Dynamics of Firms and Trade in General Equilibrium. Robert Dekle, Hyeok Jeong and Nobuhiro Kiyotaki USC, Seoul National University and Princeton

Transcription

1 Dynamics of Firms and Trade in General Equilibrium Robert Dekle, Hyeok Jeong and Nobuhiro Kiyotaki USC, Seoul National University and Princeton

2 Figure a. Aggregate exchange rate disconnect (levels) 28.5 Thousand million yen, constant prices (log scale) Real Effective Exchange Rate index (log scale) Aggregate Exports Aggregate Imports

3 Figure b. Aggregate exchange rate disconnect (HP filtered).25.2 Aggregate Exports Aggregate Imports Real Ef. Exchange Rate.5 Log-deviation from HP trend Corr(Exp, REER) =.47 (.) Corr(Imp, REER) =.9 (.6)

4 Table. Exports regression, Kaigin panel () (2) (3) (4) (5) (6) (7) All High Low Big Small Big Small Sample Profitability Profitability Employment Employment Sales Sales log RER (.49)*** (.)** (.54)*** (.6)*** (.68)*** (.63)*** (.65)*** log Y* (.55)*** (.25)** (.6)*** (.72)*** (.76)*** (.73)*** (.73)*** log Agg TFP (.8)*** (.8)*** -.89 (.4)*** (.)*** (.5)*** (.6)*** log Firm TFP (.79)*** (.69)*** (.89)*** (.2)*** (.)*** (.)*** (.2)*** Cons (.596)*** (3.6)** (.77)*** (2.83)*** (2.9)** -2.9 (2.7)*** F-stat Adj. R-sq # Obs. 9,997 2,34 7,963 3,549 6,448 3,89 6,98 Size differentiation is done by 75th percentile. * p <.; ** p <.5; *** p <..

5 In Kaigin data, the average total sales of exporters is twice as large as non-exporters! Consistent with Melitz (23) But Correlation between rm size and export dummy is weak :9 Correlation between rm size and export share of exporters is even weaker :3 Many rms have negative pro t, 8% in total and % among exporters! We consider heterogeneous productivity of each product and each rm produces multiple products

6 4 (%) Figure. Decomposition of shipment change continuing products increase continuing products decrease extensive margins entry extensive margins exit intensive margins add intensive margins drop n.e.c total change

7 Small Open Economy Model A continuum of home rm h 2 H t : Firm h produces I ht number of di erentiated products for home and export market q H hit = a hit Z t 2 6B 4@ l H hit L l F hit L C B L C B m H hit L m F hit C A L ; for i = ; 2; ::; I ht L qhit F C = a hit Z t A 7 5 ; for i = ; 2; ::I ht L L Home output for home and export markets are produced as Q H t = Q F t = 2 Z Z 6 4 h2h t h2h t I ht X i= I ht X i= q H hit q F hit 3 7 C A dh C A dh

8 A new entrant who pays a sunk cost Et at date t draws an opportunity of producing a new products from date t+ with probability E. The productivity of the new product is distributed as Prob (a hit a) = F (a) = a ; for a 2 [; ) where > and > : A rm must pay the xed maintenance cost for each product in order to produce and maintain its productivity a hit+ = 8 >< >: a hit ; with probability ; with probability In addition, each maintained product yields an opportunity to produce another new product with probability < with the same Pareto distribution.

9 Each rm can produce many products. Each product multiplies and dies like "amoeba." Home nal goods market Q H t = C t + Et N Et + N t N Et is measure of entering rms, N t is measure of di erentiated products maintained, and Et = N Et N E A ; > ()

10 The representative household supplies labor L t ; consumes nal goods C t and holds home and foreign real bonds D t and Dt to maximize its expected utility U = E X t= t subject to the budget constraint L += B C t + = + t ln Dt C t + E N Et + N t + D t + t D t = w Lt L t + t + R t D t + t R t D t C A t : utility (liquidity) shock to foreign bond holding

11 Foreigners do not hold home bond! D t = Foreign bond holding of home household where M H t D t = R t D t + p F t Q F t M H t is total import of intermediate input Foreign aggregate demand for home exports are given by where Y t Q F t = (p F t ) ' Y t is an exogenous foreign demand

12 Competitive Equilibrium All rms choose to pay the xed maintenance cost N t+ = ( + ) N t + E N Et (2) Price of di erentiated goods is a mark-up over the unit cost and the price index of home nal goods at home is = p H t = 2 Z 6 4 h2h t I ht X i= p H hit C A dh = - w t an t Z t (3) w t = (w Lt ) L L t ; a Z a df (a) + Only products with higher than a t productivity is exported. a t = ( + ) az t N t ' t Y t (-)+(+-)(-') A (4)

13 The input composite market equilibrium is X t = L t L L C B M H t L L C A = L ( C t ) = Xt H a t Free entry condition is w L+ t ( L)(+ ) t C A L (5) N t (6) Et = E E t ( t;t+ V t+ ) : free entry (7) where the value function of the average product V t = t + ( + )E t ( t;t+ V t+ ) (8) where t;t+ = C t =C t+ and t = w t X t ( )N t a t (9)

