77374 the world bank economic review, vol. 15, no. 3 367–391 Where Has All the Education Gone? Lant Pritchett Cross-national data show no association between increases in human capital attribut- able to the rising educational attainment of the labor force and the rate of growth of output per worker. This implies that the association of educational capital growth with conventional measures of total factor production is large, strongly statistically signifi- cant, and negative. These are “on averageâ€? results, derived from imposing a constant coefficient. However, the development impact of education varied widely across countries and has fallen short of expectations for three possible reasons. First, the institutional/ governance environment could have been sufficiently perverse that the accumulation of educational capital lowered economic growth. Second, marginal returns to educa- tion could have fallen rapidly as the supply of educated labor expanded while demand remained stagnant. Third, educational quality could have been so low that years of schooling created no human capital. The extent and mix of these three phenomena vary from country to country in explaining the actual economic impact of education, or the lack thereof. To be a successful pirate one needs to know a great deal about naval war- fare, the trade routes of commercial shipping; the armament, rigging, and crew size of potential victims; and the market for booty. To be a successful chemical manufacturer in early twentieth century United States required knowledge of chemistry, potential uses of chemicals in different intermediate and final products, markets, and problems of large scale organization. If the basic institutional framework makes income redistribution (piracy) the preferred economic opportunity, we can expect a very different devel- opment of knowledge and skills than a productivity-increasing (a twenti- eth century chemical manufacturer) economic opportunity would entail. The incentives that are built into the institutional framework play the de- cisive role in shaping the kinds of skills and knowledge that pay off. —Douglass North (1990) Lant Pritchett is an economist on leave from the World Bank and is currently at the Kennedy School of Government. His e-mail address is lant_pritchett@harvard.edu. The author is grateful for discussions with and comments from Harold Alderman, Jere Behrman, Bill Easterly, Deon Filmer, Mark Gersovitz, Dani Rodrik, Harry Patrinos, Marlaine Lockheed, Peter Lanjouw, David Lindauer, Michael Walton, Martin Ravallion, Jonathan Temple, Alan Krueger, Kevin Murphy, Paul Glewwe, Mead Over, and participants in the Johns Hopkins development seminar. © 2001 The International Bank for Reconstruction and Development / THE WORLD BANK 367 368 the world bank economic review, vol. 15, no. 3 People with more education have higher wages. This is probably the second (after Engel’s law) most well-established fact in economics. It would seem to follow naturally that if more individuals are educated, average income should rise; if there are positive externalities to education, average income should rise by even more than the sum of the individual effects. The belief that expanding education promotes economic growth has been a fundamental tenet of development strategy for at least 40 years.1 The post–World War II period has seen a rapid, histori- cally unprecedented expansion in educational enrollments. Since 1960, average developing country (gross) primary enrollments have risen from 66 to 100 per- cent, and (gross) secondary enrollments from 14 to 40 percent. How has this experiment in massive educational expansion turned out? Is there now strong evidence of the growth-promoting externalities to education? This is an area where growth theory and empirical estimates are potentially impor- tant. Positive externalities should mean that the impact of education on aggre- gate output is greater than the aggregation of the individual impacts. To test for externalities, we need macroeconomic and microeconomic models of education’s impacts that are consistent. The augmented Solow model is just such a model because it predicts that the “no externalityâ€? impact of education should be the share of educational capital in factor income. This impact can be estimated from microeconomic evidence on the wage increments to capital. Within the augmented Solow model, the estimated growth impact of education is consistently less than would be expected (rather than more) from the individual impacts. The cross- national data suggests negative externalities and present something of a “micro- macroâ€? paradox. The path to resolving this paradox begins with an acknowledgment that the impact of education on growth has not been the same in all countries (Temple 1999). I discuss three possibilities for reconciling the macro and micro evidence and explaining the differences across countries. The first possibility is North’s (1990) metaphorical piracy: Education has raised productivity, and there has been sufficient demand for this more productive educated labor to maintain or increase private returns, but the demand for educated labor comes, at least in part, from individually remunerative yet socially wasteful or counterproductive activities. In this case, the relative wage of each individual could rise with educa- tion (producing the micro evidence), even while increases in average education would cause aggregate output to stagnate or fall (producing the macro evidence). The second possibility is that expansion of the supply of educated labor when demand is stagnant could cause the rate of return to education to fall rapidly. In this case, the average Mincer returns (Mincer 1974) estimated in the 1960s and 1. The idea that either the “newâ€? growth theory or the “neoclassical revivalâ€? has “discoveredâ€? the importance of human capital is belied by even a casual reading of Kuznets (1960), Lewis (1956), or Dennison (1967). Gunnar Myrdal’s (1975) Asian Drama, written mostly in the late 1950s, already treats the importance of human capital along with physical capital in development as the conventional wisdom. Pritchett 369 1970s overstated the actual marginal contribution to output from educational expansion in those instances where the demand for educated labor did not ex- pand rapidly enough. Third, schooling quality may be so low that it does not raise cognitive skills or productivity. This could even be consistent with higher private wages if education serves as a signal to employers of some positive char- acteristics, such as ambition or innate ability. I. Expansion of Education and Growth-Accounting Regressions The first approach is to do what we would do if we did not know it was not going to work. That is, we will take the standard production function specifica- tions of growth at the macroeconomic level, build aggregate measures of educa- tion capital from microeconomic data on education and its returns, and then examine the relationship between them. How Much Should Education Matter? The Augmented Solow Model Mankiw and others (1992) extend the Solow aggregate production function framework to include educational capital: (1) Yt = A(t) * Ktαk * Htαh * Ltαl, assuming constant returns to scale (α k + α h + α l = 1), normalizing by the labor force, and taking natural logs to produce a linear equation in levels. But this “linear in log levelsâ€? specification can also be expressed in rates of growth. Because estimation in levels raises numerous problems (to which I return below), I focus on the relationship among percent per annum growth of output per worker (y] = dln (Y/L)/dt), growth of physical capital per worker, and educational capital per worker:2 (2) y] = â + α k * k} + α h * h}. In the context of this model, â is the growth rate of the growth-accounting re- sidual—and I will reluctantly follow convention and call this total factor pro- ductivity (tfp), even though it is not (Pritchett 2000a). (3) T}FP = y] – α k * k} – α h * h}. The extended Solow approach facilitates simple nonregression-based estimates of how much the expansion of educational capital “oughtâ€? to matter. Because 2. Growth for each variable is calculated as the logarithmic least squares growth rate over the entire period for which the data are available. This makes the estimates of growth rates much less sensitive to the particular endpoints than if changes from the beginning period to the end period were calculated. This means the time period over which I calculate the growth rate does not always correspond exactly to the time period for the education data, but because both are per annum growth rates, this difference does not matter much. 370 the world bank economic review, vol. 15, no. 3 the weights in the aggregate Cobb-Douglas production function represent the fac- tor shares of national income, the coefficient on educational capital in a growth- accounting regression ought to be equal to the share of educational capital in gross domestic product (gdp) that can be estimated based on microeconomic data. With constant returns to scale, labor share is one minus the physical capital share. A physical capital share of around 0.4 is somewhat high, but is consistent with a variety of evidence—the estimates from national accounts and from re- gression parameters—and with capital output ratios (if the capital-output ratio, K/Y, is 2.5 and the rate of return to capital is 16 percent, then the share of capi- tal, rK/Y, is 40 percent). This implies a labor share of 0.6. How much of the labor share is due to human (or educational) capital? One simple way of estimating the share of the wage bill attributable to human capi- tal is to use the ratio of the unskilled—or “zero human capitalâ€?