Feldstein–Horioka puzzles

European Economic Review 72 (2014) 98–112

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European Economic Review journal homepage: www.elsevier.com/locate/eer

Feldstein–Horioka puzzles Yanqin Chang a,n, R. Todd Smith b a Department of Business Administration, Gerald Schwartz School of Business, St. Francis Xavier University, Antigonish, Nova Scotia, Canada B2G 2W5 b Department of Economics, 8-14 Tory Building, University of Alberta, Edmonton, Alberta, Canada T6G 2H4

a r t i c l e in f o

abstract

Article history: Received 28 August 2013 Accepted 2 September 2014 Available online 22 September 2014

The high correlation between national saving and investment rates in advanced economies—the Feldstein–Horioka puzzle—has been referred to as the “mother of all puzzles.” Perhaps more puzzling is that for emerging economies saving–investment correlations tend to be significantly lower, though still positive. This deepens the Feldstein–Horioka puzzle because the mobility of capital is generally believed to be much lower in emerging economies than in advanced economies, and a country with less mobile capital should have a tighter relationship between local saving and investment rates. This paper develops a DSGE model that, without resorting to any real or financial friction, simultaneously explains these two aspects of the Feldstein–Horioka puzzle: positive saving–investment correlations in both advanced and emerging economies and significantly lower saving– investment correlations in emerging economies than in advanced economies. The main features of the model include long-run risk, an endogenous world interest rate, and crosscorrelations of national and global shocks. The findings hold for both quarterly time series and long-run averages. & 2014 Elsevier B.V. All rights reserved.

JEL classification: E210 F410 Keywords: Saving–investment correlations Feldstein–Horioka puzzle DSGE models

1. Introduction The high correlation between national saving and investment in advanced economies—the Feldstein–Horioka (FH) puzzle, first documented by Feldstein and Horioka (1980)—has been referred to as the “mother of all puzzles” (Obstfeld and Rogoff, 2000, p. 175). As Baxter and Crucini (1993) observe: One of the most stable regularities observed in the data is the fact that national saving rates are highly correlated with national investment rates, both in time-series analyses of individual countries and in cross sections in which each country is treated as a single data point. (Baxter and Crucini, 1993, p. 416) Even more puzzling perhaps is that saving–investment correlations for emerging economies tend to be significantly lower than for advanced economies, though still positive.1 This deepens the FH puzzle because the mobility of capital is generally believed to be lower for emerging economies and a country with a lower degree of capital mobility should arguably have a tighter relationship between saving and investment. This paper develops a DSGE model that, for both n

Corresponding author. E-mail addresses: [email protected] (Y. Chang), [email protected] (R.T. Smith). 1 Dooley et al. (1987) and Summers (1988) are the standard early references that document positive but smaller saving–investment correlations in emerging economies. See Coakley et al. (1998) for a review of empirical studies. See Bai and Zhang (2010) for a recent empirical confirmation of the FH puzzle and that the saving–investment correlation is higher in advanced economies. http://dx.doi.org/10.1016/j.euroecorev.2014.09.001 0014-2921/& 2014 Elsevier B.V. All rights reserved.

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quarterly time series and long-run averages, simultaneously explains these two features: positive saving–investment correlations in both advanced and emerging economies (the “FH1 puzzle”) and significantly higher saving–investment correlations in advanced economies than in emerging economies (the “FH2 puzzle”). While standard RBC-type open-economy models generally face more challenges matching data moments than their closed-economy counterparts (e.g. Backus et al., 1992), the FH1 puzzle is not in fact a challenge for these models, at least in time series data for a given country. Baxter and Crucini (1993) show that such models produce high saving–investment correlations. The intuition is that a positive transitory productivity shock raises current income more than permanent income and thus saving rises, while investment also rises to capture the temporarily higher return on capital. A limitation of their work is that its focus is on saving–investment correlations at high frequency (quarterly), whereas the FH puzzle is most often associated with co-movement in long-run averages (5 years or more). Moreover, while Baxter and Crucini's (1993) insight may be important for explaining the FH1 puzzle (at least in high frequency data), their standard RBC model is less helpful for understanding the FH2 puzzle. Their two-country model has complete markets, and the only possible difference between the two countries is their relative size. They show that the saving–investment correlation tends to be increasing in relative country size simply because the larger country behaves more like a closed-economy in which saving and investment must be equal. This argument may not be a full explanation for the FH2 puzzle because stage of economic development (rather than size of national economies) has been the relevant distinction in empirical studies. Some recent explanations of the FH puzzle emphasize external financial frictions (Castro, 2005; Bai and Zhang, 2010). National saving and investment will be more closely related when countries face external financial frictions (e.g. constraints on external borrowing). External financial frictions help explain the FH1 puzzle, but not the FH2 puzzle at least insofar as advanced economies face lower external financial frictions than emerging economies. Internal financial frictions (e.g. less efficient domestic capital markets) could, however, be helpful in explaining the FH2 puzzle. The reason is that if advanced economies have lower internal financial frictions (relative to emerging economies) then this will work in the direction of raising the relative saving–investment correlation, because a more efficient financial system will make it easier to translate domestic saving into domestic investment. We take a different approach. Our model contains three notable features. First, we build on recent work (e.g. Aguiar and Gopinath, 2007a, b; Neumeyer and Perri, 2005) that emphasize very different shock processes and associated macroeconomic dynamics in emerging small open economies from those in advanced small open economies. Our belief is that these differences might reasonably be expected to matter for saving–investment correlations. The specific modeling assumption we make is that technology shock processes may contain both transitory and trend shocks. Variations of this framework have been used to explain some of the most stubborn puzzles in economics, such as the equity premium puzzle and the real exchange rate puzzle (Bansal and Yaron, 2004; Colacito and Croce, 2010, 2011), but it has not been used in the FH literature. Aguiar and Gopinath (2007a) show that significant trend shocks help explain why emerging economies display strongly countercyclical trade balances, sudden stops in capital flows, and higher volatility of consumption, GDP, and the trade balance.2 It is noteworthy that these authors assume a constant world interest rate, whereas other authors (e.g. Chang and Fernandez, 2010; Uribe, 2012) have argued that long-run risk is less important and international interest rates more important for business cycle dynamics in emerging economies. This motivates the second notable feature of our model, namely, that the interest rate applicable to international lending is endogenously determined in a global DSGE model. The influence of the world interest rate on national economies is determined partly by the third notable feature of our model: national and global shocks are cross-correlated. Global shocks determine the behavior of the world interest rate, and the correlations between national and global shocks regulate co-movement between international borrowing costs and national economic shocks. Kose et al. (2003) find that all economies share a common component with the global economy, but this common component is larger for advanced economies. Recent work by Crucini et al. (2011) suggests that this common component may be due largely to common technology shocks. In our model, co-movement is driven precisely by this feature. This approach is consistent with the arguments of Neumeyer and Perri (2005) and Aguiar and Gopinath (2007b) that to explain emerging market economic dynamics, interest rates should be correlated with productivity shocks. Our main conclusion is that the model is consistent with both the FH1 and FH2 puzzles, both in quarterly data and in data averaged over long periods of time. The predominant role of transitory shocks in advanced economies, and trend shocks in emerging economies, is the major factor behind FH1 and FH2 in our model, but it is not the whole story. World interest rates, and thus the shocks underlying them, also play a role. There are two mechanisms at work here. First, higher volatility of global shocks/world interest rates lowers a SOEs saving–investment correlation. This is because national saving and investment respond oppositely to any independent movement of the world interest rate. Second, higher correlation of

