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American Economic Journal: Macroeconomics 2010, 2:1, 207–223 http://www.aeaweb.org/articles.php?doi=10.1257/mac.2.1.207 Contents Development Accounting † 207 Researchers have made much progress in the past 25 years in I. Proximate Development Accounting 208 accounting for the proximate determinants of income levels: physi- cal capital, human capital, and Total Factor Productivity (TFP). But we still know little about why these factors vary. We argue that TFP exerts a powerful influence on output not only directly, but also A. Physical Capital 209 indirectly, through its effect on physical and human capital accu- mulation. We discuss why TFP varies across countries, highlighting B. Human Capital 210 misallocation of inputs across firms and industries as a key determi- nant. (JEL E22, E23, F21, F35, O10, O40) C. Hours Worked per Person 211 esearch on income differences can arguably be classified into one or more R arrows in the following chain of causality: D. Residual TFP 212 Geography,Climate, Luck ⇒ Human Capital, Physical Capital, TFP ⇒ Income ⇓ Institutions, Culture ⇒ Human Capital, Physical Capital, TFP ⇒ Income II. Why Does Physical Capital Vary? 212 ⇓ Policies, RuleofLaw,Corruption⇒ HumanCapital,Physical Capital,TFP⇒ Income III. Why Does Human Capital Vary? 216 Our focus is on the right-most arrows, or what is sometimes called “development accounting.” First, we describe research from the past 25 years about the proximate role of physical capital, human capital, and TFP in accounting for income differ- IV. Why Does TFP Vary? 220 ences across countries. The current state of the debate is as follows: human capital is important (accounting for 10–30 percent of country income differences), physical capital also matters (accounting for about 20 percent of country income differences), V. Conclusion 222 and residual TFP remains the biggest part of the story (accounting for 50–70 percent References222 of country income differences). Second, we will contend there are important positive feedback effects between human capital, physical capital, and TFP. In particular, the level of TFP of different sectors (investment versus consumption, human capital versus final goods) can influ- ence the incentive to accumulate physical and human capital. We will also argue that a key determinant of aggregate TFP is the efficiency of input allocation across firms and industries. 60637 and National Bureau of Economic Research (e-mail: email@example.com); Klenow: 579 SerraL Mall, Stanford University, Stanford, CA 94305 and the National Bureau of Economic Research (e-mail: pete@ klenow.net). We gratefully acknowledge the financial support of the Kauffman Foundation, the Alfred P. Sloan Foundation (Hsieh), and the Stanford Institute for Economic Policy Research (Klenow). We thank Chad Jones and Da†id Romer for detailed comments that vastly improved the paper. To comment on this article in the online discussion forum, or to view additional materials, visit the articles page at: http://www.aeaweb.org/articles.php?doi=10.1257/mac.2.1.207. 208 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JANUARY 2010 Along the way, we will highlight some of the many open questions that remain. In a short paper such as this, however, many important topics must be left out. In the interest of brevity, this survey neglects the work that has been done on any of the left-most or vertical arrows in the simple schematic laid out at the start of this paper. That is, we neglect the growing and important literature on how geography and climate affect institutions and culture, which, in turn, determine policies (e.g., tax and tariff rates), corruption, and ultimately physical capital, human capital, and TFP. I. Proximate Development Accounting First and foremost, the reader should see the survey by Francesco Caselli (2005). Ours is a comparatively quick overview of this large literature. Second, we wish to clarify the two main ways the literature has done proximate development account- ing. Imagine the simple aggregate production function (1) Y i A K ih i ) i i 1−α, where Y ripresents real gross domestic product (GDP) in country i, A is resid- i ual TFP, K ii real physical capital, h is iuman capital per person, and L is hoursi worked per person. Dividing equation (1) by population N, and rearranging, yields a i conventional expression for accounting: α Yi K i hiL i 1−α (2) _N = A ai N_ b a _N__ b . i i i If one takes logs of both sides of equation (2), one can then linearly decompose the differences in income levels between any two countries (say each country versus the United States, or the ninetieth versus the tenth percentile of country