > 1, then that correlation will be negative when ϕ < 1 2a H 2. In this model, real exchange rates and relative consumption will either be perfectly positively or negatively correlated, depending on the values of a H and ϕ. A low elasticity of substitution turns out to have other appealing effects. Heathcote and Perri [22], for instance, show that lowering the elasticity of substitution under financial autarky significantly increases the volatility of the real exchange rate and the terms of trade to levels that are roughly consistent with the data. However, one problem with this approach is that, to obtain higher exchange rate volatility and a negative correlation between the real exchange rate and relative consumption, the elasticity of substitution needs to be relatively low. For instance, assuming a typical value for a H of.8, implies that ϕ must be lower than.6, which is at the lower end of the range of estimated values for that elasticity. For instance, Chari, Kehoe, and 6

9 McGrattan [21] suggest a value of 1.5, while Heathcote and Perri [22] estimate it to be.9. Nevertheless, we view this exercise as providing interesting insights for how an open-economy model can account for the seeming lack of international risk sharing. To potentially account for the data in Table 1, a model needs to not only have incomplete asset markets but also features in the goods market that, just like a low elasticity of substitution, increase the volatility of real exchange rates and the terms of trade. In the next section, we introduce a model with distribution costs that, consistent with the data, has the potential to generate volatile real exchange rates and terms of trade and, ultimately, improves the match between the model and the data on international risk sharing. 3 A model with international goods and asset markets segmentation Goods, inputs and market structure The world economy is a version of Corsetti and Dedola [22] with flexible wages and competitive labor markets. It consists of two countries of equal size, denoted H and F. Each country is specialized in onetypeoftradableintermediategoods, produced in a number of varieties or brands defined over a continuum of unit mass. Brands of tradable goods are indexed by h [, 1] in the Home country and f [, 1] in the Foreign country. In addition, each country produces an array of differentiated nontradable goods, indexed by n [, 1]. Non-traded goods are either consumed, or used to make intermediate tradable goods h and f available to domestic consumers. In what follows, we describe our set up focusing on the Home country, with the understanding that similar expressions also characterize the Foreign economy whereas starred variables refer to Foreign firms and households. Firms producing tradables and nontradables are monopolistic suppliers of one brand of goods only. These firms employ a technology linear in domestic labor inputs and whose productivity level is determined by a random disturbance common across firms in the same sector, Z H,t and Z N,t. 5 Firms operating in the distribution sector, instead, are assumed to operate under 5 There is no labor mobility across countries. 7

10 perfect competition. They buy tradable goods and distribute them to consumers using non-traded goods as the only input in production. 6 In the spirit of Erceg and Levin [1995] and Burstein, Neves and Rebelo [2], we assume that bringing one unit of traded goods to consumers requires η units of a basket of differentiated non-traded goods Z 1 η = η(n) θ 1 θ dn θ θ 1. (6) We note here that the Dixit-Stiglitz index above also applies to the consumption of differentiated non-traded goods. In equilibrium, then, the basket of non-traded goods required to distribute tradables to consumers will have the same composition of the basket of nontraded goods consumed by the representative domestic household. Preferences The representative home agents in the model desire to maximize the expected value of his lifetime utility, given by: ( " X t 1 #) X E U [C t (j),`t(j)] exp ν (U [C t (j),`t(j)]) t= τ= where the instantaneous utility U is a positive function of a consumption index C(j) to be defined below and leisure, (1 `(j)). Foreign agents preferences are symmetrically defined. These preferences guarantee the presence of a locally unique steady state, independent of initial conditions. 7 Households consume all types of domestically produced non-traded goods, and both types of traded goods. So, C t (n, j) is consumption of brand n of Home non-traded good by agent j at time t; C t (h, j) andc t (f,j) are the same agent s consumption of Home brand h and Foreign brand f. Foreach type of good, we assume that one brand is an imperfect substitute to all 6 For symmetry, distribution costs should also be incurred in the case of non-traded goods. For notational and computational simplicity, we ignore distribution costs for nontraded goods, noting that these are homothetic to change in the level of productivity in the nontradable sector. 7 The presence of a unique invariant distribution of wealth, under these preferences, will allow us to use standard numerical techniques to solve the model when an international bond is traded (see Obstfeld [199], Mendoza [1991], and Schmidt-Grohé and Uribe [21]). 8

