Real exchange rates and primary commodity prices: Mussa meets Backus-Smith
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Ayres, João; Hevia, Constantino; Nicolini, Juan Pablo Working Paper Real exchange rates and primary commodity prices: Mussa meets Backus-Smith IDB Working Paper Series, No. IDB-WP-1281 Provided in Cooperation with: Inter-American Development Bank (IDB), Washington, DC Suggested Citation: Ayres, João; Hevia, Constantino; Nicolini, Juan Pablo (2021) : Real exchange rates and primary commodity prices: Mussa meets Backus-Smith, IDB Working Paper Series, No. IDBWP-1281, Inter-American Development Bank (IDB), Washington, DC, https://doi.org/10.18235/0003838 This Version is available at: https://hdl.handle.net/10419/290087 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/3.0/igo/legalcode
Real Exchange Rates and Primary Commodity Prices: Mussa Meets Backus-Smith João Ayres Constantino Hevia Juan Pablo Nicolini IDB WORKING PAPER SERIES Nº IDB-WP-1281 December 2021 Department of Research and Chief Economist Inter-American Development Bank
December 2021 Real Exchange Rates and Primary Commodity Prices: Mussa Meets Backus-Smith João Ayres* Constantino Hevia** Juan Pablo Nicolini*** * Inter-American Development Bank ** Universidad Torcuato Di Tella *** Federal Reserve Bank of Minneapolis and Universidad Torcuato Di Tella
Cataloging-in-Publication data provided by the Inter-American Development Bank Felipe Herrera Library A yres, João (João Luiz). Real exchange rates and primary commodity prices: Mussa Meets Backus-Smith / Joao A yres, Constantino Hevia, Juan Pablo Nicolini. p. cm. — (IDB Working Paper Series ; 1281) Includes bibliographic references. 1. Primary commodities-Prices-Developed countries-Econometric models. 2. Foreign exchange rates-Developed countries-Econometric models. I. Hevia, Constantino. II. Nicolini, Juan Pablo. III. Inter-American Development Bank. Department of Research and Chief Economist. IV. Title. V. Series. IDB-WP-1281 Copyright © Inter-American Development Bank. This work is licensed under a Creative Commons IGO 3.0 AttributionNonCommercial-NoDerivatives (CC-IGO BY-NC-ND 3.0 IGO) license (http://creativecommons.org/licenses/by-nc-nd/3.0/igo/ legalcode) and may be reproduced with attribution to the IDB and for any non-commercial purpose, as provided below. No derivative work is allowed. Any dispute related to the use of the works of the IDB that cannot be settled amicably shall be submitted to arbitration pursuant to the UNCITRAL rules. The use of the IDB's name for any purpose other than for attribution, and the use of IDB's logo shall be subject to a separate written license agreement between the IDB and the user and is not authorized as part of this CC-IGO license. Following a peer review process, and with previous written consent by the Inter-American Development Bank (IDB), a revised version of this work may also be reproduced in any academic journal, including those indexed by the American Economic Association's EconLit, provided that the IDB is credited and that the author(s) receive no income from the publication. Therefore, the restriction to receive income from such publication shall only extend to the publication's author(s). With regard to such restriction, in case of any inconsistency between the Creative Commons IGO 3.0 Attribution-NonCommercial-NoDerivatives license and these statements, the latter shall prevail. Note that link provided above includes additional terms and conditions of the license. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the Inter-American Development Bank, its Board of Directors, or the countries they represent. http://www.iadb.org 2021
a Abstract 1 We show that explicitly modeling primary commodities in an otherwise totally standard incomplete markets open economy model can go a long way in explaining the Mussa puzzle and the Backus-Smith puzzle, two of the main puzzles in the international economics literature. Keywords: Primary commodity prices, Mussa puzzle, Backus-Smith puzzle. JEL classifications: F31, F41. 1We thank Manuel Amador, Oleg Itskhoki, Alejandro Izquierdo, Tim Kehoe, David Kohn, Andy Neumeyer, Fabrizio Perri, Andy Powell, and Pedro Teles for comments. We give special thanks to Stephanie Schmitt-Grohe for a very insightful discussion. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis, the Federal Reserve System, or the InterAmerican Development Bank. 1
1 Introduction Primary commodity prices are known to be very volatile and very persistent. This has been especially true since the oil price shocks of the early 1970s. The small open economy literature has long recognized the e↵ect that shocks to commodity prices have on the economy in general and on the real exchange rate in particular. Their importance has been identified so strongly in the literature that it is commonly acknowledged in the policy debate in small commodity-producing countries. In contrast, in studies of the behavior of the real exchange rate between large developed economies, the role of these markets has been largely ignored, particularly so during the last three decades.2The most probable reason is that the value added of primary commodities in total economic activity is small in these countries. We show that although primary commodities’ share in total output may appear small, the volatility of primary commodity prices is so high that it can potentially have large e↵ects on real exchange rates. In a recent paper (Ayres, Hevia and Nicolini,2020), we documented a strong and robust co-movement between the real exchange rates of Germany, Japan and the United Kingdom against the US dollar and a handful of primary commodity prices during the last half century. We also showed that a simple static model had the potential to deliver much higher volatility and persistence in real exchange rates than a model that ignores the commodity sector.3In this paper, we go a few steps beyond, solve a truly dynamic model, and quantitatively address two famous puzzles in international economics. The first one, known as the Mussa puzzle, documents a substantial increase in the volatil2An earlier literature did discuss and evaluate the role of primary commodity markets in the behavior of real exchange rates among developed economies. Cˆot´e (1987) provides a discussion of a mechanism by which real exchange rates and primary commodity prices jointly respond to shocks; that mechanism is very close to the workings of the model we describe in Section 3. On the empirical side, Sachs (1985) and Dornbusch (1985a,b,1987) are important contributions. 3The model is formally dynamic, but we impose a zero trade balance every period, so the solution of the model is static. 2
ity of real exchange rates since the breakdown of the Bretton Woods system of fixed exchange rates in 1973. The second one, known as the Backus-Smith puzzle, documents a low correlation, and in many cases a negative one, between the bilateral real exchange rate of any two given countries and the ratio of consumption between those same two countries. In complete markets models, this correlation ought to be very close to 1.4 We also show another strong pattern in the data, which we call the “Mussa meets BackusSmith puzzle”. This is the generalized fact that the correlation between the real exchange rate and the ratio of consumption is even lower in the period following 1973 when compared with the period before. In other words, the Backus-Smith puzzle becomes quantitatively larger in the post-1973 period than in the period before. This feature of the data has received much less attention in the literature.5 The key ingredient of the model is the interaction between incomplete markets and shocks that move prices of primary commodities.6We document how the transmission mechanism implied by this interaction helps reconcile the main puzzles. We study a labor-only open economy three-country model. Each country produces a final nontraded good, a traded intermediate good and (potentially) three primary commodities. Labor is used in all technologies, commodities are used to produce the intermediate good, and the intermediate goods are used to produce the final good. We show that as long as countries have di↵erent production structures, the real exchange rate is a↵ected by shocks that change primary commodity prices. We illustrate the mechanism in a simplified version of the model that can be solved analytically. We then calibrate the general version of the model for the US and Japan, because as we show, this is the country pair for which the puzzles are quantitatively more 4Results similar to the ones in Backus and Smith (1993) were independently reported in Robert Kollman’s unpublished PhD dissertation in 1990. The main results were published in Kollmann (1995). 5Two notable exceptions are Colacito and Croce (2013) and Itskhoki and Mukhin (2019). 6Incomplete markets are essential to studying the Backus-Smith puzzle and are also important in generating volatile real exchange rates, as shown by Heathcote and Perri (2002). 3