incomes). Alternatively, one could do a variance decomposition using a sample of many coun- tries. A capital elasticity of about one-third is typically assumed based on observed labor shares, following Douglas Gollin (2002). Compared to regression studies, this accounting approach need not require that, say, TFP be orthogonal to physical or human capital. Anyaccountingprovidestheanswertoaspecificquestion.Accountingwithequa- tion (2) asks the hypothetical question: how much would output per person increase in response to variation in one of the following factors: physical capital per person, effective labor per person, or residual TFP, holding the other two factors fixed. One objection to accounting with equation (2) is that physical capital per person will endogenously increase in response to increases in effective labor or TFP. Because investments in physical capital are final goods, unlike human capital or TFP, any increase in output will tend to bring forth higher physical capital. Put differently, holding fixed physical capital per person, while increas- ing human capital or TFP, requires a decrease in the investment rate in physical capital. It is not obvious why this is a useful thought experiment given that the investment rate in physical capital is presumably driven by factors such as the VOL. 2 NO. 1 HSIEH AND KLENOW: DEVELOPMENT ACCOUNTING 209 effective tax rate on capital income and the relative price of capital, but not the level of human capital or TFP, per se. An alternative accounting in the literature asks a different question by rearrang- ing the production function into an intensive form. For example, α/(1−α) __i 1/(1−α) __i ____i (3) N i= A i aYi a N ib. Here, the thought experiment is a change in effective labor per person or resid- ual TFP, allowing capital per person (but not the capital-output ratio) to change in response. As pointed out by N. Gregory Mankiw, David Romer, and David N. Weil (1992), this question is compatible with the steady state of a neoclassical growth model in which the level of human capital or TFP has no direct effect on the steady state capital-output ratio. For comparing large, persistent differences across coun- tries, a steady-state assumption may be a good approximation. The bigger exponents on residual TFP (i.e., 1/(1−α) instead of 1) and on effective labor input (1 rather than 1 − α) in equation (3) reflect the impact of these variables on output both directly and indirectly through capital per worker. A valid objection to accounting with equation (3) is its asymmetry. It asks how much output per person differs when the capital-output ratio changes, holding fixed the levels of human capital and residual TFP. One could, instead, argue that physical capital is an important input to accumulation of human capital and investments in higher TFP. In this spirit, Mankiw, Romer, and Weil (1992) carried out accounting that incorporated an effect of physical capital on human capital. This channel is weaker, however, if investments in human capital and TFP are intensive in human capitalmorethanphysicalcapital.And,incontrasttothewell-understoodendogene- ity of physical capital in the neoclassical growth model, the determinants of human capital and TFP are much less well understood. Still, we will describe the results of accounting with both equations (2) and (3), and then return to the issue of what may be driving differences in human capital and TFP. A. Physical Capital Using equation (3), Klenow and Rodríguez-Clare (1997) and Robert E. Hall and Charles I. Jones (1999) attribute about 20 percent of variation in income per worker to variation in capital-output ratios. Their variance decomposition evenly splits the covariance terms between any two of the following: physical capital, human capital, and TFP. Caselli (2005) uses equation (2), which gives more weight to physical capi- tal, but also looks at relative variances rather than assigning the covariance terms. These differences roughly offset each other so that he also credits about 20 percent of income variationto physical capital.Despitethis broad agreement,open questions remain about measuring the quality of physical capital across countries given pos- sibly differing vintage (e.g., Roc Armenter and Amartya Lahiri 2006) and efficiency 1See Klenow and Andrés Rodríguez-Clare (2005) and Juan Carlos Córdoba and Marla Ripoll (2008) for models in which TFP endogenously responds to the levels of human and physical capital per worker. 