11 other brands, with constant elasticity of substitution. Consumption of Home and Foreign goods by Home agent j is defined as: Z 1 C H,t (j) Z 1 C N,t (j) C t (h, j) γ 1 γ dh γ γ 1, C t (n, j) θ 1 θ dn θ θ 1, Z 1 CF,t (j) γ C t (f,j) γ 1 γ 1 γ df, where θ and γ are the elasticity of substitution for non-traded and traded goods, respectively. Consumption of different goods by Foreign agent j Ct (n, j ), Ct (h, j )andct (f,j ) and the corresponding consumption indexes CN,t(j ), CH,t(j )andcf,t(j ) are similarly defined. The utility from consumption of tradeable goods of individuals j and j is: C T,t (j) [a H C H,t (j) ρ + a F C F,t (j) ρ ] 1 ρ, ρ < 1, (7) where a H and a F are the weights on home and foreign traded goods, respectively, and ρ determines the constant elasticity of substitution between these goods. Similarly, the full consumption basket in each country is C t (j) h a T C T,t (j) φ + a N C N,t (j) φi 1 φ, φ < 1. (8) Price indices A notable feature of our specification is that, because of distribution costs, there is a wedge between the producer price and the consumer price of each good. Let p t (h) andp t (h) denote the price of brands h expressed in the Home currency, at producer and at consumer level, respectively. Let P N,t denotes the price index of the bundle of non-traded goods that are necessary to distribute the good (later to serve as a numeraire and to be normalized to 1). With competitive firms in the distribution sector, the consumer price of good h is simply p t (h) =p t (h)+ηp N,t. Using these definitions, we can derive the utility-based consumption price index following the usual steps, that is, denoting with P H the (utility-based) consumer price index of home tradeable goods in Home currency, we have Z 1 1 P H,t = [p t (h)+ηp N,t ] 1 γ 1 γ dh. (9) 9

12 The price indexes P N,t and P N,t are analogously defined. We hereafter write the utility-based price indexes of tradables: P T,t = a 1 1 ρ H P H,t (j) ρ 1 ρ 1 + a and the utility-based CPIs: P t = a 1 P T,t (j) φ 1 φ 1 + a 1 φ T 1 ρ F 1 φ N ρ 1 P F,t (j) ρ ρ ρ 1, (1) φ 1 P N,t (j) φ φ φ 1. (11) The foreign price indices, denoted by an asterisk and expressed in the same currency as the domestic ones, are similarly defined. In the remainder of thepaper,wedefine the price of Home aggregate consumption P t to be the numeraire. Hence, the real exchange rate will be defined as usual as the price of Foreign aggregate consumption Pt in terms of P t. Budget constraints and asset markets Home and Foreign agents hold an international uncontingent bond, B H, which pays in units of Home aggregate consumption, and a well diversified portfolio of domestic firms. They earn labor income W`. The individual flow budget constraint for agent j in the Home country is therefore: 8 P H,t C H,t (j)+p F,t C F,t (j)+p N,t C N,t (j)+b H,t+1 (j) (12) W t (j)`t(j)+(1+i t )B H,t (j)+ Z 1 Π(h, j)dh + Z 1 Π(n, j)dn, where i t is the bond s yield, paid at the beginning of period t but known at time t 1; and R Π(h, j)dh + R Π(n, j)dn is total dividend revenue from equities, from all firms h and n in the economy. A similar expression holds for the representative individual j in the Foreign country. As the international bond is assumed to be in zero net-supply, we have: Z 1 B H,t (j)dj + Z 1 so that in the aggregate B H,t = B H,t. B H,t (j )dj =, (13) 8 The notation conventions follow Obstfeld and Rogoff [1996, ch.1]. Specifically, M t (j) denotes agent j s nominal balances accumulated during perod t and carried over into period t + 1, while B H,t (j) andb F,t (j) denote agent j s bonds accumulated during period t 1 and carried over into period t. 1

