A. Commodity Export Shares

The first empirical task that we set out to do is to assess the size of the share of commodity exports in a typical EME. To answer this we assemble a large (unbalanced) annual panel using the World Bank’s Word Development Indicators (WDI) covering 189 countries between the years 1960 and 2013. For each country, the panel contains the share of three broad groups of commodities in total exports: agricultural, fuel and metals. We average the sum of these three shares across time to obtain country-specific commodity export shares. Finally we separate countries between 61 EMEs and 128 non-EMEs. The latter is also further subcategorized into 74 advanced and 54 low-income economies⁴.

The main descriptive statistics are reported in Table 1. The table documents the median export share across all groups of countries.⁵ It also displays Mann-Whitney tests for the equivalence between non-EMEs groups and EMEs, and Kruskal-Wallis for equivalence across all groups. The results in this Table allow us to define a first stylized fact:

- Stylized Fact 1: The share of commodities in total exports in the average EME is more than double that of advanced economies. While the median export share in EMEs is 25.7 percent, that in advanced is 11.2 percent. Furthermore, a Mann - Whitney test easily rejects equivalence between the two distributions at 1 percent significance level. It fails to reject that hypothesis when emerging economies are compared to low-income economies, but continues to accept it when EMEs are compared to non-EMEs, mainly due to the smaller number of observations for low-income countries relative to those for advanced economies. Kruskal-Wallis tests easily reject equivalence across these three groups of countries. This stylized fact is robust to two alternative measures of the relative importance of commodities: the gross and net share of commodity exports to GDP (see Appendix).

B. Cyclicality

We now explore the cyclicality of commodity prices. For that purpose we use another, more refined, quarterly panel dataset of country-specific commodity price indexes for EMEs, between 1980.Q1 and 2014.Q4. The indices are constructed by averaging the time series of the international prices of 44 commodity goods using as constant weights the (country-specific) average shares of each of these commodities in total exports between 1999 and 2004. Formally, country n’s commodity price index in quarter t, $P_{n,t}^{Co},$, is defined as

where θ_i,n is the export share of commodity good i in total commodity exports by n, and $P_{t,i}^{Co}$ is the real USD spot price of commodity i in world markets. The share θ_i,n is computed by averaging the shares of commodity i in total commodity exports by n between the years 1999 and 2004, using United Nations’ Comtrade data. $P_{t,i}^{Co}$ is obtained by deflating the monthly commodity prices indices reported by the IMF’s Primary Commodity Price Database with the US consumer price index.⁶

We study the comovement of these indices with several country-specific macro variables. Formally, we compute the serial correlation $\rho \left(X_{n,t},P_{n,t+j}^{Co}\right)$ with j = −4, …, 4; where X is sequentially replaced by real output, real private consumption, real investment, trade balance, real exchange rates, and external interest rate premia faced by EMEs in world capital markets. The latter is proxied with JP Morgan’s EMBIG and CEMBI spreads. Unfortunately, imposing a minimum range of time series data to make the analysis valid reduces the sample to 13 EMEs.⁷ Each of the serial correlations is depicted on a subplot in Figure 2. Statistics reported are simple averages across the 13 countries (EME13) in the sample and confidence bands denote +/-1.5 standard deviations. We also report results for a subset of these countries that we call LAC4 (Brazil, Chile, Colombia, and Peru) which will be explored more closely later in the paper. We use the Hodrick-Prescott filter to extract the cyclical component of all variables.⁸ Inspecting the panels in this figure a second stylized fact can be defined:

- Stylized Fact 2: The country-specific commodity prices in EMEs are procyclical and lead the cycle of output, consumption and investment. In addition, they are countercyclical to real exchange rates and measures of external risk premia. The average contemporaneous correlation between the commodity price index and real GDP is about 0.5, and is slightly higher when the index is lagged one quarter (panel a, Figure 2). This correlation further increases to 0.6 if real income is computed by deflating GDP with the CPI (panel b). We present this alternative measure of real income because earlier works have demonstrated how real GDP tends to underestimate the changes in real domestic income following terms of trade movements (Kohli, 2004). The strong procyclicality and leading property of the indices remains when X is replaced with real consumption and investment (panels c and d). This explains why lagged values of the index are negatively correlated with the trade balance but commove contemporaneously, although the correlations are less tightly estimated (panel e).

Panel f in Figure 2 reveals that commodity price indices are negatively correlated with the real exchange rate, defined in terms of a basket of foreign goods. Hence increases in the indices are accompanied by real appreciations of the exchange rate. Lastly, panels g and h document a negative comovement between commodity price indices and interest rate spreads in EMEs. Such negative co-movement is actually stronger when considering only corporate risk premia, as proxy by the CEMBI. Thus, when commodity prices are high (low), the cost of issuing debt in foreign capital markets decreases (increases) for EMEs.⁹

C. Common Factors

A last dimension that we explore empirically is the presence of common factors in our measures of commodity prices indices across EMEs. The evidence is presented in Figure 3, which plots time series of the (cyclical) indices for each of the EMEs in our sample. More formal principal component analysis is also conducted but is presented in the Appendix to economize space. This evidence leads us to define the third and final stylized fact of this section:

- Stylized Fact 3: There is a preponderant role of common factors when accounting for the dynamics of commodity price indices across EMEs. This also extends to the dynamics of real gross domestic product. A look at the time series dynamics in Figure 3 reveals the presence of strong comovement in the country-specific commodity price indices for the 13 EMEs that we study. Principal component analysis further corroborates this: the first principal component accounts for as much as 78 percent of the variance in the indices across these EMEs. This does not occur mechanically because the commodity exporting profiles of the countries in our sample are similar. In fact they differ substantially.¹⁰ Instead, the main reason comes from the fact that the international prices of various commodity goods comove. To verify this, we extend the principal component analysis across the prices of the 44 commodity goods in our sample, which we group into five categories according to the Standard International Trade Classification (SITC, fourth revision)’s one level aggregation and also extract their cyclical component.^11,12 The first principal component accounts for 55 percent of the variance in commodity prices across the five SITC categories.