210 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JANUARY 2010 of the component due to government infrastructure investments (e.g., Lant Pritchett 2000). B. Human Capital To measure levels of human capital, Mankiw, Romer, and Weil (1992) used the secondaryschoolenrollmentrateasaproxyfortheinvestmentrateinhumancapital. They attributed about 50 percent of income differences to human capital differences in their 1985 sample of 98 nonoil countries. But primary and tertiary schooling must matter as well. And attainment of the workforce—as opposed to the enrollment rate of the school-age population—should be what matters for the human capital of workers. Klenow and Rodríguez-Clare (1997) use years of schooling attainment from Robert J. Barro and Jong-Wha Lee (1993), which covers primary, secondary, and tertiary schooling. They also propose that a useful way to capture the impact of attainment is to look at how wages vary with schooling within countries. Based on evidence in the labor literature, they assume a Mincerian log linear relationship between years of schooling and human capital: φ S hit B e it iti. Here, S iityears of schooling in country i in year t; φ is the itincerian return” to a year of schooling; and B captites factors such as the quality of schooling, human capital accumulated in early life, and human capital accumulation on the job. The Mincerian return may also be affected by the quality of schooling or, for that matter, early childhood stimulation, nutrition, and so on. Given data on S , we need to know φ and B to implement the Mincerian it it it approach to estimate human capital across countries. Klenow and Rodríguez-Clare (1997) impose φ = 0.it5 for all country-years, and allow B to vary acrositcoun- tries as a function of estimated teacher human capital and differences in capital- output ratios. If human capital production is as intensive in physical capital as the production of other goods, they find human capital differences explain about 30 percent of income differences. If, instead, they put more weight on student time and teacher human capital, and less weight on physical capital inputs, they find human capital differences explain only about 10 percent of income differences. Caselli (2005) goes further in incorporating nonstudent inputs in measuring human capital, including teacher-pupil ratios, human capital of teachers, human capital of parents, classroom materials per student, experience, and even health and 2 nutrition. He finds that such factors could, in principle, allow human capital to explain the full 80 percent of income variation not attributable to physical capital. But each time he finds that the required elasticity of human capital with respect to these inputs (and/or the amount of variation in these inputs) is much larger than the 2 See Weil (2007) for creative use of micro evidence to try to measure the impact of health differences on income differences across countries. VOL. 2 NO. 1 HSIEH AND KLENOW: DEVELOPMENT ACCOUNTING 211 limited micro evidence available. He concludes that human capital explains between 10 percent and 30 percent of income variation. Many estimates, including those by Klenow and Rodríguez-Clare (1997), Lutz Hendricks (2002), and Caselli (2005), explicitly attempt to incorporate differences in the quality of schooling that do not show up in the Mincerian return. That not- withstanding, recent papers by Rodolfo Manuelli and Ananth Seshadri (2007); Andrés Erosa, Tatyana Koreshkova, and Diego Restuccia (2007); and Benjamin F. Jones (2008) emphasize the shortcomings of using the Mincerian approach alone to infer variation in human capital across countries. Imagine the log of human capital (of individual or country i) is a function of years of schooling siand schooling inputs xi: lnh i f(s ,ix i. Then the Mincerian return to schooling is d lnh i ∂f ∂f ∂x i _____ = ___ + ______ . dsi ∂s i ∂x is i Micro-Mincer regressions that run across individuals within a country should cap- ture not only the direct effect of a higher quantity of schooling, but also the indirect effect of the higher quality of schooling of those individuals who tend to get more education within countries. But the macro-Mincer relationship that growth econo- mists are interested in can be different. The quality of schooling may covary more withschoolingattainmentacrosscountriesthanitdoeswithincountries.Thisiswhat happens in Manuelli and Seshadri (2007) and Erosa, Koreshkova, and Restuccia (2007) because TFP in producing school inputs is higher in rich countries, but all 3 individuals within countries face the same price of school inputs. They posit lower prices of school inputs (relative to the wage) in rich countries because some school inputs are books, equipment, and buildings. Whereas the micro-Mincer semi-elas- ticity may be 10 percent, the macro-Mincer semi-elasticity may be 20 to 30 percent. These papers have the potential to overturn the conventional