Endogenous Trade Participation with Incomplete Exchange Rate Pass-Through

Endogenous Trade Participation with Incomplete Exchange Rate Pass-Through Yuko Imura Bank of Canada June 28, 23

Disclaimer The views expressed in this presentation, or in my remarks, are my own, and do not necessarily represent those of the Bank of Canada. Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 / 9

Exporter Characteristics and Dynamics Exporter characteristics Only 2% of US manufacturing plants exported in 992. (Bernard, Eaton, Jensen & Kortum 23) 2-8% more productive, 48% higher capital/worker, 2-45% more employment than non-exporters (Bernard & Jensen 999) Significant export costs 7-7% of a shipment s value (Alessandria et al. 2) Time-varying extensive margin of trade figure Entry rate = 3.9%, exit rate = 2.6% (Bernard & Jensen 24) Incomplete exchange rate pass-through 23% in short run, 42% in long run (Campa & Goldberg 25) Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 / 9

Objective This paper studies implications of endogenous trade participation for international business cycles, dynamics of trade participation, and exchange rate pass-through in an environment with nominal rigidities. Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 2 / 9

Main Findings With price rigidities, limited adjustments along intensive margin of trade lead to procyclical movements in the number of exporters, resulting in larger responses of export price and trade balance, in contrast to existing studies under flexible prices. Quantitative effect of extensive margin of trade on exchange rate pass-through is negligible, preserving incomplete pass-through in the presence of nominal rigidity. Entry and exit lead relatively more productive firms to dominate the export market. The model explains delayed response of trade balance and terms of trade to currency depreciation, with substantial adjustments along intensive and extensive margins. Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 3 / 9

Related Literature Exporter entry and exit Export hysteresis in partial equilibrium Baldwin (988), Baldwin and Krugman (989), Dixit (989) DSGE for business cycles Ghironi and Melitz (25), Alessandria and Choi (27) Incomplete exchange rate pass-through Demand curvature and market structure Atkeson and Burstein (28), Gust, Leduc and Vigfusson (2) Local costs Burstein, Neves and Rebelo (23), Corsetti and Dedola (24) Price rigidities Devereux and Engel (22), Bacchetta and van Wincoop (23) Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 4 / 9

Model Overview: Two-country DSGE model Representative household Competitive final-good producers [ D t = ω yt H ] γ ρ [ γ γ ρ (i) γ di + ( ω) yt F i Θ t ] γ γ γ (i) γ di ρ ρ ρ ρ Monopolistically competitive intermediate-good firms Each producing a differentiated product Heterogeneous in prices, productivity, entry costs and continuation costs for exporting These features drive individual firms state-dependent export decisions. Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 5 / 9

Model Overview All intermediate-good producers sell in their own country. y t (i) = z t (i)a t K t (i) ν L t (i) ν z t (i) = current firm-specific productivity A t = aggregate productivity To enter the export market, a firm pays entry cost, η G E (η). Upon entering the export market, an entrant sets a new price for its exports. To continue exporting, a firm pays a continuation cost, ξ G(ξ). Price-adjustment hazard increasing in the age of a price Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 6 / 9

Potential Entrant Potential entrant with productivity z c drawing entry cost η solves: Vt E (z c, η) = max { +βe t λ t+ λ t max P X,t (zc) n z c= [ P,t(z X c) Q t τy,t(z X c) w tl X,t(z c) r tk,t(z X c) ηw Pt t } π c ch,t+ ( z c, z c, ξ ) ], βe t λ t+ λ t n z c= π c cv E t+(z c, η ) Maximum entry cost η E t (z c ) this firm will pay to enter export market: βe t λ t+ λ t n z π c cv E c= t+(z c, η P,t(z X c) ) = Q t τy,t(z X c) w tl X,t(z c) r tk,t(z X c) P X t η E t (z c)w t + βe t λ t+ λ t n z c= π c ch,t+ ( z c, z c, ξ ) where H,t (z c, z s, ξ) = α V,t(z c, ξ) + ( α )V,t (z c, z s, ξ). Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 7 / 9

