Rates of return and investment rates in poor countries

In this section, we examine whether the two main implications of the neo-classical model are verified in the data: Are returns and investment rates higher in poor countries?

2.1.

2.1.1. Physicalcapital

• Indirectestimates

One way to look at this question is to look at the interest rates people are willing to pay. Unless people have absolutely no assets that they can currently sell, the marginal product of whatever they are doing with the marginal unit of capital should be no less than the interest rate: If this were not true, they could simply divert the last unit of capital toward whatever they are borrowing the money for and be better off.

There is a long line of papers that describe the workings of credit markets in poor countries [Banerjee (2003) summarizes this evidence]. The evidence suggests that a substantial fraction of borrowing takes place at very high interest rates.

A first source of evidence is the “Summary Report on Informal Credit Markets in India” [Dasgupta (1989)], which reports results from a number of case studies that were commissioned by the Asian Development Bank and carried out under the aegis of the National Institute of Public Finance and Policy. For the rural sector, the data is based on surveys of six villages in Kerala and Tamil Nadu, carried out by the Centre for Devel­opment Studies. The average annual interest rate charged by professional moneylenders (who provide 45.6% of the credit) in these surveys is about 52%. For the urban sec­tor, the data is based on various case surveys of specific classes of informal lenders, many of whom lend mostly to trade or industry. For finance corporations, they report that the minimum lending rate on loans of less than one year is 48%. For hire-purchase companies in Delhi, the lending rate was between 28% and 41%. For auto financiers in Namakkal, the lending rate was 40%.

Several other studies reach similar conclusions. A study by Timberg and Aiyar (1984) reports data on indigenous-style bankers in India, based on surveys they carried out: The rates for Shikarpuri financiers varied between 21% and 37% on loans to members of local Shikarpuri associations and between 21% and 120% on loans to non-members (25% of the loans were to non-members). Aleem (1990) reports data from a study of professional moneylenders that he carried out in a semi-urban setting in Pakistan in 1980-1981. The average interest rate charged by these lenders is 78.5%. Ghate (1992) reports on a number of case studies from all over Asia: The case study from Thailand found that interest rates were 5-7% per month in the north and northeast (5% per month is 80% per year and 7% per month is 125%). Murshid (1992) studies Dhaner Upore (cash for kind) loans in Bangladesh (you get some amount in rice now and repay some amount in rice later) and reports that the interest rate is 40% for a 3-5 month loan period. The Fafchamps (2000) study of informal trade credit in Kenya and Zimbabwe reports an average monthly interest rate of 2.5% (corresponding to an annualized rate of 34%) but also notes that this is the rate for the dominant trading group (Indians in Kenya, whites in Zimbabwe), while the blacks pay 5% per month in both places.

The fact that interest rates are so high could reflect the high risk of default. However, this does not appear to be the case, since several of studies mentioned above give the de­fault rates that go with these high interest rates. The study by Dasgupta (1989) attempts to decompose the observed interest rates into their various components,^[269] and finds that the default costs explain 7 per cent (not 7 percentage points!) of the total interest costs for auto financiers in Namakkal and handloom financiers in Bangalore and Karur, 4% for finance companies and 3% for hire-purchase companies.

Finally, it does not seem to be the case that these high rates are only paid by those who have absolutely no assets left. The “Summary Report on Informal Credit Markets in India” [Dasgupta (1989)] reports that several of the categories of lenders that have already been mentioned, such as handloom financiers and finance corporations, focus almost exclusively on financing trade and industry while Timberg and Aiyar (1984) report that for Shikarpuri bankers at least 75% of the money goes to finance trade and, to lesser extent, industry. In other words, they only lend to established firms. It is hard to imagine, though not impossible, that all the firms have literally no assets that they can sell. Ghate (1992) also concludes that the bulk of informal credit goes to finance trade and production, and Murshid (1992), also mentioned above, argues that most loans in his sample are production loans despite the fact that the interest rate is 40% for a 3-5 month loan period.

Udry (2003) obtains similar indirect estimates by restricting himself to a sector where loans are used for productive purpose, the market for spare taxi parts in Accra, Ghana. He collected 40 pairs of observations on price and expected life for a particular used car part sold by a particular dealer (e.g., alternator, steering rack, drive shaft). Solving for the discount rate which makes the expected discounted cost of two similar parts equal gives a lower bound to the returns to capital. He obtains an estimate of 77% for the median discount rate.

Together, these studies thus suggest that people are willing to pay high interest rates for loans used for productive purpose, which suggests that the rates of return to capital are indeed high in developing countries, at least for some people.