wisdom described here, that human capital explains only 10–30 percent of income differences. Open questions remain about this approach, namely estimating key parameters for human capital production at home, at school, and on the job—including the importance of nonteacher inputs in human capital accumulation. But the appar- ently large wage gains to immigrants from poor to rich countries, as documented by Hendricks (2002), are damaging to the view that human capital varies so much that there is little residual variation in TFP across countries. We return to some of this work when we ask why human capital is higher in rich countries. C. Hours Worked per Person A much smaller literature has investigated differences in hours worked per person across countries. Olivier Blanchard (2004) and Edward C. Prescott (2004) attribute the bulk of G7 income differences in the mid-1990s to differences in hours worked per person. But Caselli (2005) does not find people work systematically more in rich 3Although richer families may send their children to higher quality schools, public funding may also tend to equalize school quality more within countries than across countries. 212 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JANUARY 2010 4 3 CHE FIN SGP FRA THA KESP GER TZA ROM GRC NLDNK LSO POHUN ISRL AUS 2 PRT JAMPER CYP GBR HKUSA ECU DZAANBRAX MYS GNB ZWEY CRINVEN ARG IRL ZMB PHLJOR TUR NPL COGHND CHN IDN FTUN CHL TWN DOM URY BRB PAK LKAG PRYL ZAFTTO MUS PPP capital-output ratiMTGO 19KENGD CMRNDBOL SYR NER GBEGHAEN GTMLV RWA EGY SLE UGA HTI 0 1/64 1/32 1/16 1/8 1/4 1/2 1 PPP GDP per worker relative to the United States in 1996 Figure 1. Capital-Output Ratios versus Income Levels versus poor countries. Across countries, the labor force participation rate increases mildly with income, the unemployment rate is unrelated to income, and the work- week falls with income. An important caveat to Caselli’s (2005) results is that there is little data on hours worked per worker outside the manufacturing (or at least urban) sector in develop- ing countries. So it remains an open question whether, say, limited market work contributes importantly to limited market income per worker in rural areas of poor economies. Stephen L. Parente, Richard Rogerson, and Randall Wright (2000) make the case that distortions would predict such low market activity. A related issue is how much informal and home production is captured in income statistics. D. Residual TFP The upshot is that 50 percent or more of cross-country income variation appears to remain unexplained by a combination of physical capital, human capital (includ- ing health), and hours worked. This broad conclusion is not sensitive to whether the accounting uses equation (2) or equation (3). II. Why Does Physical Capital Vary? We now turn to work on the underlying causes of factor differences, starting with physical capital. Figure 1 shows purchasing power parity (PPP) capital-output ratios across 97 countries in 1996, derived from data in Penn World Table 6.1 (see Alan VOL. 2 NO. 1 HSIEH AND KLENOW: DEVELOPMENT ACCOUNTING 213 60 COG TKM 50 THA 40 KNA JOR SVK KOR SGP JAM SYR ATGE IDN GRD HKG 30 ALB SWZ BLZ JPN TJK VNM AZE VCTDMA HUN LKA PHLECU RUSANBWA CHL PRT AUT MLI NPL MDA KGZ UKR BLRTULBNAIRNEX SVNR NZL ISR NOR 20 BGDBE MKDPERHMAR POLBRA ESPGANLD LUX ZMB SEN AGINPAK LVA ARGRC BROMIRL BEN YEM KAZ GBRNRAKTA TZA CMR CIVBOL EGY VENTTO SWE MMDGA GEO FJI URY BHS BMU 10 BGR SLE 0 1996 percent investment rate at domestic prices (US = 1) 1/32 1/16 1/8 1/4 1/2 1 1996 PPP GDP per worker (US = 1) Figure 2. Domestic Price Investment Rates versus Income Levels Heston, Robert Summers, and Bettina Aten 2002). The ratios differ by a factor of about four across rich and poor countries, from a low of about three-fourths in the poorest countries to a high of about three in the richest countries. Behind this graph (Figure 1) is one of the strongest relationships established in the empirical growth literature: the positive correlation between the investment rate in physical capital and the level of output per worker (see Ross Levine and David Renelt 1992 and Xavier X. Sala-i-Martin 1997). Why is the PPP investment rate higher in richer countries? A first thought is that the savings rate is simply lower in poorer countries. Parente and Prescott (2000), for example, document lower savings rates in poorer countries. Possible reasons include subsistence savings needs, financial underdevelopment (low returns to savers and high cost of borrowing for investment), and high implicit tax rates on capital income (taxes,expropriation,corruption)inpoorercountries.Ashallowlocalsavingspooland inability to tap foreign pools may limit opportunities to finance