Finally, we also conduct principal component analysis on the cyclical component of real GDP across the 13 EMEs in our sample. The results point also in the direction of a strong common factor, virtually as strong as that in the commodity price indices: the first principal component accounts for 76 percent of the variance of economic activity.¹³

Taken together, the stylized facts presented in this section contribute to further improving the understanding of the main patterns exhibited by EMEs’ business cycles. On one hand they shed light on the strong comovement between aggregate macro variables in these economies and the prices of the commodities that they export. In addition, because the relative share of these commodities is shown to be large in these economies and movements in their price are largely exogenous, they can be regarded as an important driver of EMEs’ business cycles. The next section builds a dynamic general equilibrium model guided by these stylized facts where we formally articulate a mechanism by which exogenous changes in commodity prices turn into fluctuations in real economic activity.

A. Setup

The setup of our model is a multi-country version of the small open economy framework first developed by Mendoza (1991), and further analyzed by Schmitt-Grohé and Uribe (2003). We take five departures from such framework. First, we add a country-specific commodity sector that faces fluctuations in the price of the good it sells in international markets. These fluctuations are exogenous, as we assume the countries are small players in these markets. The commodity good is an endowment that is entirely sold abroad and the income generated accrues directly to households who own the sector. Second, there are foreign (f) and (country-specific) home (h) goods, which are imperfect substitutes when consuming them or using them to produce investment goods. Home goods are produced domestically using capital and labor and a random domestic productivity shock. Foreign goods are imported from the rest of the world. Third, there is a sector that produces investment goods using home and foreign goods as inputs. As in the standard framework, households in each EME can issue non state-contigent, one-period bonds in international financial markets. Such bonds will pay a premium over the world interest rate. Both the premia and the world interest rate are exogenous and stochastic, acting as two additional driving forces.

The structure with which we model commodity prices constitutes a fourth novelty of our framework. We model them with a dynamic factor structure that incorporates a latent common factor in addition to idiosyncratic shocks. This structure is intended to capture the strong comovement across EMEs in the data documented in the previous section. Fifth, the multi-country structure of our framework comes from jointly modelling a collection of N EMEs that interact with the rest of the world as small open economies. The sole source of comovement across these EME comes from shocks to the common factor in the prices of the commodity goods that they sell in international markets.¹⁴

There are four agents in each EME considered in the model: households, firms, investment goods producers, and the rest of the world (which does not include the other EMEs in the model). Households consume final goods, defined as a bundle of home and foreign goods; decide how much labor and capital supply to domestic firms; and issue bonds in foreign markets. They also purchase investment goods to replace depreciated capital and increase the net stock of capital for which they face capital adjustment costs. Besides income from the commodity sector, they receive profits from firms, as well as capital and labor income. Firms maximize profits, defined as the revenue from selling home goods net of costs from renting labor and capital from households. Home goods are produced with a standard neoclassical technology and sold either to households, investment good producers or the rest of the world. Investment goods producers use a technology that combines home and foreign goods. They later sell these goods to households for capital accumulation purposes. The fourth agent is the rest of the world. It provides funding for households at a stochastic premium over the world interest rate. It also demands home goods for its own consumption as a function of both their relative price and a price elasticity, as well as exogenous external demand shocks. Finally, it provides (foreign) goods that are imported by households for their own consumption or used as inputs by investment good producers.

In the following subsections we formally describe the actions by each of the agents in a representative j^th EME in the model. However, we omit the country index to simplify the notation and only use it when common and idiosyncratic variables interact. The full set of equilibrium and optimality conditions is included in the Appendix.

B. Households

Hence, the real exchange rate is defined in the model as the inverse of the consumption good’s price, ${\left(p_t^c\right)}^{-1}$.¹⁶

C. Production of h Goods

Firms in the domestic sector maximize profits, ξ_t, subject to a standard neoclassical production technology that uses capital and labor. Formally, the static optimization problem for domestic firms is

D. Investment

E. Market Clearing

F. Driving Forces

G. Equilibrium

Given initial conditions K_j,−1 and D_j,−1, and exogenous state-contingent sequences of idiosyncratic and common shocks $\left\{v_{j,t}^{Co},v_{j,t}^R,{\epsilon }_{j,t}^z,{\epsilon }_t^{f^{Co}},{\epsilon }_t^{R^{*}},{\epsilon }_t^{Y^{*}}\right\}$ in economy j, an equilibrium is a set of state-contingent allocations²²

and prices

such that, for all j′s EMEs in the sample, given the laws of motion of shocks:

1. The allocations solve the consumer’s problem given prices and the laws of motion for the capital stocks.

2. The allocations solve the firm’s problem given prices.

3. Markets clear for capital, labor, investment goods, and home goods.

H. A Commodity Price Shock: Inspecting the Mechanism

What happens in economy j after it receives an income shock following an exogenous increase in the price of the commodity good that it exports? A full-blown quantitative answer to this question will be given in the following sections when we take the model to data from emerging economies. At this point, however, it is instructive to describe, in a qualitative manner, the main mechanism at work.

Because the commodity sector is an endowment, real economic activity will only be affected in this economy insofar as the market of home goods is affected. Looking at a (log-linearized version) of the market clearing condition for this market:

where lower-case variables are log deviations from their steady state levels (x_t = ln (X_t/X)), reveals that economic activity will be affected by three distinct effects. A first effect is a demand channel by which households increase demand for home goods as an optimal response to the income shock, which will mainly depend on the intratemporal elasticity of substitution between h and f goods, η_c, the relative sizes of consumption and the commodity sector in steady state which defines the magnitude of the revenue shock. Such a demand channel will have real effects to the extent that it will boost the relative price of these goods, p^h, making it optimal for home good producers to increase production. This effect is illustrated in panel a. of Figure 4 by an outward shift in the demand curve for consumption of h-goods that takes the new equilibrium from point A to B.

A second effect operates via the market of new investment goods. The increased production of domestic goods raises the rental price of capital (panel b.) and pushes the demand for new investment goods by households increasing their price (panel c.). This generates a further outward shift in the demand curve for home goods from point B to C (panel a.). Here, again, the strength of this channel will mainly depend on the intratemporal elasticity of substitution between h and f goods in the production of investment goods, η_x, the relative sizes of investment in steady state, and the magnitude of the revenue shock.

