Financial Integration, Entrepreneurial Risk and Global Dynamics

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Financial Integration, Entrepreneurial Risk and Global Dynamics Vasia Panousi and George-Marios Angeletos 2010-54 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Financial Integration, Entrepreneurial Risk and Global Dynamics∗ George-Marios Angeletos Vasia Panousi MIT and NBER Federal Reserve Board October 5, 2010 Abstract How does (cid:28)nancial integration impact capital accumulation, current-account dynamics, and cross-country inequality? This paper investigates this question within a two-country, generalequilibrium, incomplete-markets model that focuses on the importance of idiosyncratic entrepreneurial risk(cid:22)a risk that introduces, not only a precautionary motive for saving, but also awedgebetweentheinterestrateandthemarginalproductofcapital. Ourcontributionisthen to show that this friction provides a simple explanation for the emergence of global imbalances, a simple resolution to the empirical puzzle that capital often fails to (cid:29)ow from the rich or slowgrowingcountriestothepoororfast-growingones,andadistinctsetofpolicylessonsregarding the intertemporal costs and bene(cid:28)ts of capital-account liberalization. JEL codes: E13, F15, F41. Keywords: Financial integration, capital-account liberalization, incomplete markets, idiosyncratic risk, entrepreneurship, current-account de(cid:28)cits, global imbalances. ∗An earlier version of the paper was entitled (cid:16)Financial Integration and Capital Accumulation.(cid:17) We thank an associate editor and two anonymous referees for very useful feedback. We also thank Daron Acemoglu, Arnaud Caustinot, Dave Donaldson, Enrique Mendoza, Dimitris Papanikolaou, and Robert Townsend for useful comments and discussions. Finally, we are particularly grateful to Dean Corbae and Ramon Marimon for encouraging us to write this paper. The views presented in this paper are solely those of the authors and do not necessarily represent those of the Board of Governors of the Federal Reserve System or its sta(cid:27) members. Email: angelet@mit.edu, vasia.panousi@frb.gov. 1

1 Introduction The last two or three decades have been characterized by signi(cid:28)cant liberalization of international capital (cid:29)ows. This, in turn, appears to have facilitated the rise of signi(cid:28)cant global imbalances(cid:22)a largeforeigndebtonthesideoftheUnitedStatesalongwithvastcurrencyreservesandbigpositive holdingsofUSTreasurybillsonthesideofemergingcountriessuchasChina. Furthermore, whereas thestandardneoclassicalparadigmpredictsthatcapitalshouldbe(cid:29)owingfromtherichtothepoor, or from the least-growing to the fastest-growing countries, the empirical evidence often suggests the opposite direction of capital (cid:29)ows (Gourinchas and Jeanne, 2006). Theseobservations,andmoregenerallythethemesof(cid:28)nancialintegrationandglobalimbalances, 1 have motivated a large body of research. In this paper, we contribute to this growing literature by studying the global macroeconomic e(cid:27)ects of (cid:28)nancial integration in the presence of a certain market friction(cid:22)uninsurable idiosyncratic entrepreneurial risk. Our focus on this friction is motivated, not only by the fact that entrepreneurship is of obvious empirical relevance, but also by the observation that this friction can play a crucial role in capital accumulation and productivity growth. Indeed, this friction introduces both a precautionary motive for saving, as entrepreneurs seek to self-insure against the uninsurable risk in their income, and a wedge between the interest rate and the marginal product of capital, as entrepreneurs require a (private) risk premium in compensation for the risk they face in their entrepreneurial activity. Furthermore, this wedge is likely to vary across countries, with, say, entrepreneurs in China presumably enjoying less risk sharing and hence facing a higher wedge than those in the United States. Our contribution is to show how cross-country di(cid:27)erences in this wedge may help explain a number of stylized facts(cid:22)such as the persistence of cross-country inequality, the emergence of global imbalances, and the failure of capital to (cid:29)ow from the rich or slow-growing countries to the poor or fast-growing ones(cid:22)while also providing a distinct set of policy lessons regarding the dynamic 2 e(cid:27)ects of capital-account liberalization. Previewofmodel. Weconductourtheoreticalexercisewithinatractable,general-equilibrium, incomplete-markets model. There are two economies (countries), each of which is populated by a continuum of households (families). Each family includes a worker and an entrepreneur. The worker supplies his labor in the domestic labor market; the entrepreneur runs a private business 1See,e.g.,Aoki,Benigno,andKiyotaki(2009),Blanchard,Giavazzi,andSa(2005),BoydandSmith(1997),Broner andVentura(2008),Caballero,Farhi,andGourinchas(2008),EngelandRogers(2006),FogliandPerri(2006),Gertler andRogo(cid:27)(1990),GourinchasandJeanne(2006),GourinchasandRey(2007),HausmannandSturzenegger(2006), Hunt and Rebucci (2005), Lane and Milesi-Ferretti (2007), Kraay et al. (2006), McGrattan and Prescott (2007), Mendoza,Quadrini,andRios-Rull(2008,2009),ObstefeldandRogo(cid:27)(2004),ReinhartandRogo(cid:27)(2004),andSong, Storesletten, and Zilibotti (2009). 2Borrowing constraints, although not explicitly considered here, are complementary sources of a wedge between the (cid:16)external(cid:17) and the (cid:16)internal(cid:17) return to capital. This o(cid:27)ers a useful re-interpretation of our contribution. As it will become clear, our key results hinge on the properties that the aforementioned wedge is positive and decreasing with wealth(cid:22)properties that may hold whether the wedge originates in idiosyncratic risk or borrowing constraints. 2

thatoperatesaconstant-returns-to-scaletechnology, employslaborfromthedomesticlabormarket, and uses the capital stock owned by her family. All households can freely trade a safe asset, but can diversify only a fraction of the idiosyncratic shocks hitting their private (cid:28)rms. The two countries di(cid:27)er in the magnitude of the uninsurable risk(cid:22)with the (cid:16)North(cid:17) enjoying better risksharing possibilities and hence less risk than the (cid:16)South(cid:17)(cid:22)but are otherwise identical. Within this model, we de(cid:28)ne (cid:16)(cid:28)nancial autarchy(cid:17) as the regime in which the market for the safe asset clears on a country-wide level, and (cid:16)(cid:28)nancial integration(cid:17) as the regime in which this market clears on a world-wide level. We then study the steady states that obtain under these two regimes, as well as the entire transitional dynamics of the global economy between the two steady states. Preview of results. Under (cid:28)nancial autarchy, the South features a lower interest rate. This is duetothestrongerdemandforprecautionarysavingimpliedbythelargeramountofundiversi(cid:28)able idiosyncratic risk (or, in an extension, due to the lower supply of the safe asset). Despite its lower interest rate, however, the South may also feature a lower capital stock and a lower level of income than the North. This is because the South faces a higher wedge between the marginal product of capital and the interest rate. It follows that, prior to (cid:28)nancial integration, the South identi(cid:28)es the poor, capital-scarce country, whereas the North identi(cid:28)es the rich, capital-abundant country. Because the South has a lower autarchic interest rate than the North, (cid:28)nancial integration triggerstheNorthtorunlargecurrent-accountde(cid:28)citsand, symmetrically, theSouthtoaccumulate a large positive foreign asset position. Intuitively, this is because the North has a comparative advantage in supplying the safe asset: the North (cid:16)exports(cid:17) this asset by running current-account de(cid:28)cits. What is more, as (cid:28)nancial integration causes interest rates to rise in the South, the opportunity cost of capital goes up and the capital stock goes down, thereby depressing domestic wages and output. Conversely, the North experiences a boom. If the North is interpreted as the United States, and the South as China or other emerging economies, these results help explain the signi(cid:28)cant (cid:16)global imbalances(cid:17) that the world economy has experienced in recent history. Furthermore, they help explain why (cid:28)nancial globalization may initially exacerbate cross-country inequality, and why capital may often fail to (cid:29)ow from the rich, capital-abundant countries to the poor, capital-scarce ones. Interestingly, though, the long-run e(cid:27)ects of (cid:28)nancial integration can be quite di(cid:27)erent. Because (cid:28)nancial integration permits the South to save abroad at higher returns than otherwise, the South is able to accumulate more and more wealth over time. As this happens, the willingness to take risk increases, the wedge between the interest rate and the marginal product of capital falls, and the capital stock increases. As a result, in the new steady state the South may well end up with higher levels of capital, wages, output and consumption than in its autarchic steady state. Our model therefore predicts that (cid:28)nancial integration may help poor countries in the long run, even as it hurts them in the short run(cid:22)and may reduce cross-country inequality in the long run, even as it increases it in the short run. 3

Furthermore, because of the aforementioned wealth accumulation and the consequent increase in risk taking, the transition in the South may feature a reallocation of saving from safe but lowreturn investment opportunities to risky but high-return ones. As a result, the South experiences anaccelerationinitsTFPgrowth, whiletheconverseistruefortheNorth. Alongwiththeproperty that the South runs current-account surpluses, while the North runs current-account de(cid:28)cits, this result means that capital (cid:29)ows from the faster growing countries to the slower growing ones(cid:22)a prediction that is the opposite of the one made by the standard neoclassical paradigm and that helps resolve the empirical puzzle documented by Gourinchas and Jeanne (2008). Combined, our results provide, not only a possible explanation to certain stylized facts, but also a distinct policy lesson: the bene(cid:28)ts of capital-account liberalization for less developed economies may be higher in the long run than in the short run. As already noted, the key intuition is that (cid:28)nancial integration helps agents in the South accumulate more wealth over time, which in turn permits them to mitigate the friction they face in their entrepreneurial activities. We reinforce this intuition by studying the welfare e(cid:27)ects of (cid:28)nancial integration in our model. Upon (cid:28)nancial integration, the South’s poor tend to lose for two complementary reasons: the increase in interest rates means an increase in the cost of borrowing; and the initial out(cid:29)ow of capital means a reduction in their wages. In contrast, the middle class and the rich gain because of the higher returns to their saving and of the lower labor costs in their private businesses. But as time passes and capital eventually reaches higher levels than under autarchy, the resulting increase in wages alleviates the burden of all poor agents and even reverses the fortunes of some of them, so that they too gain in the long run. Once again, this highlights the distinct short-run and long-run 3 e(cid:27)ects that our analysis brings to light. Related literature. Our paper belongs to a large, and growing, literature that uses Bewleytype models to study various macroeconomic implications of incomplete markets. Key references includeAiyagari(1994),Huggett(1997),KrusellandSmith(1998),andRios-Rull(1995);seeHeathcote, Storesletten, and Violante (2008) and Krusell and Smith (2006) for eclectic reviews. The bulk of this literature focuses on idiosyncratic endowment or labor-income risk. Important exceptions are Angeletos and Calvet (2000, 2006) and Angeletos (2007), which are among the (cid:28)rst papers to emphasize the distinct implications of idiosyncratic investment risk for aggregate saving within the 4 context of the neoclassical growth model. Our paper starts by extending Angeletos (2007) to a two-country open-economy setting. Our contribution is then to study how cross-country di(cid:27)erences inthelevelofidiosyncraticinvestmentriskimpactglobalmacroeconomicdynamics. Inindependent parallel work, Corneli (2010) undertakes a similar exercise and obtains closely related results. 3Complementary in this regard is Aoki, Benigno and Kiyotaki (2009), which also stresses the importance of studying the intertemporal costs and bene(cid:28)ts of (cid:28)nancial integration, albeit in a di(cid:27)erent model than ours. 4Otherpapersthattouchthesametheme,butfocusondi(cid:27)erentquestions,includeAngeletosandPanousi(2009), Basin, Benhabib and Zhu (2009), Cagetti and De Nardi (2006), Goldberg (2010), Quadrini (2000), Covas (2006), Mall (2009), Meh and Quadrini (2006), Kitao (2007), and Panousi (2010). 4

