Topic 3: Global Imbalances Econ 2530b, Gita Gopinath

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1 Topic 3: Global Imbalances Econ 2530b, Gita Gopinath Facts Mendoza, Quadrini, Rios-Rull (2009 JPE) Precautionary Savings (Demand for assets) Caballero, Farhi, Gourinchas (2008 AER) Quality of financial instruments (supply of assets) Dooley, Folkerts-Landau, Garber 2004 Mercantilist reserve accumulation

2 Global Imbalances What explains the large current account surpluses of several emerging markets that financed the large current account deficits of the U.S.? Why does the U.S. have positive net foreign asset position in FDI while strongly negative in debt in debt?

3 % of World GDP 1.5% 1.0% 0.5% 0.0% -0.5% -1.0% -1.5% -2.0% USA, Australia, UK EU Japan ROW (a) Current Account by Region (percent of world output)

4 world-short real US-long real (b) World and US Real Interest Rates

5 !"!#$%!#&' ()&*)& (c) Share of US Assets in Rest of the World s Output and Financial Wealth

6 4 A NFA in debt and international reserves 2 Percent of world GDP United States OECD countries except US Emerging economies B NFA in portfolio equity and FDI

7 10 Emerging economies B NFA in portfolio equity and FDI 2 Percent of world GDP United States OECD countries except US Emerging economies Figure 3: Net foreign asset positions in debt instruments and risky assets. The graphs are constructed using data from Lane and Milesi-Ferretti (2006). See appendix A.

8 Mendoza, Quadrini and Rios-Rull (2008) Why are the savings rates so much higher in emerging markets? Why don t they invest more in their own country? Why has capital flowed to the U.S. from emerging markets? Financial development differences combined with financial liberalization.

9 Autarky: Countries with worse financial markets have higher levels of precautionary savings and therefore lower autarkic interest rates. Opening up implies that world interest rate is higher than autarky interest for EM causing them to send capital abroad. Also have investment shocks. U.S. has a comparative advantage in investing in the risky asset.

10 AUS AUT BEL CAN DEN DEU ESP FIN FRA 3 GBR GRC ITA JPN NLD NOR PRT SWE USA 1 B Index of financial liberalization OECD countries Emerging economies Figure 1: Indices of financial markets heterogeneity. The index in panel A is from IMF (2006). The index in panel B is from Abiad, Detragiache and Tressel (2007). See appendix A for the definition of variables.

11 3 A Index of capital account openness 2.5 Standardized measure United States OECD countries except US All countries except US

12 Model Two countries Complete financial markets: Arrow-Debreu securities traded Incomplete financial markets: Risk-free bond only No aggregate uncertainty Precautionary Savings Heterogenous agents within each country Compare autarky to integration

13 Endowment only economy Only endowment shocks. Each country has a continuum of agents of total mass 1. Each agent maximizes E β t U(c t ) t=0 U (c) > 0, U (c) < 0, U(0) =, U (c) > 0 Marginal utility is convex. Precautionary savings

14 Endowment only economy Agents receive an idiosyncratic stochastic endowment, w t. Define s t = w t. g(s t, s t+1 ) is the conditional probability distribution for s t+1 No aggregate shocks. No aggregate fluctuations. Can trade state contingent claims b(s t+1 ) Define net worth a t a(s t ) = w(s t ) + b(s t ) Budget constraint a(s t ) = c(s t ) + b(s t+1 )qt(s i t, s t+1 ) s t+1

15 Financial development Contracts are not perfectly enforceable due to the limited (legal) verifiability of shocks. Agents can divert a part of their endowment, but they lose a fraction φ i of the diverted income. Everyone knows it is being diverted it is just not verifiable in court. No asymmetric information. This is the only feature that differentiates countries. There is limited liability and agents cannot be excluded from the market after defaulting.

16 Endowment only economy In case of diversion the agent will claim that it is the worst state s 1 = w 1 Net worth after diversion w 1 + b 1 + (1 φ i )(w j w 1 ) = a(s 1 ) + (1 φ i )(w j w 1 ) If do not divert net worth will be w j + b j = a(s j ) Since the value function (which will be a function of net worth) is monotonic for incentive compatibility a(s j ) a(s 1 ) + (1 φ i )(w j w 1 ) a(s j ) a(s 1 ) (1 φ i )(w j w 1 )

17 Endowment only economy Variation in net worth cannot be smaller than (1 φ i ) of the variation in income: a(s j ) a(s 1 ) (1 φ i )[w j w i ] Limited Liability (borrowing limit) a(s j ) 0 j {1,..., J}. J is the number of possible realizations of the shock. s 1 is the worst realization.