A third and final effect comes from the fall in the demand for home goods by the rest of the world. This negative effect comes from the fact that these goods become relatively more expensive for foreigners. Its strength will mainly be a function of the price elasticity of foreign demand, ∊_j,e, and the relative size of (non-commodity) exports in steady state. Assuming that such a shock generates an inward shift in the demand curve for home goods that is not enough to counterbalance the previous two effects, as depicted in panel a. from points C to D, the net effect on real economic activity of the commodity price shock will be positive. In that case, the labor market will accommodate an increase in labor demand from home good producers (panel d).²³ This assumption will be later verified when the model is taken to the data. Importantly, note that this new equilibrium in the model will be one where the real exchange rate will appreciate, driven by the increase in the relative price of home goods, p^h. Thus, periods of booming commodity prices are characterized as episodes of real exchange rate appreciation. Note, however, that the opposite happens with productivity shocks. Indeed, a positive productivity shock in the home goods sector would bring about an outward shift in the supply curve, decreasing p^h, and causing a real depreciation.²⁴

The next couple of sections will take this model to the data of emerging economies with the main goal of quantitatively assessing the strength of this mechanism by which commodity price shocks lead to movements in real economic activity and compare it with alternative driving forces of the business cycle in these economies.

A. A Representative Group of EMEs

From the pool of 13 countries studied in Section 2, we pick a sample of four EMEs to estimate the model: Brazil, Chile, Colombia and Peru.²⁵ We do so mainly for two reasons. First, we want to have a reduced number of countries for tractability, while still keeping a pool that is both large enough and with sufficient heterogeneity in the production of commodities to pin down the common factors in the model. Second, as will be shown below, the calibration of the model’s steady state presents some further data requirements that are binding for several of the 13 countries studied in Section 2.

This pool of four economies is, nonetheless, representative of the type of economies modeled in our theoretical framework. The four countries are all well-known commodity exporters, with a median commodity export share of 35.4.²⁶ In addition, as depicted in Figure 2, this group of countries reproduces well the average cyclicality documented in the larger pool of 13 EMEs.²⁷

There is also strong evidence in favor of common factors affecting the macro dynamics in these four countries. The first principal component explains 81 and 67 percent of the variance in the commodity prices indices and real output across the four economies, respectively (see Appendix). Such numbers are even more supportive of the kind of common factors embedded in our model given that the commodity exporting profiles are fairly heterogenous and trade linkages are small across these four economies. The Appendix presents evidence on the average commodity export shares for these four countries. Brazil’s largest shares are soybeans and iron; Chile’s top two are copper and fish; Colombia’s two are oil and coal; and in Peru they are gold and copper. This little overlap between the commodities that these four countries export implies that the common factor in commodities does not come mechanically from these countries exporting the same type of commodity goods. Data on the low trade linkages between the four economies and their other trading partners is also presented. For example, Brazil’s exports to Chile, Colombia and Peru are, respectively, 0.2, 0.1, and 0.1 percent of output. In contrast, trade with its main trading partners is nearly twenty times that share (10.1 percent). Similar orders of magnitudes are observed for the other three countries.

B. Calibrating the Steady State of the Model

When assigning values to the parameters in the model, we follow a strategy that uses both calibration and formal estimation methods. A subset of the parameters in the model, in particular those that determine the steady state of the model, are either taken from previous studies or calibrated so as to match certain long-run ratios in the data. The latter is an important prerequisite to disciplining the quantitative exercise.

The calibrated parameters are summarized in Table 3. Table 4 presents the long-run ratios from the data used in the calibration and the model’s performance in matching them. We assume that, across all households in the economies considered, the risk aversion coefficient, σ, equals 2 and the Frisch elasticity, 1/γ_c, equals 1.72, in line with what is usually found in the business cycle literature. We assume an annual depreciation rate of capital, δ, of 10 percent across all countries, and calibrate the share of capital in the production function, α, to match the consumption and investment ratios to GDP in each country. Following Adolfson et al. (2007) we set the price elasticity of exports, ∊_j,e, to 1.18. The elasticities of substitution in the consumption and investment bundles, η_c and η_x, are set to 0.43 consistent with the cross country evidence of Akinci (2011) for a sample of developing economies. The parameters α_c and α_x are calibrated so that the steady state of the model reproduces the average import shares of consumption and investment goods in the data presented in Table 4. This disciplines the model as it assigns realistic relative weight to f and h goods.

The parameters $\overline{D}$ and $\overline{C}o$ are calibrated so as to match the long run shares of external debt and commodity exports. This is crucial as it disciplines the calibration of the model so that it delivers realistic income effects from shocks to interest rates and commodity price shocks. The share of non-commodity exports to GDP adjusts to satisfy the balance of payments identity. We assume that the steady state (gross annual) real world interest rate, $\overline{R^{*}}$, is 1.01 and we calibrate $\overline{z^R}$ to match the long-run value of the country risk premium for each economy. The discount factor, β, for each economy is pinned down as the inverse of the country’s real interest rate. We calibrate the scale parameter in the labor supply, ψ^c, so that labor in the steady state is set to 0.3. We normalize to 1 the steady state levels of productivity and foreign demand, ${\overline{z}}_j$ and $\overline{Y^{*}}$. Finally, we set the debt elastic parameter Ω_u to a minimum level, 0.001, that guarantees that debt is stationary.

The performance of the model in matching the key long-run shares is quite acceptable. By and large, the most important of all long-run ratios is the relative size of the commodity sector, which the model matches by construction in all four countries. As mentioned above, this guarantees that the size of the commodity price shocks will have realistic revenue implications for the countries considered. Likewise, for the propagation mechanism of a commodity price shock to be properly quantified, it is also of paramount importance that the model matches the relative size of home/foreign components in the total flows of consumption and investment of the countries considered,²⁸ as well as the relative size of total investment. As presented in Table 3, these dimensions are also among those that the model can perfectly match. Likewise, for the possible financial channel to be properly disciplined we make sure that the model reproduces the historical interest rate premia faced by these four countries as well as their historic debt-to-output ratio observed. The model cannot perfectly match the relative size of consumption, imports or exports. It nonetheless accomplishes a pretty satisfactory fit along those lines, as documented in Table 3,²⁹

C. Bayesian Estimation

The remaining subset of parameters are estimated using Bayesian techniques. They govern the short-run dynamics of the model, but not its steady state. Namely, the persistence of the six driving forces $\left\{{\varphi }_{Co},{\rho }_j^{Co},{\rho }_j^{z^R},{\rho }_{R^{*}},{\rho }_{Y^{*}},{\rho }_j^z\right\}$, the standard deviation of their shocks $\left\{{\sigma }^{f^{Co}},{\sigma }_j^{Co},{\sigma }_j^R,{\sigma }^{z^R},{\sigma }^{Y^{*}},{\sigma }_i^z\right\}$; the loading factors in the dynamic common factor $\left\{w_j^{Co}\right\}$,³⁰ and those that determine the cost of adjusting the capital stock {a_j}.

