Long-Run Price Elasticity of Trade and the Trade-Comovement Puzzle

Transcription

1 Long-Run Price Elasticity of Trade and the Trade-Comovement Puzzle Lukasz A. Drozd Sergey Kolbin Jaromir Nosal FRB Philadelphia Amazon Boston College The views expressed in this paper are those of the authors and do not necessarily reflect those of the Federal Reserve Bank of Philadelphia or the Federal Reserve System. June 2018

2 Motivation Countries with closer trade ties have more synchronized business cycles Frankel and Rose (1998), Clark and van Wincoop (2001), Calderson Chong and Stein (2002), Otto, Voss and Willard (2001), Bordo and Helbling (2003), Baxter and Kouparitsas (2005), Kose and Yi (2006) Inklaar, Jong-A-Pin and de Haan (2008), digiovanni and Levchenko (2010), Johnson (2014) Table: Updated Frankel and Rose (1998) regression. Dependent Variable: GDP correlation ij OLS OLS bottom 50% OLS top 50% trade ij (0.0154) (0.03) (0.025) 10th to 90th percentile corr up by.11, relative to median 0.52

3 Motivation Countries with closer trade ties have more synchronized business cycles Frankel and Rose (1998), Clark and van Wincoop (2001), Calderson Chong and Stein (2002), Otto, Voss and Willard (2001), Bordo and Helbling (2003), Baxter and Kouparitsas (2005), Kose and Yi (2006) Inklaar, Jong-A-Pin and de Haan (2008), digiovanni and Levchenko (2010), Johnson (2014) Puzzle for IRBC theory (Kose and Yi, 2006) productivity shocks, labor-leisure choice, some financial integration

4 Motivation Countries with closer trade ties have more synchronized business cycles Frankel and Rose (1998), Clark and van Wincoop (2001), Calderson Chong and Stein (2002), Otto, Voss and Willard (2001), Bordo and Helbling (2003), Baxter and Kouparitsas (2005), Kose and Yi (2006) Inklaar, Jong-A-Pin and de Haan (2008), digiovanni and Levchenko (2010), Johnson (2014) Puzzle for IRBC theory (Kose and Yi, 2006) productivity shocks, labor-leisure choice, some financial integration No compelling resolution to date (without changing shock structure)

5 This Paper

6 This Paper Analytically characterize the source of the puzzle in standard theory

7 This Paper Analytically characterize the source of the puzzle in standard theory Show puzzle attributed to counterfactual assumption: SRE=LRE

8 This Paper Analytically characterize the source of the puzzle in standard theory Show puzzle attributed to counterfactual assumption: SRE=LRE Propose resolution of the puzzle: modeling of low SRE & high LRE

9 This Paper Analytically characterize the source of the puzzle in standard theory Show puzzle attributed to counterfactual assumption: SRE=LRE Propose resolution of the puzzle: modeling of low SRE & high LRE Show it works quantitatively in an exercise a la Kose and Yi (2006)

10 Basic Idea Δ Trade Δ Co-movement

11 Basic Idea Δ Trade Δ Co-movement Δ Trade cost

12 Basic Idea Δ Trade Δ Co-movement Δ Trade cost

13 Basic Idea Δ Trade Δ Co-movement LRE Δ Trade cost

14 Basic Idea Δ Trade Δ Co-movement LRE Δ Trade cost

15 Basic Idea Δ Trade Demand complementarity Risk-sharing Δ Co-movement LRE Risk-sharing Δ Trade cost

16 Basic Idea Δ Trade Demand complementarity Risk-sharing Δ Co-movement LRE Risk-sharing Δ Trade cost Incomplete market setup close to implementing perfect risk-sharing

17 Basic Idea Δ Trade Demand complementarity Risk-sharing Δ Co-movement LRE Risk-sharing Δ Trade cost Incomplete market setup close to implementing perfect risk-sharing Terms of trade movements generate risk-sharing even under autarky

18 Roadmap

19 Roadmap Literature / contribution Theory: Puzzle and its resolution analyze forces behind the puzzle and link them to modeling assumptions of standard theory Quantitative analysis show modeling trade elasticity has quantitatively significant effects

20 Related Literature 1. Empirical relation between trade and business cycle comovement - Frankel and Rose (1998), Clark and van Wincoop (2001), Calderson Chong and Stein (2002), Otto, Voss and Willard (2001), Bordo and Helbling (2003), Baxter and Kouparitsas (2005), Kose and Yi (2006), Inklaar, Jong-A-Pin and de Haan (2008), digiovanni and Levchenko (2010) 2. Trade-comovement puzzle and its resolution - Kose and Yi (2006) - trade-comovement puzzle - Liao and Santacrue (2015), Johnson (2014): TFP comovement correlated with trade, Johnson shows that given sectoral correlations it is insufficient to resolve the puzzle - de Soyres (2017), digiovanni and Levchenko (2010): Trade-linkages that strengthen complementarity

