Capital Flows to Developing Countries: The Allocation Puzzle

Transcription

1 Capital Flows to Developing Countries: he Allocation Puzzle Pierre-Olivier Gourinchas University of California at Berkeley Olivier Jeanne IMF May 10, 2007 Abstract According to the consensus view in growth and development economics, cross country differences in per-capita income largely reflect differences in countries total factor productivity. We argue that this view has powerful implications for patterns of capital flows: everything else equal, countries with faster productivity growth should invest more, and attract more foreign capital. We show that the pattern of net capital flows across non-industrialized countries are robustly inconsistent with this prediction. Capital flows more to countries that invest less and grow less. We argue that this result which we call the allocation puzzle constitutes an important challenge for economic research. We would like to thank Chris Carroll, Sebnem Kalemli-Ozcan, Federico Sturzenegger, Alberto Martin for useful comments and especially Chang-ai Hsie and Chad Jones for insightful discussions. We also thank seminar participants at Stanford University and Johns Hopkins University, the 2006 NBER-IFM summer institute (Cambridge), 2007 AEA meetings (Chicago) and 2007 CEPR meeting on Global Interdependence (Dublin). Also affiliated with the National Bureau of Economic Research (Cambridge), and the Center for Economic Policy Research (London). Contact address: UC Berkeley, Department of Economics, 693 Evans Hall #3880, Berkeley, CA Also affiliated with the Center for Economic Policy Research (London). he views expressed in this paper are those of the author and should not be attributed to the International Monetary Fund, its Executive Board, or its management. A first draft of this paper was completed while the author was visiting the Department of Economics of Princeton University, whose hospitality is gratefully acknowledged.

2 1 Introduction Between the years 1980 and 2000, the investment to GDP ratio averaged 32 percent in Korea and only 2.8 percent in Madagascar. Over the same period, Korea experienced an economic miracle, with a growth rate of output per worker of 5.4 percent per year. Madagascar was less lucky: output per worker declined by 1.3 percent per year. By 2000, PPP-adjusted output per worker reached $22,022 in Korea and only $1,599 in Madagascar. Modern growth theory teaches us how to interpret such enormous differences in economic performance. Hall and Jones (1999) and the subsequent literature on development accounting (see Caselli (2004)) argue conclusively that a substantial share of the differences in output per worker can be attributed to productivity. Indeed, standard growth decomposition exercises tell us that total factor productivity growth averaged 4.48 percent p.a. in Korea and percent p.a. in Madagascar. What does this imply for international capital flows? he standard growth model delivers an unambiguous answer to this question. High productivity growth in countries like Korea increases the marginal product of capital, which attracts foreign capital. Korea should have borrowed abroad to finance a share of its rapidly growing capital stock. Madagascar, facing no or little upward prospects, should not have accumulated much net international debt. Consider what happened instead. Between 1980 and 2000, both countries had a fairly open capital account. Yet Korea received almost no net capital inflows. In Madagascar, by contrast, net capital inflows averaged 6 percent of output. Figure?? documents the same pattern across a large number of developing countries. It shows that the average share of net capital inflows in GDP between 1980 and 2000 (on the vertical axis) seems to be, if anything, negatively correlated with the investment-to-gdp ratio (on the horizontal axis). Far from being outliers, Korea and Madagascar are typical of the crosscountry correlation between investment and capital inflows shown in Figure??. Both countries are close to the regression line. If investment and capital flows were driven primarily by changes in domestic productivity, as suggested by the development accounting literature, countries that invest more should receive more capital from abroad. We observe the exact opposite. Patterns such as Figure?? are just one illustration of a range of results that point in the same direction: standard models cannot account for the allocation of international capital flows across developing countries. Capital flows from rich to poor countries are not only low (as argued by 1

3 Lucas (1990)), but their allocation across developing countries is the opposite of the predictions of standard textbook models: capital does not flow more to the countries that invest more or have a higher marginal product of capital, in the way that standard open economy growth models would predict. We argue that the pattern of capital flows across developing countries constitutes a major puzzle and its resolution will be an important challenge of economics. We call it the allocation puzzle. his paper s main objective is to document and establish this puzzle in the behavior of international capital flows. he allocation puzzle is different from the Lucas puzzle (Lucas (1990)), which is about the small size of capital flows from rich to poor countries. In fact, our results are not inconsistent with the Lucas puzzle: as Figure 1 shows, capital inflows amount to a much smaller share of GDP than investment on average (3.9 percent against 15.4 percent in our sample). We would argue that the small size of aggregate capital flows toward developing countries as a whole is not especially puzzling given the overall lack of productivity catch-up in these countries. Indeed, we will show that a calibrated model can predict the order of magnitude of capital flowstodevelopingcountries pretty well without assuming any international financial friction. Our explanation is consistent with Lucas original guess: capital flows to poor countries are low because these countries are not very productive and face domestic distortions in the return to capital. It is also important to observe that introducing an external credit constraint into the model can reduce the predicted size of capital inflows, but cannot make capital flow more towards the countries that invest less (it cannot make capital flow upstream!). hus, explaining the puzzle requires more than a neoclassical growth model with international credit frictions. Our puzzle is related to the allocation of the capital flows across developing countries rather than their overall level. Our calibrated open economy growth model predicts capital inflows to Asia that are much larger than those we observe in the data. Conversely, it predicts relative large capital outflows from Latin America and Africa. his rather provocative result reflects a straightforward implication of a standard open economy growth model: the countries whose productivity declines relative to the rest of the world should export, not import capital. Our empirical approach consists in calibrating a simple neoclassical growth model. Our model and calibration methods are closely related to the recent literature on development accounting 2