Closely related in this regard is Mendoza, Quadrini, and Rios-Rull (2008). Like our paper, this work studies how cross-country di(cid:27)erences in domestic risk sharing can help explain signi(cid:28)cant and persistent global imbalances. See also Willen (2004) for an earlier take on the same key insight. However, unlike our paper, this work rules out endogenous capital accumulation and/or idiosyn- 5 cratic investment risk. It is precisely the combination of these two features that distinguishes our theoretical exercise and that explains the novelty of our results. AlsocloselyrelatedareBueraandShin(2010)andSandri(2010). BueraandShin’smodelshares the two key features of our model, namely capital accumulation and entrepreneurial risk, but adds a number of other ingredients, such as borrowing constraints, occupational choice, and cross-sectional distortions in the allocation of capital. By assuming that capital-account liberalization comes in tandem with a structural reform that removes these distortions, they obtain an acceleration in TFP growth. At the same time, a surge in current-account surpluses occurs for reasons similar to ours. 6 Their paper and ours are thus highly complementary. Sandri, on the other hand, considers a onecountry model that also features entrepreneurial risk, but focuses on a di(cid:27)erent policy exercise. In particular, hestudiesareformthatpermitssomeagentstoswitchfrom(cid:16)farmers(cid:17) to(cid:16)entrepreneurs(cid:17). Because entrepreneurial activity is assumed to face more risk than farming, this means an increase in the level of idiosyncratic risk and hence a surge in precautionary saving, which in turn helps generate current-account surpluses. A similar mechanism operates in Carroll and Jeane (2009), except that there the driving force is an increase in idiosyncratic labor-income risk. Our paper also shares with Caballero, Farhi, and Gourinchas (2008) the idea that global imbalances are explained, in a certain sense, by a shortage of assets in the South. But whereas that paper assumes that the South has a lower capacity in supplying any asset, we only assume that the North has a comparative advantage in supplying the relatively safer assets. This in turn can be the case, not because of di(cid:27)erent technologies, but simply because the North has a weaker demand for precautionary saving. Furthermore, that paper rules out capital accumulation, thus also ruling out the distinct dynamic e(cid:27)ects that are at the core of our contribution. Layout. The rest of the paper is organized as follows. Section 2 introduces the model and Section3characterizesthegeneralequilibrium. Section4studiestheautarchicandintegratedsteady states, section 5 the transitional dynamics between the two, and section 6 the welfare implications. Section 7 considers a useful extension. Section 8 concludes. The proofs are delegated to the Appendix. 5Mendoza et al. (2008) allow for a certain type of investment risk, but rule out capital accumulation: the investment opportunity in that paper is an exogenous (cid:16)Lucas tree(cid:17). Mendoza et al. (2009), on the other hand, allow for capital accumulation, but rule out idiosyncratic investment risk. Finally, Willen (2004) studies an endowment economy, thus ruling out both capital accumulation and idiosyncratic investment risk. 6The comparative advantage of their paper is that it contains a richer quantitative exercise, while that of our analysis rests on its increased tractability and the consequent clarity of the theoretical insights. 5

2 The model Our model is a two-country variant of the closed-economy model of Angeletos (2007). There are two countries, indexed by j ∈ {1,2}, and a single good, which can be used for either consumption or investment purposes. Each country is populated by a continuum of in(cid:28)nitely-lived households, indexedbyianddistributeduniformlyover[0,1]. Eachhouseholdincludesaworkerandaproducer ((cid:16)entrepreneur(cid:17)). The worker supplies his labor inelastically to the domestic labor market. The entrepreneurrunsaprivately-held(cid:28)rm((cid:16)familybusiness(cid:17)). Eachhouseholdcanfreelysaveorborrow in the riskless bond(cid:22)up to a natural borrowing constraint(cid:22)and can accumulate physical capital withinitsownfamilybusiness. Firmsarehitbyidiosyncraticshocks, whichthehouseholdscanonly partially diversify. Finally, to maintain tractability, we abstract from any aggregate uncertainty. We also let the time be continuous, indexed by t ∈ [0,∞). Preferences take an Epstein-Zin speci(cid:28)cation, which permits us to distinguish intertemporal substitution from risk aversion. Fix a household i in county j. Her preferences are de(cid:28)ned as the limit, for ∆t → 0, of the solution to the following recursive speci(cid:28)cation: (cid:40) (cid:41) 1 (cid:16) (cid:17)1−1/θ 1−1/θ U = (1−e−β∆t) c 1−1/θ + e−β∆t E [ U1−γ ] 1−γ , (1) ijt ijt t ijt+∆t where β > 0 is the discount rate, γ > 0 is the coe(cid:30)cient of relative risk aversion, and θ > 0 is the 7 elasticity of intertemporal substitution. The (cid:28)nancial wealth of this household, denoted by x , is the sum of its holdings in private ijt capital, k , and in the riskless bond, b : ijt ijt x = k +b . (2) ijt ijt ijt The evolution of x is given by the following budget constraint: ijt dx = dπ +[R b +ω −c ]dt+dT . (3) ijt ijt t ijt jt ijt ijt Here, dπ is the household’s capital income (i.e., the pro(cid:28)ts from the private (cid:28)rm it owns), R is ijt jt the interest rate on the riskless bond, ω is the wage rate, c is the household’s consumption, and jt ijt dT is a transfer that captures risk-sharing opportunities (to be de(cid:28)ned later on). ijt Whereas the sequences of the wage and the interest rate are deterministic (due to the absence of aggregate risk), (cid:28)rm pro(cid:28)ts, and hence household capital income, are subject to undiversi(cid:28)ed 7Standard expected utility is nested for θ =1/γ; in this case, U ijt =E t (cid:82) t ∞e−βsU(c ijs )ds, where U(c)= c 1 1 − − 1 1 / / θ θ . Weallowforθ(cid:54)=1/γ soastofacilitateamorepreciseunderstandingoftheunderlyingforcesinourenvironmentand a better calibration. However, none of our results rest on letting θ(cid:54)=1/γ. 6

idiosyncratic risk: dπ = [F(k ,n )−ω n −δk ]dt+σ k dz . (4) ijt ijt ijt jt ijt ijt j ijt ijt Here, n istheamountoflaborthe(cid:28)rmhiresinthecompetitivelabormarket, δ isthemeandepreijt ciation rate, and F is a constant-returns-to-scale neoclassical production function. For simplicity, we assume a Cobb-Douglas speci(cid:28)cation: F(k,n) = kαn1−α, with α ∈ (0,1). Idiosyncratic risk is introduced through dz , a standard Wiener process that is i.i.d. across ijt agents and time. Literally taken, dz represents a stochastic depreciation, or productivity, shock. ijt However, we wish to interpret this shock more broadly as encompassing various sources of idiosyncratic risk in the entrepreneurial activity and, more generally, in the returns to private investment. The scalar σ then parameterizes the level of this risk in country j. j Since this risk is purely idiosyncratic, agents would be able to obtain full insurance against it if (cid:28)nancial markets were complete. A number of reasons(cid:22)moral hazard, adverse selection, costly state veri(cid:28)cation, ine(cid:30)cient legal and enforcement systems, or mere lack of sophistication(cid:22)may explain why this does not happen in the real world. In this paper, as in most other papers in the Bewley tradition, we abstract from the deeper micro-foundations of incomplete markets. Instead, we exogenously impose that the available risk-sharing possibilities are limited, and more severely so in the South. We capture this by assuming that: dT = −λ σ k dz , (5) ijt j j ijt ijt for some λ ∈ (0,1). This assumption can also be justi(cid:28)ed by introducing an exogenous asset j structure that permits agents to diversify only certain components of their idiosyncratic risk, or by letting them sell equity on only a fraction of their pro(cid:28)ts. Either way, the scalar λ measures the j fraction of idiosyncratic risk that agents are able to diversify in country j; this is what de(cid:28)nes the level of (cid:28)nancial development in our model. Combining conditions (3)-(5), we get that the household budget reduces to: dx = dπ˜ +[R b +ω −c ]dt , (6) ijt it t ijt jt ijt where dπ˜ ≡ dπ +dT = [F(k ,n )−ω n −δk ]dt+(1−λ )σ k dz . ijt ijt ijt ijt ijt jt ijt ijt j j ijt ijt It is then evident that the quantity σ˜ ≡ (1−λ )σ measures the amount of undiversi(cid:28)able idiosynj j j cratic risk in country j. We henceforth impose σ˜ < σ˜ , which permit us to identify country 1 as 2 1 the country with a lower level of uninsurable entrepreneurial risk(cid:22)and, in this particular sense, as the country with the more advanced (cid:28)nancial markets. We accordingly refer to country 1 as the (cid:16)North(cid:17) or the (cid:16)developed(cid:17) economy, and to country 2 as the (cid:16)South(cid:17) or the (cid:16)developing(cid:17) economy. 7

At this point, we would like to invite the reader to maintain a (cid:29)exible interpretation of the assumption that σ˜ > σ˜ . For example, entrepreneurial risk may be higher in developing economies 2 1 because, in comparison to developed economies such as the United States, developing economies such as China, India, and Mexico appear to face more severe agency and/or enforcement problems. Government corruption and weak property rights also contribute to higher levels of idiosyncratic entrepreneurial risk in developing economies: some times the entrepreneur is the fortunate recipient of preferential treatment by corrupt politicians and bureaucrats, some times he is the unfortunate victim. Finally, as tax and regulatory policies tend to be more volatile in these economies, the idiosyncraticincidenceofthesepoliciesappearstobemorevolatileaswell,contributingtoadditional risk in entrepreneurial activity. 3 Equilibrium Let Y ,C ,N ,K , and B denote the aggregate levels of output, consumption, employment, jt jt jt jt jt capital, and bond holdings in country j at date t (that is, the cross-sectional averages of y ,c ijt ijt and so on). We consider two policy regimes. In the (cid:28)rst, countries are in (cid:28)nancial autarchy: the riskless bond cannot move across borders. In the second, they are (cid:28)nancially integrated: countries can borrow and lend to one another. We de(cid:28)ne the corresponding equilibrium concepts as follows. De(cid:28)nition 1. An autarchic equilibrium consists of a deterministic sequence of country-speci(cid:28)c interestrates,wages,andmacroeconomicquantities,{R ,ω ,Y ,C ,N ,K } forj ∈ {1,2}, jt jt jt jt jt jt t∈[0,∞) and a collection of individual contingent plans, {c ,n ,k ,b } for i ∈ [0,1],j ∈ {1,2}, ijt ijt ijt ijt t∈[0,∞) such that the following are true: (i) individual plans are optimal given the sequences of prices; (ii) macroeconomic quantities are obtained by aggregating individual plans; (iii) labor and bond markets clear at the country level, namely N = 1 and B = 0 for all j,t. jt jt De(cid:28)nition 2. An integrated equilibrium consists of a deterministic sequence of word-wide interest rates, {R } , a deterministic sequence of country-speci(cid:28)c wages and macroeconomic quant t∈[0,∞) tities, {ω ,Y ,C ,N ,K } for j ∈ {1,2}, and a collection of individual contingent plans, jt jt jt jt jt t∈[0,∞) ({c ,n ,k ,b } ) for i ∈ [0,1],j ∈ {1,2}, such that the following are true: (i) indiijt ijt ijt ijt t∈[0,∞) i∈[0,1] vidual plans are optimal given the sequences of prices; (ii) macroeconomic quantities are obtained by aggregating individual plans; (iii) labor markets clear at the country level, namely N = 1 for all jt j,t; (iv) the bond market clears at the world level, namely B +B = 0 for all t. 1t 2t In the remaining of this section, we (cid:28)rst characterize the individual household’s problem for a given sequence of wages and interest rates. We then proceed to characterize the general equilibrium under both regimes. 8