domestic investment. As noted, there is evidence of lower savings rates in poorer countries. But if low savings rates explain the low PPP investment rates in poor countries, then we expect the investment rate to be low in poor countries at domestic prices. These terms are related as follows: I __j PPP Investment Rate in Country j = Y ; j P I Domestic Price Investment Rate in Country j = _____ j. P Y Y, jj 214 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JANUARY 2010 50% SLV PRY 40% CIV EGY BWA MUS COG BOL MAR 30% URYF BDI ECU TUN CTTO PHL VEN JOR MEX 20% LKAPER DZA Naïve MPK in 1996 JAM MYS ZMB CRI SGP IRL PAN KOR NZL ISRLDS NOR PRT ESGBR DAUT ITA USA 10% JPNSWE FRA BEL GRC CHE 0% 0 10,000 20,000 30,000 40,000 50,000 60,000 PPP GDP per worker in 1996 Figure 3. NaÏve MPK versus Income Levels Ijand Y jenote the value of investment goods and output, respectively, in country j valued at a common set of international (PPP) prices. P and P are the domestic I,j Y,j prices investment and output, respectively, in country j, relative to the international prices of investment and output. Figure 2, taken from Hsieh and Klenow (2007), shows that in 1996 there was no tendency for richer countries to invest a higher frac- tion of their GDP at domestic prices. Foreign capital inflows (including official aid) must have fully offset low domestic savings in poorer countries. Thus, the key to understanding the low PPP investment rates in poor countries is to understand their high domestic relative price of investment (compared to the international relative price of investment). A corollary to Figure 2 is that the marginal product of capital looks higher in poor countries at international prices, but not at domestic prices. Caselli and James Feyrer (2007) make this point, and further adjust the marginal product of reproduc- ible capital (equipment and structures that go into K) by subtracting payments to nonreproducible capital (land, minerals). In their definitions, α j j α j Y, j jnts j Naïve MPK = ____ Corrected MPK ≡ ____________ . j K j PK,j j 4 PPP prices are a weighted average of prices in different countries (Heston, Summers, and Aten 2002). VOL. 2 NO. 1 HSIEH AND KLENOW: DEVELOPMENT ACCOUNTING 215 50% 40% 30% 20% SLV Corrected MPK in 1996 BWA SGP URY MUS ISR 10% CHL KOR ESP NLD IRL USA PHL PMPRY JOR MZAF PRT JPNSWER FCANUS NORLA JLKA COL PANTUN MYS GRC CHE BOL EGY VEN TTO NZL ZCOGCIV ECUIDZA 0% BDI 0 10,000 20,000 30,000 40,000 50,000 60,000 PPP GDP per worker in 1996 Figure 4. Corrected MPK versus Income Levels Figures 3 and 4 use data from Caselli and Feyrer (2007) on the marginal product of capital in 52 countries in 1996. In Figure 3, naïve marginal products hover around 10 percent in the OECD countries, and range from 15 percent to almost 50 percent in poorer countries. So it looks as though capital flows fail to equalize marginal products. It is as if risk or implicit tax payments mandate higher marginal products in poorer economies. Figure 4 displays marginal products for the same 52 countries, only corrected for local differences in the price of capital, relative to output, and for payments to nonreproducible capital. Strikingly, marginal products now appear lower in most countries outside the OECD. Figure 4 suggests that rates of return are far more equalized than previously imagined. This is because the price of investment relative to output is higher in poor countries, and a higher fraction of capital income goes to nonreproducible capital in poor countries (e.g., in land-intensive agriculture). The relative price adjustment conjures a second hypothesis for low PPP invest- ment rates in developing countries—expensive investment goods relative to rich 5 countries. Jonathan Eaton and Samuel Kortum (2001) establish that most devel- oping countries import most of their equipment, so transportation costs and trade barriers (tariffs and nontariff barriers alike) might make investment more expensive in poor countries. Hsieh and Klenow (2007) show that this is not the case if one compares Penn World Table prices of investment goods across countries. Figure 5, taken from Hsieh and Klenow (2007), plots the price of equipment (relative to the 5 The high relative price of investment in poor countries has been well known since at least Barro (1991). 