Capital Flows to Developing Countries: The Allocation Puzzle

That countries with faster productivity growth should receive more net capital inflows – a prediction the paper derives from the textbook neoclassical growth model and motivates from the development-accounting literature. Two conclusions from that literature do the motivating work (§1, p. 1487). First, “a substantial share of the cross-country inequality in income per capita comes from cross-country differences in TFP,” so “the economic take-off of a poor country, therefore, results from a convergence of its TFP toward the level of advanced economies.” Second, “developing countries are able to accumulate the level of productive capital that is warranted by their level of TFP,” citing Caselli and Feyrer (2007) that properly measured returns to capital are similar across rich and poor countries. Taken together, “an open economy version of the basic neoclassical growth model should be a reasonable theoretical benchmark to think about the behaviour of capital flows toward developing countries,” and the paper claims to be “the first, to our knowledge, to quantify the level of capital flows to developing countries in a calibrated open economy growth model and compare it with the data.”

Lucas’s puzzle is about the small aggregate level of flows from rich to poor countries; this one is about their allocation across developing countries, and the paper argues the level is not the anomaly. Because average productivity catch-up in the sample is slightly negative, “we should not expect a lot of capital to flow from advanced to developing countries” (§3.3, p. 1494). The paper’s reading of its own calibration is that the low aggregate level “is not especially puzzling given the relatively low rate of productivity growth in these countries,” which it describes as consistent with Lucas’s own hypothesis. What the model cannot reproduce is the cross-section: “our calibrated open economy growth model predicts large capital inflows to Asia and large capital outflows from Latin America and Africa… By contrast, in the data, we observe that capital has flowed to all three regions, and more so (in proportion of investment or GDP) to Africa and Latin America than to Asia.”

A deterministic small open economy, Cobb-Douglas in capital and labour, borrowing and lending freely at an exogenous world interest rate, with an exogenous productivity path that may converge on or diverge from a frontier growing at a constant rate. Labour supply equals population, factor markets are perfectly competitive, capital is owned by residents, and there is no default risk so the country pays the riskless rate (§2.1, pp. 1488-1489). Perfect capital mobility equates the net marginal product of capital to the world rate, which pins the capital stock per efficient unit of labour at a constant; net inflows are then investment minus national saving, “with both terms playing an important role in the analysis.” The paper defends unconstrained borrowing as “a theoretical benchmark” and as “not an implausible assumption to make in light of Caselli and Feyrer (2007)’s finding that the real returns to capital are equalized across the world,” and it checks the direction of the result under a borrowing constraint: with a debt ceiling rising in output or capital, “capital flows to capital-scarce countries are lower than in the absence of constraint but it remains true that a country without initial debt or capital scarcity receives a positive level of capital inflows if and only if it catches up relative to the world technology frontier, and that the volume of capital inflows is increasing with productivity growth” (§2, fn. 10). The paper also names the structural reason the saving channel is so powerful: “the saving component is very responsive to growth in the model because of the assumption that consumers are infinitely lived and can perfectly smooth consumption,” and “in the limit case where households cannot access financial markets, the saving component would equal zero” (§3.3, p. 1496 and fn. 22).

Depreciation 0.06, capital share 0.3, frontier productivity growth 1.7 percent, discount factor 0.96 and log preferences, implying a world gross interest rate of 1.0594. The frontier is US TFP, so its growth rate is “the observed growth of U.S. total factor productivity between 1980 and 2000” (§3.1, pp. 1492-1493). The interest rate follows from the discount factor and the frontier growth rate; the paper checks it against Caselli and Feyrer’s reported average marginal return to capital of 6.9 percent for poor countries with a standard deviation of 3.7 percent, and calls log preferences “rather conservative, given the uncertainty about whether the intertemporal elasticity of substitution is larger or smaller than one.” Productivity catch-up is measured as trended TFP in 2000 relative to trended TFP in 1980 grown forward at the frontier rate, minus one, with the trend from a Hodrick-Prescott filter whose smoothing parameter of 1600 on annual data “filters out more than 70% of cycles of periodicity lower than 32 years.” The paper reports that varying the discount factor or the intertemporal elasticity “has a very small impact on the results” (§4.2, fn. 31).