13 Firms optimization and endogenous pricing to market While many elements of our setup are standard in the literature, distributive trade and monopolistic competition in the goods market are two distinctive features of our model that enable us to account for endogenous pricing-to-market. In this section, we briefly addressthefirms pricing problem. We start by characterizing optimal pricing by firms producing nontradables in the Home market. These firms face the following demand for their product C(n)+η (n) =[p t (n)] θ P θ N,t It is easy to see that their optimal price will be: µz 1 Z 1 C N,t + η C t (h)dh + C t (f)df. (14) p t (n) =P N,t = θ W t. (15) θ 1 Z N,t In the tradable good sector, instead, even if the elasticity of substitution γ among different brands of type h (f) good is the same in the two countries, the need for distribution services intensive in local non-traded goods implies that the elasticity of demand for the h (f) will usually differ across markets. Thus, in general, firms will want to charge different prices at Home and in the Foreign country. To see this, consider the profit maximization problem faced by the representative Home firm (where p(h) andp (h) are the prices in common currency charged to domestic and foreign retailers, respectively): Max p(h),p (h) [p t (h)c t (h)+p t (h)c t (h)] W t Z H,t [C t (h)+c t (h)] where C t (h)+c t (h) =[p t(h)+ηp N,t ] γ P γ H,tC H,t + h p t (h)+ηp N,ti γ ³ P H,t γ C H,t Making use of (15), the optimal prices p(h) andp (h) are (where W t W t again the relative wage in a common currency): p t (h) = γ Ã 1+ η γ 1 γ 11 θ θ 1 Z H,t Z N,t denotes! Wt Z H,t (16)

14 p t (h) = γ Ã 1+ η γ 1 γ θ θ 1 Z H,t ZN,t Wt! Wt (17) W t Z H,t Observe that in general p (h) falls, but less than one to one, with a depreciation of the exchange rate. Most crucially, unless η = the optimal prices of intermediate tradeable goods do not obey the law of one price: p t (h) 6= p t (h). Monopolistic firms take into account the effect of distribution on the demand elasticity across countries. Thus, they find it optimal to charge different wholesale prices to firms distributing in the Home and in the Foreign market. The consumer price of the good h in each market is then calculated adding the distribution costs (ηp N and η P N)totheoptimal producer prices above. 9 In addition to explaining deviations from the law of one price, distribution costs also have key implications for the optimal degree of exchange rate passthrough. In the Home market, the price elasticity of the demand for the good h depends on relative productivity across domestic sectors: C t(h) p(h) θ/γ θ 1 p t (h) C t (h) = γ p t (h) = γ 1+η p t (h)+ηp N,t 1+η θ Z H,t Z N,t Z H,t, θ 1 Z N,t while in the export market the price elasticity of the demand for the good h depends on productivity shocks at Home and abroad, and the exchange rate: C t (h) p (h) p (h) Ct (h) = γ p (h) p (h)+ηpn,t 1+η θ/γ Wt Z H,t θ 1 W t ZN,t = γ 1+η θ Wt Z H,t θ 1 W t ZN,t. Specifically, the price elasticity of export demand is increasing in the wholesale price a sufficient condition for incomplete exchange-rate passthrough, as shown by the literature on international trade. 1 Note that the above price elasticities are monotonic functions of the distribution margin, defined as the share of distributive trade in the consumer price of the good 9 While charging (16) and (17) would maximize firms profits,however,arbitragein the good markets may prevent optimal price discrimination between domestic and foreign distributors. See Corsetti and Dedola [22] for an analysis of this case. 1 As far as the elasticity of substitution between the tradable good and the nontradable bundle in the retailer distribution technology is less than 1, the producer s price elasticity will be increasing in p (h). 12

15 h, i.e. ηp N,t/p t (h) andηp N,t /p t (h) intheexportandthedomesticmarket, respectively. In either market, the higher the distribution share, the lower the price elasticity. 4 Consumption, the real exchange rate, and sector-specific shocks In this section we employ standard numerical techniques to solve the model developed above, with the goal of quantifying the effects of deviations from the law of one price due to distribution services on the link between the real exchange rate and the level of consumption across countries. Namely, we will examine the model s prediction comparing unconditional moments to their empirical counterparts and through impulse-response analysis. To facilitate an intuitive understanding of the model, when analyzing impulse responses we choose a streamline benchmark calibration in which supply shocks are not correlated across sectors and countries. This assumption is clearly unrealistic, and is therefore relaxed in the other experiment. We will compute unconditional moments, and in particular the correlation between the real exchange rate and relative consumption, adopting the more general process for the sectoral labor productivity that we estimated for the U.S. and Canada. Finally, we conduct some sensitivity analysis to assess the robustness of our results, under the benchmark calibration. In particular, we will assess the sensitivity of our results to changes in η, the fraction of the retail price accounted for by distribution services, as well as the tradables 1 elasticity of substitution and the import share. 1 ρ 4.1 Calibration In order to be able to gauge the quantitative implications of the model, we have to pick baseline values for the parameters. Table 2 reports our benchmark choices, which we assume symmetric across the two countries. Several parameters values are similar to those used in Stockman and Tesar [1995] and Chari, Kehoe, and McGrattan [21], who calibrate their model to the United States and a set of OECD countries. 13