216 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JANUARY 2010 8 MKD SYR 4 GAB NGA 2 COGYEM CIV EGY UZB FINDNK BEN SEN LBNOR ATG GRC QAAFRIRLR MDA GIN UKR EST HSVNRT NGBOMNDTA LUX 1 BOLALB LVATUFTUPOLBRAKCARG ESP USA TZA MDG KEN VNM CMR AZE KAZROMPAN MKNA ISR JAM GRD TUN BHRBHSBRB SGP MLI TJKSLE KGZ MAR TTO MUS KOR HKG ARM PHLDN SWZ BLZ NPL LKA 191/2equipment price (US = 1) ZWE BGDPAK TKM 1/4 1/32 1/16 1/8 1/4 1/2 1 1996 PPP GDP per worker (US = 1) Figure 5. Equipment Prices versus Income Levels Source: Hsieh and Klenow (2007) US price) against relative income across countries in 1996. The price of equipment varies more among poor countries, but appears no higher in poor countries on aver- age. Any import barriers seem to be offset by lower mark-ups or lower local distribu- 6 tion costs. If investment is not particularly expensive in poor countries, then consumption must be cheap. Figure 6, also from Hsieh and Klenow (2007), confirms that PPP consumption prices are lower in poor than rich countries. As an explanation, we pro- posed that poor countries have lower TFP in producing investment goods (relative to consumption goods). This relative TFP explanation can simultaneously rationalize why poor countries have lower PPP investment rates, similar domestic price invest- ment rates, similar investment good prices (at least for tradable investment), and lower consumption good prices. The upshot is that relative TFP can exert a powerful indirect effect on income differences through its impact on capital accumulation. III. Why Does Human Capital Vary? Figure 7 combines Penn World Table 6.1 incomes with Barro and Lee (2000) data on educational attainment. Average schooling attainment ranges from about 3 years in the poorest countries to about 12 years in the richest countries. Earlier, we dwelled 6An important caveat regards data quality. PPP prices are supposed to be quality-adjusted prices. Eaton and Kortum (2001) suggest this might not be the case, given that many developing countries produce some equipment but rarely export it, as if it is not competitively priced for the global market. VOL. 2 NO. 1 HSIEH AND KLENOW: DEVELOPMENT ACCOUNTING 217 4 MKD 2 CHE SWEN NOR FGEAUT NGA ISLLDEL LUX SYR NGBRISRITA 1 GRCESP AUSUSA ATG PRT KORCAN HKG YEM ARGNBHS URY BHR JAM HDMA CHLA ECUVCTTHALZETTO 1/2 COG TUROL MEX QAT TZA ZMB EST HUN OMN BOL LVA RUS GAIRN CZE MDBEN SEN PHL LTU SVK CIV ALB IDN BWA BRB MWILI CMR PALKA MEGY 1/4 KEN AZED GEO BGRROM TUN MUS ARKGZWEKR BLRSWZ SLEM MDA GIN 1996 consumption price (TJK= 1)PL 1/8 TKM 1/16 1/32 1/16 1/8 1/4 1/2 1 1996 PPP GDP per worker (US = 1) Figure 6. Consumption Prices versus Income Levels 15 USA 12 NZL CANR SWE KOR AUS GERHE POL ISRFIN ROM IRLELPNG HUNARG CYP ISL 9 FJIN GRCRBN AUT PHL PER CHLY FRA VENX ESP ITSGP LKAJOR MYS GUYN ECU CRIWAZAF MUS 6 ZMB BOL SYR PRT COG ZWE EJAMDZIRNLUR HNDD IDNLV TUNBRA KENO PAK GHA UTGO CMR GTM ZAR TZA MWI HTI PNG 1996 years of schooling attainmNPLSEN GMB GMLI 0 1/64 1/32 1/16 1/8 1/4 1/2 1 1996 PPP GDP per worker (US = 1) Figure 7. Schooling Attainment versus Income Levels 218 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JANUARY 2010 6 Secondary 5 Primary 4 3 2 1 School fees relative to 1996 level 0 1996 1997 1998 1999 2000 2001 2002 2003 2004 Year Figure 8. Public School Fees in China from 1996 to 2004 Source: Hsieh and Klenow (2007) on whether the Mincerian return across countries was closer to 10 percent (so that schooling contributes a factor of 2.5 to income differences) or 30 percent (implying income differences closer to a factor of 15). Here, we ask why schooling attainment is higher in richer countries. We hasten to add that this section is more speculative than the previous one on physical capital. As we note below, we will omit many factors that could be critical for explaining schooling differences across countries. A first candidate is that richer countries may provide greater public subsidies to education. Consider, for example, the case of Mexico. From 1991 to 2004 the share of government expenditures devoted to schooling rose from 15 percent to 26 percent. Public spending per student rose from 5 percent of GDP per capita to 15 percent of GDP per capita. This more generous public funding may have helped boost Mexico’s secondary school enrollment rate from 45 percent in 1991 to 67 percent in 2004. 7 Now consider China, which reduced public support for education at the same time. The share of public expenditures for education fell from 21 percent in 1994 to 15 percent in 2004, forcing students to finance more of their education out of tuition and fees, which rose from 7 percent to 32 percent of school spending over the same period. These ratios understate the decline in support for primary and secondary schooling in China because at the same time China increased public support for uni- versities. Figure 8 plots fees (in constant prices) for public primary and secondary schools in China from 1996 to 2004. Despite the increasing cost of public schooling, the enrollment rate in secondary schooling in China rose from 50 percent to 70 per- cent from 1991 to 2004—almost parallel to the increase in Mexico. 