Consumption and real exchange rates in dynamic economies with non-traded goods

Four or five, and the authors treat the PPP one as about as solid as anything in the discipline. “Probably the most striking feature of international macroeconomic data is the regularity of large, persistent departures from purchasing power parity (PPP) apparent in national price indexes and foreign exchange rates,” documented by Isard (1977), Roll (1979), Frenkel (1981), Mussa (1986) and Huizinga (1987) “among many others, with the result that departures from PPP are one of the most clearly established empirical regularities in economics” (Section 1, p. 1). The second fact is the low cross-country consumption correlation: “the most obvious implication of complete markets in a one-good world economy is that consumption by every individual and country should be deterministically related to aggregate, or world, consumption; with identical homothetic preferences, consumption in one country should be perfectly correlated with consumption in every other country. In fact the correlations are considerably less than one, and are similar to cross-country output correlations” (pp. 1-2, citing Leme 1984 and Scheinkman 1984). The third is that “real interest rates exhibit sizable differences across countries” (Isard 1983, Cumby and Obstfeld 1984, Mishkin 1984, Mark 1985, Cumby and Mishkin 1986). The authors also note two further applications of the device: nontraded goods have been used “to account for imperfect international diversification” (Eldor, Pines and Schwartz 1988; Stockman and Dellas 1989) and to explain “high correlations between savings and investment, country by country” (Engel and Kletzer 1989; Tesar 1992).

Because price indexes mix traded and nontraded prices, and the nontraded ones exist only domestically. “The mechanism is fairly simple. Although the law of one price holds, in the sense that each good sells for a single price in all countries, PPP may not: price indexes combine prices of both traded and nontraded goods, and because the latter are sold in only one country their prices, and hence price indexes, may differ across countries” (p. 1). The authors are careful about the standing of the law of one price itself. Evidence of its failure exists (Isard 1977; Kravis and Lipsey 1977, 1978; Richardson 1978; Krugman 1987; Lapham 1992), but “this generally is based on comparisons of price indexes for disaggregated but nevertheless heterogeneous groups of goods,” whereas Protopapadakis and Stoll (1983, 1986) imply that “with homogeneous commodities, like metals and agricultural products, deviations from the law of one price are much smaller than departures from PPP.” Hence the reading they adopt: “One therefore might follow the interpretation that all final goods contain a positive nontraded component. In that case even price comparisons between seemingly similar goods in different locations are affected by changes in relative prices of nontraded goods” (p. 1).

Not a new mechanism but a joint restriction: it derives several implications of the device at once and shows they must move together. “The strength of this approach is thus its potential for reconciling a wide range of international evidence by a single theoretical device. While nontraded goods have been suggested as an explanation for many features of international macroeconomic data, the focus of this paper is on general equilibrium restrictions. We derive several implications of nontraded goods simultaneously and point out relations between them” (Section 1, p. 3). The particular relation: “if fluctuations in the nontraded sector account for large variability in the ratio of two countries’ consumptions then their real exchange rate also should be relatively variable in competitive equilibrium. Moreover, relative consumptions and relative prices in the theory have similar dynamics and are positively correlated over time” (p. 3). This is what makes the test an internal-consistency test rather than a fit exercise – the device is allowed to explain any one fact, and is then held to what explaining that fact implies for the others.

A finite-horizon stochastic exchange economy with I countries, one traded good and one country-specific nontraded good, extending Lucas (1984) to many agents (Section 2, pp. 3-4). “Our theoretical world is a stochastic exchange economy; the structure and notation extend Lucas (1984) to a multiagent setting. There are I countries… each represented by a single consumer who lives from date 0 to date T.” Events are publicly observed, and “for mathematical simplicity, T is finite and each event is drawn from a finite set.” Each country is endowed “with quantities of the traded good and their own nontraded good,” so there are I+1 goods in each state. Equilibria are computed by the Mantel-Negishi algorithm – a social planner maximising Pareto-weighted utilities subject to a world resource constraint on the traded good and a country-by-country constraint on each nontraded good. Section 3 works the benchmark with no nontraded goods, where “it is clear that PPP holds exactly” and each country’s consumption is monotonically related to every other’s, so the two target facts cannot arise at all.

That isoelastic period utility is enough to force the bilateral real exchange rate and the consumption ratio to move together, state by state. “Let the period utility function be isoelastic as in (4.4). Then along any equilibrium path there is a monotone relation between the bilateral real exchange rate, eij, and the consumption ratio ci/cj: if the real exchange rate is higher in one state than in another, then so is the consumption ratio” (Section 4, p. 9). The proof substitutes the planner’s first-order conditions into the price-index definition to obtain the exact relation that the ratio of Pareto weights times the consumption ratio raised to gamma equals the real exchange rate. On generality, the authors make two points. The functional form “is of interest because many applications use period utility with this form.” And an alternative assumption gets there too: “Some other studies use additive separability… which is stronger but also will give the result in the proposition more generally even without the isoelastic utility function (e.g. as in Stockman and Dellas, 1989)” (p. 9). So the target is not one exotic specification but the standard preference structures the literature was already using.