16 Preferences and production Consider first the preference parameters. We assume a utility function of the form: U [C t (j),`t(j)] = α ln C t (j)+(1 α)ln(1 `t(j)), < α < 1 (18) wherewesetα so that so that in steady state one third of the time endowment is spent working.. We follow Gomme and Greenwood [1995] and assume that the endogenous discount factor has the following form: ν (U [C t (j),`t(j)]) = ln (1 + ψ [α ln C t (j)+(1 α)ln(1 `t(j))]), where the constant ψ is set so that the steady-state real interest rate is 1% per quarter. To choose a value for φ, we need to get an estimate of the elasticity of substituiton between traded and non-traded goods. We use Mendoza [1991] s estimate for industrialized countries and set that elasticity to.74. Stockman and Tesar [1995] estimate a lower elasticity of.44. However, developing countries were also included in their data set. The range of estimates used in quantitative works for the elasticity of substitution between traded goods varies greatly. For instance, Backus, Kydland, and Kehoe [1995] use a value of 1.5, whereas Heathcote and Perri [22] estimate the elasticity to be.9. For our benchmark calibration, we set it equal to 1, as in Stockman and Tesar [1995], but we also report our results for different values of that parameter. We set the weights of domestic and foreign traded goods, a H and a F, in the consumption basket for traded goods, C T, so that imports, in steady state, represent 1% of aggregate output (the import share) and using the normalization a H +a F = 1. We also report results with a higher import share of 15%, in order to take into account the positive trend in this quantity in the data. To choose a value for a T and a N, the weight of traded and non-traded goods in the full consumption basket C, we refer to empirical work by Kravis et al. [1982], suggesting that the share of nontradables in the industrialized countries is in the range of 4-54 percent of GDP. Using a similar decomposition of GDP by sector, Stockman and Tesar [1995] find that non-traded goods comprise roughly 5 percent of output in the seven largest OECD countries. We therefore set a T to match that ratio and use the normalization a T + a N = 1 to determine a N. 14

17 Finally, we need to pick up baseline values for η, γ, and θ, the parameters determining the fraction of the retail price of traded goods accounted for by local distribution services and the elasticity of substitution across brands of goods, respectively. We follow Burstein, Neves and Rebelo [2] and set η =.82, which implies that 45% of the retail price of traded goods is made up by local retailing. Values for the elasticity of substitution are in general chosen drawing from the evidence on the size of markups note that the markup in the θ nontraded-goods sector is given by the standard constant. Assuming θ 1 asteady-statemarkupof1.11impliesthatθ =1.9. Such values are on the lower side of those estimated in the literature. Estimates in Morrison [199] range between 1.2 and 1.4 for sixteen out of her eighteen industries, while estimates in Domowitz, Hubbard and Petersen [1988] range between 1.4 and 1.7 for seventeen out of their nineteen industries. In the macroeconomics business cycle literature, calibrated markups range between 1.11 in Chari, Kehoe and McGrattan [21], 1.5 in Hornstein [1993] and Christiano, Eichenbaum and Evans [21], and 2 in Rotemberg and Woodford [1989]. However, in the presence of distribution services, sectoral markups will not be equal in steady state. For instance, the markup in the Home traded-good sector can be written as: Λ H = γ Ã 1+ η! θ Z H. γ 1 γ θ 1 Therefore, for a given η, and assuming equal productivity levels Z across sectors in the long-run, we set γ to equalize the markups between the nontraded and traded sectors. Productivity shocks Consider next the technology parameters for traded and nontraded goods. The disturbances to technology, defined by the state vector Z (Z H,Z F,Z N,ZN), are assumed to follow a stationary AR(1) process Z N Z = λz + u, (19) where u (u H,u F,u N,u N) has variance-covariance matrix V (u), λ is a 4x4 matrix of coefficients describing the autocorrelation properties of the shocks. Since we assume that the two countries in our model are symmetric, we also 15

