Advanced International Finance Part 3

Transcription

1 Advanced International Finance Part 3 Nicolas Coeurdacier - nicolas.coeurdacier@sciences-po.fr Spring 2011

2 Global Imbalances and Valuation Effects (2) - Models of Global Imbalances Caballerro, Fahri and Gourinchas (2008) Coeurdacier, Guibaud and Jin (2011)

3 Models of Global Imbalances: quick literature review - Differences in ability to capitalize output between emerging Asia and developed countries Caballero, Fahri and Gourinchas (2008) - Capital misallocation Benhima (2009), Song, Storesletten and Zilibotti (2009) - Precautionary savings Ranciere and Jeanne (2006), Jeanne and Caroll (2009)

4 together with difference in financial markets development (financial markets completeness): Mendoza, Quadrini and Rios-Rull (2009) - Corporate savings and frim liquidity constraints Benhima and Bachetta (2011), Sandri (2010) - Saving story based on differences in household credit constraints (development of credit markets) Coeurdacier, Guibaud and Jin (2011)

5 Caballero, Fahri and Gourinchas (2008) Motivation: 3 stylized facts - global imbalances: current account deficits in the US (and UK) financed by surpluses in Asia and Europe - fall in world interest rates - rising share of US financial assets

6 Current accounts by region

7 World interest rates

8 Share of US assets (% of world financial assets or world output)

9 Caballero, Fahri and Gourinchas (2008) - Main contribution: To provide a framework to analyze equilibrium in global financial markets and the impact of regional macroeconomic shocks. - Important side product: To shed some light on the mechanisms that could be generating these important facts as an equilibrium

10 Basic elements of the model (closed economy) Continuous time OLG; birth rate = death rate = θ One good. output = X t grows at rate g Consume when dies: C = θw (wealth = W ) One tree / no physical investment Capitalizable and non-capitalizable output: δ = share of capitalizable output X t = δx t + (1 δ)x t

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12 r aut = δθ + g - Countries with higher growth rates will have higher interest rates in autarky - Countries with higher supply of financial assets will have higher interest rates in autarky Main novelty: asset supplies matter for interest rates.

13 Key mechanism if capital market integration: - Europe has a low g, if open up to the US, capital outflows towards the US (high interest rate country). - Asia has a low δ, if open up to the US, capital outflows towards the US (high interest rate country). Thus if g in Asia not too high compared to the US. - US interest rates falls. Similar mechanism if fall in g in Europe (and markets inegrated) and fall in δ in Asia (Asian crisis).

14 Small open economy Take world interest rate r as given

15 Metzler diagram

16 Europe (E)-US (U) World Same δ but fall in growth g E in Europe r t = [ x U t g + ( 1 x U t ) g E ] + δθ

17 - Fall in world interest rates: r t = [ x U t g + ( 1 x U t ) g E ] + δθ = r U aut ( 1 x U t ) g E - In the short run V U V E raises. So does relative wealth W U W E (due to non-capitalized income). - Consumption raises in the US and falls in Europe. Europe runs a trade surplus

18 A fall in ge

19 Asia (R)-US (U) World Fall in δ R in Asia (Asian crisis) with g R = g: δ R = δ δ R r t = g + x U t δθ + ( 1 x U t ) δ R θ such that r R aut r t r U aut

20 Metzler diagram for drop in δr

21 A fall in δ R when g R = g

22 - Again fall in world interest rates: r t = r U aut ( 1 x U t ) δ Rθ - Again V U V R raises as share of capitalized asset is falling in Asia. - Asia runs a trade surplus [supply of asset scarcity in Asia and buy abundant US assets] Note: if g R > g, demand for assets rises faster than supply.this implies that r t continues to fall, further expanding the asymptotic current account deficit in the US.

23 Three country world: Asia (R) Europe (E) US (U) Combination of both shocks. Consistent with the 3 broad facts presented above. Note if the crash in δ R takes place in a world where g E < g, then the asset appreciation is much larger in U than E and capital flows mostly from R to U

24 A fall in ge followed by a fall in δr

25 Coeurdacier, Guibaud and Jin (2011) Motivation: Over the last 25 years, the world experienced: - Fast growth in Emerging Asia - An increase in private savings in Emerging Asia and a fall in private savings in Advanced Economies - Emergence of Global Imbalances (see above) - A fall in World Long-Term Interest Rate (see above)

26 Fast Growth in Emerging Asia Emerging Asia and Developed Countries Growth Experience Real Growth Rate in Advanced Economies (5 years average) Real Growth Rate in the US (5 years average) Real Growth Rate in Emerging Asia (5 years average) Source PWT

27 Fast Growth in Emerging Asia Real GDP Growth in Emerging Asia Emerging Asia (share of Advanced Countries GDP in %) China (share of Advanced Countries GDP in %) Source: Maddison

28 An increase in private savings in Emerging Asia and a fall in private savings in Advanced Economies Savings in Emerging Asia % of GDP Private Savings in Developed Countries % of GDP Private Savings in Emerging Asia % of GDP Private Savings in the US % of GDP

