New Terrain in International Trade

Transcription

1 New Terrain in International Trade Samuel Kortum, Yale University Society for Economic Dynamics, Warsaw 27 June 2015

2 Map of the Terrain Starting Point: Ricardian Trade: Multiple countries, with Jonathan Eaton (2002) Counterfactuals, with Dekle and Eaton (2007, 2008) New Terrain: Intranational Trade and Labor Mobility New Terrain: Dynamics and Global Accounting

3 Navigational Tools Focus on two ideas/tools we ve found useful: 1. Extreme-value distributions to model producers in many countries 2. Hat algebra to calibrate to data

4 Navigational Tools Focus on two ideas/tools we ve found useful: 1. Extreme-value distributions to model producers in many countries 2. Hat algebra to calibrate to data These ideas also prove useful navigating new terrain, as I ll show

5 Navigational Tools Focus on two ideas/tools we ve found useful: 1. Extreme-value distributions to model producers in many countries 2. Hat algebra to calibrate to data These ideas also prove useful navigating new terrain, as I ll show As in the world of Lucas (2009), they didn t come out of nowhere: 1. Modeling idea: antecedent in McFadden and discrete choice models 2. Calibration idea: antecedent in growth accounting and CGE modeling

6 Recent Contributions Bridging models: Arkolakis, Costinot and Rodríguez-Clare (ACR 2012) Estimating the trade elasticity: Simonovska and Waugh (2014) Quantitative analyis of NAFTA: Caliendo and Parro (2015) Quantitative analysis of trade wars and policy: Ossa (2014) Overview, coining exact hat algebra : Costinot and Rodríguez-Clare (2014)

7 Simplest Ricardian Setting Endowments: L i, for countries i = 1,..., N Preferences: tradables share α, symmetric over j [0, 1] Technology: effi ciency z i (j) (effi ciency in services a i will disappear) Labor perfectly mobile across sectors Iceberg trade costs (shipping to n from i) d ni 1 and d ii = 1

8 I. Modeling Idea Summarize effi ciencies with Fréchet distribution: Pr [z i (j) z] = e T iz θ Most effi cient producer of j has same distribution: T = k T k

9 I. Modeling Idea Summarize effi ciencies with Fréchet distribution: Pr [z i (j) z] = e T iz θ Most effi cient producer of j has same distribution: T = k T k Probability low-cost producer for n is from country i: π ni = T i (w i d ni ) θ k T k (w k d nk ) θ

10 II. Calibration Idea Data on bilateral trade shares (of n s tradable spending imported from i): X ni αx n = π ni = T i (w i d ni ) θ Nk=1 T k (w k d nk ) θ

11 II. Calibration Idea Data on bilateral trade shares (of n s tradable spending imported from i): X ni αx n = π ni = T i (w i d ni ) θ Nk=1 T k (w k d nk ) θ Use them to calibrate T i s and d ni s to calculate change in trade shares if wages are w k instead (ŵ k = w k /w k):

12 II. Calibration Idea Data on bilateral trade shares (of n s tradable spending imported from i): X ni αx n = π ni = T i (w i d ni ) θ Nk=1 T k (w k d nk ) θ Use them to calibrate T i s and d ni s to calculate change in trade shares if wages are w k instead (ŵ k = w k /w k): π ni = T i (w i ŵ i d ni ) θ Nk=1 T k (w k ŵ k d nk ) θ = π ni (ŵ i ) θ Nk=1 π nk (ŵ k ) θ

13 An ACR Detour Given wages w k, home share is: ( ) θ X ii wi = π ii = T i αx i p i /γ Why not invert it? (don t forget equation 15 in EK!) w i p i = γ ( Ti π ii ) 1/θ Real wage relative to autarky: W W A = (π ii) α/θ

14 Table 1: Welfare Relative to Autarky Basic Multiple Sectors Country Model & Intermediates Poland USA Calculations based on Costinot and Rodriguez- Clare (2014)

15 General Equilibrium Income: Y i = w i L i Trade imbalances: X n = Y n + D n Market clearing: Y i (1 α) (Y i + D i ) = n π ni α (Y n + D n ) If α = 1 and d ni = 1 then D s drop out, otherwise affect specialization