3.1 Individual behavior Since employment is chosen after the capital stock has been installed and the idiosyncratic shock hasbeenobserved, optimalemploymentmaximizespro(cid:28)tsstate-by-state. Furthermore, byconstant returns to scale, optimal employment and pro(cid:28)ts are linear in own capital. We therefore have that: n = n¯ k and dπ = r¯ k dt+σ k dz , (7) ijt jt ijt ijt jt ijt j ijt ijt where n¯ = n¯(ω ) ≡ argmax [F(1,n)−ω n] and r¯ = r¯(ω ) ≡ max [F(1,n)−ω n]−δ. As in jt jt n jt jt jt n jt Angeletos (2007), the key (cid:28)nding here is that households face linear, albeit risky, returns to their capital. This linearity, together with the homotheticity of preferences, ensures that the household’s consumption-saving problem reduces to a tractable homothetic optimization problem, much like in Samuelson’s and Merton’s classic portfolio analysis. It then follows that the optimal policy rules are linear in wealth, as shown in the next lemma. Lemma 1. Let {ω ,R } be equilibrium price sequences (with R = R = R if the world is jt jt t∈[0,∞) 1t 2t t integrated) and let h jt ≡ (cid:82) t ∞ e− (cid:82) t sRjτdτω js ds denote the present value of labor income (a.k.a. human capital). Then, optimal consumption, investment and bond holdings are given by c = m (x +h ), k = φ (x +h ), and b = (1−φ )(x +h )−h , (8) ijt jt ijt jt ijt jt ijt jt ijt jt ijt jt jt where m denotes the marginal propensity to consume and φ the marginal propensity to invest in jt jt private capital. The marginal propensity to consumer solves the following recursion: m˙ jt = m +(θ−1)ρˆ −θβ , (9) t jt m t where ρˆ ≡ ρ − 1γφ2 σ˜2 denotes the risk-adjusted return to saving and ρ ≡ φ r¯ +(1−φ )R jt jt 2 jt j jt t jt jt t the mean return to saving. Finally, the marginal propensity to invest is given by r¯ −R jt jt φ = . (10) jt γσ˜2 j Condition (8) establishes the linearity of optimal consumption, capital and bond holdings in wealth. Condition(10)identi(cid:28)esthepropensitytoinvestintheriskyassetasanincreasingfunction of the risk premium, µ ≡ r¯ −R , and a decreasing function of the amount of uninsurable risk, t t t σ˜ = (1−λ )σ. Finally, condition (9) is essentially the Euler condition: it describes the growth j j rate of the marginal propensity to consume as a function of the anticipated path of risk-adjusted 8 returns to saving. 8Notethathigherrisk-adjustedreturnsreducethepropensitytoconsume(i.e.,increasethepropensitytosave)if and only if the elasticity of intertemporal substitution θ exceeds one; this is is due to the familiar tension between the income and substitution e(cid:27)ects implied by an increase in the rate of return. 9

3.2 General equilibrium Let f(K) ≡ F(K,1) = Kα. From Proposition 1, we have that the equilibrium values of the propensity to invest and the risk-adjusted return to saving are given by φ = φ(K ,R ,σ˜ ) and jt jt t j ρˆ = ρˆ(K ,R ,σ˜ ), where jt jt t j (f(cid:48)(K)−δ−R) (f(cid:48)(K)−δ−R)2 φ(K,R,σ˜) ≡ and ρˆ(K,R,σ˜) ≡ R+ . γσ˜2 2γσ˜2 Furthermore, the equilibrium wage satis(cid:28)es ω = f(K )−f(cid:48)(K )K = (1−α)f(K ). Using these jt jt jt jt jt facts,aggregatingthepolicyrulesoftheagents, andimposingmarketclearingfortherisk-freebond, we arrive at the following tractable characterization of the general equilibrium of the economy. Proposition 1. In either the autarchic or the integrated equilibrium, the aggregate dynamics of country j satisfy the following ODE system C +K˙ +B˙ = f(K )−δK +R B (11) jt jt jt jt jt jt jt C˙ jt = θ(ρˆ −β)+ 1γσ˜2φ2 (12) C jt 2 j jt jt H˙ = R H −(1−α)f(K ) (13) jt jt jt jt B = (1−φ )(K +B )−φ H , (14) jt jt jt jt jt jt where φ = φ(K ,R ,σ˜ ) and ρˆ = ρˆ(K R ,σ˜ ). The autarchic equilibrium is then obtained by jt jt jt j jt jt jt j letting R (cid:54)= R and requiring that, for each j, R adjusts so that 1t 2t jt B = 0 . (15) jt In contrast, the integrated equilibrium is obtained by imposing R = R = R and requiring that 1t 2t t R adjusts so that t B +B = 0 . (16) 1t 2t Conditions (11) and (12) give, respectively, the resource constraint and the aggregate Euler condition. Condition (13) gives the law of motion for human capital, whereas condition (14) gives the equilibrium level of aggregate holdings of the riskless bond or, equivalently, the net foreign asset position of the country. Conditions (15) and (16) then complete the characterization of the equilibrium: under (cid:28)nancial autarchy, the domestic interest rate of each country must be such that the net foreign asset position of that country is zero; under (cid:28)nancial integration, the world-wide interest rate must be such that the asset positions of the two countries balance one another. At this point, it is important to recognize how idiosyncratic risk impacts the general-equilibrium system. When σ˜ = 0, arbitrage imposes that R = f(cid:48)(K ) − δ = ρˆ , and the Euler condition j t jt jt 10

reduces to its familiar complete-markets version, C˙ jt = θ(R −β). When instead σ˜ > 0, there Cjt t j are two important changes. First, the precautionary motive for saving introduces a positive drift in consumption growth, represented by the term 1γσ˜2φ2 in the Euler condition (12). This is the 2 j jt key force in Bewley-type models such as Aiyagari (1994) and Mendoza et al. (2008). Second, the fact that investment is subject to undiversi(cid:28)able idiosyncratic risk introduces a wedge between the risk-free rate and the marginal product of capital, so that R < ρˆ < f(cid:48)(K )−δ. This wedge jt jt jt plays a crucial role in the results of our paper and distinguishes it from the aforementioned work. 4 Steady state In this section we (cid:28)rst explain how long-run wealth accumulation impacts the wedge between the interest rate and the marginal product of capital, and thereby the steady-state level of capital for given interest rate. This identi(cid:28)es the key mechanism behind the long-run e(cid:27)ects in our framework. We then complete the characterization of the autarchic and integrated steady states by studying the determination of the interest rate. 4.1 Long-run wealth accumulation and the wedge on investment In steady state, whether under autarchy or under integration, the growth rate of aggregate consumption in each country must be zero. The Euler condition (12) then reduces to the following: 1γ ρˆ = β− σ˜2φ2 . (17) j 2θ j j This condition simply requires that the risk-adjusted return to saving in country j be lower than the discount rate as much as it takes for the associated negative intertemporal substitution e(cid:27)ect to justo(cid:27)setthepositiveprecautionarymotive. Usingthefactsthatρˆ = R + 1 µ2 andφ = 1 µ , j j 2γσ˜2 j j γσ˜2 j j j where µ = f(cid:48)(K )−δ−R is the risk premium, we can restate condition (17) as follows: j j j (cid:115) 2θγσ˜2(β−R ) f(cid:48)(K )−δ = R + j j . (18) j j θ+1 We infer that this condition pins down the combinations of the domestic capital stock and the interest rate that are consistent with stationarity of aggregate consumption(cid:22)equivalently, with stationarity of aggregate wealth(cid:22)in country j. If there were no uninsurable idiosyncratic risk (σ˜ = 0), condition (18) would have reduced to the familiar condition f(cid:48)(K)−δ = R; that is, the marginal product of capital would have been equated to the interest rate. Furthermore, this would have implied that the capital stock is a decreasing function of the interest rate. Now, instead, we have that the marginal product of capital exceeds the interest rate: f(cid:48)(K)−δ > R. This is because agents require a positive risk premium in order 11

to be willing to hold their risky entrepreneurial capital. In addition, the steady-state value of this premium, which is given by the square-root term in (18), is decreasing in the interest rate. This is because a higher interest rate permits the domestic agents to accumulate more wealth in the long run, which in turn increases their willingness to take risk and thereby reduces the wedge between the interest rate the marginal product of capital. Indeed, for any given initial level of aggregate wealth, a higher interest rate necessarily increases the mean return to saving and therefore also increases the level of aggregate wealth in subsequent periods. It follows that the long-run level of aggregate wealth also increases. The accumulation of more wealth, in turn, increases agents’ willingness to take risk(cid:22)due to diminishing absolute risk aversion(cid:22)and thereby reduces the premium they require in order to hold any given amount of capital. Hence, the overall impact of the interest rate on capital accumulation is now ambiguous: a higher interest rate may actually induce more investment in the long run, due to the wealth e(cid:27)ect on risk taking. This wealth and risk-taking e(cid:27)ect plays a central role in the results of our paper; we will revisit it shortly. Going back to the determination of the steady state, we now note that, because the interest rate and the wage are constant in steady state, the present value of labor income is also constant. In particular, it is given by H = (1 − α)f(K )/R . Using this into condition (14), we infer j j j that aggregate bond holdings(cid:22)equivalently, the net foreign asset position(cid:22)of country j satisfy the following condition: 1−φ (1−α)f(K ) j j B = K − . (19) j j φ R j j Combining this result with the one in condition (18), we reach the following lemma. Lemma 2. (i) There exist continuous functions K,B : (0,β)×R → R such that, under either + autarchy or integration, the steady-state levels of aggregate capital and bond holdings satisfy K = K(R ,σ˜ ) and B = B(R ,σ˜ )K (20) j j j j j j j These functions are de(cid:28)ned by 1−φ(R,σ˜) (1−α)f(K(R,σ˜)) K(R,σ˜) ≡ (f(cid:48))−1(R+µ(R,σ˜)+δ) and B(R,σ˜) ≡ − , φ(R,σ˜) RK(R,σ˜) (cid:113) where µ(R,σ˜) ≡ 2θγσ˜2 (β−R) and φ(R,σ˜) ≡ 1 µ(R,σ˜) . 1+θ γσ˜2 (ii) ∂K(R,σ˜) > 0 if and only if φ(R,σ˜) < θ , which in turn is true if and only if R > Rˆ(σ˜), ∂R 1+θ where Rˆ(σ˜) ≡ β − θ γσ˜2 < R¯ . 1+θ 2 ∂K(R,σ˜) (iii) < 0 necessarily. ∂σ˜ ∂B(R,σ˜) (iv) > 0 necessarily. ∂R (v) ∂B(R,σ˜) > 0 if and only if R > R, where 0 < R ≡ β 2θ(1−α) < R¯ . ∂σ˜ α+(2−α)θ 12