2 It is tempting, but not necessarily valid, to associate strongly countercyclical trade balances with lower saving–investment correlations. Take a very simple example. Suppose we measure the cyclicality of the trade balance by cov½ððS  IÞ=YÞ; Y ¼ covðS=Y; YÞ  covðI=Y; YÞ. Suppose also that S ¼ αI, 0o α o 1. Thus, the smaller is α, the more countercyclical the trade balance is, but the saving–investment correlation is unity. If we instead used the correlation rather than the covariance in the first expression, the trade balance is again countercyclical but the saving–investment correlation is still unity. Similar examples can also be constructed to show that the variance of the trade balance does not necessarily contain precise information on saving–investment correlations. The point is that a model that explains second moment properties of trade balances in emerging economies versus advanced economies (e.g. Aguiar and Gopinath, 2007a) does not necessarily make specific predictions about saving–investment relationships in the two economies.

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global and national shocks raises a SOEs saving–investment correlation. The intuition can be illustrated with an example: If national shocks were identical to global shocks and thus their correlation is unity, this SOE will behave exactly the same way as the global economy does, including that saving and investment co-move perfectly. As advanced economies share a larger common component with the global economy than do emerging economies, they will also have higher saving–investment correlations. 2. Model 2.1. A small open economy There is a single good in the world economy (a two-good model is considered in Section 5). There are two possible representative SOEs we are concerned with, an emerging economy (EE) and an advanced economy (AE). Both of these representative SOEs have a negligible influence on the global economy. An SOE is indexed by i, where i A fEE; AEg, and the representative agent maximizes: 1

U i;t ¼ Et ∑ β j¼0

1γ j C i;t þ j

1γ

;

ð1Þ

where β denotes the subjective discount factor, and γ 40 is the coefficient of relative risk aversion. The representative agent owns the domestic capital stock, K i;t , and combines this with labor to produce the good. Labor supply is inelastic and normalized to unity.3 Output obeys the technology: Y i;t ¼ Z i;t ðAi;t Ni;t Þα K 1i;t α ¼ Z i;t Aαi;t K 1i;t α ;

ð2Þ

where Z i;t and Ai;t are referred to as transitory and trend shocks respectively. Specifically, denote z ¼ logðZÞ, then: zi;t ¼ ϕi zi;t  1 þ εzi;t ; where ε

is i.i.d. with zero mean and standard deviation σ   Ai;t log ¼ logðGi;t Þ ¼ g i;t ¼ ð1  ρi Þg i þ ρi g i;t  1 þ εgi;t ; Ai;t  1 z i;t

ð3Þ z i.

The shock Ai;t satisfies: ð4Þ

where g i is the unconditional mean growth rate of productivity, and εgi;t is i.i.d. with zero mean and standard deviation σ gi . Note that (4) defines a stochastic trend of the Solow residual. Both shocks are in general correlated with their global shock counterparts. While formally the shocks faced by a SOE are typically associated with technology shocks, it is reasonable to interpret them more broadly. Aguiar and Gopinath (2007a) explain this succinctly: While we use a standard real business cycle model, we do not claim that market imperfections are unimportant. The differences in the Solow residual processes between developed and emerging markets may well be a manifestation of deeper frictions in the economy. Shocks to trend output in emerging markets are often associated with clearly defined changes in government policy, including dramatic changes in monetary, fiscal, and trade policies. Chari et al. (2007), for instance, show that many frictions, including financial frictions, can be represented in reduced form as Solow residuals. From the perspective of private agents in our economy, these shocks appear as exogenous shifts in productivity. Our analysis provides support for models with frictions that are reflected in the persistence of Solow residuals rather than frictions that distort the response of investment and consumption to underlying productivity. (Aguiar and Gopinath, 2007a, pp. 72–73) Capital accumulation obeys:   I K i;t þ 1 ¼ Ψ i;t K i;t þ ð1  δÞK i;t ; K i;t

ð5Þ

where δ is the depreciation rate. The function Ψ captures capital adjustment costs, and is assumed to be increasing and concave. The resource constraint is Y i;t ¼ C i;t þI i;t þ NX i;t :

ð6Þ

Net exports determine the change in the SOEs international asset position. Countries may borrow or lend internationally by trading one-period bonds. These bonds play a vital role in consumption smoothing. The SOEs international net liability position is P i;t þ 1 Bi;t þ 1 ¼ NX i;t þBi;t ¼  ðY i;t  C i;t  I i;t Þ þBi;t ;

ð7Þ

3 The relative roles of trend and transitory shocks in emerging and advanced SOEs are found by Aguiar and Gopinath (2007a, b) to be invariant to whether labor supply is elastic or not, and thus for simplicity we assume the latter.

