Why Doesn't Capital Flow from Rich to Poor Countries?

That under free competitive trade in capital goods, all new investment should go to the poorer country until capital-labour ratios, wages and returns are equalised – and this follows “from entirely standard assumptions on technology alone.” Lucas states the logic in three steps (p. 92): two countries produce the same good with the same constant-returns production function relating output to homogeneous capital and labour; if production per worker differs, “it must be because they have different levels of capital per worker: I have just ruled everything else out!”; and then “the Law of Diminishing Returns implies that the marginal product of capital is higher in the less productive (i.e., in the poorer) economy.” The conclusion drawn is not that capital flows are somewhat too small but that under the theory “one would expect no investment to occur in the wealthy countries in the face of return differentials of this magnitude.”

With US production per person about fifteen times India’s and a Cobb-Douglas capital share of 0.4, the implied Indian marginal product of capital is about 58 times the American one. The sources and steps are stated plainly (p. 92): production per person in the United States “is about fifteen times what it is in India,” from Summers and Heston (1988, Table 3, pp. 18-21); output per worker follows y = Ax raised to the capital share, with a common intercept in both countries; and in terms of production per worker the marginal product of capital scales as output per worker raised to a power of one minus the capital share over the capital share. Setting the capital share to 0.4, “an average of U.S. and Indian capital shares,” again for both countries, yields a factor of fifteen raised to 1.5 – “about 58 times the marginal product of capital in the United States.” Lucas is explicit about why he bothers: “I worked out the arithmetic for this example to make it clear that there is nothing at all delicate about this standard neoclassical prediction on capital flows.”

It cuts the predicted return ratio from about 58 to about 5, by cutting the income ratio per effective worker from 15 to 3. The first candidate explanation is that the introductory calculation treats effective labour input per person as equal across countries, “ignoring differences in labor quality or human capital per worker” (§I, p. 92). Lucas uses Anne Krueger’s (1968) study, which he calls “the best attempt to correct measured labor inputs for differences in human capital” while noting its estimates rest on 1950s data – defended on the grounds that “the percentage income differentials between very rich and very poor countries have not changed all that much in the last 25 years and, in any case, a rough estimate is better than none at all.” Krueger’s method combines each country’s mix of workers by education, age and sector with US estimates of how those factors affect productivity as measured by relative earnings, and her Table III (p. 653) reports, for 28 countries, the per capita income each could attain with US physical capital per worker: from about .38 for India, Indonesia and Ghana to unity for Canada and .84 for Israel (§I, p. 93). Because these figures have the dimension of relative human capital stocks raised to labour’s share, taking labour’s share at .6 implies relative human-capital endowments from about .2 to unity – “each American or Canadian worker was estimated to be the productive equivalent of about five Indians or Ghanians.” Lucas adds a sanity check in wage terms: compensation per employed civilian in the United States in 1987 was about $24,000, “so this estimate implies that a typical worker from India or Ghana could earn about $4800 in the United States.” Reinterpreting income as income per effective worker makes the US-India ratio 3 rather than 15 and the predicted return ratio 3 raised to 1.5, “= 5 rather than 58.”

Because a factor of five is still far larger than observed flows can bear, and because a complete resolution along these lines would create a worse problem with labour migration. On the first point: “This is a substantial revision, but even so, it leaves the original paradox very much alive: a factor of 5 difference in rates of return is still large enough to lead one to expect capital flows much larger than anything we observe” (§I, p. 93). The second point is the more interesting one and is worth stating in full, because it is the constraint that disciplines the whole exercise: under constant returns, equal capital returns imply equal wages for equally skilled labour, so if human-capital adjustment alone eliminated the return differential there would be no economic motive for labour flows either – “Yet we see immigration at maximal allowable rates and beyond from poor countries to wealthy ones. We do not want to resolve the puzzle of capital flows with a theory that predicts, contrary to the evidence provided by millions of Mexicans, that Mexican workers can earn equal wages in the United States and in Mexico.”