18 Endowment only economy If φ is high can maintain constant net worth/constant consumption. Full insurance. If φ = 0 only non-contingent claims are feasible. Constraint binds. a(s j ) a(s 1 ) = [w j w i ]

19 Endowment only economy The solution to the agent s problem yields decision rules for consumption, c i t(s, a), and contingent claims b i t(s, a, s ). M i t(s, b): Distribution of agents over s and a.

20 Endowment only economy Autarky: s,b,s b i τ (s, b, s )M i t(s, b)g(s, s ) = 0 for eachi Integrated markets: i q i τ = g(s, s ) 1 + r i t for eachi s,b,s b i τ (s, b, s )M i t(s, b)g(s, s ) = 0 q 1 τ = g(s, s ) 1 + r 1 t = g(s, s ) 1 + r 2 t = q 2 τ

21 Endowment only economy No aggregate uncertainty q i t(s t, s t+1 ) = g(s t, s t + 1) 1 + r i t q i t(s t, s t+1 ) is the price of one unit of consumption goods contingent on the realization of s t+1 r i t is the equilibrium interest rate.

22 Endowment only economy Complete Markets: Assume the borrowing limit does not bind First order conditions c(w i ) = c(w j ) U (c) = β(1 + r t )U (c(w )) β(1 + r t ) = 1 If β(1 + r t ) 1 then all agents have either positive or negative consumption growth. This cannot be an equilibrium because aggregate output is constant.

23 Endowment only economy Incomplete Markets: Assume the borrowing limit does not bind First order conditions U (c) = β(1 + r t )E[U (c(w ))] β(1 + r) < 1 Because U is convex if β(1 + r) 1 expected next period consumption is bigger than current consumption for all agents. Therefore next period aggregate consumption is also greater than today s consumption. This cannot be an equilibrium. U (c) E[U (c(z ))] > U (E(c(z ))) c < E(c(z )

24 Endowment only economy 1 E(b(r),phi_1) E(b(r),phi_2) r_w r_2 r_1 E(a(r) ) E(a(r) ) phi_1<phi_2 Low φ higher asset demand at each interest rate. Increases precautionary savings and lowers interest rates.

25 Endowment and Fixed Capital Each country has a unit supply of a non-reproducible, internationally immobile asset traded at price P i t Like land. Asset can be used by each agent to produce a homogenous good with a one period lag, ν < 1 y t+1 = z t+1 k ν t k t is the quantity of asset used at time t

26 Endowment and Fixed Capital z t+1 is an idiosyncratic shock: Investment shock No capital accumulation. (Do this in another paper) No aggregate shocks. s t (w t, z t ) Define net worth a t a(s t ) = w(s t ) + b(s t ) + z t kt 1 ν + k t 1 Pt i Budget constraint a(s t ) = c(s t ) + b(s t+1 )qt(s i t, s t+1 ) + k t Pt i s t+1

27 Endowment and Fixed Capital: Financial Constraints a(s j ) a(s 1 ) (1 φ i )[(w j + z j k ν t ) (w i + z 1 k ν t )] Limited Liability a(s j ) 0 Assumption: φ i pertains to the country of residency. Ability of an agent to divert investment income generated abroad depends on the institutional, legal and contractual environment of the residence country. Relax this in section 5.

28 P 1 τ = P 2 τ Endowment and Fixed Capital Autarky: bτ i (s, a, s )Mt(s, i b, k)g(s, s ) = 0 s,b,k,s kτ i (s, a)mt(s, i k, b) = 1 s,b,k qτ i = g(s, s ) 1 + rt i Integrated markets: i for eachi for eachi bτ i (s, a, s )Mt(s, i k, b)g(s, s ) = 0 s,b,k,s kτ i (s, a)mt(s, i k, b) = 2 i s,b,k q 1 τ = g(s, s ) 1 + r 1 t = g(s, s ) 1 + r 2 t = q 2 τ

29 Endowment shocks only and fixed capital Supply of K Supply of K 1 r_1 r_w Aggregate demand for Savings, phi_1 r_2 Aggregate demand for Savings, phi_2 E(a(r) ) E(a(r) ) phi_1<phi_2 With Capital: Only endowment shocks

30 Investment shocks only Productivity shock z is stochastic Endowment is constant Can distinguish debt instruments from risky instruments like FDI.

