The Consumption-Real Exchange Rate Anomaly: Non Traded Goods and Distribution Sevices Vicente Tuesta∗ CENTRUM Católica and Prima AFP January 2011
Abstract In the data, real exchange rates tend to move in opposite directions with respect to the relative consumption across countries. Chari, Kehoe, and McGrattan (2002) refer to the inability of models to replicate the previous stylized fact as the consumption-real exchange rate anomaly. In this paper, it is shown that an international real business cycles model, similar to the one proposed by Chari et al. but extended by considering non-traded goods and an incomplete asset market structure, can solve the anomaly. Non-tradable goods amplify wealth effects arising from the incomplete assets market structure, generating a negative comovement between the real exchange rate and relative consumption. Adding distribution services improves the performance of the model in some other dimensions. In particular, distribution services help to generate countercyclical net exports. Keywords: Non-traded goods, incomplete markets, distribution services. JEL Classification: F31; F32; F41
Chari, Kehoe, and McGrattan (2002) attempted to explain the volatility and persistence of the real exchange rate by building a model with sticky prices and local currency pricing. Their main finding was monetary shocks and complete markets, along with a high degree of risk aversion and price stickiness, are enough to account for real exchange rate volatility and to a lesser extent, its persistence. However, the model could not account for the observed negative correlation between ∗ 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.Correspondence concerning this article should be addressed to Vicente Tuesta, Professor of CENTRUM Católica, Pontificia Universidad Católica del Perú. E-mail:
[email protected]
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real exchange rates and relative consumption across countries, a fact Chari et al. labeled the consumption-real exchange rate anomaly. In addition, Chari et al. show that the most widely used form of asset market incompleteness does not eliminate the anomaly. Chari et al. argued their results stemmed from the fact wealth effects arising from market incompleteness are too small. Backus and Smith (1993) reported the same puzzle in an international real business cycle model (IRBC) with non-traded goods. Obstfeld and Rogoff (2000) listed the “disconnect” puzzle among the central unresolved puzzles in international macroeconomics. In this paper, the consumption real exchange anomaly is addressed by generating meaningful wealth effects in a dynamic stochastic general equilibrium model with imperfect competitors. In achieving this goal, I build an economy along the lines of Chari et al. (2002) and Stockman and Tesar (1995), modified to allow for some features expected to help the model produce fluctuations like those in the data. First, I consider an incomplete asset market structure as did Chari et al. (2002), but unlike them, the net foreign assets position (NFA) is stationary. Second, I introduce non-traded goods as did Stockman and Tesar (1995) in order to generate meaningful wealth effects. The key difference in the analysis relative to Chari et al. (2002) is the introduction of non-traded goods. I argue it is the absence of non-traded goods in Chari et al.’s model that inhibits wealth effects and makes the model deliver almost perfect risk sharing, even with incomplete markets. Finally, following Burstein, Neves, and Rebelo (2003), I add distribution services in terms of non-traded goods that endogenously generate deviations from the law of one price at both consumer and producer level.1 Distribution services, while accounting for the consumption-real exchange anomaly, in addition, help to account for countercyclical net exports and the cross-correlation of output and consumption across borders. In the model, fluctuations in the real exchange rate are generated by the presence of nontraded goods in addition to the standard home bias channel. Non-traded goods are appealing in an incomplete market setup because they capture important wealth effects arising from the associated traditional transfer problem.2 Lane and Milesi-Ferretti (2001) argued a model with 1
Corsetti and Dedola (2005) have also considered the role of market segmentation in the tradable sector generated by the presence of non-tradable goods in a two-period monetary model. 2 Under the transfer effect, a positive home trade balance implies that home production exceeds its consumption
2
only tradable goods may neglect the potential impact on transfers from the relative price of nontraded goods. Hence, the wealth effect stemming from the level of net foreign assets on the labor supply may be better captured in a heterogeneous sector model. In addition, Betts and Kehoe (2006) and Burstein, Eichenbaum, and Rebelo (2006) highlighted the role of non-traded goods in explaining real exchange rate volatility. Burstein, Eichenbaum, and Rebelo found at least one third of real exchange variance is explained by fluctuations in the relative price of non-traded goods to traded goods. The quantitative framework yields the following main results. First, the benchmark model with incomplete asset markets and non-tradable goods is able to explain the consumption-real exchange rate anomaly. The predicted correlation between the real exchange rate and relative consumption is consistently negative. Results are obtained with a realistic value of the elasticity of substitution between tradable goods. Thus, adding non-traded goods to a standard open economy model with incomplete markets alters the real exchange rate dynamics. In the benchmark model, a productivity shock in the traded sector delivers an appreciation of both the terms of trade and the real exchange rate vis-à-vis an increase in relative consumption. Following the shock, domestic consumption and output increase and foreign consumption decreases, so relative consumption increases. Furthermore, the increase in output is larger than the increase in consumption; hence, it follows that the country accumulates net foreign assets. Unlike what Chari et al. (2002) predicted, a large NFA accumulation is achieved by the presence of non-traded goods. Thus, a meaningful wealth effect induces a decrease in labor supply and, therefore, real wages increase, causing an increase in domestic prices, generating an appreciation of both the terms of trade and the real exchange rate.3 Thus, the results give support to the evidence presented by Betts and Kehoe (2006) and Burstein et al. (2006) with respect to the importance of non-traded goods.4 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 exports increases. Accompanying this change is a fall in home’s real wage, its real exchange rate, and its terms of trade. In this context, debtor (creditor) countries tend to have more depreciated (appreciated) real exchange rates. See Lane and Milesi-Ferretti (2004) for recent evidence on the transfer problem. 3 Corsetti, Dedola, and Leduc (2006) provide empirical evidence supporting the idea that a productivity shock generates simultaneous terms of trade and real exchange rate appreciations. 4 In a recent paper, 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
3
Second, including distribution services to the benchmark economy helps to explain the consumptionreal exchange rate anomaly, and in addition, by dampening the expenditure-switching effect, generates countercyclical net exports. Furthermore, in the model with distribution services, consumption is less cross-correlated than is output across countries, matching the ranking in the data. As is well known, IRBC models typically yield the opposite result. Hence, distribution services help in this dimension. Third, the sensitivity analysis shows that the model with only tradable goods predicts a close to perfect correlation between the real exchange rate and relative consumption; therefore, movements in the terms of trade are sufficient to yield perfect risk-sharing. Hence, the lack of non-tradability mitigates wealth effects in an important way. The model also indicates that with low values of the elasticity of substitution between tradable goods across countries, the negative correlation between the real exchange rate and relative consumption becomes smaller. Other authors have proposed similar avenues to address the consumption-real exchange rate anomaly. Corsetti, Dedola, and Leduc (2008) show a low price elasticity of demand for imported goods, generated by the presence of distribution services, can hinder risk sharing and might contribute to explain the anomaly.5 Here, the model generates a terms of trade improvement following a productivity traded good increase, dynamics that are supported by Corsetti et al.’s (2006) empirical evidence. Corsetti et al. (2008) developed a model that can generate a terms of trade appreciation in response to a traded good productivity improvement. However, Corsetti et al.’s model relies on rather unpalatable assumption, namely, the model requires a substitution elasticity between domestic and imported tradables that is much smaller than empirical estimates of that elasticity. G. Benigno and Thoenissen (2008) introduced non-tradable goods in a model with incomplete markets where prices were perfectly flexible and markets competitive. Similar to my findings, they attributed a key role for non-tradable goods in explaining the anomaly.6 In played a minor role in explaining the behavior of the real exchange rate, 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 neighborhood of 5 to 6. Most of the NOEM models consider values of 1 for this elasticity that arises from the assumption of Cobb-Douglas preferences in aggregate consumption. 6 Similarly, Ghironi and Melitz (2005) findings suggested the Balassa-Samuelson dominates the home bias effect,
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contrast to Corsetti et al. (2008) and G. Benigno and Thoenissen (2008), a model with imperfect competition in production, similar to Chari et al.’s (2002) model, was developed, so deviations from the law of one price both at the border and at the consumer level were generated. Thus, the sticky price model does a great job of generating real exchange rate persistence whereas a model with flexible price fails on this dimension. Finally, other contributions have also included distribution services to explain the real exchange rate dynamics and in particular, to account for differences between import prices and consumer prices (cf. Burstein, Eichenbaum, & Rebelo, 2005). I take an additional step, modeling distribution services in a set up with monopolistic competitors in a dynamic general equilibrium model. Distribution services coupled with monopolistic competitors permit the model to generate deviations from the law of one price both at wholesale and retail price levels. Corsetti and Dedola (2005) introduced the same mechanism in a model with nominal rigidities, although in their framework they did not evaluate the merits of this extension in a dynamic setting. The rest of the paper is structured as follows. Section 1 introduces the model with distribution services. The benchmark model is obtained by eliminating distribution services. In Section 2, the quantitative properties of the model are analyzed and the key mechanism behind the findings illustrated. I then perform a sensitivity analysis. Finally, Section 3 concludes the paper.