striking, and because the Ministry of Economy, Trade, and Industry of Japan publishes a bilateral Japan-US input-output table that we use to discipline our calibration. The third country is taken to be the rest of the world. The rest of the world is subject to shocks in its excess demand for commodities. The key step in our calibration is to choose the volatility of these shocks in order to match the volatility and persistence of the primary commodity prices we see in the data for each subperiod. We want to emphasize at the outset that we do not explain why the prices of primary commodities are so volatile. A key aspect of our calibration that we wish to highlight is that the sizes of value added created in the primary commodity sectors in the model are as small as they are in the data. Our analysis shows that, in spite its size, the high volatility of the shocks to primary commodity markets has a substantial e↵ect on the real exchange rate and on its correlation with the ratio of consumption. And these e↵ects are more pronounced after 1973, when primary commodity prices became more volatile. In a nutshell, the benchmark calibrated model can account for a large share of the puzzles mentioned above. Specifically, we show that by calibrating the model preand post-1973 (the end of the Bretton Woods period), the model generates substantially more volatile real exchange rates in the post-Bretton Woods period (the Mussa puzzle), as observed in the data. The calibrated model also exhibits a correlation much lower than one between the real exchange rate and the ratio of consumption. Interestingly, the model also generates a lower correlation of the real exchange rate and the ratio of consumption for the post-1973 period (the Mussa meets Backus-Smith puzzle), as in the data. In describing the stylized facts, we first show that the puzzles hold very generally. We illustrate this fact using data for 15 bilateral pairs between the US and 15 other OECD countries. We also show that these moments have substantial statistical uncertainty due to the high persistence of both the bilateral real exchange rates and the primary commodity prices. For this reason, we focus on the US-Japan bilateral relation and compute the entire small sample 4
distribution of the statistics of interest. We find these distributions to be quite dispersed and skewed. For example, the point estimate of the standard deviation of the US-Japan real exchange rate after 1973 is about 19 percentage points, but the associated small sample distribution implies that one could quite likely observe values that are 50 percent smaller or 50 percent larger than that. For this reason, we focus on the entire small sample distributions of the statistics of interest instead of the point estimate. To evaluate the performance of our model, we compare these estimated distributions with analogous distributions obtained from model simulations. The model has no frictions other than the lack of contingent asset markets. Thus, it is unable to match the deviations from the uncovered interest rate parity observed in the data— just one risk-free bond, as we assume, is enough for the uncovered interest rate parity (UIP) to hold in the model. Thus, we see the results of our paper as complementary to e↵orts in the literature that explore frictions in the setting of prices (as in Chari, Kehoe and McGrattan (2002)aswellasmanyothers)orsegmentationinassetmarkets(suchastherecentworkby Itskhoki and Mukhin (2019,2021)). To highlight the transmission mechanism, we choose to keep the model as simple as possible. Thus, there is no physical capital in the model, and production functions are assumed to be Cobb-Douglas except in the production of primary commodities, for which we allow the elasticity of substitution to be smaller than one, as suggested by the evidence. We also ignore realistic microeconomic features like time-to-build restrictions in investment, the role of inventories and political economy considerations, which are very relevant for understanding primary commodity markets, as emphasized, for instance, in Baumeister and Kilian (2016). The paper proceeds as follows. In Section 2,wedescribethemainfeaturesofthedata. In Section 3, we briefly present the model, which, as mentioned earlier, is very standard. We discuss in detail a simplified version of the model that can be solved analytically and helps develop intuition for the transmission mechanism. It also highlights the type of demand 5
Japan real exchange rate, the distribution of the Backus-Smith correlation for the USA and Japan, and the distribution of the volatility and persistence of US-Japan relative consumptions. We also compute the distribution of the volatility and persistence of the three primary commodity price indices that we use to calibrate our model below (energy, agriculture, and metals and minerals). We estimate these small sample distributions using a bootstrapping procedure with the following statistical model. We divide our sample before and after 1973:Q1 and detrend the data using the log-linear trend discussed above. The first subsample has 52 quarters of observations and the second has 188. For each subsample, we run a VAR of order 1 using the following five variables: i) a price index of energy normalized by the US CPI, ii) a price index of agriculture normalized by the US CPI, iii) a price index of metals and minerals normalized by the US CPI, iv) the bilateral US-Japan real exchange rate, and v) the relative per-capita consumption of the USA and Japan.16 With the estimated parameters, we construct artificial time series of the five variables in the VAR, with a length of 55 for the first subperiod and 188 for the second, by drawing with replacement from the fitted residuals of the VAR. For each artificial time series, we compute the statistics of interest, such as the standard deviation of the bilateral real exchange rate. We repeat the procedure and construct 5,000 artificial time series for each of the five variables in the VAR, from which we estimate the small sample distribution of the statistics. The top panel of Figure 5displays the estimated small sample distribution of the standard deviation of the US-Japan real exchange rate before (in blue) and after (in orange) 1973. In this type of figure, the claim that the real exchange rate became more volatile is represented by a shift to the right of the estimated distributions. As noted above, the point estimate in the second subperiod is 19.6, but the distribution of the statistic has a wide range, from about 10 to 30 percentage points. Moreover, the distribution is right-skewed, with the mode (of about 15 percentage points) smaller than the mean (of about 17 percentage points), which, in 16We choose the lag length of the VAR using the Schwarz information criterion. Increasing the number of lags does not lead to significant di↵erences. 12
Figure 5: Small sample distributions of the standard deviation and autocorrelation of the US-Japan real exchange rate (a) Standard deviation of the US-Japan real exchange rate 0 5 10 15 20 25 30 (b) Autocorrelation of the US-Japan real exchange rate 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 turn, is smaller than the point estimate of 19.6 percentage points. For the first subperiod, the small sample distribution of the volatility of the real exchange rate is more concentrated at lower values of the standard deviation and is less skewed than the distribution of the second subperiod. The point estimate of 4 is close to both the mean and mode of the distribution. The bottom panel of the figure shows the estimated small sample distributions of the coefficient of autocorrelation of the bilateral real exchange rate before and after 1973. While there is a large area of overlap between the two distributions, that for the first subperiod has more mass in lower values of the autocorrelation coefficient, consistent with the observation of the previous subsection that the persistence of real exchange rates may have increased after 1973. The moral of Figure 5is that it could be misleading to evaluate the performance of the model using just the point estimates. Therefore, to evaluate the model, we will compare the small sample distribution of the statistic estimated from the data, as discussed above, 13
Figure 6: Small sample distribution of the correlation between the US-Japan real exchange rate and relative consumption -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 with the analogous distribution generated by simulating the model 5,000 times, drawing histories of artificial time series of 55 and 188 observations for the first and second subperiods, respectively, and computing the equivalent statistics that we computed using the actual data. As for the Backus-Smith puzzle, Figure 6shows that for both subperiods, the distributions of the correlation between the US-Japan real exchange rate and the ratio of consumption per capita have wide supports. Yet, the Mussa meets Backus-Smith puzzle is evident in that most of the mass of the distribution for the second subperiod is concentrated in negative values of the correlation, while that for the first subperiod is concentrated in positive values. But the dispersion is huge: while the point estimate of the correlation for the second subperiod is -0.47, it could be as low as -0.8 or as high as 0.3. In any case, these values are far away from one, which constitutes the Backus-Smith puzzle. On the other hand, the point estimate of the correlation in the first subperiod is 0.38, but there is a non-trivial mass of the distribution with values above 0.8, in which case the correlation could hardly be called a puzzle. In sum, the figure shows that there is considerable statistical uncertainty in the estimate of the Backus-Smith correlation, even larger than that of the volatility of the real exchange rate, but also that the observation that the correlation was less of a puzzle during the Bretton Woods period still holds. Finally, Figure 7shows the estimated small sample distributions of the standard deviation and autocorrelation of the three relative commodity prices before and after 1973. In the case of the volatility, the distributions are more concentrated and take smaller values in the 14
Figure 7: Small sample distribution of the standard deviation and autocorrelation of commodity prices (a) Energy: standard deviation 0 10 20 30 40 50 60 70 (b) Energy: autocorrelation 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (c) Agriculture: standard deviation 0 5 10 15 20 25 30 35 40 (d) Agriculture: autocorrelation 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 (e) Metals and minerals: standard deviation 0 5 10 15 20 25 30 35 40 45 50 (f) Metals and minerals: autocorrelation 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 first subperiod than in the second one, similar to what we observe with the small sample distributions of the volatility of the real exchange rate. Regarding the autocorrelation, the higher persistence of commodity prices after 1973 is reflected by the fact that the small sample distributions have more mass at higher values of the autocorrelation coefficient after 1973 than before. 15