21 Theory Mechanisms Underlying Trade-Comovement Puzzle

22 Setup Two symmetric countries (home/foreign) Country-specific goods: G(d, f) = ( 1 ρ 1 2 (d/2) ρ + 1 ρ 1 ρ 2 (f/2) ρ ) ρ 1 Iceberg trade cost: d + d + τd = y f + f + τf = y Quasi-linear labor-leisure choice: u(d, f, l) = log(g(d, f)) l Productivity shocks: y = Al y = A l Complete markets

23 Setup Asset UU cc = log(cc) ll UU cc = log c ll trade GG(dd, ff) GG(ff, dd) ττ yy = AAAA yy = AA ll DOMESTIC COUNTRY FOREIGN COUNTRY

24 Household problem Representative household solves: t s t β t {u(d(s t ), f(s t ), l(s t ))} subject to d(s t ) + p(s t )f(s t )(1 + τ) + Q(s t+1 )B(s t+1 ) = B(s t ) + w(s t )l(s t ), s t+1 where good d is the numéraire (globally); s t is history of shocks.

25 Household problem Representative household solves: t s t β t {u(d(s t ), f(s t ), l(s t ))} subject to d(s t ) + p(s t )f(s t )(1 + τ) + Q(s t+1 )B(s t+1 ) = B(s t ) + w(s t )l(s t ), s t+1 where good d is the numéraire (globally); s t is history of shocks. Foreign household budget constraint: p(s t )f (s t )+d (s t )(1+τ)+ s t+1 Q(s t+1 )B (s t+1 ) = B (s t )+p(s t )w (s t )l (s t ).

26 Firm problem Wages given by marginal product: w(s t ) = A(s t ) w (s t ) = A (s t )

27 Feasibility and Market Clearing Production and trade in goods d(s t ) + d + τd (s t ) = y(s t ) = A(s t )l(s t ) f(s t ) + f (s t ) + τf (s t ) = y (s t ) = A (s t )l (s t ) Asset trade B(s t ) + B (s t ) = 0 Competitive equilibrium defined as usual. Welfare theorems apply.

28 Measurement: Trade Steady-state level of trade x = Imports GDP = p f(1 + τ) d + p f(1 + τ)

29 Measurement: Trade-Comovement Link Business-cycle comovement: spillover S S = d log y d log A impact of foreign productivity on domestic GDP monotonic with correlation for one parameterization of the model

30 Measurement: Trade-Comovement Link Business-cycle comovement: spillover S S = d log y d log A impact of foreign productivity on domestic GDP monotonic with correlation for one parameterization of the model Trade-comovement link: L L = ds d x = ds dτ( x) dτ d x comparison across parameterizations of the model if we change τ to induce different level of steady state trade x, how does spillover change 1 we know that τ( x) = ( 1) ρ x

31 Trade Elasticity Short-run trade elasticity (business cycle response to terms of trade p) SRE = d log(d/f) d log p Long-run trade elasticity (steady-state response to trade cost τ) d log d/f LRE = d log(1 + τ) Lemma SRE = LRE.

32 Assumptions Assumption (Gravity) ρ > 1 so that dτ( x)/d x < 0. Assumption (Home-bias) 0 x < 1/2.

33 Mechanisms Underlying Trade-Comovement Puzzle Proposition To a first order approximation, L < 0.

34 Mechanisms Underlying Trade-Comovement Puzzle Proposition To a first order approximation, L < 0. Model s dynamics around SS can be represented as follows: ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â) where R(s t ) = B(s t ) Q(s t+1 )B(s t+1 ) + (1 p(s t ))(1 + τ( x))f(s t ) s t+1 s t

35 Mechanisms Underlying Trade-Comovement Puzzle Proposition To a first order approximation, L < 0. Model s dynamics around SS can be represented as follows: ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â) where d + f(1 + τ( x)) = wl + R d (1 + τ( x)) + f = w l R

36 Mechanisms Underlying Trade-Comovement Puzzle Proposition To a first order approximation, L < 0. Model s dynamics around SS can be represented as follows: where ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â) u(d(s t ), f(s t ), l(s t )) (1 + τ( x)) = u(f (s t ), d (s t ), l (s t )) d(s t ) d (s t )

37 Mechanisms Underlying Trade-Comovement Puzzle Proposition To a first order approximation, L < 0. Model s dynamics around SS can be represented as follows: ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â) where 1 c(s t ) G d(s t )(1 + τ( x)) = 1 c (s t ) G d(s t )