1
The Model
The model developed is a modification of the model presented by Chari et al. (2002), allowing for the presence of non-tradable goods in the line of Stockman and Tesar (1995). The model is extended to generate deviations from the law of one price at the border due to the introduction of distribution services in the line of Burstein, Neves, and Rebelo (2003). Firms producing tradable and non-tradable goods are monopolistic competitors.7 In addition, the model contains triggering appreciations in the real exchange rate vis as vis an increase in relative consumption. The mechanism relies on aggregate productivity shocks rather than sector specific shocks. 7 Coresetti et al. (2008) introduced distribution services in an standard IRBC model with a perfect competitive setting. Instead, the model developed allows for monopolistic competition. This assumption generates deviations from the law of one price at the border.
5
an incomplete asset market structure with stationary net foreign asset positions and sticky prices in the non-traded sector.
1.1
Preferences
I assume that there are two countries, home (H) and foreign (F ), of equal size.8 Brands of traded goods are indexed by h ∈ [0, 1] in the home country and by f ∈ [0, 1] in the foreign country. Similarly, households and workers are indexed by h and f in the domestic and foreign country, respectively. Brands of non-tradable goods are indexed by n ∈ [0, 1] . The generic preferences of a household in country H are9 ∞ h Uth = E0 β t U (Ct+s , Lht+s ,
(1)
t=0
where E0 denotes the expectation conditional on the information set at date t = 0, and β is the inter-temporal discount factor, with 0 < β < 1. Ct and Lt denote the level of consumption and labor in period t, respectively. The consumption index is defined as ε ε−1 T ε−1 N ε−1 1/ε 1/ε ε ε Ct Ct Ct ≡ γ + (1 − γ) ,
(2)
where ε is elasticity of substitution between tradable (CtT ) and non-tradable (CtN ) goods, and γ is the share of tradable goods in the consumption basket at home. The sub-index of consumption for traded goods is defined as CtT
θ θ−1 θ−1 θ−1 1 1 H θ F θ θ θ ≡ λ Ct + (1 − λ) Ct ,
(3)
where θ is elasticity of substitution between home and foreign tradable goods, and λ, represents the degree of home bias in preferences. CtH and CtF are indexes of consumption across the 8
The population in each country is normalized to one. It is straightforward to allow for different populations in each country, as in Clarida, Gali, and Gertler (2002) and P. 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.
6
continuum of differentiated goods produced in country H and F , and are given by CtH
≡
1
ct (h)
σ−1 σ
0
dh
σ σ−1
, CtF
≡
1
ct (f)
σ−1 σ
df
0
σ σ−1
,
(4)
where σ > 1 is the elasticity of substitution across goods produced within country H, denoted by ct (h), and country F , denoted by ct (f). Similarly, the consumption of non-traded goods in the home country is given by CtN
≡
1
0
σ σ−1
σ−1 σ dn cN t (n)
,
(5)
where cN t (n) denotes the consumption of each individual non-traded good. Individual demands for home and foreign tradable and non-tradable goods are given by −θ T −ε pt (h) −σ PtH Pt Ct , Pt PtH PtT −θ T −ε Pt pt (f ) −σ PtF ct (f) = (1 − λ)γ Ct , and F T Pt Pt Pt N −σ N −ε pt (n) Pt N ct (n) = (1 − γ) Ct . N Pt Pt ct (h) = λγ
In this context, the consumer price index corresponding to the previous specification is given by 1
1−ε N 1−ε 1−ε T + (1 − γ) Pt , Pt ≡ γ Pt
(6)
where the price index for tradable goods has the following form 1
1−θ 1−θ 1−θ PtT ≡ λ PtH + (1 − λ) PtF ,
(7)
with prices of home and foreign tradable goods, and non-tradable goods defined, respectively as PtH
≡
1
pt (h)
1−σ
0
1 1−σ
F dh , Pt ≡
1
1−σ
pt (f )
0
PtN
≡
0
1
1 1−σ
1−σ pN dn t (n)
7
,
df
1 1−σ
,
where pt (i) for i = h, f, and pN t (n) are prices sold in the home country, in home currency, and at ∗
∗
consumer level, for both tradable and non-tradable goods, respectively. Prices Pt∗ , PtH , PtF and ∗
PtN are analogously defined. I define the real exchange rate, Qt =
St Pt∗ Pt ,
as the relative price
between the aggregate foreign prices expressed in domestic currency and domestic prices, where St is the nominal exchange rate. A feature of the specification is the presence of distribution costs that imply a wedge between producer and consumer prices. This follows Burstein et al. (2003) closely. With competitive firms in the distribution sector, the consumer price of good h is given by pt (h) = pt (h) + κPtN
(8)
where pt (h) denotes the price of home goods at the producer level, and κ are the units of a basket of differentiated non-traded goods necessary to bring one unit of traded goods to the consumers. κ=
1
κ(n)
0
σ−1 σ
σ σ−1 dn
(9)
The Dixit-Stiglitz index also applies to the consumption of differentiated non-traded goods.10 For the rest of the paper, the upper bar represents prices at producer level. In a model without distribution services, the law of one price holds at every period. Distribution services along with the assumption of monopolistic competition permit the model to generate deviations from the law of one price both at the border and at the consumer level. Note that purchasing power parity (PPP) does not hold in the model because of the presence of both home bias in preferences and non-traded goods.
1.2
Budget Constraints and Asset Markets
For modeling simplicity, I chose to model incomplete markets following P. Benigno (2009), where two risk-free, one-period nominal bonds are traded and a cost of foreign bond holdings is intro10
For simplicity, I assume no distribution costs in delivery of non-tradable goods exists.
