Understanding rates of return and investment rates in poor countries: aggregative approaches

For Lucas, the inability to fit the cross-country differences into an aggregative growth model was direct evidence in favor of abandoning the assumption of equal TFP: Allow­ing the TFP level to be lower in India than in the U.S.

Allowing TFP differences across countries can also explain why the poor countries do not invest more and ultimately why there is no growth convergence: Once we assume fixed productivity differences, the steady states in different countries will be different and there is no presumption that poorer countries should grow faster.

For rest of this section, we will therefore proceed under the assumption that it is possi­ble to resolve the “macro puzzles” by introducing cross-country differences in TFP. We focus on the so-called new growth approaches, which are theories within the aggregative growth framework that aim to explain persistent cross-country TFP differences, recog­nizing that these “new” growth theories, like “old” growth theories, make no attempt to deal with the obvious problems with the aggregate production function.

3.1. Access to technology and the productivity gap

The dominant answer, within growth theory, of why TFP should be lower in poorer countries comes down to technology. There is a now a large literature - due to Aghion and Howitt (1992), Grossman and Helpman (1991) and others - that emphasizes tech­nological differences as the source of this TFP gap.

By itself, this explanation focuses on investment in technology and cannot directly account for the lack of investment in human capital in LDCs or why the returns there often seem so low. However, if there is strong complementarity between human capital investment and investments in new technology,^[282] then the slow growth of TFP could explain the relative absence of investment in human capital in LDCs, assuming that we accept the rather mixed evidence, reviewed above, on the responsiveness of investment in human capital to the expected returns.

If the productivity gap between the U.S. and India has to be fully accounted for by technological differences in an aggregative model (i.e., if we rule out any differences in the interest rates), then TFP in the U.S. would have to be about twice that of India. How plausible is a TFP gap of 1 : 2 in a world of efficiently functioning markets? One way to look at this is to observe that U.S. TFP growth rates seem to be on the order of 1-1.5% a year. Even at 1.5%, TFP takes about 45 years to go up by 200%.^[283] Therefore in 2000, Indians would have been using machines discarded by the U.S. in the 1950s.

This is also clearly very far from being true of the better Indian firms in most sectors. The McKinsey Global Institute’s [McKinsey Global Institute (2001)] recent report on India, reports on a set of studies of the main sources of inefficiency in a range of indus­tries in India in 1999, including apparel, dairy processing, automotive assembly, wheat milling, banking, steel, retail, etc.

However, most firms do not make use of these technologies. And, according to the same McKinsey report, it is not because these technologies are not economically viable in this sector: The report on the apparel industry tells us that in the apparel industry:

“Although machines such as the spreading machine provide major benefits to the production process and are viable even at current labor costs, they are ex­tremely rare in domestic (i.e., non-exporting) factories” [McKinsey Global Insti­tute (2001)].

Despite this, technological backwardness is not one of the main sources of ineffi­ciency that is highlighted in their report on the apparel industry. They focus, instead, on the fact that the scale of production is frequently too small, and in particular, on the fact that the median producer is a tailor who makes made-to-measure clothes at a very small scale, rather than a firm that mass produces clothes. TFP is low, not because the tailors are using the wrong technology given their size, but because tailoring firms are too small to benefit from the best technologies and therefore should not exist.

Reports from a number of other industries show a similar pattern. Certain specific types of technological backwardness are mentioned as a source of inefficiency in both the dairy processing industry and the telecommunications industry, but in both cases it is argued that while all firms should find it profitable to upgrade along these dimensions [McKinsey Global Institute (2001)], only a few of them do.

In these two cases, however, there is also a reference to the gains (in terms of produc­tive efficiency) from what the report calls “non-viable automation”.