• Directestimates

Some studies have tried to come up with more direct estimates of the rates of returns to capital. The “standard” way to estimate returns to capital is to posit a production func­tion (translog and Cobb-Douglas, generally) and to estimate its parameters using OLS regression, or instrumenting capital with its price. Using this methodology, Bigsten et al. (2000) estimate returns to physical and human capital in five African countries. They estimate rates of returns ranging from 10% to 32%. McKenzie and Woodruff (2003) estimate parametric and non-parametric relationships between firm earnings and firm capital. Their estimates suggest huge returns to capital for these small firms: For firms with less than $200 invested, the rate of returns reaches 15% per month, well above the informal interest rates available in pawn shops or through micro-credit programs (on the order of 3% per month). Estimated rates of return decline with investment, but remain high (7% to 10% for firms with investment between $200 and $500, 5% for firms with investment between $500 and $1,000).

Such studies present serious methodological issues, however. First, the investment levels are likely to be correlated with omitted variables. For example, in a world without credit constraints, investment will be positively correlated with the expected returns to investment, generating a positive “ability bias” [Olley and Pakes (1996)]. McKenzie and Woodruff attempt to control for managerial ability by including the firm owner’s wage in previous employment, but this may go only part of the way if individuals choose to enter self-employment precisely because their expected productivity in self-employment is much larger than their productivity in an employed job.

Banerjee and Duflo (2004) take advantage of a change in the definition of the so- called “priority sector” in India to circumvent these difficulties. All banks in India are required to lend at least 40% of their net credit to the “priority sector”, which includes small-scale industry, at an interest rate that is required to be no more than 4% above their prime lending rate. In January, 1998, the limit on total investment in plants and machinery for a firm to be eligible for inclusion in the small-scale industry category was raised from Rs. 6.5 million to Rs. 30 million. In 2000, the limit was lowered back to Rs. 10 million. Banerjee and Duflo (2004) first show that, after the reforms, newly eligible firms (those with investment between 6.5 million and 30 million) received on average larger increments in their working capital limit than smaller firms. They then show that the sales and profits increased faster for these firms during the same period. The opposite happened when the priority sector was contracted again. Putting these two facts together, they use the variation in the eligibility rule over time to construct instrumental variable estimates of the impact of working capital on sales and profits. After computing a non-subsidized cost of capital, they estimate that the returns to capital in these firms must be at least 74%.

There is also direct evidence of very high rates of returns on productive investment in agriculture. Goldstein and Udry (1999) estimate the rates of returns to the production of pineapple in Ghana. The rate of returns associated with switching from the traditional maize and Cassava intercrops to pineapple is estimated to be in excess of 1200%! Few people grow pineapple, however, and this figure may hide some heterogeneity between those who have switched to pineapple and those who have not.

Evidence from experimental farms also suggests that, in Africa, the rate of returns to using chemical fertilizer (for maize) would also be high.

To estimate the rates of returns to using fertilizer in actual farms in Kenya, Duflo, Kremer and Robinson (2003), in collaboration with a small NGO, set up small scale ran­domized trials on people’s farms: Each farmer in the trials designated two small plots. On one randomly selected plot, a field officer from the NGO helped the farmer apply fertilizer. Other than that, the farmers continued to farm as usual. They find that the rates of returns from using a small amount of fertilizer varied from 169% to 500% depending on the year, although of returns decline fast with the quantity used on a plot of a given size. This is not inconsistent with the results in Foster and Rosenzweig (1995), since by the time this study was conducted in Kenya, chemical fertilizer was a well established and well understood technology, which did not need many complementary inputs.

The direct estimates thus tend to confirm the indirect estimates: While there are some settings where investment is not productive, there seems to be investment opportunities which yield substantial rates of returns.

• How high is the marginal product on average?

The fact that the marginal product in some firms is 50% or 100% or even more does not imply that the average of the marginal products across all firms is nearly as high. Of course, if capital always went to its best use, the notion of the average of the marginal products does not make sense. The presumption here is that there may be an equilibrium where the marginal products are not equalized across firms.

One way to get at the average of the marginal products is to look at the Incremen­tal Capital-Output Ratio (ICOR) for the country as a whole. The ICOR measures the increase in output predicted by a one unit increase in capital stock. It is calculated by extrapolating from the past experience of the country and assumes that the next unit of capital will be used exactly as efficiently (or inefficiently) as the last one. The inverse of the ICOR therefore gives an upper bound for the average marginal product for the economy - it is an upper bound because the calculation of the ICOR does not control for the effect of the increases in the other factors of production which also contributes to the increase in output.^[271] For the late 1990s, the IMF estimates that the ICOR is over 4.5 for India and 3.7 for Uganda. The implied upper bound on the average marginal product is 22% for India and 27% in Uganda. This is also consistent with the work of Pessoa, Cavalcanti-Ferreira and Velloso (2004) who estimate a production function using cross­country data and calculate marginal products for developing countries which are in the 10-20% range. It seems that the average returns are actually not much higher than 9% or so, which is the usual estimate for the average stock market return in the U.S.