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where P i;t þ 1 is the bond price, and the borrowing cost is Ri;t þ 1 ¼ 1=P i;t þ 1 . We assume: Ri;t ¼ 1 þ r f ;t þ ψ ½expðB~ i;t  B~ i Þ  1;

ð8Þ

where r f ;t is the world net interest rate between period t  1 and t. The parameter ψ links the borrowing cost to the level of indebtedness. B~ i;t is normalized debt, B~ i;t ¼ Bi;t =Ai;t  1 , which adjusts debt for the size of the economy. The other term in the exponential function, B~ i , is the SOEs steady-state normalized debt level. Note that agents do not internalize the upward-sloping supply of foreign loans. The purpose of the debt-elastic interest rate in our model is purely technical: namely, this is one method to “close” models of SOEs, i.e. to make debt stationary in the linearized model (see Schmitt-Grohe and Uribe, 2003). 2.2. The world economy: co-movement, and the global interest rate Empirical work has shown that national economies share a common component with the world economy and that this common component is relatively less important—and purely local shocks more important—in emerging economies than in advanced economies (Kose et al., 2003). For our focus, co-movement between a national economy and the world economy will matter because of the associated co-movement between the world interest rate and national economic conditions. If the underlying shocks in the world economy are of the same structure as in our SOEs, then co-movement between a national economy and the world interest rate will be driven in large part by the covariances between national and global transitory and trend shocks. Solving the world economy model explicitly will enable us to compute correlations between national and world macroeconomic variables in the model which we then combine (see Section 3) with the corresponding data moments to inform our calibration of cross correlations of national and world shock processes. In a similar fashion, we estimate parameters of the world shock processes that will govern the volatility and persistence of the world interest rate. An alternative approach is to specify exogenously a global interest rate process. In Neumeyer and Perri (2005) the global interest rate is an AR(1) process estimated from U.S. interest rate data with shocks assumed to be independent of national shocks (in Aguiar and Gopinath (2007a, b) the world interest rate is constant). In principle, one could extend their specification to allow for correlations between world interest rate shocks and national technology shocks. Instead, we model the world economy directly and derive a world interest rate process from within this model. This approach identifies which variables are important for driving the global interest rate process and the parameters that govern co-movement between an SOE and the world economy. As discussed in Section 5, some aspects of the approach of Neumeyer and Perri (2005) might be worth considering in future work. The world economy model has tastes and technology analogous to our representative SOEs. The world economy is described by (1)–(5) plus: Y w;t ¼ C w;t þI w;t ;

ð9Þ

because of the restriction that the net foreign asset position must be zero for the world economy. 2.3. Solving the models We solve the world economy model and the SOE model using standard methods.4 First, we normalize variables to induce stationarity: for a variable X, we define X~ as the normalized variable: X~ t ¼ X t =At  1 . Second, the system of first-order conditions for the world economy and for an SOE is log-linearized around the non-stochastic steady state in the normalized variables: denote by x^~ the deviation of logðX~ t Þ from the non-stochastic steady state. Logarithms are not taken for debt and interest rates (see Uribe, 2012). Third, the equilibrium for an economy is computed from the linearized systems using the method of undetermined coefficients. To conserve space, we only present the main variables of interest. The solution for the equilibrium world interest rate has the following form: ^ r^ f ;t þ 1 ¼ prg g^ w;t þ prz z^ w;t þprk k~ w;t ;

ð10Þ

where x^ denotes the deviation from the steady state value, and the coefficients “pab ” are functions of the underlying parameters of the world economy model. Saving is defined in the model as S ¼ Y C, which is gross domestic saving (as Y is GDP), the same definition used by FH and the subsequent empirical literature. The solutions for saving and investment in a SOE have the form: ^ ^ ^ s^~ i;t ¼ Si;gi g^ i;t þ Si;zi z^ i;t þ Si;ki k~ i;t þ Si;bi b~ i;t þ Si;gw g^ w;t þ Si;zw z^ w;t þ Si;kw k~ w;t ;

ð11Þ

^ ^ ^ ^~ i i;t ¼ I i;gi g^ i;t þI i;zi z^ i;t þ I i;ki k~ i;t þI i;bi b~ i;t þ I i;gw g^ w;t þ I i;zw z^ w;t þI i;kw k~ w;t ;

ð12Þ

where the coefficients on the state variables are functions of the underlying parameters of both the SOE and the world economy. Note that saving and investment are, of course, functions of the world interest rate; in writing (11)–(12) we have used (10). 4 A mathematical appendix containing the full details of the solution of the models is available at the Dropbox link https://www.dropbox.com/sh/ 9qbkmt5ezrahdmi/_31yZk55Dz.

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Table 1 Baseline parameter values.

Long-run productivity growth rate, g Depreciation rate, δ RRA, γ Labor's share, α Investment adjustment cost, ζ Debt-elastic interest rate, φ Steady-state debt-output ratio, ι Persistence of trend shocks, ρ Std. dev. of trend shocks, σ g Cross-corr. of trend shocks, corrðεgi;t ; εgw;t Þ Persistence of transitory shocks, ϕ Std. dev. of transitory shocks, σ z Cross-corr. of transitory shocks, corrðεzi;t ; εzw;t Þ

World

Emerging

0.0065 0.025 2 0.68 0.1

0.0066 0.025 2 0.68 0.0433 0.001 0.42 0.001 0.0213 0.26

0.0073 0.025 2 0.68 0.0575 0.001 0.1 0.29 0.0047 0.72

0.95 0.0053  0.28

0.97 0.0063  0.11

0.45 0.005 0.90 0.003

Advanced

The relationship between saving and investment in many empirical studies is measured based on saving and investment as shares of GDP. For inducing stationarity this is similar to our normalization method in the model, but it could matter for saving–investment correlations. We will therefore consider both measures. We also consider two measures of co-movement between saving and investment. First, using (11)–(12) we compute their unconditional correlation. Second, the “savingretention coefficient,” defined as the estimated slope parameter in a least-squares regression of normalized investment on normalized saving:

τi ¼ covðs^~ i;t ; ^~i i;t Þ=varðs^~ i;t Þ;

ð13Þ

and similarly when variables are normalized by GDP. The above measures of co-movement are based on a model calibrated to quarterly data. In contrast, much of the FH literature is concerned with co-movement in long-run averages of the data. It is important therefore to study also saving– investment correlations in long-run averages of the quarterly model. 3. Model parameterization Many parameter values are the same in all model economies to focus the analysis on the role of the shock processes and the endogenous world interest rate. For reference, Table 1 contains a summary of all parameter values. The remainder of this section justifies this calibration. 3.1. Preferences and technology parameters The value of the parameter α, labor's share, is set at 0.68, a standard value in the literature. The depreciation rate, δ, is set at a quarterly rate of 0.025.5 The risk aversion parameter is set at γ ¼ 2, which is broadly in-line with much of the related literature.6 The parameter ψ governing the debt-elastic portion of the country interest rate is set at 0.001, which is commonly used. We set β ¼ 0:993, which results in a world steady-state return on capital of 8 percent (annualized). The steady-state debt-output ratio ι is set at 0.1 for an advanced SOE (following Aguiar and Gopinath, 2007a) and 0.42 for an emerging SOE, which is the value used in Neumeyer and Perri (2005). Turning to the investment adjustment costs, it is standard to impose structure on the adjustment cost function so that the steady-state levels of variables would be the same whether there are investment adjustment costs in the model or not. These assumptions are: ~ K~ Þ ¼ I= ~ K~ : Ψ ðI=KÞ ¼ Ψ ðI=

ð14Þ

~ K~ Þ ¼ 1: Ψ 0 ðI=KÞ ¼ Ψ 0 ðI=

ð15Þ

Next, define as ζ the following:

ζ¼

5 6

 Ψ ″ðI=KÞI=K : Ψ 0 ðI=KÞ

We also considered a depreciation rate of 0.05 with similar results. The results are qualitatively similar for γ equal to 3 and 5.