29 An increase in private savings in Emerging Asia and a fall in private savings in Advanced Economies

30 Coeurdacier, Guibaud and Jin (2011) (preliminary) On the top of these facts show that current account mostly driven by savings (and particularly private savings) especially in the cross-section. Dispersion in savings accounts for 75% of the cross-section dispersion of current accounts (of which more than 50% on average due to private savings). Need a model where dispersion in savings rate across countries are key. Challenging since standard models predict exactly the opposite of what is observed (see above) Coeurdacier, Guibaud and Jin (2011) develops an OLG model with household credit constraints. Credit constraints heterogeneity across countries are key to reproduce the main stylized facts.

31 The Basic Model Basic intuition 3 generations: the young borrowers, the middle-aged workers and savers, the old retired. Key ingredient: borrowing constraints for the young; can only borrow up to a fraction of their discounted future wage income In autarky, in Asia where the constraint is tighter, aggregate savings are high and interest rate is low in the steady-state. Opposite in the rest of the world.

32 Basic intuition 1. Capital market integration If Asia opens up its capital account, capital flows from Asia to the rest of the World. As the interest rate falls, easier to borrow so savings fall a bit in the US. 2. Growth in Asia Suppose now that Asia grows much faster for a long time period, world interest rate falls even more as growth comes from the high saving country: this reduces further savings in the ROW while Asian savings will tend to rise (why?). Higher dispersion of savings across the world and larger imbalances. Key element: asymmetric response of private savings to changes in the world interest rates.

33 Set-up Two countries i = {H, F }. One good used for consumption and investment. Three generations: the young (y), the middle-aged (m), and the old (o). Agents work when middle-aged and consume in every period of their lives. The lifetime utility of an agent born at t in country i {H, F } is U i t = u(ci y,t ) + βu(ci m,t+1 ) + β2 u(c i o,t+2 ), u(c) = c1 1 σ 1 1 σ with c i γ,t denote the consumption in period t of an agent at state γ {y, m, o}

34 Set-up Budget constraints s i γ,t denote the savings in period t of generation γ {y, m}, wi t the wage in period t and Rt+1 i the gross interest rate earned between periods t and t + 1. An agent born in period t faces the following sequence of budget constraints: c i y,t + s i y,t = 0 c i m,t+1 + si m,t+1 = wi t+1 + Ri t+1 si y,t c i o,t+2 = Ri t+2 si m,t+1

35 Set-up Credit constraints Young agents cannot borrow more than a fraction θ i of the present value of their future labor income s i y,t θiwi t+1 Rt+1 i. For sake of simplicity in the presentation, we assume that θ i is such that the constraint is binding in both countries.

36 Savings function Binding constraint imply: s i y,t = θ iwi t+1 Rt+1 i, First-order condition for middle-aged: ( ) c i 1/σ ( ) m,t+1 = βr i t+2 c i 1/σ o,t+2 This gives the following savings function for the middle-aged: s i m,t+1 = β σ (R i t+2 )1 σ(1 θi )w i t+1 Remark: Log-utility case σ = 1 (constrained); constraint binds if θ i < (1 + β + β 2 ) 1, s i m,t+1 = β ( 1+β 1 θ i ) wt+1 i.

37 Savings function In the steady-state without growth, where Rt i = R and wi t = wi ( s i y + si m = θi R + 1 θ i ) 1 + β σ R 1 σ w i For low θ i, this is decreasing in R for σ < 1 (the standard case) as the income effect dominates. For high θ i, this is increasing with R since young can borrow more if R low (wealth effect of the young dominates).

38 Savings function (s i y + si m ) for θ i = 0.4 and θ i = Parameter values: w i = 1, σ = 1/2, β = ; x-axis: r = R 1/20 1

39 Production Output is produced using capital K i t and labor Li m,t : Yt i = ( A i tl i ) α ( ) m,t K i 1 α t = A i t L i m,t(kt) i 1 α k i t = Ki t A i t Li m,t denote the capital labor ratio (per efficiency unit) Assuming markets are competitive, wages and rental rate for capital are: w i t = αa i t ( k i t ) 1 α r i t = (1 α) ( k i t ) α The gross return on capital (net of depreciation δ) is: R i t = 1 δ + ri t = 1 δ + (1 α) ( k i t ) α

40 Capital market equilibrium in autarky The market clearing condition for capital in autarky is K i t+1 = Li y,t si y,t + Li m,t si m,t Using savings function and FOC of the firms, we get: k i t+1 = θiα ( k i t+1 R i t+1 ) 1 α + Ai t Li m,t A i t+1 Li m,t β σ (Rt+1 i )1 σ(1 θi )α ( kt i ) 1 α

