International Macroeconomics and Finance Session 4-6

International Macroeconomics and Finance Session 4-6 Nicolas Coeurdacier - nicolas.coeurdacier@sciences-po.fr Master EPP - Fall 2012

International real business cycles - Workhorse models of international business cycles fluctuations Explore basic frameworks and draw its limitations. - International business cycles: one good model Complete markets and incomplete markets (riskfree bond only) - International business cycles with multiple goods Complete markets and some insights on incomplete markets models.

International real business cycles: one good models (complete and incomplete markets ) - International business cycles facts - One good real business cycle model with complete markets Backus, Kehoe, Kydland, JPE 1992; "Quantity Puzzle" - One good real business cycle model with incomplete markets Kollmann (1996, JEDC), Baxter and Crucini (1995, IER)

International Business Cycles Facts

International Business Cycles Facts

International Business Cycles Facts

A two country/one good endowment economy (complete markets) See Obstfeld and Rogoff Chapter 5. Set-up Two countries Home and Foreign (H and F ). Discrete time economy with two periods t=0,1. t=0: output is given in both countries = y 0. Consumption c 0,i t=1, output risk is realized. S states of nature with probability π(s).country i produces y 1,i (s) in state s and consumes c 1,i (s) in state s. At date t=0: Trade in Arrow-Debreu Securities [each AD securities s gives one unit in state s]

Intertemporal Utility U i = u(c 0,i ) + βe 0 u(c 1,i ) = c 0,i + β s π(s)u(c 1,i (s)) c t,i =aggegate consumption at date t in country i et β=discount factor u(c) = c1 σ 1 σ with σ = CRRA coefficient Budget constraints: c 0,i = y 0,i s p b (s)b i (s) λ i 0 c 1,i (s) = y 1,i (s) + b i (s) βλ i 1 (s)

Ressource constraints (denoting y w = world output) i i c 0,i = i c 1,i (s) = i y 0,i = y w,0 y 1,i (s) = y w,1 (s) Asset market clearing condition i b i (s) = 0 FOC u (c 0,i ) = λ i 0 π(s)u (c 1,i (s)) = λ i 1 (s)

Euler equation for Arrow-Debreu Securities p b (s)u (c 0,i ) = βπ(s)u (c 1,i (s)) p b (s) = βπ(s) u (c 1,i (s)) u (c 0,i ) This is true for both countries [agents must agree on asset prices!] u (c 1,H (s)) u (c 0,H ) = u (c 1,F (s)) u (c 0,F ) ( ) σ ( c1,h c1,f = c 0,H c 0,F ) σ c 1,H c 0,H = c 1,F c 0,F Consumption growth rates are equalized across countries due to perfect risksharing. This relationship will show up in any model with 1) one good 2) complete markets 3) separability between leisure and consumption.

Notice that neither country has constant consumption across states. However, each country s consumption is internationally diversified in the sense that any consumption risk it faces is entirely due to uncertainty in global output, or in systematic output uncertainty. Using market-clearing conditions: c 1,i c 0,i = y w,1 y w,0 for i = H, F Remark: If countries are symmetric ex-ante (same initial endowment y 0 ): c 1,H (s) = c 1,F (s) = 1 2 y 1,i (s) = 1 2 y w,0 i

Implications (1) 1) Simple models with one good and complete asset market imply that MRS in consumption should be equalized across countries. Under the additional assumption of CRRA utility, consumption growth rates should be equal across countries. 2) More generally consumption co-movements should be higher across countries than output co-movements. Is it true? No, this is known as The quantity puzzle.