68 developing countries – 65 non-OECD plus Korea, Mexico and Turkey – over 1980-2000, with flows cumulated from current-account deficits and PPP-deflated by the price of investment goods. The period is chosen because financial openness rose sharply from the late 1980s (the Chinn-Ito index averaged -0.38 in 1980 and 0 in 2000 for the sample) and because “we want as long a sample as possible, since the focus is on long-term capital flows. Results over shorter periods may be disproportionately affected by a financial crisis in some countries or by fluctuations in the world business cycle” (§3.2, p. 1493). Output, capital and productivity come from Penn World Table 6.1, with capital built by perpetual inventory. Initial net external debt comes from Lane and Milesi-Ferretti’s External Wealth of Nations Mark II, as the negative of the net international investment position less errors and omissions cumulated 1970-1980. Net inflows come from IMF current-account deficits, “keeping with the usual practice that considers errors and omissions as unreported capital flows.” The deflator choice is explained rather than assumed: trade balances should be deflated by the traded-goods price, which the Penn World Tables do not report, so the investment-goods price is used as “a good proxy because investment goods are mostly tradable – as suggested by the fact that their price varies less across countries than that of consumption goods,” and the paper notes “the PPP adjustment tends to reduce the estimated size of capital flows relative to output in poor countries.” It also states that “the allocation puzzle… does not hinge on the particular assumptions that we make in constructing those estimates. We tried other deflators, which did not affect the thrust of our results” (§3.2, p. 1494).

Negative, sizeable, and present in both the regional and the income breakdowns. Plotting average TFP growth against average net inflows over 1980-2000, the regression slope is -0.72 with a p-value of 0.1 percent, with some countries receiving more than 10 percent of GDP in inflows (Mozambique, Tanzania) and Taiwan exporting about 7 percent (§1, p. 1485 and fn. 3). Group averages make the same point: average catch-up is -0.10 for the whole sample, 0.19 for Asia, -0.24 for Latin America and -0.17 for Africa, while cumulated inflows relative to initial output are 11.28 percent for Asia against 36.89 for Latin America and 39.09 for Africa (§3.3, Table 1, pp. 1494-1495). By income, “poorer countries experienced lower productivity catch-up and so should export more capital… Observed capital inflows run in the exact opposite direction: actual capital flows decrease with income per capita, from 56% of output for low-income countries to −58% for high-income non-OECD countries.” The paper is careful that regional averages conceal heterogeneity – catch-up is -0.34 for the Philippines, 0.28 for Chile and 0.47 for Botswana (§3.3, fn. 19).

Observed flows are of the same order of magnitude as the investment component of the prediction but negatively rather than positively related to catch-up – so the model reproduces the size of flows much better than their allocation. Plotting observed inflows against catch-up together with the predicted investment and saving components, “most countries are located in the ‘wrong’ quadrant of the figure, with negative productivity catch-up but positive capital inflows,” with a fitted slope of -0.68 (standard error 0.18, p < 0.01) (§3.3, pp. 1495-1496). The predicted slopes are +2.14 for the investment component and +5.25 for the saving component, so the saving channel is the more extreme: “for a country such as Korea, with a productivity catch up [of] 0.61, the model predicts investment and saving components of net capital inflows each in excess of 130% of initial output. Conversely, for Madagascar, with a relative productivity decline [of] −0.47, the model predicts investment and saving components of net capital outflows each in excess of 100% of initial output!” Against this, “the ratio of the sum of the absolute value of the observed net inflows amounts to 76% of the model prediction based on the investment component. We conclude that the model is able to reproduce the magnitude of capital flows… much better than their allocation across countries.”

