A Solution to Two Paradoxes of International Capital Flow

1. A Solution to Two Paradoxes of International Capital Flow Jiandong Ju and Shang-Jin Wei * Personal views, not those of the IMF

2. Motivation • Cross-border capital flow reached nearly $6 trillion in 2004. Less than 10% goes to developing countries. • The paradox of too little capital flow: in a one-sector model, marginal product of capital is lower in rich country, but the amount of capital from rich to poor countries is too small (the Lucas Paradox) Example: India vs the U.S. (5800% difference in MPK) • The paradox of too much capital flow: in a 2-sector, 2-factor model, factor prices are equalized in a free trade world (FPE due to Samuelson). So there is no incentive for any capital to flow.

3. Objectives of the paper • Existing explanations of the Lucas paradox do not survive in a generalization to a 2X2 model • To build a micro-founded non-neo-classical theory to solve the two paradoxes • To highlight (possibly different) roles of financial development and property rights institutions in international capital flows

4. Existing explanation of the Lucas paradox within a neo-classical framework • Difference in effective labor • Missing factor (e.g. human capital) • Sovereign risk (Reinhart and Rogoff) • Trade cost (Obstfeld and Rogoff) • Difference in TFP (of which institution is a special case) Common problem: They do not survive in a generalization to a neo-classical two sector, two factor model

5. Chain rule of FPE Lemma 1: Let # factors = m. All other neo-classical assumptions apply. For any two countries, factor prices are equalized if the countries can be linked by a sequence of country pairs, and if the countries within each pair produce a common set of m products. • Example: Two factors (land and capital) • US and India may not produce anything in common, and may not even trade with each other. But FPE could hold if • US-Greece (apple & apricot) • Greece-Thailand (beer and bottle) • Thailand-India (cabbage and carriage)

6. If existing explanations of the Lucas paradox don’t work, what about textbook reasons that break the FPE in the 2X2X2 model? • Difference in technology • No eqbm in general (Panagariya) • We are NOT saying that FPE is realistic, • but that it is much more difficult to escape from the tyranny of FPE that the existing literature may have realized.

7. Intuitive outline of our model • We work with a two-sector model but with two twists • To resolve the Lucas paradox, we introduce a financial contract between entrepreneurs and investors: Each only gets a slice of the marginal product of physical capital. • To move away from FPE, we introduce heterogeneous entrepreneurs, which result in sector- level DRS (despite firm-level CRS).

8. Re-do Lucas’ example: India vs the U.S. • India’s K/L ratio is only 1/15 of the U.S. • Its financial system is also much less efficient • In the absence of capital flow, the return to financial investment is lower in India than in the U.S. • India experiences an outflow of financial capital • At the same time, because Indian’s return to physical capital is higher -> Inflow of FDI Inflow of FDI is bigger than it would have been if its financial system had been more efficient • Return differential is smaller than Lucas’ calculation • Much smaller friction can stop the capital flows

9. Roadmap • The Model • Two key parameters • Financial development • Control of expropriation risk (property rights protection) • Comparative Statics • Free trade in goods • Financial capital flow • FDI • World capital market equilibrium • Some very preliminary/suggestive evidence

10. Model Description • Within an economy (2 sectors, 2 factors) • For a given sector: • Labor • Capitalists (each endowed w one unit of capital) • Entrepreneurs + financial investors • Linked by financial contracts • 2-period production; Liquidity shock in 2nd period • Moral hazard problem • Two country world economy • Various scenarios of capital flows

11. Time line of the model

12. The Model

14. Financial Contract:

15. Solution

16. Allocation of Capital within and across Sectors • Lemma 2:The more productive entrepreneurs enter the heterogeneous sector, while the less productive ones enter the homogeneous sector. In the heterogeneous sector, relatively more productive entrepreneurs manage more capital.

17. Free Entry Conditions

18. A “Stolper-Samuelson Plus” theorem holds: (Prop 1) • When p ↑ → r ↑ but w↓ • When λ↑ → r ↑ but w↓ • When θ ↑ → r ↑ but no change in w • When N1↑ → r↓ but w↑ But FPE does not hold!

19. Determination of Factor Prices • Proposition 1: An increase in N1 will decrease r but increase w. An improvement in the level of financial development will increase r but has no effect on w. Lower expropriation risk increases r but decrease w.

20. Equilibrium Conditions

21. A “Rybczynski Plus” theorem holds: (Prop 2) (under a modified non-reversal of factor intensity) • When K↑ (or L↓) → N1↑, y1↑more than y2↑, and p↓ • When θ ↑ → y1 ↑ and y2↑ proportionately, but no change in p (or N1) • When λ↑ → N1&N2 ↓, y1& y2↑ proportionately, but no change in p

22. Comparative Statics • Proposition 2: The increase in K will increase N1, and decrease the relative price of good 1. The improvement in the level of financial development, however, has no effect on outputs and the commodity price. Lower risk expropriation decreases N1 and N2, but has no effect on p.