38 Mechanisms Underlying Trade-Comovement Puzzle Proposition To a first order approximation, L < 0. Model s dynamics around SS can be represented as follows: ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â) where w(s t )(1 + τ( x)) = (1 + τ( x))p(s t )w (s t ))

39 Mechanisms Underlying Trade-Comovement Puzzle Proposition To a first order approximation, L < 0. Model s dynamics around SS can be represented as follows: ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â) where p(s t ) = w(st ) w (s t ) = A(st ) A (s t )

40 Mechanisms Underlying Trade-Comovement Puzzle Proposition To a first order approximation, L < 0. Model s dynamics around SS can be represented as follows: (risk-sharing) ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â) where R(s t ) = B(s t ) Q(s t+1 )B(s t+1 ) + (1 p(s t ))(1 + τ( x))f(s t ) s t+1 s t

41 Mechanisms Underlying Trade-Comovement Puzzle Proposition To a first order approximation, L < 0. Model s dynamics around SS can be represented as follows: (complementarity) ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â) where R(s t ) = B(s t ) Q(s t+1 )B(s t+1 ) + (1 p(s t ))(1 + τ( x))f(s t ) s t+1 s t

42 Decomposition of Trade-Comovement Relation in Model Implied decomposition of trade-comovement link: L = L C + L R L C = L R = [χµ] τ [η(π + θµ)] τ dτ( x) d x [ SC = η(π + θµ) S R = χµ dτ( x) d x ]

43 Complementarity Channel Lemma L C = 1 [S C = η(π + θµ) = x] since η = x and π + θµ = 1.

44 Complementarity Channel Lemma L C = 1 [S C = η(π + θµ) = x] since η = x and π + θµ = 1. Recall the decomposition: Ŝ C effect of p on l + effect of A on p ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â)

45 Complementarity Channel Lemma L C = 1 [S C = η(π + θµ) = x] since η = x and π + θµ = 1. Recall the decomposition: Ŝ C effect of p on l + effect of A on p (CP I = (1 x) + xp) ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â)

46 Complementarity Channel Lemma L C = 1 [S C = η(π + θµ) = x] since η = x and π + θµ = 1. Recall the decomposition: Ŝ C effect of p on l + effect of A on p (CP I = (1 x) + xp) (risk-sharing & quasi-linear utility) ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â)

47 Complementarity Channel Lemma L C = 1 [S C = η(π + θµ) = x] since η = x and π + θµ = 1. Recall the decomposition: Ŝ C effect of p on l + effect of A on p (CP I = (1 x) + xp) (risk-sharing & quasi-linear utility) ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â) Trade increases comovement 1-to-1 L C = 1.

48 Risk-Sharing Channel Lemma L R < 1 [S R = χµ] where χ = 1 and µ = x((ρ 1)(1 2 x) + ρ). Recall the decomposition: Ŝ R effect of R on l + effect of A on R ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â)

49 Risk-Sharing Channel Lemma L R < 1 [S R = χµ] where χ = 1 and µ = x((ρ 1)(1 2 x) + ρ). Recall the decomposition: Ŝ R effect of R on l + effect of A on R (income effect of R) ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â)

50 Risk-Sharing Channel Lemma L R < 1 [S R = χµ] where χ = 1 and µ = x((ρ 1)(1 2 x) + ρ). Recall the decomposition: Ŝ R effect of R on l + effect of A on R (income effect of R) (optimal risk-sharing transfer) ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â)

51 Risk-Sharing Channel Lemma L R < 1 [S R = χµ] where χ = 1 and µ = x((ρ 1)(1 2 x) + ρ). Recall the decomposition: Ŝ R effect of R on l + effect of A on R (income effect of R) (optimal risk-sharing transfer) ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â) Trade & trade cost lowers comovement more than 1-to-1 L R < 1.

52 Risk-Sharing Channel & Trade Elasticity ρ Figure: L R = d(χµ(τ)) dτ dτ τ( x) dx τ( x) as a function of SRE generated by φ vs. ρ. d[χμ(τ)]/dτ ρ d[τ(x)]/dx ρ x=10% L R 0-5 L> ρ

53 Theory Long-run Trade Elasticity and Trade-Comovement Puzzle

54 Setup Convex adjustment cost of adjusting import share d/f u(d, f, l) = log(g(d, f)) Φ(d, f) l where ( f Φ(d, f) = φ d d f 1 ) 2

55 Trade Elasticity Short-run trade elasticity (business cycle response to terms of trade p) SRE = d log(d/f) d log p Long-run trade elasticity (steady-state response to trade cost τ) d log d/f LRE = d log(1 + τ) Lemma LRE is independent of φ and SRE is strictly decreasing in φ.

56 LR Trade Elasticity and Trade-Comovement Puzzle Proposition To a first order approximation, L > 0 for sufficiently high φ.