ð16Þ

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1

Then ζ is the elasticity of the steady-state investment capital ratio ðI=KÞ with respect to the marginal q, which equals
0 1=Ψ I=K in equilibrium. We set ζ ¼ 0:0433 for emerging SOE and ζ ¼ 0:0575 for advanced SOE based on Aguiar and Gopinath's (2007a) estimates of capital adjustment costs for Mexico and Canada. These values are within the range that Baxter and Crucini (1993) suggest in order for their model to exhibit reasonable investment volatility. Assigning a value to ζ for the world economy is harder because there is not a large literature on this property of the global economy. Studies that use aggregates based on a relatively small number of advanced economies (such as G3 or G7) may or may not be an adequate proxy for the global economy, but regardless, to our knowledge these studies do not offer clear estimates of capital adjustment costs. Thus, we follow the approach of Baxter and Crucini (1993) and assign a value to the world adjustment cost parameter that equates investment volatility in the world economy model with its empirical counterpart—the empirical counterpart is discussed below. This value is ζ ¼ 0:1. That this is higher than the values for SOEs is intuitive since the world economy is borrowing constrained. 3.2. Parameterization of the shock processes The world economy and the two SOEs each has a pair of shock processes (3)–(4), and each pair of shock processes is defined by five parameters fg; ρ; ϕ; σ g ; σ z g. In addition, co-movement between a SOE's shock processes and the world economy shock processes is defined by two parameters, fcorrðεgi;t ; εgw;t Þ; corrðεzi;t ; εzw;t Þg. Thus, parameterization of the shock processes requires assigning 19 parameter values. For the emerging and advanced SOEs the values of fg; ρ; ϕ; σ g ; σ z g are from Aguiar and Gopinath (2007a).7 For the world economy, there is little direct evidence in the literature to guide us in calibrating these shock processes. We therefore estimate fg; ρ; ϕ; σ g ; σ z g directly for the world economy by using GMM to match theoretical (unconditional) second moments of the macro variables from the world economy model with their empirical counterparts, as well as the first moment of output (which is informative for estimating the long-run mean growth rate of productivity, g). All moments are based on the log-differences of the raw non-normalized variables.8 The world economy data is discussed in Appendix A. Table 2 reports estimates of the parameters using various moments.9 The estimates are quite robust to alternative specifications. All the parameters are tightly estimated and significant. The values in Table 1 are chosen based on the estimates in Table 2. Finally, we must identify reasonable values for the cross correlations between national and world shock processes. While correlated national and global economies are reflected in calibrations of DSGE open-economy models (e.g., Baxter and Crucini, 1993; Backus et al., 1992, and subsequent work), the literature does not provide much direct guidance on the correlations between national and global transitory/permanent shocks, especially for emerging economies. Our approach is to estimate these correlations directly for a range of emerging and advanced SOEs which will then inform our calibration. Specifically, we estimate the cross correlations using GMM where the criterion involves matching covariances between national and global (log-differenced) output, consumption, and investment in the data with those computed from the model economy. Table 3 presents the results. Consider first the cross correlation of trend shocks. The estimates are much higher for advanced SOEs than for emerging SOEs, and within each group the estimates are fairly similar. Compared to trend shocks, the estimated cross correlations of transitory shocks are less precise, and much lower, with negative average values for both groups of SOEs. We use the average values of the estimates for each group in calibrating the model. However, as there is some variation in estimated cross correlations, we will assess the sensitivity of our main findings to the cross correlations in the calibrated model. 4. Results Table 4 (Panel A) reports the results for the quarterly model. Saving and investment are positively related in both country groups, but their co-movement is markedly lower in emerging economies. This pattern is consistent with the FH1 and FH2 puzzles. The model has been calibrated based on quarterly data, so an important question is whether these findings apply also to long-run averaged data as the latter has been the focus of much of the FH literature. Using large-sample simulation analysis, Table 4 (Panel B) reports the results when quarterly time series are averaged over periods ranging from 1 to 30 years (30 years is at the upper end of empirical work). The results are virtually the same as those in the quarterly model. These results 7 The model in Aguiar and Gopinath (2007a) differs from ours in that the world interest rate is constant and exogenous in their model. This could in principle matter for the estimated parameters of the shock processes for the SOEs. Aguiar and Gopinath emphasize that the critical difference in the shock processes for an advanced SOE and an emerging SOE is the ratio of the variances of the innovations to permanent and transitory shocks, σ gi =σ zi , which is much larger in the emerging SOE than in the advanced SOE. Our baseline values for the parameters of the shock processes for the SOEs are consistent with this key difference emphasized by Aguiar and Gopinath. Note also that in a related paper, Aguiar and Gopinath (2007b) find almost identical estimates of the parameters of the shock processes when their model is extended to include endogenous country interest rate premiums. 8 We use log differences of the level variables rather than filtering the level variables to remove a trend because our focus is not specifically on business cycles. 9 Aguiar and Gopinath (2007a) thoroughly examine which moments are informative for the shock parameters and conclude that consumption and output are most informative.

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Table 2 World economy parameter estimates.

σ gw σ zw

ρw ϕw gw Moments used

(1)

(2)

0.0039 (0.0004) 0.0033 (0.0005)

0.0039 (0.0004) 0.0033 (0.0005)

σc ; σy

0.0065 (0.0007) σ c ; σ y ; Ey

(3)

(4)

0.47 (0.034) 0.86 (0.044)

0.0046 (0.0008) 0.0025 (0.0003) 0.43 (0.053) 0.88 (0.029) 0.007 (0.0005) Full

σ c ; σ y ; AC c ; AC y

Note: “Full” denotes the set of moments fEy; σ c ; σ y ; σ i ; AC c ; AC y ; Covðy; iÞg, where AC denotes the auto-covariance. Robust standard errors in parentheses.