The estimation uses as observables quarterly time series data on seven variables from each of the four countries considered which have a direct mapping onto the variables in the structural model: real private consumption, real income, real investment, the trade balance to GDP ratio, the EM-BIG spread, the real effective exchange rate, and the commodity price index described in Section 2. Two additional observables are the 3-month real US TBills rate, and the United States’s real GDP, as proxies for the world interest rate and foreign aggregate demand, respectively. Thus, in total, the estimation uses 30 quarterly time series that are mapped onto the model’s counterpart through measurement equations.³¹ We add measurement errors in consumption, investment, the trade balance share, and the real effective exchange rate as they are the only variables that do not have a shock directly linked to them. The model is estimated on a balanced panel that covers the period 2000.Q1 to 2014.Q3.³² In the measurement equations the data are expressed in log-deviations from the Hodrick-Prescott trend and are measured in percent. Interest rates and EMBI are measured in logs of gross rates. As mentioned earlier, Kohli (2004) demonstrated how real GDP may underestimate the increase in real domestic income following terms of trade movements. We thus follow Kehoe and Ruhl (2008) by using real income instead of real GDP in the set of observables.

Fairly agnostic priors for the Bayesian estimation are used. We assume a Beta distribution with mean 0.5 and standard deviation 0.15 for the autoregressive coefficients in all six driving forces, implying a prior highest density region at 90 percent probability between 0.25 and 0.74. The prior distribution for a_j is Gamma with mean 0.5 and standard deviation 0.25, implying a large range for possible values of the parameter that governs the capital adjustment costs. Finally, we choose a rather conservative approach and center the prior distribution for $w_j^{Co}$ around zero (i.e., no common factor) using a normal distribution with standard deviation 0.015. In this case, the 90 percent bounds of the prior higher density region are (−0.025, 0.025).

A. Posterior Distributions and Common Factors

Posterior distributions of the estimated parameters are reported in Table 4.³³ Overall the posterior densities are considerably different from the loose priors that we choose, implying that the data contain information on the estimated parameters. In terms of the parameters associated with the driving forces, the most salient result comes from the somewhat persistent and highly volatile commodity shock processes estimated. The AR(1) coefficient in the common factor of commodity prices, ${\varphi }_{Co}$, has a posterior mean of 0.73. Moreover, shocks to this common factor display an estimated standard deviation, ${\sigma }^{f^{Co}}$, of 6.31 percent, at least an order of magnitude larger than those of the other global shocks, implying an important role for common factors in commodity prices. The AR(1) parameters associated with the idiosyncratic components in commodity prices, ${\rho }_j^{Co}$, are also high, in most cases higher than those for the other idiosyncratic forces. It is also worth noticing that the presence of commodity prices reduces both the persistence of the (country-specific) productivity processes and the size of their shocks relative to previous business cycle studies. The posterior mean estimates of ρ_z range between 0.39/0.40/0.51 in Brazil/Chile/Colombia to 0.68 for Colombia; while the estimated standard deviation σ^z ranges between 0.84/0.89 percent in Peru/Colombia to 1.32/3.39 for Brazil/Chile.

Another salient result comes from the estimated coefficient of the loading factor, $w_j^{Co}$, which captures the degree of transmission from movements in the common factor to the country-specific commodity price index, relative to the normalized value chosen for Colombia (equal to one). Chile displays the strongest response in relative terms, with the highest value for the posterior mode of $w_j^{Co}$, equal to 1.53. Peru and Brazil, in contrast, display relatively less resposnes with posterior modes for $w_j^{Co}$ equal to 0.89, and 0.53, respectively.

Another salient result comes from the estimated coefficient of the loading factor, $w_j^{Co}$, which captures the degree of transmission from movements in the common factor to the country specific commodity prices. Relative to the normalized (to one) value chosen for Colombia, Chile exhibits the highest value for this parameter with a mode of 1.53, followed by Peru (0.89) and Brazil (0.53).

Lastly, Figure 5 presents the time series evolution of the common factor, f^Co, which we back out from the Kalman filter smoothing evaluated at the posterior mean, together with the 90 percent distribution bands. It is tightly estimated and displays large and short-lived deviations from trend, particularly in the second half of the sample, post 2005, reaching sometimes near 30 percentages points–hence the allusion of a roller coaster ride that we make in the title of this paper. The increase in the years preceding the financial crisis was followed by a sharp fall during the crisis, and then a vigorous recovery within the next two years, only to fall once more in the last couple of years of the estimated period.

B. Business Cycle Drivers

We now use the estimated model to document the main business cycle drivers. Our first tool to accomplish this is the forecast error variance decomposition (FEVD) of real income across the four countries and at various forecast horizons, summarized in Table 5. Statistics are reported using posterior means. The upper left panel of the table presents the unconditional contribution of each of the six structural shocks in each country. The other three panels report FEVD conditioning the exercise at alternative forecast horizons of one, four, and twelve quarters. Commodity price shocks play a large role, only comparable to that of productivity shocks. Their share in the unconditional FEVD of income displays a median of 42 percent, ranging from 27.5 percent in Brazil, up to 77.1 percent in Chile, with Colombia (43.5) and Peru (40.4) in between the two. Moreover, in all four countries a considerable amount of this share is related to the common factor in commodity prices. The remaining three external shocks to foreign demand, the world interest rate and spreads do not account for a large share of output’s unconditional FEVD, with the exception of Brazil where interest rate shocks do play a role. The latter is related to the considerably large stock of external debt that Brazil has, relative to that in the other countries (see Table 3 again).