18 impose symmetry on the autocorrelation and variance-covariance matrices of the process. Consistent with our model, we identify the technology shocks as labor productivity in each sector and we use data on labor productivity per hour worked in manufacturing and services industries in Candada and the U.S. as proxies for tradables and nontradables. The bottom panel of Table 1 reports the parameter estimates of the exogenous process in detail. As previous studies found, our estimation procedure yields very persistent technology shocks and a relatively low spillovers across countries and sectors Main findings We now explore the relationship between the consumption ratio and the real exchange rate in our model economy at business cycle frequencies. We begin by analyzing impulse-response functions conditional to a shock to sectoral productivity. We then look at the (unconditional) correlation properties of the model The dynamics of sector-specific shocks This section shows that the link between the real exchange rate and the consumption ratio depends crucially on the nature of the shocks hitting our model economy. Based on standard impulse-response functions, our experiments consist of shocking the exogenous process for productivity once at date, when both countries are at their symmetric, deterministic steady state, by one standard deviation (amounting to an increase of.7 percentage point). We first discuss the response of the Home and Foreign economies to an unexpected increase of nontraded-goods productivity in the Home country. Next we investigate the effects of an unexpected increase of the productivity in the Home export sector. 11 The persistence of the estimated shocks, though in line with estimates both in the closed (e.g., Cooley andprescott [1995]) and open economy (Backus et al. [1992]) literature, is higher than that reported by Stockman and Tesar [1995]. There are at least two reasons for this difference, due to their following two departures from the above mentioned literature. First, Stockman and Tesar [1995] use annual data - while we use quarterly data; second, they compute their Solow residuals out of filtered data - while we compute them from logged levels. 16

19 Nontraded-goods productivity Figure 1 depicts the response of key economic variables in each country to a one standard deviation shock to the level of technology in the nontraded-goods sector. The figure reports the response of (a) the real exchange rate, where the latter is defined as the relative price of the Foreign consumption bundle in terms of the Home one; (b) the terms of trade, defined as the relative price of Home imports in terms of Home exports; (c) relative consumption across countries, defined as the ratio of Home aggregate consumption to Foreign aggregate consumption; and (d) relative output across countries, defined as the ratio of Home aggregate output to Foreign aggregate output. Since a different share of distribution services in the final price of traded goods affects the transmission of shocks in the economy, we report impulse-responses for different value of η. Ineachgraphs, the solid and dotted lines denote a variable s behavior when η =,η =.82, amounting to a. and.5 distribution margin, respectively. Following an increase in the productivity of the domestic nontradables, the relative price of nontraded goods falls and the Home consumption bundle becomes less expensive than the Foreign bundle. Therefore, the real exchange rate depreciates according to a standard Balassa-Samuelson effect. Moreover, the increase in nontraded-goods consumption at home leads to a rise in both domestic aggregate consumption and relative consumption. As a result, the correlation between the latter and the real exchange rate is positive and very close to 1. This is the basic mechanism at the heart of the Backus and Smith anomaly: consumption increases in the country where it happens to be cheaper (i.e. that is experiencing a real depreciation). Strikingly, however, in our model this occurs through the effect of shocks to the nontraded-good industry, regardless of asset markets incompleteness. To understand the importance of distribution services, note that, absent retail trade (η = ), the domestic prices of export goods rise due to the shift in labor towards the non-traded goods sector. The terms of traded therefore improve on impact as home tradable output falls. However, for positive values of η, instead, monopolistic wholesalers cannot but take into account developments in the nontraded-goods sector when making their pricing decisions. In particular, domestic firms realize that rising productivity in the non-traded good sector reduces the marginal costs of retail services, and make the final demand for their goods more elastic. Thus, this channel lowers their markup and the price they charge to Home retailers. The larger η, the bigger the downward pressure on the domestic 17