• Variations in the marginal products across firms

To reconcile the high direct and indirect estimates of the marginal returns we just dis­cussed and an average marginal product of 22% in India, it would have to be that there is substantial variation in the marginal product of capital within the country. Given that the inefficiency of the Indian public sector is legendary, this may just be explained by the investment in the public sector. However, since the ICOR is from the late 1990s, when there was little new investment (or even disinvestment) in the public sector, there must also be many firms in the private sector with marginal returns substantially below 22%. The micro evidence reported in Banerjee (2003), which shows that there is very sub­stantial variation in the interest rate within the same sub-economy, certainly goes in this direction. The Timberg and Aiyar (1984) study mentioned above, is one source of this evidence: It reports that the Shikarpuri lenders charged rates that were as low as 21% and as high as 120%, and some established traders on the Calcutta and Bombay com­modity markets could raise funds for as little as 9%. The study by Aleem (1990), also mentioned above, reports that the standard deviation of the interest rate was 38.14%. Given that the average lending rate was 78.5%, this tells us that an interest rate of 2% and an interest rate of 150% were both within two standard deviations of the mean. Unfortunately, we cannot quite assume from this that there are some borrowers whose marginal product is 9% or less: The interest rate may not be the marginal product if the borrowers who have access to these rates are credit constrained. Nevertheless, given that these are typically very established traders, this is less likely than it would be otherwise.

Ideally we would settle this issue on the basis of direct evidence on the misallocation of capital, by providing direct evidence on variations in rates of return across groups of firms. Unfortunately such evidence is not easy to come by, since it is difficult to consistently measure the marginal product of capital. However, there is some rather suggestive evidence from the knitted garment industry in the Southern Indian town of Tirupur [Banerjee and Munshi (2004), Banerjee, Duflo and Munshi (2003)]. Two groups of people operate in Tirupur: the Gounders, who issue from a small, wealthy, agricul­tural community from the area around Tirupur, who have moved into the ready-made garment industry because there was not much investment opportunity in agriculture. Outsiders from various regions and communities started joining the city in the 1990s. The Gounders have, unsurprisingly, much stronger ties in the local community, and thus better access to local finance, but may be expected to have less natural ability for garment manufacturing than the outsiders, who came to Tirupur precisely because of its reputation as a center for garment export. The Gounders own about twice as much capital as the outsiders on average. They maintain a higher capital-output ratio than the outsiders at all levels of experience, though the gap narrows over time. The data also suggest that they make less good use of their capital than the outsiders: While the outsiders start with lower production and exports than the Gounders, their experience profile is much steeper, and they eventually overtake the Gounders at high levels of experience, even though they have lower capital stock throughout. This data therefore suggests that capital does not flow where the rates of return are highest: The outsiders are clearly more able than the Gounders, but they nevertheless invest less.^[272]

To summarize, the evidence on returns to physical capital in developing countries suggests that there are instances with high rates of return, while the average of the marginal rates of return across firms does not appear to be that high. This suggests a coexistence of very high and very low rates of return in the same economy.

2.1.2. Humancapital

• Education

The standard source of data on the rate of return to education is Psacharopoulos and Patrinos (1973,1985,1994,2002) who compiles average Mincerian returns to education (the coefficient of years of schooling in a regression of log(wages) on years of school­ing) as well as what he call “full returns” to education by level of schooling. Compared to Mincerian returns, full returns take into account the variation in the cost of schooling according to year of schooling: The opportunity cost of attending primary school is low, because 6 to 12-year-old children do not earn the same wage as adults; and the direct costs of education increase with the level of schooling.

On the basis of this data, Psacharopoulos argues that returns to education are sub­stantial, and that they are larger in poor countries than in rich countries. We re-examine the claim that returns to education are larger in poor countries, using data on traditional Mincerian returns, which have the advantage of being directly comparable. We start with the latest compilation of rates of returns, available in Psacharopoulos and Patrinos (2002) and on the World Bank web site. We update it as much as possible, using studies that seem to have been overlooked by Psacharopoulos, or that have appeared since then (the updated data set and the references are presented in Table 1).^[273] We flag the observa­tions that Bennell (1996) rated as being of “poor” or “very poor” quality. We complete

Table 1

Rate of returns to education and years of schooling

Ch. 7: GrowthTheorythroughtheLensofDevelopmentEconomics 485

Table 1 (Continued)

486 A.V. Banerjee andE. Duflo

Table 1 (Continued)

Ch. 7: GrowthTheorythroughtheLensofDevelopmentEconomics 487

Notes: This table updates Psacharopoulos and Patrinos (2002). The last column indicates which rate of returns were added by us. The data rating quality is from Bennell (1996), and concerns only African Countries.

this updated database by adding data on years of schooling for the year of the study when it was not reported by Psacharopoulos.

Using the preferred data, the Mincerian rates of returns seem to vary little across countries: The mean rate of returns is 8.96, with a standard deviation of 2.2. The maxi­mum rate of returns to education (Pakistan) is 15.4%, and the minimum is 2.7% (Italy). Averaging within continents, the average returns are highest in Latin America (11%) and lowest in the Europe and the U.S. (7%), with Africa and Asia in the middle.