The role of commodity price shocks is positively related to the forecasting horizon in the FEVD decomposition exercise, as documented in the remaining panels of Table 5. When the FEVD is computed at only one quarter forecast horizon (upper right panel in Table 5) the share of output’s FEVD accounted by commodity price shocks decreases considerably, between 1/10 and 1/2 to the one computed unconditionally. The domestic productivity shock accounts for the highest share, while the contribution of the remaining four shocks continues to be very small. This is related to the strong persistence in commodity prices, as documented earlier.

In order to gauge when, historically, commodity price shocks have contributed the most to business cycles in the four countries considered, we decompose the observed time series of output into the structural shocks of the model. For expositional purposes, the results, reported in Figure 6, group the six shocks into four groups: (i) Productivity Shocks captures domestic TFP shocks (ε^z); (ii) Commodity Shocks includes both common factor and country-specific shocks to commodity prices $\left({\epsilon }^{f^{Co}},v_j^{Co}\right)$; (iii) Spread Shocks which alludes to the idiosyncratic risk premia shock $\left(v_{j,t}^R\right)$; and Foreign Shocks that puts together the world’s demand and riskless interest rate shocks $\left({\epsilon }^{Y^{*}},{\epsilon }^{R^{*}}\right)$. A common feature across the four decompositions is the preponderant role of only two groups: Commodity and Productivity Shocks, in line with the FEVD results above. The influence of the former group is more marked in the second half of the sample, with Chile being the exception where its influence is large throughout all the sample. This coincides with the period where the common factor exhibits the largest fluctuations, as discussed earlier in the context of Figure 5. The contribution is more marked in the two-year boom that preceded the world financial crisis, which abruptly turned negative during the 2009 recession when, again, these shocks’ contribution was large. Remarkably, these shocks turned positive in the recovery of the 2009 recession and helped all the countries recover from the recession. This helped counterbalance the negative contributions of domestic shocks, mostly in Brazil and Chile.

Table 6 presents further evidence on the role played by the structural shocks in the model from a historical perspective by running various counterfactual experiments on the historical decompositions. Starting from the second row, the table reports the standard deviation (S.D) of real income predicted by the model if one or several shocks are counterfactually turned off. The numbers are reported as percentage of the observed S.D reported in the first row of the table. One of the most salient findings is that the counterfactual S.D. falls considerably relative to the observed one when the two commodity price shocks are turned off (second to last row in Table 6). A fall that is only compared to the one observed when productivity shocks are shut down. In Peru, for instance, the counterfactual S.D when commodity price shocks are turned off is 69.6 percent of the observed one, followed by Chile (72.1), Colombia (75.4), and, to a lesser extent, Brazil (91.1). Similar qualitative results pointing to the preponderant role of commodity price shocks are obtained when all shocks are turned off except the two commodity price shocks (last row in Table 6). Chile stands out from the other countries where the counterfactual volatility actually increases above the observed one, implying that in this country other shocks have helped smooth out the massive volatility coming from commodity prices.³⁴

C. Quantifying the Mechanism

Earlier, when presenting the model, we gave a qualitative description of the mechanism in place following a commodity price shock. We now provide a quantification of this mechanism using the estimated model’s impulse response function (IRF) following an unexpected 1 S.D. common shock in commodity prices, which equates to assuming that the common factor increases by 6.3 percentage points above its long run mean. The IRFs of several of the variables in the model for all four countries are reported in Figure 7. Numbers reported are percentage deviations from steady state values.

Chile stands out as the country where more real effects following the shock are observed. This is consistent with the results from Tables 5 and 6 that showed the common factor to be particularly relevant for this country. Nonetheless, the other three countries exhibit non-trivial real effects as well.

The two upper panels in Figure 7 display the IRFs of two proxies of real economic activity: on the left we have plotted the quantities of the home good produced (Y_t), and on the right our proxy for real income as defined above, GDP_t/$p_t^c$. The production of home goods follows a hump-shape behavior, peaking between one tenth and a little over a half of a percentage point. The income shock triggered by the movement in commodity prices manifests as a rise of real income, which considerably increases on impact, ranging from 3 to 0.5 percentage points across all four countries and then steadily decreases.

The following panels in Figure 7 quantify the three effects that were described before. First, total private consumption increases, mainly driven by the boost in consumption of home goods. The latter increases between half and one full percentage point relative to its steady state. It is also noteworthy the strong persistence in the response of consumption, which is inherited from the long memory that commodity shocks display, as already mentioned.

The second effect, the response of investment, is also pronounced and hump-shaped. At its peak, approximately 4 to 5 quarters after the shock, it deviates between 0.5 and 3.5 percentage points from its long run value. As argued earlier, higher investment is driven to a large extent by the increase in the rental price of capital as home good producers demand more capital goods. The real rental return increases on impact between 10 and 100 basis points.

The third effect materializes as a fall in the non-commodity exports that ranges between one half and three percentage points. This is linked to the fact that the equilibrium relative price of home goods increases substantially, leading to an appreciation of the real exchange rate across countries between half and two percentage points. The contractionary effect of the fall in the non-commodities exports is, however, not large enough to offset the expansion driven by the first two effects. Thus home good production expands. In the process, the labor market expands as labor demand increases, driving up real wages.

A last feature that stands out in the set of IRFs is that the common factor shock has the ability to generate sufficient comovement across countries. We now turn to a more formal evaluation of the model’s performance.

D. Model’s Performance

Table 7 presents the cross correlation of real income across the four countries predicted by the model (numbers below the main diagonal) and compares it to the one observed in the data (numbers above). Two model-based correlations are presented: the one coming from the benchmark model with a common factor in commodity prices (”CF”), and another one coming from an alternative model where we turn off the common factor in commodity prices (”NCF”). To be precise, in the latter case we set $w_j^{Co}=0\forall j$ and reestimate the model.

The benchmark model does a good job when bringing the model closer to the observed cross-correlations of output in the data. The average cross correlation in the data is 0.45 while the one predicted from the benchmark model is 0.32. This is, to a very large extent, the work of the common factor in commodity prices. In the alternative model, where the only common drivers are world interest rates (R*) and external demand (Y*), the average cross correlation falls to virtually zero (0.02). This is corroborated by the considerable fall of the alternative model’s marginal likelihood relative to that of the benchmark model, reported in the bottom of Table 7.