20 producer price of Home tradeables. As the distribution margin rises, the increase in the productivity of the nontraded-good sector counterweights the upward movement in domestic export prices caused by the shift in labor. By the same token, the fall in the retailing cost of their goods to Home consumers will also exert a downward pressure on the export prices charged by foreign monopolists. Overall, the terms of trade worsens for the home country, under our calibration. Therefore, the combination of goods markets segmentation and incomplete asset markets tends to dampen the response of relative consumption, following an increase in nontraded-goods productivity, while at the same time magnifying the response of the real exchange rate. For the benchmark retail margin of 45%, the latter is up to three times more volatile than its fundamentals. Traded-goods productivity The effects of an increase in the productivity of the domestic tradable is shown in Figure 2, reporting our results for the same set of variables as the previous exercise. Consider first the straightforward case with no distribution (η =).From (16) and (17) it is clear that, as the law of one price holds, the increase in productivity of the Home traded-goods industry lowers the domestic and Foreign price of Home tradables in proportion to the additional quantities produced and by the same amount. As a result, Home and Foreign consumption rise and the terms of trade worsen for the Home country. But because of the presence of home-bias in preferences, Home aggregate consumption rises by more than that in the foreign country and the fall in the domestic aggregate price index is greater than abroad. Absent distribution, the model therefore generates a strong positive correlation between relative consumption and the real exchange rate. When retailing is introduced, the depreciation of the real exchange rate and the worsening of the terms of trade are amplified. Since foreign nontraded goods are necessary to bring domestic imports to foreign consumers, foreign labor is shifted from the production of traded goods to the production of non-traded goods. Therefore, the production of foreign traded goods falls and their prices rise, which amplifies the adverse movement on the domestic country s terms of trade and magnifies the depreciation of the real exchange rate. Note that these effects of productivity shocks on the terms of trade and the real exchange rate are in line with standard models with product 18

21 specialization and homothethic preferences (e.g., Lucas [1982]). 12 Finally, the real exchange rate and relative consumption are negatively correlated following a technological shock to the export sector. Indeed, relative consumption falls in the face of a depreciating domestic currency. Again, this is due to worsening terms of trade at Home. Because Foreign wholesalers increase the price they charge Home retailers, Home agents face higher prices at the consumer level. They therefore cut back on their consumption of imports. In a nutshell, the worsening of the terms of trade, following a positive shock in the Home traded-goods industry, contributes both to the depreciation of the real exchange rate and to the fall in relative consumption Volatility and correlation properties We now look at the unconditional correlation between relative consumption and the real exchange rate in the model, as well as the volatility of some variables of interest, when both traded- and nontraded-goods industry productivity shocks hit the economies simultaneously. Throughout our exercises, we will compute statistics by logging and filtering the model s artificial time series using the Hodrick and Prescott filter and averaging moments across1 simulations. The H-P filtered statistics for the data, the baseline economy and some variations on that economy are reported in Tables 3. As we discussed in section 2, Table 1 describes the extent of the anomaly highlighted by Backus and Smith [1993] and Chari, Kehoe and McGrattan [21]. While for the United States relative to an aggregate of OECD countries this correlation is basically zero (.2), for other country pairs it ranges between -.48 and.4, but with a predominance of negative correlations. At any rate, these correlations are substantially lower than what is predicted by most standard open-economy models. To emphasize the impact of distribution services on the level of risk sharing in our model, Figure 3 reports the correlation between the real exchange rate and the consumption ratio. The figure first demonstrates that, under our standard calibration, introducing incomplete markets per se is not suf- 12 This result is seldom highlighted in models with nontraded goods, as in general tradables are assumed to be perfectly homogeneous and thus there are no terms of trade fluctuations (e.g. Stockman and Dellas [1989] and Tesar [1993]). Therefore, a technological advance in the traded-good sector typically brings about an appreciation of the domestic currency due to an increase in the domestic relative price of nontradables. 19

22 ficient to resolve the puzzle: the correlation when η = is close to unity, due to the fact that terms of trade movements foster risk sharing through the international transmission of shocks. However, this correlation falls as we increase the distribution margin. In fact, when the share of retail services in final goods prices is between 4-5%, the model generates a correlation between relative consumption and the real exchange rate that is close to zero or even negative. Note also that introducing retail trade has a similar impact on that correlation whether we look at HP-filtered or first-differenced data. As shown by Ravn [21], the last aspect is also important, because the availability of an international bond should imply that the (expected) relative growth rate of consumption across countries be positively and strongly correlated with the (expected) real rate of depreciation. Table 3 shows that our benchmark model succeeds in generating correlations between the real exchange rate and relative consumption very close to these data, and substantially less than one in absolute value. In fact, when the model is calibrated so that 45% of consumers prices is accounted for by distribution services, the correlation between relative consumption and the real exchange rate is.2, which is exactly what is found in the data. The correlation between the terms of trade and relative consumption in our model is, however, slightly more negative than we observe empirically. As is well known, real exchange rates do not exhibit a tight link with relative output across countries either (see, for instance,stockman [1998]).We therefore report that correlation in Table 3. Our results shows that a plausible value of the distribution margin also helps improving the match between the model and the data along that dimension. Although the real exchange rate and relative output are still highly correlated in our environment (.61), the latter value is significantly less than that in the model with no retailing (.94). As we discussed in the section describing the impulse-response functions, increasing the distribution margin amplifies the movements of the terms of trade and the real exchange rate. The volatility of the real exchange rate relative to that of output is 3.66% in our model when s=45%, nearly the same as we find in the data. The simulated terms of trade are also very volatile, being three times as volatile as output. The statistics in Table 3 also highlight the importance of distribution services in generating our results. Without distribution services, our standard framework replicate the Backus-Smith anomaly: a depreciation of the real 2