Price-adjusting Incumbent Price-adjusting incumbent exporter with current productivity z c drawing export cost ξ solves: V,t(z c, ξ) = max { +βe t λ t+ λ t max P X,t (zc) n z c= [ P,t(z X c) Q t τy,t(z X c) w tl X,t(z c) r tk,t(z X c) ξw Pt t } π c ch,t+ ( z c, z c, ξ ) ], βe t λ t+ λ t n z c= π c cv E t+(z c, η ) Max. continuation cost ξ t (z c ) the firm will pay to continue exporting: βe t λ t+ λ t n z π c cv E c= t+(z c, η P,t(z X c) ) = Q t τy,t(z X c) w tl X,t(z c) r tk,t(z X c) P X t ξ t (z c)w t + βe t λ t+ λ t n z c= π c ch,t+ ( z c, z c, ξ ) Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 8 / 9

Non-price-adjusting Incumbent Value of non-price-adjusting incumbent of type (z c, j, z s ) drawing continuation cost ξ: V j,t (z c, z s, ξ) = max [ +βe t λ t+ λ t Pj,t(z X s) Q t τyj,t(z X c, z s) w tl X j,t(z c, z s) r tkj,t(z X c, z s) ξw Pt X t ] n z c= π c ch j+,t+ ( z c, z s, ξ ), βe t λ t+ λ t n z c= π c cv E t+(z c, η ) Maximum cost ξ j t (z c, z s ) the firm will pay to continue exporting: βe t λ t+ λ t n z π c cv E c= t+(z c, η Pj,t(z X s) ) = Q t τyj,t(z X c, z s) w tl X j,t(z c, z s) r tkj,t(z X c, z s) P X t ξ j t (z c, z s)w t + βe t λ t+ λ t n z c= π c ch j+,t+ ( z c, z s, ξ ) Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 9 / 9

Probabilities of Export Participation Probabilities of entering export market: ζ E t (z c ) = G E ( η E t (z c ) ) for c =,, n z Probabilities of remaining in the export market: a) if adjusting prices ζ t (z c ) = G ( ξ t (z c ) ) for c =,, n z b) if not adjusting prices ( ) ζ j t (z c, z s ) = G ξ j t (z c, z s ) for c =,, n z, s =,, n z and j =,, J evolution Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 / 9

Household Representative household chooses C t, L t, K t+, B t+ (s t+ ), and M t : subject to max E t t= β t [log C t + χ log ( Mt P t ) ] + χ 2( L t) P tc t+p ti t+ s t+ q(s t+ s t )B(s t+ )+M t P tw tl t+p tr tk t+b(s t )+M t +P td t+t M t where ( ) It K t+ = ( δ)k t + I t φ K t K t B(s t+ ) = holdings of state-contingent, home-denominated bond q(s t+ s t ) = price of B(s t+ ) in units of home currency in state s t Tt M = lump-sum government transfer = Mt s Mt s Mt s = money supply, Mt s = µ t Mt, s log µ t+ = ρ µ log µ t + ε µ t+ φ( ) = convex capital adjustment cost function, φ(δ) =, φ (δ) = Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 / 9

Calibration The model frequency is quarterly. Data Model Sources Mass of exporters.2.2 Bernard et al. (23) Continuation rate.97.87 Bernard & Jensen (24) Entry rate.4.4 Bernard & Jensen (24) Imports/GDP ratio.2.2 Drozd & Nosal (2) Productivity relative to.2-8.3 Bernard & Jensen (999) non-exporters Mean price adjustment.7-3.27 2.66 Bils & Klenow (24) frequency Nakamura & Steinsson (28) parameters Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 2 / 9

Business Cycle Moments Data Model Flex-price Standard deviations relative to GDP Consumption.83.43.54 Investment 2.73 4.88 3.52 Labor.65.26.42 Net exports/gdp.5.2.5 Correlations with GDP Consumption.84.87.94 Investment.94.94.97 Labor.86.79.97 Net exports/gdp -.3 -.35 -.26 Autocorrelations GDP.86.66.69 Consumption.88.8.73 Investment.88.5.66 Labor.9.4.66 International correlations GDP.4.34.6 Consumption.2.56.65 Investment.8.7 -.32 Labor.27.46 -.3 Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 3 / 9

