Chapter 34 The intertemporal approach to the current account

From a theoretical impulse and a set of events that existing models could not handle (§1). Intertemporal analyses “became common in the early 1980s as a result of papers by Buiter (1981), Obstfeld (1982), Sachs (1981), Svensson and Razin (1983), and many others, although the approach had explicit precursors in work on trade and growth by Bardhan (1967), Bruno (1970), and Hamada (1969).” The theoretical motivation was the Lucas critique: “Lucas’s insistence on grounding policy analysis in the actual forward-looking decision rules of economic agents suggested that open-economy models might yield more reliable policy conclusions if demand and supply functions were derived from the optimization problems of households and firms rather than specified to match reduced-form estimates based on ad hoc econometric specifications.” The empirical impulse was the oil shocks: “[t]he divergent patterns of current-account adjustment by industrialized and developing countries raised the inherently intertemporal problem of characterizing the optimal dynamic response to external shocks,” on which existing monetary and Keynesian models “offered [no] reliable guidance.” A third was debt sustainability: “[t]he need to evaluate developing-country debt levels again led naturally to the notion of an intertemporally optimal current-account deficit.” The authors delimit the term deliberately, reserving “intertemporal approach” for “models with international borrowing and lending but not necessarily with complete international markets in state-contingent claims,” and referring complete-markets models to another Handbook chapter.

As a synthesis rather than a replacement (§2). The current account “includes not only exports less imports (broadly defined to include all the income on and payouts on cross-border assets …), but also net capital gains on existing foreign assets,” and because foreign asset holdings were long small, “[a] focus on the current account as the net export balance led some economic thinkers to view relative international prices as its central determinant. Thus was born the elasticities approach.” The accounting identity that the current account is national saving less domestic investment produced the absorption approach, which “stresses how macroeconomic factors must ultimately determine international borrowing or lending patterns.” The intertemporal approach extends absorption by making saving and investment forward-looking, and recovers what elasticities had: it “achieves a synthesis of the absorption and elasticities view … by accounting for the macroeconomic determinants of relative prices and by analyzing the impact of current and future prices on saving and investment.”

Two omissions, each large enough to matter for the empirical literature the chapter goes on to survey (§2). Reported accounts omit capital gains on existing foreign assets, and they are nominal: “it is changes in real, not nominal, asset holdings that matter for a country’s welfare. Thus, NIPA measures of the current account, even if corrected to include nominal capital gains and losses, must be adjusted as well to correct for the inflationary erosion of foreign assets’ real values.” The illustration is the US in 1991, where “the true dollar U.S. current-account deficit … is probably much closer to -$3.7 billion + $67.8 billion - $172.8 = -$108.7 billion than to its simple NIPA measure” – and even that “reflects only partial coverage of international asset holdings.” The authors do not treat this as a footnote: “[t]hese problems plague all of the empirical literature discussed in section 4, although it would be possible to remedy them somewhat for a few industrial countries. In empirically evaluating theories it is obviously crucial to achieve the best possible match between the conceptual framework and the data brought to bear in testing it.”

Imbalances under the classical gold standard far larger than most modern ones, including for countries without close ties to the main lender (§2). Using saving, investment and current-account data for a dozen countries over 1885-1913, “[t]he graphs indeed show several examples of large and protracted current-account imbalances, indicators of extensive trade across time. Canada ran persistent deficits which, by the early twentieth century, approached 20 percent of gross national product,” flows the authors partly attribute to Canada’s “close political and cultural links with the United Kingdom, the largest lender.” But the argument does not rest on that: “even countries without such close ties to potential lenders were able to draw extensively on international capital markets. Japan ran an external deficit of 10 percent of national expenditure in financing its 1905 war with Russia.”

As a tractable starting point, with three reasons given and an explicit fallback (§3.1.1). “The intertemporal separability of preferences … will form the backbone of our formal analysis,” and the defence is stated as a methodological choice rather than a claim of realism: a fully general non-separable utility function “would yield few concrete and testable behavioral predictions. Instead we prefer to begin with a tractable basic setup … with strong implications. Preferences then can be generalized if the basic setup seems to be leading us astray.” Second, “[a]ggregation, across both goods and individuals, may cause intertemporal dependencies approximately to cancel out at the level of total per capita consumption.” Third, at macroeconomic time-aggregation levels separability “is not implausible,” and “while empirical research on data at these frequencies has raised interesting questions about the time-separable preference model, it does not clearly point to a superior nonseparable alternative.” The deterministic models more generally are justified on two grounds: they “elucidate a number of questions for which uncertainty is of secondary importance,” and they “provide a benchmark against which to measure the predictions of richer stochastic models” – a benchmark that turns out to be close, since “stochastic models in which real bonds are the only assets countries trade imply responses to shocks similar to the impulse responses of deterministic models.”