Table 3 Estimated cross correlations for SOEs. corrðεzi;t ; εzw;t Þ

p-Value

corrðεgi;t ; εgw;t Þ

p-Value

(A) Emerging SOEs Argentina Brazil Israel Korea Malaysia Mexico Peru Slovakia S. Africa Thailand Turkey Average

 0.084  0.447  0.678  0.214  0.200 0.646  0.692  0.746  0.351  0.794 0.436  0.284

0.850 0.145 0.003 0.405 0.602 0.037 0.009 0.017 0.080 0.032 0.432 0.237

0.251 0.235 0.177 0.383 0.176 0.270 0.303 0.237 0.241 0.282 0.305 0.260

0.008 0.004 0.065 0.000 0.099 0.000 0.019 0.081 0.000 0.006 0.036 0.029

(B) Advanced SOEs Australia Austria Belgium Canada Denmark Netherlands N. Zealand Portugal Spain Sweden Switzerland Average

 0.160  0.262  0.093 0.040 0.037 0.039  0.128  0.136  0.094  0.184  0.164  0.112

0.340 0.005 0.330 0.808 0.797 0.818 0.613 0.090 0.427 0.167 0.035 0.394

0.821 0.663 0.680 0.920 0.799 0.829 0.520 0.757 0.815 0.323 0.667 0.716

0.000 0.000 0.000 0.000 0.000 0.000 0.014 0.000 0.000 0.355 0.000 0.031

Note: GMM estimates using covariances of national and world output, consumption and investment (in log differences). Country data is from Aguiar and Gopinath (2007a) and world data is as described in the paper.

refer to co-movement between saving and investment when averaged over long periods of time within a given country. They can also be interpreted as cross-sectional correlations between average saving and investment for advanced or emerging economy groups with different initial conditions (but the same parameter values within a group). As noted in Section 3, there is some variation across SOEs in the estimated cross correlations of the shock processes. The significance for our main results of using cross correlations different from the baseline values is addressed in Table 5. There are two main observations. First, the precise cross-correlation of national and global transitory shocks is not particularly important. Second, the cross-correlation of national and global trend shocks can be important, but Table 5 shows that our main findings would be altered significantly only if these cross-correlations were greatly different from the baseline values, especially for emerging SOEs. This possibility, however, has no support from the empirically estimated values reported in Table 3. We conclude that, while one might argue that our baseline values for the shocks' cross correlations are somewhat too high or too low, the main findings would not be altered by reasonable alternative values of the cross correlations.

4.1. Interpretation of results We turn to impulse response analysis to illustrate the effects of shocks. To simplify comparisons of different shocks, the magnitude of shocks is fixed at 1 percent. Impulse responses of variables expressed as shares of GDP for (orthogonalized) national shocks are shown in Fig. 1 for the emerging SOE (they are qualitatively identical for the advanced SOE). National transitory shocks produce strong co-movement of saving and investment on impact and in the longer run (due to high

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Table 4 Saving–investment co-movement. Emerging SOE

Advanced SOE

Correlation – normalized variables Correlation – variables/GDP Retention coefficient – normalized variables Retention coefficient – variables/GDP

0.24 0.15 0.41 0.28

0.75 0.41 0.75 0.45

(B) Long-run correlations Saving and investment averaged Saving and investment averaged Saving and investment averaged Saving and investment averaged Saving and investment averaged Saving and investment averaged Saving and investment averaged

0.24 0.23 0.22 0.23 0.19 0.17 0.21

0.74 0.74 0.74 0.73 0.69 0.70 0.72

(A) Quarterly model

over over over over over over over

1 year 5 years 10 years 15 years 20 years 25 years 30 years

Note: Panel B simulation results are for normalized variables and are computed as average correlations across 50 samples, each sample with 24,000 quarters.

persistence). In comparison, national trend shocks produce negative co-movement of saving and investment in the short run but a positive one in the longer run. As a result, the effect of national trend shocks on the unconditional saving– investment correlation is reasonably expected to be weaker than transitory shocks. The two FH puzzles are consistent with the predictions of the model because in advanced SOEs transitory shocks are more important than trend shocks, and the converse is true for emerging SOEs. Further, saving–investment correlations are similar in the quarterly model and long-run averages because national transitory shocks are highly persistent and the trend shocks have permanent effects on productivity. Increased investment in response to national trend and transitory shocks is financed partly by reduced net exports (foreign borrowing), more so for trend shocks. Markets are incomplete in this model as the only financial asset is the bond. While it is impossible to share risk ex ante, foreign debt serves as an important tool for the agent to adjust to shocks ex post, in particular as a consumption-smoothing device. Specifically, a favorable productivity shock (whether permanent or temporary) that encourages higher investment induces the agent to finance some of that investment by borrowing abroad. Transitory shocks cause output to rise more than consumption initially, whereas a trend shock increases consumption more than output initially. The world interest rate is constant in these national-shock experiments and thus the response of consumption is due to a pure wealth effect—there is no substitution effect (see Baxter, 1995). The relative magnitudes of these wealth effects cannot be ascertained from the impulse responses for C/Y as the output response differs. To quantify the relative wealth effects we compute utility levels with and without the shocks. For the emerging SOE—the advanced SOE yields similar results—we find the following: utility increases by 0.3% for the transitory shock and 0.9% for the trend shock. The wealth effect is therefore larger for a trend shock.10 We now turn to impulse responses for global shocks. There are two potential consequences of the global economy for national saving–investment correlations. The first consequence is the “volatility effect.” The volatility effect is the influence on saving and investment of the world interest rate fluctuating, ignoring common shocks to national and global economies. The volatility effect produces strong negative co-movement between saving and investment. The intuition for the volatility effect is that any independent movement in the global interest rate affects national saving and investment oppositely. If a global shock, say, raises the global interest rate, the higher interest rate will increase national saving and reduce investment (because the return on capital is relatively less attractive than the return on bonds). Fig. 2 shows the volatility effect of the two global shocks for the emerging SOE (the advanced economy ones are qualitatively and quantitatively very similar). All variables respond oppositely to global trend shocks than to global transitory shocks. The reason for this is apparent from the bottom charts: global transitory shocks lower interest rates while trend shocks raise them. Fig. 2 also shows for consumption the dynamic Hicksian wealth and substitution effects following King (1991) and Baxter (1995). The substitution effect is the main influence on consumption in these experiments. The quantitative response of the interest rate is greater for global trend shocks and this, in turn, leads to larger movements in all variables compared to global transitory shocks. Specifically, from the interest rate function (10), the relevant coefficients are prg ¼ 0:1587 and prz ¼  0:0064, so the global interest rate responds 25 times more strongly to global trend shocks than to global transitory shocks. The reason is that trend shocks create a larger difference between saving and investment than do transitory shocks, but because saving and investment must be equal in the global economy the interest rate responds more strongly to trend shocks.