—wage, w0, to the average wage, w: (4) HUMAN CAPITAL SHARE (FROM WAGES) = 1 – w0 / w. A calculation based on the distribution of wages in Latin America estimates a human capital share of wages of between 50 and 75 percent. Mankiw, Romet, and Weil (1992) use the historical ratio of average to minimum wages in the United States to estimate that half of wages are due to human capital.3 Either of these calculations suggests a human capital coefficient (αh) of at least 0.3. Another approach to estimating the educational capital share is to assume a wage increment to education (taking the micro evidence discussed below at face value), and then use data on the fraction of the labor force in each educational attainment category to derive the educational capital share. Table 1 shows the results of two calculations. The top half shows the fraction of the labor force in various educational attainment categories in various regions. One can calculate the share of the wage bill due to educational attainment by assuming a wage premium for each attainment category and applying equation 5: K ∑ (wi −w0) ∗ γi (5) EDUCATIONAL CAPITAL SHARE OF WAGES BILL = i=0 wL where i represents each of the seven educational attainment categories and γi are the shares of the labor force in each educational attainment category. 3. Using data on the distribution of workers’ earnings (World Bank 1993a), we take the ratio of the average wages up to the 90th percentile (to exclude the effect of the very long tails of the earnings dis- tribution) to the wage of those workers in either the 20th or 30th percentile (to proxy for the wage of a person with “noâ€? human capital). The estimates of human capital share of the wage bill are 62 and 47 percent, respectively. If the top 10th percentile is included (and I take the ratio of average wages to the 20th or 30th percentile), the estimates of human capital share are even higher—74 and 63 percent, respectively. Although these are considerably higher that other estimates, they are estimates of all hu- man capital, not just educational capital. In the United States, the ratio of the average to the minimum wage (taken as a proxy for the “unskilledâ€? wage) has hovered around 2. Table 1. Share of Educational Capital in Wage Bill Wage premia by Share of work force by educational attainment, 1985 educational attainment (percent except where noted) under assumption set: Developing Sub-Saharan Latin American South A B countries Africa and Caribbean Asia oecd No schooling 1.00 1.00 49.7 48.1 22.4 69.0 3.3 Some primary 1.40 1.56 21.3 33.2 43.4 8.9 19.4 Primary complete 1.97 2.44 10.1 8.5 13.2 4.8 18.3 Some secondary 2.77 3.42 8.7 7.7 8.4 8.8 20.7 371 Secondary 3.90 4.81 5.9 1.6 5.5 5.3 20.1 Some tertiary 5.47 6.06 1.4 0.2 2.5 0.9 7.7 Tertiary 7.69 7.63 3.0 0.8 4.6 2.3 10.5 Average years of schooling 3.56 2.67 4.47 2.81 8.88 Calculated share of wage bill due to educational capital across regions under each assumption (percent) Assumption set A 36 26 43 30 62 (wage increment is constant at 10 percent) Assumption set B 49 38 56 42 73 (wage increments are: primary 16 percent, secondary 12 percent, tertiary 8 percent) Source: Data on educational attainment by region from Barro and Lee (1993). 372 the world bank economic review, vol. 15, no. 3 Under assumption set A (constant wage increment of 10 percent per year of schooling), the educational share of the wage bill varies across regions, from 26.3 percent in Sub-Saharan Africa (ssa) to 62.1 percent in the Organisation for Eco- nomic Cooperation and Development (oecd); and it is 36.4 percent for devel- oping countries as an aggregate. Under assumption set B (wage increments are proportionately higher for a year of primary than for a year of secondary, and higher for secondary than for tertiary, at 16, 12, and 8 percent, respectively), the share of educational capital in the total wage bill averages 49 percent—al- most exactly half—for all developing economies, varying from 38 percent in ssa to 73 percent in oecd. Both methods suggest that the educational capital share of the wage bill should be between 0.35 and 0.7. Hence the growth-accounting regression coefficient on educational capital (αh) ought to be between 0.21 and 0.42—with 0.3 in the middle of the range. Data and Specification for Physical and Educational Capital Using two recently created cross-national time-series data sets, I create estimates of the growth rate of per worker educational capital. The two data sets use dif- ferent methods to estimate the educational attainment of the labor force. Barro and Lee (1993) estimate the educational attainment of the population age 25 and above using census or labor force data where available and create a full panel of five yearly observations over the period 1960–85 for a large number of coun- tries by filling in the missing data using enrollment rates. Nehru and others (1995) use a perpetual inventory method to cumulate enrollment rates into annual esti- mates of the stock of schooling of the labor force–aged population, creating annual observations for 1960–87. From these estimates of years of schooling of the labor force, I create a mea- sure of educational capital from the microeconomic specification of earnings used by Mincer (1974). I assume the natural log of the wage (or more generally, earn- ings per hour) is a linear function of the years of schooling: (6) ln(wN) = ln(w0) + r * N, where wN is the wage with N years of schooling, N is the number of years of schooling, and r is the wage increment to a year’s schooling. The value of the stock of educational capital at any given time, t, can then be defined as the dis- counted value of the wage premia due to education: T (7) HK(t) = Σ t δt * (wN – w0), where w0 is the wage of labor with no education. Substituting the formula for the educational wage premia (equation 6) into the definition of the stock (equa- tion 7) and taking the natural log gives equation 8 for the log of the stock of educational capital, we get T (8) ln(HK(t)) = ln( ∑ δt) + ln(w0(t)) + ln(erN – 1). t=0 Pritchett 373 Therefore, the proportional rate of growth of the stock of educational capital is approximately4 (9) hk{(t) ≅ dln(expRN(t) – 1) / dt. Based on existing surveys of the large number of micro studies,5 I calculate the growth of educational capital using equation 9, the data on years of schooling from either Barro and Lee (1993) or Nehru and others (1995), and an assumed r of 10 percent constant across all years of schooling.6 In addition to the measures of educational capital, I use two series created by a perpetual inventory accumulation of investment and an initial estimate of the “capitalâ€? stock, based on an estimate of the initial capital-output ratio (King and Levine 1994; Nehru and Dhareshwar 1993). As I have argued elsewhere, series constructed in this way cannot be treated as estimates of the physical capital stock relevant to the production function, because there is no underlying theoretical or empirical justification for doing so when governments are the main investors. Hence, they should be called by a purely descriptive acronym: cudie (cumulated, depreciated investment effort) (Pritchett 2000a). The two cudie series are highly correlated and give similar results, with the principal difference being that King and Levine (1994) use investment data from the Penn World Tables, Mark 5 (pwt5; Summers and Heston 1991), while Nehru and Dhareshewar (1993) use invest- ment data from the World Bank. The dependent variable is growth of gdp per worker from pwt5. This is con- ceptually more appropriate in growth-accounting regressions than gdp per per- son or per labor force–aged person (but, as argued below, the findings are robust).7 4. There are two reasons this formula is only an approximation. First, the discount factor is as- sumed constant and hence is factored out in the time rate of change. It does depend on the average age of the labor force (because the discount is only until time T, retirement), which certainly varies system- atically across countries, but I am assuming that changes in this quantity over time are small. The sec- ond, potentially more serious problem is that I dropped out the growth rate of ln(w0(t))—the evolution of the unskilled wage term. This means my growth rate of human capital is really that component of the growth of human capital due to changes in years of schooling. For instance, Mulligan and Sala-i- Martin (1997) estimate a human capital stock in which increases in unskilled wages reduce human capital; this is technically correct, but certainly counterintuitive. 