4 (although in this version of the paper we do not consider human capital explicitly). his literature has emphasized productivity growth as the main proximate cause of economic development (Hall and Jones (1999); Caselli (2004)). his view has implications for the behavior of capital flows that have not been systematically explored in the literature (by contrast with investment, whose relationship with productivity is well understood and documented). Whether the observed pattern of capital flows to developing countries is consistent with the dominant theory of growth is an interesting question in its own right, and might teach us one lesson or two on the determinants of growth themselves. Our paper is the first, to our knowledge, to quantify the level of capital flows to developing countries in a calibrated open economy growth model and compare it to the data. he Section 2 begins with a simple frictionless small open economy model in the tradition of Ramsey, Cass and Koopmans. he model assumes a common technology frontier: in the long run, all countries grow at the same rate. his can result from the diffusion of ideas and technology across countries, as in Parente and Prescott (2000), or Eaton and Kortum (1999). Given this common long-run growth, countries can experience two sorts of transitions. First, capital-scarce countries can converge to their conditional steady state. hese convergence dynamics have been widely studied in the literature and are by now well understood (see Mankiw, Romer and Weil (1992)): countries further from their conditional steady state tend to grow faster. he implications for international capital flows are also straightforward, although their quantitative importance have been less explored (see King and Rebelo (1993) for an important exception). Second, countries can experience a productivity catch-up towards the productivity frontier. We take this productivity catch-up as exogenous, although, following Hall and Jones (1999) one could interpret it as the result of a permanent increase in a country s social infrastructure, i.e., the set of institutions and government policies that determine the environment within which individuals accumulate skills, and firms accumulate capital and produce output (Hall and Jones (1999)). As our discussion of the relative experience of Korea and Madagascar illustrates, these productivity catch-ups are essential to the process by which countries experience economic development. We calibrate the model using Penn World able (PW) data on investment and output as well as IMF data on currrent account (under balance of payment accounting, the opposite of net capital inflows). Section 3 presents our main empirical findings. Using the model of section 2, we compare 3

5 estimates of actual and predicted capital flows to and from a large number of developing economies between 1980 and We find that developing countries were not very scarce in capital at the beginning of the sample period, potentially explaining the small size of capital flows from rich to poor countries (the Lucas puzzle). We also find that the cross-country allocation of capital flows during the period in response to productivity changes is always opposite to that predicted by the theory. Countries with faster productivity growth attract less capital. his is the allocation puzzle. Section 4 proposes some extensions and studies in greater detail the composition of net capital inflows. Using data from the World Bank (Global Development Finance), it proposes a decomposition of net and gross capital inflows into public and private components, FDI and reserve accumulation. We find that whereas FDI behaves in accordance with a standard neoclassical model most other flows do not, and those flows dominate the sign of the correlation with growth in the data. his paper contributes to the literature on the determinants of capital inflows to developing countries and the role of capital flows in economic development. Aizenman, Pinto and Radziwill (2004) construct a self-financing ratio indicating what would have been the stock of capital in the absence of capital inflows. hey find that 90 percent of the stock of capital in developing countries is self-financed, and that countries with higher self-financing ratios grew faster in the 1990s. Prasad, Rajan and Subramanian (forthcoming 2007) also find a negative cross-country correlation between the ratio of capital inflows to GDP and growth. Manzocchi and Martin (1996) empirically test an equation for capital inflows derived from an open-economy growth model on cross-section data for 33 developing countries and find relatively weak support. Our approach is different: we use the theory to help us estimate the size and direction of international capital flows for developing countries. his allows us to estimate separately the contribution of convergence dynamics and productivity catch-up to observed capital flows. We do so under a number of different scenarios. he paper is also related to the literature on savings and growth. his literature has established a positive correlation between savings and growth, which is puzzling from the point of view of the permanent income hypothesis since high-growth countries should borrow abroad against future income to finance a higher level of consumption (Carroll and Summers (1991), Carroll and Weil (1994)). he allocation puzzle that we present in this paper is related to the savings puzzle but it is stronger. Our finding is that the difference between savings and investment (capital outflows) is 4