If we run an OLS regression of the rates of returns to education on the average ed­ucational attainment (number of years of education), using the preferred data (updated database without the low quality data), the coefficient is -0.26, and is significant at 10% level (Table 2, column (3)). The returns to education predicted from this regres­sion range from 6.9% for the country with the lowest education level to 10.1% for the country with the highest education level. This is a small range (smaller than the varia­tion in the estimates of the returns to education of a single country, or even in different specifications in a single paper!): There is therefore noprima facie evidence that returns to education are much higher when education is lower, although the relationship is in­deed negative. Columns (1) and (2) in the same table show that the data construction matters: When the countries with “poor” quality are included, the coefficient of years of education increases to -0.45. When only the 38 countries in the latest Psacharopoulos update are included (most countries are dropped because the database does not report years of education, even for countries where it is clearly available - Austria for exam­ple), the coefficient more than doubles, to -0.71. On the whole, this strong negative number does appear to be an artifact of data quality.

In column (4), we directly regress the Mincerian returns to education on GDP, and we find a small and significant negative relationship. However, this is counteracted by the fact that teacher salary grows less fast than GDP, and the cost of education is thus not proportional to GDP: In column (5) we regress the log of the teacher salary on the log of GDP per capita.^[274] The coefficient is significantly less than one, suggesting that teachers are relatively more expensive in poor countries. This is to some extent attenuated by the fact that class sizes are larger in poor countries (which tends to make education cheaper). We then compute the returns to educating a child for one year as the ratio of the lifetime benefit of one year of education (assuming a life span of 30 years, a discount rate of 5%, a share of wage in GDP of 60%, and no growth), to the direct cost of education (assuming that teacher salary is 85% of the cost of education). In column (6), we regress this ratio on GDP: There is no relationship between this measure of returns and GDP^[275] If we factor in indirect costs (as a fraction of GDP) (in column (7)), the relationship becomes slightly more negative, but still insignificant. On balance, the returns to one more year of education are therefore no higher in poor countries.

Table 2

Returns to education

Source: The data on returns to education was compiled starting from Psacharopoulos and Patrinos (2002) and extended by surveying the literature. Table 1 lists the data and the sources. The data on teacher salary is from Freeman and Oosterkberke. The data on pupil teacher ratio is from the UNESCO Institute for Statistics database, available at http://www.uis.unesco.org/.

Ch. 7: GrowthTheorythroughtheLensofDevelopmentEconomics 489

• Health

Education is not the only dimension of human capital. In developing countries, in­vestment in nutrition and health has been hypothesized to have potentially high returns at moderate levels of investment. The report of the Commission for Macroeconomics and Health [Commission on Macroeconomics and Health (2001)], for example, esti­mated returns to investing in health to be on the order of 500%, mostly on the basis of cross-country growth regressions. Several excellent recent surveys [Strauss and Thomas (1995, 1998), Thomas (2001) and Thomas and Frankenberg (2002)] summarize the ex­isting literature on the impact of different measures of health on fitness and productivity, and lead to a much more nuanced conclusion.

There is substantial experimental evidence that supplementation in iron and vita­min A increases productivity at relatively low cost. Unfortunately, not all studies report explicit rates of returns calculations. The few numbers that are available suggest that some basic health intervention can have high rates of returns: Basta et al. (1979) studies an iron supplementation experiment conducted among rubber tree tappers in Indone­sia. Baseline health measures indicated that 45% of the study population was anemic. The intervention combined an iron supplement and an incentive (given to both treatment and control groups) to take the pill on time. Work productivity in the treatment group in­creased by 20% (or $132 per year), at a cost per worker-year of $0.50. Even taking into account the cost of the incentive ($11 per year), the intervention suggests extremely high rates of returns. Thomas et al. (2003) obtain lower, but still high, estimates in a larger experiment, also conducted in Indonesia: They found that iron supplementation experiments in Indonesia reduced anemia, increased the probability of participating in the labor market, and increased earnings of self-employed workers. They estimate that, for self-employed males, the benefits of iron supplementation amount to $40 per year, at a cost of $6 per year.^[276] The cost benefit analysis of a de-worming program [Miguel and Kremer (2004)] in Kenya reports estimates of a similar order of magnitude: Taking into account externalities (due to the contagious nature of worms), the program led to an average increase in school participation of 0.14 years. Using a reasonable figure for the returns to a year of education, this additional schooling will lead to a benefit of $30 over the life of the child, at a cost of $0.49 per child per year. Not all interventions have the same rates of return however: A study of Chinese cotton mill workers [Li et al. (1994)] led to a significant increase in fitness, but no corresponding increase in productivity. Likewise, the intervention analyzed by Thomas et al. (2003) had no effect on earnings or labor force participation of women.

In summary, while there is not much debate on the impact of fighting anemia (through iron supplementation or de-worming) on work capacity, there is more heterogeneity amongst estimates of economic rates of return of these interventions. The heterogene­ity is even larger when we consider other forms of health interventions, reviewed, for example, in Strauss and Thomas (1995), or when one compares various human capital interventions. As in the case of physical capital, there are instances of high returns, and substantial heterogeneity in returns.