Evidence for OECD countries (1973-92): Obstfeld-Rogoff corr(c, c W ) corr(y, y W ) Canada 0.56 0.70 France 0.45 0.60 Germany 0.63 0.70 Italy 0.27 0.51 Japan 0.38 0.46 UK 0.63 0.62 US 0.52 0.68 OECD 0.43 0.52 Dev. countries -0.10 0.05

Implications (2) 3) In state s, net exports of country H are equal to: NX H (s) = y 1,H (s) c 1,H (s). Due to the resource constraint, this must equal net imports of country F = c 1,F (s) y 1,F (s)! If countries are symmetric: NX H (s) = 1 [ 2 y1,h (s) y 1,F (s) ]. Countries ship goods abroad when output is high to smooth consumption across states of nature. Net exports are procyclical. Is it true? No, next exports are counter-cyclical for most developed countries [see previous tables]

What are the missing ingredients? 1) Capital accumulation and production? 2) Market incompleteness? 3) Multiple goods and different consumption baskets across countries? We will explore sequentially these three dimensions. Let us start with 1).

The single good IRBC model with complete markets (or the simplest is more interesting than you think!) Model of intertemporal trade only: single good Complete markets: can perfectly insure against idiosyncratic risk Production economy: capital accumulation will play a key-role No money, competitive firms, competitive input markets Abstract from government for simplicity Reference: Backus, Kehoe and Kydland, JPE, 1992. (BKK)

Basic Set-up - Two countries Home (H) and Foreign (F ). One good used for consumption and investment (= numeraire) - Each country (i) produces output using CRTS technology (labour inputs=l it and capital=k it ). Production is subject to stochastic technology shocks z i,t : y it = z i,t (l i,t ) 1 θ (k i,t ) θ - Capital internationally mobile but not labor - Complete markets

- Intertemporal Utility U i = E 0 t=0 β t u(c it, l it ) Remark: we will follow BKK and use u(c it, l it ) = (cµ it (1 l it) 1 µ ) 1 σ 1 σ - Capital accumulation: k it+1 = (1 δ)k it + I it AC it where AC it = ϕ 2 [k it+1 k it ] 2 denotes the adjustment costs to changes in the capital stock [BKK use time-to-build but does not make much of a difference] - Resource constraint i (c it + I it ) = i y it

Computation of Competitive Equilibrium Markets are fully competitive Exploit welfare theorems and compute Pareto efficient allocation make use of central planner Complete asset markets implies constant welfare weights [no reallocation of wealth along the equilibrium path] This allocation can be decentralized (check it as an exercise).

Planner s problem max ω H t=0 β t u(c Ht, l Ht ) + ω F t=0 β t u(c F t, l F t ) with ω H + ω F = 1 st: i (c it + I it ) = z i,t (l i,t ) 1 θ (k i,t ) θ (λ t ) i k it+1 = (1 δ)k it + I it ϕ 2 (k it+1 k it ) 2 k i0 is given

FOC (1) c it : ω i u c (c it, l it ) = λ t (2) l it : ω i u l (c it, l it ) = λ t (1 θ) z i,t (l i,t ) θ (k i,t ) θ u l (c it, l it ) = u c (c it, l it ) (1 θ) z i,t (l i,t ) θ (k i,t ) θ (3) k it+1 : λ t [1 + ϕ (k it+1 k it )] = { [ E t βλt+1 (1 δ) + θzi,t+1 (l i,t+1 ) 1 θ (k i,t+1 ) θ 1 + ϕ (k it+2 k it+1 ) ]} [1 + ϕ (k it+1 k it )] = E t { t,t+1 [ (1 δ) + θzi,t+1 (l i,t+1 ) 1 θ (k i,t+1 ) θ 1 + ϕ (k it+2 k it+1 ) ]} where t,t+1 is the SDF (pricing-kernel) = β λ t+1 λ t = β u c(c it+1,l it+1 ) u c (c it,l it )

Interpretation Eq (1): c it condition: Marginal utility of consumption equalized across countries apart from time-invariant Negishi weight = Fundamental risk-sharing condition (in a single good economy with PPP). Due to complete markets, the optimal allocation is the one in which marginal utility of consumption is equalized across locations since shadow price of c Ht = shadow price of c F t ω H u c (c Ht, l Ht ) = ω F u c (c F t, l F t ) The condition hold at all dates, state-by-state = complete risk-sharing. Does not necessarily imply consumption equalized across countries state-by-state: (a) Non-separability between consumption and leisure in utility function: although marginal utility equalized state-by-state, consumption is not. (b) One could allow for taste shocks (=shocks to the marginal utility of consumption as in Stockman and Tesar (1995))