Three, and they survive not knowing the preference parameters or the endowment processes (Section 4, pp. 9-11). Because “Proposition 2 applies state by state and hence applies to moments, when they exist,” the isoelastic form suggests studying growth rates, yielding the restriction that gamma times the change in the log consumption ratio equals the change in the log real exchange rate. First: “a pair of countries for which the growth rate in the ratio of aggregate consumptions has a relatively large mean or standard deviation will have a real exchange rate with similar properties. The means and standard deviations of the two growth rates will not be equal unless gamma = 1, but the monotonicity implication can be tested using cross-section correlations of the moments, which are robust to the value of gamma, or cross-section rank correlations of the moments, which also are robust to some measurement error.” Second: “The autocorrelations of the two growth rates are equal in the theory.” Third: “the time series cross-correlation between the growth rate of relative consumptions and the growth rate of relative prices should be unity for all pairs of countries.” The authors underline the point: “Although the endowments of nontraded goods are unobservable, Proposition 2 thus suggests several simple tests of the theory, for any values of rho, gamma, and alpha” (p. 10). Their own summary of why the failure matters: the results “are striking because they are based on weak assumptions. They do not require us to restrict parameter values, to make auxiliary assumptions about detrending, to specify laws of motion for the endowment processes, or to identify specific categories of consumption goods as traded or nontraded (although implicit separability is required for aggregation into these two groups)” (p. 15) – the parenthetical being the one assumption they do carry.

Quarterly consumption and deflators for eight OECD countries over 1971-1990, giving 28 bilateral pairs (Section 5, p. 14). “The tests in this section use data from eight OECD countries: Australia (A), Canada (C), France (F), West Germany (G), Japan (J), Sweden (S), the U.K. (K), and the U.S. (U) for 1971-1990… Consumption series are measured as quarterly, seasonally adjusted, real, total private consumption expenditures. Their deflators are used with quarterly average nominal exchange rates to construct real exchange rates.” Figures plot moments of real exchange rate growth against moments of consumption-ratio growth pair by pair: standard deviations (times 100), first-order autocorrelations, and means (times 100). The horizontal axes themselves reproduce the motivating facts – “the variability in real exchange rate changes,” “the persistence in growth rates of relative prices,” and “their small means” – which the authors note “can be compared with that of Mussa (1986).”

Theory puts the points on upward-sloping lines through the origin; the data give clouds with negative or near-zero rank correlations. “Proposition 2 shows that, in the theoretical economy with standard preferences and nontraded goods, scatterplots of these moments lie around upward-sloping lines… More specifically, the theoretical points in Figures 1 and 3 lie on a line through the origin with slope 1/gamma while those in Figure 2 lie on a 45-degree line through the origin” (Section 5, p. 15). The authors note the individual observations that do look right – “Canada-U.S. real exchange rate growth has the smallest variance among values for these pairs of countries and… the growth rate of the Canada-U.S. consumption ratio also is among the least variable,” and “in Figure 3 there is a positive relationship between mean growth rates if Japan is excluded” – before the verdict: “In general, though, the cloud-like patterns found in the Figures provide little support for the theoretical model. The rank correlations in the three Figures are -0.263, -0.466, and 0.074.” With n = 28 the normal approximation gives a standard error of 0.192, so “only the negative rank correlation in Figure 2 (autocorrelations) is significant at conventional significance levels. Thus there certainly is no evidence of positive rank correlation, and Figures 1-3 show no positive relationships” (p. 15). Note the calibrated phrasing: no evidence of the predicted positive relation, with one significant relation of the wrong sign – not a claim that the correlations are reliably negative across the board.

Figure 3 (means), because transitivity means only 7 of its 28 points are independent – and correcting for that would make the test more, not less, hostile to the theory. “This diagram contains only 7 observations, because the rest follow from transitivity.” The reasoning: in theory the mean growth of the consumption ratio and of the real exchange rate share the same sign, so the graph should lie in the first and third quadrants as well as slope up – “If consumption grows more rapidly in country i than in country j on average then country i’s real exchange rate with country j should depreciate on average. When this implication holds, points ij, jk, and ik lie on a straight line, sloping up, by transitivity. Here the standard error quoted above would be too small, because in fact n = 7.” Their conclusion is explicitly self-adverse: “Thus, including all 28 points biases the case in favour of the theory; even so, no significant positive relation can be detected” (p. 15). They also note the geometry fails in the other quadrants: “For points in the second and fourth quadrants this straight-line relation does not hold, despite transitivity, because of reflection in one axis.”