Yes, and the interaction with financial openness goes the wrong way for the model. Regressing observed inflows on the four variables the model identifies – initial capital abundance, initial debt, working-age population growth and productivity catch-up – leaves the catch-up coefficient significantly negative at -0.586, while “the other variables do not enter significantly, except initial debt, which has a positive coefficient as predicted by theory but much smaller in magnitude”: 0.006 estimated against 1.14 predicted (§3.3, Table 2, pp. 1496-1497 and fn. 23). Adding the Chinn-Ito openness index, either additively or interacted with catch-up, does not rescue the model: “One would a priori expect a better fit between the model and the data for more financially open countries. Yet we find the opposite to be true: the coefficient on productivity catch-up remains strongly negative, the more so for more financially open economies.” Other unreported checks constrain the initial-condition coefficients to their theoretical values and exclude African countries, “where arguably many countries may be too poor to export capital,” without changing the result.

They are a diagnostic device to locate which first-order condition the data violate, not an explanation of the puzzle. The paper states this before introducing them: “We should not interpret these wedges as an explanation for the allocation puzzle, but rather as a diagnosis tool that points to the first-order conditions that exhibit the largest discrepancies with the data – and may then guide us toward the type of changes to the model that may explain the puzzle” (§4, p. 1498). The capital wedge means investors receive only a fraction of the gross return on capital, interpretable “as a tax on gross capital income, or as the result of other distortions – credit market imperfections, expropriation risk, bureaucracy, bribery, and corruption,” or as inefficiency in producing investment goods that raises the relative price of capital. The saving wedge enters the household budget constraint and “functions like a tax on capital income that increases current consumption relative to future consumption,” with revenue from both wedges rebated lump sum so that only the intertemporal distortion is at work, and with the saving wedge set to zero after the transition so consumption growth converges to the world rate. Crucially, “because of perfect capital mobility, there is a Fisherian separability between the two wedges, in the sense that the capital wedge required to explain the observed investment rate can be computed independently of the saving wedge.” The paper is candid that with both wedges “the model replicates perfectly, but trivially, the observed capital flows” (§4.2, p. 1502). The methodological ancestor is Chari, Kehoe and McGrattan’s business-cycle accounting, with the difference that “while [they] look at real business fluctuations, we focus here on long-term growth” (§1, p. 1487).

The capital wedge averages 11.5 percent, falls with income, and the investment rate is dominated by the trend component, which moves inversely with the wedge. The proposition decomposes the average investment rate into a convergence term (the investment needed to bring capital to its equilibrium level), a productivity term (the extra investment warranted by catch-up) and a trend term (replacing depreciation, adjusted for productivity and population growth) (§4.1, p. 1499, Proposition 2). Investment rates range from 8.49 percent of output for low-income countries to 28.52 percent for high-income non-OECD, and 10.26 percent in Africa against 19.59 in Asia; the fitted capital wedge runs from 18.92 percent for low-income countries down to 1.55 percent for high-income non-OECD, and from 16.05 percent in Africa to 6.88 in Asia (Table 3). The paper’s summary: “most of the variation in the investment rate is accounted for by the trend component, which itself is strongly correlated with the capital wedge… To a first order of approximation, countries with a high investment rate are those that maintain a high capital-to-output ratio because of a low distortion on capital accumulation.”