Interpretation Eq (2): l it condition: equalizes the marginal cost of working an additional hour to the marginal marginal productivity of labor. Across countries the ratio of marginal cost of labour = the ratio of marginal productivity of labour: the country with higher marginal productivity is assigned a higher marginal cost of labor (i.e must work more). ω H u l (c Ht, l Ht ) ω F u l (c F t, l F t ) = z H,t(l H,t ) θ (k H,t ) θ z F,t (l F,t ) θ (k F,t ) θ

Interpretation Eq (3): k it+1 condition: relative price of extra unit of capital equals discounted expected future marginal utility times the gross marginal productivity of capital. When combined across countries: E t { t,t+1 [ (1 δ)+θzf,t+1 (l F,t+1 ) 1 θ (k F,t+1 ) θ 1 +ϕ(k F t+2 k F t+1 ) ]} [1+ϕ(k F t+1 k F t )] = E t { t,t+1 [ (1 δ)+θzh,t+1 (l H,t+1 ) 1 θ (k H,t+1 ) θ 1 +ϕ(k Ht+2 k Ht+1 ) ]} [1+ϕ(k Ht+1 k Ht )] Apart from adjustment costs, expected marginal product of capital equalized across countries. Adjustment costs means this equalization happens gradually over time.

Implications in simple case Log-utility; no adjustment costs; symmetric countries (ω i = 1/2) u(c it, l it ) = µ log(c it ) + (1 µ) log(1 l it ) - Consumption risk-sharing implies: c Ht = c F,t Consumption perfectly correlated across countries. - Intratemporal consumption-leisure condition: c it 1 l it = (1 θ) z i,t (l i,t ) θ (k i,t ) θ

Cross-country version: 1 l F t = z H,t(l H,t ) θ (k H,t ) θ 1 l Ht z F,t (l F,t ) θ (k F,t ) θ Cross-country allocation of leisure/work determined by relative productivity only. An increase in z H,t z means an increase in l Ht F,t l (k F t i,t is predetermined). - Investment condition: 1 = E t { t,t+1 [ (1 δ) + θzi,t+1 (l i,t+1 ) 1 θ (k i,t+1 ) θ 1]} for i = H, F Cross-country division of capital determined by relative expected marginal return on investment.

Anomalies... 1) Perfect cross-country consumption correlation 2) Non-perfectly correlated productivity shocks have a tendency for imply negative cross-country correlation of hours worked: increase in z H,t z means an F,t increase in l Ht l - a strong tendency for negative cross-country correlation of F t output. 3) Strong tendency for negative cross-country comovements of investment as capital is moved towards its most productive use. Investment too volatile (but this is sensitive to adjustment costs) More or less opposite of what is observed in the data!. 1) and 2) together lead to the so-called "Quantity Puzzle".

Do we have good news? Yes, net exports are countercyclical due to the presence of capital accumulation As investment increases faster than GDP (especially true if shocks are very persistent), a country hit by a positive positive productivity shocks runs a trade deficit to finance investment (capital moves towards the most productive country). After the trade deficit, the country moves towards a surplus.

The "Quantity Puzzle"

Backus, Kehoe and Kydland, Journal of Political Economy, 1992 - Non-separable preferences between leisure and consumption (σ > 1) Risk-sharing implies: ( ) (1 µ)(σ 1) c Ht = c 1 lf t 1+µ(σ 1) F t 1 l Ht No longer implies perfect consumption correlation. Changes in hours worked affect the link between consumption across countries- the country that works harder is rewarded with higher consumption. - inventory stock in production function - time-to-build instead of quadratic adjustment costs

Calibration (based on quarterly data): Two symmetric countries (Europe and US) c/y = 0.75; β = 0.99; δ = 0.025; θ = 0.36; 4 quarters to build; σ = 2; µ = 0.34 Productivity shocks: ( ln(zht+1 ) ln(z F t+1 ) ) = ( 0.906 0.088 0.088 0.906 ) ( ln(zht ) ln(z F t ) ) + ( εht ε F t ) Correl (ε Ht ; ε F t ) = 0.25; var(ε Ht ) = 0.00852 2

The role of incomplete markets. Does it help? It help in some dimensions but overall does not makes a big difference in many models... Unless: - Highly persistent shocks that generate strong wealth effects (Kollmann (1996), Baxter and Crucini (1995, IER) in one-good models, see also Corsetti, Dedola, Leduc (2007) in a two good model).