On other hand, it is clearly true that there are many firms that, for some reason, have opted not to adopt the best practice despite the fact that others within the same economy find it profitable to do so and, at least according to McKinsey, they too would benefit from moving in this direction. In other words, while there is a technology gap, it is largely a within-country phenomenon and not, as the models of technology production and adoption imply, a problem at the level of the country.^[284]

3.2. Human capital externalities

Another reason why there may be persistent TFP differences across countries is that there are aggregate increasing returns. As emphasized in the introduction, for this to be true it is not enough to have firm-level increasing returns. We need externalities across firms, or more generally across investors, which may arise, for example, because there are human capital externalities: It has been argued that human capital is not just valuable to those who own and use it, but also to others.

Externalities in human capital would tend to limit the extent of diminishing returns with respect to human capital in the production function, keeping as given the share of human capital in total production.

Externalities could also explain a puzzle we did not discuss until now, pointed out by Acemoglu and Angrist (2001) and Bils and Klenow (2000): The high correlation between human capital and income that is observed in the cross-country data [e.g., Mankiw et al. (1992)] is hard to reconcile with the micro evidence we have reviewed earlier, which suggested relatively low returns to education. To see this, note that the difference in average schooling between the top and bottom deciles of the world edu­cation distribution in 1985 was less than 8 years. With a Mincerian returns to schooling of about 10%, the top decile countries should thus produce about twice as much per worker as the countries in the bottom decile. In fact, the output-per-worker gap is about 15. One possibility is that the Mincerian rate of return understates the true rate of re­turns to education, because it does not take into account positive externalities generated by educated workers. More specifically, the human capital externalities on the order of 20-25% (more than twice the private return) would be necessary to explain the cross­country relationship between education and income, which sounds implausible.

Early evidence [e.g., Rauch (1993)] suggested that externalities were positive, but not of that order of magnitude. Using variation in education across U.S. cities, Rauch (1993) estimated that the human capital externalities may be on the order of 3% to 5%. Moreover, even this evidence is to be taken with caution, since cities where workers are more educated vary in many other respects. Using variation in average education gener­ated by the passage of compulsory schooling laws, Acemoglu and Angrist (2001) find no evidence of average education on individual wages, after controlling for individual education.

In Indonesia, Duflo (2003) actually finds evidence that those who invest in their ed­ucation may inflict negative pecuniary externalities on others.

To summarize, the available evidence does not suggest that there are strongly increas­ing returns to human capital. It appears that if human capital externalities are important they must take a very different form. One possibility is that they play a role in the inter- generational transmission of learning: For example, it is possible that parents or teachers do not fully internalize the benefits that their investment in human capital confer on the next generation of scholars. However as the figures above makes clear, in order to fit the data the extent of this miscalculation has to be substantial.

3.3. Coordination failure

Another source of lower aggregate productivity is the possibility of coordination fail­ures, which reduces aggregate productivity through a demand effect. There is a long line of work, starting with Rosenstein-Rodan (1943), that has emphasized the role of coor­dination failure in explaining why certain countries successfully industrialize, while others remain poor and non-industrialized. Murphy, Shleifer and Vishny (1989) explore models where industrialization in a sector creates demand for the products of another sector (through higher wages for the workers), and which leads to multiple equilibria. A coordinated “big push”, where all industries start together, can place the country on a permanently higher level of investment and income. Developing countries may have low investments and low returns to capital because such a “big push” has not happened. A large literature explores different forms of strategic complementarities. Since the ar­gument involves an entire economy’s coordination, it is difficult to use micro-evidence to provide much direct evidence about these aggregate externalities.^[285] However, while these theories certainly have some relevance, the fact countries trade will tend to sub­stantially mitigate the effect of local demand. It is therefore not clear that aggregate demand effects can be so powerful as to generate the necessary gap in TFP between, say, India and the U.S.

Another possible mechanism is suggested by Acemoglu and Zilibotti (1997). They argue that when one firm invests, others benefit, because each firm is subject to indepen­dent shocks and increasing the number of firms expands the ability of an individual firm to diversify its risk. When there are few firms around, risk diversification opportunities are limited and risk averse investors limit their investment.