8
duced to achieve stationarity.11 One bond is denominated in domestic currency and the other one in foreign currency. Then, the real budget constraint of the domestic household h is given by h BH,t
Pt (1 + it )
+
h St BF,t SB Pt (1 + i∗t ) φ tPtF,t
≤
h h h + St BF,t−1 + Mt−1 BH,t−1 Mh − t Pt Pt
+
Wth Lht T Rht Πh − Cth + + t Pt Pt Pt
(10)
where Wth is the nominal wage in the tradable and non-tradable sectors. it is the home country nominal interest rate, and i∗t is the foreign country nominal interest rate. Pt is the consumer price level. Πht are nominal profits for home consumer. I assume each consumer holds one firm in each sector and domestic firms are located in the interval [0, 1], and there is no trade in firms’ shares. T Rth is a nominal transfer that individual h receives from the government and Mth are h is household h’s holding of the risk the holding of real money balances by household h. BH,t h is household h’s holding of the risk-free nominal bond free nominal bond, in home currency. BF,t
in foreign currency. The function φ (.) depends on the real holdings of the foreign assets in the entire economy, and therefore is taken as given by the domestic household.12 The function φ (.) allows one to obtain a well-defined steady state and capture the costs of undertaking positions in the international asset market.13 The government has a budget constraint given by
0
n
Mth dh −
0
n
h Mt−1 dh +
11
0
n
T Rht dh = 0
Schmitt-Grohe and Uribe (2003) and Kollmann (2002) 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 P. Benigno (2009) pointed out, some restrictions on φ (.) are necessary: φ (0) = 1; assumes the value 1 only if BF,t = 0; are differentiable and decreasing in the neighborhood 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 (.) .
9
The first order conditions with respect to the labor supply for tradable and non-tradable sectors imply
Wh UL Lht = UC (Ct ) t Pt
(11)
I further assume that the initial level of wealth is the same across all households belonging to the same country. This assumption, combined with the fact that all households within a country work for all firms sharing the profits in equal proportions, implies that within a country, all households face the same budget constraints. In their consumption decisions, households will choose the same path of consumption. Hence, I can then drop the index h and consider a representative household for each country. The conditions characterizing the allocations of domestic and foreign consumption and holding of nominal bonds are the following: Pt UC (Ct ) = (1 + it ) βEt UC (Ct+1 ) Pt+1 Pt∗ ∗ ∗ ∗ UC (Ct ) = (1 + it ) βEt UC (Ct+1 ) ∗ Pt+1 BF,t St Pt St+1 ∗ UC (Ct ) = (1 + it ) φ βEt Uc (Ct+1 ) Pt Pt+1 St
(12) (13) (14)
Equations (12) and (13) correspond to the Euler equations of the home and foreign countries, respectively. Equation (14) represents household H’s Euler equation, derived by maximizing the holdings of the nominal bond denominated in foreign currency.
1.3
Price Setting with Distribution Sector (Imperfect Pass-through)
In order to obtain a tractable model, I assume prices are sticky only in the non-tradable sector, whereas prices are flexible in the tradable one. I also include distribution costs in order to obtain deviations from the law of one price and consequently, intermediate degrees of pass-through. As previously mentioned, monopolistic competition is a key assumption to obtain deviations from the law of one price at the border once distribution services are taken into account. This section shows how a representative firm endogenously charges different prices across countries due to the
10
presence of distribution services. I focus on domestic firms because price setting for foreign firms can be derived analogously. 1.3.1
Non-Tradable Sector
The firms’ price-setting decision behavior is modeled through a Calvo-type mechanism. Prices are subject to changes at random intervals. In each period, a seller faces a fixed probability (1 − α) of adjusting the price, irrespective on how long it has been since the last change occurred. In this model, suppliers behave as monopolists in selling products. The objective of a home firm selling non-traded goods is to maximize the expected discounted value of profits14 ∞ N,d h MaxpN Et αk ζ t,t+k { pN t,t+k (n) − Wt+k Lht+k } t+k (n) y t (n)
(15)
k=0
subject to
ytN,d (h)
where
=
pN t (h) PtN
−σ CtN,d + κdt (n) ,
−ε PtN = (1 − γ) Ct , Pt 1
1 d κt (n) = κ ct (h)dh + ct (f)df 0 0 −θ F −θ T −ε PtH Pt Pt = κγ λ + (1 − λ) Ct , T T Pt Pt Pt CtN,d
(16)
(17) (18) (19)
ytN,d (n) is the total individual demand for a given type of non-traded good, which is further composed by the demand of non-traded goods for consumption, CtN,d , and the demand for distribution services by the tradable firms, κdt (n) . The supplier maximizes (15) with respect to pN t (n) given the demand functions and taking ∗ ∗ ∗ ∗ as given the sequences of prices PtH , PtF , PtT , PtN , Pt , Ct and PtH , PtF , PtT , PtN , Pt∗ , Ct∗ .
U (Ct+s ) t ζ t+s = β s CPt+s UCP(C is the pricing Kernel associated to the first order condition for the recursive comt) petitive equilibrium. 14
11
Each firm produces according to a linear technology ytN (n) = ZtN LH t (n)
(20)
where ZtN is the country-specific AR(1) productivity shock to the non-tradable sector at time t. The optimal choice of pN t (n) is as follows: pN t (n) =
σ (σ − 1)
Et
∞
Wh
t+k N,d k t,t+k (n) k=0 α ζ t,t+k Z N y t+k ∞ k N,d Et k=0 α ζ t+k yt,t+k (n)
(21)
Finally, Calvo-price setting implies the following state equation for PtN
1.3.2
N 1−σ N 1−σ 1−σ Pt = α Pt−1 + (1 − α) pN t (n)
(22)
Tradable Sector
In this model the tradable sector is completely flexible. The presence of distribution services intensive in local non-traded goods will imply different demand elasticity across markets; therefore, firms will charge different prices in each market. Firms face the following maximization problem: Wth d H d H ∗ ∗d Maxpt (h),p∗t (h) (1 − τ ) [P t Ct (h) + St P t Ct (h)] − T yt (h) Zt
(23)
subject to ytd (h) = cdt (h) + cd∗ t (h) −σ H −θ T −ε pt (h) + κPtN Pt Pt d ct (h) = λγ Ct , H T Pt Pt Pt ∗ ∗ −σ ∗ −θ ∗ −ε∗ pt (h) + κPtN PtH PtT d∗ ct (h) = (1−λ) γ Ct∗ , ∗ ∗ Pt∗ PtH PtT
(24) (25) (26)
where ZtT is the country-specific AR(1) productivity shock to the tradable sector at time t. Foreign profits are valued back in home country currency using the nominal exchange rate. τ is
12
a time-invariant tax on sales.15 The optimal prices at producer level, pt (h) and p∗t (h) are pt (h) =
p∗t (h)
=
1 σ Wt κ N = + Pt 1 − τ (σ − 1) ZtT σ
(27)
T 1 σ Wt κ N∗ = + Pt , 1 − τ (σ − 1) St ZtT σ
(28)
H Pt
H∗ Pt
The marginal cost for tradable goods varies as a function of the prices of non-traded goods. Under the presence of distribution costs, the elasticity of demand for domestic goods is not the same at home and abroad, and firms will charge different prices in each market. Optimal price setting ∗ implies deviations from the law of one price P H,t = St P H,t unless the degree of distribution margin, κ, is equal to zero.