6 positively correlated with growth, which means that savings not only has to increase with growth, but has to increase more than investment. Finally this paper belongs to a small set of contributions that look at the implications of the development accounting literature for international economics. In Gourinchas and Jeanne (2006) we use a development accounting framework similar to that in this paper to quantify the welfare gains from capital mobility and find them to be relatively small. In this paper, by contrast, we look at the positive implications of development accounting for the direction of capital flows. In a related contribution that is discussed in more detail in section 4, Caselli and Feyrer (2005) show that the return to capital, once properly measured in a development accounting framework, is very similar in advanced and developing countries, which might explain why we observe so little capital flow from the former to the latter. he paper is structured as follows. Section 2 derives the predictions of the basic neoclassical model of growth for international capital flows. Section 3 calibrates the model and compares the model predictions with the data on capital flows to developing countries. Section 4 explores the robustness of our results. Section 5 presents a brief review of what we view as the main possible explanations for the puzzle. Section 6 concludes. 2 Capital Flows in the extbook Growth Model We begin with a small open economy version of the standard Ramsey-Cass Koopmans growth model. We focus on the model s implications for net capital inflows. 2.1 he model Consider a set of small open economies that can borrow and lend at an exogenously given world gross real interest rate R. ime is discrete and, for the time being, there is no uncertainty. In each economy, the population N t grows at an exogenous rate n: N t = n t N 0. he population can be viewed as a large family whose stand-in representative maximizes the welfare function: X U t = β s N t+s u (c t+s ). (1) s=0 c t denotes consumption per capita (more generally, lower case variables are normalized by population) and u (c) c 1 γ 1 / (1 γ) is a constant relative risk aversion (CRRA) utility function 5

7 with coefficient γ>0. In the case where γ =1, the utility function is u (c) =ln(c). Each economy produces a single homogeneous good using two inputs, capital and labor, according to a common Cobb-Douglas production function: Y t = K α t (A t L t ) 1 α, 0 <α<1 (2) he notation is standard: K t is the stock of domestic physical capital, L t the labor supply, and A t the level of technology. he labor supply is exogenous and equal to the population (L t = N t ). Factor markets are perfectly competitive so each factor is paid its marginal product. echnology grows at a gross rate g t A t /A t 1,whichmaydiffer across countries in the short run but converges towards the same value for all countries: 1 lim g t = g (3) t + g can be interpreted as the growth rate of a world productivity frontier A t A t. It reflects the advancement of knowledge, which is not country specific. 2 his assumption guarantees that no country s share of world output converges to 0 or 100 percent. However, it does not presume any convergence in the level of GDP per capita since country specific differences in the level of technology could persist forever. In order to account for long-run cross country differences in investment rates, we assume a distortion τ in the return to capital. Denote R t the marginal product of capital, net of depreciation: α (k t /A t ) α 1 +1 δ, where δ measures the depreciation rate. Investors receive only a fraction (1 τ) of the gross return on capital R t,whereτ 1. 3 We call τ the capital wedge. It is a short hand for the gap between the gross social return to capital R t and the private return. One can interpret τ as a tax on gross capital income, but other interpretations are also possible: credit market imperfections, expropriation risk, bureaucracy, 1 We assume further that βng (1 γ) < 1 so that utility is always well defined. 2 Models of idea flows such as Parente and Prescott (2000) or Eaton and Kortum (1999) imply a common long run growth rate of productivity. 3 In the long run of the model, the investment rate is equal to α (δ + ng 1) / (R / (1 τ)+δ 1). Without a capital wedge (τ = 0), the investment rate varies only with the population growth rate n. Empirically, this source of variation is not sufficient to account for the large cross-country differences in investment rates. A higher wedge implies a lower investment rate. 6

8 bribery, and corruption would also introduce such a wedge between social and private returns. 4 In order to focus on the distortive aspects of this wedge, the revenue per capita z t = τr t k t generated by this wedge are rebated in a lump sum fashion. he stand-in representative resident issues external debt d t and owns all the domestic capital k t. Given our assumptions, the country s budget constraint is: n (k t+1 d t+1 )=(1 τ) R t k t R d t + w t + z t c t, (4) where w t is the wage, equal to the marginal product of labor (1 α) k α t A 1 α t. A country is characterized by an initial capital stock per capita k 0, debt d 0, population growth rate n, productivity A 0 together with a productivity path {A t } 0 that satisfies (3), and a capital wedge τ. We assume that all countries are financially open at time t = 0 and use the model to estimate the size and the direction of capital flows from time t =0onward. Financial integration means that domestic investors can borrow and lend at the world interest rate R (recall that each country we consider is small). From the perspective of each small economy, the rest of the world is composed of developed economies that have already achieved their steady state. hen, the world interest rate R coincides with the steady state rate of return, equal to the growth-adjusted discount factor: R = g γ /β (5) his ensures that financial integration does not tilt consumption profiles in developing countries in the long run. Capital mobility equates the private return on domestic capital and the world real interest rate: (1 τ) R t+1 = R. (6) Substituting the expression for the gross return on capital, this implies a constant capital stock per efficient unit of labor k = k/a (more generally, tilde-variables denote per capita variables in 4 τ distorts intertemporal decisions and has much the same interpretation as the intertemporal wedge in Chari, Kehoe and McGrattan (2002). 7