5. A survey by Psacharopoulos (1993) shows wage increments by region: ssa 13.4 percent; Asia 9.6 percent; Europe, Middle East, and North Africa 8.2 percent; Latin America 12.4 percent; oecd 6.8 percent; and an unweighted average of 10.1. In any case, the cross-national differences in the growth rate of educational capital are very robust to variations in the value of r. 6. One confusion (among many) in this literature is between the wage increment and the rate of return to education. The often-repeated assertion that “returns are higher to primary schoolingâ€? (as reported, for example, by Psacharopolous [1993]) seems true not because the increment to wages from a year of primary school is higher than for other levels, but because the opportunity cost of a year of primary schooling is much lower. This is due to the fact that the typical forgone wage attributed to a primary-age unschooled child is very low (Bennell 1996). What is relevant to growth accounting is the increment to wages, not the cost-inclusive return. 7. This output variable does raise one problem. My estimates of human capital are based on esti- mates of the educational capital of the labor force–aged population, whereas my output is output per estimated labor force (although not corrected for unemployment), so that systematic differences in the 374 the world bank economic review, vol. 15, no. 3 Regression Results for Growth and TFP The results for estimating the growth-accounting equation (2) for the entire sample of countries8 are reported in column 1 of Table 2. The partial scatter plot is displayed as figure 1. The estimates for cumulated physical investment (cudie) correspond reasonably well to national accounts-based estimates of the capital share (although 0.52 is somewhat on the high side) and are strongly sig- nificant (t = 12.8). Very much on the other hand, the estimate of the impact of growth in educational capital on growth of per worker gdp is negative (–0.049) and insignificant (t = 1.07). Adding the initial level of gdp per worker (column 2) has no impact on the negative estimates of the effect of education (–0.038). Columns 8 and 9 of table 2 show the results of regressing tfp growth on the growth of physical cudie and educational capital. In column 9, the assumed fac- tor shares used in creating tfp are 0.4 (physical) and 0.3 (educational). The growth of educational capital shows a large, statistically very significant (t = 6.91) and negative (–0.338) effect on tfp growth. In column 10, I make the educa- tional capital share as small as is consistent with growth accounting by assuming the physical capital share is on the high side (0.5) and the share of educational capital in the wage bill is on the low side (0.33 | , so that the educational capital | ) share is as low as it can reasonably be (1/2 × 1/3 = 0.167). It is still the case that educational capital accumulation is strongly statistically significant and nega- tively related to tfp growth. Of course, except for fixing the physical capital share, this tfp regression is equivalent to a t-test that finds the estimated human capi- tal share equal to 0.167. Using the results of column 1, this hypothesis is easily rejected (t = [–0.049 – 0.167] / 0.046 = 4.72). These tfp results are a simple arithmetic trick, but this trick is useful because it changes a typically uninteresting “failure to rejectâ€? to a convincing rejection of an interesting and policy-relevant hypothesis. The findings are not a “low- poweredâ€? failure to reject zero—they are a “high-poweredâ€? failure to reject, because although the data do not reject zero, they do in fact reject a wide range of interesting hypotheses—including the hypothesis that the growth impact is as large as the microeconomic data would suggest. After all, the primary reason to use aggregate data to estimate the impact of schooling is to find out whether the evolution of the labor force versus the labor force–aged population (say, through differential female labor force participation) could affect the results. The question of whether or not changes in female labor force participation (cross-national level differences would not affect the results) are an important part of the story is beyond the scope of this article. With the currently available gender-disaggregated data, this is an active research question, with some arguing that female education is more important for growth, and others arguing that it is less important, than male schooling. 8. Four countries have been dropped from all regressions because of obvious data problems: Ku- wait, because pwt5 gdp data are bizarre; Gabon, because labor force data (larger than the population) are clearly wrong; Ireland, because the Nehru and others (1995) data report an average of 16 years of schooling (immigration has distorted these numbers); and Norway, because Barro and Lee (1993) re- port an impossible increase of 5 years in schooling over a period of 5 years. Table 2. Growth-Accounting Regressions of gdp per Worker Growth with Educational Capital and cudie per Worker Growth Per annum growth of gdp per worker (gdppw ) Level gdppw tfp as defined in text 1 2 3 4 5 6 7 8 9 iv ols ols ols (w/ Nehru (sample of ols (factor (factor ols ols ols and others iv countries (on level in shares, shares, (entire (with initial (on just iv [1995] educ. (w/ similar with test 1985, whole αK = 0.4, αK = 0.5, Dependent variable sample) gdppw) sample) capital data) country) scores) sample) αH = 0.3) αH = 0.167) Growth of education –0.049 –0.038 –0.091 –0.120 –0.088 0.058 0.136 –0.338 –0.205 capital per workera (1.07) (0.795) (1.61) (1.42) (0.593) (0.229) (1.97) (6.91) (4.19) Growth of 0.524 0.526 0.458 0.460 0.527 0.592 0.612 0.126 0.026 cudie per workera (12.8) (12.8) (10.19) (10.18) (12.42) (6.78) (14.88) (3.08) (0.651) 375 ln (initial gdp 0.0009 0.0009 0.0009 per worker) (0.625) (0.625) (0.0625) Test score 0.014 (normalized, mean = 1) (1.31) Test score * EK –0.485 (1.27) Number of 91 91 70 70 77 25 96 91 91 countries R2 0.653 0.655 0.611 — — 0.71 0.909 0.419 0.205 Note: t-statistics in parentheses. aExcept in column 7, which uses levels. Source: Author’s calculations. 376 the world bank economic review, vol. 15, no. 3 Figure 1. Partial Scatterplot of Growth of gdp per Worker and Educational Capital per worker, Conditioned on cudie per Worker 0.1 0.08 Human capital growth|CUDIE per worker growth 0.06 0.04 0.02 0 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 -0.02 -0.04 -0.06 GDP per worker growth|CUDIE per worker growth impact is higher (or lower) than expected from the microeconomic data, and hence to provide some indication of the presence (or absence) of externalities. But to speak to this question, growth regressions using aggregate data must demon- strate not only that the educational capital coefficient is not zero but that it is higher than the value expected, given the microeconomic evidence applied to the same growth model. This is a seemingly modest standard, but one that has never been met. Before proposing explanations of this apparent micro-macro paradox of negative externalities, I first show that this result is robust to sample, data, and technique and that it is not the result of “pureâ€? measurement error or failure to account for school quality.9 The estimated coefficient is not the result of a peculiar sample or a few ex- treme or atypical observations. To ensure robustness against outliers, individual observations identified as influential were sequentially deleted up to 10 per- cent of the sample size, with no qualitative change in results.10 The negative 9. I do not show that the results are robust to the introduction of other covariates (Levine and Renelt 1992). This is because I am interested in growth accounting within a specific growth model that takes a production function approach. Thus there is no scope to introduce other covariates arbitrarily, as in the “reduced formâ€? literature. 