Part (i) follows from conditions (18) and (19). The functions K and B give, respectively, the domestic capital stock and the net foreign-asset position that are consistent with stationarity of aggregate wealth when the interest rate is R and the level of risk is σ. These functions will turn out to be particularly helpful in the characterization of the steady states. Parts (ii) through (iv) then provide us with the comparative statics of these functions with respect to the interest rate and the level of risk. Part (ii), in particular, establishes that the steady-state capital stock is a U-shaped function of the interest rate. What lies behind this Ushaped relation is our wealth-and-risk-taking e(cid:27)ect: for su(cid:30)ciently high R, this e(cid:27)ect dominates the familiar opportunity-cost e(cid:27)ect, guaranteeing that a higher interest rate increases the capital stock in the steady state. This result plays a crucial role in our subsequent analysis. Part (iv), then, complements this result by showing that, as the interest rate increases, the propensity to save in the bond also increases: as the risk-free rate increases, saving in the riskless asset (bond) increases relative to aggregate saving in the risky asset (capital). Finally, parts (iii) and (v) establish that, for any given interest rate, an increase in the level of risk necessarily reduces the steady-state capital stock, while it increases the propensity to save in the bond as long as the interest-rate is not too low. These properties capture, respectively, the risk-aversion and precautionary-saving e(cid:27)ects of higher idiosyncratic risk. Combined, these results facilitate the characterization of the autarchic and integrated steady states. To sharpen this characterization, we now introduce the following assumption, which we will invoke for a subset of our results. Assumption 1. Suppose that either of the following conditions holds: (cid:115) 2αβ(1+θ) α−saut θ j σ˜ > or < , j θγ(α+θ(2−α)) 1−saut 1+θ j where saut ≡ δKaut/f(Kaut) is the autarchic steady-state saving rate of country j. j j j Thisassumption requireseither(i)thattheuninsurableidiosyncraticriskexceedssome minimal level, or (ii) that the elasticity of intertemporal substitution, θ, is su(cid:30)ciently high relative to saving rates. Itcanbeshownthattheformerpropertyimpliesthelatter(seeAppendix). Theadvantageof the former property is that it is stated in terms of purely exogenous parameters, thus guaranteeing the existence of economies for which the assumption holds. The advantage of the latter property is that it can easily be mapped to data. In particular, consider the following back-of-the envelope exercise. Using US data, we can set α ≈ .36 and saut ≈ .23. It then follows that Assumption 1 is satis(cid:28)ed for the United States if θ > .2. For countries with higher saving rates, this condition might be satis(cid:28)ed for even lower values of θ. Since most recent estimates of θ are almost always above .5, and often above 1, we conclude that Assumption 1 is a very plausible benchmark. 13

In any event, the role of this assumption is to guarantee that the autarchic steady states lie in the increasing portion of the function K. In words, this means that, in the neighborhood of the autarchic steady state, the wealth-and-risk-taking e(cid:27)ect of a higher interest rate dominates the standard opportunity-cost e(cid:27)ect. 4.2 Autarchy We are now ready to provide our (cid:28)rst main result, which concerns the characterization of the autarchic steady state. Proposition 2. There always exists an autarchic steady state, it is unique, and it features the following properties: (i) The autarchic interest rates are given by Raut, where Raut solves B(Raut,σ˜ ) = 0, and satisfy j j j j R < Raut < Raut < R¯ , 2 1 where R¯ is the complete-markets interest rate, R¯ = β. (ii) The autarchic capital stocks are given by Kaut = K(Raut,σ˜ ). Furthermore, under Assumpj j j tion 1, 0 < Kaut < Kaut < K¯ , 2 1 where K¯ is the complete-markets capital stock, de(cid:28)ned by f(cid:48)(K¯) = β+δ. (iii) The autarchic consumption levels are given by Caut = f(Kaut)−δKaut. Furthermore, under j j j Assumption 1, 0 < Caut < Caut < C¯, 2 1 where C¯ is the complete-markets consumption level, de(cid:28)ned by C¯ = f(K¯)−δK¯ . The existence and the uniqueness of the autarchic steady state follow from the continuity and monotonicity of the function B with respect to R (which we established in Lemma 2), along with appropriate limit properties (which we establish in the Appendix). Part (i) characterizes the steady-state levels of the interest rate: it establishes that the interest rate is lower than the discount rate in both countries, and more so in the South than in the North. The (cid:28)rst property, namely that the autarchic interest rates are lower than the discount rate, re(cid:29)ects thepresenceofaprecautionarymotiveforsaving. Asnotedearlier, thisissimilartoAiyagari(1994) andMendozaetal. (2008). Thesecondproperty,thattheinterestrateintheSouthislowerthanthe one in the North, is then a consequence of the fact that the precautionary motive is stronger in the South, due to the higher level of idiosyncratic risk. Formally, this is captured by the monotonicity of the function B with respect to σ: the higher the level of undiversi(cid:28)able idiosyncratic risk, the higher the steady-state demand for the risk-free asset for any given R; but since the net supply of 14

this asset is zero when the economy is in autarchy, it must be that the autarchic interest rate is lower the higher is σ. This result is also illustrated in Figure 1. The interest rate is on the horizontal axis. The solid line is the curve B for the North; the dashed line is the curve B for the South. These curves can be interpreted as the aggregate demand for the safe asset in each country (normalized, though, by the corresponding capital stocks). Both curves are increasing in R, but the one for the South lies above the one for the North, re(cid:29)ecting the stronger precautionary motive in the South. The autarchic steady-state interest rates are given by the intersections of the two curves with the horizontal zero line. Clearly, the South has a lower autarchic interest rate, Raut < Raut . 2 1 Part (ii) characterizes the steady-state levels of the capital stock: it establishes, under Assumption 1, that the capital stock is lower than its complete-markets counterpart in both countries, and moresointheSouththanintheNorth. The(cid:28)rstproperty, namelythattheautarchiccapitalstocks are lower than their complete-markets counterparts, revisits the key result in Angeletos (2006). As mentioned in the introduction, this is a core prediction that di(cid:27)erentiates our framework from prior work, including Aiyagari (1994), Krusell and Smith (1998), Mendoza et al. (2008, 2009), and most other Bewley-type models where incomplete risk sharing is typically associated with higher capital accumulation. Furthermore, this prediction is obviously more consistent with the data than the alternative featured in the aforementioned class of models: our framework predicts that the least (cid:28)nancially developed countries are the poorest ones, not the richest ones. The key for this di(cid:27)erence is the type of risk featured in those models versus the type of risk in our model. In those models, agents face only idiosyncratic labor-income risk. This risk introduces a precautionary motive for saving, which reduces the interest rate, but does not break the equality between the interest rate and the marginal product of capital. In contrast, our model features entrepreneurial, or capital-income, risk. This risk introduces not only a precautionary motive, but also a positive wedge between the interest rate and the marginal product of capital; this wedge is the risk premium on private investment. It follows that, while incomplete risk-sharing necessarily encourages more capital accumulation in Bewley models by reducing the interest rate, it can discourage capital accumulation in our model by introducing the risk-premium wedge. The conditions in Assumption 1 then su(cid:30)ce for this wedge to dominate the reduction in the interest rate, thus guaranteeing that the capital stock is lower than under complete markets. Finally, the result that the autarchic capital stock is lower in the South than in the North re(cid:29)ects the fact that the wedge is higher in the South. Formally, this last result follows combining the facts that σ is higher in the South, that R is lower in the South, that the function K is necessarily decreasing in σ, and that, under Assumption 1, this function is also increasing in R for all R ≥ Raut . j Finally, part (iii) characterizes the steady-state level of consumption: it establishes, under Assumption 1, that the aggregate level of consumption is lower than its complete-markets counterpart in both countries, and more so in the South than in the North. 15

Combined, the above results show that, under autarchy, the South(cid:22)the economy with more severe (cid:28)nancial frictions(cid:22)features a lower risk-free rate, a higher marginal product of capital, and lower levels of aggregate capital, wealth and consumption. 4.3 Financial integration We now proceed to our second main result, the characterization of the integrated steady state. Proposition 3. Anintegratedsteadystateexists, anditnecessarilyfeaturesthefollowingproperties: (i) The interest rate is given by Rint, where Rint solves (cid:80) B(Rint,σ˜ )K(Rint,σ˜ ) = 0, j∈{1,2} j j and satis(cid:28)es Raut < Rint < Raut < β . 2 1 (ii) The foreign asset positions are given by Bint = B(Rint,σ˜ )Kint and satisfy j j j Bint < 0 < Bint . 1 2 (iii) The capital stocks are given by Kint = K(Rint,σ˜ ). Furthermore, under Assumption 1, j j Kaut < Kint < Kint < Kaut . 2 2 1 1 (iv) The consumption levels are given by Cint = f(Kint)−δKint+RintBint. Furthermore, under j j j j Assumption 1, Caut < Cint < Cint < Caut . 2 2 1 1 Part (i) establishes that the interest rate in the integrated steady state falls between the two autarchicvalues, whilepart(ii)statesthatintheintegratedsteadystatetheSouthisanetcreditor, while the North is a net debtor. As we will see in the next section, this steady-state position is attained after a long transition throughout which the North runs persistent current-account de(cid:28)cits (and, symmetrically, the South runs persistent current-account surpluses). These two results contain the explanation that our model o(cid:27)ers for global imbalances: Corollary 1. Along the transition from the autarchic to the integrated steady state, the North must accumulate a negative foreign asset position, that is, it must run a series of current-account de(cid:28)cits. Intuitively, this is because the North has a comparative advantage in supplying the riskless asset. More precisely, the autarchic price of the riskless asset is lower (i.e., the autarchic interest rate is higher) in the North than in the South because of the weaker precautionary motive in the North. Extrapolating from standard trade theory, one would thus expect that the North will become a net supplier of the riskless asset once the two countries are allowed to trade. Of course, this intuition could have been misleading both because we are talking here about capital (cid:29)aws, not goods trade, 16

and because of the rich dynamics that are involved in our environment. Nevertheless, our results show that this basic intuition is largely correct. Parts (ii) and (iii) then study the long-run implications of (cid:28)nancial integration for economic activity and world-wide inequality. In particular, part (ii) establishes that the South has a higher capital stock in the integrated steady state than in the autarchic one. Formally, this is a direct implicationofourearlierresultinLemma2thatthefunctionKisincreasinginR. Moreintuitively, this is because of the dynamics of wealth accumulation that we highlighted earlier: agents in the South enjoy a higher capital stock in the integrated steady state because a prolonged access to higher safe returns permits them to accumulate more wealth, and therefore to take more risk. The converse is true for the North. Part (iv) spells out the implications for aggregate consumption. The South enjoys a higher level ofconsumptionintheintegratedsteadystatethanunderautarchy, bothbecauseithasaccumulated more capital domestically and because it has accumulated a positive position against the North. Once again, the converse is true for the North. Clearly, similar properties as those for capital and consumption hold if we look at GDP, wages, and labor productivity. This gives the key prediction of our model regarding the long-run impact of (cid:28)nancial integration on cross-country inequality: Corollary 2. In the long run, (cid:28)nancial integration reduces cross-country inequality. As we will see next, however, the short-run e(cid:27)ects are quite di(cid:27)erent. 5 Transitional dynamics and numerical example In this section we examine in more detail the dynamic responses of the two countries to the integration of their (cid:28)nancial markets, starting from an initial position that coincides with the autarchic steady states. For this purpose, we henceforth have to abandon generality and focus on a particular numerical exercise. While we base this numerical exercise on a somewhat plausible calibration of themodel, weinvitethereadernottofocusontheprecisenumbers: thesimplicityofourmodeland data limitations preclude a rich, serious quantitative assessment. That being said, the numerical exercise indicates that the e(cid:27)ects can be of non-trivial magnitude. Furthermore, the qualitative patterns we identify with this particular numerical exercise are extremely robust: as one should anticipate from our earlier theoretical results, they obtain for a wide range of parameters that we have experimented with as long as Assumption 1 is maintained. 5.1 Parameterization The two economies are parameterized by (α, β, γ, δ, θ, σ˜ , σ˜ ), where α is the income share of 1 2 capital, β is the discount rate, γ is the coe(cid:30)cient of relative risk aversion, δ is the depreciation rate, 17