That the current account responds to gaps between current and permanent values, plus a tilting term – with each prediction hedged (§3.1.1). The equation decomposes the surplus into excess interest income over its permanent level, output less permanent output, minus government consumption and investment less their permanent levels, plus a tilting term, and the authors note that the predictions “each … require[] a ceteris paribus clause.” Three readings are given. On interest rates the sign depends on the net position: “[i]f the economy is a net foreign claimant and the world interest rate is above its permanent average, then the current account will be in greater surplus as people smooth consumption in the face of temporarily high foreign interest income. If the economy is a net foreign debtor, temporarily high interest rates will have an opposite current-account effect.” On quantities: “[o]utput above its permanent level will contribute to a higher current-account surplus, again due to consumption smoothing. Similarly, the private sector will use foreign borrowing to cushion its consumption from abnormally high government consumption and investment needs.” On tilting: when the home country is on average more impatient than the rest of the world there is “a secular tendency toward current-account deficits, and thus toward secularly increasing foreign debt and declining consumption,” an effect “proportional to the economy’s ‘permanent’ resources” and “stronger the higher is the ease of intertemporal substitution.”

A prediction off by roughly an order of magnitude, which they present as a failure and use to motivate richer models (§3.1.1, §5). In the growing Cobb-Douglas small economy, “a growing economy can run a current-account deficit indefinitely,” and the steady state gives a striking magnitude: “[s]uppose the world real interest rate r is 8 percent per year, [growth] is 4 percent per year, and [the intertemporal elasticity] = 0.4. Then A/Y = -20, and the economy’s trade balance surplus each period must be 80 percent of GDP!” The reaction is immediate: “[s]uch large debt levels and debt burdens are never observed in practice … The anomalous prediction points to some shortcomings of the model.” Three are named: “[w]ith finite lifetimes, individuals currently alive wouldn’t be able to borrow against the entire present value of the economy’s output”; “[t]here is no allowance in the model for sovereign risk”; and the small-country assumption is internally strained, since a country growing faster than the world indefinitely “would cease being small and the fixed interest rate assumption would be violated.” The conclusion restates the puzzle as unresolved: “it is a puzzle that ratios of foreign debt to output seldom exceed 1:1 when plausible parameter estimates suggest that ratios of 5:1 or 10:1 could easily be sustainable and even optimal.”

As a real regularity that does not bear the weight placed on it, and emphatically not as support for Feldstein’s policy conclusion (§4.1). They set out the logic fairly: since “[a] basic premise of the intertemporal approach is that capital is to some degree internationally mobile,” an “empirical finding that national saving rates affect domestic investment rates with unit coefficients would therefore appear to be strong evidence against the applicability of the intertemporal approach.” They reproduce the original regression for 16 OECD countries over 1960-74 – a saving coefficient of 0.887 with a standard error of 0.074 and R-squared of 0.91 – and note that the association weakens but persists, with a coefficient of 0.622 and R-squared of 0.69 for the OECD over 1982-91 excluding Luxembourg and Turkey, “a weakening, but still very significant, positive association.” They also record that the ratios “suffer from all the conceptual deficiencies discussed at the end of section 2.” The key distinction they draw is between description and prescription: “[a]lthough the intertemporal approach is consistent with a world in which changes in saving behavior impinge on domestic investment, it certainly does not support the policy conclusion, preferred by Feldstein, that government measures to raise a country’s saving rate will automatically cause a long-run pari passu increase in its investment rate.”

They are logically distinct, and the authors give a historical case where they diverge sharply (§4.1). The cross-section “captures the association between low-frequency or ‘sustained’ changes” while contemporaneous detrended series capture “the coherence of high-frequency changes,” and “[t]he time-series and cross-section aspects of the saving-investment relationship are quite distinct: the time-series relationship could be close and the cross-section relationship not, or vice versa.” Their example is the pre-war UK: “[i]t is apparent that the short-run saving-investment correlation is very close. Nonetheless, the U.K. ran current-account surpluses approaching 10 percent of GDP in this same period.” They also make a consistency objection to the immobility reading: “it is hard to see how capital could be truly immobile in the long run but not in the short run, since the long run is just a succession of short runs. And even if international trade in long-term instruments or long-lived assets were highly limited – a hypothesis that the data do not support – short-term instruments can be rolled over.” The modern time-series correlation is reported as a “stylized fact,” explicitly “somewhat sensitive to the detrending method adopted”: across OECD countries over 1974-90, “the average correlation between saving and investment rates is 0.495 over 1974-90 after linear time detrending. The correlation is 0.512 when the data are first-differenced,” with Norway singled out as “the most glaring” exception.