8 Clearly, other factors besides government funding are important for schooling attainment in China, and presumably elsewhere. To hint at some explanations for 7The source of the numbers cited in the paragraph for school enrollment and spending in Mexico is the World Development Indicators. 8 Figure 8 and the share of tuition and fees in total spending are from Emily Hannum et al. (2008). Public spending on schools as a share of government spending and secondary school enrollment are from the World Development Indicators. VOL. 2 NO. 1 HSIEH AND KLENOW: DEVELOPMENT ACCOUNTING 219 schooling attainment in China, imagine that the marginal cost and benefit of addi- tional schooling are MC = iirect Cost + Opportinity Cost = P (S ) i i i MB = ____________) i . i δ(r i g iT −iS ) i The direct cost is tuition, and the opportunity cost is foregone earnings, both of which are presumably increasing with the level of schooling S. The marginal ben- efit is the present discounted value of additional earnings. Here φ represents the i Mincerian return to schooling. W (S ) is thi waie for an individual with school- ing S ,iand δ is an appropriate discount rate. The effective discount rate should be increasing in the real interest rate r , decreasing in the growth rate of wages g , and i i increasing in the number of years working T − S , where Tiis thi retirement ige. For simplicity, let T = ∞ so that δ = r − g . Then, equating the marginal cost i i i i and marginal benefit of schooling yields _______i) i _____)i ______i P(i )i= ri− g i ⇒ W (S ) = ri− g i . i i Although not necessary for the qualitative points we wish to make, we can obtain a closed-form solution if we assume the cost of schooling relative to the wage is _____)i = ___i S , W iS i W i i where P isithe price of inputs to schooling, W is the wage,iand β > 1. Combining the previous two equations yields φ 1/β S i a_____________i b . (P/i ) ·i(r − g i i So, optimal years of schooling are increasing in the Mincerian return (φ ), i decreasing in the relative price of schooling (P/W ), and decreasing in the effec- i i tive discount rate (δ = ri− g )i Do rich countries have higher schooling because of higher Mincerian returns, say, due to skill-biased technology? Abhijit V. Banerjee and Esther Duflo (2005) say no. They conclude that Mincerian returns are relatively flat across countries with high versus low schooling attainment. Might rich countries have lower discount rates because of better financial systems or better protection of property rights? If so, then the marginal product of capital should be lower in rich countries, contrary to the evidence in Caselli and Feyrer (2007). Related, if dis- count rates are lower in rich countries, then we might expect to see lower Mincerian returns in rich countries, contrary to the Banerjee and Duflo (2005) evidence. See David Card (2001) and Todd Schoellman (2009) for expositions closely tying the Mincerian return to discount rates and the relative price of schooling. It is possible, of course, that discount rates and skill-biased technology differ in offsetting ways 220 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JANUARY 2010 across countries. That is an open question for future research, as is the potential role for heterogeneity in discount rates across individuals. Might the relative price of schooling fall with development? The Mexico versus China comparison notwithstanding, perhaps rich countries subsidize schooling at a higher rate. Caselli (2005) finds little evidence for this in the Barro and Lee (2000) data on schooling expenditures. In China, growth in TFP may be reducing the price of nontime inputs to schooling (books, equipment, buildings) relative to the wage per unit of human capital. This is precisely the thesis of Manuelli and Seshadri (2007) and Erosa, Koreshkova, and Restuccia (2007). Another possibility is that teacher salaries are lower relative to average wages in richer countries. One would need a richer model to take to the data. This simple model does not incorporate many factors that surely affect schooling decisions, such as liquidity constraints, the ability to learn (presumably endogenous to early childhood invest- ments), life expectancy, schooling costs not tied to the general level of wages, any direct consumption value of schooling, and cultural and institutional differences (in attitudes toward girls, for example). But, as of now, we lack information on critical parameters even for this simple model. What does the human capital production function look like? What is the price of schooling across countries? What is the curvature parameter β? We leave these vital questions for future research in