31 Autarky when φ = φ, complete markets Assume the borrowing limit does not bind First order conditions c(z) is constant U (c) = β(1 + r t )U (c(z )) U (c) = βe(r t+1 (k, z )U (c(z )) E(R t+1 (k, z ) = 1 + r t β(1 + r t ) = 1 If β(1 + r t ) 1 then all agents have either positive or negative consumption growth. This cannot be an equilibrium because aggregate output is constant. There is no marginal premium for investing in the productive asset and k is the same for all agents. Agents can perfectly insure. No need for precautionary savings.

32 Autarky when φ = 0, Bonds only markets Assume the borrowing limit does not bind First order conditions U (c) = β(1 + r t )E[U (c(z ))] U (c) = βe[(r t+1 (k, z )U (c(z ))] Marginal risk premium for the risky asset. ER t+1 (k, z ) (1 + r t ) = Cov(R t+1(k, z ), U (c(z )) EU (c(z )) β(1 + r) < 1 Because U is convex if β(1 + r) 1 expected next period consumption is bigger than current consumption for all agents. Therefore next period aggregate consumption is also greater than today s consumption. This cannot be an equilibrium.

33 Integrated markets: φ 1 = φ, φ 2 = 0 r < 1 β 1 Country 1 has a negative net NFA position, but a positive position in the productive asset. The average return of country 1 s foreign assets is larger than the cost of its liabilities.

34 Integrated markets: φ 1 = φ, φ 2 = 0 β(1 + r) 1 cannot be an equilibrium. When β(1 + r) < 1. Agent s in country 1 experience negative consumption growth until the limited liability constraint binds. a(s t ) = c(s t ) + s t+1 b(s t+1 )q i t(s t, s t+1 ) + k t P i t = 0 NFA 1 < 0 In country 1 ER(k, z ) = 1 + r and in country 2 ER(k, z ) > 1 + r which implies that k 1 > k 2 The average return being higher follows from the concavity of the production function (even though marginal return is the same). In the general case where there are both endowment and investment shocks details about NFA depend on the relative size of shocks etc.

35 Caballero, Farhi and Gourinchas (AER, 2008) Supply of Assets Supply of Assets constraint (δ) Denote by PV t the present value of the economy s future output: PV t = t X s e s r t τ dτ ds δ represents the share of PV t that can be capitalized today and transformed into a tradable asset. V t = δpv t δ captures the pledgeability of future revenues. (Fraction of capital share) δ: Index of financial development. Extent to which property rights over earnings are well defined and tradable in financial markets.

36 Demand for Savings At birth, agents receive (1 δ)x t which they save in its entirely until they die. Consume all accumulated resources at the time of death. In its extreme form, there is no savings decision here. Save all endowment at birth and consume your wealth when you die. Contrast with Mendoza, Quadrini and Rios-Rull (2008) No inter-temporal euler equation for consumption. No uncertainty.

37 Standard infinitely lived agent Need the change in δ to effect interest rates. Standard infinitely lived agent consumption = f(wealth) wealth = financial wealth + human wealth = δpv t + (1 δ)pv t Changes in δ have no effect on total wealth. δ increases the supply of assets, but also increases the demand for assets one for one since non-capitalizable future income N t falls by the same amount. Interest rates unchanged.

38 Non-Ricardian Feature consumption = f(wealth) wealth = financial wealth + β t human wealth β t < 1. In the model β t = 0. Claim: Blanchard (1985) model of perpetual youth in reduced form works as in this paper. See working paper version.