1.4
Monetary Policy
Monetary policy is established with a Taylor rule that targets expected CPI inflation and output deviation from steady-state values: ¯ (1−ρi ) (1 + it−1 )ρi Et (1 + it ) = R
Πt+1 Π
(1−ρi )γ π
Yt Y
(1−ρi )γ y
(29)
where Πt denotes CPI inflation, Yt denotes the real GDP, and a variable without time subscript represents its target variable.
1.5
Market Clearing
The market clearing condition in the tradable good sector at home is YtH = CtH + CtH
∗
(30)
∗
where CtH denotes the demand for home tradables by the foreign household. The market clearing for the non-tradable goods sector is YtN = CtN + κt
(31)
15 I introduce this tax in order to eliminate the distortion generated by distribution services 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.
13
where
−ε PT,t PH,t −θ PF,t −θ κt = κγ λ + (1 − λ) Ct , PT,t PT,t Pt
(32)
The aggregate budget constraint is obtained by aggregating the equilibrium budget constraint of households with that of the government and profits of the firms: St BF,t SB ≤ t F,t−1 + NXt St BF,t Pt ∗ Pt (1 + it ) φ Pt
(33)
where net exports are given by H∗
F
St P t P ∗ NXt = CtH − t CtF Pt Pt
(34)
Because it will be convenient in characterizing the full log-linear model, I define aggregate domestic real output,
PtY Pt
Yt as the sum of the value of the sectorial outputs: PN PtY 1 H H ∗ ∗ Yt = Pt Ct + St PtH CtH + t YtN Pt Pt Pt
(35)
where PtY is the nominal domestic producer price index. In general, PtY may differ from Pt because domestic consumption may differ from domestic output. In a steady state, however, the trade balance is zero, implying PtY = Pt is the long-run equilibrium price level.
2
Simulation of the Model
I solve the model by taking log-linear approximations around a steady state with stationary net foreign assets. In the Appendix, the log-linear version of the full economy is summarized. Lower case letters (i.e., ct ) will denote that the variable is expressed as the percentage deviations of a variable from its steady state value. Given the parameters and the structure of shocks, a system of linear difference equations using the DYNARE toolkit is solved. The model’s statistics are computed by logging and filtering the model’s artificial time series using the Hodrick and Prescott filter. 14
2.1
Calibration
In Table 1, the benchmark calibration is reported. The main values for the parameters are taken from Chari et al. (2002) and Stockman and Tesar (1995). As is standard in IRBC models, I assume a symmetric economic structure across countries and impose symmetry on the autocorrelation and variance-covariance matrices of shocks. Shocks are assumed to follow autoregressive processes of the form Zt = Zt−1 + εt where ∗ ] and χ is a 4x4 matrix describing the autoregresive component of the Zt ≡ [ZT , ZNT , ZT∗ , ZNT
disturbance. The disturbances are εt ≡ εT,t , εNT,t , ε∗T,t , ε∗NT,t . The structure of the shock
process is taken from Stockman and Tesar (1995). In section (2.4) a sensitivity analysis is
performed by changing the matrix of shocks.16 I adopt the same utility function as Stockman and Tesar (1995),
h
U (Ct , Lt ) = Et
∞ s=t
β
s−t
1 1−ρ η (Ct ) (1 − Lt ) , 1−ρ
(36)
setting a quarterly discount factor, β, equal to 0.99, which implies an annualized rate of interest of 4%. For the coefficient of constant risk aversion, ρ, we choose a value of 2 as in Stockman and Tesar (1995). The inverse of the elasticity of leisure, η is set equal to 3.17. As is standard in the real business cycle literature, I assume households dedicate 20% of their time to work activities. The value of the elasticity of substitution between traded and non-traded goods, ε, is set to 0.74 following Mendoza’s (1995) estimate for a sample of industrialized countries. The value of the elasticity of substitution between traded goods, θ, is set equal to 1.5 as Chari et al. (2002).17 In section (2.4) a sensitivity analysis was performed regarding this parameter. The weight associated with traded goods, γ, is set equal to 0.45, and it was calibrated by taking into account the share of traded goods in the consumption bundle for the United States (cf. Stockman & Tesar, 1995). 16
In order to compare results with those provided by the existing literature, that the economy is hit by productivity shocks (traded and non-traded) was assumed. However, I am aware of the important of demand shocks in explaining both gross domestic product (GDP) and real exchange rate behaviors (see Rabanal & 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) presents 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.
15
Following G. Benigno and Thoenissen (2008) and Corsetti et al. (2006), I calibrate the degree of home bias, λ, equal to 0.72. For the debt elasticity premium parameter, χ, we choose a value of 0.007 given recent evidence by Rabanal and Tuesta (2010) and Selaive and Tuesta (2003, 2009).18 I further assume that the steady state level of debt is zero. I choose a degree of monopolistic competition, σ, equal to 10, which implies an average markup of 11% over the marginal cost in the baseline model without distribution services (see Basu 1 κ ∗ & Fernald, 1997). I set τ = τ = 1 − 1−κ 1 + (σ−1) so that the law of one price at consumer
level holds in the steady state. I set the distribution cost parameter, κ, equal to 0.5 which implies
a margin of 50% of the retail price of consumer goods due to distribution costs. Burstein et al. (2003) show that distribution costs are large and account for about 40-60% of the retail price in the United States. I parameterize the policy rule, following Rabanal and Tuesta (2007): ρi = 0.88, γ π = 2.05, γ y = 0.91. The coefficients on the Taylor rule are quite similar to previous estimates in the literature starting in 1985 (see Clarida, Galí, & Gertler, 2000). Finally, I set the parameters associated to the degree of nominal rigidities α = α∗ equal to 0.75 which is standard in the literature.
2.2 2.2.1
Explaining the Consumption Real Exchange Rate Anomaly Impulse Response Functions
One can obtain some sense of the quantitative results reported in the next sub-section by analyzing the impulse response dynamics following a tradable productivity shock. Figure 1 depicts the responses to a 1% home productivity shock in the tradable sector that decays with an autoregressive coefficient of 0.95.19 The dynamics of the benchmark model without distribution services (solid line) are compared with respect to the one predicted in a model with distribution services (dashed line). The novel result is that the benchmark economy predicts a negative co-movement 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.
16
between the real exchange rate (RER) and relative consumption following the shock. In fact, the productivity shock in the tradable sector leads to an increase in relative consumptions vis-à-vis a real exchange rate appreciation. Note that the real exchange rate appreciation is larger in the benchmark model. Hence, given the calibrated value for trade elasticity (θ = 1.5) and the fact that sticky prices are included in the non-tradable sector, distribution services do not make relative prices more sensitive to tradable productivity shocks. In the benchmark economy, following the positive shock in tradable productivity, output (↑ yt ) and consumption (↑ ct ) increases, and because the increase in output is of larger magnitude, an asset accumulation occurs (↑ bt ) . Foreign consumption also increases, but less than the domestic ∗ one, so an increase in relative consumptions ↑ cR t = ct − ct is observed. Wealth effects, due to the presence of non-traded goods, also induces a decrease in the labor supply in the tradable sector and, consequently, an increase in real wages is observed (↑ wt ). Prices in the tradable sector increase because wealth effects more than compensate for the expected negative effect of tradable productivity over prices ↑ pH t . The increase in domestic prices further generates a terms of 20 trade appreciation ↓ tott = pFt / ↑ pH Because wages are homogeneous across sectors, wages t .
in the non-tradable sector also increase, triggering an increase in the price of non-traded goods N ↑ pt , which, in turn, causes a reduction in the relative price of tradable to non-tradable goods ↓ rertN .21 Both effects, the terms of trade appreciation and the reduction in the relative price of non-traded to traded goods, cause an overall appreciation of the real exchange.