Figure 8 presents further evidence on the model’s performance by focusing on the serial correlation of macro variables with commodity price indices within countries. Again, data and benchmark model-based statistics are compared. The model is capable of reproducing the procyclicality of commodity prices relative to income, consumption and investment processes. It also captures the trade balance to GDP process appropriately, and the countercyclicality of real exchange rates. Overall the fit is pretty acceptable considering that these moments were not used as specific targets in the estimation.

Finally, Table 8 documents the model’s performance along other second moments that are more standard in the literature and compares them to the data. The first two columns document the volatility of the main variables. The model does a proper job in accounting for the absolute and relative (to income) volatility of all the variables: a volatility of commodity prices that is close to four times that of income; that of investment and the real exchange rate that is nearly twice that of income; and that of consumption and the trade balance share that is less than that of income. The model also replicates in a satisfactory way the moderately high serial autocorrelation of the series as well as their comovement with real income. In particular, it reproduces the strong positive comovement of commodity prices, investment and consumption with income, and the negative one observed for the real exchange rate.³⁵

A. Comparison with a SVAR

As a first robustness, we compare the results of our DSGE model in terms of the relevance of commodity price shocks as drivers of business cycles in emerging economies against those from a SVAR. As suggested in a recent contribution by Schmitt-Grohé and Uribe (2015), comparing SVAR and DSGE may be a good way to assess the performance of the DSGE when assigning a role to terms of trade fluctuations when explaining business cycles given that usually SVARs are believed to impose less structure in the data than DSGE do. Hence they “let the data speak” more freely. Their approach, however, does not look particularly at commodity price shocks as ours do.

The strategy we follow is simple. We first estimate the SVAR in Schmitt-Grohé and Uribe (2015) with data for the same four economies on which we estimate the DSGE model, except that we replace terms of trade in their SVAR with our measure of country-specific commodity price indices. Then we compare the results of each of the two models, SVAR and DSGE, when it comes to gauging the relevance of commodity price shocks. Formally, for each country, we estimate the VAR model:

and $x_t=\left[p_t^{Co},t{b}_t,y_t,c_t,i_t,re{r}_t\right]$, where $p_t^{Co}$ is the country-specific commodity price that we build, tb_t is the trade balance share, y_t is real income, c_t is real private consumption, i_t is real investment, and rer_t is the real exchange rate; u_t is a 6x1 vector with mean zero and variance-covariance matrix Σ, and A is a 6x6 matrix of coefficients. Additionally, we impose the same two identifying restrictions in Schmitt-Grohé and Uribe (2015). First, we assume that $p_t^{Co}$ is exogenous and that it follows an AR(1) process, thus the off-diagonal elements of the first row of A are zero, a_1j = 0 for j = 2,6; where a_1j denotes the element (i, j) of the matrix A. Second, we assume that u_t = Π∈_t, where Π is a 6x6 matrix and ∊_t is a 6x1 vector of white noise mean zero and identity variance-covariance matrix. Thus, Σ = ΠΠ′. Also following this work, we pick Π to be the lower-triangular Cholesky decomposition of Σ. The SVAR is estimated with filtered quarterly data for each of the four countries on which we estimate the DSGE model, in the same sample period.

The results from the comparison between the two models are gathered in Figure 9 and Table 9. Figure 9 plots the time series of y_t in the data against the predicted series for this variable from the DSGE and the SVAR models. The predicted time series for each model are obtained by recovering the history of structural shocks in commodity prices and simulating both models using only these shocks. Thus, they are the predicted time series by the two models if only commodity shocks had been realized. Table 9 presents some further comparison between the two models in terms of the unconditional variance decomposition of output explained by shocks to $p_t^{Co}$, among others.

The main result coming out of this evidence is that, while not identical, the implications of the SVAR are aligned with those from the DSGE in that they also point to a considerable role of commodity price shocks. In the SVAR, the mean/median share of shocks to $p_t^{Co}$ in the unconditional variance of output across the four countries is 49/50 percent, while that from the DSGE is 47/42 percent. Some differences remain nonetheless. The predicted share in Brazil (15) and Chile (53) by the SVAR are lower than their DSGE counterparts, (28 and 77, respectively), while in Colombia they are pretty much aligned (47 and 44, respectively), and in Peru the SVAR predicted share is 80 percent, twice that of the DSGE.

The resemblance between the two models increases when the predicted time series from the two models using only $p_t^{Co}$ shocks are compared, as can be seen from Figure 9, particularly during the second half of the sample. The median correlation between the two predicted series is equal to or above 0.9 for all countries but Chile (panel E in Table 9). In the latter case, however, the DSGE model tracks much more closely the observed data than the SVAR (panel D). Furthermore, the mean standard deviation of the simulated time series from the SVAR, relative to that in the data, is 67 percent while that of the DSGE model is 62 percent (panel B). Lastly, we also conduct the opposite experiment, where all shocks but those from commodities are used to simulated both models (panel C). In this case, again, both models continue to yield very close results.

Overall, the results point to the SVAR being consistent with our benchmark results derived from the DSGE in that commodity prices account for a large part of output fluctuations in EMEs. This contrasts with the results from Schmitt-Grohé and Uribe (2015) who find that only a median share of 10 percent of output’s variance can be associated with terms of trade shocks. While there could be several reasons why our results differ from theirs, we think a good place to start is the link between commodity prices and terms of trade. This clearly goes beyond the scope of this paper so we postpone it for future research.³⁶

B. Countercyclical Spreads

To keep the analysis simple and the transmission mechanism of a commodity shock as tractable as possible, the benchmark model assumed the simplest structure for risk spreads as AR(1) processes (see Eq. 20). However, spreads may react to country fundamentals as well, and vice versa. As argued by the seminal works of Neumeyer and Perri (2005) and Uribe and Yue (2006), this may generate an amplification mechanism for real shocks. In this subsection we follow these works and extend the benchmark framework to allow explicitly for such interaction between country fundamentals and spreads. We do so by modifying the model in two dimensions. First, the risk premia process is now allowed to be affected by country fundamentals, in the form of TFP and commodity prices. Formally, Eq. (20), in log deviations, becomes now:

where a hat, “^”, denotes log deviations from steady state values; and $\left\{{\eta }_j^z,{\eta }_j^{Co}\right\}$ govern the degree of responsiveness of spreads to expected deviations of productivity and commodity price indices from their long-run values. The inclusion of TFP in (23) is not new and follows Neumeyer and Perri (2005). What is novel is the inclusion of (expected) changes in commodity prices. This captures the idea that commodity prices contain information on the creditworthiness of the borrower EME to the extent that they are a determinant of its repayment capacity. Thus expectations of future commodity prices may determine current’s risk premium.