The India-U.S. comparison is perhaps the worst example one could pick for apply­ing this theory, since between the 1920s and the 1940s the Indian stock market was comparable to that in many OECD countries in terms of number of listed firms and vol­ume of trade. However, lack of financial development is clearly a serious problem for many developing countries. However, within an aggregative model the lack of financial development can at best explain why all the firms underinvest. As emphasized earlier, the more important sources of inefficiency seem to come from the fact that some firms underinvest much more than others, and in particular that some firms adopt the latest technologies, while others do not.

3.4. Takingstock

While the evidence is somewhat impressionistic, it seems unlikely that the aggregative theories discussed above can explain the entire TFP gap. Of course, if we were prepared to give up the idea that the entire problem comes from a lower aggregate productivity, for example by accepting that the marginal product is lower in India, the problem of fitting the data would be easier. For example, if the TFP gap were 1.5 higher in the U.S. (on top of what is predicted by the difference in the productivity of labor), the fact that the U.S. has 18 times more capital-per-worker would imply that output-per-worker would be (1.5)(2)(18)⁰∙⁴ = 9.5 times higher in the U.S., and the marginal product of capital would be 285) = 1.9 times higher in India. These are both clearly in the ballpark, although the output gap between the U.S. and India predicted by this model is still too low (the output gap is about 11 : 1 in the data) and the ratio of the marginal product of capital between India and the U.S., which was too high in a model with identical TFP, is now too low (the ratio in the data is about 2.5).

It is worth noting that in order to get closer to 11 : 1 ratio in the data, the TFP ratio would need to be higher than 1.5, which is perhaps already too big. Moreover, this would further reduce the predicted ratio between the marginal product of capital in India and in the U.S., which was already too low when the TFP gap was 1.5. In other words, we are facing a new problem: Given the existing capital stock, if a difference in TFP was the reason why the output per worker is so low in India, the marginal product of capital should be even lower in India than what it is. Indeed, there is no way to adjust the TFP ratio to improve the fit along both dimensions - we can increase the gap in output-per- worker by raising the TFP ratio, but only at the cost of making the ratio of marginal product even smaller. The problem is quite basic: With a Cobb-Douglas production function, the average product of capital is proportional to its marginal product. But then output-per-worker must be proportional to the product of the marginal product of capital and capital-per-worker. If the marginal product in India is 2.5 times that of the U.S., but capital-per-worker is 18 times greaterin the U.S., output-per-worker has to be 28 = 7∙2 times larger in the U.S. and not 11 times larger, irrespective of what we assume about the ratio of TFP in the two countries. In other words, the only way we can hope to really fit what we see in the data is by abandoning the standard Cobb-Douglas formulation. This is useful to keep in mind when, in later sections, we discuss ways to improve the fit between the theory and the data.

To sum up, Lucas’ question about why capital does not flow from the U.S. to India was, in some sense, where it all started, but from the vantage point of what we know today, this is in some ways the lesser problem. We know now that there are differences in the marginal product of capital within the same economy that dwarf the gap that Lucas calculated from comparison of India and the U.S., and found so implausibly large that he set out to rewrite all of growth theory. The harder question is why capital flows do not eliminate these differences.

Lucas’ resolution of the puzzle was to give up the key neo-classical postulate of equal TFP across countries. Based on the McKinsey report, this seems to be the obvious step, but the problem is less that people in developing countries do not find it profitable to adopt the latest (and best) technologies and more that many firms do not adopt tech­nologies that are available and would be profitable if adopted. The key question, once again, is why the market allows this to be the case.

The premise of the aggregative approach to growth was that markets function well enough within countries that we can largely ignore the fact that there is inefficiency and unequal access to resources within an economy when we are interested in dynam­ics at the country level. The evidence suggests that this is not true: The cross-country differences in marginal products or technology that we want to explain are of the same order of magnitude as the differences we observe within each economy. A theory of cross-country differences has to based on an understanding and an acknowledgment of the reasons why rates of returns vary so much within each country. This is what we turn to next: In Section 4, we first review the various reasons that have been proposed. In Section 5, we will then calibrate their impact to evaluate whether they can form the basis of an explanation for the puzzles we observed.

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