23. Combining Propositions 1 and 2 • When K/L↑ → N1↑ (prop 2) → r↓ but w ↑ (prop 1) • The intuition from a one-sector model is restored in this two-sector, two-factor model! • Question: Is the Lucas Paradox also restored? • No! The differential in returns to capital depends on c1f/(1+f), which can be very small • Evidence: Caselli and Feyrer (2005)

24. Moving from closed to open economy Four-step discussion • Free trade in goods • Just financial capital flow (+ free trade) • Just FDI (+ free trade) • Both types of capital flows (free trade)

25. Free Trade in Goods • Two countries differ in factor endowments and levels of financial development and property rights protection. • Prop 3: The Heckscher-Ohlin theorem still holds: Each country exports the good that uses its more abundant factor intensively.

26. Financial Capital Flow • Proposition 4: If the two countries have the same level of property rights protection and financial development, financial capital will flow out of the capital abundant country, and into the capital scarce one. If the two countries have the same capital-labor ratio, financial capital will flow out of the country with lower financial development or poorer property rights protection and into the other one.

27. Foreign Direct Investment • Proposition 5:Suppose trade in goods is free and expropriation risk in the two countries are the same, FDI will flow out of the capital abundant country to the labor abundant country. If the two countries have the same K/L ratio, then FDI will go from the country with poor property rights protection to the other.

28. Free capital mobility + free goods trade • If a country has low K/L and low θ, then it experiences two way gross flows (outflow of financial capital but inflow of FDI), and a small net flow e.g. China • If a country has a low K/L and low λ, then outflow of financial capital + outflow of FDI • e.g. Zimbabwe

29. Contrasting effects of poor financial development vs. poor property rights protection • A lower level of financial development results in a lower r, which generates an outflow of financial capital. As a result, w becomes lower, which attracts more FDI than otherwise. • Worse property rights protection results in both a lower profit, leading to less FDI, and a lower r, leading to outflow of financial capital • Empirical evidence: Wei 2006

30. Property rights protection, financial development, and composition of capital flow (Wei, 2006, “connecting two views on financial globalization …”) Measure of Institutions – Average of Six World Bank Indicators

31. Capital Bypass Circulation, or transfusion • Proposition 6:A unique equilibrium: Inefficient financial system is completely bypassed. • In the transition to the eqbm, the country with a higher initial K/L always exports capital on net (i.e. running a CA deficit) • So a scenario in which the US runs a current account (CA) deficit, China CA surplus can in principle be rationalized w/o • Exchange rate policy • Mercantilist trade strategy • Fiscal deficit Free capital mobility + free trade + free mobility of entrepreneurs

32. F O* K+K* B* Y1 FCF FDI K H C A* E A Y2 B O L L+L* Capital Bypass Circulation

33. Capital Bypass Circulation, or transfusion

34. Capital Market Equilibrium: Different Expropriation Risk

35. Different Expropriation Risk • In equilibrium, wage is always higher in the country with better financial institution or lower expropriation risk.

36. Prop 5: • Suppose the two countries are diversified in the equilibrium with free trade and free capital mobility, then the wage rate is always (at least weakly) higher in the country with better property rights protection or with better financial development

37. Conclusions • Existing explanations of the Lucas paradox don’t survive in a model with two sectors and two factors. It is difficult to simultaneously resolve Lucas paradox and FPE in a neo-classical framework • We build a micro-founded non-neoclassical model • Key twists: • Financial contracts • Heterogeneous firms • The model highlights (potentially different) roles of financial development and property rights protection • It generates predictions about gross as well as net capital flows. It avoids both the Lucas paradox and FPE.

38. Future Work (I) • Solution to other puzzles in int’l finance? • Feldstein-Horioka puzzle • Shutting down risk-sharing motivation • Small friction to capital mobility → ∆investment = ∆saving • Home bias in equity holdings • Equity instead of direct financing contracts • Small friction to capital mobility

39. Future Work (II) • Empirics • Dynamics • Welfare analysis • /conflict of interest • Alternative financial contracts • Frictions to capital flow

40. Financial development, corruption, and composition of capital flows: Preliminary evidence Challenge: measures of institutions may be endogenous Instrumental variable for government corruption: • Initial cost to colonizers –mortality rate of European settlers before 1850 • Acemoglu, Johnson, and Robinson (AER 2001) • Alternative: initial population density in 1500

41. Instrumental variables for financial development: • Legal origins: La Porta, Lopez-de-silanes, Shleifer, and Vishny (JPE 1998) • Settler mortality

42. (History-based) instrumental variables • Corruption is mostly affected by settler mortality but not by legal origin • Financial development is affected by both legal origins and settler mortality.

43. The basic specification: • Composition(j) = β1 Corruption(j) + β2 FinDev(j) + Z(j)Γ + e(j) Zj is a vector of control variables, β1, β2, and Γ are parameters ej is a random error.

44. Table 7: Adding more control variables (IV Regressions)

45. Explaining the Ratio of FDI/ Total Foreign Liabilities in 2003

46. First Stage Regressions:Using Histories to Instrument Modern-day Institutions

47. Evidence is still preliminary, but intriguing • More needs to be done

48. Welfare Impacts: Financial Capital flow • The welfare effect of financial capital outflow is determined by the trade off between investors' gain and entrepreneurs' loss. If the later dominates the former, welfare is reduced at home due to financial capital outflow.