2.1.3. Taking stock: returns on capital

The marginal product of physical and human capital in developing countries seems very high in some instances, but not necessarily uniformly. The average of the marginal products of physical capital in India may be as low as 22%, though even reasonably large firms often have marginal products of 60%, or even 100%.

As long as we remain in the world of aggregative growth theory, the average marginal product is of course equal to the marginal product, since marginal products are always equated. Moreover even if there is some transitory variation in the marginal product, the relevant number from the point of view of any investor, should be the maximum and not the average: Capital should flow to where the returns are highest. The investments with returns of 60% or more should be the ones that guide investment, and not the 22%, and this ought to favor convergence.

That being said, there is nothing in what we have said that tells us whether 22% is lower than what we would have predicted based on an aggregative growth model that predicts convergence, or is exactly right. Lucas (1990), in a well-known paper, suggests an approach to this question. He starts with the observation that according to the Penn World Tables [Heston, Summers and Aten (2002)], in 1990, output-per-worker in India at Purchasing Power Parity was 1/ 11th of what it was in the U.S. To obtain a productivity gap per effective use of labor, we need to adjust this ratio by the differences in education between the two countries. Based on the work of Krueger (1967), Lucas (1990) argues that “one American worker is equal to five Indian workers” in terms of human capital. In our case, since we are comparing productivity in 1990, and Krueger’s estimates of human capital are from the late 1960s, we presumably adjust the correction factor. Between 1965 and 1990, years of schooling among those 25 years or older went from 1.90 years to 3.68 years in India and from 9.25 years to 12 years in the United States, i.e., from approximately 20% of the U.S. level, which fits with the 5 : 1 gap in productivity that Krueger suggested, to about 30%.^[277]

To show what this implies, Lucas starts with the assumption that net output is pro­duced using a production function Y = AL¹~^αK^α, where K is investment and L is the number of workers.^[278]

From this, it follows that output per worker is y = Ak^α, where k is investment per worker in equipment. Assuming that firms can borrow as much as they want at the rate r, profit maximization requires that αAk^α-1 = r, from which it follows that

If we assume that the only difference between the TFP levels in the two countries is due to the productivity per worker, the fact that Indian workers are only 30% as productive as the U.S. workers and the share of capital is assumed to be 40% implies that:

With these parameters, the 11-fold difference between y_u and y₁ would imply that ri = (3.3)³∣²ru ≈ 6r_u. r is naturally thought of as the marginal product of capital. In other words, if we take 9% for the marginal product of capital in the U.S., this would imply a 54% rate for India.

Lucas, at this point, did not even wait to look at the data: If the difference in the returns were indeed so large, all the capital would flow from the U.S. to India. Hence, Lucas argued, the rate of returns cannot possibly be that high in India. As we know, this is something of a leap of faith, since capital does not flow even when there are large differences in returns within the same country.

On the other hand, our estimates of the average marginal product is 22%. So Lucas was right in insisting that the actual rates of returns are much lower than what we would expect if the model were correct.

This is strictly only true if we estimate the marginal product from the data on output per worker; however if we calculate it directly from the capital-labor ratio, the problem shows up elsewhere. To see this, recall from Equation (4) that assuming that workers are only 30% as productive is equivalent to assuming that TFP in India should be approxi­mately 50% of what it is in the U.S. This, combined with the fact that, according to the Penn World Tables, the U.S. has 18 times more capital-per-worker than India implies that the marginal product of capital ought to be 2 (18)⁰∙⁶ = 2.8 times higher in India, which tells us that the marginal product in India ought to be about 25%, which is prob­ably close to what it is. However if we now put in the numbers for capital-per-worker into the production function, the ratio of output per worker in the two countries turns out to be:

In the data this ratio is 11 : 1. In other words, the problem is still there: Earlier when we used the capital-labor ratio implied by the low level of worker productivity it told us that the return on capital should be much higher than it is. On the other hand, when we use the actual capital-labor ratio, we see that the implied return on capital is quite reasonable, but the predicted worker productivity is much higher than it is in the data. Either way, it seems clear that we need to go beyond this model.