Four, each with its own counter-evidence noted (§4.1). First, current-account targeting: governments have sometimes adjusted policy to avoid large imbalances, though “[t]he evidence on this current-account targeting hypothesis is mostly anecdotal … and there are of course prominent instances (like the United States in the 1980s) in which macroeconomic policies have instigated major external imbalances.” Second, stochastic steady states: OECD countries “may be sufficiently well endowed with capital to have reached stochastic steady states for their external debt or asset levels,” which would make long saving-investment averages small – an interpretation “borne out by the cross-sectional results for developing countries prior to the onset of their debt crisis in 1982,” where “the cross-sectional saving-investment association is much looser.” Third, the Gertler-Rogoff channel by which investment responds to retained earnings, with a caveat the authors supply themselves: “private domestic owners of firms may pierce the corporate veil and offset corporate saving decisions through their own consumption,” and foreign-owned firms’ retained earnings raise foreign rather than domestic saving. Fourth, demographics, where they report both sides: Feldstein-Bacchetta and Summers “have dismissed this line of explanation,” but Taylor, controlling for domestic relative prices, age structure, and its interaction with output growth, “finds that for a number of country samples the cross-sectional saving-investment association disappears.” Their overall statement is comparative: “[i]t seems likely that of the many potential explanations … no single one fully explains the behavior of all countries. Taken together, however, and combined with other evidence indicating substantial international mobility of capital, the arguments suggest that the Feldstein-Horioka finding provides no basis at all for dismissing the basic premises of the intertemporal approach.”

Because the required discount rate is unclear and the answer is hypersensitive to a persistence parameter that cannot be pinned down empirically (§4.2.1). On the rate: “[m]ost of the studies surveyed below use fairly low discount rates, in the range of 2 to 4 percent per year. These numbers correspond roughly to average ex post real returns on U.S. Treasury bills post-World War II. But is a (nominally) riskless rate the appropriate one for discounting very risky future output flows?” – with Bernanke’s estimate that “an annual real interest rate as high as 14 percent is needed to rationalize U.S. consumption-income relationships” cited as the opposite pole. On sensitivity: at a 3 percent rate, expected output twenty years ahead “though discounted, still has a weight more than half that of current output,” so with an AR(1) output process, “[w]hen [the AR coefficient] = 1 … permanent output = current output, regardless of the value of r. But when r = 0.03 and [the coefficient] = 0.97 (a value differing from 1 by an amount generally too small to detect empirically), [the ratio] drops to only 0.5: permanent output is half of current output.” Raising the rate helps – 0.824 at 14 percent, 0.943 at 50 percent – but “[r]eal interest rates high enough to make [permanent output] insensitive to [the coefficient] in the vicinity of a unit root appear implausible.” The authors link this to Deaton’s paradox in the closed-economy consumption literature.

Partial support, with the model’s implied responses often the wrong size (§4.2.2). Hercowitz, on Israeli data for 1950-81, “presents some support for an intertemporal model but also finds that the model exaggerates the current account’s response to output fluctuations.” Johnson, on Canada for 1952-76, “rejects Ricardian equivalence, but concludes that Canada’s private sector can plausibly be modeled in line with a version of the intertemporal approach that allows for some liquidity-constrained consumers.” Ahmed’s work is highlighted for its identification: British wartime spending was “largely exogenous and … almost certainly viewed as temporary by the public,” so the theory predicts wartime external deficits, and using data back to 1701 gives “a more demanding testing ground than the twentieth century alone, as the period is punctuated by many wars.” The authors are careful about what a negative correlation between spending surges and the current account proves: it “is fully consistent with theories other than the intertemporal approach.” Their own re-estimation with serial-correlation correction is reported as unhelpful to the theory: “neither current or permanent government spending coefficient is individually significant,” followed by the interpretive difficulty they name repeatedly – “it is unclear whether the intertemporal approach is simply false, or whether the many extraneous simplifications and maintained hypotheses imposed by the econometrician are to blame.”