10. An observation is identified as influential based on the difference in the estimate with and with- out the observation included (Belsley and others 1980). Temple (1999) working on a different data set, Pritchett 377 coefficient on schooling growth persists if (a) only developing countries are used, (b) all observations from ssa are excluded, or (c) regional dummies are included. The results are also robust to variations in the data used for education, cudie, or gdp. All the regressions in table 2 were also estimated using Nehru and oth- ers’ (1995) estimates of educational capital, and the educational capital coeffi- cient estimates are similar: consistently negative.11 Changing the data on growth and using World Bank growth rates of gdp in constant prices in local currency instead of the pwt5 gdp data gives similar results. Using growth of gdp per per- son or per labor force–aged population produces an even larger negative esti- mate for education. Relaxing the assumption of constant returns to scale does not alter the negative estimate on educational capital. Using weighted least squares with either (log of) population, gdp per capita, or total gdp because the weights also gives nearly identical results. The finding using level-on-level specifications of the augmented Solow equa- tion in table 2, column 7 shows a coefficient of 0.13 (t = 1.97)—which contin- ues to reject H0 : αh = 0.3, t = 2.37. However, there are good reasons to believe level-on-level coefficients will be biased upward. If this educational capital co- efficient is biased upward by as much as the cudie results appear to be (by about 0.1), then the small negative coefficient in the growth-on-growth regres- sions are consistent with the small positive coefficients in the level-on-level regressions. Although both sets of educational attainment data have been roundly criti- cized on a number of legitimate grounds (Behrman and Rosenzweig 1993, 1994), I use two different instruments to show that this particular result on educational capital is not the result of pure measurement error in the estimates of years of schooling. Using the growth of Nehru and others’ (1995) educational capital as an instrument for Barro and Lee’s (1993) educational capital (the correlation of the two series’ growth rates is.67), the coefficient becomes slightly more nega- tive: –0.12 (column 4 of table 1) versus –0.091 for ordinary least squares (ols) in the same sample (column 3). In addition, I also match each country with a similar country, usually picking the geographically closest neighbor, based on the idea that educational capital growth rates in similar countries are likely to be correlated (the actual correlation was Ï? = 0.316), whereas the pure mea- surement error in similar countries’ reported enrollment and attainment rates is plausibly uncorrelated (and certainly less than perfectly correlated). This iv coefficient in table 2, column 5 is also negative (–0.088). Correcting for pure finds that there is substantial parameter homogeneity and that a significant fraction the sample must be dropped to recover a significant positive coefficient on education. I take this to indicate not a lack of robustness but substantial parameter heterogeneity—a point to which I return below. 11. These are reported in Pritchett (1996), an earlier version of this article. In that paper, the basic ordinary least squares regression using the other data set was y] = c +0.501k}(15.4) – 0.104(2.07)h}, N = 79, r2 = 0.557 (t-statistics in parentheses). 378 the world bank economic review, vol. 15, no. 3 measurement error makes the estimates more negative (which is to be expected, as measurement error produces attenuation bias), and hence only deepens the puzzle.12 Recently, Krueger and Lindahl (2000) have criticized Benhabib and Spiegel (1994), based on the latter’s older estimates of educational stocks. Krueger and Lindahl (2000) claim that Benhabib and Spiegel’s (1994) findings are not ro- bust to pure measurement error. However, this criticism is not relevant to the present article (for which much of the work was done several years before the Krueger and Lindahl paper) for three reasons. First, I use newer data sets, not the Kyriacou (1991) data used in Benhabib and Spiegel (1994). Second, my use of iv to correct to measurement error is exactly the same conceptual approach as Krueger and Lindahl’s (2000), and I do not find that iv reverses any findings. Third, Krueger and Lindahl (2000) focus particularly on the measurement error of growth rates over short (e.g., five-year) periods, and argue, rightly, that mea- surement error is a larger concern in differenced data. In any case, the results in Krueger and Lindahl’s (2000) table 5, column 5, which are the most similar to those presented here (in that they control for physical capital with an uncon- strained coefficient and instrument for the education variable), find an empiri- cally modest but statistically insignificant impact of schooling (t = 0.41). The bound of two standard deviations on Krueger and Lindahl’s estimate of the aggregate equivalent of the Mincerian rate of return ranges from negative 44 percent to positive 67 percent. The major difference between our results is that I use the percentage rate of growth in the value of educational capital (which is essentially a logarithmic specification; see equations 6–9), whereas they use ab- solute change in the years of schooling. A different, deeper notion of measurement error is that while the years of schooling are correctly measured, the true problem is that years of schooling do not reflect learning. However, while differences in educational quality can ac- count for heterogeneity in the impact of schooling, it should not explain a low average impact. In fact, due to the “general underlying positive covariance be- tween quantity and quality of schoolingâ€? (Schultz 1988), one would expect that excluding quality would bias the estimated return upward, as more schooling is accumulated where quality is high.13 For lack of quality adjustment to explain the results or quantities in the aggregate, there would have to be a very strong inverse cross-national relationship between quality and the expansion of quan- tity—a relationship for which there is no evidence. The quality of schooling across countries is impossible to measure without internationally comparable test examinations of comparable groups of students, 12. Using instruments for physical cudie and educational capital simultaneously, to correct for measurement error in both has very little impact on the estimates of educational capital. 13. For instance, Behrman and Birdsall (1983) have shown, for Brazil, that not controlling for school quality leads to overestimating the impact of years of schooling by a factor of two. Pritchett 379 and these, unfortunately, exist for very few countries.14 Hanushek and Kim (1995) use test score data to show that test score performance has a positive and statis- tically significant coefficient as an independent variable in a growth regression.15 However, in this case the interest is in the impact of an increase in educational capital, and the expected functional form when schooling quality matters would be an interactive effect: the impact of an additional unit of educational capital is higher when the quality of schooling is higher. I estimate this functional form using a single observation on test scores for each of the 25 countries used by Hanushek and Kim (1995), normalized to a mean of one, to interact with the growth of the educational capital stock. As shown in table 2, column 7, while the estimated impact of education is higher with higher quality (although the interactive coefficient is statistically insignificant), it is still the case that, evalu- ated at the average level of quality (test score = 1), the education impact is sub- stantially less than zero (0.06 – 0.48 = –0.42). This suggests that, as expected, the lack of control for quality causes an upward bias, so the negative estimates that do not control for quality are not negative enough. Relationship to Other Empirical Results on Schooling As surprising as these negative results may seem, they are similar to what other researchers have found when they examined the relationship between education and growth using either growth-on-growth or level-on-level regressions. Benhabib and Spiegel (1994) and Spiegel (1994) use a standard growth-accounting frame- work that includes initial per capita income and estimates of years of schooling from Kyriacou (1990), and find a negative coefficient on growth of years of schooling.16 Lau and others (1991) estimate the effects of education by level of schooling (primary versus secondary) for five regions and find that primary edu- cation has an estimated negative effect in Africa and Middle East North Africa, 14. One possible way out of the lack of quality measures is to use proxies for quality. However, there is no particular reason to believe that physical indicators (such as teacher-to-pupil ratio or re- sources expended per student) will adequately proxy quality, and many reasons to believe they will not. Hanushek and Kim (1995) explore the connections between these indicators and test scores to extrapolate a quality when it is not available, but with little success. Because schooling is typically publicly provided, there is no reason to believe that dollars spent will be closely associated with output (that is, one cannot apply the usual theory about the relationship between inputs and outputs derived from production theory of profit maximizers). There is a huge amount of literature on the impact on achieve- ment of various physical and financial measures of resources expended per student, with generally ambiguous results (see, for example, Filmer and Pritchett [1999]). 