2.2. Investment rates in poor countries

2.2.1. Is investment higher in poor countries?

Prima facie, it does not seem to be the case that investment rates are higher in poor countries. On the contrary, there is a robust positive correlation between investment rates in physical capital and income per capita, when both are expressed in terms of purchasing power parity. In fact, Levine and Renelt (1992) and Sala-i-Martin (1997) identified investment per capita as the only robust correlate of income. For example, Hsieh and Klenow (2003) estimate that in 1985, the correlation between PPP invest­ment rate and PPP income per capita for the 115 countries present in the Penn World Tables was 0.60. The coefficients they estimate suggest that an increase in one log point in income per capita is associated with about a 5 percentage point higher PPP invest­ment rate (the mean investment rate is 14.5%). The same positive correlation obtains with investment in plant and machinery. The relationship between investment rate and income per capita is much less strong when both of them are expressed in nominal terms rather than in PPP terms [Eaton and Kortum (2001), Restuccia and Urrutia (2001) and Hsieh and Klenow (2003)]. The coefficient drops by a third when all investments are considered, and becomes insignificant when the measure of investment includes only plant and machinery. According to Hsieh and Klenow (2003), the fact that poor coun­tries have a lower investment-to-GDP ratio, when expressed in PPP, is explained by the low relative price of consumption, relative to investment: While there is no correlation between investment prices and GDP, there is a strong positive correlation between con­sumption prices and GDP. It is not clear, however, that knowing this helps us explain why there is not more investment in poor countries. First, because the high rates that we found in some firms in developing countries and the lower, but still much higher than U.S., rates that we found on average are there despite the high price of capital goods. This, by itself, should encourage investment, unless income effects are unusually strong. Moreover, even if we measure everything in nominal terms, there is no strong negative correlation between investment and GDP.

There are, of course, examples of poor countries with large investment-to-GDP ratios. Young (1995) shows that a substantial fraction of the rapid growth of the East-Asian economies in the post-WWII period can be accounted for by rapid factor accumulation (including increase in the size of the labor force, factor reallocation, and high invest­ment rates). In particular, according to the national accounts, between 1960 and 1985, the capital stock in Singapore, Korea, and Taiwan grew at more than 12% a year (in Hong Kong, it grew only at 7.7% a year). Between 1966 and 1999, the capital-output ratio has increased at an average rate of 3.4% a year in Korea, and 2.8% in Singa­pore. In Singapore, for example, the constant investment-to-GDP ratio increased from 10% in 1960 to 47% in 1984. In Singapore, Korea, and Taiwan, this increase in the stock of capital alone is responsible for about 1% out of the average yearly 3.4% to 4% of the “naive” Solow residual. Based on these results, Young (1995) concluded that the East-Asian economies are perfect examples of transitional dynamics in the neo-classical model. However, in subsequent research, Hsieh (1999) questioned the validity of the na­tional account data for investment for Singapore. He observes that if the capital-to-GDP ratio had grown at that speed, one would have observed a commensurate reduction in the rental price of capital. In practice, there was indeed a steady fall in the rental price of capital (both the interest rates and the relative price of capital fell) in Korea, Taiwan and Hong Kong. The drop is particularly large in Korea, where the national account statistics also suggest a large increase in the capital stock. However, in Singapore, there is no evidence that the rental rate declined over the period. If any thing, it seems to have increased.

As for investment in physical capital, there is no prima facie evidence that poor coun­tries invest more in education. The data is poor and extremely partial, since it is difficult to estimate private expenditure on education. What we can measure easily, government expenditure on education as a fraction of GDP, however, is not higher in poor countries, though there is significant variation across countries. In 1996, according to the country level data disseminated by the World Bank “edstat” department, government investment on education was 4.8% in Africa, 4% in Asia, 4.1% in Latin America, 4.8% in North America and 5.6% in Europe. The correlation between the log of government expendi­ture on education as a fraction of GDP and GDP-per-capita is strong (in current prices): The coefficient of the log of GDP was 0.18 in 1990, and 0.08 in 1996, larger than the comparable estimate for rate of investment in physical capital.

As we noted earlier, the fact that teachers are relatively more expensive in developing countries may imply that true returns to education may be much lower than the Min- cerian returns. Can this explain why there is not greater investment in education in poor countries? Withinthe neo-classical model, the answer is no: Banerjee (2004) shows that in the neo-classical world the same forces that raise the relative price of teachers in poor countries (or in countries with low education levels) also raise the wages paid to edu­cated people, and on net the rate of return has to be higher rather than lower. And, in any case, it is not true that public investment in education is higher when returns are higher: We found no correlation between government expenditure on education as a fraction of GDP and rate of returns to education (the coefficient of the rates of return to education on government expenditure in education in 1996 is -0.008, with a standard error of 0.013).

In summary, while there are isolated cases of high investment rates in relatively poor countries (Taiwan and Korea), this by no means seems to be a general phenomenon. We have already suggested one reason why this might be the case - it does not look like returns are especially high. It may also be that investment is not particularly responsive with respect to returns. This is the issue we turn to next.

2.2.2. Does investment respond to rates of return?

There is little doubt that people do take up many investment opportunities with high potential returns. Investment flowed into Bangalore when it became a hub for the soft­ware industry in India. When, in the 1990s, Tirupur, a smallish town in South India, became known in the U.S. as a good place to contract large orders of knitted garments, the industry in the city grew at more than 50% per year, due to substantial investments of both the local community (diversifying out of agriculture) and outsiders attracted to Tirupur [Banerjee and Munshi (2004)]. Or, to take a last example from India, new hy­brid seeds and fertilizers spread rapidly during the “green revolution”, leading to very rapid yield growth (yields were multiplied by 3 in Karnataka and 2.5 in Punjab [Foster and Rosenzweig (1996)]).