θ is the elasticity of intertemporal substitution, and σ˜ is the undiversi(cid:28)able risk in country j. j The time period is interpreted as one year. All the preference and technology parameters are set in a manner that is broadly consistent with the macro and macro-(cid:28)nance literatures. In particular, the discount rate is β = 0.05. The elasticity of intertemporal substitution is θ = 1, a 9 value broadly consistent with recent micro and macro estimates, while the coe(cid:30)cient of relative risk aversion is chosen to be γ = 8, a value commonly used in the macro-(cid:28)nance literature to help generate plausible risk premia. Finally, the depreciation rate is δ = 0.10 and the share of capital in production is α = 0.40. This leaves us with σ˜ or, equivalently, with σ and λ . We (cid:28)rst focus on σ , which we interpret j j j j as the idiosyncratic volatility of the rate of return that an individual entrepreneur faces in his investment, regardless of whether this risk is insurable or not. This interpretation is analogous to the notion of idiosyncratic volatility for stock market returns, except that here we are primarily 10 interested in privately-held businesses. Unfortunately, there is no direct measure σ in the US economy because of the unavailability of data about entrepreneurial returns. However, there are various indications that idiosyncratic investment risks in the United States are signi(cid:28)cant. For instance, the probability that a privately held (cid:28)rm survives (cid:28)ve years after entry is less than 40%. Furthermore, even conditional on survival, the risks faced by entrepreneurs and private investors appear to be very large: as Moskowitz and Vissing-Jłrgensen (2002) document, not only is there a dramatic cross-sectional variation in the returns to private equity, but also the volatility of the book value of an index of private (cid:28)rms is twice as large as that of the index of public (cid:28)rms. Since this index already diversi(cid:28)es the (cid:28)rmspeci(cid:28)c risk in private equity, and since the volatility of the entire pool of public (cid:28)rms is about 15% per annum, this gives another indication of the signi(cid:28)cant risks faced by entrepreneurs. Finally, if one takes the idiosyncratic volatility of public (cid:28)rms as a proxy for that of private (cid:28)rms, this would suggest a value of σ over 50% for the United States. This is actually the value preferred by Moskowitz and Vissing-Jłrgensen (2002), Bitler et al. (2005) and Roussanov (2009). Another indirect estimate for the private-sector volatility in the US could be motivated by the work of Davis et al. (2006), who use the Longitudinal Business Database (LBD). They (cid:28)nd that in 2001 the ratio of private to public volatility of employment growth rates was in the range of 1.43- 1.75. Given that the average annual standard deviation of returns for public (cid:28)rms over 1990-1997 was0.11accordingtoCampbelletal. (2001), andthatthereis, atleastinthecontextofthepresent model, a close relationship between the volatility of pro(cid:28)ts and the volatility of labor demand, a choice of σ near 0.20 for the US economy could be justi(cid:28)ed from this perspective. Finally, if one also takes into account that, in the data, sales and pro(cid:28)ts are more volatile than employment (at 9SeeAngeletos(2007)foramorethoroughdiscussionoftherelevanceofthisparameterwithinthetypeofmodel we have employed here, and also for references on the empirical estimates of this parameter. 10Note, though, that idiosyncratic risk may a(cid:27)ect the investment decisions of public traded (cid:28)rms as well. See Papanikolaou and Panousi (2010) for evidence. 18

least for public (cid:28)rms), this would suggest even higher values for σ. Combiningtheaboveobservations,andinterpretingtheNorthinourmodelastheUnitedStates, we conclude that a value for σ near 0.5 is a plausible benchmark. However, as already mentioned, 1 the entrepreneur could actually be able to diversify away a fraction λ of that risk, so that the volatility of the remaining undiversi(cid:28)able risk is in fact lower than σ. Furthermore, our model assumes that all capital is held in private businesses, whereas in reality an important fraction is held in publicly-traded companies. For these reasons, we next proceed to discuss the value of λ and/or σ˜. 11 Althoughwehavenotexplicitlymodeledthedistinctionbetweenprivateandpublicequity, the followingconceptualexerciseprovidesapossiblemappingbetweenourmodelandthedata. Suppose that each household in our model is able to split its family business in two accounting identities. The one, which takes a fraction λ of the business’s output and pro(cid:28)ts, (cid:16)goes public(cid:17): it is sold in the market for its expected value, so that the household diversi(cid:28)es the risk in that component. The other, which takes the residual (1 − λ) of the business’s output and pro(cid:28)ts, (cid:16)stays private(cid:17): the household has to bear the risk in that component. This interpretation then suggests that λ can be matched to the ratio of public (cid:28)rm pro(cid:28)ts over total pro(cid:28)ts in the United States, where total pro(cid:28)ts are the sum of privately held (cid:28)rm pro(cid:28)ts plus corporate pro(cid:28)ts. In the National Income and Product Accounts (NIPAs), the ratio of proprietors’ pro(cid:28)ts over total pro(cid:28)ts (proprietors plus corporate) is 47% on average over the period 1981-2006. This gives a value for λ around 0.5 or 0.6, 1 12 which is consistent with other estimates of the size of public equity relative to total capital. Finally, a direct calibration of the uninsurable risk σ˜ can be obtained as follows. In our model, 1 the idiosyncratic volatility of individual consumption growth is proportional to σ˜ . We could then 1 ask what is the value of σ˜ that makes our model’s prediction about idiosyncratic consumption 1 volatility match the one found in the data. Using studies that estimate this idiosyncratic variance of consumption growth in US data, such as Ait-Sahalia et al. (2001) and Malloy et al. (2006), we then infer that the appropriate value for σ˜ is close to 0.2. On the basis of this observation and all 1 the preceding discussion, we pick σ = 0.5, λ = 0.6 and σ˜ ≡ (1−λ )σ = 0.2 as our favorable 1 1 1 1 1 parameterization for the North. TurningtotheSouth,wenotethatdataonentrepreneurialactivityandidiosyncraticinvestment risk are even more scarce in developing countries than in the United States. Nevertheless, there are multiple indications that idiosyncratic risk is higher in developing countries. For lack of a better alternative, we assume that the overall amount of risk σ in the South is the same as the one 2 assumed for the North. We then set λ at the conservative value of 0.2. This is at the upper range 2 of available estimates of the ratio of public equity to total capital in less advanced economies such 11Incidentally, note that this distinction is unclear in the data too, since ownership of many public companies is often concentrated in the hands of few key investors. 12See Moskowitz and Vissing-Jłrgensen (2002) for a more extensive discussion of the relative size of private and public equity in the United States. 19

Preferences and technologies Risk: South Risk: North Parameter β θ γ α δ σ λ σ˜ σ λ σ˜ 1 1 1 2 2 2 Value 0.05 1 8 0.40 0.10 0.50 0.60 0.20 0.50 0.20 0.40 Table 1: Baseline parameter values. as China, India, Brazil and Mexico (e.g., Demirguc and Levine, 1996; La Porta et al., 1997). This approach gives σ = 0.5, λ = 0.2 and σ˜ ≡ (1−λ )σ = 0.4 as our favorable parameterization for 2 2 2 1 1 the South. In any event, what matters for the qualitative properties of all the results we document below is merely the fact that σ˜ is higher than σ˜ , not the precise numbers we have picked. With this 2 1 quali(cid:28)cation in mind, we summarize the baseline parameterization of our model in Table 1 and proceed to document the dynamic e(cid:27)ects of (cid:28)nancial integration. 5.2 Dynamic responses Wearenowreadytoconducttheexperimentofinterest,namelyareformthatletsthetwoeconomies integrate their (cid:28)nancial markets (i.e., to trade the riskless asset). This reform is assumed to be unexpected and irreversible. Before this reform, the two economies are assumed to rest at their respective autarchic steady states. The objective is then to study the dynamics responses of these economies to this reform. Tracking the transitional dynamics of incomplete-market models is often a daunting exercise. This is not the case here, thanks to the low dimensionality of the general-equilibrium system of our model. In particular, note from Lemma 1 that, when θ = 1, the marginal propensity to consume out of total wealth reduces to m = β for all j,t. It then follows from Proposition 1 jt that the transitional dynamics of the world economy can be reduced to a simple system of four (cid:28)rst-order ODE’s in (X ,H ) , where X ≡ K +B . Our numerical algorithm then works jt jt j∈{1,2} jt jt jt as follows. First, we solve for both the autarchic and the integrated steady-state aggregates. Next, we numerically solve the aforementioned ODE system using the autarchic steady-state values of capital, X ≡ Kaut, as initial conditions and the integrated steady-state values of human wealth, j0 j Hint, as terminal conditions. j The dynamic path of the South is illustrated in Figure 2, and that of the North in Figure 3. Time in years is on the horizontal axis, and levels of several macroeconomic variables are on the vertical axis. The dotted lines indicate the levels of the variables at the autarchic steady state. The dashed lines indicate the levels of the variables at the integrated steady state. The solid lines show the dynamic response of the variables. Figure 2 shows that, immediately upon integration, the capital stock in the South falls below its autarchic steady-state level. But after this initial fall, the capital stock starts recovering. In fact, 20

it is back to the autarchy level in about thirty years and it keeps increasing after that, eventually converging to the new, higher, integrated steady state. In other words, the South faces a bleak picture in the short run, with a signi(cid:28)cant out(cid:29)ow of capital immediately after integration, but this picture is reversed in the long run, as capital starts (cid:29)ying back into the country, eventually reaching a higher level than under autarchy. In particular, the capital stock in the South falls by almost 4% immediately after integration, compared to its autarchic steady state. But, at the long-run integrated steady state, the capital stock in the South has increased almost 9% above its autarchic level. The same qualitative picture is true for the other aggregate variables, such as aggregate output, consumption, and the wage. For example, aggregate output in the South falls by almost 2% in the short run, and it increases by almost 3% in the long run, compared to its autarchic value. Figure 3 demonstrates the exact opposite picture for the North. Immediately upon integration, the North experiences an in(cid:29)ow of capital, and capital remains above its autarchic level for about (cid:28)fty years. However, in the long run, capital settles at an integrated level lower than the autarchic one. The same is true for the other aggregate variables. The interest rate jumps down from the autarchicsteadystateuponintegration, anditsettlesatanevenlowerlevelinthelongrun. Finally, in the long run the North ends up borrowing from the South. In other words, the North experiences an initial period of prosperity, but in the long run this picture is reversed. For example, capital in the North increases by about 2.5% upon integration, but it falls by about 5% in the long-run steady state, compared to its autarchy level. And aggregate output in the North increases by 1% upon integration, but it falls by 2% in the long run, compared to autarchy. The intuition behind these results is as follows. While in autarchy, the South faces higher levels ofidiosyncraticriskandthereforefeaturesahigherdemandforprecautionarysavingthantheNorth. This stronger precautionary motive keeps the domestic (risk-free) interest rate suppressed in the South relative to the North. Upon integration, however, the precautionary saving of the South is partly absorbed by the North, implying that the domestic interest rate has to increase in the South (and decrease in the North). This in turn has very di(cid:27)erent implications for the macroeconomic outcomes of the South depending on whether we look at the short run or the long run. In the short run, the increase in interest rates means an increase in the opportunity cost of capital, causing a reduction in the capital stock of the South. In the long run, however, this increase in interest rates permits the residents of the South to accumulate more wealth. As they do so, they become willing to undertake more investment risk, which explains why the capital stock recovers over time. The fact that the capital stock eventually increases beyond its autarchic value then follows from Proposition 3. Finally, note that, along the transition to the new steady state, the South runs signi(cid:28)cant current-account surpluses, so that it keeps increasing its (cid:28)nancial position abroad. Conversely, the North runs signi(cid:28)cant current-account de(cid:28)cits, eventually reaching a dramatic level of foreign debt, equal to about 3.5 times its GDP. Clearly, this is the manifestation of the precautionary saving of 21