15. However, one could easily suspect that any variable—for example, test scores—on which coun- tries such as Singapore (the highest, 72.1) and Hong Kong (71.8) do well and countries such as Nigeria (38.9) and Mozambique (27.9) do poorly, might well be capturing more in a growth regression than just labor force quality. 16. Spiegel (1994) shows that the finding of a negative effect of educational growth is robust to the inclusion of a wide variety of ancillary variables (e.g., dummies for ssa and Latin America, size of the middle class, political instability, share of machinery investment, inward orientation), and to the inclu- sion of samples. 380 the world bank economic review, vol. 15, no. 3 insignificant effects in South Asia and Latin America, and positive and signifi- cant effects only in East Asia. Jovanovich and others (1992) use annual data on a different set of capital stocks and Nehru and others’ (1995) education data and find negative coefficients on education in a non-oecd sample. Behrman (1987) and Dasgupta and Weale (1992) find that changes in adult literacy are not significantly correlated with changes in output. The World Bank’s World Development Report on labor also reports the lack of a (partial) correlation between growth and education expansion (World Bank 1995, figure 2.4). Newer studies using panels to allow for country-specific effects consistently find nega- tive signs on schooling variables (Islam 1995; Caselli and others 1996; Hoeffler 1999).17 Some very early studies used enrollment rates in growth regressions (Barro 1991; Mankiw and others 1992), but this approach had and has two deep prob- lems. First, especially in Mankiw and others (1992), secondary enrollment rates alone were used—but without any clear or compelling reasoning as to why both primary and tertiary enrollment rates should have been excluded. Second, en- rollment rates are a terrible proxy for growth in years of schooling.18 The as- sumption that current (or average) enrollment rates adequately proxy a country’s steady-state stock is true only if enrollment rates are constant over time across countries—but this is contradicted by the massive recent expansion of school- ing in developing countries (Schultz 1988). The correlation between the growth of educational capital and secondary enrollment rates is –0.41. This is because the growth of educational attainment depends not on the current enrollment rate but on the difference in the enrollment rate between the cohort leaving the labor force and the cohort entering the labor force.19 17. However, these studies are susceptible to the Krueger and Lindahl (2000) critique about exac- erbation of measurement error in short (five-year) panels. Moreover, the dynamic properties of the educational series, which tend to have little time series variation within countries, make it difficult to identify impacts of education in any case (Pritchett 2000b). 18. This does raise the question of why, if they are not a valid proxy for accumulation of schooling, initial secondary enrollment rates are a reasonably robust correlate of subsequent growth rates. My conjecture is the nature of “conditional convergenceâ€? regressions—that is, both the initial level of in- come and initial secondary enrollment rate are on the right-hand side of the equation with growth on the left-hand side. It is not unreasonable to assume that high secondary enrollment rates conditional on income level may signal something good about a country’s growth prospects (e.g., the government’s provision of good schools might mean it does other things well, the country has a substantial middle class, or people anticipate the country will do well; but it could also mean income is temporarily low), quite independent of the impact via accumulation of educational capital. 19. Comparing Korea and Great Britain provides a simple illustration. Korea’s secondary enroll- ment rate in 1960 was 27 percent, while Great Britain’s was 66 percent. But the level of schooling of Great Britain’s labor force in 1960 was 7.7 years, and the level of Korea’s was 3.2 years. Subsequently, Great Britain’s enrollment rate increased to 83 percent by 1975 and then remained relatively constant, whereas Korea’s enrollment rate increased from 27 to 87 percent by 1983. Given these differences in initial stocks and the large changes in enrollment rates, Korea’s average years of schooling expanded massively from 3.2 to 7.8 by 1985, but Great Britain’s expanded only modestly from 7.7 to 8.6, even though Great Britain’s enrollment rate was higher than Korea’s for most of the period. Pritchett 381 Another section of the literature uses the initial level of the stock of education to explain growth of output per capita. Benhabib and Spiegel (1994) show that if the initial level of education is added to a growth-accounting regression, the initial level of education is positive, whereas the mildly negative impact of the growth of educational capital persists. This finding of a level effect is actually much more puzzling than is generally acknowledged, as the spillover effects of knowledge that might be captured by an effect of the level of education in the endogenous growth literature should be in addition to rather than instead of the usual direct productivity effects. Finding only a spillover impact is grossly in- consistent with the microdata: If the entire return to education at the aggregate level is spillover effects, then why is the wage premium observed at the individual level? Moreover, a regression with growth rates on the left-hand side and level of education on the right-hand side is either misspecified or a complicated way of imposing parameter restrictions. The obvious fact that growth rates are station- ary (without drift) while the stock of education is nonstationary and secularly increasing implies there cannot be a stable relationship between the growth of output and the level of education (Jones 1995).20 Growth regressions that in- clude initial levels of both education and output are only justified if education levels (nonstationary) are cointegrated with levels of income (nonstationary). But in that case, this specification still begs the original question, because to fully implement the error correction model one must still estimate the cointegrating relationship. II. Why (and Where) Has Schooling Contributed to Growth? So there is an apparent micro-macro contradiction. The microeconomic evidence is commonly (if naively) taken to mean that substantial wage increments from additional schooling are nearly universal and that additional schooling will lead to growth. The macroeconomic data in an entirely standard growth accounting model suggest that education has not uniformly had the growth impact the microeconomic data would suggest. The obvious resolution is that the impact of education has varied widely across countries (Temple 1999).21 The question 20. Ben-David and Papell (1994) use Angus Maddison’s historical data and find that growth rates are stationary after allowing for one structural break. This criticism applies to all endogenous growth models that make growth rates a function of any nonstationary variable (such as the magnitude of re- search and development or the stock of knowledge) while growth rates are stationary (Jones 1995). 21. Not surprisingly, the data, when unconstrained, do not say that schooling has contributed to output to exactly the same degree in Korea, Zaire, Paraguay, and Hungary. Parameter homogeneity does not change the fact that the unconstrained estimates are well below the expected level, on average. Hence, there must be a number of countries for which education appears to have had less than the expected “standard augmented Solow model no externalityâ€? growth impact if wage increments were on the order of 10 percent. 