International Real Business Cycles

The paper asks whether a two-country real-business-cycle model can account simultaneously for the familiar closed-economy comovements (the relative volatility of consumption, investment, and hours with respect to output) and for international comovements – cross-country correlations of output and consumption, the correlation of net exports with output, and the correlation between saving and investment rates. Closed-economy real business cycle theory had already been shown to match several postwar U.S. facts; the authors extend this “to open economies” to see whether the interaction between country-specific technology shocks and international borrowing/lending can “have a substantial influence on the magnitude and character of aggregate fluctuations” (Introduction, pp. 1-2). The study follows earlier dynamic-general-equilibrium studies of international business cycles by Cantor and Mark (1988), Dellas (1986), and Stockman and Svensson (1987), but gives the theory quantitative content by parameterizing it and comparing simulated moments directly to international time-series data (p. 4).

Using Hodrick-Prescott filtered quarterly data for twelve developed countries (the universe of usable data in the IMF’s International Financial Statistics) plus a European aggregate, the authors document that business cycles “exhibit a great deal of regularity across countries”: investment is much more volatile than output, consumption less volatile, hours about as volatile, and all three are procyclical; net exports is consistently countercyclical in every one of the twelve countries; and – the fact the model will most dramatically fail to replicate – “output fluctuations are more highly correlated across countries than are consumption fluctuations” (Section I, pp. 5-8). For the U.S. specifically (1954-1989), the standard deviation of output is 1.71 percent, consumption (nondurables and services) is about half as volatile as output, investment more than three times as volatile, and net exports/output has a contemporaneous correlation with output of -0.28 (Table 1). Across the twelve countries, output correlations with the U.S. are positive for all but South Africa (0.22 to 0.48 for Japan and the major European economies), while consumption correlations are uniformly smaller – e.g., 0.46 versus a 0.70 output correlation for the European aggregate, and a maximum of 0.65 (Canada) for any individual country (Table 2). Saving/investment correlations (defined as output minus consumption and government purchases, to sidestep the ambiguity of “saving” under international asset trade) are large and positive for Germany, Japan, and the United States, replicating the Feldstein-Horioka (1980) finding, though the authors note this pattern “shows no clear pattern” in general.

The authors’ interest in this statistic follows from “a well-known property of complete markets: in economies with one good and stationary, additively separable preferences, consumption by every agent is deterministically and positively related to consumption by every other agent”; with identical, homothetic preferences, the relation is linear and consumption paths of any two agents are perfectly correlated “regardless of the correlation of their incomes” (Section I, p. 6, citing Scheinkman 1984). This makes the cross-country consumption correlation “a direct measure of how well such models mimic the international economy” – which is exactly why the model’s failure on this dimension is diagnostic rather than a minor miss.

The model is a two-country extension of Kydland and Prescott’s (1982) closed economy, retaining a single homogeneous produced good and complete markets for state-contingent claims, but departing from the original in two respects: countries experience different technology shocks each period, and agents participate in international capital markets (Section II, p. 8). In each country the representative consumer maximizes expected utility E₀Σβᵗ U(cₜ,ℓₜ) with U(c,ℓ) = [c^μ ℓ^(1-μ)]^γ/γ (Cobb-Douglas over consumption and leisure, with curvature parameter γ governing risk aversion and intertemporal substitution, benchmark value γ = -1, not the special case γ = 0 of additively separable log utility). Output in each country follows a CES aggregator over a Cobb-Douglas capital/labor composite and inventories, F(λ,k,n,z) = [(λk^θn^(1-θ))^(-ν) + σz^(-ν)]^(-1/ν), with a country-specific technology shock λ. Investment follows Kydland and Prescott’s (1982) time-to-build structure, with J = 4 quarters required to complete a unit of capital. World output is allocated to consumption, fixed investment, and inventory accumulation, with net exports defined as output minus domestic absorption. The planner’s problem – equivalent to the competitive equilibrium under the Negishi (1960)/Mantel (1971) welfare-weight construction, computed at ψ = 1/2 – is solved via a quadratic approximation around the model’s non-stochastic steady state.