16 Counterfactual Trade Balance Given data on Y i and π ni, moving from our world to a world of D = 0 implies wage changes satisfying: Y i = ŵ iy i = n π niŵny n π ni = π ni (ŵ i ) θ Nk=1 π nk (ŵ k ) θ

17 Table 2: Rebalancing Counterfactual CA deficit Counterfactual change from 2004 base (% of GDP) change in GDP Real GDP 2004 mobile immobile theta=1 theta=1 Germany Greece USA From Dekle, Eaton, and Kortum (2008)

18 Issues Raised by Counterfactual Modeling labor immobility Modeling trade deficits Modeling trade elasticities (short and long run) Modeling slow wage adjustment Explore first two issues in new terrain

19 New Terrain: Intranational Trade

20 Burst of Activity Allen and Arkolakis (2014); Ahlfedlt, Redding, Sturm, and Wolf (2015) Ramondo, Rodríguez-Clare, and Saborio (2014) Redding (2015); Monte, Redding, and Rossi-Hansberg (2015) Tombe and Zhu (2015); Fajgelbaum, Suárez-Serrato, and Zidar (2015) Follow: Caliendo, Dvorkin, and Parro (CDP 2015)

21 New Elements Ricardian model: but locations i within and between countries Cost of moving from n to i is τ ni (can be prohibitive) Dynamic discrete choice as in Artuç and McLaren (2010) Amenity draws a i,t (ω) distributed Fréchet (ɛ)

22 CDP Model Let V n,t be the value of residing in location n at date t: [ { } ] V n,t = ln(w n,t /p n,t ) + E max ρvi,t+1 + ln a i,t+1 (ω) ln τ ni i Migration shares (of individuals in n relocating to i), letting u i,t = e V i,t: (( ui,t+1 ) ρ /τ ni ) ɛ µ ni,t+1 = (( ) ρ ) ɛ k uk,t+1 /τ nk State variables L i,t evolve according to these migration shares

23 Counterfactuals Counterfactual: dynamic response to a new path, such as { ˆT i,t+1 } ( hat now means temporal change, ˆx t+1 = x t+1 /x t ) Condition on data Y i,t, L i,t, π ni,t, and µ ni,t for initial period only leaving only three parameters! θ, ɛ, and ρ Perfect foresight: initial û n,t s get you on path to the steady state of...

24 (ûn,t ) ɛ = i µ ni,t ( ˆT i,t+1 /ˆπ ii,t+1 ) ɛ/θ (ûi,t+1 ) ρɛ µ ni,t+1 = µ ni,t (ûi,t+1 ) ρɛ k µ nk,t (ûk,t+1 ) ρɛ L n,t+1 = i µ in,t+1 L i,t π ni,t+1 = π ni,t ˆT i,t+1 (ŵi,t+1 ) θ Nk=1 π nk,t ˆT k,t+1 (ŵk,t+1 ) θ, ŵ i,t+1 ˆL i,t+1 Y i,t = n π ni,t+1 ŵ n,t+1 ˆL n,t+1 Y n,t,

25 New Terrain: Dynamics What happend to world trade?...

26 Log Index (2008Q3=0) Data 08Q3 09Q Q1

27 Log Index (2008Q3=0) Data 08Q3 09Q Q1

28 Log Index (2008Q3=0) Data 08Q3 09Q Q1

29 Contributions Alessandria, Kaboski, and Midrigan (2010, 2011) Fitzgerald (2012) Mutreja, Ravikumar, and Sposi (2014) Kehoe and Ruhl (2014) Follow: Eaton, Kortum, Neiman, and Romalis (EKNR 2015)

30 New Elements Ricardian trade, country as unit of observation, discrete time Factors of production: L i fixed (share β) and K i,t evolving Tradeable goods invested to build capital (effi ciency of invest χ i,t ): K i,t+1 = χ i,t ( Ii,t ) η ( Ki,t ) 1 η (1 δ)ki,t Nontradable goods consumed to max log preferences (shocks φ i,t ) Solved by a global social planner (weights ω i ), complete markets

31 EKNR Relationships Consumption spending: X C i,t = ω iφ i,t Investment spending: X I i,t = p i,ti i,t Value of GDP: Y i,t = X C i,t + n π ni,t X I n,t Payments to labor: w i,t L i = βy i,t Payments to capital: r i,t K i,t = (1 β)y i,t Bilateral trade equations unchanged...