382 the world bank economic review, vol. 15, no. 3 is why. In those countries that have had substantial improvements in educational attainment of the labor force yet still face declining real wages and slow eco- nomic growth, the question must be asked: Where has all the education gone? I do not propose a single answer, but put forward three possibilities that could account for the results: • The newly created educational capital has gone into piracy; that is, privately remunerative but socially unproductive activities. • There has been slow growth in the demand for educated labor, so the sup- ply of educational capital has outstripped demand and returns to school- ing have declined rapidly. • The education system has failed, so a year of schooling provides few (or no) skills. These possibilities are not mutually exclusive; all are likely to be present to varying degrees in every country. I will discuss each briefly, with some indication of the evidence that would support or contradict each approach in a given country. (For a more extensive discussion, see Pritchett 1996.) Are Cognitive Skills Applied to Socially Productive Activities? Rent seeking in our [African] economies is not a more or less important phenomenon, as would be the case in most economies. It is the center- piece of our economies. It is what defines and characterizes our economic life. —Meles Zenawi, Prime Minister of Ethiopia, September 5, 2000 One way to reconcile high wage increments to schooling with a small (and dif- ferential) macroeconomic impact of education is to argue that social and private rates of return to education diverge due to distortions in the economy. North’s (1990) powerful metaphorical comparison of piracy and chemical manufactur- ing in the introduction suggests the problem. Rent seeking and directly unpro- ductive activities can be privately remunerative but socially dysfunctional and reduce overall growth. If the improved cognitive skills acquired through educa- tion are applied to piracy, this could explain both the micro returns (rich pirates) and small macro impact (poor economies). Several pieces of evidence suggest this is at least part of the puzzle. In many developing economies, the public sector has accounted for a large share of the expansion of wage employment in the 1960s and 1970s (table 3). This is not to equate government or the magnitude or growth of government employment with the magnitude of rent seeking. Nor am I saying that the ex- pansion of education in government is necessarily unproductive. On the con- trary, the most successful of developing countries have had strong and active governments and highly educated civil servants hired through a very competi- Pritchett 383 Table 3. Share of Wage Employment Growth Accounted for by Public Sector Growth in Selected Developing Countries Average growth of wage employment (percent per annum) Public sector (percentage of Country Period Public Private Total total increase) Public sector employment growth positive, private wage employment growth zero or less Ghana 1960–78 3.4 –5.9 –0.6 Zambia 1966–80 7.2 –6.2 0.9 418 Tanzania 1962–76 6.1 –3.8 1.6 190 Peru 1970–84 6.1 –0.6 1.1 140 Egypt 1966–76 2.5 –0.5 2.2 103 Brazil 1973–83 1.4 0 0.3 100 Public sector employment growth more than half of total wage employment growth Sri Lanka 1971–83 8 0.9 3.9 87 India 1960–80 4.2 2.1 3.2 71 Kenya 1963–81 6.4 2 3.7 67 Public sector growth faster, but less than half of total wage employment growth Panama 1963–82 7.5 1.8 2.7 45 Costa Rica 1973–83 7.6 2.8 3.5 34 Thailand 1963–83 6.3 5.5 5.7 33 Venezuela 1967–82 5.1 3.4 3.7 27 Unweighted mean 5.5 0.3 2.4 Source: Derived from Gelb and others (1991), table 1. tive process (World Bank 1994).22 The question is not whether educated labor flows into the government, but why the government hires educated workers (ac- tual need versus employment guarantee) and what they do once they are in the government (productive versus unproductive or rent-seeking activities). Murphy and others (1991) present a simple model of the allocation of talent in which, if returns to ability are the greatest in rent seeking, then economic growth is inhibited by drawing the most talented people away from productive sectors into rent seeking. Anecdotal evidence that rent seeking attracts educated labor abounds. There is the possibly apocryphal (but nevertheless instructive) story of one West African nation with an employment guarantee for all univer- sity graduates. In a year when the exchange rate was heavily overvalued (and hence, there was a large premium on evading import controls), 60 percent of university graduates in all fields designated the customs service as their prefer- ence for government employment. Explicit or implicit government guarantees of employment for the educated have been common and have led to large distortions in the labor market. In Egypt, 22. Wade (1990) asserts that college graduates are as likely to enter government service in Korea and Taiwan as in African economies. 384 the world bank economic review, vol. 15, no. 3 government employment guarantees led to notoriously overstaffed enterprises and bureaucracies. In 1998, the government and public enterprises employed 70 percent of all university graduates and 63 percent of those with education at the intermediate level and above (Assaad 1997). Gersovitz and Paxson (1995) calculate that in 1986–88 in Côte d’Ivoire, 50 percent of all workers between age 25 and 55 that had completed even one grade of postprimary education worked in the public sector. Gelb and others (1991) built a dynamic general equilibrium model in which government responds to political pressures from potentially unemployed educated job seekers and becomes the employer of last resort for educated labor force entrants. They show that when both employment pressures are strong and the government is highly responsive to those pressures, the employment of surplus educated labor in the public sector can reduce growth of output per worker by as much as 2 percent a year (from a base case growth of 2.5 percent). Stagnant Demand for Educated Labor A second explanation for smaller growth returns from expanding education than from wage increments might suggest that the marginal return to adding an addi- tional year of schooling economy-wide can be dramatically different from the average returns estimated from a cross-sectional Mincer (1974) regression on wage employment at a single point in time. Depending on the shift in the de- mand for and supply of educated labor, and on the mechanism of labor market adjustment, the wage premia can rise or fall. In different countries there is evi- dence of rising, falling, stable, or vacillating returns to schooling. Mincer coeffi- cients in the United States have increased (at the median) from 0.063 to 0.096 (Buchinksy 1994). The returns to schooling in Egypt fell significantly in the 1980s (Assaad 1997). Funkhouser (1994) shows quite stable Mincer returns for five Central American countries over several years. Montenegro (1995) shows that the Mincer coefficient in Chile varied from 0.095 to 0.167 between 1960 and 1993—falling, then rising, then falling again over this period. There are two basic stories to explain the demand for educated labor (includ- ing by the self-employed). One is that education conveys skills that make labor more productive. In this case, the demand for educated labor will rise when the skill intensity of the economy rises. The second is that more educated individu- als are able to adapt more quickly to disequilibrium (Schultz 1975). In this case, the demand for educated labor will rise when there are greater gains to adapting to disequilibrium. These two stories of the source of returns to education are difficult to distinguish empirically, but both suggest that growth of educational capital would have a larger impact on output growth when policies are in place to ensure either that sectoral shifts lead to higher skill intensity, or that the cre- ation or assimilation of knowledge is higher (even within the same sector), or both. One can easily imagine a scenario in which a Mincer regression based on wage employment shows very high returns and yet, in the absence of expansion of the Pritchett 385 wage employment sector (assume, for now, this is the skill-intensive sector), these returns could fall very fast so that the marginal return to additional education is very small. Table 4 (adapted from Bennell 1996) shows that in many African countries, expansion of the number of newly educated laborers has often exceeded expansion of wage employment by more than an order of magnitude. Under these conditions, the returns to education could fall very fast. Even without sectoral shifts, the returns to education would be higher where technological progress was rapid, thus requiring constant adaptation to techno- logically induced disequilibrium. Schultz (1975) argues that in a technologically stagnant agricultural environment the production gains from education would be zero, as even the least educated could eventually reach the efficient allocation of factors. In this case, only when new technologies and inputs are available does education pay off, and then only in transition to the new equilibrium. Foster and Rosenzweig (1996) find that the return to five years of primary schooling versus no schooling in the average Indian district studied was a modest 11 per- cent (an average increase of 446 rupees in farm profits). However, returns to schooling were higher in those districts where agricultural conditions were in- trinsically conducive to the adoption of Green Revolution technologies (which they proxy by the exogenous increase in average farm profits). In a district where farm profits are one standard deviation above the average due to technical Table 4. Growth of Enrollments and of Wage Employment in Selected Sub-Saharan African Countries Change in Change in Ratio, expansion Wage employment enrollments wage employment of enrollment to as percentage of Country (thousands) (thousands) wage employment total labor force Enrollment growth positive, wage employment falling Zambia 446 –4.3 — 13.1 Côte d’Ivoire 323 –7.7 — 9 Enrollment growth exceeds wage employment growth by an order of magnitude Sierra Leone 257 8.9 29 4.9 Uganda 225 13.2 17 4.7 Ghana 1312 80 16 3.8 Burkina Faso 351 35.4 10 3.8 Lesotho 142 14.9 10 5.4 Enrollment growth higher by factor of 4 Senegal 180 45.4 4.0 5.5 Kenya 1709 436 3.9 14.1 Malawi 546 143 3.8 13.7 Rough equality of enrollment and wage sector growth Botswana 157 122 1.3 50.4 Zimbabwe 135 111.1 1.2 36.6 Note: Growth rates of enrollments and wage sector growth are calculated from the beginning date of the study estimating Mincerian return to 1990 (or the most recent data). Source: Bennell (1996), table 5. 