3 The model We study a simple dynamic general equilibrium model featuring three large countries. There are three sectors of production in each country: nontradable final goods, tradable intermediate goods, and tradable primary commodities. Countries 1 and 2 represent the USA and Japan, respectively, while country 3 is the rest of the world. There are two types of shocks in the model. First, there are standard productivity shocks in countries 1 and 2. For simplicity, we assume an aggregate productivity shock that a↵ects all sectors in each country.17 In addition, there are shocks to the endowments of primary commodities in the rest of the world, which are designed to generate volatile and persistent primary commodity prices. We could also introduce demand shocks for commodities in the rest of the world. We do so in a simplified version of the model below and show that they are equivalent ways to generate volatile commodity prices, since all that matters are shocks to the excess demand from the rest of the world. Thus, for parsimony, the calibrated model has only shocks to the endowment of commodities. Time is discrete and denoted by t=0,1,2,.... Households in each country consume a single nontradable final good and can internationally trade a single non-contingent bond that pays in units of primary commodity 3.18 Households in country i=1,2,3 make their consumption-savings decision in order to maximize the expected lifetime utility E0"1 X t=0 t(Ci t)1 1#, where E0[·] is the expectation operator conditional on information at time t=0,2(0,1) is the discount factor, and >0 is the risk aversion parameter. All technologies in the model feature constant elasticities of substitution, and all goods 17These shocks are known to generate too little volatility in real exchange rates. Thus, allowing for di↵erent shocks across sectors has little hope of being of any quantitative relevance. 18Since we log-linearize the model, the unit in which the non-contingent bond pays is irrelevant. 16
and inputs are traded in competitive markets. Country i=1,2,3 produces a final nontradable good, Ci t, using labor and three intermediate tradable goods, each produced in a di↵erent country.19 The technology to produce the intermediate good, denoted by Qi t,uses labor and three tradable primary commodities. In addition, countries 1 and 2 are able to produce the three primary commodities using labor and a commodity-specific fixed endowment of natural resources, while country 3 receives stochastic endowments of the three primary commodities. Throughout the paper, a superscript in a variable is used to denote a given country, and a subscript refers to a particular good. For example, x1 3,t is the demand for commodity 3 by country 1 at time t,andsoon. We assume Cobb-Douglas technologies—unit elasticity of substitution—for the final goods and intermediate goods to reduce the number of parameters in the model. With CobbDouglas technologies, we can calibrate all parameters directly from observed input-output tables. However, we do allow for arbitrary elasticities of substitution in the production of the commodities, since there is ample micro evidence that it is substantially lower than one. Thus, the production functions are given by Ci t=Zi tqi 1,t↵i 1qi 2,t↵i 2qi 3,t↵i 3ni c,t↵i 4, Qi t=Zi txi 1,ti 1xi 2,ti 2xi 3,ti 3ni q,ti 4, Xi j,t =Zi t2 41i jei j,t i xj 1 i xj+i j⇣ni xj,t⌘ i xj 1 i xj3 5 i xj i xj 1 , where Zi tdenotes aggregate productivity (TFP) in country i,whichiscommonacrosssectors; qi 1,t,qi 2,t,andqi 3,t are the inputs of intermediate goods used to produce final goods; xi 1,t,xi 2,t, and xi 3,t are the inputs of primary commodities used to produce the intermediate good; ni c,t, ni q,t, and ni xj,t are the labor inputs allocated to each sector; Xi j,t denotes the production of commodity j;andei j,t is a commodity-specific fixed endowment of natural resources. The 19The final good is nontradable and can be used only for consumption, so we simply denote it by C. 17
parameters ↵i jand i jare the factor shares, which sum to one in each sector, and i j2(0,1). The parameter i xjdenotes the elasticity of substitution between inputs. Our assumption that the rest of the world does not produce the commodities but rather receives endowments is equivalent to assuming that 3 j=0forj=1,2,3.20 Uncertainty is then represented by the aggregate productivity shocks in countries 1 and 2 and the stochastic endowments of primary commodities in country 3. We assume the following (stationary) autoregressive processes: ln (Z1 t)=(1⇢z1)ln(Z1)+⇢z1ln (Z1 t1)+"z1 t, ln (Z2 t)=(1⇢z2)ln(Z2)+⇢z2ln (Z2 t1)+"z2 t, ln (X3 1,t)=(1⇢x3 1)ln(X3 1)+⇢x3 1ln (X3 1,t1)+"x1 t, ln (X3 2,t)=(1⇢x3 2)ln(X3 2)+⇢x3 2ln (X3 2,t1)+"x2 t, ln (X3 3,t)=(1⇢x3 3)ln(X3 3)+⇢x3 3ln (X3 3,t1)+"x3 t, where the vector of innovations ["z1 t," z2 t," x1 t," x2 t," x3 t] is normally distributed with zero mean and arbitrary covariance matrix. Variables without time subscripts represent long-run means. Markets are competitive, and given prices, firms solve a static profit maximization problem in every period. For the calibration, we assume that in steady state, the three countries have a zero net asset position. To simulate the model, we impose a small quadratic adjustment cost to changes in the stock of the single non-contingent bond, as is customary in the literature, to avoid the inherent unit root when using linearization techniques. As the model and the solution technique are totally standard, we leave the complete description of the equilibrium and the details of the computation to the Online Appendix. Before showing the quantitative results, we discuss the closed-form solution of a simplified version of the model. This version is useful for understanding the transmission mechanisms of the di↵erent shocks that we study in the dynamic quantitative model below. 20This assumption simplifies the calibration, since it allows direct control of the supply of the commodities in the rest of the world. 18
3.1 A simplified economy We make three assumptions to simplify the general model. First, we assume financial autarky, so all countries must satisfy a zero trade balance condition. In this case, the solution of the model becomes static and preferences are irrelevant. So, in what follows, we do not make explicit the time dependence of the variables. Second, we simplify the production structure and eliminate the intermediate goods. And third, we consider only two commodities. Country 1 produces commodity 1, and country 2 produces commodity 2. The rest of the world receives endowments of the two commodities. To simplify notation, we use Xto denote commodity 1 and Mto denote commodity 2. In addition, all prices are measured in an international numeraire that is common across countries.21 We derive explicit expressions for the real exchange rate and for the ratio of consumption between the two countries to theoretically address the Mussa and Backus-Smith puzzles. Moreover, for this example, we allow for di↵erent productivity shocks across sectors to clarify why they have little chance of accounting for the puzzles quantitatively. 3.1.1 Country 1 The technology to produce the final good in country 1 is given by C1=Z1x1↵xm1↵ml1↵l, where Z1is productivity, C1is the final good, and x1,m1and l1are the inputs of commodity X,commodityM, and labor allocated to the production of the final good. The technology is constant returns to scale, so ↵x+↵m+↵l=1. 21Defining national currencies and nominal exchange rates is redundant. 19
The cost minimization conditions imply Pxx1=↵x ↵l W1l1,(1) Pmm1=↵m ↵l W1l1,(2) where Pxand Pmare the prices of the two commodities, and W1is the wage. Moreover, since markets are competitive, the price level in country 1 satisfies P1=1 Z1✓W1 ↵l◆↵l✓Px ↵x◆↵x✓Pm ↵m◆↵m . Zero trade balance means that Px(Xx)=Pmm1, where Xis the total amount of the commodity produced in country 1. Combining this expression with equations (1)and(2)gives PxX=↵x+↵m ↵l W1l1.(3) We use this equation to replace W1in the expression for the price level and obtain P1=k11 Z1✓X l1◆↵l (Px)↵x+↵l(Pm)↵m,(4) where k1is a constant. Equation (4) makes clear that the price of final consumption in country 1 is homogeneous of degree one in commodity prices. The reason is that since country 1 produces commodity X,thereisadirectlinkbetweenthedomesticwageandPx, described in equation (3). This is the reason why the share of Pxin the price level is given by its direct e↵ect, represented by the parameter ↵x, plus an indirect e↵ect,givenby↵l. 20
In addition, trade balance combined with equations (1)and(2) implies x1=X↵x ↵x+↵m and m1=X↵m ↵x+↵m Px Pm.(5) The technology to produce commodity Xis given by X=Zx(1 1)e11 1 1+1n11 1 11 11 , where Xis total production; Zxis a stochastic productivity parameter; e1is the endowment of a natural resource, which we assume constant over time; and n1is labor allocated to the production of commodities. The optimality condition with respect to labor is W1n11 1=1Px(Zx)1 1 1(X)1 1.(6) If we use equation (3) to replace the wage W1above, we obtain ↵l ↵x+↵m✓X Zxn1◆1 1 1 =1 l1 n1, which, using the production function of the commodity, can be written as ↵l ↵x+↵m2 4(1 1)✓e1 n1◆1 1 1 +13 5=1 l1 n1.(7) Equation (7) and the equilibrium condition in the labor market, n1+l1=N1,(8) determine the allocation of labor, where N1is the endowment of labor in country 1. Since the endowment of natural resources is constant, it follows that the labor allocation 21