Technology shocks in the two countries follow a bivariate autoregression λₜ₊₁ = Aλₜ + εₜ₊₁, where the off-diagonal elements of A (“spillovers”) capture the extent to which a shock to one country’s technology gradually affects the other, and the innovations εₜ have a covariance matrix V that allows contemporaneous correlation between home and foreign shocks (Section II, Eq. 7, p. 10-11). The authors estimate this process by least squares on Solow residuals for the United States and a European aggregate (Austria, Finland, Germany, Italy, Switzerland, U.K.) over 1970:1-1986:4, obtaining an estimated A with diagonal elements near 0.90-0.91 and positive off-diagonal “spillover” elements of 0.05 and 0.15, innovation standard deviations of 0.0091 (U.S.) and 0.0080 (Europe), and a correlation between innovations of 0.258 (Section III, p. 15). For the symmetric benchmark economy they use the unique symmetric matrix with the same eigenvalues (0.994 and 0.818) as the estimated asymmetric one, giving A with diagonal 0.906 and off-diagonal 0.088, with both innovation standard deviations set to 0.00852 (the average of the US/Europe estimates) and correlation 0.258 as estimated. All other parameters (capital share 1-θ = 0.64, depreciation δ = 0.025, discount factor β ≈ 0.99, curvature γ = -1, time-to-build J = 4) are taken directly from Kydland and Prescott’s (1982, 1988) closed-economy calibration, “set without regard for their international implications” (p. 4).

In the benchmark economy, output volatility (1.55 percent) is 91 percent of the U.S. figure, and the consumption/output volatility ratio (0.40) is close to the data’s 0.49, but investment volatility relative to output (10.94) is more than three times the data’s 3.15, and the standard deviation of net exports/output (2.90 percent) is about seven times the U.S. figure (0.42 percent) and larger than any of the twelve countries in Table 2 (Section IV, Table 4, pp. 16-17). Net exports is “essentially uncorrelated with output” in the model (-0.02) rather than countercyclical as in the data, and saving/investment correlations, while positive, are not strongly so. Most strikingly, “output [is] negatively correlated in the model, while in the data they are positively correlated in all but one of the twelve countries,” and “foreign and domestic consumption are much more highly correlated in the model than they are in the data”: the model’s consumption correlation (0.88) “far exceeds” its output correlation (-0.18), the reverse of every country pair examined.

Impulse responses to a one-time, one-standard-deviation home-country technology shock (Figure 2) show that the shock raises home productivity, investment (by far the largest response), consumption, and output, with the investment-plus-consumption increase exceeding the output increase – financed by imports, producing a trade deficit at home. In the foreign country, the technology spillover eventually raises foreign productivity, but foreign output and investment both fall initially as “resources are shifted to the more productive location, the home country” – both capital (investment rises at home, falls abroad) and labor move toward the more productive country. Foreign consumption, however, rises slightly even as foreign output falls, so “the equilibrium responses of foreign and domestic consumption have the same sign, but those of foreign and domestic output do not” – which is exactly what produces a negative cross-country output correlation alongside a strongly positive consumption correlation (Section IV, p. 17).

Using the actual (unsymmetrized) estimated spillover matrix for the U.S. and Europe rather than the symmetric benchmark changes some correlations substantially – the home country’s investment/output correlation falls from 0.27 to -0.08 and its saving/investment correlation falls from 0.28 to -0.04 (though the foreign country’s analogous correlations are 0.39 and 0.34) – showing the saving/investment correlation is “sensitive to modest perturbations of the technology process,” but investment and net exports remain much more volatile than in the data and consumption remains more correlated across countries than output (Section IV, Table 5, p. 18). Pushing further, an extreme “large spillovers” experiment – raising the off-diagonal element of A from 0.088 to 0.2 and the innovation correlation from 0.258 to 0.5, changes the authors describe as probably going “beyond what can be justified from the data” – lowers investment and net-export volatility by more than 70 percent and raises the cross-country output correlation from -0.18 to 0.38, but the consumption correlation moves further from the data, rising from 0.88 to 0.95: “in this last respect the model still has a large discrepancy with the data” (p. 19).