To illustrate the previous result, note that in the benchmark economy, the real exchange rate in log-linear form, can be decomposed in the following way: qt = (2λ − 1) tott + (1 − γ) (rernt − rern∗t ) where T OTt =
PtF PtH
denotes the terms of trade, and RERNt ≡
20
PT PN T
and RERNt∗ ≡
(37) PT∗ ∗ PNT
denote
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 VAR with long-run restrictions to identify productivity shocks. 21 This mechanism is called the Balassa-Samuelson effect, which contributes towards an appreciation of the real exchange rate and switched demand from home to non-traded to traded goods.
17
the relative prices of traded to non-traded goods at home and abroad, respectively. The first term captures the traditional home-bias channel (2λ − 1) tott , , and the second term accounts for the traditional Balassa-Samuelson effect, (1 − γ) rertN − rertN∗ . Remarkably, in the benchmark
calibration, even with θ larger than one, a tradable productivity shock generates an improvement in the terms of trade and an increase in the relative price of non-traded goods, so both effects tend to appreciate the real exchange rate as noted from equation (37). The question that arises is how does the model with distribution services help to account for some international co-movements. As depicted in Figure 1, the model with distribution services makes all real variables less volatile. Hence, one expects to see less volatile international relative prices. Thus, contrary to the predictions of Corsetti et al. (2008), distribution services increase the effective price elasticity of aggregate import demand, leading to a smaller adjustment in international relative prices. The previous result stems from the relative high value of the elasticity of substitution between tradable goods. However, as will be shown in the next section, the DS model helps to account for the negative correlation between the RER and relative consumption. Furthermore, the DS model helps in accounting for the negative correlation between net exports and output observed in the data. Note the benchmark model implies a positive correlation between output and the net foreign assets (i.e. positive net exports). The model with distribution services, by reducing the expenditure-switching effect, generates a net foreign asset deccumulation, inducing a negative co-movement between output and net exports.
18
Real Exchange Rate
Rel. Consump
Output
0.2
0.15
0.4
0
0.1
0.3
−0.2
0.05
0.2
0
0.1
Base DS
−0.4 −0.6
10
20
30
40
−0.05
10
Consumption
20
30
40
0
TOT 0
0
0.15
−0.5
−0.2
0.1
−1
−0.4
0.05
−1.5
−0.6
10
20
30
40
−2
10
Wages 0
0.1
−0.1
0
−0.2
−0.1
−0.3 10
20
30
40
−0.8
10
Hours
0.2
−0.2
20
30
40
−0.4
20
30
40
30
40
30
40
RERN
0.2
0
10
20 NFA
1 0.5 0
10
20
30
40
−0.5
10
20
Figure 1: Impulse response function, tradable productivity shock 2.2.2
Non Tradable Goods and the Anomaly
As shown in the impulse response functions, non-traded goods play a key role in amplifying wealth effects. For simplicity, assume preferences are separable in the benchmark economy. In terms of this simplification, the net foreign assets accumulation equation and the implied risk-sharing condition can be expressed, respectively, as follows22 : βbt − bt−1 = (1 − λ) γqt − 2 (1 − λ) γλ (θ − 1) tott +
(38a)
(1 − λ) γ (1 − ε) (1 − γ) (rernt − rern∗t ) − (1 − λ) γ (ct − c∗t ) ρEt 22
ct+1 − c∗t+1 − (ct − c∗t ) = Et (qt+1 − qt ) − χbt
(39)
Selaive and Tuesta (2003, 2009) test the risk-sharing condition and find that growth factors of consumption and real exchange rates behave in a manner that may be consistent with a significant role for the net foreign asset position. See Rabanal and Tuesta (2007, 2010) for a structural estimation using Bayesian techniques.
19
It is well know that in a model with tradable goods only (γ = 1), symmetric preferences λ = 1/2, the coefficient ρ equal to 1, and with a unitary elasticity of substitution between tradable goods (θ = 1) , the adjustment in the terms of trade is sufficient to yield perfect risk sharing. In that case, there is no need for any adjustment in the current account. For simplicity, assume that γ = 1,λ = 1/2 and θ = ρ = 1. Under the previous parameterization, the RER is constant and both the NFA accumulation and the risk-sharing condition boil down to bt − βbt−1 = 1/2cR t R Et cR t+1 − ct = −χbt
(40a) (41)
∗ where cR t = (ct − ct ) denotes relative consumption. Given the assumption of φ (.) , χ denotes the
coefficient in the adjustment cost function for foreign bonds and should be positive. bt is the change in the net foreign assets position relative to the steady state and it is a predetermined variable with initial value b−1 = 0. Hence the NF A position is zero at every period, achieving perfect risk sharing. In contrast, in a model with non-traded goods, even under the previous parameter values, risk-sharing is broken down. Moreover, the real exchange rate is not constant and depends upon the relative price of traded to non-traded goods across countries. Thus, equations (38a) and (39), after replacing the real exchange rate dynamics into the NF A accumulation equation, can be re-written as follows:
R bt − βbt−1 = (1 − λ) γ (2 − γ − ε) rernR t − Ct
R R R Et cR t+1 − ct = (1 − γ) Et rernt+1 − rernt − δbt
(42a) (43)
∗ where rernR t = (rernt − rernt ) denotes the relative price of tradable to non-traded goods across
countries. Notice that after a productivity shock in the traded sector, the relative price of home non-traded goods increases ↓ rernR t goes down , which can be consistent with an increase in
relative consumption and a real exchange rate appreciation.
20
As emphasized in the above analysis, standard IRBC with incomplete markets and non-traded goods can account for the consumption-real exchange rate anomaly, given that the equilibrium dynamic response to tradable productivity shock generates substantial positive wealth effects.
2.3
Quantitative Properties of the Model
In this section, the quantitative performance of the model is analyzed. The results of the simulations are summarized in Table 2. I evaluate the unconditional correlation between the RER and relative consumption as well as some other statistics. The first column in Table 2 reports H-P filtered statistics for the data from quarterly time series taken from Chari et al. (2002) and Corsetti et al. (2008). The benchmark economy without distribution services (second column of Table 2, headed NDS) demonstrates that an economy with non-tradable goods and incomplete markets can successfully account for the consumption-real exchange rate anomaly. The novel finding is the correlation generated by the model is -0.26 , against the data -0.41. Table 2 also shows a positive correlation between the RER and the terms of trade (0.18). A positive sign of this correlation is a key feature in the data. A model with tradable goods only and home bias will, unambiguously, predict a positive correlation between the real exchange rate and the terms of trade. In a model with non-tradable goods, this is not necessarily the case. In the model, conditional to a productivity shock in the tradable sector, both the terms of trade and the relative prices of non-traded goods move in the same direction, and the positive co-movement between the RER and the terms of trade is obtained. In the same line as noted by G. Benigno and Thoenissen (2008), the main limitation of the model is the low volatility of the RER.23 Note, however, the model generates a very volatile terms of trade. Finally, the sticky price model does a great job of matching the real exchange rate persistence (0.79 in the model versus 0.83 in the data). Sticky prices are crucial to obtain this result.24 23
Rabanal, Rubio-Ramirez, and Tuesta (2010) showed a benchmark international real business cycle model allowing for co-integrated TFP processes could generate a RER three times more volatile with respect to output than could 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.