386 the world bank economic review, vol. 15, no. 3 progress, the return to primary schooling was 32 percent—almost three times higher. However, the converse of high returns with rapid progress is that the estimated returns to schooling were negative in those districts in which progress was low.23 Rosenzweig (1996) uses data across districts of India to show the pitfalls in cross- sectional regressions when technological progress varies exogenously. In a cross- section of Indian districts, education is correlated with economic growth. But Rosenzweig (1996) shows that once varying exogenous technical progress is in- troduced, this technological progress explains both the higher economic growth and higher returns to education (and the higher returns lead to greater expansion in the amount of education). Although schooling has paid off handsomely where the Green Revolution brought technological advances, education has not been an important determinant of local growth in technologically stable areas, and the apparent impact of education from cross-district regressions disappears. If some countries’ policies are more conducive to the creation or assimilation of technical progress or to development patterns that are skill intensive, then one could expect that the output impact of a given expansion of schooling could be higher or lower. For instance, many argue that more open trade regimes in de- veloping countries would facilitate catch-up and lead to more rapid technical progress, and that the returns to education would depend, at least in part, on complementary policies such as reasonable outward orientation (World Bank 1994). Did Schooling Create Skills? Direct evidence from internationally comparable examinations shows substan- tial variation in schooling quality—and that children in some developing coun- tries lag far behind oecd and East Asian countries. Low quality of schooling is consistent with the macroeconomic evidence and is obviously consistent with the household evidence of little or no wage increment from additional schooling. However, in countries where there is a reliably demonstrated microeconomic return but no apparent macroeconomic impact of schooling, a more sophisti- cated “low qualityâ€? explanation of the paradox is needed. A signaling model of the labor market is consistent with schooling that creates few skills and yet sub- stantial observed wage impacts. If workers with high initial (or innate) ability have an easier time staying in school than workers with low initial ability, em- ployers will pay more for schooled workers even though schooling has no im- pact on skills or productivity (Spence 1976). 23. When average district farm profits were more than two-thirds of a standard deviation below the country average, the point estimate of education was negative. This explanation of the interaction of demand and supply for education due to different rates of technological progress might suggest the reason education appears not to have paid off in such places as ssa. Several recent studies have found very little return to education in farming in Africa (Gurgand 1995; Joliffe 1995). If there has been little exogenous change in the technical production functions appropriate for more educated farmers to adopt, it is because Green Revolution innovations were not appropriate for African agriculture. Pritchett 387 There is mixed evidence of a signaling function of schooling. “Sheepskinâ€? effects—in which the completion of a level of education has substantially more labor market impact than would be expected from the skills acquired at that level—are common and can be taken as indication of schooling as a filter. How- ever, there are at least three sources of evidence against an argument that the entire wage impact of schooling is signaling. First, several studies from develop- ing countries with data on ability, skills, and schooling suggest that signaling effects are small (Knight and Sabot [1990], containing data on Kenya and Tan- zania; Glewwe [1991] with data on Ghana; and Alderman and others [1996], with data on Pakistan). Second, the limited evidence of the impact of education on the productivity of farmers (Jamison and Lau 1982) or the self-employed is harder to explain by signaling. Finally, even for ssa countries, where one might suspect low educational quality, evidence from the Demographic and Health Surveys shows a 24 percent lower child mortality rate where women have a pri- mary education as opposed to no education (Hobcraft 1993). This is hard to explain if schooling has no impact on knowledge.24 III. Conclusion In the decades since 1960, nearly all developing economies have seen educational attainment grow rapidly. The cross-national data show, however, that on aver- age, education contributed much less to growth than would have been expected in the standard augmented Solow model. Where did all the education go? There are three possible explanations for the differences across countries in the impact of schooling on growth in economic output: • In some countries, schooling has created cognitive skills and these skills have been in demand, but to do the wrong thing. In other countries, the institu- tional environment has been sufficiently bad that the bulk of newly acquired skills has been devoted to privately remunerative but socially wasteful or counterproductive activities—that is, the expansion of schooling has meant the country just has better-educated pirates. • The rate of growth of demand for educated labor (due in part to different sectoral shifts, in part to policies, in part to exogenous differences in tech- nological progress) has varied widely across countries, so countries with the same initial individual returns and equal subsequent expansions in the supply of educated labor could have seen the marginal returns to educa- tion fall dramatically, stay constant, or rise. • In some countries, schooling has been enormously effective in transmitting knowledge and skills, while in others it has been essentially worthless and has created no skills. 24. But it is not impossible to explain, as the education–health linkage might be entirely the result of intergenerationally correlated endowments or preferences. 388 the world bank economic review, vol. 15, no. 3 No two countries follow exactly the same pattern, and each explanation con- tributes a different amount to explaining the overall impact of schooling on growth in different countries. None of the arguments in this article suggest that governments should invest less in basic schooling, for many reasons. For one thing, most (if not all) societies believe that at least basic education is a merit good, so that its provision is not and need not be justified on economic grounds at all—a position with which I strongly agree. To deny a child an education because of a small expected economic growth impact would be a moral travesty. In addition, schooling has a large number of direct beneficial effects beyond raising economic output, such as lower child mortality. All education can raise cognitive skills, with everything that implies. The implication, therefore, of a poor past aggregate payoff from increased cognitive skills in a perverse policy environment is not “don’t educate,â€? but rather “reform now so that investments (past and present) in cognitive skills will pay off.â€? References The word “processedâ€? describes informally reproduced works that may not be commonly available through library systems. Alderman, Harold, Jere Behrman, David Ross, and Richard Sabot. 1996. “The Returns to Endogenous Human Capital in Pakistan’s Rural Labor Market.â€? Economica 5(2):167–85. Assaad, Ragui. 1997. “The Effect of Public Sector Hiring and Compensation Policies on the Egyptian Labor Market.â€? World Bank Economic Review 11:85–118. Barro, Robert. 1991. “Economic Growth in a Cross Section of Countries.â€? Quarterly Journal of Economics 106(1):407–43. Barro, Robert, and Jong-Wa Lee. 1993. “International Comparisons of the Educational Attainment.