A test with a sharp null and a mostly negative verdict (§4.2.3). The model in differenced form says “the current account balance tends to be negative when net cash flow is expected to rise, and positive when it is expected to fall,” with net cash flow defined as output less government consumption less investment, and differencing chosen because the level may contain a unit root. The methodological advance is informational: “as long [as] the information set used by the econometrician does not contain all the information available to private agents, then past values of [the current account] contain information useful in constructing estimates of agents’ expectations,” so estimating a VAR in the cash-flow change and the current account and imposing the model yields the null that the coefficient vector equals [0 1]. Results: “Sheffrin and Woo find that the restriction … is rejected for Canada, Denmark, and the U.K. in their 1955-85 sample, although it is not rejected for Belgium. Ghosh, whose sample period is 1960-88, finds that the restriction is not rejected for the U.S., but that it fails for Canada, Germany, Japan, and the United Kingdom.” Even the weaker implication that the current account should Granger-cause the cash-flow change is, in Ghosh’s full sample, “still passed only by the United States data,” and Otto “rejects the present-value model for Canada and the U.S.”

As informative but with a specific reason for discounting it (§4.2.3). “While the formal evidence therefore is very mixed, Ghosh, Sheffrin and Woo, and Otto all stress that the informal evidence obtained by simply lining up actual current accounts with the model’s predictions can be quite impressive. This perspective is useful, because no empirical model is likely to be literally true.” But the caution is immediate and technical: “one should not make too much of such pictures, either, since the lagged current account, used in constructing the VAR estimates, is likely to be a good predictor of today’s current account regardless of the validity of the present-value model.” Their own examples cut both ways: “[t]he model performs very well for Sweden, but poorly for the United Kingdom,” possibly because it omits oil prices. Extending Britain’s data to 1870-1991 with a 4 percent real rate “yields a dramatically better fit than when one estimates the model over post-World War II data alone,” yet “the model still fails a formal test of the restriction,” with the estimated coefficient vector [-0.26 0.54] differing significantly from [0 1].

Too volatile relative to the model – the opposite of the Feldstein-Horioka reading (§4.2.3). “A common theme in the graphical evidence … is that the actual current account is often far more volatile than the predicted current account. This seems to contradict the Feldstein-Horioka conclusion that current account movements are relatively small compared to what one would expect in theory.” Formally, Ghosh finds the actual variance higher except for the US, where equality cannot be rejected, and “Otto similarly finds that Canada’s current account is six times as volatile [as] that of the predicted series.” Ghosh reads this “as evidence of ’too much’ capital mobility, in contrast to the Feldstein-Horioka claim of too little.” The authors offer a reconciling conjecture rather than a conclusion, tying it back to the persistence problem: since assuming a unit root in income “can lead to the conclusion that consumption is too smooth, it can also produce the result that saving or the current account is too volatile. This may help explain the Ghosh-Otto volatility results, though further investigation is required.”

A large one, and it is the chapter’s clearest example of the theory doing better once specified correctly (§4.2.4). The criticism of the earlier tests is that they implicitly assume “all shocks to cash flow are purely idiosyncratic,” whereas “[o]utput shocks which identically impact all countries should … express themselves primarily through the global interest rate, and not in individual countries’ current accounts,” so that on the corrected equation “only country-specific shocks affect current accounts.” Glick and Rogoff use annual G-7 data for 1960-90, “treating these countries as the world (which, in terms of economic size, isn’t a bad approximation for most of their sample period),” and split shocks two ways – subtracting a mean-GNP-weighted world average, and taking residuals from a regression on an index of other countries’ cash flows – finding the two “yield similar results.” Global shocks are large: “roughly 50 percent” of total G-7 productivity shocks. And the correction works: “the global versus country-specific distinction greatly improves the ability of the intertemporal approach to explain actual current accounts: the coefficients on the global shocks are invariably much smaller than those on the country-specific shocks, and are usually insignificant.” The authors also flag unreconciled contrary evidence from Costello and Stockman, whose industry-level results “apparently point[] to a greater role for country-specific shocks, and it remains to reconcile it with the results discussed in the text.”