price of commodity X. On the other hand, shocks to the world supply of commodity Mas well as to the world demand of commodity X,drivenbyanincreaseinx, make the relative price of commodity Xto increase. 3.1.6 The Mussa puzzle If we put the equilibrium relative prices (13) into the real exchange rate equation (11), use Corollaries 1 and 2, and take logs, we obtain ln ✓P1 P2◆/ln ✓Z2 Z1◆+ln (Zx)↵l (Zm)l!+(1(↵m+x)) ln 0 @ amZm+⇣x m+x⌘M3 axZx+⇣m m+x⌘X31 A,(14) where amand axare positive constants and the symbol /means that we are ignoring an additive constant.25 The first term on the right hand side, ln(Z2/Z1), captures the direct e↵ect of productivity shocks on the relative marginal costs to produce final goods in each country. The second term captures the impact that productivity shocks in the domestic commodity sectors translate, through a common labor market, into changes in wages and, hence, in the marginal cost to produce final goods. These e↵ects of productivity shocks are standard in open economy models and known to generate too little volatility in real exchange rates because of their relatively low volatility in the data. The third term is the new e↵ect brought about by shocks to primary commodity markets. This term is multiplied by (1(↵m+x)), which is close to 1 to the extent that commodities have a low share in the production of final goods in the two countries. This term captures how shocks to the world supply (M3and X3)ordemand(mand x) of commodities can a↵ect the bilateral real exchange rate between countries 1 and 2 through changes in equilibrium relative prices. To the extent that these shocks are volatile and persistent, the real exchange rate will inherit these same properties, somewhat dampened by the term (1 (↵m+x)), 25Given that the labor inputs and natural resources are fixed, we can normalize variables so that the output of Xand Mare equal to Zxand Zm, respectively. 28
which is lower than but close to one for most economies. Notice, also, that the productivity shocks Zxand Zmin the commodity sectors also a↵ect equilibrium prices and therefore appear in this last term. Yet, since these shocks are of relatively low volatility, they have a much smaller impact on equilibrium relative prices than shocks to the world supply or demand of commodities. 3.1.7 The Backus-Smith puzzle Likewise, using the equilibrium relative prices (13) in equation (12)weobtain ln ✓C2 C1◆/ln ✓Z2 Z1◆+ln (Zm)1l (Zx)1↵l!(↵m+x)ln0 @ amZm+⇣x m+x⌘M3 axZx+⇣m m+x⌘X31 A.(15) Note that world supply and demand shocks for commodities also a↵ect the ratio of consumption, but these shocks are muted, since the last term is multiplied by (↵m+x), which is a relatively small number for the economies we are studying. The sign and magnitude of the correlation between the (log) real exchange rate and the (log) ratio of consumption depend on the type of shock hitting the economy, as can be seen by comparing equations (14) and (15). First, productivity shocks in the final goods sectors, captured by the term log(Z2/Z1), impart a correlation of 1 between the real exchange rate and the ratio of consumption. This result, which parallels that in an economy with complete financial markets, is obtained in an economy with an extreme form of market incompleteness. Intuitively, a TFP shock to the final good’s technology has the simultaneous e↵ect of decreasing the domestic price level and increasing domestic consumption because of a positive wealth e↵ect. This behavior results in a positive correlation between the real exchange rate and the ratio of consumption that equals 1 in this example. This same intuition applies to an economy with a single non-contingent bond, as the productivity shock still has a wealth e↵ect that increases consumption and simultaneously reduces the price level. Second, in the economically relevant case that ↵m+x<1—so that commodity sectors 29
are relatively small—all shocks (supply or demand) to primary commodity markets in the rest of the world impart a correlation of -1 between the log real exchange rate and log ratio of consumption. Mechanically, this result follows because the term 1 (↵m+x)is positive in equation (14)and(↵m+x) is negative in equation (15). Intuitively, a world shock that increases the relative price Px/Pmgenerates a positive wealth e↵ect in country 1, which produces commodity X, and a negative wealth e↵ect in country 2, which imports commodity X. As a result, consumption increases in country 1 and decreases in country 2. Simultaneously, an increase in Px/Pmincreases the price of final goods in country 1 relative to those in country 2, leading to a correlation of -1 between the real exchange rate and the ratio of consumption. The impact of productivity shocks to the commodity sectors is subtler, as there are direct and indirect e↵ects through changes in relative prices. For simplicity, consider a two-country version of this model, with X3=M3= 0. In this case, and ignoring irrelevant constants, equations (14) and (15) collapse to ln ✓P1 P2◆/(m↵m)lnZx(↵xx)lnZm, ln ✓C2 C1◆/2↵m+↵x+x 2ln Zx2x+↵m+m 2ln Zm. The sign of the correlation between ln (P1/P2)andln(C2/C1) depends on the symmetry of technologies between countries. If the share of commodities in the production function of both countries is the same, so that ↵m=mand ↵x=x, the real exchange rate does not move with Zxor Zmand the correlation is zero. But if each country uses in the production of its final goods more of the commodity that it produces than that of the other country, so that ↵x> xand m>↵ m,thenshockstoZxand Zmimpart a correlation of -1 between the real exchange rate and the ratio of consumption. The previous discussion shows that there are forces that a↵ect the correlation in both directions. So the correlation will depend on the covariance matrix of the vector of shocks to 30
the economy. To the extent that shocks to primary commodity markets dominate, one would expect a negative correlation between the real exchange rate and the ratio of consumption. This stark conclusion depends critically on the assumption of financial autarky, since it is well known that with complete markets, the correlation ought to be equal to 1. In the incomplete markets, one-bond economy we consider next, the equilibrium exhibits insurance, a feature that makes the correlation move closer to 1. Yet, if productivity shocks and shocks to primary commodity markets are highly persistent, as we argue below, the ability of a single-bond economy to efficiently smooth consumption over states of nature deteriorates, and the intuition derived from this simplified model extends to the one-bond economy. On the other hand, if shocks have little persistence, a single non-contingent bond does a good job of smoothing consumption, and the economy looks more like a model with complete financial markets, as we show in the quantitative exercises below. 3.2 The role of nominal variables The model discussed above has no frictions in the setting of prices, so only relative prices matter. As money is neutral, monetary policy need not be specified, so we do not specify it. It is trivial to show that the model is consistent with inflation targeting policies, whereby inflation rates are made roughly constant, as they have been in most countries during the last decades. In this case, almost all of the volatility in real exchange rates would come about through changes in the nominal exchange rate, as has also been documented by Mussa (1986). It is certainly not the purpose of this paper to argue that price frictions are irrelevant in explaining the puzzles we address. In fact, Mussa (1986) also presents evidence from the endings of fixed exchange rate regimes, in which the real devaluation follows the nominal devaluation. It is this evidence that has been used more forcefully to argue for the frictions in the setting of prices. This evidence is much harder to reconcile with our model. Our purpose is to explore the role of real shocks arising from primary commodity markets in explaining the behavior of real exchange rates. To highlight that role, we adopted a flexible 31
prices model, in which the exchange rate regime is irrelevant. The previous discussion highlights that our theory of real exchange rate fluctuations departs from most of the literature in that the breakdown of the Bretton Woods system plays no role. The interpretation that we endorse of the events is that the collapse of the Bretton Woods system happened to occur at roughly the same period in which primary commodity markets started operating in a very di↵erent way, for independent reasons. There is ample evidence supporting the notion that the oil market went through a transformation that started slowly in the 1960s, took speed by 1970, and had fully taken e↵ect by the time of the first oil price shock in 1973. A very compelling case is developed in detail in a fascinating book by Garavini (2019). The series of events described by Garavini (2019) transformed a market that had traditionally been controlled by a cartel of a few international firms known as the majors. The oil producing countries played a very passive role. The relationship between the companies and the oil producing countries was based on long-term contracts with fixed posted prices. These posted prices were closely related to the price in the US, which was fixed by the government. The foundation of the OPEC by the end of the 1950s was an attempt by the oil producing countries to change the relationship with the majors. But for the OPEC countries, progress was slow, and only by the early 1970s did the manage to change the rules of the game. This occurred at a time in which global demand for oil was increasing dramatically because of the boom in total world output, as it has been thoroughly documented by Baumeister and Kilian (2016), for instance. The oil market after 1973 became one without long-term contracts and no posted prices, with oil producing countries playing a prominent role. At the same time, swings in global demand became larger as a result of the growth miracles in Southern Europe, Southeast Asia and eventually China and India. Other primary commodity markets went through similar transformations. For instance, the tin market was regulated through the International Tin Agreement, signed by over 20 32