41 Model dynamics in autarky This gives a law of motion for k of the form U i (k i t+1 ) = V i (k i t ): [ 1 + β σ (R i t+1 )1 σ] ( kt+1 i + θiα kt+1 i R i t+1 ) 1 α = 1 θi 1 + gt+1 i α ( kt i ) 1 α where g i t+1 = Ai t+1 Li m,t+1 A i t Li m,t 1 is the growth rate of effective labor in country i

42 Model dynamics in autarky Log-utility/full depreciation case. (σ = 1 and δ = 1) k i t+1 = β (1 + β) ( 1 + gt+1 i ) α(1 α)(1 θi ) ( ) k i 1 α 1 α + αθ t. i Steady state: A i L i m grows at the world growth rate g R i( θ i) + k i = β α(1 α) ( 1 θ i) 1 + β (1 + g) ( 1 α + αθ i) 1/α = k i( θ i) = r i = (1 α)(k i ) α = 1 + β α + αθi (1 + g)1 βα 1 θ i Tighter constraints imply a lower autarky interest rate

43 Model dynamics under capital market integration Capital market integration imposes that R H t = R F t = R t = 1 δ + (1 α) ( k i t ) α Capital-to-effective-labor ratios are equalized across countries kt H = kt F = k t. Capital markets equilibrium condition is Kt+1 i = ( L i y,t s i y,t + Li m,t si m,t i=h,f i=h,f ).

44 Model dynamics under capital market integration Binding constraints: s i y,t = θiαai t+1 k1 α t+1 ; s i m,t R = 1 t β σ R 1 σ t+1 (1 θ i )αa i t k1 α t The capital market equilibrium condition can be written as [ 1 + β σ Rt+1 1 σ ] [ ( k t+1 + α i ) λi k 1 α ] t+1θi t+1 R t+1 = α [ i ] λ i t+1 (1 θi ) 1+g i t+1 k 1 α t where λ i t j Ai t Li m,t A j t Lj m,t is country size relative to the world (in terms of effective labor). Again difference equation of the form U(k t+1 ) = V (k t )

45 Model dynamics under capital market integration Investment I i t K i t+1 (1 δ)ki t = A i t+1 Li m,t+1 ki t+1 (1 δ)ai tl i m,tk i t. Aggregate savings S i t L i y,ts i y,t + L i m,t[s i m,t (1 δ)s i y,t 1 ] Li o,t(1 δ)s i m,t 1 Current account and Net Foreign Assets CA i t = Si t Ii t. With the convention that NF A i t is measured at the beginning of period t, NF A i t = (1 δ) NF Ai t 1 + CAi t 1.

46 Model dynamics under capital market integration Log-utility/full depreciation case. (σ = 1 and δ = 1) k t+1 = β 1 + β α(1 α) [ i 1 α + α λ i t+1 1+g i t+1 (1 θ i ) ( ) λ i t+1 θi i ] k 1 α t. Steady state: growth rates constant and equal across countries, g i t = g: k = βα(1 α) (1 + β) (1 + g) 1 α + α i λ i (1 θ i ) ( i λ i θ i ) 1/α, R = (1 α)k α

47 Capital market integration experiment Log-utility/full depreciation case. (σ = 1 and δ = 1) World interest rate after integration R = i j λ i (1 θ i ) λ j (1 θ j ) Ri = i µ i R i where R i = 1 + β α + αθi (1 + g)1 βα 1 θ i = Autarky gross rate of interest and µ i = λi (1 θ i ) λ j (1 θ j ). Note that i j if λ i is high or θ i is low. µ i = 1. Country i has a greater weight µ i

48 Capital market integration experiment More generally, with δ = 1 and for any elasticity of intertemporal substitution σ, the steady-state world interest rate satisfies F (R) = i µ i F (R i ) with F (R) = R 1 + β σ R 1 σ Hence if θ H > θ F, R H > R > R F : capital market integration will generate a current account deficit in country H. Associated fall in R in country H will decrease savings in that country. Everything else equal, larger effects in the smaller country/the less constrained country

49 Capital market integration experiment Calibration: Country H (Developed countries) are at their steady-state g H = g = 2% Country F (Asia) is assumed to be capital scarce before opening ( kf initial kinitial H and less productive λ F initial = 0.2 = 2%) Capital market integration occurs after one period. θ F = 0.05; θ H = 0.35 Labour share α = 0.72 On a annual basis: δ = 10%, β = 0.99

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51 Emerging markets growth experiment (under integration) Let s now assume high productivity growth in country F (remember that θ F < θ H ) g = g H = 2% per year. We assume that country F starts from λ F initial = 0.2 and ends up at λf = 0.8 after 2 periods = 40 years (g F = 6.25% per year in the first period of fast growth and g F = 5% in the second period) Both countries starts from their steady-state values before the growth experience (g H = g F = 2%)

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53 Capital market integration and emerging markets growth experiment Timing: Asia is assumed to start growing fast one period before the capital market integration (g F = 6.25%) g F = 5% in the period at which capital markets open. Afterwards: g H = g F = g = 2% Other parameters values are identical to previous experiments.

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