21
Consider the rest of statistics for the benchmark economy reported in the second column of Table 2. Consumption is more volatile in the model (0.97) than in the data (0.75). This result can be easily fixed by including habit formation in consumption or investment dynamics. Comovements of output, consumption, and hours are all positive, consistent with the evidence. The cross-country correlation of output (0.55) is very close to that observed in the data (0.60). Note that the cross-correlation of consumption (0.63) is larger than that of the data (0.38) , and it is also larger than the cross-correlation of output across countries. Thus, the model does not help in this dimension. In particular, standard IRBC models that deliver very low volatility of the RER also predict a higher correlation of consumption across countries with respect to outputs under either a bond economy or complete markets. Finally, the model performs badly in accounting for countercyclical net exports (0.23 in the model versus -0.41 in the data). Consider the benchmark economy with distribution services (third column of Table 2, headed DS ). The model performs better in some dimensions. First, notice the DS model generates a negative correlation between the RER and relative consumption (−0.71). Consumption is less crosscorrelated than is output across countries, matching the ranking reported in the data. As mentioned above, IRBC models have difficulty matching these cross-correlations simultaneously. This limitation is referred as the “quantity anomaly”.25 The DS model does not suffer from this anomaly. Therefore, distribution services appear to play an important role in this result because a correlated increase in consumption in tradables across countries triggers an increase in the production of the non-tradables required to provide distribution services. Although the above results show that distribution services are not necessary to account for the consumption-real exchange anomaly, the results also show important advantages to including them into the benchmark model. Some Policy Implications The results of the paper highlight the importance of adding incomplete markets in order to match the co-movement between the real exchange rate and relative consumption. At the empirical level, it is well established that markets are far from being complete. On this front, the model 25
See Backus, Kehoe, and Kydland (1995).
22
could be used to measure the benefits of approaching a world (or pair of countries) where markets are less incomplete or, to some extent, are approaching a complete asset market environment (i.e. the Euro area). In addition, recently, active and flexible monetary policies might be helping to mitigate output and consumption volatility, or the well known great moderation, but at the cost of allowing for larger real exchange rate volatility. Thus, because the model better approaches matching the data in several dimensions, it could be useful to provide a quantitative assessment of the trade-off a policy maker could face between stabilizing output and the exchange rates simultaneously. Finally, the model showed distribution services help to match countercyclical net exports. In this respect, the model could be also helpful for establishing the link between the degree of distribution services and net exports and verify whether the data validates this relationship.
2.4
Sensitivity Analysis
In this section, the sensitivity of the findings are examined by varying assumptions about five of the benchmark model’s features. I evaluate the importance of non-traded goods by excluding them from the model. Remarkably, the simulated exercise delivers a positive and high value of the correlation between the RER and relative consumption; therefore, I conclude that a model with tradable goods only is not able to explain the anomaly. I perform a sensitivity analysis with respect to the elasticity of substitution between tradable goods, θ, and find that the smaller the elasticity, the closer the baseline model to fit for both the cross-correlation between the real exchange rate and relative consumption and countercyclical next exports. Finally, I check the robustness of the results under shock processes suggested by G. Benigno and Thoenissen (2008) and Corsetti et al. (2008), respectively. I find that under those shocks structures, the benchmark model fails to account for the anomaly while the model with DS does a good job. 2.4.1
Tradable Goods Only (γ = 0.999)
As was documented in the previous section, a key element in explaining the main features of the RER dynamics is the presence of non-tradable goods. In order to highlight their importance, in 23
column 4 of Table 2, the statistics for the benchmark model shutting down the non-tradable goods sector is reported. I eliminate non-traded goods by setting the share of final traded consumption goods in overall consumption bundle equal to 0.999.26 Abstracting from non-traded goods, the model generates a correlation between the RER and relative consumption close to one (0.94). This result is consistent with that of Chari et al. (2002). In fact, wealth effects are almost inhibited once non-tradable goods are absent. In addition, net exports become more procyclical compared to the baseline model. Furthermore, the absence of non-traded goods increases the cross-correlation of consumption across borders (from 0.63 in the NDS model to 0.93 in a model without non-traded goods), making it much higher than that of output across borders (0.58 in the model without non-traded goods). This result goes against the data. In short, it seems that any theory of real exchange rate determination cannot be successful at matching the data without considering non-traded goods. 2.4.2
Elasticity of Substitution Between Tradable Goods (θ)
In this section the role of the inter-temporal elasticity between tradable goods is considered. I perform a sensitivity analysis under two values of the parameter θ, a low elasticity (0.9) and a high elasticity (6.0). Results are reported in columns 5 and 6 (NDS and DS model, respectively). Recall that this parameter determines the degree to which the terms of trade responds to productivity shocks. Ceteris paribus, one should expect that the larger the elasticity of substitution, the lower the terms of trade volatility. Thus, a larger elasticity implies a stronger adjustment in quantities than in prices, so the model predicts a decrease in the volatility of the terms of trade for larger values of this elasticity. In fact, the volatility of the terms of trade decreases from 4.92 in the benchmark economy to 3.32 in a high elasticity scenario (θ = 6). In spite of the decrease in the terms of trade volatility, this does not translate into smaller RER volatility. The source of this result is to be found in the dynamics of the relative price of non- traded goods. Regarding the anomaly, clearly, θ is a crucial parameter, and as it becomes larger, it makes it 26
Spillover terms from the matrix of shocks arising from the non-traded sector are also eliminated.
24
more difficult to match the negative correlation between the RER and relative consumption.27 In fact, note that with smaller values of θ, the model does better in terms of the consumption-real exchange rate anomaly. This later result is consistent with the values G. Benigno and Thoenissen (2008) obtained in a model without distribution services. Indeed, in a model with distribution services, the reduction of the elasticity of substitution between tradable goods is endogenous whereas in this sensitivity exercise, the reduction of the elasticity is exogenous. 2.4.3
Different Structures of Shocks
In this sub-section I evaluate the robustness of our findings to alternative structure of shock. The 7-10 columns of Table 2 (heading "BT" and "CDL" respectively), consider productivity shocks structures as suggested by G. Benigno and Thoenissen (2008) and Corsetti et. al., re spectively. The autocorrelation ΩBT , ΩCDL and variance-covariance matrices V BT , V CDL for
both shocks structure are the following
BT
Ω
V
=
BT
0.84 0 0.22 −0
=
3.76 0.72 1.59 0.51
0 0.30 0 0 0.72 0.51 0.44 0.21
0.22 0 0.84 0 1.59 0.51 3.76 0.72
0 0 0 0.30
CDL ,Ω =
0.44 0.21 0.72 0.51
0.82 −0.02 −0.06 0.02
CDL ,V =
4.7 0.9 2.2 0.4
0.1 0.96 0.24 0.01
−0.06 0.02 0.82 −0.02
0.9 0.9 0.4 −0.1
2.2 0.4 4.7 0.9
0.24 0.01 0.1 0.96
0.4 −0.1 0.9 0.9
Given the above two structures of shocks the benchmark model (NDS) fails in matching the negative correlation between the RER and relative consumption. However, the model with distribution services (DS) does a good job in matching both the consumption real exchange rate anomaly and the countercyclical net exports. In addition, the model with distribution services has also a good performance in terms of the quantity anomaly. 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-real exchange rate anomaly. For instance, Stockman and Tesar’s (1995) shocks are not persistent, and that is why I obtain that result.