10 This result is not sensitive to the level of adjustment costs: using an adjustment cost parameter two standard errors higher or lower (see Table 4 in Aguiar and Gopinath (2007a)) than our baseline value alters utility levels at the third decimal.

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Table 5 Sensitivity of saving–investment correlations to cross-correlations of shocks. corrðεzi;t ; εzw;t Þ

Emerging SOE

Advanced SOE

corrðεgi;t ; εgw;t Þ

Emerging SOE

Advanced SOE

1.0 0.75 0.5 0.25 0  0.25  0.50  0.75  1.0

0.29 0.28 0.27 0.26 0.25 0.24 0.23 0.21 0.20

0.78 0.77 0.77 0.76 0.75 0.75 0.74 0.74 0.73

1.0 0.75 0.5 0.25 0.00  0.25  0.50  0.75  1.0

0.55 0.39 0.30 0.23 0.18 0.15 0.12 0.09 0.07

0.85 0.76 0.69 0.63 0.58 0.53 0.49 0.45 0.42

Transitory Shock 0.04

Trend Shock 0.04

S/Y and I/Y

0.03

0.03

0.02

0.02

0.01

0.01

0

1

7

13

19

25

31

37

0

investment 0.5

saving

7

13

19

investment 0.5

NX/Y

25

31

37

saving

NX/Y

0.2

0.2 -0.1 1

7

13

19

25

31

37

-0.1 1

-0.4

-0.4

-0.7

-0.7

-1

-1

-1.3

-1.3

0.001

-0.001

1

-0.01

-0.01

0

S/Y and I/Y

0.001

C/Y 1

7

13

7

19

25

31

37

0

-0.001

-0.002

-0.002

-0.003

-0.003

-0.004

-0.004

-0.005

-0.005

-0.006

-0.006

13

19

25

31

37

C/Y 1

7

13 19 25 31 37

Fig. 1. Impulse responses for national shocks. Note: A 1% shock occurs at t¼ 4. The shocks are purely local shocks (i.e. they can be interpreted as orthogonalized national shocks). Reported results are for the emerging economy. All variables are expressed as output shares and are log deviations from steady state values.

The second consequence of the global economy arises from correlated national and global shocks. We label this the “correlation effect.” The intuition is illustrated clearly with an extreme example. If national shocks were identical to global shocks and thus their correlation is unity, this SOE will behave as the global economy does, including that saving and

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Transitory Shock 0.02 -0.005

-0.03

Trend Shock 0.02

S/Y and I/Y 1

7

13

19

25

31

-0.005

37

-0.03

-0.055

-0.055

-0.08

-0.08 investment

4

7

13

4

19

25

1

1

0

31

37

saving

NX/Y

3 2

0 1

0.004 0.002 0 -0.002 1 -0.004

7

13

19

25

31

C/Y 7

13

19

consumpon

25

31

37

37

-1

wealth effect

7

13

7

13

19

25

31

37

C/Y 7

13

19

consumpon

25

31

37

wealth effect

subst. effect

int. rate

1

1

0.004 0.002 0 -0.002 1 -0.004

subst. effect 0.0022 0.0018 0.0014 0.001 0.0006 0.0002 -0.0002

1

investment

2

-1

S/Y and I/Y

saving

NX/Y

3

107

19

25

31

37

0.0022 0.0018 0.0014 0.001 0.0006 0.0002 -0.0002

int. rate

1

7

13

19

25

31

37

Fig. 2. Impulse responses for global shocks – volatility effects. Note: A 1% shock occurs at t ¼4. The shock is assumed to affect the national economy only through the interest rate (i.e. the shock can be interpreted as an orthogonalized shock to the global economy). Reported results are for the emerging economy. Variables are expressed as output shares and are log deviations from steady state values, except the interest rate which is the level deviation from the steady state.

investment co-move perfectly. More generally, the higher the correlation between national and global shocks, the higher is the SOEs saving–investment correlation. To investigate the overall consequences of fluctuating interest rates and correlated national and global shocks consider the experiments shown in Fig. 3. Panel (a) shows how saving and investment respond to a 1 percent global shock that has unit correlation with a simultaneous national shock of the same type. Panel (b) shows the pure effect of the interest rate fluctuation (i.e. the volatility effect), and panel (c) shows the pure effect of the spillover (i.e. the national shock). There are two main observations. First, for transitory shocks the volatility effect is small and thus the impulse response from simultaneous national and global shocks is mostly due to the national shock. Second, for trend shocks this is not the case: the volatility effect is large and the impulse response from simultaneous national and global trend shocks is quite different from the impulse response from just the national trend shock. Specifically, a national trend shock (panel (c)) causes saving and investment to diverge on impact, but when this shock coincides with a global trend shock, this divergence is weakened considerably. These experiments show that a higher correlation between national and global trend shocks raises saving–investment correlations significantly. To understand why, recall that a global trend shock raises the interest rate. For positive cross correlation of trend shocks this means that the interest rate rises at the same time as the SOE wishes to save less and invest more. Clearly this will push saving and investment closer together, just as it must do in the global economy. In contrast, the cross correlation between national and global transitory shocks is less important to saving–investment correlations because such shocks have a relatively small impact on the global interest rate. Because the volatility effects are small, the total effects are driven mostly by the spillover of the transitory shock.

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Total Effect Transitory Shock 0.15 0.1 0.05 0 -0.05 1 -0.1

Trend Shock

S/Y and I/Y

7

13

19

25

investment

31

37

0.15 0.1 0.05 0 -0.05 1 -0.1

saving

S/Y and I/Y

7

13

19

25

investment

31

37

saving

Volatility Effect 0.15 0.1 0.05 0 -0.05 1 -0.1

S/Y and I/Y

7

13

19

25

investment

31

37

0.15 0.1 0.05 0 -0.05 1 -0.1

saving

S/Y and I/Y

7

13

19

25

investment

31

37

saving

Spillover with Interest Rate Constant 0.15 0.1 0.05 0 -0.05 1 -0.1

S/Y and I/Y

7

13

19

investment

25

31

37

saving

0.15 0.1 0.05 0 -0.05 1 -0.1

S/Y and I/Y

7

13

investment

19

25

31

37

saving

Fig. 3. Impulse responses for global shocks: the role of cross correlations. Notes: Shock occurs at t¼ 4. Reported results are for the emerging SOE. All variables are expressed as output shares and are log deviations from steady state values. (a) The global shock is 1% and the national trend shock size is ðc  σ T =σ w Þ  :01, where c ¼ 1 is the correlation between national and global shocks, σ T is the standard deviation of the national shock and σ w is the standard deviation of the global shock. (b) Global shock size is 1%, no spillover. (c) No global shock; local shock size as in (a).