How to specify incomplete markets? Exogenous incomplete markets (covered in class): - Financial Autarky - Trade only in non-contingent debt contracts = one period bond (Kollmann (1996), Baxter and Crucini (1995, IER)) Endogenous incomplete markets (not covered in class): - Kehoe and Perri (2002)

Incomplete markets versus complete markets in a one good model: key differences Kollmann (1996, JEDC), Baxter and Crucini (1995, IER) Consider the same set-up with one perfectly traded good and production as before (BKK, 1992). Trade only in non-contingent debt contracts = one period bond Buy one bond at t at price p b t, tomorrow they pay out 1 unit of the good irrespective of the realized state of nature - here written as a zero coupon bond All countries can buy and sell bonds at the same price and can borrow at interest rate that is unrelated to amount of assets: integrated bond financial markets

Each country i faces the following flow budget constraint at date t: p b tb it+1 + c it + I it = y it + b it where b it+1 =quantity of bonds purchased at period t; will deliver b it+1 goods at date t + 1. Bonds market clearing condition: b Ht + b F t = 0

The competitive equilibrium conditions with trade in bonds only: max t=0 β t u(c it, l it ) st: y it + b it = p b tb it+1 + c it + I it (λ it ) k it+1 = (1 δ)k it + I it ϕ 2 (k it+1 k it ) 2 y it = z i,t (l i,t ) 1 θ (k i,t ) θ

FOC c it : u c (c it, l it ) = λ it l it : u l (c it, l it ) = λ it (1 θ) z i,t (l i,t ) θ (k i,t ) θ u l (c it, l it ) = u c (c it, l it ) (1 θ) z i,t (l i,t ) θ (k i,t ) θ k it+1 : λ it [1 + ϕ (k it+1 k it )] = { [ E t βλit+1 (1 δ) + θzi,t+1 (l i,t+1 ) 1 θ (k i,t+1 ) θ 1 + ϕ (k it+2 k it+1 ) ]} [1 + ϕ (k it+1 k it )] = E t { t,t+1 [ (1 δ) + θzi,t+1 (l i,t+1 ) 1 θ (k i,t+1 ) θ 1 + ϕ (k it+2 k it+1 ) ]} where it,t+1 is the SDF in country i = β λ it+1 λ it = β u c(c it+1,l it+1 ) u c (c it,l it )

FOC for bonds (b it+1 ): p b tλ it = E t βλ it+1 p b t = E t β u c(c it+1, l it+1 ) u c (c it, l it ) Cross country version: p b t = E t β u c(c Ht+1, l Ht+1 ) u c (c Ht, l Ht ) = E t β u c(c F t+1, l F t+1 ) u c (c F t, l F t ) Non transversality conditions lim t [ β t λ it+1 b it+1 ] = 0; limt [ β t λ it+1 k it+1 ] = 0

Complete vs Incomplete Markets With incomplete markets, countries no longer able to enter into risk sharing agreements - allocations now subject to redistribution of wealth and subject to idiosyncratic risk. The latter is reflected in the appearance of λ it rather than λ t in the first-order conditions - an increase in y it (together for instance with a decrease in y jt ) now affects the allocation since λ it and λ jt are affected while this is not the case under complete markets. Thus the wealth effect of idiosyncratic shocks is the key difference. Idiosyncratic risk in not shared intratemporally as in the complete markets (no more consumption risk sharing across states through AD securities) but consumption smoothing intertemporally through trade in bonds. Incomplete markets implies consumption smoothing through borrowing and lending (complete markets implies risk sharing through transfers of goods and leisure).