25
3
Conclusions
A central puzzle in international macroeconomics is the lack of risk sharing across countries. Standard complete and incomplete market models with tradable goods only predict a high and positive correlation between the real exchange rate and relative consumption, while in the data, the opposite is observed. The failure of these models to explain the data in this dimension is referred by Chari et al. (2002) as the consumption real exchange rate anomaly or Backus and Smith’s puzzle in a context of an IRBC model. As shown in Chari et al. (2002), wealth effects arising from incomplete markets are very small to break ties between the real exchange rate and relative consumption. In this paper I have taken a step toward solving the consumption real exchange rate anomaly. First, I highlighted the need to combine incomplete markets and non-traded goods in an open economy model in order to account both for the negative co-movement between the real exchange rate and relative consumption. I showed quantitatively that non-tradable goods generate sizeable wealth effects so that NFA movements induce a reduction in international relative prices, triggering a real exchange rate appreciation and an increase in relative consumption. In the simulations, I also considered an elasticity of substitution between tradable goods larger than one, and the model still performed reasonably well. Thus, due to the presence of non-traded goods, the standard paradigm that movements in terms of trade are sufficient to yield perfect risk sharing is broken down. I further evaluated the merits of distribution services in terms of international co-movements. I found that distribution services are useful to account for some other international co-movements observed in the data. In particular, it helped in matching countercyclical net exports and the cross-correlation across borders between output and consumption. Empirical evidence has put into debate the success of estimated structural open economy models in fitting the data and in particular, the real exchange rate dynamics. Lubik and Schorfheide (2005, 2007) and Rabanal and Tuesta (2007, 2010) have started to estimate small-scale open economy models with data for the United States and Europe. Justiniano and Preston (2010a, 2010b)
26
performed a structural estimation for small open economy. All previous contributions considered models with tradable goods only. Their estimations, with traditional structural shocks, could not account for the real exchange rate dynamics. Thus, the findings in this the paper suggest other modeling structures, in particular the introduction of non-traded goods, could help to improve the fit of estimated international models. It is important in further research that attention be paid to modeling and estimating movements in the real exchange rate that arise from movements in the relative prices of traded to non-traded goods.
27
References [1] Backus, D., Kehoe, P., & Kydland, F. (1995). International real business cycles: Theory and evidence. In T. F. Cooley (Ed.), Frontiers of Business Cycle Research (p. 331-56). Princeton, Princeton University Press. [2] Backus, D., & Smith, G. (1993). Consumption and real exchange rates in dynamic economies with non-traded goods. Journal of International Economics 35, 297-316. [3] Basu, S., & Fernald, J. G. (1997). Returns to scale in U.S. production: Estimates and implications. Journal of Political Economy, 105, 249-283. [4] Baxter, M., & Crucini, M. (1995). Business cycles and the asset structure of foreign trade. International Economic Review 36, 821-54. [5] Benigno, P. (2009). Price stability with imperfect financial integration. Journal of Money Credit and Banking, 4(1), 121-149. [6] Benigno, P., & Benigno, G. (2003). Price stability in open economies. Review of Economic Studies, 70(4), 743-764. [7] Benigno, G., & Thoenissen, C. (2008). Consumption and real exchange rates with incomplete markets and non-traded goods. Journal of International Money and Finance, 27, 926-948 . [8] Betts, C., & Kehoe, T. (2006). U.S. real exchange rate fluctuations and relative price fluctuations. Journal of Monetary Economics, 53, 1297-1323 [9] Burstein, A., Neves, J., & Rebelo, S. (2003). Distribution costs and real exchange rate dynamics during exchange-rate-based-stabilizations. Journal of Monetary Economics, 50, 1189-1214 [10] Burstein, A., Eichenbaum, M., & Rebelo, S. (2005). Large devaluations and the real exchange rate. Journal of Political Economy, 113, 742-784.
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[11] Burstein A., Eichenbaum, M., & Rebelo, S. (2006). The Importance of Nontradable Goods’ Prices in Cyclical Real Exchange Rate Fluctuations. Japan and the World Economy. 18(3): 247-253. [12] Chari, V. V., Kehoe, P. J. & McGrattan, E. R. (2002). Can sticky prices explain the persistence and volatility of real exchange rates? Review of Economic Studies, 69, 533-563. [13] Clarida, R., Galí J., & Gertler, M. (2000). Monetary policy rules and macroeconomic stability: Evidence and some theory. Quarterly Journal of Economics 115, 147-180. [14] Clarida, R., Gali, J., & Gertler, M. (2002). A simple framework for international monetary policy analysis. Journal of Monetary Economics, 49(5), 879-904. [15] Corsetti, G., & Dedola, L. (2005). Macroeconomics of international price discrimination. Journal of International Economics 67, 129-55. [16] Corsetti, G., Dedola, L., & Leduc, S. (2006). Productivity, external balance and exchange rates: Evidence on the transmission mechanism among G7 countries. NBER International Studies on Macroeconomics 2006. [17] Corsetti, G., Dedola, L., & Leduc, S. (2008). International risk sharing and the transmission of productivity shocks. Review of Economic Studies, 75(2), 443-473. [18] Ghironi, F., & Melitz, M. J. (2005). international trade and macroeconomic dynamics with heterogeneous firms. The Quarterly Journal of Economics, 120(3), 865-915. [19] Heathcote, J., & Perri, F. (2002). Financial autarky and international business cycles. Journal of Monetary Economics 49(3), 601-627. [20] Justiniano, A., & Preston, B. (2010a). Can structural small open economy models account for the influence of foreign shocks? Journal of International Economics, 81(1), 61-74. [21] Justiniano, A., & Preston, B. (2010b). Monetary policy and uncertainty in an empirical small open economy. Journal of Applied Econometrics, 25(1), 93-128. 29
[22] Kollmann, R. (2002). Monetary policy rules in the open economy: effect on welfare and business cycles, Journal of Monetary Economics 49, 989-1015. [23] Lane, P., & Milesi-Ferretti, G. M. (2001). Long-term capital movements. NBER Macroeconomics Annual 2001. [24] Lane, P., & Milesi-Ferretti, G. M. (2004). The transfer problem revisited: Net foreign assets and the real exchange rates. The Review of Economics and Statistics, 86(4), 841-857. [25] Lubik, T., & Schorfheide, F. (2005). A Bayesian look at new open economy macroeconomics. NBER Macroeconomics Annual 2005. [26] Lubik, T., & Schorfheide, F. (2007). Do central banks respond to exchange rate fluctuations: A structural investigation. Journal of Monetary Economics, 54(4), 1065-1087. [27] Mendoza, E. (1995). The terms of trade, the real exchange rate, and economic fluctuations. International Economic Review 81(1), 101-137. [28] Obstfeld, M., & Rogoff, K. (2000). The six major puzzles in international macroeconomics: Is there a common cause? NBER Macroeconomics Annual 2000. [29] Rabanal, P., & Tuesta, V. (2007). Non-traded goods and the real exchange rate, La Caixa working paper. [30] Rabanal, P., & Tuesta, V. (2010). Euro-dollar real exchange rate dynamics in an estimated two country model: An assessment. Journal of Economic Dynamics and Control, 34, 780-797. [31] Rabanal, P., Rubio-Ramirez, J., & Tuesta, V. (2010). Cointegrated TFP processes in international macroeconomics. Journal of Monetary Economics forthcoming. [32] Schmitt-Grohe, S., & Uribe, M. (2003). Closing small open economy models. Journal of International Economics 61, 163-185. [33] Schneider, M., & Fenz, G. (2010). Transmission of business cycle shocks between the US and the Euro area. Applied Economics, in press. 30
[34] Selaive, J., & Tuesta, V. (2003). Net foreign asset and imperfect pass-through: The consumption- real exchange rate anomaly (IFDP Report No. #764), Washington, USA, Board of Governors of the Federal Reserve. [35] Selaive, J., & Tuesta, V. (2009). Net foreign assets and imperfect financial integration: An empirical testing, Journal of CENTRUM Cathedra, 1(2), 53-77. [36] Stockman, A., & Tesar, L. (1995). Tastes and technology in two-country model of the business cycle: Explaining international co-movements. American Economic Review 85, 168-185.