the South rushing for safety in the North. Our (cid:28)ndings thus provide a novel perspective on the ongoing debate on the costs and bene(cid:28)ts of capital-market liberalization. In particular, while many fear that such a reform may cause an out(cid:29)ow of capital, and while this fear seems to be validated by the recent emergence of global imbalances, here we (cid:28)nd that this e(cid:27)ect may be reversed in the long run thanks to the endogenous accumulation of capital. Corollary 3. Financial integration can trigger an out(cid:29)ow of capital from the poor country in the short run, thereby exacerbating cross-country inequality. These e(cid:27)ects, however, are reversed in the long run. 6 Welfare implications In this section we examine the welfare e(cid:27)ects of integration within each country. In so doing, we 13 are interested to distinguish how these e(cid:27)ects may vary between the poor and the rich, as well as across di(cid:27)erent generations. This motivates us to consider two exercises. The (cid:28)rst studies welfare at the moment the reform takes place, taking into account the entire transitional dynamics that will follow; the second compares welfare across the two steady states. More precisely, the (cid:28)rst exercise seeks to answer the following question. Suppose that a country rests in its autarchic steady state and the current generation contemplates the option to undertake a reform that would let it integrate with the other country. Pick a particular level of wealth. What istheminimalcompensationanagentwiththatparticularlevelofwealthwouldbewillingtoaccept in return for the failure of the reform to take place? The second exercise, on the other hand, seeks to answer the following question. Suppose that future generations are o(cid:27)ered the option to be born in the autarchic steady state versus be born in the integrated steady state. Fix a particular ranking in the wealth distribution (say, the 7-th percentile). What is the minimal compensation an agent with that particular ranking would have to receive under the autarchic steady state in order to be as happy as an agent with the same ranking under the integrated steady state? In short, the (cid:28)rst exercise studies how (cid:28)nancial integration impacts the welfare of the poor and the rich in the current generation, while the second exercise studies how it impacts the welfare of the poor and the rich in generations in the distant future. 13Atthispoint,wenotethatourbaselinemodelfeaturesanexplosivelevelofwealthinequalitywithineachcountry. Thisisbecauseindividualdynamicsfollowarandomwalkinsteadystate. To(cid:28)xthisissue,wecanmodifythemodel toletsomeagentsdiewithaconstantPoisonrateν >0andgetreplacedwithotheragentswho(cid:16)inherit(cid:17) theaverage level of wealth; see Panousi (2010) for further details on this approach. We can then adjust the subjective discount ratesothatthee(cid:27)ectivediscountrate,whichisnowβ+ν,remainsthesameasinourbaselinemodel. Thisguarantees thattheaggregatedynamicsofthemodi(cid:28)edmodelremainexactly thesameasthoseofourbaselinemodel, whileat the same time the modi(cid:28)ed model admits a unique, well-de(cid:28)ned steady-state wealth distribution. For our numerical exercise, we set ν =1/150; this is motivated by the fact that the average mortality rate is about 1/75 per year and the fact that agents are imperfectly altruistic towards future generations. 22

South North Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 (cid:16)short run(cid:17) −8.44 −2.79 −1.11 0.91 3.33 1.24 0.52 −0.67 (at time of reform) (cid:16)long run(cid:17) 3.76 3.81 1.82 −0.75 −11.61 −3.00 0.81 6.82 (across steady states) Table 2: Welfare E(cid:27)ects. Thistablesummarizesthewelfaree(cid:27)ectsof(cid:28)nancialintegrationacross di(cid:27)erent quartiles of the wealth distribution. Q1 is the (cid:28)rst quartile, Q2 is the second quartile, and so on. The numbers is the cells of the table report the within-quartile averages of the short-run and long-run compensating di(cid:27)erentials. The latter are measured as percent of permanent income. The (cid:16)short run(cid:17) refers to welfare at the moment integration takes place, while the (cid:16)long run(cid:17) compares welfareacrosstheautarchicandintegratedsteadystates. (Seethemaintextfordetailedde(cid:28)nitions.) Formally, (cid:28)x a country j and let Vj (x), Vj (x) and Vj (x) denote the value functions ∞,aut 0,int ∞,int at, respectively, the autarchic steady state, the time the reform initiates, and the integrated steady state. The (cid:28)rst welfare exercise is to compute, for each level of (cid:28)nancial wealth x, a compensating di(cid:27)erential τ (x) such that Vj (x + τ (x)) = Vj (x). The second exercise is to compute a j ∞,aut j 0,int compensating di(cid:27)erential τ(cid:48)(x) such that Vj (x+τ(cid:48)(x)) = Vj (gj(x)), where gj(x) is the level j ∞,aut j ∞,int of wealth that corresponds to the same relative wealth position under the integrated steady state as the one obtained with wealth x under the autarchic steady state. For either of these two exercises, we then express the corresponding compensating di(cid:27)erential as a fraction of the agent’s permanent 14 income. The resulting number represents a welfare gain if it is positive, and as a welfare loss if it is negative. Finally, to (cid:28)x language, and notwithstanding the fact that both exercises concern life-time utility, we refer to the e(cid:27)ects that are computed with the (cid:28)rst exercise as the (cid:16)short-run(cid:17) welfaree(cid:27)ects, andtotheonesthatobtainfromthesecondexerciseasthe(cid:16)long-run(cid:17) welfaree(cid:27)ects. These welfare gains and losses are then illustrated in Table 2 and in Figure 4, for each of the two countries and for di(cid:27)erent levels of wealth. Table 2 summarizes the welfare gains and losses across thefourdi(cid:27)erentquartilesof theautarchic steady-state wealthdistribution. Figure4gives asimilar but (cid:28)ner picture, by illustrating the welfare e(cid:27)ects across all percentiles of the wealth distribution. The solid line in this (cid:28)gure represents the (cid:16)short-run(cid:17) welfare e(cid:27)ects (that is, those obtained by the (cid:28)rst of the aforementioned welfare exercises), while the dashed line represents the (cid:16)long-run(cid:17) welfare e(cid:27)ects (that is, those obtained by the second exercise). We (cid:28)rst consider the South, which is in panel (a) of Figure 4. On impact (solid line), (cid:28)nancial integration bene(cid:28)ts the rich at the expense of the poor: the poor of the current generation su(cid:27)er losses, whereas the rich enjoy gains. These e(cid:27)ects, however, are reversed in the long run (dashed line): the poor of future generations are better o(cid:27) living under integration than under autarchy, 14That is, a number equal to, say, 5% means that the agent must receive either a lump sum equal to 5% of his e(cid:27)ective wealth or, equivalently, a perpetuity with annual dividend equal to 5% of his permanent income. 23

while the converse is true for the rich. For example, as shown in Table 2, agents at the bottom 25% of the wealth distribution su(cid:27)er an average loss equal to −8.5% of their permanent income on impact, but enjoy an average gain of +3.8% in the long run. The corresponding numbers for the top 25% of the wealth distribution are +0.9% and −0.8%. The intuition behind these results is as follows. In the short run, (cid:28)nancial integration causes the South’s wages to fall and its interest rates to rise, as we have seen in Figure 2. Both these forces tend to reduce the present discounted value of wages, that is, the human wealth of the households. In turn, this hurts all agents, but more so the poorer ones, since a larger fraction of poor agents’ e(cid:27)ective wealth comes from labor income. At the same time, the reduction in wages means that privatebusinessnowhavetofacelowlaborcosts,aforcethatincreasestheaveragereturnonprivate investment. Alongwiththefactthattheinterestratehasalsoincreased, thismeansthattheoverall return to saving has increased. This e(cid:27)ect tends to bene(cid:28)t the rich, who have large amounts of (cid:28)nancial wealth relatively to human wealth. In our example, this positive e(cid:27)ect is strong enough to o(cid:27)set the negative e(cid:27)ect of the reduced human wealth for richer agents, and it explains why richer agents gain whereas poorer agents lose from integration at impact. Inthelongrun, ontheotherhand, wageseventuallysettleatahigherlevelthanunderautarchy. This tends to increase human wealth. The increase in interest rates contributes in the opposite direction, but does not o(cid:27)set the positive e(cid:27)ect of higher wages. The long-run increase in human wealth then bene(cid:28)ts both the poor and the rich. Along with the fact that the wealth distribution shifts to the right, this explains why the poor and the middle class of future generations are most likely to bene(cid:28)t from integration. The rich, however, may end up losing because the new steady state is associated with higher labor costs and lower mean returns to entrepreneurship. We next consider the North, which is illustrated in panel (b) of Figure 4. In the short run (solid line), the poor and the middle class gain, while the very rich lose. Once again, these e(cid:27)ects are reversed in the long run (dashed line): the poor lose and the rich gain. For example, as shown in Table 2, the bottom 25% make gain of +3.3% in the short run and a loss of −11.6% in the long run, while the top 25% make a loss of −0.7% in the short run and a gain of +6.8% in the long run. The intuition for these results is analogous to that for the South. The North’s poor gain immediately upon integration because of the increase in human wealth, while the rich lose because of the lower return to their bond holdings and the higher labor costs in their private businesses. But as time passes and capital starts going down, the consequent reduction in wages hurts the poor, while it bene(cid:28)ts the rich, and welfare e(cid:27)ects are reversed. In Table 3, we study the sensitivity of the aforementioned (cid:28)ndings to three variant parameterizations of the model. For simplicity, we focus on long-run welfare e(cid:27)ects (comparisons across steady states). The (cid:28)rst variant raises the level of uninsurable risk in the South, from σ˜ = 0.4 to σ˜ = 0.6. 2 2 The second variant raises the income share of capital in both countries to α = 0.7; this is meant to capture the broader de(cid:28)nition of capital one may wish to use for long-run considerations. The third 24

South North Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 baseline 3.76 3.81 1.82 −0.75 −11.61 −3.00 0.81 6.82 σ˜ = 0.6 5.15 5.80 2.62 −1.69 −15.27 −3.63 1.18 9.29 2 α = 0.7 53.26 0.64 0.73 2.18 −16.05 0.50 0.57 6.81 σ˜ = 0.6,α = 0.7 65.17 2.49 2.37 2.28 −15.22 0.28 0.51 7.07 2 σ˜ : 0.4 → 0.2 40.23 29.98 22.85 13.90 0.00 0.00 0.00 0.00 2 Table 3: Sensitivity analysis. This table revisits the long-run welfare e(cid:27)ects of (cid:28)nancial integration for three alternative parameterizations and a variant policy reform. variant combines the aforementioned two variants. In all cases, the poor continue to make gains in the South and to su(cid:27)er loses in the North. However, the poor’s gains in the South now tend to be much bigger, while the poor’s losses in the North are not much di(cid:27)erent. Furthermore, the long-run bene(cid:28)ts of integration are now more widespread in the South, with all quartiles actually gaining in the last two variants. Notwithstanding the limitations of our quantitative exercises, these (cid:28)ndings suggest that the long-run welfare gains of capital-account liberalization are likely to be highest for economies where idiosyncratic risk impacts a broad range of entrepreneurial, investment, and human-capital choices. Finally, intherowcolumnofTable3, wereturntothebaselineparameterizationbutconsideran alternative policy exercise: we now assume that (cid:28)nancial integration permits the South to obtain access, not only to the higher safe returns of the North, but also to the improved risk-sharing possibilities of the latter. That is, we let (cid:28)nancial integration be associated with an increase of λ 2 from0.2to0.6, andhencewithareductioninσ from0.4to0.2. Theimpliedwelfaregainsarethen 2 much bigger than those of our baseline policy exercise, and also more widespread in the population. For example, the bottom 25% gain +40.2% instead of +3.8%, and the top 25% gain 13.9% instead of losing −0.8%, as in the benchmark. This (cid:28)nding underscores that the bene(cid:28)ts of capital-account liberalization for developing economies are likely to be maximal if the reform helps these countries alleviate their own agency, enforcement and institutional problems by gaining access to the more e(cid:30)cient (cid:28)nancial institutions of developed economies. Thenumerical(cid:28)ndingswehavereportedinthissectionare,ofcourse,onlyillustrative. Aserious quantitative exercise would require a richer model, one that would allow for more sources of heterogeneity (e.g., di(cid:27)erent levels of entrepreneurial ability), for diminishing returns in entrepreneurial investment, and for endogenous occupational and educational choices. Nevertheless, the qualitative properties we have uncovered are likely to be robust and highlight the distinct short-run and long-run e(cid:27)ects that are at the focus of our analysis. 25