Evidently, Eq. (23) models risk premia in a reduced form and is not derived from first principles. A more complete model of the determination of fluctuations in country risk and their interaction with commodity prices is beyond the scope of this paper because our main goal is to analyze the extent to which this interaction matters for business cycles. There is, nonetheless, both theoretical and historical evidence of this link. Calvo and Mendoza (2000) link volatility in financial conditions for EMEs in world markets to the cyclicality of their terms of trade and other fundamentals in the context of informational frictions where uninformed investors cannot extract information from prices but rather do so from noisy information about specialists’ trades. In a historical context, Eichengreen (1996) documented that during the crash of 1929 the sharp drop in the price of Brazilian coffee led foreign bankers to stop extending loans to Brazilian borrowers. And Min et al. (2003) found that improved terms of trade are associated with lower yield spreads to the extent that such improvements imply an increase in export earnings and better repayment capacity.³⁷

The second modification to the model aims at capturing the other direction of the linkage: from spreads to economic activity. We do so following the literature by introducing a working capital constraint that creates a direct supply-side effect of changes in spreads, and hence in interest rates, on the demand for labor by home-good producers. Formally, this is done by assuming that the profit function of the firm is now:

We take this modified model to the data including the three new parameters per country, ${\eta }_j^z,{\eta }_j^{Co}$, and ψ_j, in the estimation. The posterior results are presented in the Appendix. We report the unconditional FEVD for output in the top-left corner of Table 10. The most interesting result is that in three of the four countries (Brazil, Colombia, and Peru) the share of variance associated with commodity prices raises relative to the benchmark case presented in the upper-left panel of Table 5. This is related to the fact that the estimated coefficients ${\eta }_j^{Co}$ and ψ_j are significantly different from 0. The share in Chile is slightly reduced, but continues to be the largest of all countries. Overall, this provides evidence in favor of the theories that link commodity prices to spreads and see the latter as a propagation mechanism for commodity price fluctuations.³⁸

C. Correlated External Driving Forces

In this subsection we relax the assumption made in the benchmark case that external driving forces are uncorrelated. In particular, we now allow for the common factor in commodity prices, $f_t^{Co}$, to be correlated with external demand, $Y_t^{*}$. The assumption of uncorrelated forces in the benchmark case is tenable insofar as the primitive shocks to the common factor in commodity prices are driven by, e.g., demand shocks that stem from one region, say China, while external demand for non-commodities produced in EMEs is coming from a separate region, say the United States. Still, one could also argue that demand shocks in the United States may also impact market equilibrium prices in commodities, thus calling for an approach that takes into account a correlation between these two forces.

Formally, we model this by modifying the stochastic processes for these two driving forces, (21) and (14), as

and $\left\{{\epsilon }_t^{Y^{*}},{\epsilon }_t^{f^{Co}}\right\}\sim N\left(0,1\right)$. This simple identification strategy assumes that primitive shocks to external demand may have a contemporaneous effect on commodity prices, governed by the parameter ${\sigma }^{Co,Y*}$, but not vice versa. This parameter is included in the set of estimated parameters in the modified model.

We report the unconditional FEVD for output in the top-right corner of Table 10. Posterior results are presented in the Appendix. The main result is that the large share of commodity price shocks remains, relative to the benchmark case. There is indeed evidence that the two forces are correlated, i.e. ${\sigma }^{Co,Y*}$ is estimated to be positive and statistically significant (with a posterior mean of 0.021), and the share associated with external demand shocks increases to an average of 5.5 percent. While this is still a moderate share, it is nonetheless a considerable increase relative to the benchmark case where the average share of these shocks was only one tenth of a percentage point. Lastly, there is also an improvement in the modified model’s overall fit judging by the increase in the marginal likelihood relative to the benchmark case.

D. Absence of Commodity Shocks

We now explore what happens if commodity shocks are turned off in the benchmark estimation. This case is interesting as the reduced model becomes much similar to the benchmark small open economy RBC model. Here, again for the sake of space, we document only the FEVD of output in bottom left panel of Table 10 and the marginal likelihood of the reduced model and report in the Appendix the posterior results as well as other second moments generated by the model.³⁹

Two results stand out. First, in three of the four countries the overwhelming share of output’s variance is now explained by TFP shocks. The exception is Brazil, where the role of commodity shocks is not replaced by TFP shocks as in the other three countries, but by interest rate shocks. We believe these results reconcile our results with those coming from previous works on business cycles of emerging economies where TFP and interest rate shocks were at center stage.

The second result is the large fall in the model’s performance, measured by its marginal likelihood, relative to the benchmark. It drops from 4530.8 to 4410.6. The Appendix reports the model’s fit in terms of second moments. A noticeable failure of this reduced model is the fact that it fails to reproduce the negative comovement between the real exchange rate and real income observed in the data. Instead it counterfactually predicts that expansions (contractions) in economic activity are accompanied by real exchange rate depreciations (appreciations). As explained in the context of Figure 4, positive productivity shocks in the home goods sector would bring about an outward shift in the supply curve of home goods, decreasing p^h, and causing a real depreciation.

E. Alternative Dynamic Factor Models

A choice made in the estimation strategy of the benchmark model is the inclusion of the parameters of the dynamic factor structure $\left\{{\varphi }_{Co},{\rho }_j^{Co},{\sigma }^{f^{Co}},{\sigma }_j^{Co},w_j^{Co}\right\}$ in the full set of parameters from the DSGE model that are estimated using full-information methods. As argued before, this choice allows the structural model to identify country-specific, commodity-related, revenue shocks via the idiosyncratic component of the commodity process. This choice, however, entails a tradeoff as it constrains the information on commodity prices used to only the sample period where the DSGE model is estimated, after the year 2000. One might also wonder how the estimation of the dynamic factor model would be if it were done outside the rigid structure imposed by the DSGE on the data.