31
Appendix: Log-Linear Approximation of the Economy with Distribution Services. The benchmark economy corresponds to the case where κ = 0 Euler equations uc,t = (it − Et πt+1 ) + Et uc,t+1 u∗c,t = i∗t − Et π∗t+1 + Et u∗c,t+1 labor supply wt = vl,t − uc,t ∗ wt∗ = vl,t − u∗c,t
marginal utility of consumption and marginal de-utility of working L lt 1−L L ∗ = −ρc∗t − η l 1−L t L = (1 − ρ) ct − (η − 1) lt 1−L L = (1 − ρ) c∗t − (η − 1) lt∗ 1−L
uc,t = −ρct − η u∗c,t vl,t ∗ vl,t
risk sharing uc,t − u∗c,t = Et uc,t+1 − Et u∗c,t+1 + Et (qt+1 − qt ) + δbt Phillips curves πN t πN t where κN ≡
∗ (1−β)(1−αβ) , κN α
≡
∗
N = κN mcN t + βEt π t+1 ∗
∗
∗
N = κN mcN t + βEt π t+1
(1−β)(1−α∗ β) α∗
32
marginal costs mcN t mcN t where tN t = log
PtN N ∗ Pt , tt
∗
= wt − ztN − tN t ∗
= wt∗ − ztN − tN t
∗
∗
= log
PtN Pt∗
relative prices at producer level when distribution costs are present = γ 1 wt − ztH + (1 − γ 1 ) tN t ∗ = γ 1 wt − ztH − qt + (1 − γ 1 ) tN t ∗ ∗ = γ 1 wt∗ − ztF + (1 − γ 1 ) tN t ∗ = γ 1 wt∗ − ztF + qt + (1 − γ 1 ) tN t
H
tt
H∗
tt
F∗
tt
F
tt H
H
H∗
where tt = log PPtt , tt
H∗
H
H∗
tt
F∗
tt
F
tt PtH H ∗ Pt , tt
F∗
t
tt
where tH t = log
F
F
= log PPt ∗ , tt = log PPtt , tt
∗
= log
PtH Pt∗
F∗
= log PPt∗ , and γ 1 ≡ t
1 H κ N tt − t 1−κ 1−κ t 1 H∗ κ N∗ = tt − t 1−κ 1−κ t 1 F∗ κ N∗ = t − t 1−κ t 1−κ t 1 F κ N = tt − t 1−κ 1−κ t =
, tFt = log
PtF Pt
∗
, tFt = log
33
∗
PtF Pt∗
σ−1 σ−1+κ
demands, T T cH = −θ tH t t − tt − εtt + ct cFt = −θ tFt − tTt − εtTt + ct cN t
where tTt = log
PtT Pt
∗
, tTt = log
cH t
∗
cFt
∗
cN t
∗
= −εtN t + ct ∗ ∗ T∗ = −θ tH − t − εtTt + c∗t t t ∗ ∗ ∗ = −θ tFt − tTt − εtTt + c∗t ∗
∗ = −εtN t + ct
∗
PtT Pt∗
relative price relation γtTt + (1 − γ) tN t ∗
γtTt + (1 − γ) tN t
∗
= 0 = 0
production functions ytN
= ztN + ltN
ytH = ztH + ltH ytN
∗
= ztN + ltN
∗
ytF
∗
= ztF + ltF
∗
∗
∗
aggregate labor lt = γltH + (1 − γ) ltN ∗
lt∗ = γltF + (1 − γ) ltN
34
∗
non-tradable output ytN
=
∗
=
ytN where
CN YN
=
CN N CN c + 1 − N κt YN t Y N C N∗ CN c + 1 − N κ∗t YN t Y
(1−γ) (1−γ)+κγ
distribution services F κt = λcH t + (1 − λ) ct ∗
κ∗t = λcFt + (1 − λ) cH t
∗
total tradable demand H ytH = λcH t + (1 − λ) ct
ytF
∗
∗
∗
= λcFt + (1 − λ) cFt
net foreign assets βbt = bt−1 + nxt net exports
where bt =
BtF St Y Pt
∗ H∗ F F nxt = (1 − λ) qt + tt + cH − t − c t t t is the debt to GDP ratio, and nxt =
NXt Y
total output
∗ H H H∗ N yt = γ λ tH + c + (1 − λ) t + c + q + (1 − γ) tN t t t t t t + yt
∗ ∗ ∗ N∗ yt∗ = γ λ tFt + cFt + y + (1 − λ) tFt + cFt − qt + (1 − γ) tN t t
35
CPI and tradable inflations πt = γπTt + (1 − γ) πN t ∗
π∗t = γπTt + (1 − γ) πN t πTt πTt
∗
F = λπH t + (1 − λ) π t
∗
∗
= λπFt + (1 − λ) πH t
∗
some relative price dynamics due to sticky prices H H tH t − tt−1 = π t − π t
tFt − tFt−1 = πFt − πt ∗
∗
∗
∗
∗
∗
H H ∗ tH t − tt−1 = π t − π t
tFt − tFt−1 = πFt − π∗t
N N tN t − tt−1 = π t − π t ∗
∗
∗
N N ∗ tN t − tt−1 = π t − π t
qt − qt−1 = ∆st + π∗t − πt where st is the of the nominal exchange rate Taylor rules it = ρi it−1 + (1 − ρi ) γ π Et πt+1 + γ y yt i∗t = ρi i∗t−1 + (1 − ρi ) γ π Et π∗t+1 + γ y yt∗ some useful relative prices: relative price of non-traded goods and terms of trade N∗ rern = − (1 − γ) /γ tN , t − tt 36
∗
tot = qt + tFt + tH t
Table 1 Benchmark Parameterization Preferences
Technology shocks
Distributions costs Incomplete Markets Taylor Rule and sticky prices
β = 0.99; σ = 10; η = 3.17; ρ = 2; θ = 1.5; ε = 0.74; γ = 0.45; λ = 0.72 0.154 0.040 −0.150 0.632 Autocorrelation matrix, Ω = −0.199 0.262 −0.110 0.125 3.62 1.23 1.21 0.51 1.23 1.99 0.51 0.27 Var-cov matrix, V = 1.21 0.51 3.62 1.23 0.51 0.27 1.23 1.99 Parametr κ = 0.5 δ = 0.007 α = α∗ = 0.75, ρi = 0.88, γ π = 2.05, γ y = 0.91
37
−0.199 −0.110 0.154 −0.015
0.262 0.125 0.040 0.632