Table 6 Accounting for differences in saving–investment correlations.

1) 2) 3) 4) 5) 6) 7)

Only national transitory shocks Only national trend shocks Both national shocks; no global shocks All shocks, cross correlations ¼ 0 All shocks, cross correlation transitory shocks ¼1 All shocks, cross correlation trend shocks¼ 1 All shocks, both cross correlations ¼ 1

Emerging SOE (baseline ¼ 0.24)

Advanced SOE (baseline ¼ 0.75)

0.88 0.00 0.27 0.20 0.24 0.56 0.62

0.89  0.30 0.78 0.58 0.62 0.85 0.86

Note: Reported values are cross correlations using normalized variables.

There are three main features of our model: trend and transitory shocks, an endogenous global interest rate, and correlated national and global shocks. To quantify the contributions of these three features to our explanation of the FH puzzles, we study the model with subsets of these features. These experiments are shown in Table 6. It is apparent from Table 6 that the model with national trend and transitory shocks and a constant world interest rate (experiment 3) is consistent with the two FH puzzles as long as trend shocks are of greater importance than transitory shocks in emerging SOEs and the converse is true for advanced SOEs. In reality, however, the world interest rate is not constant and global and national shocks are correlated. The important question is whether those matter for saving–

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investment correlations. The answer is that they may. It is important to bear in mind that the baseline case has very different cross correlations for the two economies, especially for trend shocks. To see the significance of this, note from Table 6 that for certain cross correlations of global and national shocks the model is not able to explain the FH2 puzzle. For example, if the cross correlation of trend shocks was high for the emerging SOE and low for the advanced SOE then the saving–investment correlations in the two economies would be essentially the same (compare experiment 6 for the emerging SOE with experiments 4–5 for the advanced SOE). In this case, the model only explains the FH1 puzzle. The significance of this possibility is limited, however, as there is little empirical support for such a possibility (Table 3). 5. Other considerations and directions for future research The model should not only explain the FH puzzle but also be consistent with macroeconomic dynamics more generally in the two types of economies. This has been established to a large degree by Aguiar and Gopinath (2007a, b), whose main objective is to show that the long-run risk model does well in matching business cycle dynamics within advanced and emerging SOEs. The behavior of the trade balance is most closely related to our focus because in the model TB ¼ S  I (as S ¼ Y  C and Y is GDP). An important question, then, is whether the properties of the trade balance in the model are reasonable. Table 7 reports the volatility of the trade balance relative to output as well as its cross-correlation with output along with the corresponding figures from the data. The properties of the trade balance in the model seem reasonable. An aspect not considered by Aguiar and Gopinath (2007a, b) is co-movement between national and world macroeconomic aggregates. Table 8 reports cross-correlations between national and world output, consumption, and investment, from the model for some alternative cross-correlations of national and world shock processes. The corresponding statistics from data for advanced and emerging SOEs are also reported. An obvious shortcoming of the model for the baseline case is the well-known “quantity anomaly”—the higher cross-correlation of consumptions than Table 7 Properties of the trade balance. Advanced economy

Std. dev (NX/Y) Corr (NX/Y,Y)

Emerging economy

Model

SOE avg.

Model

SOE avg.

1.16  0.12

1.02  0.17

2.76  0.46

3.22  0.51

Note: SOE avg. is from the data, obtained from Aguiar and Gopinath (2007a), Tables 1 and 2. The cross-correlation uses HP-filtered output series. Model statistics computed from simulations. Standard deviations are in percent.

Table 8 Macroeconomic variables' cross correlations in model and data. Emerging SOE corrðyi ; yw Þ

Advanced SOE corrðci ; cw Þ

corrðii ; iw Þ

corrðyi ; yw Þ

corrðci ; cw Þ

corrðii ; iw Þ

(A) Sensitivity to cross-correlations of transitory shocks
corr εzi ; εzw 0.9 0.3568 0.1847 0.5 0.2716 0.1690 0.25 0.2184 0.1592 0 0.1652 0.1493  0.25 0.1120 0.1395  0.50 0.0588 0.1296 Baseline 0.1057 0.1383 Data 0.18 0.08

0.3652 0.2683 0.2073 0.1460 0.0843 0.0222 0.0768 0.17

0.7371 0.5201 0.3845 0.2488 0.1131  0.0226 0.1891 0.38

0.4702 0.4076 0.3674 0.3264 0.2845 0.2416 0.3081 0.21

0.7869 0.5665 0.4239 0.2774 0.1266  0.0287 0.2116 0.26

(B) Sensitivity to cross-correlations of trend shocks
corr εgi ; εgw 0.9 0.5408 0.8244 0.5 0.2686 0.3821 0.25 0.0989 0.1285 0  0.0705  0.1105  0.25  0.2394  0.3364  0.50  0.4081  0.5509 Baseline 0.1057 0.1383 Data 0.18 0.08

 0.0494 0.0416 0.0781 0.1079 0.1333 0.1557 0.0768 0.17

0.2569 0.1066 0.0134  0.0793  0.1715  0.2631 0.1891 0.38

0.4955 0.1076  0.0917  0.2682  0.4271  0.5721 0.3081 0.21

0.2165 0.2087 0.2079 0.2085 0.2102 0.2124 0.2116 0.26

Note: All correlations computed using log-differences of variables. The “Data” row entries are average cross-correlations for emerging SOEs (Argentina, Brazil, Korea, Malaysia, Mexico, South Africa, Thailand, and Turkey) and advanced SOEs (Australia, Austria, Belgium, Canada, Denmark, Finland, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, and Switzerland).