In this subsection we undertake several extensions that relax this initial choice. First, we estimate the dynamic factor model (DFM) structure, (14) - (16), in isolation from the structural model, using only data from country-specific commodity price indices. This allows us to use data on commodity prices that goes as far back as 1980 when our time series on single commodity goods prices begin. For this case we also consider using the full range of 13 EMEs in our empirical analysis. We also study the case of only the 4 countries studied in the DSGE model, starting the estimation in 1980 and 2000.⁴⁰

The estimated common factor for each of these alternative cases, together with the benchmark case, that we reproduce for comparison, are reported in Figure 10. The most noticeable result that can be drawn from this figure is that all robustness cases track down pretty well the common factor estimated in our benchmark estimation. Another noticeable result is that the volatility exhibited in the post-2005 subperiod continues to stand out even when one looks at a longer historical period.

F. Alternative Filtering

In the empirical analysis of Section 2, as well as in the estimation of the structural model, we detrend the data using a Hodrick-Prescott filter. We do so in order to keep the analysis within a business cycle frequency. However, as is well known, results may differ depending on the filter used when detrending the data. In this subsection we assess the sensitivity of our results when using simple growth rates as alternative detrending method. For the sake of space, the Appendix reproduces the same set of stylized facts as those reported in Figure 2, and the bottom-right panel in Table 10 reports the results of the FEVD of output from the structural model when the observable data used in the estimation are on growth rates.⁴¹

The stylized facts remain strongly robust to the change in filtering methodology. Commodity price indices continue to correlate vigorously with the other macro variables considered. Likewise, the results of the FEVD derived from the structural model continue to point to a preponderant role of commodity price shocks as a key driving force of the business cycle in the economies considered. The only economy for which the share of variance drops relative to the benchmark case is Chile, although it continues to remain above half. In the remaining three countries the share associated with commodity price shocks increases relative to the benchmark results. The median share of output explained by commodity shocks is now 68.1 percent. Thus, if anything, the benchmark result in terms of the preponderant role of commodity price shocks for business cycles strengthens when considering an alternative data detrending technique.

G. Cyclical Production of Commodities: A Discussion

Arguably the assumption of an endowment flow of commodity goods in the model is not without loss of generality. Ideally a more complete model of an emerging economy would include production in this sector along other features associated to the economics of commodities like storage capacity, optimal management of inventories, foreign ownership of capital, monopolistic rents, speculation, etc.⁴² Yet we believe that such realistic features would likely make the analytical framework less tractable, and would obscure the main propagation channel that we think is the most important from a business cycle perspective: the revenue shock that comes with movements in the world markets of commodity goods.

Nonetheless, we think that further discussion about the validity of this assumption is warranted. Thus, in this subsection we present the available evidence regarding the cyclicality of commodity production over the business cycle and discuss its implications. Figure 11, panels (a) to (h), report the serial correlation between the volumetric production of the two most important commodities in each of the four countries considered in the estimation of the structural model with the international market price of each commodity. The sample period over which the correlations are computed is the same as the one used when estimating the structural model. The results indicate no systematic co-movement whatsoever between quantities and prices. Indeed, in most cases, commodity production does not react to changes in prices at business cycle frequencies.⁴³ A more formal analysis with the use of Granger-causality tests between the two variables reveals no causality in either direction (see Appendix). This not only provides evidence of the absence of a response of commodity production to changes in commodity prices, but also backs the assumption that these countries are price takers in international markets.

The remaining two subplots in Figure 11, (i) and (j), present further evidence related to the propagation mechanism of the revenue shock implied by the model. Subplot (i) reports the serial correlation between the simple average of the non-commodities GDP for the four countries studied in the structural estimation and their country-specific commodity price indices.⁴⁴ Subplot (j) looks instead at the nontraded GDP and its comovement with commodity prices across countries. Because constraints on data availability are less stringent for non-traded output, the latter is done for a wider pool of EMEs. Regardless of which of the two measures of real economic activity one looks at, there is a considerable comovement between them and country commodity price indices. This goes in line with the main prediction of the model’s propagation mechanism following a commodity shock: that economic activity, mainly the one that is unrelated to the commodity sector, comoves with commodity prices, driven by changes in real income which, in turn, come from exogenous fluctuations in those prices.

H. The Role of Fiscal Policy: A Discussion

A potentially important agent that is absent from the theoretical framework is the government, which may be the recipient of a large part of the revenue from commodity exports, either because it owns a stake in the commodity sector, or because it collects taxes levied on this sector.⁴⁵ This, in turn, may bear importance for the source of the propagation mechanism following a commodity price shock. Indeed, it would imply that government expenditure may be an important part of the channel through which the real effect propagates.⁴⁶ More generally, this possibility opens the door for the conduct of fiscal policy to become a crucial element. If policy is conducted with a fiscal rule, this may help dampen commodity shocks. On the other hand, absent a fiscal rule, governments may amplify the business cycle effects of those shocks.⁴⁷

We view the analysis, both positive and normative, of the role of fiscal policy in the face of commodity price fluctuations as an important topic that deserves a careful analysis, which goes well beyond the scope of this paper.⁴⁸ However, a simple first look at the data suggests that this mechanism does not have first order importance. This assertion is supported by the serial correlations reported in Figure 12 where, once more, we correlate country commodity price indices with economic activity across EMEs, except that this time we compare the results when such activity is measured with and without the flow of government expenditure. The left panel reports the results for LAC4, and the center panel reports results for a wider pool of 12 EMEs. The right panel directly computes the correlations between real government expenditure and commodity prices in the two sets of countries. Real government is not positively correlated with commodity prices, and real economic activity, if anything, marginally increases its comovement with commodity prices when public expenditure is removed.⁴⁹

It may be argued that the measures of government expenditure used above do not incorporate direct transfers from the government to households and that these can be an alternative mechanism for channeling resources from the commodity sector.⁵⁰ In this case, however, our model would be isomorphic to this case as households are the ultimate recipients of revenues from the commodity sector.