Badly enough that the persistence result has the wrong sign almost universally, and the correlation predicted to be one averages 0.045. “Figure 2 shows that the growth rates of all 28 bilateral real exchange rates are positively autocorrelated, while 27 of the growth rates of consumption ratios are negatively autocorrelated. In addition, the cross-correlation between the growth rate of the consumption ratio and the growth rate of the real exchange rate, averaged across countries, is 0.045, with a range of [-0.08, 0.17]. Thus there is little evidence in favor of either of these implications of the theory” (Section 5, p. 16). The range matters: the abstract-level claim in the introduction is that “the correlation between relative price movements and relative consumption movements is low (less than 0.17) for all of the pairs of countries studied,” so the failure is not an averaging artefact concealing some pairs that fit. A further implication is checked by citation rather than by the authors: “A related prediction from the first-order conditions is that log(ci), log(cj), and log(eij) are cointegrated, if integrated. Kollmann (1991) finds that this implication can be statistically rejected in several data sets, including the OECD data studied here.”

Per capita measurement, annual frequency, and a narrower consumption concept; none changes the conclusion. “The conclusions do not change when we measure consumption in per capita terms. In annual, per capita data the rank correlations in the counterparts to Figures 1-3 are -0.114, -0.045, and 0.170. The average correlation between relative price growth and real consumption growth is -0.056, with a range of [-0.63, 0.21].” The authors note that the figures themselves move even though the findings do not – “because Australian population grew much faster in these two decades than did German population, for example.” Also: “We also find no support for the theory when we measure consumption only of nondurables and services. We have found similar results for other transformations and also for moments of interest rates.” And a statement of what is left undone: “Further evidence could be collected for a longer span of annual data or for additional countries” (p. 16).

One second-order feature: the relative variability of prices and quantities points to gamma greater than one. “From Proposition 2 and Example 2, the means and standard deviations of the growth rates of the price ratios exceed those of the quantity ratios if gamma is greater than 1, that is if there is less intertemporal substitution than that characterized by the logarithmic period utility function. From Figures 1 and 3 we observe that real exchange rates tend to be more variable and have larger means (in absolute value) than do consumption ratios, which facts are consistent with gamma greater than 1” (Section 5, pp. 14-15). The examples make the same point structurally: “the consumption ratio is smoother and less sensitive to differences in growth rates of the endowments of nontraded goods than is the real exchange rate if gamma is greater than 1, and the reverse if gamma is less than 1” (Section 4, p. 13). The load-bearing verb is “consistent with” – this is an ordering the theory can accommodate, not evidence for the theory, since the relation the theory actually predicts is the one the data reject.

Five candidate directions, with taste shocks the most developed and none endorsed (Section 6, pp. 16-17). The conclusion first restates the negative finding in its own terms: “growth rates of relative consumption tend to be negatively autocorrelated, whereas growth rates of real exchange rates tend to be positively autocorrelated. And there is no systematic cross-correlation between the two growth rates. Moreover, pairs of OECD countries with relatively stable consumption ratios do not have relatively stable real exchange rates. Yet such parallels should be found if fluctuations in the nontraded good sector account for international fluctuations, under standard models of preferences.” On the repairs: “One possibility would be to admit demand-side shocks (such as taste shocks), in addition to the endowment shocks studied here. Taste shocks lead to a negative correlation between changes in relative consumption and in the real exchange rate in contrast to the positive correlation arising from endowment shocks. The relative importance of the two types of shocks might be identified from the empirical correlations given in section 5, which are near zero (see also Stockman and Tesar 1990).” But the authors immediately note this does not fix everything: “the theory still predicts that pairs of countries with volatile relative consumptions will have volatile relative prices, unless there is considerable heterogeneity across countries either in preferences or in the relative importance of the two types of shocks. Figure 1 provides little evidence of this property.” The remaining candidates are listed without development: “(i) wealth effects (i.e. departures from homotheticity, which could be studied by simulation) (ii) measurement error in these data (e.g. from the use of fixed-weight indexes), (iii) incomplete markets. A further possibility is that the empirical evidence can be accounted for by a model with non-competitive features and spatial separation or segmentation (pricing to market).” The closing sentence is deliberately open: “Perhaps future work, as well as evidence for other countries and time periods, will help us distinguish among these alternatives.”

It has shown that nontraded goods “in principle can account for each of these phenomena” while the joint restriction they imply is not in the data; it has not shown that nontraded goods are unimportant, nor identified what replaces them. The abstract states both halves in sequence: “A dynamic, exchange economy is used to show that nontraded goods in principle can account for each of these phenomena. In the theory there is a close relation between fluctuations in consumption ratios and those in bilateral real exchange rates, but we find little evidence for this relation in time series data for eight OECD countries.” The introduction’s formulation is likewise scoped to the joint claim rather than to the device as such: “The main empirical finding is that there is little support for a central role for nontraded goods in accounting for the consumption and relative price evidence simultaneously” (p. 3, emphasis on the last word). What the tests reject is a competitive complete-markets exchange economy with nontraded goods and standard separable or isoelastic preferences as the explanation of both facts at once, for these eight countries over these two decades.