57 LR Trade Elasticity and Trade-Comovement Puzzle Proposition To a first order approximation, L > 0 for sufficiently high φ. Recall: ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â) where R(s t ) = B(s t ) Q(s t+1 )B(s t+1 ) + (1 p(s t ))(1 + τ( x))f(s t ) s t+1 s t

58 Complementarity Channel Lemma L C = 1 [S C = η(π + θµ) = x] since η = x and π + θµ = 1.

59 Complementarity Channel Is the Same Lemma L C = 1 [S C = η(π + θµ) = x] since η = x and π + θµ = 1. Recall decomposition of Ŝ C effect of p on l + effect of A on p (CP I (1 x) + xp) (risk-sharing & quasi-linear utility)

60 Risk-sharing Channel (φ ) Lemma L R (φ) x > 1 [S R = χµ] where χ = 1 and µ x(2 x 1). Recall decomposition of Ŝ R effect of R on l + effect of A on R ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â)

61 Risk-sharing Channel (φ ) Lemma L R (φ) x > 1 [S R = χµ] where χ = 1 and µ x(2 x 1). Recall decomposition of Ŝ R effect of R on l + effect of A on R (income effect of R) ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â)

62 Risk-sharing Channel (φ ) Lemma L R (φ) x > 1 [S R = χµ] where χ = 1 and µ x(2 x 1). Recall decomposition of Ŝ R effect of R on l + effect of A on R (income effect of R) (optimal risk-sharing transfer size) ŷ(s t ) = αâ + ηˆp(st ) + χr(s t ) ˆp(s t ) = π(â Â) + θr(st ) R(s t ) = µ(â Â)

63 Decomposition of Trade-Comovement Relation Decomposition of Trade-comovement link L = L C + L R : L C = L R = [χµ] τ [η(π + θµ)] τ dτ( x) d x [ SC = η(π + θµ) S R = χµ dτ( x) d x ]

64 Risk-Sharing Channel & Trade Elasticity ρ Figure: L R = d(χµ(τ)) dτ dτ τ( x) dx τ( x) as a function of SRE generated by φ vs. ρ. d[χμ(τ)]/dτ d[χμ(τ)]/dτ ρ x=10% /ϕ d[τ(x)]/dx ρ x=10% /ϕ x=5% L R 0 L> ρ L>0 d[τ(x)]/dx L R /ϕ

65 Summary Δ Trade Demand complementarity Risk-sharing Δ Co-movement LRE Risk-sharing Δ Trade cost

66 Robustness: Nonseparable Utility Function u(c, l) = (cζ (L l) 1 ζ ) 1 σ 1 σ 10 (σ=2, ζ=1/3) 10 (σ=5, ζ=1/3) ρ ρ x x Figure: The negative region of the trade-comovement link L for nonseparable CRRA utility function, σ = 2, ζ = 1/3 (left panel) and σ = 5, ζ = 1/3 (right panel).

67 Quantitative Model Are the qualitative effects strong quantitatively?

68 Quantitative Model Are the qualitative effects strong quantitatively? Extend Backus, Kehoe and Kydland (1995): extended to a 3 country system (H,F,ROW) infinite time horizon the same adjustment friction other standard business cycle features (capital, convex adjustment costs etc...)

69 Quantitative Model Key parameters: elasticity ρ, adjustment friction φ to match long-run and short-run elasticities as in Drozd & Nosal (2012)

70 Quantitative Model Key parameters: elasticity ρ, adjustment friction φ to match long-run and short-run elasticities as in Drozd & Nosal (2012) Compare comovement within country pair between median an 90% percentile of trade intensity: 0.85% to 3.8%, controlling openness data-implied slope: model-implied slope: % of the data relationship

71 Quantitative Model Key parameters: elasticity ρ, adjustment friction φ to match long-run and short-run elasticities as in Drozd & Nosal (2012) Compare comovement within country pair between median an 90% percentile of trade intensity: 0.85% to 3.8%, controlling openness data-implied slope: model-implied slope: % of the data relationship frictionless: 0 financial autarky: negative

72 Quantitative Model Key parameters: elasticity ρ, adjustment friction φ to match long-run and short-run elasticities as in Drozd & Nosal (2012) Compare comovement within country pair between median an 90% percentile of trade intensity: 0.85% to 3.8%, controlling openness data-implied slope: model-implied slope: % of the data relationship frictionless: 0 financial autarky: negative Improves business cycle statistics

73 Conclusions Trade-comovement puzzle intimately related standard model s counterfactual assumption of equal short- and long-run trade elasticity Modeling high long-run and low short-run trade elasticity promising in resolving trade-comovement puzzle More broadly, trade elasticity relevant for shock transmission in a large class of models