countries in the 1950s. The agreement was meant to regulate the tin market and avoid excessive fluctuations in prices. As described in detail in Mallory (1990), the agreement formally collapsed in 1985, after a few years of disagreements among its members. 4 Calibration We divide the calibration of the model in two blocks. In the first block, we calibrate all parameters of preferences and technologies using steady state conditions or standard values in the literature. The second block of the calibration is concerned with the parameters that govern the evolution of the five stochastic processes in the model. We set those parameters by matching moments in the data with the equivalent moments generated by the model. Importantly, we do not use data on real exchange rates or consumption to calibrate the parameters of the model. They are used to evaluate the performance of the model. 4.1 Matching steady state conditions To calibrate the first block of parameters, we proceed in three steps. First, we set the discount factor and coefficient of risk aversion to standard values: =0.99 and =2. The second step consists of calibrating the parameters of the production functions, which correspond to the factor shares and elasticities of substitution. As our benchmark case, we set all elasticities of substitution to be one (Cobb-Douglas technologies). In Section 5.1.3 we show that using lower elasticities of substitutions in the production function of commodities actually improves the quantitative performance of the model. To calibrate the share parameters, we use the 2005 Japan-US input-output table published by the Ministry of Economy, Trade, and Industry of Japan. We map each of the 174 sectors in the input-output table into the three sectors considered in our model: final goods, intermediate goods, and primary commodities. We then further divide the primary commodity sectors into three groups: energy, metals and minerals (referred to as metal), and the rest (referred to as 33
agriculture). The exact mapping is discussed in the Online Appendix. The group of all final goods in the US is assumed to be C1, and the group of all intermediate goods is assumed to be Q1.WedothesameforC2and Q2in the case of Japan. The input-output table contains data on the payments to each of the factors of production, such as intermediate inputs, compensation of employees, and operating surplus. We compute the shares of each factor of production considered in the model to pin down the share parameters of the production functions described in Section 3. For the intermediate and final good sectors, we assume that the payments to labor input are equal to the value added in the data. In the primary commodity sector, on the other hand, the labor share is computed as the share of compensation of employees in value added. With this information, we calibrate the parameters of the production functions in the USA, country 1, and Japan, country 2. They are reported in the first and second columns of Table 1. Table 1: Calibration: factor shares (%) Country 1 (USA) Country 2 (JPN) Country 3 (ROW) Final good Ci intermediate good qi 1↵1 1= 23.5↵2 1=0.4↵3 1=2.8 intermediate good qi 2↵1 2=0.2↵2 2= 26.3↵3 2=1.3 intermediate good qi 3↵1 3=3.3↵2 3=1.6↵3 3= 34.9 labor ni c↵1 4= 73.0↵2 4= 71.7↵3 4= 61.0 Intermediate good Qi primary commodity xi 11 1=8.62 1=5.43 1=9.9 primary commodity xi 21 2=3.92 2=4.23 2=7.0 primary commodity xi 31 3=3.32 3=5.73 3=5.1 labor ni q1 4= 84.22 4= 84.73 4= 78.0 Primary commodity Xi 1 labor ni x11 1= 29.62 2= 48.4 natural resource ei 111 1= 70.412 2= 51.6 Primary commodity Xi 2 labor ni x21 1= 34.32 2= 20.3 natural resource ei 211 1= 65.712 2= 79.7 Primary commodity Xi 3 labor ni x31 3= 68.52 3= 38.7 natural resource ei 311 3= 31.512 3= 61.3 We do not have a similar input-output table for the rest of the world (ROW). Besides 34
the information regarding the transactions with the rest of the world in the Japan-US inputoutput table, we use data from the 10-sector database available from the Groningen Growth and Development Center, trade data from Comtrade, and nominal GDP and population data from the World Bank Development Indicators to pin down the remaining parameters. We impose zero trade balance in the steady state, so the share of the final good sector in GDP is equal to the share of labor in the final good sector, ↵i 4. Using the 10-sector database, we set ↵3 4equal to the GDP-weighted average of the share of the final good sector in the rest of the world.26 Next, the input-output table reports the rest of the world’s consumption of intermediate goods produced in the USA and Japan. We pin down ↵3 1and ↵3 2using data from the World Development Indicators to compute the GDP for the rest of the world. Finally, given that factor shares sum to one, we set the parameter ↵3 3as a residual. Next, we move to the parameters of the production of intermediate goods in country 3. We calibrate 3 4together with the endowments of natural resources in commodities to match the share of primary commodities in the rest of the world’s GDP together with other moments. That process is described in the third step below. The remaining shares, 3 1,3 2, and 3 3, are distributed according to their shares in primary commodity trade in 2005 from Comtrade. The resulting factor shares are presented in the third column of Table 1. The third and final step consists of calibrating the relative size of each economy in steady state together with the composition of the primary commodity sectors in each country and the share of the primary commodity sector in the rest of the world’s GDP, as mentioned above. Again, we use data from the World Development Indicators to compute the shares of the rest of the world’s GDP, the 10-sector database to compute the shares of the primary commodity sector in rest of the world’s GDP, and the US-Japan input-output table to compute the composition of GDP in the primary commodity sector in the USA and Japan. We normalize aggregate productivity in each country to one and use population data in 2005 to compute the relative endowment of labor in each country. So we are left with the en26We compute the weights using nominal GDP in USD from the 2005 World Development Indicators. 35
Table 2: Composition of GDP within and across countries USA JPN ROW (Country 1) (Country 2) (Country 3) Model Data Model Data Model Data Shares (%) Sectoral composition of GDP Final good 74 61 72 58 61 61 Intermediate good 23 36 26 39 29 29 Primary commodity 3 3 2 3 10 10 Composition of commodity sector GDP X1: Energy 59 39 0 0 46 45 X2: Agriculture 16 43 58 61 31 32 X3: Metals and minerals 25 18 42 39 23 23 Share of world GDP 37 27 16 10 47 63 dowments of natural resources in countries 1 and 2, the endowments of primary commodities in country 3, and the share of labor in the production of the intermediate goods in country 3. Because of strong non-linearities, an exact match between the moments in the model and in the data is not feasible, so we set their values to achieve a good approximation by means of minimizing the distance between the model generated moments and the value observed in the data. We report the endowment values in the Online Appendix. The corresponding GDP composition within and across countries is reported in Table 2, which also includes some non-targeted moments, such as the share of the final good sectors in countries 1 and 2. Table 2shows that our model does a decent job in matching the data on GDP composition in the world. And, more importantly, it shows that our calibrated model does not overestimate the size of the primary commodity sector in the economies. It is as small as in the data. 4.2 Calibration of the stochastic processes There are two types of shocks in the model. First, there are country-specific productivity shocks, {ln Z1 t,ln Z2 t}. We choose the parameters of these processes so as to match the standard deviation and autocorrelation of output in each country and their correlation 36
over the period 1973–2019. Since these parameters can be chosen to perfectly match those moments, we do not report them.27 Importantly, we assume that the stochastic process for the productivity shocks is orthogonal to the one for commodity shocks and remains the same over the entire sample period, from 1960 to 2019. Next, we calibrate the shocks to the rest of the world’s supply of primary commodities. While we formally assume shocks to the endowment of commodities in the rest of the world, what really matters in the mechanism that we propose is to generate shifts in the excess demand of commodities in the rest of the world. Fluctuations in these shocks then drive fluctuations in equilibrium relative primary commodity prices.28 Given the calibrated values for the productivity shocks, we choose the parameters of the stochastic process for the endowment of primary commodities in the rest of the world to match the standard deviation, first-order autocorrelation, and cross correlations of the three primary commodity price indices that we observe in the data. The target moments that we consider are the average values of the associated small sample distributions of the corresponding estimates that we constructed in Section 2.2. More specifically, we divide our sample in two. The first subperiod goes from 1960 until 1973. We remove a linear trend from the three series of primary commodity prices, just as we did for the real exchange rates, and compute their persistence, volatility, and correlations. We then calibrate the parameters of the stochastic processes for the endowments of commodities in the rest of the world so as to minimize the distance between the moments in the model and the moments in the data. We repeat the same procedure for the second subperiod, the one that goes from 1973 until 2019. 27The calibration of the two types of shocks can be done independently because relative price shocks do not a↵ect the proper measure of output, as Kehoe and Ruhl (2008) explain in detail. The Online Appendix provides a formal proof. In contrast, relative price shocks do a↵ect relative consumption. 28Of course, productivity shocks also drive fluctuations in equilibrium commodity prices, but to a lesser extent, because of their lower volatility. 37