Implications Consumption allocation p b t = E t β u c(c Ht+1, l Ht+1 ) u c (c Ht, l Ht ) = E t β u c(c F t+1, l F t+1 ) u c (c F t, l F t ) Thus expected marginal rates of substitution are equalized across countries (while the realized marginal rate of substitution is equalized across countries under complete markets). Consider the example (symmetric countries ex-ante): u(c it, l it ) = µ log(c it ) + (1 µ) log(1 l it ) CM: IM: c Ht = c F t E t β c Ht = E t β c F t c Ht+1 c F t+1

Or if we consider a log-linearized version: CM: ĉ Ht = ĉ F t c Ht+1 ĉ Ht = IM: E t c Ht+1 ĉ Ht = E t c F t+1 ĉ F t c F t+1 ĉ F t while consumption levels are equalized under CM, expected consumption growth rates are equalized under IM. But IM condition does NOT tie down level of consumption - this is a reflection of the wealth effect. Equalization of realized MRS implies that expected MRS are also equalized, but the opposite is not true. This means that levels of consumption can drift apart under IM but not under CM. This happens in particular when productivity shocks are highly persistent.

Intuition For example, if there is a negative home technology shock that lowers output, you can borrow abroad to boost consumption. Since you are a large country, your desire to borrow raises the world interest rate, and this induces foreign country to lower its consumption and lend to you. So consumption falls also in the foreign country, and this helps offset part of the fall in consumption in home country. Consumption still moves together. Whether this happens or not depends on the persistence of the technology shock. Story above applies for a temporary shock, where want to borrow to smooth consumption. For permanent shocks permanent income fall more with current income. As most technology shocks are thought to be pretty persistent, can lower the correlation of consumption across countries. Kollmann finds that for an autocorrelation of shocks = 0.95, the cross-country consumption correlation falls from 0.72 to 0.38.

Kollmann (1996) Same set-up as BKK, 1992 (except adjustment cost instead of time-to-build). Adjustment costs set to match volatility of investment. Same calibration for key parameters except for productivity shocks [no spillover, higher persistence] Productivity shocks: ( ln(zht+1 ) ln(z F t+1 ) ) = ( 0.95 0 0 0.95 ) ( ln(zht ) ln(z F t ) ) + ( εht ε F t ) Correl (ε Ht ; ε F t ) = 0.2; var(ε it ) = 0.007 2

Baxter and Crucini (1995) Business Cycles and the Asset Structure of Foreign Trade Very similar exercise as Kollmann (1996). Same set-up but discuss further the results when using different processes for productivity shocks. Use first the process of BKK with positive spillovers: ( ) ( ) ( ln(zht+1 ) 0.906 0.088 ln(zht ) = ln(z F t+1 ) 0.088 0.906 ln(z F t ) ) + ( εht ε F t ) Correl (ε Ht ; ε F t ) = 0.25; var(ε Ht ) = 0.00852 2.

With such a calibration, allocation CM and IM are almost identical: not enough persistence & spillovers that are substitute for risk-sharing. Basically, the induced wealth effects are too small to make much difference.

Baxter and Crucini (1995) Then, assume productivity shocks follow a random walk without spillovers ( ) ( ) ( ) ( ) ln(zht+1 ) 1 0 ln(zht ) εht = + ln(z F t+1 ) 0 1 ln(z F t ) ε F t Correl (ε Ht ; ε F t ) = 0.25; var(ε Ht ) = 0.00852 2. Hence: It s not market incompleteness as such that matters, but the interaction between market completeness and the persistence of shocks.

Remark: Non-stationarity Model implies permanent effects of temporary shocks on the level of consumption (and wealth). Where does the problem come from? The domestic and foreign Euler equations imply that in steady-state p b = β - nothing ties down the steady-state level of consumption. This can be solved in various ways: - second-order approximation around a risky steady state (see Coeurdacier, Rey and Winant, 2011) - endogenous discount factor; portfolio rebalancing costs; debt elastic interest rates (see Schmitt-Grohe and Uribe) However: The properties of model with and without these features are very similar