9 efficiency units: x = X/AN) equalto: 5 µ k t+1 = k α 1/1 α R. (7) / (1 τ)+δ 1 Equation (7) makes clear that the intertemporal wedge τ is the only source of variation in the steady state capital stock per efficient unit of labor across countries. A higher wedge, equivalent to a higher implicit tax on capital, depresses domestic capital accumulation and yields a lower k. We complete the characterization of the model by noting that the Euler equation for consumption c γ t = βr c γ t+1 implies that consumption per capita grows at the constant rate g, c t = c 0 g t. 2.2 Net Capital Flows Accounting It will be convenient to define π t = A t / A 0 g t, the ratio of domestic productivity to the trend productivity assuming no catch-up. We denote by π =lim t π t the long-run technological catchup of the economy. 6 When π =1, the economy s relative technology does not change in the long run. When π>1,the economy moves toward the technology frontier. 7 When π<1,the economy falls further behind. We obtain after some simple manipulations the following proposition: Proposition 1 (Net Capital Flows Accounting) : Given an initial debt d 0, capital stock k 0, relative productivity process {π t } t=1 and steady state capital k, the net external debt d t stabilizes at the level: d = d 0 π + k k 0 + π 1 π π k w + z X µ ng t π π t + R R. (8) π Proof. See the appendix. o interpret equation (8), consider first the case of a country whose technology grows at the constant rate g. his implies π t = π = 1 since there is no long-run technological catch-up. Sub- 5 Observe for future reference that a constant capital stock k implies a that the wage w t and revenues z t are proportional to technology: w t =(1 α) k α A t and z t = τr k / (1 τ) A t. 6 echnically, the existence of a finite π requires a slightly stronger form of equation (3), ensuring that lim t t s=1 ln (g s/g ) <. We assume this condition is satisfied in what follows. 7 Since A t/a t = A 0/A 0π t, the case of full technology catch-up corresponds to π = A 0/A 0. t=0 8

10 stituting into equation (8), this equation simplifies to: d d 0 = k k 0 (9) he pattern of capital flows is controlled by the initial capital scarcity k k 0. o understand why, observe that under financial autarky, a capital scarce country would accumulate physical capital domestically and asymptotically reach k. Under financial integration, and in the absence of financial frictions, the country will instead optimally borrow the amount k k 0. Notice that in this simple case, saving does not change since consumption adjusts immediately to its new permanent income level. Second, consider a country without initial debt ( d 0 = 0) nor capital scarcity ( k 0 = k ), but in which productivity grows at a rate different from g. Equation (8) yields: d = π 1 π k + w + z R X µ ng t π π t R π t=0 (10) his expression has two terms, each with an intuitive interpretation. Consider the first term on the right hand side: d i π 1 π k (11) It represents the external borrowing that goes toward financing domestic investment. oseethis, observe that since capital per efficient unit of labor remains constant at k, capital per capita needs to increase more when there is a productivity catch-up. Without productivity catch-up, capital per capita at time would be k A 0 g. Instead, it is k A. he difference, (π 1) k A 0 g, normalized by productivity A,equals k (π 1) /π. In the limit of, this converges to ³ d i. his expression makes clear that capital should flow into d > 0 countries that get closer ³ to the world productivity frontier (π >1) and flow out of d < 0 countries that move further away from the productivity frontier (π <1). he second term on the right-hand-side of (8), d s w + z R X µ ng t π π t R, (12) π t=0 represents the change in external debt brought about by changes in domestic saving. It is tied to thetimepathofdisposableincomew t +z t. Faster relative productivity growth implies higher future 9

11 income, leading to an increase in consumption and a dcrease in savings. Since current income is unchanged, the stand-in representative domestic agent borrows on the international markets. It is important to emphasize that what controls the size and direction of capital flowsisthelong run productivity catch-up, i.e., productivity growth relative to g as summarized by π. Countries are expected to borrow, only insofar as they catch-up to, or fall behind, the productivity frontier. Notice also that faster productivity growth unambiguously reduces savings here. he reason is that the usual substitution effects faster productivity growth raises the marginal product of capital and interest rates are absent in a small open economy facing a constant exogenous rate of return to capital. By contrast, in a closed economy, faster productivity growth leads to additional investment only insofar as it successfully mobilizes national savings through higher interest rates. 8 While the results are very stark in our simple model, the Fisherian separation of savings and investment is at the core of the economics of capital flows in the neoclassical growth model. 9 o summarize, the investment and consumption channels lead to the same prediction that countries growing faster should borrow more. Before turning to the data, let us highlight briefly some empirical shortcomings of the simple model developed above. First, we assume perfect international financial integration. In reality, financial frictions may limit severely perhaps eliminate altogether the ability of developing countries to borrow in order to smooth consumption profiles. Yet, we would argue that, while international financial frictions may be important, they are unlikely to reverse by themselves the direction of capital flows, or the sign of their correlation with productivity growth. In the presence of international financial frictions, countries will be able to borrow less, much less perhaps. But countries with brighter prospects, as measured by π 1, shouldstillbeabletoborrowmore, not less, than countries facing little or no prospects for productivity improvements (π 1). International financial frictions can reduce the predicted size of capital inflows, but cannot make capital flow more towards the countries that invest less or flow less toward the countries that invest more. Second, equation (12) assumes perfect foresight: the path of future productivity, as embodied in {π} t=0 is known as of time t = 0. Uncertainty about the future path of productivity would 8 his is the main reason our results are different from Chen, Imrohoroglu and Imrohoroglu (2006) who study the Japanese saving rate from the perspective of a closed economy. 9 Equation (12) makes clear that the time preference parameter β and the intertemporal elasticity of substitution 1/γ enter this expression only via their impact on the world interest rate R = g γ /β. A higher world interest rate (either because of a lower discount factor β or a lower elasticity of substitution 1/γ) reduces d s. 10