â€? Journal of Monetary Economics 32(3):363–94. Behrman, Jere. 1987. “Schooling in Developing Countries: Which Countries Are the Over and Underachievers and What Is the Schooling Impact?â€? Economics of Education Review 6(2):111–27. Behrman, Jere, and Nancy Birdsall. 1983. “The Quality of Schooling: Quantity Alone Is Misleading.â€? World Bank Reprint Series (International) 311:928–46. Behrman, Jere, and Mark Rosenzweig. 1993. “Adult Schooling Stocks: Comparisons among Aggregate Data Series.â€? Processed. ———. 1994. “Caveat Emptor: Cross-Country Data on Education and the Labor Force.â€? Journal of Development Economics 44:147–71. Belsley, David A., Edwin Kuh, and Roy E. Welsch. 1980. Regression Diagnostics: Iden- tifying Influential Data and Sources of Colinearity. New York: J. Wiley. Ben-David, Dan, and David H. Pappell. 1994. The Great Wars, the Great Crash, and the Unit Root Hypothesis: Some New Evidence about an Old Stylized Fact. Working Paper 4752. National Bureau of Economic Research, Cambridge, MA. Benhabib, Jess, and Mark Spiegel. 1994. “Role of Human Capital in Economic Devel- opment: Evidence from Aggregate Cross-Country Data.â€? Journal of Monetary Eco- nomics 34:143–73. Pritchett 389 Bennell, Paul. 1996. “Rates of Return to Education: Does the Conventional Pattern Pre- vail in Sub-Saharan Africa?â€? World Development 24:183–99. Buchinsky, Moshe. 1994. “Changes in the U.S. Wage Structure 1963–1987: Applica- tion of Quantile Regression.â€? Econometrica 62(2):405–58. Caselli, Francesco, Gerardo Esquivel, and Fernando Lefort. 1996. “Reopening the Con- vergence Debate: A New Look at Cross-Country Growth Empirics.â€? Journal of Eco- nomic Growth 1(3):363–89. Dasgupta, Partha, and Martin Weale. 1992. “On Measuring the Quality of Life.â€? World Development 20(1):119–31. Denison, Edward Fulton.1967. Why Growth Rates Differ. Brookings Institution: Wash- ington, D.C. Filmer, Deon, and Lant Pritchett. 1999. “What Education Production Functions Really Show: A Positive Theory of Education Expenditures.â€? Economics of Education Re- view 18(2):223–39. Foster, Andrew D., and Mark R. Rosenzweig. 1996. “Technical Change and Human Capital Returns and Investments: Evidence from the Green Revolution.â€? American Economic Review 86(4):931–53. Funkhouser, Edward. 1994. “The Returns to Education in Central America.â€? Univer- sity of California, Santa Barbara, December. Processed. Gelb, Alan, J. K. Knight, and Richard H. Sabot. 1991. “Public Sector Employment, Rent Seeking, and Economic Growth.â€? Economic Journal 101:1186–99. Gersovitz, Mark, and Christina Paxson. 1995. “The Revenues and Expenditures of Af- rican Governments: Modalities and Consequences.â€? World Bank, Washington, D.C. Processed. Glewwe, Paul. 1991. Schooling, Skills, and the Returns to Government Investment in Education. Living Standards Measurement Survey Working Paper 76. World Bank, Washington D.C. Gurgand, Marc. 1993. “Les effets de l’éducation sur la production agricole: application à la Côte Ivoire.â€? Revue de l’économie du developpement 10(4):37–54. Hanushek, Eric A., and Dongwook Kim. 1995. “Schooling, Labor Force Quality, and Economic Growth.â€? National Bureau of Economic Research Working Paper 5399. Cambridge, MA. Hobcraft, J. 1993. “Women’s Education, Child Welfare, and Child Survival: A Review of the Evidence.â€? Health Transition Review: The Cultural, Social, and Behavioral Determinants of Health 3(2):159–75. Hoeffler, Anke Elisabeth. 1997. “The Augmented Solow Model and the African Growth Debate.â€? Oxford University, Center for Study of African Economics. Processed. Islam, Nazrul. 1995. “Growth Empirics: A Panel Data Approach.â€? Quarterly Journal of Economics 110(4):1127–70. Jamison, Dean, and Lawrence Lau. 1982. Farmer Education and Farm Efficiency. Johns Hopkins University Press: Baltimore, MD. Jolliffe, Dean. 1998. “Skills, Schooling, and Household Income in Ghana.â€? World Bank Economic Review 12(1):81–108. Jones, Chad. 1995. “R&D-Based Models of Economic Growth.â€? Journal of Political Economy 103(August):759–84. Joyanavich, Boyan, Saul Lach, and Victor Lavy. 1992. “Growth and Human Capital’s Role as an Investment in Cost Reduction.â€? New York University, New York. Processed. 390 the world bank economic review, vol. 15, no. 3 King, Robert, and Ross Levine. 1994. “Capital Fundamentalism, Economic Development, and Economic Growth.â€? Carnegie-Rochester Series on Public Policy 40:259–300. Knight, J. B., and Richard Sabot. 1990. Education, Productivity and Inequality: The East African Natural Experiment. New York: Oxford University Press for the World Bank. Krueger, Alan, and Mikael Lindahl. 2000. “Education for Growth: Why and for Whom?â€? National Bureau of Economic Research Working Paper 7591, Cambridge, MA. Kuznets, Simon. 1966. Modern Economic Growth: Rate, Structure, and Spread. New Haven: Yale University Press. Kyriacou, George. 1991. “Level and Growth Effects of Human Capital: A Cross-Coun- try Study of the Convergence Hypothesis.â€? New York University Economic Research Report: 91-26, p. 25. Lau, Lawrence, Dean Jamison, and Larry Louat. 1991. “Impact of Education by Region.â€? World Bank, Washington, D.C. Processed. Levine, Ross, and David Renelt. 1992. “Sensitivity Analysis of Cross-Country Growth Regressions.â€? American Economic Review 82(4):942–63. Lewis, W. Arthur. 1955. The Theory of Economic Growth. London: Allen and Unwin. Mankiw, Gregory, David Romer, and David Weil. 1992. “A Contribution to the Empirics of Economic Growth.â€? Quarterly Journal of Economics 107:407–37. Mincer, Jacob. 1974. Schooling, Experience, and Earnings. New York: Columbia Uni- versity Press. Montenegro, Claudio. 1995. “The Structure of Wages in Chile 1960–1993: An Applica- tion of Quantile Regression.â€? World Bank, Washington, D.C. Processed. Mulligan, Casey B., and Xavier Sala-i-Martin. 1997. “A Labor-Income-Based Measure of the Value of Human Capital: An Application to the States of the United States.â€? Japan and the World Economy 9(2):159–91. Murphy, Kevin M., Andrei Shleifer, and Robert Vishny. 1991. “Allocation of Talent: Implications for Growth.â€? Quarterly Journal of Economics 106(2):503–30. Myrdal, Gunnar. 1968. Asian Drama: An Inquiry into the Poverty of Nations. New York: Twentieth Century Fund. Nehru, Vikram, and Ashok Dhareshwar. 1993. “A New Database on Physical Capital Stock: Sources, Methodology and Results.â€? Revista de Analysis Economico 8(1):37– 59. Nehru, Vikram, Eric Swanson, and Ashutosk Dubey. 1995. “New Database on Human Capital Stock in Developing and Industrial Countries: Sources, Methodology and Results.â€? Journal of Development Economics 46:379–401. North, Douglass. 1990. Institutions, Institutional Change and Economic Performance. Cambridge: Cambridge University Press. Organization for Economic Cooperation and Development (oecd) 1993. National Ac- counts. Paris: oecd. Pritchett, Lant. 1996. “Where Has All the Education Gone?â€? World Bank Policy Re- search Working Paper #1581. World Bank, Washington, D.C. ———. 2000a. “The Tyranny of Concepts: cudie (Cumulated, Depreciated, Investment Effort) Is Not Capital.â€? Journal of Economic Growth 5:361–84. ———. 2000b. “Understanding Patterns of Economic Growth: Searching for Hills among Plateaus, Mountains, and Plains.â€? World Bank Economic Review 14(2):221–50. Pritchett 391 Psacharopoulos, George. 1993. “Returns to Investment in Education: A Global Update.â€? Policy Research Paper 1067. World Bank, Washington, D.C. Rosenzweig, Mark. 1996. “Schooling, Economic Growth, and Aggregate Data.â€? Depart- ment of Economics, University of Pennsylvania. Processed. Schultz, T. P. 1988. “Education Investments and Returns.â€? In H. Chenery and T. N. Srinivasan, eds., Handbook of Development Economics, vol. I. Amsterdam: Elsevier Science. Schultz, Theodore W. 1975. “The Value of the Ability to Deal with Disequilibria.â€? Journal of Economic Literature 13(3):827–46. Spence, Michael. 1976. “Competition in Salaries, Credentials, and Signaling Prerequi- sites for Jobs.â€? Quarterly Journal of Economics 90(1):51–74. Spiegel, Mark. 1994. “Determinants of Long-Run Productivity Growth: A Selective Sur- vey with Some New Empirical Results.â€? Department of Economics, University of Rochester, Rochester, New York. Processed. Summers, Robert, and Alan Heston. 1991. “The Penn World Table (Mark 5): An Ex- panded Set of International Comparisons, 1950–88.â€? Quarterly Journal of Econom- ics 106(2):327–68. Temple, Jonathan. 1999. “A Positive Effect of Human Capital on Growth.â€? Economics Letters 65 (1):131–34. Wade, Robert. 1990. Governing the Market: Economic Theory and the Role of Govern- ment in East Asian Industrialization. Princeton, NJ: Princeton University Press. World Bank. 1993. The Story of Poverty in Latin America. Washington, D.C. ———. 1994. Priorities and Strategies for Education: A World Bank Sector Review. Education and Social Policy Department. Washington, D.C. ———. 1995. World Development Report 1995: Workers in an Integrating World. Washington, D.C.: Oxford University Press for the World Bank.