growth, labor, and development fields. IV. Why Does TFP Vary? As described, development accounting yields sizable residual TFP terms. In the previous two sections, we have argued that TFP can indirectly affect physical and human capital accumulation through the relative price of physical and human capi- tal. The natural next question is why TFP itself varies. One can decompose aggregate TFP into the (unweighted) average of firm-level TFPs,andtheefficiencyofinputallocationacrossfirms.ParenteandPrescott (2000) examine some of the many factors that affect TFP at the firm level, such as disem- bodied TFP, work rules, government ownership, and corruption. Here we focus, instead, on how TFP can be affected by the efficiency of resource allocation across firms. This is an old idea, but there has been a recent surge of mod- els and evidence on misallocation. Restuccia and Rogerson (2008) show that modest distortions can have nontrivial effects on aggregate TFP in a Lucas span-of-control model. Hugo Hopenhayn and Rogerson (1993) present an early model on misalloca- tion of labor due to firing costs. Caselli and Nicola Gennaioli (2003) model misal- location of capital due to capital market imperfections, as do Francisco J. Buera and Yongseok Shin (2008). Nezih Guner, Gustavo Ventura, and Yi Xu (2008) analyze the consequences for TFP of size-dependent policies. Jones (2009) demonstrates that complementarities across industries can allow modest industry-level distortions to have larger effects on aggregate TFP. 9 factors.elli and Seshadri (2007) and Erosa, Koreshkova, and Restuccia (2007) incorporate several of these VOL. 2 NO. 1 HSIEH AND KLENOW: DEVELOPMENT ACCOUNTING 221 India 0.25 0.20 0.15 0.10 0.05 0 1 4 16 64 256 1,024 4,096 16,384 United States Percent of plants 0.20 0.15 0.10 0.05 0 1 4 16 64 256 1,024 4,096 16,384 Number of workers in plant Figure 9. Distribution of Plant Size, India versus the United States Regarding the magnitude of resource misallocation, Banerjee and Duflo (2005) present suggestive evidence that India’s low TFP in manufacturing relative to the United States could reflect misallocation of capital across plants. In Hsieh and Klenow (2009), we compare misallocation in China and India to that in the United States. We document much wider dispersion in the value marginal products of capi- tal and labor within manufacturing industries in China and India. We argue that misallocation could explain about one-third of the manufacturing TFP gap between China or India and the United States. In China, allocative efficiency appeared to improve over our 1998–2005 sample, as inefficient state-owned enterprises faded in importance and manufacturing TFP surged. In India, we find no such improvement in the period 1987–1994 despite reforms, consistent with India’s tepid manufacturing TFP growth. InHsiehandKlenow(2009),wealsoreportathicklefttailofsmallplantsinIndia even within the formal manufacturing sector. Here, we show how thick the left tail of small plants in India is when we include both formal and informal firms. Figure 9 compares the distribution of plant size (in terms of employment) in Indian versus US manufacturing, where Indian plants include formal and informal firms. US data are from the 1997 Census of Manufactures, and Indian data are from combining 222 AMERICAN ECONOMIC JOURNAL: MACROECONOMICS JANUARY 2010 the 1999 Annual Survey of Industries (which covers larger plants) with the 1999 National Sample Survey (which covers even the smallest plants). The majority of plants in Indian manufacturing have 5 or fewer workers, whereas most US plants have more than 40 workers. Major questions for future research include the following: how much of the dis- persion is real versus a by-product of measurement error? What specific distortions (man-made or natural) generate greater dispersion in marginal products in poorer countries? How large are the misallocations across sectors? Why is the distribution of firm size so left-skewed in poor countries? We hope to see progress on these ques- tions in the years to come. V. Conclusion We have learned a great deal in the last two decades about the proximate deter- minants of income differences. Although important questions remain, particularly about the role of human capital differences, there is a broad consensus that differ- ences in human capital account for 10–30 percent of country income differences, physical capital accounts for 20 percent of country income differences, and residual TFP may be the biggest part of the story (accounting for 50–70 percent of country income differences). But, we have much less understanding as to why these factors differ. 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