It ranges from about -6 percent for Taiwan and Singapore to about 6 percent for Rwanda and Angola, averages 1 percent, and is strongly negatively correlated with productivity catch-up – which is what makes the allocation puzzle a saving puzzle. “First, we observe that the saving wedge needed to account for aggregate saving ranges from −6% for countries such as Taiwan or Singapore, to 6% for countries such as Rwanda or Angola, with an average of 1%. This may seem relatively small but the cumulative impact on initial consumption of such annual wedges applied for twenty years is large” (§4.2, p. 1502). The pattern is systematic: “countries whose productivity catches up… are also countries that ‘subsidize’ saving… while countries that fall behind… are countries that ’tax’ saving,” and because the relationship is roughly linear through the origin, “on average, countries that catch-up twice as much in terms of productivity ‘subsidize’ their saving twice as much.” By region, Asia’s saving wedge is -1.14 percent while Latin America’s and Africa’s are 1.83 and 1.79 percent; the wedge also falls with the level of development (§4.2, p. 1504). The conclusion the paper draws is stated as a diagnosis of where the model breaks: “adjusting investment rates to account for physical capital accumulation is not enough to account for patterns of capital flows across countries. The saving wedge is essential to account for the observed pattern of net capital flows across developing countries.” The paper allows a distortionary reading – a saving subsidy could reflect “domestic financial repression that prevents residents from borrowing against their future income” – but flags the constraint that reading faces: “the distortion would need to be positively correlated with productivity growth to account for” the observed pattern (§4.2, fn. 32).

In the frictionless model it should not, by a Barro-Ricardian argument – so the fact that it does is itself informative. If public flows were government borrowing financing a lump-sum transfer, “the predictions of the model would remain valid for net capital flows because of a form of Barro-Ricardian equivalence: any change in public flows would be offset one-for-one by a corresponding change in the private sector’s external borrowing,” which can be verified by simply redefining debt as total public plus private external debt (§5, p. 1504). “However, Ricardian equivalence may fail to hold if private capital flows are constrained by financial frictions that do not affect public flows to the same extent… In addition, capital controls could prevent changes in public flows from being completely offset by private flows.” The paper then adopts a deliberately extreme benchmark – “we make the extreme assumption that those flows are not offset by any other type of capital flows” – and says so. It also states the ambiguity in the prior: public flows should be positively related to growth if they finance development-relevant public investment, but “there is a selection bias if the countries that have been receiving public flows over long periods of time are those that have failed to develop (as would be the case for humanitarian aid flows)” (§5, fn. 34).

Private inflows are positively related to catch-up; public flows are strongly negatively related and larger in magnitude. Using Aguiar and Amador’s definition – net public inflows are the change in public and publicly guaranteed debt minus the change in international reserves, with private flows the residual – and losing six countries to data availability (Angola, Hong Kong, Iran, Mozambique, Taiwan and South Africa), the fitted slope on catch-up is -0.79 (p < 1 percent) for public inflows and +0.29 (p = 4 percent) for private inflows (§5, pp. 1505-1506 and fn. 40). Group averages: high-income non-OECD economies received private inflows of 70.69 percent of initial output against 27.73 percent for low-income countries, while their public flows were -100.58 percent against +28.32 percent. Across regions the private picture is muddier – “all three regions received about the same amount of private capital (between 27% and 36%) despite vastly different productivity performance.” Two extreme cases are excluded from the figures and named: Botswana’s and Singapore’s net public capital outflows of -248 and -261 percent of initial output, with the paper noting “adding them would only strengthen our results.” Regressions confirm the pattern with controls: the public-flow coefficient on catch-up is -0.843, rising in magnitude to -1.182 with an openness interaction of -0.693 (§5, Table 6, p. 1507).

Reserves account for much of the public-flow pattern, and financial openness amplifies rather than attenuates the puzzle. “According to the estimates, open developing countries that experience a 10% increase in their productivity catch-up between 1980 and 2000 accumulated international reserves accounting for about 30% of their initial output,” with the paper adding a scope note: “these estimates are obtained on a pre-2000 sample. Therefore, they do not include the rapid rise in international reserve holdings of major emerging economies that occurred since then, especially after China’s accession to the WTO” (§5, p. 1508). The openness result is the one that most sharply resists a frictions-only reading: “the interaction term between financial openness and productivity on total capital inflows is negative and significant, indicating that the allocation puzzle applies more strongly to financially more open economies. The reason… is that public outflows respond more strongly than private inflows to productivity growth in more open economies. Thus, financial openness does not reduce the allocation puzzle, it exacerbates it.” The paper is careful that the split “does not per se resolve the allocation puzzle but it leads us to reformulate the question in a more precise way”: why do faster-growing countries have larger public outflows, and why are those not offset by private inflows even where the financial account is very open?