39 Model details Agents born at rate θ per unit time and die at the same rate. Population mass is constant and equal to 1. Agents receive a perishable endowment (1 δ)x t which they save entirely and consume when they die. Single savings vehicle: Identical trees that produce an aggregate dividend of δx t per unit time. V t : value of trees. Return on the trees r t = δ X t V t + V }{{} t V }{{} t dividend-price ratio capital gains

40 Model details W t : Savings accumulated by agents up to date t Ẇ t = θw }{{} t + (1 δ)x t + }{{} r t W }{{} t withdrawals new savings return on savings

41 Closed Economy Equilibrium Equilibrium: Interest rate: W }{{} t = V }{{} t savings valueoftrees W t = X t θ r t = δ X t V t + V }{{} t V }{{} t dividend-price ratio capital gains r t = Ẋt X t + δθ r t = g + δθ

42 Closed Economy Equilibrium r aut = g + δθ g raises the rate of growth of financial wealth demand (W ) and hence the capital gains from holding a tree. δ increases the share of income that is capitalizable and hence the supply of assets. θ lowers financial wealth demand and hence asset prices. Country with higher financial development has higher autarky interest rates.

43 Small open economy equilibrium Trade Balance: Current account: TB t X t θw t CA t Ẇ t V t }{{} net asset demand (savings)

44 Small open economy equilibrium Lemma 1: Consider a path for interest rates such that lim t r t = r, with g < r < g + θ. Then, Asymptotic supply of assets, normalized by size of economy. Decreasing in r. Iterate forward r t = δ X t V t + V }{{} t V }{{} t dividend-price ratio capital gains V t X t }{{} t δ r g Gordon s formula

45 Small open economy equilibrium Asymptotic demand for assets, normalized by size of economy. Increasing in r. Iterate backward Ẇ t = θw }{{} t + (1 δ)x t + }{{} r t W }{{} t withdrawals new savings return on savings W t X t }{{} t 1 δ g + θ r

46 Metzler Diagram r W X = 1 δ g+θ r (Demand) r aut V X = δ r g (Supply) W/X, V/X Figure 2: The Metzler diagram.

47 Asymptotic current account CA t X t }{{} t TB t X t (r aut r) g (g + θ r)(r g) }{{} t (r aut r) (g + θ r) If r < r aut asymptotic current account deficit, TB surplus. If r > r aut asymptotic current account surplus, TB deficit.

48 World Economy Two large regions, i = U, R, Only possible difference in δ. r t = δ i X t i Vt }{{} i + dividend-price ratio W u t = θwt i }{{} withdrawals + (1 δ i )Xt i }{{} new savings V i t V i t }{{} capital gains + r t W i t }{{} return on savings

49 World supply of assets World demand for assets V t = V U t W t = W U t World market clearing for goods + V R t + W R t World interest rate x R X R X t θw t = X U t + X R t = X t r t = g + (δ U x R (δ U δ R ))θ

50 Metzler Diagram r W U /X U (Demand) r NA R = NA U > 0 W R /X R (Demand) r U aut r B A NA U < 0 C V U /X U (Supply) r R aut B A D C V R /X R (Supply) W U /X U, V U /X U W R /X R, V R /X R Figure 3: The Metzler diagram for a permanent drop in δ R. In summary, the model is able to generate, simultaneously, large and long lasting current account deficits Decrease in δ R. V R /X R shifts to the left. Reduce in supply of assets. in U (Fact 1); a decline in real interest rates (Fact 2) and an increase in the share of U s assets in global portfolios (Fact 3). Importantly, Increase CA U t in /XU tdemand does not vanish forasymptotically assets, Was it R converges /X R, shifts to: to the right. CA U t X U t (δ U δ R )x R θ = g (θ + g r + ) (r + g) < 0.

51 Thoughts Compare to the Ricardian set-up. Drop in asset demand matches drop in supply. Here an increase in asset demand because of savings/consumption assumptions. Compare to Mendoza et. al. In both cases the less financially developed economy has lower interest rates in autarky. In Mendoza less financial development is an increase in demand for assets. (increased savings). Need uncertainty. Here less supply of assets. In Mendoza et. al. study the impact of financial liberalization. In Caballero et al. study the impact of shocks to δ. (East asian crisis.)

52 Dooley, Folkerts-Landau, Garber 2004 Mercantilist reserve accumulation Need to absorb labor from rural to urban areas Support pro-export policies. Depreciated RER Reserve accumulation