32 Investment Euler equation: cost of building one more unit of capital p i,t ηχ i,t ( Ii,t K i,t ) 1 η equals benefit ρ r i,t+1 + (1 η)p i,t+1i i,t+1 ηk i,t+1 + (1 δ)p i,t+1 ηχ i,t+1 ( ) 1 η Ii,t+1 K i,t+1 Trade deficit: D i,t = X I i,t n π ni,t X I n,t = X C i,t + XI i,t Y i,t

33 Computing a Perfect Foresight Path Shocks paths: { ˆdni,t+1 }, { ˆT i,t+1 }, {ˆφi,t+1 }, {ˆχi,t+1 }, eventually 1 Condition on initial data Y i,t, X C i,t, XI i,t, and π ni,t Initial ˆK i,t+1 s get you on perfect-foresight path to steady state of: change in consumption spending: ˆX C i,t = ˆφi,t price change equation: ˆp i,t+1 = ŵ β i,t+1ˆr1 β i,t+1 (ˆπii,t+1 / ˆT i,t+1 ) 1/θ...

34 trade share evolution: π ni,t+1 = π ni,t ˆT i,t+1 (ŵβ Nk=1 π nk,t ˆT k,t+1 (ŵβ i,t+1ˆr1 β i,t+1 ˆd ni,t+1 ) θ k,t+1ˆr1 β k,t+1 ˆd nk,t+1 ) θ GDP changes, wage changes, and rental rate changes Euler equation to solve for change in investment spending Update change in capital with ˆK i,t+2 (1 δ) = ˆχ i,t+1 ˆX I i,t+1 ˆp i,t+1 ˆK i,t+1 η ( ˆK i,t+1 (1 δ) )

35 The Algorithm Starting from 2012:Q4, shocks fixed thereafter, solve for ˆK s Work backwards using data to form paths for the ˆK i,t+1 Using capital paths (in changes) back out shocks during data period Intertemporal preference shock is easy: ˆφi,t = ˆX C i,t Other three are a bit deeper!

36 Backing out Shocks Trade Frictions: ) (ˆπni,t+1 ˆpn,t+1 ˆd ni,t+1 = ˆπ ii,t+1 ˆp i,t+1 Productivity : ˆT i,t+1 = ˆπ ii,t+1 ( (ŵi,t+1 ) β (ˆri,t+1 ) 1 β /ˆpi,t+1 ) θ Effi ciency of investment: ˆχ i,t+1 = ˆX I i,t+1 ˆp i,t+1 ˆK i,t+1 η ˆK i,t+2 (1 δ) ˆK i,t+1 (1 δ)

37 Counterfactuals for Accounting Perfect foresight path, given the shocks we back out, reproduces the data Assess contributions: compute with only a single set of shocks Breaks the Euler equation at the date when new future becomes apparent If a shock can explain the data on its own, its important Global analog of Chari, Kehoe, and McGratten (2007)

38 Log Index (2008Q3=0) Data 08Q3 09Q Q1

39 Log Index (2008Q3=0) Data 08Q3 09Q2 11Q1 Productivity

40 Log Index (2008Q3=0) Data 08Q3 09Q2 11Q1 Trade Frictions Productivity

41 Log Index (2008Q3=0) Data 08Q3 09Q2 11Q1 Trade Frictions Productivity Demand

42 Log Index (2008Q3=0) Data 08Q3 09Q2 11Q1 Trade Frictions Productivity Demand Investment Efficiency in Durables

43 The Cross-Country Dimension

44 Aggregate Demand Shocks MEX POL Changes in Counterfactual JPN ROU CAN SWE IND DNK FRA CZE FIN ESP ROW DEU KOR AUT GRC ITA USA CHN GBR Changes in Trade/GDP in Data

45 Investment Efficiency in Durables Shocks Changes in Counterfactual JPN IND CHN AUT CAN ROW KOR DEUGRC FIN ITA USA FRADNK SWE ESP CZE ROU GBR MEX POL Changes in Trade/GDP in Data

46 All Demand and Investment Efficiency Shocks Changes in Counterfactual JPN IND SWE CAN KOR CZE AUT FIN DEU ROW DNK FRA GRC ITA CHN USA ESP ROU GBR MEX POL Changes in Trade/GDP in Data

47 Conclusion