structure between countries.32 The level of aggregation that we used in our model implies abstracting from many dimensions of heterogeneity contained in the data. For instance, when calibrating the size of the commodity sectors, we started with 26 di↵erent commodities contained in the inputoutput table and aggregated them into the three commodities of the model. This aggregation muted substantial degrees of heterogeneity that may a↵ect the transmission mechanism of the model. To quantify this e↵ect, let ↵USA jand ↵JPN jdenote the share of commodity sector value added generated by commodity j=1,...,26, for each country. We can define an index of heterogeneity by H(USA, JPN)= 1 26 26 X j=1 ↵USA j↵JPN j, where |x|is the absolute value of x. This index has a minimum value of 0 whenever ↵USA j= ↵JPN jfor all j, so that countries are identical, and a maximum value of 1 when countries produce di↵erent sets of commodities. Using the 26 di↵erent commodity sectors in the inputoutput table, the value of the index is H(USA, JPN)=0.5. But when we aggregate the 26 sectors into three, as we did to calibrate the model, the index falls to 0.3. This is one specific dimension in which aggregation reduces the true heterogeneity in the data.33 To provide a quantitative measure of the relevance of this heterogeneity, we simulated the model with the following variations. First, we choose the endowment of natural resources so that the relative sizes of the three commodity sectors are equal for Japan and the USA. In this homogeneous economy, the index H(USA, JP N)=0.Wealsosimulateaheterogeneous economy, in which we set the value added of commodities 2 and 3 in the USA to be 0, and the value added of commodities 1 and 2 in Japan to be 0. That is, the USA fully specializes in the production of energy, while Japan fully specializes in the production of agriculture. This is a case in which the countries are as heterogeneous as possible in the production of commodities, and the index H(USA, JPN)=1. 32In fact, it is easy to prove that if the two countries are identical except for the productivity shocks, the real exchange rate is given by the ratio of productivities. 33This e↵ect is also present when aggregating the intermediate goods. 44
Figure 13: Changes in the heterogeneity of the commodity sectors (a) Standard deviation of RER 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 (b) Correlation of RER and relative consumption -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure 13 displays the results of these experiments. The top panel shows the case in which the two countries are made homogenous, the middle panel the benchmark calibration, and the bottom panel the case of the extreme heterogeneity. The figure shows that the homogeneous economy performs very poorly. The volatility of real exchange rates barely increases, and most of the mass of the correlation between the real exchange rate and the relative consumption is positive in both subperiods. At 45
the other extreme, by making the countries more heterogeneous in commodity production, the distribution of the volatility of the real exchange rate after 1973 moves further to the right, with a mean value around 22 percent, substantially higher than in the data.34 The heterogenous case also generates an average correlation between the real exchange rate and the consumption ratios that is closer to the data both in the first and second subperiods. The most remarkable feature of Figure 13 is that small changes to the model can have substantial e↵ects in the standard deviation of real exchange rates and in the correlation between real exchange rates and relative consumption. We say these changes are small because they happen within a sector that represents only 3 percent of the economies we analyze. 5.1.3 Lower elasticity of substitution in the commodity sectors In the baseline calibration, we assumed that the elasticity of substitution between labor and the natural resources in the commodity sectors is unity. The simple model in Section 3.1 implies that the results are invariant to changes in the elasticity of substitution. Here, we analyze to what extent this invariance result extends to the general model without complete specialization in commodity production and in which countries have access to financial markets through a risk-free bond. Figure 14 shows the results of reducing the elasticity of substitution from 1 to 2/3 in the commodity sectors in both countries.35 As becomes clear in the figure, with a lower elasticity of substitution, the model does a better job at matching the Mussa puzzle but barely changes the results regarding the Mussa meets Backus-Smith puzzle. 34The mean standard deviation also increases in the first subperiod, but since the volatility and persistence of primary commodity prices are much lower in that case, the di↵erence is smaller. 35The algorithm had problems of convergence for lower values of the elasticity. 46
Figure 14: Lower elasticity of substitution in the commodity sectors (a) Standard deviation of RER 0 5 10 15 20 25 30 0 5 10 15 20 25 30 (b) Correlation of RER and relative consumption -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 5.1.4 The structure of financial markets In this section, we focus on the role of financial markets by considering two extremes: an economy with complete financial markets, and an economy in financial autarky. The model with financial autarky di↵ers from the simple model discussed in Section 3.1 in that it has the more general production structure of the baseline economy. Not surprisingly, the model with complete financial markets implies a counterfactual correlation of 1 between the real exchange rate and relative consumption, as confirmed in the upper right panel of Figure 15.ButthismodelalsofailstosolvetheMussapuzzle, as the distribution of the volatility of the real exchange rate barely increases after 1973. The reason behind this result is that, relative to the baseline model, in the economy with complete financial markets, there is substantially more reallocation of labor across sectors that moderate the impact of commodity shocks on the relative prices of final goods between countries. At the other extreme, the model with financial autarky implies a larger shift to 47
Figure 15: The structure of financial markets (a) Standard deviation of RER 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 (b) Correlation of RER and relative consumption -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 the right of the distribution of volatilities after 1973 and a more clear distinction between the distribution of the correlation between the real exchange rate and relative consumption, as shown in the bottom right panel of Figure 15.Intuitively,wealthe↵ectsinthiseconomy are stronger and therefore also magnify the movements in relative consumption associated with equilibrium changes in commodity prices. 48
5.1.5 Persistence of shocks to world commodity markets We now consider the role of persistence. In particular, we consider an economy in which shocks to world commodity markets are less persistent than in the baseline model and another economy in which they are more persistent. As mentioned above, we recalibrate the volatility of the innovations to the commodity shocks so as to match the volatility of commodity prices observed in the data. The results of this experiment are shown in Figure 16. Figure 16:Changingthepersistenceofshockstocommoditymarkets (a) Standard deviation of RER 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 (b) Correlation of RER and relative consumption -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 49
The model with lower persistence in world commodity shocks performs worse, both in terms of solving the Mussa puzzle and in terms of solving the Backus-Smith puzzle. On the other hand, in the model with more persistent shocks, the volatility of the real exchange rate increases more after 1973, and the distribution of the correlation between the real exchange rate and relative consumption moves slightly to the left, with more mass in negative values of the correlation. The reason for these results is that as we keep increasing the persistence of world commodity shocks, the model more and more resembles an economy in financial autarky because the risk-free bond is a less useful hedge against persistent shocks. Conversely, as we reduce the persistence of commodity shocks, the risk-free bond does a better job of insuring against shocks, and the economy tends to look more like an economy with complete financial markets. 5.2 Relative consumption Following the literature, so far we have focused the analysis on the fluctuations of the real exchange rate and its correlation with relative consumption. However, the model also makes predictions about the volatility and persistence of relative consumption before and after 1973. Therefore, in this section, we discuss those predictions and how they match features of the data. We first present evidence regarding the behavior of the ratio of consumption preand post-1973, as we did in Section 2.Thenweshowthepredictionsofthemodel. The left panel of Figure 17 displays the volatility before and after 1973 of the log-di↵erence of detrended consumption for the group of OECD countries analyzed in Section 2, relative to that of the USA. The right panel shows the persistence of relative consumption. As with the real exchange rates, we observe a clear increase in both the volatility and persistence of relative consumption after 1973.36 The same observation holds when we focus on the Japan-US pair, as shown in the upper panels of Figure 18. These figures show the bootstrapped small sample distributions of 36Portugal is the only country in which the volatility of relative consumption decreased after 1973. 50