That an economy’s technology level is the average human capital of its workers raised to a power, with that exponent estimated at 0.36 from Denison’s US 1909-1959 data. Lucas notes one could always resolve the puzzle by assuming returns are equalised and backing out the implied technology-level differences, and says that is “almost what I will do in this section, but I will do so in a way that has more content,” by making the technology term an external effect of average human capital, multiplying the productivity of a worker at any skill level exactly as a technology intercept would (§II, p. 93). The estimation uses Denison’s (1962) comparison of US productivity in 1909 and 1958: over 1909-1959 US output per man-hour grew about one percentage point a year faster than capital per man-hour, and Denison estimates human-capital growth of .009 attributed entirely to schooling; combined with a capital share of .25 these imply a spillover exponent of .36 – “That is to say, a 10 percent increase in the average quality of those with whom I work increases my productivity by 3.6 percent” (§II, p. 94). Lucas attaches the caveat himself: “This estimate is based on the assumption that the total stock of human capital grows at the same rate, .009, as that part of the stock that is accumulated through formal schooling. I do not have any idea how accurate an assumption this is.”

It closes it: the predicted India-US return ratio becomes 1.04. Taking the Krueger estimate that five Indians equal one American, “the predicted rate of return ratio between India and the United States becomes… 1.04. That is, taking the external effects of human capital into account in the way I have done entirely eliminates the predicted return differential” (§II, p. 94). Lucas is careful to note this is not built in: “the value of [the spillover exponent] estimated from the 1909-58 U.S. comparison exactly eliminates the return differential in a 1959 India-U.S. comparison,” and he says he is “surprised how well it works in a cross-country comparison.”

That knowledge spillovers across national boundaries are exactly zero. “But it is important and troublesome, I think, to note that the cross-country comparison is based on the assumption that the external benefits of a country’s stock of human capital accrue entirely to producers within that country. Knowledge spillovers across national boundaries are assumed to be zero” (§II, p. 94). He observes that ordinary experience suggests some external benefits of individual knowledge are local – confined to single cities or even neighbourhoods – while “others are worldwide in scope,” and then states the binding limit on the exercise: “without some real evidence on the scope of these external effects, I do not see how to advance this quantitative discussion any further.” The summary he draws from Sections I and II together is deliberately a range rather than a point: correcting for human-capital differentials “reduces the predicted return ratios between very rich and very poor countries from about 58 at least to about 5, and possibly, if knowledge spillovers are local enough, to unity.”

By noting that the discussion so far has been static, and that a return differential at a point in time implies flows of goods over time – which in a one-good setting are borrowing contracts that someone must be able to enforce. Lucas describes the pattern: goods flow from advanced country A to backward country B for a phase, followed by a phase “(which lasts forever) in which goods flow from B to A in the form of interest payments or repatriated profits” (§III, p. 94). For that to be a competitive equilibrium, “it is evident that there must be an effective mechanism for enforcing international borrowing agreements. Otherwise, country B will gain by terminating its relationship with A at the point where the repayment period begins, and, foreseeing this, country A will never lend in the first place.” This is the imperfection usually labelled political risk.

The historical record before 1945, when contract enforcement in much of the Third World was as effective as at home, and capital-to-effective-labour ratios were still not equalised. “A serious difficulty with political risk as an explanation for the inadequacy of capital flows lies in the novelty of the current political arrangements between rich and poor nations” (§III, pp. 94-95). Until around 1945 much of the Third World had been under European-imposed legal and economic arrangements for decades or centuries, and “a European lending to a borrower in India or the Dutch East Indies could expect his contract to be enforced with exactly the same effectiveness and by exactly the same means as a contract with a domestic borrower.” Hence the question Lucas poses and does not answer: “Even if political risk has been a force limiting capital flows since 1945, why were not ratios of capital to effective labor equalized by capital flows in the two centuries before 1945?” His response is candid – “I do not know the answer to this question” – followed by the suggestion that the colonial powers should not be assumed to have simply enforced laissez-faire.

An imperial power with exclusive control over the colony’s trade but facing a free colonial labour market chooses capital per worker to maximise repatriated profit, and the resulting first-order condition sets the colony’s marginal product of capital above the world return – about 2.5 times it, at a capital share of 0.4. The setup, “very much in the spirit of Adam Smith’s (1776/1976) analysis of an earlier phase of colonialism,” assumes at one extreme that the colony has no capital of its own and no ability to accumulate any, so the imperialist chooses capital per worker and repatriates the entire income (§III, p. 95). The objective is total production less competitively determined wage payments less the opportunity cost of capital at the world return; the first-order condition equates the colony’s marginal product of capital to the world return plus the derivative of the colonial real wage with respect to capital per worker. Lucas identifies the active channel precisely: “It is the imperialist’s monopsony power over wages in the colony that is crucial. His optimal policy is to retard capital flows so as to maintain real wages at artificially low levels.” With the Cobb-Douglas technology and a capital share of .4, “the return on capital in the colony should be about 2.5 times the European return. These are quantitatively interesting rents.” He takes institutional support from “the carving up of the Third World by the European powers, and the frequent granting of exclusive trading rights to monopoly companies.”