12 dampen the willingness the domestic household to borrow against future income, reducing d s. We will consider a variant of the model with stochastic productivity in section 4.1. Again, while this may affect the magnitude of capital flows, it should still be the case that countries that grow more should borrow more. Lastly, it is important to realize that richer environments could deliver different predictions for the aggregate relationship between saving and growth, and thus modify the implications of the model for capital flows. For instance, in Modigliani s original life cycle model, faster growth increases aggregate savings by increasing the saving of richer young cohorts relative to the dissaving of poorer older cohorts. As we have mentioned in the introduction, other models have been developed to explain the positive association between faster growth and national saving that is observed in the data. We will discuss that literature in section 5. 3 Capital Flows Accounting he natural question to consider is whether the data support the model s prediction concerning capital flows. o be more specific, we want to investigate whether those industrializing countries with faster productivity growth (high π) and larger initial capital scarcity ( k k 0 ) receive more capital inflows. his requires an estimate of initial and steady state capital stock; of technological catch-up (π); and of realized cumulated capital flows. We start by assuming preferences are identical across countries. More precisely, we assume logarithmic preferences (γ = 1) and set the discount factor β to 0.96 (a period is a year). Next, we set the capital share of output α equal to 0.3, and the depreciation rate δ to 6%. 10 Lastly, we set the growth rate of world productivity g to his corresponds to the U.S. annual multifactor productivity growth between 1980 and Given these parameter values, the world real interest rate equals R 1=5.94 percent per year. Data on output and capital come from Version 6.1 of the Penn World ables (Heston, Summers and Aten (2004)). he capital stock K t is constructed with the perpetual inventory method from 10 his assumption will be relaxed in section 4. Recent estimates by Gollin (2002) suggest that the capital share is roughly constant within countries, and varies between 0.2 and

13 time series data on real investment (also from the PW). 11 From (2), we obtain the level of technology A t as (y t /k α t ) 1/(1 α) and the level of capital stock per efficient unit of labor k t as (k t /y t ) 1/(1 α). 12 We focus on the period his choice of period is motivated by two considerations. First, countries need to be financially open over at least part of the period we study. Indicators of financial openness indicate a sharp increase starting in the late 1980s and early 1990s. 13 Second, we want as long a sample as possible, since the focus is on long-term capital flows. Results over shorter periods may be disproportionately affected by financial crisis or fluctuations in the world business cycle. 14 Our final sample consists of 69 non-oecd countries. 15 We measure n as the growth rate of working age population. For the productivity catch-up parameters π, for lack of a better alternative, we assume that productivity growth is constant and equal to g, after Assumption 1 (finite time productivity catch-up) π +s = π for s 0. Under assumption 1, we can measure π as exp(ln Ā2000 ln Ā1980)/g 20, where ln Āt is obtained as the trend component of the Hodrick-Prescott filter of ln A t. 16 his detrending removes short term fluctuations in productivity due to mismeasurement or business cycle factors. he next step consists in constructing the steady state capital level k. From equation (7), this is equivalent to constructing the capital wedge τ. We can make this dependency explicit in the notations by writing k as a function of τ, k (τ). Our approach is to calibrate the capital wedge so as to match investment rates in the data. In other words, we calibrate the model so as to account for the pattern of cross-country physical capital accumulation. he next proposition characterizes the average investment rate between 1980 and See Caselli (2004) for details. Following standard practice, we set initial capital to I/(g i + δ) wherei is the initial investment level from the PW and g i istherateofgrowthofrealinvestmentforthefirst 10 years of available data. 12 We measure output and capital per working-age capita using data on the fraction of the population of working age (typically ages 15 to 64) from the World Bank. 13 See Chinn and Ito (2002) or Quinn (1997). For instance, the Chinn-Ito index indicates an average increase from -0.70in1985to0.38in2005forthecountriesinoursample. 14 For instance, the Asian financial crisis of 1997, or the debt crisis of the early 1980s. 15 For a small set of countries, the sample period starts later and/or end earlier, due to data availability. he list of countries and sample period is reported in the appendix. 16 Consistent with this approach, g satisfies ln g = ln Ā US 2000 ln Ā1980 US /20. 12