Figure 17: Volatility and persistence of (log) relative consumption before and after 1973 (a) Standard deviation of relative consumption 0123456789 0 1 2 3 4 5 6 7 8 9 Japan (b) Autocorrelation of relative consumption 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Japan the standard deviation and first order autocorrelation of the (log) relative consumption of Japan against the USA. The increase in volatility and persistence is reflected as a shift of the distributions to higher values after 1973. These movements in the distributions of the volatility and persistence of relative consumption mimic those of the real exchange rate. In the bottom panels of Figure 18, we see that the benchmark model is able to match the distributions of the volatility and persistence of relative consumption before and after 1973. We emphasize again that we did not use any data on consumption to calibrate the model, so the results are due solely to the increase in the volatility and persistence of primary commodity prices and the transmission mechanism generated by the model. In the simplified economy of Section 3.1, the increase in the volatility of shocks to world commodity markets (summarized by shocks to X3and M3) translate into higher volatility of relative consumption, although it is of a smaller magnitude than that of the real exchange rate (compare equations (14)and(15), noting that ↵m+x<1(↵m+x)). Moreover, the persistence of relative consumption inherits the persistence of shocks to world commodity markets. 51
Figure 18: Volatility and persistence of relative consumption of Japan versus the USA (a) Standard deviation of relative consumption 012345678910 012345678910 (b) Autocorrelation of relative consumption 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 6 Conclusion We showed that explicitly modeling primary commodities in an otherwise standard quantitative multi-country model can go a long way in explaining two puzzles in the international economics literature. This is the case even though both production and use of primary commodities account for a small fraction of the economy. The key features of the model are incomplete markets and volatile shocks to the primary commodity markets. A calibrated model in which shocks to primary commodity markets are chosen so as to match the moments of primary commodity prices in the data, can explain most of the increase after 1973 in the volatility of real exchange rates between the USA and Japan. In addition, it also explains a sizable fraction of the low correlation between real exchange rates and the ratio of consumption. Importantly, in the calibrated model, the sizes of the primary commodity sectors are as low as in the data. We also show, through a series of robustness exercises, that distributions of the key mo52
ments are quite sensitive to relatively small changes in parameters. Together with the high statistical uncertainty that we document, this fact strengthens the notion that documenting the puzzles with point estimates ought to be done with extreme caution and, more importantly, may be subject to substantial changes even following small changes in the production structure of countries. For instance, the model implies that the fracking technology that changed the oil sector in the USA in the last couple of decades could have a substantial e↵ect on the impulse response of the real exchange rate after a supply shock to the oil market. In our theory of real exchange rate behavior, there is no role for exchange rate systems. Thus, the interpretation we adopted in the paper is that the breakdown of the Bretton Woods system in the early 1970s happened to coincide, by chance, with developments that made the primary commodity markets much more volatile. There is an alternative interpretation, though, raised as a question by a discussant of this paper. According to that interpretation, the turbulence in primary commodity markets that became evident by the early 1970s may have contributed to the final collapse of the Bretton Woods system, which had already showed signs of weaknesses during the previous decade. We find this a very interesting hypothesis, since it is typically the case that fixed exchange rates endogenously collapse owing to economic forces, and the end of the Bretton Woods system was not an exception. This view challenges the standard assumption in the literature, which takes the collapse of the Bretton Woods system as the exogenous change that cause the increased volatility of real exchange rates. The proper causality may be to go from changes in primary commodity markets to the collapse of the Bretton Woods system and more volatile real exchange rates. We leave this fascinating discussion for further research. 53
A.2 Volatility of commodity prices before and after 1973 Figure 1: Standard deviation of primary commodity prices before and after 1973 (a) Prices expressed in deutsche marks (euros after 2000) and normalized by German CPI 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 energy agriculture metal (b) Prices normalized by the price of wheat 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 energy agriculture metal 3
B Appendix: Model B.1 Log-linearized equilibrium equations This appendix presents the (log-linearized) equilibrium equations of the model described in Section 3 in the main text. We use the log-linearized version of the model to compute the model simulations based on the method of undetermined coefficients discussed in Uhlig (1999). Variables without time subscripts denote steady state values, and e X denotes the log-deviation of variable Xfrom its steady state level. We begin by describing the equilibrium equations related to the household problem in country i2{1, 2, 3} . The household inelastically supplies the endowment of labor and natural resources, and the optimal choices of consumption and bond holdings are characterized by the following equations: PciCif Pci t+PciCif Ci t+Pbg Bi t+1=WiNif Wi t+Pei 1ei 1f Pei 1 t+Pei 2ei 2f Pei 2 t+Pei 3ei 3f Pei 3 t+Px3f Bi t, (1) f Pb t+Pci Px3 g Bi t+1=f Ci t+f Pci t-Et ] Ci t+1-Etg Pci t+1. (2) Equation (1) is simply the budget constraint, in which Pb denotes the price of the uncontingent bond B that pays in units of commodity X3 . Equation (2) is the standard Euler equation, in which E[·] is the expectation operator and the parameter > 0 determines the cost of moving bond holdings away from their steady state level (assumed to be zero). 1 The latter is expressed in units of the final good in each country. Next, we move to the final good sector in country i2{1, 2, 3} . The equilibrium conditions are represented by the feasibility constraint and the optimality conditions for 1We set =1.0e-5. It is a device to make bond holdings stationary. 4
the choice of inputs: f Ci t=f Zi t+↵i 1g qi 1,t+↵i 2g qi 2,t+↵i 3g qi 3,t+↵i 4g ni c,t, (3) f Pq1 t+g qi 1,t=f Pci t+f Ci t, (4) f Pq2 t+g qi 2,t=f Pci t+f Ci t, (5) f Pq3 t+g qi 3,t=f Pci t+f Ci t, (6) f Wi t+g ni c,t=f Pci t+f Ci t. (7) The assumption of a Cobb-Douglas production function implies that input costs are a fixed proportion of total revenues. This means that their log-deviations from steady state must be the same, as equations (4)–(7) show. The same applies to the intermediate good sector: f Qi t=f Zi t+i 1f xi 1,t+i 2f xi 2,t+i 3f xi 3,t+i 4g ni q,t, (8) f Px1 t+f xi 1,t=f Pqi t+f Qi t, (9) f Px2 t+f xi 2,t=f Pqi t+f Qi t, (10) f Px3 t+f xi 3,t=f Pqi t+f Qi t, (11) f Wi t+g ni q,t=f Pqi t+f Qi t. (12) We assume a CES production function in the primary commodity sectors j= 1, 2, 3, so the proportions of input costs are allowed to vary. The equilibrium equations in the 5
primary commodity sector Xi jin country i2{1, 2}are g Xi j,t=f Zi t+⇣i j⌘1 i xj Xi j Zini xj!1-i xj i xjg ni xj,t, (13) f Pei j t=f Pxj t+i xj-1 i xjf Zi t+1 i xjg Xi j,t, (14) f Wi t+1 i xjg ni xj,t=f Pxj t+i xj-1 i xjf Zi t+1 i xjg Xi j,t. (15) We assume that labor cannot move across countries, only across sectors within each country. That implies the following market-clearing condition for labor in country i2{1, 2} : 0=ni cg ni c,t+ni qg ni q,t+ni x1g ni x1,t+ni x2g ni x2,t+ni x3g ni x3,t. (16) The market-clearing condition for labor in country 3 is similar, with the exception that labor is not used in the production of primary commodities: 0=n3 cg n3 c,t+n3 qg n3 q,t. (17) Finally, the following market-clearing conditions must hold in equilibrium for the tradable goods and bond holdings: q1 1g q1 1,t+q2 1g q2 1,t+q3 1,tg q3 1,t=Q1f Q1 t, (18) q1 2g q1 2,t+q2 2g q2 2,t+q3 2,tg q3 2,t=Q2f Q2 t, (19) q1 3g q1 3,t+q2 3g q2 3,t+q3 3,tg q3 3,t=Q3f Q3 t, (20) x1 1f x1 1,t+x2 1f x2 1,t+x3 1,tf x3 1,t=X1 1g X1 1,t+X2 1g X2 1,t+X3 1g X3 1,t, (21) x1 2f x1 2,t+x2 2f x2 2,t+x3 2,tf x3 2,t=X1 2g X1 2,t+X2 2g X2 2,t+X3 2g X3 2,t, (22) x1 3f x1 3,t+x2 3f x2 3,t+x3 3,tf x3 3,t=X1 3g X1 3,t+X2 3g X2 3,t+X3 3g X3 3,t, (23) f B1 t+f B2 t+f B3 t=0. (24) 6