Precautionary saving, durables, and nontradables, each with a quantitative or interpretive caveat (§4.2.5). Ghosh and Ostry add a precautionary-saving term built on Caballero’s closed-form solution under exponential utility, and find “their precautionary variable usually enters significantly and with the correct sign,” with magnitudes for developing countries “of the order of magnitude of 5 percent of imports for the African region, 4 percent for commodity exporters, and 14 percent for fuel exporters” – obtained after negotiating the measurement problem that the conditional variance must be estimated over intervals “long enough … for accurate measures” but not so long as to exhaust the time series. Burda and Gerlach argue durable-goods imports should be far more sensitive to expected real exchange rate movements than nondurables, and find such expected price changes significantly correlated with the US current account over 1970-88, though the authors note comparison is hard because “the Burda-Gerlach setup, with its very general lag structure, imposes much less theoretical structure.” Rogoff’s nontradables model shows that “even a temporary rise in traded-goods output raises [tradables consumption] permanently because of consumption smoothing,” so intertemporal smoothing “might account for the persistence of innovations in real exchange rates” – a result for which “[a] country’s ability to borrow and lend in international markets is the key,” and which finds “some support, though further testing is required.”

For questions the alternatives cannot pose, including persistent imbalances and the consequences of demographic change (§5). “Even in its most rudimentary forms, the intertemporal approach … has proved valuable for analyzing a host of important problems,” specifically “the current-account and world interest rate effects of oil price shocks” and “episodes of capital-market disruption, such as the developing-country debt crisis of the 1980s” – where “the standard intertemporal models must be extended to take account of default risk but … the main qualitative insights do not change.” The general claim: “models that fail to integrate investment, saving, and growth make it virtually impossible to understand why some countries have persistent current account imbalances. Why, for example, are Canada’s and Australia’s current accounts perennially in deficit, and Japan’s in surplus, despite wide swings in their currencies’ real exchange rates?” And overlapping-generations variants “are indispensable for thinking about how, say, the aging of Japan’s population could eventually lead to a fall in Japan’s persistent trade surpluses.”

Uneven descriptive performance, the debt puzzle, and weak support for a robust prediction of the finite-horizon versions (§5). “As positive descriptions of the current account, the simple intertemporal theories are not without their limitations. As we saw above, time-series models based on consumption smoothing seem to work fairly well for some countries (for example, Sweden) but, in other cases, clearly miss much of the action,” and they suggest that “[f]urther research allowing for time-varying interest rates, multiple goods, durables, nominal price rigidities, and some liquidity-constrained consumers might lead to better descriptive power.” On finite-lived-dynasty models, which rationalise observed debt levels better: “such models, while capable of embracing a wider set of empirical phenomena, also pose empirical puzzles. A fairly robust implication is that government deficits lead to current-account deficits, but the empirical evidence supporting this prediction, while suggestive, is hardly a basis for strong conclusions. The striking industrial-country correlation observed over 1976-1985 is not clearly evident later on.”

Because both alternatives fail in ways they specify, and the argument is comparative (§5). “The models we have discussed in this chapter provide only a starting point. Obviously, the task of building and empirically applying richer and more realistic intertemporal models will not be an easy one. But there is no avoiding this challenge, since the two leading alternatives to the intertemporal model are seriously flawed.” Against complete markets: if it held, “the current account is little more than an accounting convention without major significance even for a country’s relative wealth position,” and the authors judge real markets “very far from the frictionless, full-information, complete-markets ideal” because of “moral hazard problems in lending at the microeconomic level, finite lifetimes, and difficulties in insuring labor income,” compounded internationally by “sovereign default risk, difficulties in insuring national government spending shocks, and cultural and institutional differences.” They concede the methodological point against themselves – “it would be vastly preferable to model explicitly these capital-market imperfections rather than simply to assume limited asset trade” – and rest on comparison: “[u]ntil these models have been more fully developed, however, the intertemporal model seems to provide a much closer description of reality than does the complete markets model.” Against Mundell-Fleming: it “ignores intertemporal choice and even intertemporal budget constraints” yet “remains overwhelmingly dominant in policy circles,” and it “offers no valid benchmark for evaluating external balance” – since “efficient trade across time often calls for an unbalanced current account,” while “[t]he intertemporal approach identifies circumstances, for example, a transitory fall in output or a rise in domestic investment productivity, that justify a current account deficit.” The normative conclusion is stated flatly: “[t]he intertemporal approach to the current account offers a viable framework for assessing macroeconomic policy, one that must supplant the Mundell-Fleming framework for normative questions.” The positive conclusion is stated as an expectation rather than a result: “as intertemporal models become more tractable and enjoy wider empirical testing, it seems to us that they must ultimately come to supplant modified Mundell-Fleming models for positive as well as normative questions.”