14 The nal goods market clearing implies C t + Et N Et + N t = an t Z t X H t () Net foreign assets evolve as t Dt = t Rt Dt + a (+-)(-') t ' t Yt ( L )w t X t () Home demand for home bond and foreign bond imply = R t E t ( t;t+ ) (2) t R t E t ( t;t+ t+ ) = t C t D t (3) ( 3) determine w t ; a t ; X t ; X H t ; C t ; t ; R t ; V t ; t, Et ; N Et, N t+ and D t as a function of the state variables M t = (N t ; D t ; Z t; t,y t ; R t )

15 Table 2a. Baseline parameterization β Discount factor.92 θ Elasticity of substitution between products 4.9 ψ Frisch elasticity of labor supply 6.2 ψ Labor disutility 2.84 γ L Labor share.85 α Productivity distribution shape parameter 3.64 ϕ Elasticity of foreign demand.75 φ Export cost 3.4 κ Maintenance cost 6.57 κ E Entry cost η Elasticity of entry cost. δ Probability of losing product.2 λ Probability of drawing new product for incumbent.49 λ E Probability of producing new product for entrant.4 σ Std. dev. of noise for sales.67 Z Steady state aggregate productivity Y Steady state foreign demand 6 G/C Steady state govt. expenditure / cons..28 ξ Steady state liquidity shock. R Steady state foreign interest rate.5

16 Table 2b. Steady state moments (aggregate and cross-sectional) Data Model C/Y ɛd /Y.2.9 Exp/Y.2.2 N E /N..5 Mean log Rev SD log Rev Mean log Dom SD log Dom.4.84 Mean log Exp SD log Exp Mean P R.3.5 SD P R.6.5 #Exp/N.39. Corr P R, log Rev.7.7 Corr ES, log Rev.7.32

17 Figure 3a. Cross sectional distribution of total sales by export status: Kaigin data Density Exporter Non exporter Total sales (log)

18 Figure 3b. Cross sectional distribution of total sales by export status: Model Density Total sales (log)

19 Table 3a. Calibration of stochastic processes Efficient Subjective Standard deviation σ Z (%) σ Y (%) σ G (%).83.6 σ ξ (%) Autocorrelation ρ Z ρ Y ρ G ρ ξ.95.27

20 Table 3b. Sample and simulated moments Data Efficient Subjective Standard deviation SD GDP (%) (.) SD Gov / SD GDP (.) SD Inv / SD GDP (.3) SD Exp / SD GDP (.7) SD RER (%) (.3) Autocorrelation AC() GDP (.5) AC() Gov (.7) AC() Inv (.3) AC() Exp (.8) AC() RER (.6) Correlation with GDP Corr Gov, GDP (.9) Corr Inv, GDP (.) Corr Exp, GDP (.9) Corr RER, GDP (.6) Data and output from the model are HP filtered. HAC robust standard errors are shown in parenthesis.

21 Figure 4. Impulse response to TFP shock Z. GDP. Consumption (C) x 3 Labor (L) Export and import value (ε P F Q F, ε M) Exports Imports α x Extensive margin (a ) exp Real exchange rate (ε) x 3 Net foreign assets (D * ) x 3 Intangible capital (N) Shocks Z Y * G ξ * 5 5 2

22 Figure 5. Impulse response to foreign demand shock Y 2 x GDP x Consumption (C) x 4 Labor (L) x 3Export and import value (ε P F Q F, ε M) Exports Imports α 8 x Extensive margin (a ) exp Real exchange rate (ε) Net foreign assets (D * ).5 x 3 Intangible capital (N) Shocks Z Y * G ξ *

23 Figure 7. Impulse response to liquidity shock ξ 2 x 3 GDP x 3 Consumption (C) x 3 Labor (L) Export and import value (ε P F Q F, ε M) Exports Imports.3.2 Extensive margin (a exp ) α.2 Real exchange rate (ε) Net foreign assets (D * ) x 3 Intangible capital (N) Shocks Z Y * G ξ * 5 5 2

24 Table 6. Panel regression on simulated data: Profitability interaction Data Model () (2) (3) (4) log RER (.65)*** (-7.4,.7) (-.2, 3.8) (., 3.84) (.8, 2.2) log RER PR (.954)* (-.3, -.23) (-4.,.56) (-.39,.27) log Y* (.55)*** (-7.9, 23.33) (-2.6, 6.6) (-.88, 6.69) (.9, 3.29) log Y* PR (.55)** (-5.72,.25) (-2.3,.43) log Agg TFP (.3)*** (-29.32, 24.36) (-8.62, 2.99) (-8.89, 2.2) (-2.77, -.7) log Agg TFP PR (.436)*** (.24, 6.4) (-.26, 3.96) log Firm TFP (.84)*** (.97,.99) Cons (.626)*** # Obs. 9,994 26,752 (536, 38688) For the model, 95% bootstrap confidence intervals (with, simulations) are shown in parenthesis.

25 Figure 8. Response of exports to the exchange rate at extensive and intensive margins