The equations above represent a system of 64 equations with 63 variables. Walras’s law implies that one equation is redundant, so we drop the budget constraint in country 3 to compute the simulations. Note that we have three state variables, B1 , B2 , and B3 , and three expectation equations represented by the Euler equation (2). Finally, we need to describe the stochastic processes of the productivities in countries 1 and 2, f Z1 t and f Z2 t , and endowments of primary commodities in country 3, g X3 1,t , g X3 2,t , and g X3 1,t . We assume the following (stationary) autoregressive processes: ln (Z1 t)=(1-⇢z1)ln (Z1)+⇢z1ln (Z1 t-1)+"z1 t, ln (Z2 t)=(1-⇢z2)ln (Z2)+⇢z2ln (Z2 t-1)+"z2 t, ln (X3 1,t)=(1-⇢x3 1)ln (X3 1)+⇢x3 1ln (X3 1,t-1)+"x1 t, ln (X3 2,t)=(1-⇢x3 2)ln (X3 2)+⇢x3 2ln (X3 2,t-1)+"x2 t, ln (X3 3,t)=(1-⇢x3 3)ln (X3 3)+⇢x3 3ln (X3 3,t-1)+"x3 t, where the vector of innovations ⇥"z1 t,"z2 t,"x1 t,"x2 t,"x3 t⇤ is normally distributed with zero mean and arbitrary covariance matrix. Variables without time subscripts represent long-run means. Complete markets The linear system characterizing the equilibrium in the economy under complete markets is similar to the one described above. The difference is that we can drop the budget constraints, and we replace the Euler equations by the following (perfect) risk-sharing conditions: f C2 t-f C1 t=f Pc1 t-f Pc2 t, (25) f C3 t-f C1 t=f Pc1 t-f Pc3 t. (26) In this case, we have a system of 59 equations and 58 variables, without any endogenous state variables or expectation equations. 7
Financial autarky The linear system characterizing the equilibrium of the economy under financial autarky is also similar to the cases above. The difference from the complete markets economy is that we replace the (perfect) risk-sharing conditions for the following zero trade balance conditions for country i2{1, 2}: 0=Pq1⇣Q1-q1 1⌘f Pq1 t+Pq1Q1f Q1 t-Pq1q1 1g q1 1,t-Pq2q1 2f Pq2 t-Pq2q1 2g q1 2,t-Pq3q1 3f Pq3 t -Pq3q1 3g q1 3,t+Px1⇣X1 1-x1 1⌘f Px1 t+Px1X1 1g X1 1,t-Px1x1 1f x1 1,t+Px2⇣X1 2-x1 2⌘f Px2 t(27) +Px2X1 2g X1 2,t-Px2x1 2f x1 2,t+X1 3g X1 3,t-x1 3f x1 3,t, 0=-Pq1q2 1f Pq1 t-Pq1q2 1g q2 1,t+Pq2⇣Q2-q2 2⌘f Pq2 t+Pq2Q2f Q2 t-Pq2q2 2g q2 2,t-Pq3q2 3f Pq3 t -Pq3q2 3g q2 3,t+Px1⇣X2 1-x2 1⌘f Px1 t+Px1X2 1g X2 1,t-Px1x2 1f x2 1,t+Px2⇣X2 2-x2 2⌘f Px2 t(28) +Px2X2 2g X2 2,t-Px2x2 2f x2 2,t+X2 3g X2 3,t-x2 3f x2 3,t. Again, we have a system of 59 equations and 58 variables, without any endogenous state variables or expectation equations. B.2 Computation of the steady state equilibrium Variables remain constant in steady state, so we suppress time subscripts. We assume that bond holdings are zero; that is, B1=B2=B3= 0. We normalize the price of primary commodity X3 to one, Px3= 1, and iterate on the prices of intermediate goods and primary commodities [Pq1,Pq2,Pq3,Px1,Px2]. Given a guess for the vector [Pq1,Pq2,Pq3,Px1,Px2] , we can compute the other prices and allocations in the economy. We start with country 1. From the cost-minimization problem of the firms, perfect competition implies that the prices of the final good Pc1 , intermediate good Pq1 , and primary commodities Px1 , Px2 , and Px3 are equal to their respective marginal 8
costs: Pc1=⇣Z1⌘-1 Pq1 ↵1 1!↵1 1 Pq2 ↵1 2!↵1 2 Pq3 ↵1 3!↵1 3 W1 ↵1 4!↵1 4 , (29) Pq1=⇣Z1⌘-1 Px1 1 1!1 1 Px2 1 2!1 2 Px3 1 3!1 3 W1 1 4!1 4 , (30) Px1=⇣Z1⌘-1⇣1-1 1⌘⇣Pe1 1⌘1-1 x1+1 1⇣W1⌘1-1 x11 1-1 x1, (31) Px2=⇣Z1⌘-1⇣1-1 2⌘⇣Pe1 2⌘1-1 x2+1 2⇣W1⌘1-1 x21 1-1 x2, (32) Px3=⇣Z1⌘-1⇣1-1 3⌘⇣Pe1 3⌘1-1 x3+1 3⇣W1⌘1-1 x31 1-1 x3. (33) Given the vector of prices for the tradable goods, we use equation (30) to solve for the wage W1 . With the wage and price of intermediate goods, we solve for the price of the final good Pc1 using equation (29) and for the price of the endowments of primary commodities using equations (31)–(33). Next, we compute the allocations. If we assume that B1= 0 in steady state, consumption C1is directly determined by the budget constraint: C1=W1 Pc1N1+Pe1 1 Pc1e1 1+Pe1 2 Pc1e1 2+Pe1 3 Pc1e1 3. (34) With prices and total consumption, we can use the optimality conditions in the final good sector to compute its input choices: q1 1=↵1 1 Pc1 Pq1C1, (35) q1 2=↵1 2 Pc1 Pq2C1, (36) q1 3=↵1 3 Pc1 Pq3C1, (37) n1 c=↵1 4 W1 Pq1C1. (38) 9
Given that the supply of the endowment of natural resources is fixed, we solve for the production of primary commodities X1 j and its labor inputs using the respective optimality conditions in the primary commodity sector j=1, 2, 3: X1 j=e1 j 1-1 j Pe1 j Pxj!1 xj⇣Z1⌘1-1 xj, (39) n1 xj=1 j✓Pxj W1◆1 xj⇣Z1⌘1 xj-1X1 j. (40) The labor input in the production of the intermediate good sector Q1 is determined by the market-clearing condition for labor in Country 1: n1 q=N1-⇣n1 c+n1 x1+n1 x2+n1 x3⌘. (41) Finally, we solve for the production of the intermediate good Q1 and its inputs of primary commodities x1 1 , x1 2 , and x1 3 , using the optimality conditions in the intermediate good sector: Q1=W1 Pq1 n1 q 1 4 , (42) x1 1=1 1 Pq1 Px1Q1, (43) x1 2=1 2 Pq1 Px2Q1, (44) x1 3=1 3 Pq1 Px3Q1. (45) Given the vector of prices for the tradable goods, we use the same procedure as above to compute the allocations and prices in countries 2 and 3, noting that country 3 receives exogenous endowments of primary commodities. After computing the production of primary commodities and intermediate goods in each country and their demand in the production of intermediate and final goods, we can check whether their market-clearing 10
conditions are satisfied. The algorithm iterates on the prices of the tradable goods until they are. B.3 Chain-weighted real GDP and productivity shocks In this appendix, we show that the chain-weighted real GDP in country 1 is proportional to its productivity shock up to a first-order approximation. The same applies to country 2. To simplify the exposition, we define GDP1 Pt1Yt2=GDPc,1 Pt1Yt2 +GDPq,1 Pt1Yt2 +GDPx1,1 Pt1Yt2 +GDPx2,1 Pt1Yt2 +GDPx3,1 Pt1Yt2(46) GDPc,1 Pt1Yt2 =Pc1 t1C1 t2-Pq1 t1q1 1,t2-Pq2 t1q1 2,t2-Pq3 t1q1 3,t2(47) GDPq,1 Pt1Yt2 =Pq1 t1C1 t2-Px1 t1x1 1,t2-Px2 t1x1 2,t2-Px3 t1x1 3,t2(48) GDPx,1 Pt1Yt2 =Px1 t1X1 1,t2, (49) GDPx,2 Pt1Yt2 =Px2 t1X1 2,t2, (50) GDPx,3 Pt1Yt2 =Px3 t1X1 3,t2. (51) GDP1 Pt1Yt2 is a measure of value added in country 1. It is defined as the sum of value added in the final good, intermediate good, and primary commodity sectors using prices from period t1 and quantities from period t2 . For example, nominal GDP in Country 1 in period tis equal to GDP1 PtYt. Let RGDP1 denote the chain-weighted real GDP in country 1, the measure of real GDP reported in the data. It evolves according to RGDP1 t RGDP1 t-1 = GDP1 PtYt GDP1 PtYt-1!1 2 ⇥ GDP1 Pt-1Yt GDP1 Pt-1Yt-1!1 2 . (52) Taking a first-order approximation of equation (52) around the steady state, we reach 2✓^ RGDP1 t- ^ RGDP1 t-1◆= ^ GDP1 PtYt- ^ GDP1 PtYt-1+ ^ GDP1 Pt-1Yt- ^ GDP1 Pt-1Yt-1, (53) 11
where f Xtdenotes the log-deviation of variable Xfrom its steady state level in period t. Using equations (46)–(51), we can decompose each term in the right-hand-side of equation (53) into GDP1 ^ GDP1 Pt1Yt2 =GDPc,1 ^ GDPc,1 Pt1Yt2 +GDPq,1 ^ GDPq,1 Pt1Yt2 +GDPx1,1 ^ GDPx1,1 Pt1Yt2 +GDPx2,1 ^ GDPx2,1 Pt1Yt2 +GDPx3,1 ^ GDPx3,1 Pt1Yt2, (54) GDPc,1 Pc1C1 ^ GDPc,1 Pt1Yt2 =f Pc1 t1+g C1 t2-Pq1q1 1 Pc1C1g Pq1 t1-Pq1q1 1 Pc1C1g q1 1,t2-Pq2q1 2 Pc1C1g Pq2 t1-Pq2q1 2 Pc1C1g q1 2,t2 -Pq3q1 3 Pc1C1g Pq3 t1-Pq3q1 3 Pc1C1g q1 3,t2, (55) GDPq,1 Pq1Q1 ^ GDPq,1 Pt1Yt2 =g Pq1 t1+g Q1 t2-Px1x1 1 Pq1Q1g Px1 t1-Px1x1 1 Pq1Q1g x1 1,t2-Px2x1 2 Pq1Q1g Px2 t1-Px2x1 2 Pq1Q1g x1 2,t2 -Px3x1 3 Pq1Q1g Px3 t1-Px3x1 3 Pq1Q1g x1 3,t2, (56) GDPx1,1 Px1X1 1 ^ GDPx1,1 Pt1Yt2 =g Px1 t1+g X1 1,t2, (57) GDPx2,1 Px2X1 2 ^ GDPx2,1 Pt1Yt2 =g Px2 t1+g X1 2,t2, (58) GDPx3,1 Px1X1 3 ^ GDPx3,1 Pt1Yt2 =g Px3 t1+g X1 3,t2. (59) where variables without time subscripts, such as GDPc,1 , denote steady state levels. Our goal is to simplify the equations above using the equilibrium equations described in Section 12
Figure 4: Homogeneous commodity sectors in countries 1 and 2 (b) Primary commodity prices 0 10 20 30 40 50 60 70 80 90 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 20 25 30 35 40 0.5 0.6 0.7 0.8 0.9 1 0 10 20 30 40 50 60 0.5 0.6 0.7 0.8 0.9 1 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 19
Figure 5: Heterogeneous commodity sectors in countries 1 and 2 (a) Real exchange rate and relative consumption 0 5 10 15 20 25 30 0.5 0.6 0.7 0.8 0.9 1 0246810 0.5 0.6 0.7 0.8 0.9 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 20
Figure 5: Heterogeneous commodity sectors in countries 1 and 2 (b) Primary commodity prices 0 10 20 30 40 50 60 70 80 90 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 20 25 30 35 40 0.5 0.6 0.7 0.8 0.9 1 0 10 20 30 40 50 60 0.5 0.6 0.7 0.8 0.9 1 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 21
Figure 6: Lower elasticity of substitution in commodity production (x=0.65) (a) Real exchange rate and relative consumption 0 5 10 15 20 25 30 0.5 0.6 0.7 0.8 0.9 1 0246810 0.5 0.6 0.7 0.8 0.9 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 22
Figure 6: Lower elasticity of substitution in commodity production (x=0.65) (b) Primary commodity prices 0 10 20 30 40 50 60 70 80 90 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 20 25 30 35 40 0.5 0.6 0.7 0.8 0.9 1 0 10 20 30 40 50 60 0.5 0.6 0.7 0.8 0.9 1 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 23
Figure 7: Complete markets (a) Real exchange rate and relative consumption 0 5 10 15 20 25 30 0.5 0.6 0.7 0.8 0.9 1 0246810 0.5 0.6 0.7 0.8 0.9 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 24
Figure 7: Complete markets (b) Primary commodity prices 0 10 20 30 40 50 60 70 80 90 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 20 25 30 35 40 0.5 0.6 0.7 0.8 0.9 1 0 10 20 30 40 50 60 0.5 0.6 0.7 0.8 0.9 1 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 25
Figure 8: Financial autarky (a) Real exchange rate and relative consumption 0 5 10 15 20 25 30 0.5 0.6 0.7 0.8 0.9 1 0246810 0.5 0.6 0.7 0.8 0.9 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 26
Figure 8: Financial autarky (b) Primary commodity prices 0 10 20 30 40 50 60 70 80 90 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 20 25 30 35 40 0.5 0.6 0.7 0.8 0.9 1 0 10 20 30 40 50 60 0.5 0.6 0.7 0.8 0.9 1 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 27
Figure 9: Lower persistence of commodity shocks (⇢=0.95) (a) Real exchange rate and relative consumption 0 5 10 15 20 25 30 0.5 0.6 0.7 0.8 0.9 1 0246810 0.5 0.6 0.7 0.8 0.9 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 28