23 exchange rate is associated with a rise in relative consumption. When η =, the correlation between these two variables is.94. And absent distribution services, the real exchange rate and the terms of trade are less volatile than output. In section 2, we discussed the importance of the elasticity of substitution in a standard model without distribution services for generating volatile exchange rates and a (perfectly) negative correlation between real exchange rates and relative consumption across countries. The last row of Table 3 presents the results from our model when we assume no distribution costs (η = ) and a low elasticity of substitution between Home and Foreign traded goods ( 1 =.5). As in Heathcote and Perri [22], our framework produces 1 ρ very volatile real exchange rates and terms of trade relative to the variability of output. And, moreover, the real exchange rate is not strongly positively correlated with relative consumption. In fact, the correlation is equal to -.21, which is less than -1, as in section 2, because of the presence of nontraded goods. The model with distribution costs and Cobb-Douglas preferences for the traded goods consumption aggregator ( 1 = 1) behaves in a similar 1 ρ fashion to the model without distribution services but with a low elasticity of substitution ( 1 =.5). The reason for this is that the need to combine 1 ρ traded goods with distribution services brings about a lower substitutability betweenhomeandforeigntradedgoods. Finally, as it should be expected from the above impulse-response analysis, the model predicts a much tighter connection between the real exchange rate and sectoral relative consumption. Namely, in the model the relative consumption of traded (nontraded) goods is more negatively (positively) correlated with the real exchange rate than in the aggregate. For instance, for our benchmark calibration, we find that the correlation between the real exchange rate and the consumption of traded (nontraded) goods is -.68 (.48). At this point, we are not aware of any stylized fact about these relationships. However, according to the evidence in Stockman and Tesar [1995], it seems that total and sectoral consumption behave roughly in the same way at business cycle frequencies. Thus, this relatively stronger prediction may turn out to be at odds with the evidence. 21

24 5 Concluding remarks The lack of a tight link between bilateral relative consumption levels and real exchange rates, first documented by Backus and Smith [1993], is among a set of riddles that challenges standard open-economy models. At the heart of the matter is the very strong prediction by a large class of models that a country with a depreciating real exchange rate should simultaneously experience a relatively higher level of consumption. Inacompellingpaper,ObstfeldandRogoff [21] argue that asset markets incompleteness is most likely one reason behind the absence of such a link between real exchange rates and relative consumption. Yet, Chari, Kehoe, and McGrattan [21] show that restricting trade in international assets markets to pure-discount bonds does not significantly alter the equilibrium allocations in their economy with nominal rigidities and local-currency pricing. In this paper, we develop a model with incomplete asset markets and a goods-trading friction that is due to the need to combine traded goods with distribution services in order to reach final consumers. In numerical examples with a plausible parameterization of our world economy, we show that the interaction of these two features with sectoral productivity shocks can account for the somehow weak link between the real exchange rate and relative consumption in the data. Similar to other models in the literature adopting the same consumption preferences as we do, the equilibrium adjustment to shocks requires large movements of the terms of trade, providing risk insurance to countries specialized in different types of goods. However, because of the combination of incomplete asset markets and distribution services in our model, these large terms of trade movements are insufficient to provide full insurance against production risk. Productivity shocks to the traded- and nontraded-goods sectors have opposite effects on the comovements between the real exchange rate and relative consumption. Even without complete asset markets, positive productivity shocks to the nontraded-goods sector depreciates the real exchange rate (consistent with the Balassa-Samuelson prediction) and raise the domestic to foreign consumption ratio. Conversely, shocks to the traded-goods sector worsen the terms of trade, reducing the relative price of exportables in the world markets. Because of the differential effects of distributive trade on 22