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Table 9 The two-good model. World home bias

Advanced SOE Corr(s,i)

Emerging SOE Corr(s,i)

Stdev(TOT)

(A) Elasticity of intratemporal substitution in SOE ¼1.5 η ¼ 0:85 0.7291

0.2909

0.0179

η ¼ 0:76

0.2949

0.0133

(B) Elasticity of intratemporal substitution in SOE¼ 0.75 η ¼ 0:85 0.7302

0.2973

0.0179

η ¼ 0:76

0.2996

0.0133

0.7351

0.7352

(C) Large country in two-country world economy η ¼ 0:85 Corr(s,i) 0.7260

η ¼ 0:76 0.7339

Note: Elasticity of intratemporal substitution ¼1=ð1þ μÞ. Corr(s,i) is the saving–investment correlation for normalized variables. Stdev(TOT) is the standard deviation of the terms of trade. Reported statistics are computed from large sample simulations (25,000).

outputs in the model in contrast to the data. Recent work by Colacito et al. (2013), featuring long-run risk, studies various specifications of preferences and technologies that help resolve the quantity anomaly. The model used here to explain the FH puzzles abstracts from some features that may be important. One is that there is a single good. With multiple goods, terms-of-trade fluctuations could matter for national wealth, real exchange rates, and asset returns, and thus affect saving and investment. We next consider an extension in which we allow for two traded goods. We model the world economy as two symmetric large economies that each consumes two traded goods but specializes in the production of only one. Suppose the home and foreign country produce, respectively, good m and n. The composition of domestic absorption is C it þI it ¼ GðMit ; Nit Þ;

i A fh; f g

ð17Þ

where the aggregator G is defined as follows: μ

μ

GðMht ; Nht Þ ¼ ½ηMht þ ð1  ηÞNht   1=μ ; μ

μ

GðMf t ; Nf t Þ ¼ ½ð1  ηÞMf t þ ηN f t   1=μ :

ð18Þ ð19Þ

Here η is the share parameter, often referred to in the literature as the “home bias coefficient.” The elasticity of substitution between the two goods is 1=ð1 þ μÞ. A SOE also produces only one good and has the above preferences. Following Colacito et al. (2013), for the two countries in the world economy we use a high correlation of trend shocks (0.85) and a low correlation of transitory shocks (0.027). The volatilities of the shocks in these two economies are equal and calibrated so that the volatility of the world shock process is the same as the estimated value in our one-good model. The correlations between the SOE's shocks and those in the world economy are the same as in the one-good model. We consider several values for the home bias coefficient in the world economy model. From the literature for large economies (e.g. the United States) we consider η ¼ 0:85 from Backus et al. (1994), and η ¼ 0:76 from Colacito et al. (2013). The degree of home bias in the SOE's is derived from average import shares computed for the two groups of SOEs—average import shares are 34% for advanced SOEs and 35% for emerging SOEs. The elasticity of substitution between the two goods in the world economy is 1.5, which is standard for large advanced economies. The literature suggests possibly lower elasticities for SOEs (e.g. Mendoza, 1995). We report results for SOEs using elasticity values of 1.5 and 0.75. Table 9 reports saving–investment correlations for SOEs from the two-good model. Also shown is the volatility of the terms of trade. It is apparent that the correlations are similar to the baseline results and thus the two-good model is also consistent with FH puzzles. We also report the saving–investment correlations for a large country in the two-country world economy. These correlations are similar to the advanced SOE, as the parameters of the shock processes are similar. Future work should examine non-traded goods, differentiation between investment and consumption goods and their degrees of home bias, recursive preferences, and alternative asset market structures. Some of these features have been suggested to resolve other puzzles in open-economy business cycle models for large advanced economies, but their significance for saving–investment correlations and the FH puzzles has not been studied. In future work it would also be desirable to formulate a model with many economies. This framework would permit analysis of cross-sectional saving– investment correlations, as these have been the focus of much empirical literature on the FH puzzle. It is also of interest to study country risk premia in interest rates. For instance, Neumeyer and Perri (2005) and Aguiar and Gopinath (2007b) model country risk premia as functions of national technology shocks. While Aguiar and Gopinath (2007b) find that this does not significantly affect the main predictions of their model, Neumeyer and Perri (2005)

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emphasize the importance of country risk premia for emerging markets. It would be of interest to examine the role of country risk premia for the FH puzzles and for our explanation of them.

Acknowledgments For helpful comments and suggestions, we thank Eric Leeper (the Editor), a referee, Marc-Andre Letendre, Connie Smith, Henry van Egteren, Runjuan Liu, and Dima Hryshko. Appendix A. Data for the world economy Estimation of the parameters of the world economy shock processes requires assembling data for the world economy. We require time series data on private consumption, investment, and GDP for the world economy. The desired sample period is 1980q1–2003q2 (quarterly data) as that is the sample from which the same parameters are estimated for the two types of SOEs by Aguiar and Gopinath (2007a). There is no quarterly time series for the true world economy for the simple reason that quarterly national accounts are not produced by many countries. Many of the larger emerging economies that do presently produce quarterly national accounts have only done so relatively recently. Specifically, quarterly national accounts for Brazil, Russia, India, and China are available only since around the mid-1990s and, even then, some of these data are potentially problematic (e.g. some are estimated well into the 2000s and, for China, the quarterly data is cumulative and de-cumulating them is difficult due to the manner in which annual data are revised). Annual data for the world economy (from 1980) is available from the IMF covering virtually all countries (189 to be exact). However, this would provide only 23 observations to estimate 5 parameters, and these parameters would be estimated from a different frequency than are those for the SOEs. For these reasons we use a proxy for the world economy. To our knowledge, the broadest country aggregate available quarterly for this sample period to proxy the world economy is the “OECD New Grouping,” which consists of 34 countries, including all the advanced economies and several emerging economies. Data on private consumption, investment (gross fixed capital formation), and GDP is available quarterly for this aggregate from the OECD for the desired sample period. These aggregates are real, PPP adjusted, expressed in U.S. dollars, and seasonally adjusted. The method of PPP adjustment uses fixed weights (see Schreyer and Koechlin, 2002). The countries included in this aggregate are: Australia, Austria, Belgium, Canada, Chile, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Israel, Italy, Japan, Korea, Luxembourg, Mexico, Netherlands, New Zealand, Norway, Poland, Portugal, Slovak Republic, Slovenia, Spain, Sweden, Switzerland, Turkey, United Kingdom and United States. Using the annual IMF data for 1980–2003, the cross correlation between GDP for their world aggregate (189 countries) and that from just the advanced economies is 0.99 in levels and 0.95 in growth rates. Our proxy for the world economy is likely very good for our sample period. Appendix B. Supporting information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j. euroecorev.2014.09.001.

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