It regards its own finding as related to both but stronger. The literature has established a positive correlation between saving and growth – puzzling under the permanent income hypothesis, “since high-growth countries should borrow abroad against future income to finance a higher level of consumption” – and, since Feldstein and Horioka, a strongly positive correlation between saving and investment (§1, p. 1486). “The allocation puzzle presented in this article is related to both puzzles, but it is stronger. Our finding is that the difference between savings and investment (capital outflows) is positively correlated with productivity growth.” It also notes that the sign is the opposite of the emerging-market business-cycle fact: current accounts are countercyclical at business-cycle frequency, whereas “the cross-country correlation between growth and the current account is the opposite.” Because of the very low frequency, the more natural comparison is the transitional-growth literature, from which the paper differs in allowing countries to catch up or fall behind relative to the frontier and in drawing out the implications for flows.

Five families of explanation, reviewed as “a tentative road map” with no attempt to choose between them. The paper says so at the outset and again in the conclusion: “No attempt is made to discriminate empirically between these explanations – the objective of the last section of the article being to propose a road map for future research rather than to establish new results,” and “the explanations reviewed below are not mutually exclusive, and may be complementary. Moreover, the most relevant explanation may not be the same for different countries or regions” (§1, p. 1486; §6, fn. 42). The families: (i) causality from growth to saving, via the life-cycle model or consumption habit, where “whether models with consumption habit can explain the allocation puzzle (i.e. that higher growth raises saving more than investment) is an open question for future research”; (ii) domestic financial frictions, since international frictions “cannot explain the allocation puzzle… they can mute the absolute size of capital flows, not change their direction,” whereas domestic frictions can constrain borrowing against future income and blunt investment’s response to productivity; (iii) precautionary saving against idiosyncratic risk, where “a positive correlation between growth and idiosyncratic risk can reverse the sign of the relationship between growth and capital flows” absent insurance mechanisms – with the open question of whether models of precautionary saving against aggregate risk, which is how reserves are usually justified, can do the same; (iv) causality from saving to growth, which “does not easily survive perfect capital mobility, which makes domestic savings a small component of the global savings pool”; and (v) explanations centred on government policy, including the “Bretton Woods 2” view in which fast-growing tradable sectors resist real appreciation through public foreign-asset accumulation plus inflow restrictions, and Aguiar and Amador’s limited-commitment model in which growth requires governments to pay down external liabilities. The paper flags the common weakness of the first four families – “they do not give a meaningful and distinct role to the government, and thus do not speak to the fact that the allocation puzzle seems to reflect the behaviour of public capital flows” – and the common requirement of the fifth: these accounts “rely, implicitly or explicitly, on the assumption that the government can control the volume of net capital flows. This is not true in the frictionless neoclassical model, because the accumulation of reserves by the government should be offset one-for-one by higher capital inflows. This must be prevented by frictions, either natural (low financial development) or policy induced (capital controls).”

Far enough to raise the question explicitly, without answering it. “This article establishes a puzzling stylized fact: capital does not tend to flow more towards countries with higher productivity growth and higher investment. This is puzzling for neoclassical models of growth – in fact, this makes one wonder if the textbook neoclassical framework is the right model at all to think about the link between international financial integration and development” (§6, p. 1508). What it claims to have established beyond the stylised fact is narrower and precise: that the puzzle is “related to (i) saving rather than investment, and (ii) the behaviour of publicly originated capital flows (and in particular, the accumulation of international reserves),” so that “the solution to the ‘allocation puzzle’ thus lies at the nexus of between growth, saving, and the accumulation of net foreign assets by the government.”