14 Proposition 2 (Average Investment Rate) : Under assumption 1, given an initial capital stock k 0,productivitycatch-upπ, and capital wedge τ, the average investment-output ratio between t =0and t = 1 can be decomposed into the following three terms: s k = 1 k (τ) k 0 k α 0 + k h i (τ) 1 α π 1/ 1 g n + k (τ) 1 α (g n + δ 1) (13) Proof. See the appendix. Equation (13) has a simple interpretation. he first term on the right hand side corresponds to the increase in investment at time t =0, from k 0 to k, normalized by initial output ỹ 0 = k 0 α. his is the convergence component. he second term reflects the additional investment needed when there is a productivity catch-up (i.e. π>1). he last term is simply the usual formula for the investment rate in steady state, with productivity growth g. It corresponds to the investment required to offset capital depreciation, adjusted for productivity and population growth. 17 Solving numerically (13), we obtain the capital wedge as a function of the average investment rate s k, π and n. 18 Everything else equal, our calibration approach assigns a high capital wedge to countries with low average investment rate. his is intuitive: countries with low investment must face some significant capital market distortions. For the average working-age population growth rate in our sample (2.64 percent p.a.), productivity catch-up (0.88), and initial capital output ratio (1.40), (13) admits a capital wedge of zero if the investment rate s k equals 32 percent of GDP. he average investment rate in our sample is only 13.3 percent, implying a capital wedge of 8.04 percent. Our approach to constructing τ assumes that countries are perfectly integrated. In the presence of international financial frictions, our estimates of the contribution of capital scarcity and productivity catch-up to capital flows are likely to be biased. Can this bias upset our results? In general, it is difficult to tell in which direction the bias goes, but we can get more specific results for the case where the capital account is completely closed. First, let us assume that there is no productivity catch-up (π = 1). In that case, with a Cobb-Douglas production function and logarithmic preferences, the saving rate is decreasing with the capital stock along the transition. 19 Hence, capital 17 Observe that when g = n =1, this last term simplifies to δ k (1 α) = δ k /ỹ. 18 When there is no initial capital scarcity, the capital wedge has an explicit solution: R τ =1 α (δ + ng π 1/ 1) / s k +1 δ. he appendix reports the values of s k,π,nand τ for each country in our sample. 19 his is not true in the general case. See Barro and Sala-i-Martin (1995), p.77 for a discussion. 13

15 (1) (2) (3) (4) (5) (6) (7) Average Investment Rate otal Convergence Productivity rend Wedge Catch-up Obs. (percent of output) s k τ π Non-OECD countries Low Income Lower Middle Income Upper Middle Income High Income (Non-OECD) Africa Latin-America Asia except China and India China and India able 1: Decomposition of Average Investment Rates between 1980 and 2000, percent of GDP. Population weighted k averages. Convergence: k 0 /ỹ 0;Productivity: k (1 α) g n π 1/ 1 ;rend: k (1 α) g n scarce countries will have higher saving and investment rates than in steady state. For these countries, our procedure will underestimate the capital wedge τ, overestimate the steady state capital stock k and therefore overestimate the size of the capital inflows. Conversely, for capital abundant countries, we would undererestimate k and therefore overestimate the size of the capital outflows. heimportantpointtonoteisthatwhilethereisanupwardbiasinthelevel of capital flows, the model still predicts accurately their direction and relative magnitude. Second, consider the case of financial autarky without capital scarcity ( k = k 0 ), but with productivity catch-up. Investment will increase for countries with a productivity catch-up (π >1), but less than under financial integration, since domestic interest rates also need to increase to mobilize domestic saving. Hence measured investment rates are lower than under financial integration. We will underestimate k and the capital inflows needed for investment ( d i > 0). Conversely, a relative productivity decline (π <1) leads to a decline in domestic interest rates that mitigates the decline in investment rates. Hence, observed investment rates are too high, and so is the calibrated steady state capital k. We will then overestimate the size of the capital outflows ( d i < 0). We should therefore interpret our predicted productivity flows d i as lower bounds on actual capital inflows. 3.1 Patterns of physical capital accumulation able 1 decomposes s k into the three components of equation (13). his decomposition yields a number of interesting results. As is well known, investment rates vary widely across regions. 14