7 TFP growth and shortage of assets Inthissectionwediscussanextensionofourmodelthathelpsaccommodatetheideathatdeveloping countries su(cid:27)er from a shortage of assets (Caballero, Farhi and Gourinchas, 2008), uncovers the possible implications of our analysis for TFP growth, and helps resolve the puzzle that capital often (cid:29)ows from fast-growing to slow-growing countries (Gourinchas and Jeanne, 2008). This extension introduces a (cid:16)safe sector(cid:17). The technology in this sector has a lower mean return thanentrepreneurialactivity, butentailsnorisk. Onecanthinkofthisas, say, (cid:16)farming(cid:17), orassome formofstoragetechnology. Thebroaderideahereisthatentrepreneursfaceatrade-o(cid:27)betweenrisk and return as they choose among an array of investment opportunities(cid:22)a trade-o(cid:27) that is known to play a crucial role in aggregate TFP and growth dynamics (e.g., Acemoglu and Zillibotti, 1997). Theproductionfunctioninthe(cid:16)safesector(cid:17) isassumedtotaketheformg (M ) = A Mα,where j jt j jt M is the corresponding level of capital and A is a productivity parameter that determines the jt j 15 size of the safe sector relative to that of the risky, entrepreneurial sector. Clearly, the equilibrium must now satisfy R = g(cid:48)(M ) for each country j and all periods t: the marginal product of jt j jt capital in the safe sector is equated to the interest rate. This pins down the capital stock of the safe sector(cid:22)which can be interpreted as the supply of safe assets(cid:22)as an increasing function of the interest rate. The rest of the equilibrium characterization then proceeds in similar lines as in our benchmark model, and is omitted here because of space limitations. Consider now the following exercise. Restrict σ˜ = σ˜ but let 0 < A < A . Letting A > A 1 2 2 1 1 2 captures the idea that the North may have a technological or institutional superiority in supplying the safe asset; restricting σ˜ = σ˜ seeks to isolate this possibility from the possibility of di(cid:27)erential 1 2 levels of uninsurable entrepreneurial risk, the implications of which we have already studied. It is then possible to check that all our (cid:28)ndings continue to hold as before. In particular, the South is poorer than the North under both autarchy and integration; the North runs persistent currentaccount de(cid:28)cits upon integration; capital initially (cid:29)ies out of the South and into the North in the short run; and (cid:28)nally this e(cid:27)ect is reversed in the long run. This extension thus o(cid:27)ers a direct re-interpretation of the preceding analysis: our results originate interchangeably in the relatively higher level of uninsurable risk faced by entrepreneurs in the South and/or in the relative superiority of the North in supplying the global economy with safe stores of value. In turn, this builds a bridge between our paper and Caballero, Farhi and Gourinchas (2008). Like this earlier work, our analysis indicates that global imbalances may originate from a shortage of assets in emerging countries. But unlike this earlier work, our analysis requires only a shortage of the relatively safe assets, not of all assets. Indeed, emerging economies appear to be producing a lot of assets in reality. Yet, most of these assets are risky and their residents seem to be searching abroad for safer assets such as US Treasury bills. It is thus the shortage of 15That the safe sector does not employ labor is for simplicity. 26

such (cid:16)quality(cid:17) assets, and not of all assets, that explains why (cid:28)nancial capital may be (cid:29)owing from emerging countries to the United States and other advanced economies. Finally, our analysis has distinct implication for aggregate TFP and growth dynamics. To see this, note that along the transition from the autarchic to the integrated steady state, agents in the South become increasingly willing to take risk. Like in our baseline mode, this is because the increase in interest rates induces agents in the South to accumulate more wealth. But now that the agents face a choice between the safe sector and the risky, entrepreneurial sector, this increase in the willingness to take risk also means a reallocation of resources from the safe sector to the more risky, but also more e(cid:30)cient, entrepreneurial sector. As this happens, the South enjoys an increase in TFP. Conversely, because the North de-cumulates wealth and reallocates capital away from its entrepreneurial sector, it experiences a drop in its TFP. This is illustrated in Figure 5, which shows 16 the dynamics of TFP in the two countries for a numerical version of the extended model. Along with our model’s prediction regarding current-account dynamics, this provides a simple resolution tothe empirical puzzledocumented byGourinchasand Jeanne (2008). Thisworkshowed that, in the data, capital often appears to (cid:29)ow from countries that experience higher productivity growth to those that experience lower productivity growth. While this fact is inconsistent with the 17 standard neoclassical growth paradigm, it is easily accommodated in our model. 8 Conclusion This paper studies the global macroeconomic implications of (cid:28)nancial integration within a tractable incomplete-markets model that features uninsurable idiosyncratic entrepreneurial risk(cid:22)a friction that introduces, not only a precautionary motive for saving, but also a wedge between the interest rate and the marginal product of capital. Because of this wedge, a (cid:28)nancially underdeveloped economy ((cid:16)South(cid:17) or (cid:16)China(cid:17)) can feature both a lower interest rate and a lower capital stock under autarchy than a more advanced economy ((cid:16)North(cid:17) or (cid:16)US(cid:17)). As the two economies open up their capital accounts, interest rates rise in the South and fall in the North; the North starts running large current-account de(cid:28)cits; and the South su(cid:27)ersanout(cid:29)owofcapital. Overtime, however, integrationpermitstheSouthtoaccumulatemore wealth, in part by saving in the North. As this happens, the bite of the aforementioned friction diminishes. Eventually, this helps boost capital accumulation and growth, thereby reducing cross- 16Thenumericalexercisehereassumesσ˜ 1 =σ˜ 2 =.50,α=0.7,and(A 1 ,A 2 )chosensothatinautarchythecapital inthe(cid:16)safesector(cid:17) accountsfor50%oftotalcapitalintheNorthandfor20%oftotalcapitalintheSouth. Also,note that TFP growth is negative in the North and positive in the South, but both countries could feature positive TFP growth if we had allowed for an exogenous constant drift in technology. The robust prediction is that integration speeds up TFP growth in the South while it slows it down in the North. 17In fact, if we focus on labor productivity (output per worker) rather than TFP, this statement holds true even forourbaselinemodel: alongthetransitionfromtheautarchictotheintegratedsteadystates,theSouthexperiences higher growth in physical capital and labor productivity than the North, and yet it is the North that is borrowing from the South. The extension of this section helps reinforce this point by establishing a similar property for TFP. 27

country inequality in the long run. Combined, these results provide a simple explanation for the emergence of global imbalances, a simple resolution to the empirical puzzle that capital often fails to (cid:29)ow from the rich or slow-growing to the poor or fast-growing countries, and a distinct set of policy lessons regarding the intertemporal costs and bene(cid:28)ts of capital-account liberalization. Underlying these (cid:28)ndings are two key properties. First, a positive wedge between the marginal product of capital and the risk-free rate. Second, the tendency of this wedge to diminish as wealth increases. In our model, the (cid:28)rst property is due to uninsurable idiosyncratic investment risk; the second property then follows from diminishing absolute risk aversion. Interestingly, these properties may naturally emerge also in models with borrowing constraints. These models feature a positive wedge between the marginal product of capital ((cid:16)internal returns(cid:17)) and the interest rate faced by savers((cid:16)externalreturns(cid:17)), eitherbecauseconstraintsbindnoworbecausetheyareexpectedtobind in the future. What is more, this wedge typically falls with wealth, as more wealth helps overcome current and future borrowing constraints. We thus conjecture that similar results would obtain in a variant of our model that would introduce realistic borrowing constraints in addition to, or in place of, the entrepreneurial risk that we have focused on in this paper. 28

9 Appendix Proof of Lemma 1 (individual policy rules). This result is essentially a variant of the Merton- Samuelson optimal portfolio problem; see the proof of Proposition 1 in Angeletos and Panousi (2009). Proof of Proposition 1 (equilibrium dynamics). For simplicity, we drop the index j. Since aggregate labor demand is (cid:82) ni = n¯(ω )K and aggregate labor supply is 1, the labor market i t t t clears if and only if n¯(ω )K = 1. It follows that the equilibrium wage satis(cid:28)es ω = F (K ,1) and, t t t L t similarly, the equilibrium mean return to capital satis(cid:28)es r¯ = F (K ,1)−δ. The bond market, on t K t the other hand, clears if and only if B = 0. We de(cid:28)ne total e(cid:27)ective wealth for an agent i as the t sum of his (cid:28)nancial wealth, which in turn is the sum of his capital holdings and bond holdings, plus human wealth (or human capital), i.e. wi ≡ ki +bi +h = xi +h . Then, in general equilibrium t t t t t t of the autarchic economy, W = K +H , which, combined with the aggregation of bond holdings t t t from (8), gives (14). Aggregating over the de(cid:28)nition of human capital in Lemma 1, we get (cid:90) ∞ H t = h t = e− (cid:82) t sRjdjω s ds . t Expressing this in recursive form gives condition (13). Aggregating the household budget, which can be written as dwi = [r¯ki +R (bi +h )−ci]dt+σkidzi, using the aggregated policy functions t t t t t t t t t from (8), using (9) and (13), and the fact, in equilibrium, r¯K + ω = F (K ,1) − δK , we get t t t t t the resource constraint (11). Finally, using C = m W , and therefore C˙ /C = m˙ /m +W˙ /W , t t t t t t t t t together with (10) and the de(cid:28)nition of ρˆ , gives the aggregate Euler condition (12). jt Proof of Lemma 2. (i) The form of the function K is evident from condition (18), while the form of the function B follows from condition (19). (ii) Using our Cobb-Douglas assumption for the production function and equation (18), we get (cid:104) (cid:105) 1 that K(R) = µ(R)+δ+R α−1. It follows that K has the same sign as 1 (µ +1). Since from α R α−1 R (18) µ(R) = (2θγσ˜2 (β −R))1/2, we get that µ = (−12θγσ˜2 )1/2(β −R)−1/2. Using this, we have 1+θ R 2 1+θ that K > 0 ⇔ R > β − 1θγσ˜2 ≡ Rˆ(σ˜˜) < β ≡ R¯ . R 2 θ+1 In addition, since W˙ = ρ¯W − C = (ρ¯ −m )W , where ρ¯ ≡ φ r¯ + (1 − φ )R , wealth t t t t t t t t t t t t stationarity requires ρ¯= m. Combining this with the Euler equation in steady state, we get θ+1 φ(f(cid:48)(K)−δ−R)−θ(β−R) = 0 . 2 Fromthis, andforsteady-statecapitaltobelowerthanundercompletemarkets,thatis,forf(cid:48)(K)− 29