However, there are many instances where investments options with very high rates of returns do not seem to be taken advantage of. For example, Goldstein and Udry (1999) find that, despite the high rates of returns to growing pineapple compared to other crops, only 18% of the land is used for pineapple farming. Similarly, Duflo et al. (2003) find that only less than 15% of maize farmers in the area where they conducted field trials on the profitability of fertilizer report having used fertilizer in the previous season, despite estimated rates of return in excess of 100%.

From a more macro perspective, Bils and Klenow (2000) argue that the observed high correlation between educational attainment and subsequent growth observed in cross-sectional data (one year of additional schooling attainment is associated with 0.30 percent faster annual growth over the period 1960-1990) must be due, at least in part, to the fact that higher expected growth rates increase the returns to schooling, and therefore the demand for schooling. As we noted earlier, the correlation between education and subsequent growth [found in many studies, e.g., Barro (1991), Benhabib and Spiegel (1994), and Barro and Sala-i-Martin (1995)] appears to be too high to be entirely ex­plained by the causal effect of transitional differences in human capital growth rates on growth rates. Bils and Klenow (2000) calibrate a simple neo-classical growth model, which requires that the impact of schooling on individual productivity has to be consis­tent with the average coefficient obtained from Mincerian regressions. Their calibration suggest that the high level of education in 1960 can only explain up to a third of the correlation between education and growth. Moreover, as we will discuss below, this correlation cannot be explained by high human capital externalities. They therefore cal­ibrate an alternative model, where they construct the optimal schooling predicted by a country’s expected economic growth. The calibration, once again, requires that the impact of education on human capital be consistent with the micro-estimates of the Mincerian returns, so that there remains a large fraction of the correlation between education and growth to explain. Higher expected growth induces more schooling by lowering the effective discount rate. They assume that a country’s expected growth is a weighted average of its real ex post growth and the growth of the rest of the world. They estimate that, starting at 6.2 years of schooling, a 1 percent increase in growth induces 1.4 to 2.5 more years of schooling, depending on the values chosen for the parameters that are imposed. A 1 percentage point higher Mincerian return to schooling increases education by 1.1 to 1.9 years.

The aggregate data is thus consistent with a strong response of schooling to growth. However, it is also consistent with the presence of an omitted variable explaining both education and growth: In fact, Bils and Klenow acknowledge that their estimates suggest an elasticity of schooling demand to returns to schooling that is higher than what is implied by existing micro-studies [reviewed by Freeman (1986)]. This problem cannot really be adequately addressed in the macroeconomic data, since there it is difficult to find a plausible instrument for growth, and the impact of expected growth on schooling must essentially be estimated as a residual impact (what remains to be explained from the correlation between growth and schooling after a plausible estimate for the impact of education on growth has been removed).

Foster and Rosenzweig, in a series of papers, use the green revolution in India as a source of partly exogenous increase in rate of returns to human capital to estimate the impact of expected growth and increases in returns to education on schooling and, more generally, investment in human capital. Foster and Rosenzweig (1996) find that re­turns to education increased faster in regions where the green revolution induced faster technological change: Their estimates imply that in 1971, before the start of the green revolution, the profits in households where the head had completed primary education were 11% higher than the profits in households were he had not. By 1982, the profits were 46% higher for districts where the growth rate was one standard deviation above average. They then turn to estimating whether educational choices were also sensitive to the higher yield growth. After instrumenting for yield growth, they find that the impact of technological change on education is indeed substantial: In areas with recent growth in yields of one standard deviation above the mean, the enrollment rates of children from farm households are an additional 16 percentage points (53%) higher, compared to average-growth areas. Foster and Rosenzweig (2000) find that technological growth also affected the provision of schools, benefiting landless households. However, on bal­ance, technological growth seems to lead to lower educational investment by landless households, perhaps because returns to education increase less for them (since they are engaged in more menial tasks) and because the fact that the withdrawal of children of landed households from the labor market increases children’s wages, and thus the opportunity cost of school attendance.

Foster and Rosenzweig (1999) consider another measure of investment in children’s human capital, namely child survival. They argue that technological growth in the vil­lage increases the returns from investing in boys’ health, while technological growth outside the village, but in the potential “marriage market”, increases the returns to in­vesting in girls (because better educated and healthier women will fetch a higher prices in regions with higher technological progress). Their results indeed suggest that the gap in boys/girls mortality rates increases with technological change in the village, but decreases with technological change in the labor market.

Other evidence that girls’ survival is affected by the expected returns to having girls include Rosenzweig and Schultz (1982), who show that the boys/girls mortality gap is negatively correlated to women’s wages, and Qian (2003), who uses the liberalization of tea prices in China as a natural experiment in female productivity. She shows that, in regions suitable to tea production, the ratio of boys to girls diminished considerably after tea production and tea prices were liberalized. Since tea is picked by women, this is evidence that higher female productivity encourage parents to invest more in their girls. In contrast, in regions suitable for orchard production (for which males have an advantage) the ratio of boys to girls increased during the period.