It reports the contrary evidence in its own footnote and raises an internal objection in the text. The footnote is direct: “According to Lance Davis and Robert Huttenback (1989), investment in the late British empire was open to firms from any country on competitive terms, which would obviously be inconsistent with this model. Moreover, they do not find rates of return in the British colonies that exceeded European returns for similar investments” (§III, fn. 1, p. 95). The text objection is about scale: in a country like India or Indonesia, where most of the workforce was and is in traditional agriculture, “it is hard to imagine that the ability to control capital inflows from abroad gave the imperialists much monopsony power over the general level of wages,” because European capital must have been a small fraction of total capital, most of which was land. Lucas concludes that for the mechanism to matter “it must have been because only a small part of the colonial labor force was skilled enough to work with imported capital in, say, goods manufacturing” – which in turn “would obviously need a more refined view of the nature of human capital than one in which five day-laborers equal one engineer.”

Lucas argues it need not have, and points to post-colonial restrictions on inflows as possible private taxation of capital. “Insofar as monopoly control over trade in capital goods was an important factor in the determination of capital-labor ratios prior to 1945, I do not see any reason to believe it ceased to be a factor after the political end of the colonial age. Monopoly returns are not of interest to Europeans only” (§III, pp. 95-96). He cites “much unsystematic evidence of heavy private taxation of capital inflows in Indonesia, the Phillipines, in the Iran of the Shah, and other poor economies that are otherwise attractive to foreign investors,” and treats the standard rationales for restricting inflows – mistrust of foreigners, reluctance to let development proceed “too fast” – as warranting “a Smithian skepticism.” The evidential status of this passage is explicitly informal (“much unsystematic evidence”), and the summary should not upgrade it.

Because three of the four hypotheses imply that transferring capital to poor countries accomplishes nothing, and only one implies it helps. “The central idea of virtually all postwar development policies is to stimulate transfers of capital goods from rich to poor countries” (§IV, p. 96). Under either of the human-capital-based hypotheses, “such transfers will be fully offset by reductions in private foreign investment in the poor country, by increases in that country’s investments abroad, or both” – because returns are already equalised, so there is no unmet arbitrage for aid to fill. Under the monopoly hypothesis, transfers are “also be fully offset by reductions in private investments,” and the reason is put memorably: “Giving goods to a monopolist does not reduce his interest in exploiting potential rents.” Only political risk leaves room: “Only insofar as political risk is an important factor in limiting capital flows can we expect transfers of capital to speed the international equalization of factor prices.”

Human-capital accumulation, and tying aid to openness to competitive foreign investment – both framed as conditional judgements rather than established results. “In a world of largely immobile labor, policies focused on affecting the accumulation of human capital surely have a much larger potential. So too, I think, do policies in which aid of any form is tied to the recipient’s openness to foreign investment on competitive terms” (§IV, p. 96). Both clauses carry hedges the paper does not remove – “surely have a much larger potential”, “So too, I think” – and neither is supported by evidence presented in this paper; they follow from whichever combination of the four hypotheses turns out to hold, a question the paper explicitly leaves open.

Not which explanation is correct, but how large the anomaly is under standard assumptions and how much of it each candidate can absorb. The paper never claims to have identified the right answer – it asks “which combination, if any, of the four hypotheses I have advanced is adequate to account for the absence of income equalizing international capital flows” (§IV, p. 96) and leaves the combination undetermined, having recorded one unanswered historical question (“I do not know the answer”), one unmeasurable parameter (the geographic scope of knowledge spillovers), and one piece of contrary evidence on the colonial model. What it does establish is quantitative: an unadjusted return gap of about 58, an adjusted gap of about 5, a candidate mechanism that could close even that, and a set of policy conclusions that depend entirely on which of these is doing the work.