The consumption-real exchange rate anomaly: nontraded goods and distribution services

Abstract

In the data, Real Exchange Rates (RERs) tend to move in opposite directions with respect to the relative consumption across countries. Chari et al. (2002) refer to the inability of models to replicate the previous stylized fact as the consumption-RER anomaly. In this article, it is shown that an International Real Business Cycle (IRBC) model, similar to the one proposed by Chari et al. but extended by considering nontraded goods and an incomplete asset market structure, can solve the anomaly. Nontradable goods amplify wealth effects arising from the incomplete assets market structure, generating a negative co-movement between the RER and relative consumption. Adding Distribution Services (DS) improves the performance of the model in some other dimensions. In particular, DS help to generate countercyclical net exports.

Keywords:

• nontraded goods
• incomplete markets
• distribution services

JEL Classification:

• F31
• F32
• F41

Acknowledgements

I am specially indebted to Pierpaolo Benigno and Jorge Selaive for very helpful comments and discussions. I would also like to thank David Backus, Ariel Burstein, Paul Castillo, Jonathan Eaton, Jon Faust, Mark Gertler, Dale Henderson, Fabrizio Perri, Pau Rabanal, John H. Rogers, Marco Vega, Jonathan Wright, and seminar participants at NYU, Federal Reserve Board of Governors, Bank of Italy, Bank of England, and the SED 2004 Conference for their comments and useful suggestions.

Notes

¹ Corsetti and Dedola (2005) have also considered the role of market segmentation in the tradable sector generated by the presence of nontradable goods in a two-period monetary model.

² Under the transfer effect, a positive home trade balance implies that home production exceeds its consumption in value, so that home is making a transfer of resources to the foreign. Home's relative wage decreases and the range of goods homes produces for export increases. Accompanying this change is a fall in home's real wage, its RER, and its terms of trade. In this context, debtor (creditor) countries tend to have more depreciated (appreciated) RERs. See Lane and Milesi-Ferretti (2004) for recent evidence on the transfer problem.

³ Corsetti et al. (2006) provide empirical evidence supporting the idea that a productivity shock generates simultaneous terms of trade and RER appreciations.

⁴ In a recent article, Rabanal and Tuesta (2010) performed Bayesian structural estimation on a monetary model similar to the one proposed by Chari et al. (2002). Rabanal and Tuesta (2010) showed that monetary shocks have played a minor role in explaining the behaviour of the RER, while both demand and technology shocks have been important.

⁵ Trade studies typically find values for the elasticity of import demand with respect to price (relative to the overall domestic consumption basket) in the neighbourhood of five to six. Most of the New Open Economy Macroeconomics (NOEM) models consider values of one for this elasticity that arises from the assumption of Cobb–Douglas preferences in aggregate consumption.

⁶ Similarly, Ghironi and Melitz (2005), findings suggested that the Balassa–Samuelson dominates the home bias effect, triggering appreciations in the RER vis-à-vis an increase in relative consumption. The mechanism relies on aggregate productivity shocks rather than sector specific shocks.

⁷ Coresetti et al. (2008) introduced DS in a standard IRBC model with a perfect competitive setting. Whereas, the model developed here allows for monopolistic competition. This assumption generates deviations from the law of one price at the border.

⁸ The population in each country is normalized to one. It is straightforward to allow for different populations in each country, as in Clarida et al. (2002) and Benigno and Benigno (2003).

⁹ The convention will be to use an asterisk to denote the counterpart in the foreign country of a variable in the home country (i.e. if aggregate consumption C is in the home country, it will be C* in the foreign country and so on). The same applies to the model's parameters.

¹⁰ For simplicity, I assume that no distribution costs in delivery of nontradable goods exist.

¹¹ Kollmann (2002) and Schmitt-Grohe and Uribe (2003) developed small open-economy models introducing the same cost to achieve stationarity. Heathcote and Perri (2002) also made a similar assumption in a two-country IRBC model. Baxter and Crucini (1995) highlighted the role of market incompleteness in IRBC. Baxter and Crucini showed that if shocks were very persistent and without spillovers, adding incomplete markets changed predictions in such models.

¹² As Benigno (2009) pointed out, some restrictions on φ(.) are necessary: φ(0) = 1; assumes the value 1 only if B _F,t  = 0; are differentiable and decreasing in the neighbourhood of zero.

¹³ Another way to describe this cost is to assume the existence of intermediaries in the foreign asset market (which is owned by the foreign households) who can borrow and lend to households of country F at a rate (1 + i*), but can borrow from and lend to households of country H at a rate of (1 + i*)φ(.).

¹⁴ is the pricing Kernel associated to the first order condition for the recursive competitive equilibrium.

¹⁵ I introduce this tax in order to eliminate the distortion generated by DS at the consumer price level in the steady state. Hence, in the model the law of one price at consumer level holds at a steady rate.

¹⁶ In order to compare results with those provided by the existing literature, the case that the economy is hit by productivity shocks (traded and nontraded) was assumed. However, I am aware of the importance of demand shocks in explaining both Gross Domestic Product (GDP) and RER behaviours (Rabanal and Tuesta, 2010). Recently, Schneider and Fenz (2010) showed that domestic shocks explain the largest share of the forecast error variances for GDP, consumer prices and interest rates in the US and the Euro area at business cycle frequencies.

¹⁷ Obstfeld and Rogoff (2000) present a survey regarding the empirical estimates of θ, indicating high values for this elasticity. Rabanal and Tuesta (2010) found estimates of this parameter in the range between 0.5 and 0.95.

¹⁸ Selaive and Tuesta (2003, 2009) estimated the implied risk sharing condition that arises from the incomplete asset market structure and found values between 0.004 and 0.01 of this elasticity. Similarly, Rabanal and Tuesta (2010) performed structural estimation of an incomplete asset markets model under different forms of international pricing with nominal rigidities. The findings gave support for the presence of cost of bond holdings.

¹⁹ In order to gain more intuition we assume an AR(1) process without spillovers effect and also that the matrix of shocks is an identity matrix.

²⁰ In the model, a productivity shock in the tradable shock improves the terms of trade, which is in line with the empirical findings reported in Corsetti et al. (2006). Corsetti et al. used a Vector Autoregression (VAR) model with long-run restrictions to identify productivity shocks.

²¹ This mechanism is called the Balassa–Samuelson effect, which contributes towards an appreciation of the RER and switched demand from home to nontraded to traded goods.

²² Selaive and Tuesta (2003, 2009) test the risk-sharing condition and find that growth factors of consumption and RERs behave in a manner that may be consistent with a significant role for the NFA position. See Rabanal and Tuesta (2007, 2010) for a structural estimation using Bayesian techniques.

²³ Rabanal et al. (2011) showed a benchmark IRBC model allowing for co-integrated Total Factor Productivity (TFP) processes could generate a RER three times more volatile with respect to output than a model that considers productivity stationary processes.

²⁴ In a flexible price version of this model, the persistence of the RER decreases significantly. Results of this exercise are available upon request from the author.

²⁵ Backus et al. (1995).

²⁶ Spillover terms from the matrix of shocks arising from the nontraded sector are also eliminated.

²⁷ This result is consistent with Corsetti et al. (2008), who find that only if shocks are very persistent, a model with high elasticity can match the consumption–RER anomaly. For instance, Stockman and Tesar's (1995) shocks are not persistent, and that is why I obtain that result.