Lowering γ from -1 to -5 (raising risk aversion, which the authors expected would strengthen the nonseparability between consumption and leisure and so lower the cross-country consumption correlation) has only a small effect: it raises the output correlation from -0.18 to -0.11 and lowers the consumption correlation from 0.88 to 0.74, but the consumption correlation “still far exceeds the output correlation.” Adding a distributed lag on leisure (using Hotz, Kydland, and Sedlacek’s 1988 estimates, α = 0.6, η = 0.1) makes leisure durable and raises hours’ volatility relative to output from 0.49 to 0.67 and investment’s from 10.94 to 12.81, but “has little effect on the difference between cross-country output and consumption correlations.” Time-to-build, by contrast, “has a strong influence on the model’s properties”: shortening it from J = 4 to J = 1 quarter raises output’s standard deviation 45 percent (to 2.24) and worsens the investment-volatility discrepancy from three times the data to ten times – and the authors note this effect is much larger in the open economy than in Kydland and Prescott’s closed economy, where investment volatility “is not very sensitive to the choice of J” (Section IV, pp. 18-20).

Adding a quadratic transport cost calibrated so the marginal cost at the benchmark’s net-export volatility is about 0.58 percent of output is “very successful in reducing the variability of trade”: the standard deviation of net exports/output falls from 2.90 to 0.16 percent, investment volatility relative to output falls by a factor of four (to 2.60), output’s own volatility falls from 1.55 to 1.38, and the output correlation across countries rises from -0.18 to 0.02 – but the consumption correlation barely moves, rising slightly from 0.88 to 0.91, so the friction “has little effect on the difference between the cross-country correlations of consumption and output” (Section V, p. 21). Eliminating trade in goods and state-contingent assets entirely (autarky) produces results “very close to” the transport-cost experiment – output volatility falls further to 1.33, and “even with trade fixed at zero, the correlation of consumption across countries is much higher than the correlation of output,” so “this discrepancy… cannot be attributed to imperfect capital markets alone, since no assets are traded in this world.” The authors attribute the positive cross-country consumption correlation under autarky instead to the permanent-income hypothesis: the foreign agent, anticipating that a home productivity shock will eventually spill over and raise his own future income, raises consumption immediately and postpones investment, even while his current output falls (Section V, p. 22).

The authors measure the welfare gain from free trade (relative to autarky) as the percentage increase in the autarky consumption path needed to match discounted expected utility under free access to international markets, and find that consumption under autarky need rise only 0.3 percent to equal welfare under free trade – “the welfare gains from trade in our theoretical economies… are remarkably small,” consistent with similar calculations by Cole and Obstfeld (1991). They suggest this smallness helps explain why even a small trading friction reproduces most of autarky’s quantitative properties: when gains from trade are small to begin with, a small cost can have a disproportionately large effect on the equilibrium quantity of trade (Section V, p. 22, citing Cole and Obstfeld 1991).

The paper’s conclusion is that the benchmark model differs from postwar international data “in several respects”: investment and net exports are too volatile, consumption is too highly correlated across countries, and output too little correlated – and while some of these gaps (investment/net-export volatility, the sign and size of the output correlation) respond to plausible changes in parameters or market frictions, the consumption/output correlation gap is the paper’s “most robust” finding and persists even under autarky, where no asset trade of any kind occurs. The authors explicitly flag that it “remains to be seen” whether non-separable preferences, taste shocks, or similar extensions pursued in contemporaneous work by Devereux, Gregory, and Smith (1990), Ravn (1990), and Stockman and Tesar (1990) can resolve what later became known as the “quantity anomaly” or “consumption correlation puzzle” in international business cycle research, and note as a further, low-frequency discrepancy that poor but fast-growing countries borrow less from richer, slower-growing countries than the theory would predict.