While these facts taken together do suggest that individuals respond to returns when making human capital investment decisions, there are possible alternative explanations for these facts. The results from Rosenzweig and Schultz (1982) and Qian (2003) can­not easily be distinguished from a women’s bargaining power effect: If mothers tend to prefer girls, and their bargaining power increases as a result of the increase of their productivity, then the outcomes will improve for girls, even if households’ decisions do not respond to returns. The results in Foster and Rosenzweig (1996, 2000) could in part be attributed to wealth effects (expected growth makes the households richer, and if education has any consumption value, one would expect growth to respond to it), although Foster and Rosenzweig (1996) estimate the wealth effect directly, and argue that it is not important. But it remains possible that the instrumented expected increase in yield captures real increases in expected wealth better than any other mea­sure (they show that land prices do adjust to the future expected yield increases, for example). Moreover, there is also direct evidence that investment in human capital does not always respond to returns: Munshi and Rosenzweig (2004) show that the rapid in­crease in the returns to English education in India in the 1990s (the returns increased from 15% to 24% in 10 years for boys, and 0% to 27% for girls) led to a convergence in the choice of English as a medium of instruction between the low and high castes amongst girls, but not amongst boys: Boys from the lower castes seem so far not to have taken full advantage of the new opportunities offered by English medium educa­tion.

Another angle for approaching this question is the sensitivity of human capital invest­ment to the direct or indirect costs of these investments. Several recent studies suggest that the elasticity of school participation with respect to user fees is high: Kremer, Moulin and Namunyu (2003) conducted a randomized trial in rural Kenya in which an NGO provided uniforms, textbooks, and classroom construction to seven schools ran­domly selected from a pool of 14 schools. Dropouts fell considerably in the schools that received the program, relative to the other schools (after five years, pupils initially en­rolled in the treatment schools had completed 15% more schooling than those enrolled in the comparison schools). They argue that the financial benefits of the free uniforms were the main reason for this increase in participation. Several programs go beyond reducing the school fees to actually pay for attendance. The PROGRESA program in Mexico provided grants to poor families, conditional on continued school participation and participation in health care. The program was initially launched as a randomized experiment, with 506 communities randomly assigned to either the treatment or control group. Schultz (2004) finds a 3.4% increase in enrollment in all children. The largest in­crease was in the transition between primary and secondary school, especially for girls. Gertler and Boyce (2002) report a similar effect on health. In this case as well, it is difficult to distinguish the pure price effect from the income effect.^[279] School meals, which is another way to pay children to attend school, have been shown to be as­sociated with increased school participation in several observational studies [Jacoby (2002), Long (1991), Powell, Grantham-McGregor and Elston (1983), Powell et al. (1998) and Dreze and Kingdon (2001)] and one experimental trial conducted among pre-school children in Kenya [Vermeersch (2002)]. The available evidence, therefore, points toward a robust elasticity of schooling decisions with respect to the cost of schooling.

While this could be indicative of households being extremely sensitive to net returns, the magnitude of these effects is hard to reconcile with this explanation. For example, using an estimate of 7% Mincerian returns per year of education, Miguel and Kremer (2004) estimate that the benefit of one year of primary schooling is in excess of $200 over the lifetime of a child. Yet, the provision of a uniform valued at $6 induced an average increase of 0.5 years in the time a child spent in school (time spent in schools increased from 4.8 years in the comparison schools on average, to 5.3 years in the treatment schools). To be consistent with a model where the only reason where the provision of uniforms increases school attendance is the increase in the rate of returns that it leads to, these numbers would mean that a large fraction of children (or their parents) were exactly indifferent between attending school or not, before the uniform is provided.

While this is certainly possible, other evidence suggests that human capital invest­ment does not always respond to rates of returns. For example, the take-up of the de-worming program studied by Miguel and Kremer (2004) was only 57%, despite the fact that the program was free, and that the only investment required was to sign an informed consent form (and some disutility for the child). Further, when a nominal fee was introduced in a randomly selected set of schools in the year after the initial exper­iment, the take-up fell by 80%, relative to free treatment [Kremer and Miguel (2003)]. While this could be due to the fact that the private benefits are perceived to be low by the parents, it is worth noting that the hike in user fees happened after one year of free treat­ment, so that parents would have had time to observe the change in the child’s health and attendance at school. Moreover, Kremer and Miguel (2003) also observe that, as long as the price was positive, there was no impact from the actual price on the take-up of the drug. This strong non-linearity between a price of zero and any positive price (which is also consistent with the evidence from school uniforms) appears to be inconsistent with an explanation of their findings in terms of rates of returns.

To sum up, the evidence suggests that, while investment seems to respond in part to the cost and the benefits of these investments, it appears to do so in ways that suggest that it does not only respond to returns as we are measuring them.

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2.2.3. Taking stock: investment rates

Investment rates, both in physical and human capital, are typically no higher in poorer countries than in rich countries. If we are willing to accept that the average marginal product is the one that guides investment, this is perhaps not a surprise, especially given that the link between investment and rates of return is also not particularly strong.

3.