δ > β, it has to be the case that θ+1 φ(β −R)−θ(β−R) < 0 , 2 which, since β−R > 0, gives θ > φ/(2−φ) or φ < θ/(θ+1) . (cid:104) (cid:105) 1 (iii) Since K(R) = µ(R)+δ+R α−1, it follows that K has the same sign as −µ . Since µ(R) = α σ˜ σ˜ (2θγσ˜2 (β −R))1/2, we get that µ = θγ (2θγσ˜2 )−1/2(β−R). Using this, we have that K < 0. 1+θ σ˜ 1+θ 1+θ σ˜ (iv) From (19) we have that K(R)α 1−φ(R) B(R) = −(1−α) + K(R) . (21) R φ(R) Consider the limits of B as R → 0+ and R → β−. Note that µ(0) = (2θγσ˜2 β)1/2 is (cid:28)nite and hence 1+θ both φ(0) and K(0) are (cid:28)nite. It follows that 1 1 lim B(R) = −(1−α)K(0)α lim +( +1)K(0) = −∞ . R→0+ R→0+ R φ(0) Furthermore, µ(β) = 0, implying φ(β) = 0 and K(β) = (f(cid:48))−1(β) is (cid:28)nite. It follows that 1 1 lim B(R) = −(1−α)K(β)α + lim ( +1)K(β) = +∞ . R→β− β R→β− φ(R) Next, note that, from (21), ∂B K(R)α (cid:20) K(cid:48)(R) (cid:21) φ(cid:48)(R) 1 = −(1−α) αR −1 − K(R)+ K(cid:48)(R) . ∂R R2 K(R) φ(R)2 φ(R) (cid:104) (cid:105) 1 (cid:113) Now note that, since K(R) = µ(R)+δ+R α−1 and φ(R) ≡ 2θ (β−R), we have α γσ˜2(1+θ) f(cid:48)(K) K(cid:48) 1 µ(cid:48)+1 φ(cid:48) γσ˜2µ(cid:48) Kα−1 = , = , and = , α K α−1f(cid:48)(K) φ2 µ2 where we suppress the dependence of K, µ, and φ on R for notational simplicity. It follows that ∂B 1−αRµ(cid:48)+R−f(cid:48)(K) γσ˜2µ(cid:48) = − − . ∂R α R2 µ2 Since µ(cid:48)(R) < 0 and R < f(cid:48)(K(R)) for all R ∈ (0,β), we have that ∂B/∂R > 0 for all R ∈ (0,β). (v) Using the formulas for µ(R) and φ(R) from above, we get ∂B ∂ B ∂ 1−α = ( ) = (φ−1−1−(1−α)Kα−1R−2) = −φ−2φ − R−1µ , σ˜ σ˜ ∂σ˜ ∂σ˜ K ∂σ˜ α 30

where φ = − 1 ( 2θ(β−R) )1/2 and µ = ( 2θγ(β−R) )1/2. Substituting this into ∂B > 0 yields σ˜ σ˜2 γ(1+θ) σ˜ 1+θ ∂σ˜ 2θβ(1−α) R > ≡ R < R¯ ≡ β . α+θ(2−α) (cid:9) Proof that the (cid:28)rst part of Assumption 1 implies its second part. Using the de(cid:28)nitions of Rˆ and R, we get (cid:9) 2αβ(1+θ) Rˆ < R ⇔ σ˜ < . (cid:9) θγ(α+θ(2−α)) In this region of interest rates, K > 0, and therefore φ < θ/(1 + θ). Next, let f(K) = Kα, R fˆ(K) = Kα+δK, and s ≡ δK/fˆ . From (19) in autarchic bond market clearing, we have that 1−φ H ω f(K)−f(cid:48)(K)K f/K −f(cid:48) = = = > , φ K RK RK f(cid:48) and therefore fˆ(cid:48)K/fˆ−δK/fˆ α−s φ < = . 1−δK/fˆ 1−s For σ˜ very small, φ (cid:39) α−s, which implies that K > 0 ⇔ α−s < θ . 1−s R 1−s 1+θ Proof of Proposition 2. (i) This part follows from the proof of Lemma 2, part (iii). The limits of B(R), together with the continuity of B(R) in R, establish the existence of an R that solves B(R) = 0. This is in fact the unique steady-state R, since B > 0 always. R (ii) The equation B(Raut,σ˜ ) = 0 is simply bond market clearing for each country. Under j j Assumption 1, we are in the region where B > 0. From (1) we have that B = B/K ≡ D. Using a σ˜ proof similar to that in Proposition 1(iv), we get that D < 0. Hence, B < 0. We also have that R R B = B R > 0, with B < 0. Therefore, it has to be that R < 0 in autarchy. In other words, σ˜ R σ˜ R σ˜ Raut > Raut. 1 2 (iii) Under Assumption 1, we are in the region where K > 0. Hence, the fact that Raut > Raut R 1 2 implies that Kaut > Kaut > 0. Since consumption is increasing in capital, we also have that 1 2 Caut > Caut. 1 2 Proof of Proposition 3. (i) Consider the function WB(R) de(cid:28)ned by WB(R) ≡ B(R,σ˜ )K(R,σ˜ )+B(R,σ˜ )K(R,σ˜ ) . 1 1 2 2 An integrated steady state is given by any solution to WB(R) = 0. Note that the function K is always positively valued, while the function B can take both signs and is increasing in R and σ˜. 31

Furthermore, recall that Raut < Raut. Whenever R ≤ Raut(< Raut), by the monotonicity of B 2 1 2 1 in R we have that B(R,σ˜ ) ≤ B(Raut,σ˜ ) = 0 and B(R,σ˜ ) < B(Raut,σ˜ ) = 0; it follows that 2 2 2 1 2 2 WB(R) < 0. Similarly, whenever R ≥ Raut, we have that WB(R) > 0. Along with the fact that 1 the function WB(R) is continuous in R, this implies that a solution Rint to WB(R) = 0 always exists and it necessarily satis(cid:28)es Raut < Rint < Raut. 2 1 (ii) Since K < 0, it follows that Kint > Kint. Since Assumption 1 ensures that K > 0, and σ˜ 1 2 R using (i), we get the desired result. (iii) Under Assumption 1, we are in the area where B > 0, which implies that Bint < Bint, σ˜ 1 2 and since the world bond market has to clear, this means that Bint < 0 < Bint. 1 2 (iv) This part follows directly from parts (ii) and (iii). 32

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aut R 2 0 aut R 1 B 0 R β Figure 1: Steady state. This (cid:28)gure illustrates the determination of the autarchic and integrated steady states. The interest rate is on the horizontal axis, the net foreign asset position of a country is on the vertical axis. The solid line is the function B(R) for the North. The dashed line is the function B(R) for the South. The intersection of these curves with the zero line gives the autarchic interest rates, where Raut < Raut. The integrated interest rate, Rint, falls in between the the two 2 1 autarchic values. 37

0.65 0.84 0.64 0.835 0.63 0.83 0.62 0.825 0.61 0.82 0.6 0.815 0.59 0.81 0.58 0.805 0.57 0.8 0 50 100 150 200 250 t 0.795 0 50 100 150 200 250 t (a) Aggregate Capital Stock (b) Aggregate Output 1.1 0.84 0.835 1.05 0.83 1 0.825 0.82 0.95 0.815 0.81 0.9 0.805 0.85 0.8 0.795 0 50 100 150 200 250 t 0.8 0 50 100 150 200 250 t (c) Labor Productivity and Wage (d) Aggregate Consumption 4.5 0.0425 4 0.042 3.5 0.0415 3 0.041 2.5 0.0405 2 1.5 0.04 1 0.0395 0.5 0.039 0 0 50 100 150 200 250 t 0 50 100 150 200 250 t (e) Interest Rate (f) Net Foreign Asset Position Figure 2: South’s dynamic adjustment to (cid:28)nancial integration. This (cid:28)gure illustrates the transition of the South from its autarchic steady state to the integrated one. Time in years is on the horizontal axis. Integration occurs at time zero. The dotted line indicates the value of the variables in the autarchic steady state. The dashed line indicates the value of the variables in the integrated steady state. The solid line indicates the dynamic path of the variables. Capital, output, consumption, and the wage are normalized by the corresponding autarchy values of the North. The net foreign asset position is given as a fraction of contemporaneous GDP. 38

1.03 1.01 1.02 1.005 1.01 1 1 0.99 0.995 0.98 0.99 0.97 0.985 0.96 0.98 0.95 0 50 100 150 200 250 t 0.975 0 50 100 150 200 250 t (a) Aggregate Capital Stock (b) Aggregate Output 1.01 1.05 1.005 1 1 0.995 0.95 0.99 0.9 0.985 0.85 0.98 0.8 0.975 0 50 100 150 200 250 t 0 50 100 150 200 250 t (c) Labor Productivity and Wage (d) Aggregate Consumption 0 0.044 −0.5 0.0435 −1 −1.5 0.043 −2 0.0425 −2.5 −3 0.042 −3.5 0.0415 0 50 100 150 200 250 t −4 0 50 100 150 200 250 t (e) Interest Rate (f) Net Foreign Asset Position Figure 3: North’s dynamic adjustment to (cid:28)nancial integration. This (cid:28)gure illustrates the transition of the North from its autarchic steady state to the integrated one. Time in years is on the horizontal axis. Integration occurs at time zero. The dotted line indicates the value of the variables in the autarchic steady state. The dashed line indicates the value of the variables in the integrated steady state. The solid line indicates the dynamic path of the variables. Capital, output, consumption, and the wage are normalized by their corresponding autarchy values. The net foreign asset position is given as a fraction of contemporaneous GDP. 39

20 15 10 5 0 −5 −10 −15 −20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 individual wealth percentiles noitpmusnoc laudividni fo tnecrep sa noitargetni morf sniag 20 15 10 5 0 −5 −10 −15 0 1 −20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 individual wealth percentiles (a) Welfare Gains/Losses for the South noitpmusnoc laudividni fo tnecrep sa noitargetni morf sniag 0 1 (b) Welfare Gains/Losses for the North Figure 4: Welfare e(cid:27)ects. This(cid:28)gureillustratesthewelfaree(cid:27)ectsof(cid:28)nancialintegrationacross di(cid:27)erent wealth levels. The horizontal axis measures wealth in terms of percentiles in the autarchic steady-state distributions. The vertical axis measures the welfare gains (positive numbers) or losses (negative numbers), evaluated as percent of individual permanent income. The solid line represents the welfare e(cid:27)ects for the current generation (the (cid:16)short-run(cid:17) e(cid:27)ects that obtain by evaluating welfare at the time of reform); the dashed line represents the welfare e(cid:27)ects for future generations (the (cid:16)long-run(cid:17) e(cid:27)ects that obtain from comparing welfare across the two steady states). 40

1.1 1 0.98 1.08 0.96 1.06 0.94 1.04 0.92 0.9 1.02 0.88 1 0.86 0 50 100 150 200 250 t 0 50 100 150 200 250 t (a) TFP of South (b) TFP of North Figure 5: TFP dynamics. This (cid:28)gure illustrates the dynamic adjustment of TFP to (cid:28)nancial integration, within the context of the extended model. Time in years is on the horizontal axis. Integration occurs at time zero. The TFP of each country, normalized by its corresponding value at the integrated steady state, is on the vertical axis. 41