16 hey also increase with income levels, from 11.4 percent for low income countries, to 29.2 percent for high-income non-oecd countries. 20 By construction, the model accounts exactly for observed differences in average investment rates. We view this as a strength of our approach: since the model is designed to reproduce the change in the capital stock over the long run for a large number of countries, we can assess precisely whether the drivers of capital accumulation are also the drivers of observed capital flows. At the same time, equation (13) and able 1 contain interesting information on the sources of capital accumulation across countries. First, the table indicates that the convergence and productivity growth components (columns 2 and 3) account for relatively little of the overall investment rates, compared to the trend component (column 4). he variation in that component is almost entirely accounted for by the capital wedge τ reported in column 5. he average capital wedge is large, at 10.25%, and decreases with income levels from 14.6% to 2.2%. Hence the ability of the model to replicate successfully average capital accumulation requires that we take into account implicit distortions along the intertemporal margin. Second, there is little overall productivity catch-up with the industrial world. Column 6 reports our estimate of π. We find π =1.24 for the entire sample, accounting for only 1.17% of the 15.39% total investment rate. Yet, closer inspection reveals an interesting geographical pattern. Most of the productivity catch-up is located in Asia, with π =1.44, while Latin America and Africa fell behind, on average. 21 Accordingly, the productivity component is positive for Asia (2.56%), and negative for Africa and Latin America (-2.22% and -3.09% respectively). Finally, the convergence component (column 2) also seems to explain very little of the overall capital accumulation, contributing less than 1 percent to the overall investment rate. 22 his is not simply because the capital gap itself is small, but also because the capital output ratio tends to be small for the poorest countries. 23 Countries do need to borrow significantly, in relation to their initial capital stock. hey need to borrow much less in relation to their output level. Overall, we find that Asia and Latin America are capital scarce ( k 0 < k ), 20 See Hsieh and Klenow (2003). 21 here are exceptions to this pattern. For instance, we find π =0.68 for the Philippines, 1.28 for Chile and 1.47 for Botswana. See the appendix. 22 It ranges from percent for Zambia, to 3.74% for Indonesia. 23 o see this, note that we can rewrite the convergence component as 1 k 0/ k k0/ k α K /Y. he term in brackets is an increasing function of the capital gap k 0/ k. he second term is the steady state capital output ratio. In our sample, the capital gap ranges from 0.54 for Indonesia to 1.89 for the Republic of Congo. In turn, the steady state capital output ratio varies between 0.24 for Uganda and 3.2 for Singapore. 15

17 while Africa is capital abundant ( k 0 > k ). he contribution of the productivity and convergence components is most dramatic when we compare Asia and Africa. While both regions have a similar trend investment rate (column 5), observed investment rates are almost twice as large in Asia than in Africa (column 1). Figure 2 reports each component of (13) against s k. he figure confirms table 1: while s k is positively correlated with each component, most of the cross country variation is explained by the changes in the capital wedge Patterns of net capital flows able 1 has strong implications for the pattern of capital flows. It implies that we should observe significantly more capital flows to Asia than to Africa. he next proposition formalizes this insight. Proposition 3 (Change in External Debt) Under assumption 1, the change in net external debt relative to initial output, D/Y 0 =[D D 0 ] /Y 0, for a country with initial debt d 0, capital stock k 0 and capital wedge τ satisfies: " D Y 0 = k (τ) k 0 (g k n) + 0 α (π 1) k (τ)+ Proof. See the appendix ew + ez R X µ ng t (π π t )# t=0 R (g n) k α 0 + d 0 k α 0 h i (ng ) 1 Proposition 3 has a similar interpretation as proposition 2. he first term represents the convergence component of net capital Inflows. he second term in brackets the productivity catch-up component, with its investment and consumption smoothing subcomponents. he third term represents the trend component due to population and trend productivity growth. 25 (14) With estimates of π, τ, n, k 0 in hand, we obtain estimates of the first two terms on the right hand side of (14). We construct estimates of the initial debt output ratio d 0 /ỹ 0 as follows. First we construct a US dollar estimate of the initial net external liability position from Lane and Milesi- Ferretti (2006) s External Wealth of Nation Mark II database (EWN), as the difference between (the opposite of) the reported net international investment position (NIIP) and the cumulated errors and omissions (EO). 26 Since we measure output and capital in constant international dollars, 24 A simple variance decomposition reveals that differences in capital wedge account for 59% of the cross country variation in s k, productivity catch-up accounts for 28 percent and initial capital scarcity for the remaining 13 percent. 25 his last term was not present in Proposition 1 because debt measured in efficient units of labor remains constant. 26 In keeping with usual practice, we interpret errors and omissions as unreported capital inflows. 16

18 this US dollar estimate is first converted into current international dollars using a price deflator P def that we will describe shortly, then into constant international dollars using the ratio of the Laspeyres constant international output (RGDP) to its current international dollar equivalent (CGDP). Hence the deflator from current US dollars into constant international dollars is = P def.cgdp/rgdp and the initial debt to GDP is: D 0 Y 0 = d 0 ỹ 0 = NIIP 0 PEO 0 P def 0 CGDP 0 (15) o construct an estimate of the real change in external position D, westartfromthenominal external accumulation equation: D $ = D$ 0 P 1 t=0 CA$ t where X$ t denotes the current US dollar value of X. 27 We then deflate each term into constant international dollars using to obtain: D = Ã 0 1! X 1 D 0 CA t. Qdef t t=0 (16) Letusnowturntothechoiceofthedeflator P def. One possibility is to deflate dollar debt and current accounts with the output deflator from the PW. his PPP-adjustment would be appropriate if current account and external positions had the same composition as output. Since poorer countries have -on average- a lower price of output, this also implies that a dollar of current account deficit for a poor country represents a larger share of their PPP adjusted resources than for arichcountry. 28 Alternatively, and this is the approach we follow in this paper, we can deflate the current account and external position using the deflator of investment goods. his is appropriate if we think that investment goods are mostly tradable, and that the trade and current account balances should be deflated by the price of tradable goods. Since investment prices are no higher in poor and rich countries, this implies that a dollar of current account deficit represents the same drain on PPP adjusted resources in rich and poor countries. 29 In other words, our procedure attempts to measure the real resource value of external deficits in terms of tradable prices. Since poor and rich countries prices differ mostly because of the lower price of (largely nontradable) consumption goods, it is inappropriate to deflate current account deficits and external debt by the 27 Alternatively, one could use Lane and Milesi-Ferretti (2006) s estimate of the net external position in year he difference between the two estimates lies in the treatment of valuation effects due to asset price and currency movements. he size and relative importance of these valuation effects has increased over time (see Lane and Milesi- Ferretti (forthcoming 2007) and Gourinchas (2007)). We do not attempt to incorporate these effects in this paper. 28 his also implies that PPP adjusted current accounts need not sum to zero. 29 See Hsieh and Klenow (2003). 17

19 (1) (2) (3) (4) (5) (6) (7) Capital Flows D/Y 0 D p /Y 0 D c /Y 0 D i /Y 0 D s /Y 0 D t /Y 0 D n /Y 0 Obs. (percent of initial output) (3) (6) (3)+(4)+(6) Non-OECD countries Low Income Lower Middle Income Upper Middle Income High Income (Non-OECD) Africa Latin-America Asia except China and India China and India able 2: Predicted and Actual Capital Flows between 1980 and 2000, percent of initial output. price of output. able 2 presents estimates of net capital inflows. Column (1) reports our estimate of observed cumulated net capital inflows, as a fraction of initial output, D/Y 0. hesizeofcumulated capital inflows is quite small, around 16 percent of 1980 output. Between the years 1980 and 2000, the countries in our sample increased their capital stock by 17.9 trillion (1996 international dollars). Yet they received only about 1 trillion in net capital inflows. Hence, the self-financing ratio, as defined by Aizenman et al. (2004), equals 94 percent: most of the capital accumulation is domestically financed. 30 Column (2) reports the total predicted net capital inflows, i.e. the sum of the convergence, productivity and trend components, according to (14). Predicted capital flows are often an order of magnitude larger than realized flows. For instance, the model predicts that capital inflows should represent about 4 times initial output on average, 25 times larger than observed net inflows. Why is there such a discrepancy? he answer lies in columns (3)-(6) of the table, reporting the various components of (14). Column (3) indicates that developing countries should have borrowed 23 percent of initial output to equate domestic and foreign returns on capital: R t+1 (1 τ) =R. his convergence component corresponds precisely to the standard Lucas (1990) calculation. While Lucas argued that too little capital was flowing from rich to poor countries, our results indicate that there is little, if any, Lucas puzzle, once differences in productivity growth and distortions along the 30 Aizenman et al. (2004) construct a self-financing ratio indicating what would have been the stock of capital in the absence of capital inflows. hey find that 90 percent of the stock of capital in developing countries is self-financed, and that countries with higher self-financing ratios grew faster in the 1990s. 18

20 intertemporal margin are accounted for. According to able 2, poor countries do not need to import large amounts of capital to equate marginal returns because they face significant capital market distortions that lower the return to private investors well below the marginal product of capital. he gap between the convergence component (22.7 percent of initial output) and observed capital flows (16.4 percent) is reasonably small. Column (6) reports the trend component D t /Y 0 = h (ng ) 1i d0 / k 0 α. his term reflects the impact of initial debt positions on capital flows. It is also relatively small and similar in magnitude to observed flows. he question remains, then: if differences in return to capital and initial debt positions do not explain the gap between predicted and actual capital flows, what does? he answer lies in the interaction of two important features of the model: relative productivity catch-up and perfect foresight. Faster expected productivity growth implies that countries will want to increase their productive capacity. he contribution of this additional investment to capital flows is captured by the term D i /Y 0 =(π 1) k (τ)(g n) / k 0 α in column (4). Even a moderate productivity catchup (π =1.25) generates sizeable capital inflows (62 percent of initial output). his is not all. Under perfect foresight, the expectation of future higher income increases consumption immediately. he term D s /Y 0 = χ (g n) / k 0 α P /R t=0 (ng /R ) t (π π t ) captures this consumption-smoothing component. As discussed earlier, this term increases with π. 31 his consumption smoothing term represents 3 times initial output and dominates total predicted inflows. Overall, the model implies that predicted capital flows should be large and positive when there is productivity catch-up (π >1) and large and negative when countries move away from the frontier (π <1). For reasons discussed earlier, we should not expect the model to do a good job of pinning down the actual amount of external borrowing by any single country. Sovereign risk, financial frictions or uncertainty about future productivity will limit the extent to which countries rely on foreign capital. Yet our approach should pin down the relative structure of external borrowing across countries quite precisely. his is what we focus on next. We argue that the true failure of the model consists in its inability to explain the allocation of capital flows across developing countries. o illustrate, consider the allocation of capital across regions. According to able 1, a significant share of Asia s capital accumulation reflects productivity catch-up. Hence, we expect significant 31 D s is constructed under the assumption that π t evolves over time according to π t = 1 + t/ (π 1) for 0 t. 19