Role of Entry and Exit: Flexible prices.5 exports imports net exports.5 -.5 2.5 -.5 2 % of output.5 -.5 2 export price index.5 number of exporters real exchange rate -.5.5.4.2-2 2 2 entry & exit no entry & exit IRFs Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 4 / 9

Role of Entry and Exit: Nominal rigidities.5 exports imports net exports.5 -.5 2.5 -.5 2 % of output.5 -.5 2 export price index.5 number of exporters real exchange rate -.5.5.4.2-2 2 2 entry & exit no entry & exit Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 5 / 9

Exchange Rate Pass-Through p X t = α + 8 β n e t n + n= 8 γ n πt n + δ y t + ɛ t n= Pass-through (n).8.6.4.2 Full 2 4 6 8 Horizon n (quarters) Full model generates short-run incomplete pass-through. Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 6 / 9

Exchange Rate Pass-Through p X t = α + 8 β n e t n + n= 8 γ n πt n + δ y t + ɛ t n= Pass-through (n).8.6.4.2 Full Flex price 2 4 6 8 Horizon n (quarters) With flexible prices, pass-through is complete immediately. Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 6 / 9

Exchange Rate Pass-Through p X t = α + 8 β n e t n + n= 8 γ n πt n + δ y t + ɛ t n= Pass-through (n).8.6.4.2 Full Fixed participation 2 4 6 8 Horizon n (quarters) The added flexibility of endogenous trade participation does not overturn incomplete pass-through arising from nominal rigidity. Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 6 / 9

Pass-Through: Composition of exporters Model without entry and exit % of firms 8 6 4 2 Price age j=5 j=4 j=3 j=2 j= j= % of firms 8 6 4 2 Current productivity z c =high z c =low 2 4 6 8 2 Time 2 4 6 8 2 Time Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 7 / 9

Pass-Through: Composition of exporters Model without entry and exit % of firms 8 6 4 2 Price age j=5 j=4 j=3 j=2 j= j= % of firms 8 6 4 2 Current productivity z c =high z c =low 2 4 6 8 2 Time 2 4 6 8 2 Time % of firms 8 6 4 2 Model with entry and exit % of firms 8 6 4 2 2 4 6 8 2 2 4 6 8 2 Time Time Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 7 / 9

Effects of monetary policy and currency movements.8.6.4.2 Money growth shock 5 5 2.2 Net exports.5.5 Real exchange rate 5 5 2 Exports.5.5 -.5 Terms of trade - 5 5 2 6 Imports % of output -.2 -.4-4 2 -.6 5 5 2 Number of exporters (Home).5 -.5 - -.5-2 5 5 2-2 5 5 2 Number of exporters (Foreign) -.2 -.4 -.6 -.8-5 5 2-2 5 5 2 Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 8 / 9

Conclusion In the presence of price rigidity, endogenous trade participation influences international business cycles, in contrast to earlier findings under flexible prices. This suggests that market structure and pricing conventions may be critical in analyzing the role of exporter entry and exit for aggregate dynamics and international transmission of shocks. Endogenous trade participation and incomplete exchange rate pass-through have important implications for the effects of currency movements and the conduct of monetary policy at both micro and macro levels. Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 9 / 9

Exporter Dynamics 3 Number of exporters RGDP 4 Number of exporters (in thousands) 25 2 2 Real GDP (in trillion $) 5 996 998 2 22 24 26 28 2 8 Year Back Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 2 / 4

Final-Good Producer Final-good producers combine home- and foreign-produced intermediate goods to produce final goods D t. y H t max P td t (i),yf t (i) Pt D (i)yt H (i)di Pt X i Θ t (i)y F t (i)di subject to D t = [ ω ] γ ρ [ yt H (i) γ γ ρ γ di + ( ω) yt F (i) γ γ di i Θ t ] γ γ ρ ρ ρ ρ γ = elasticity of substitution b/w goods produced in the same country ρ = elasticity of substitution b/w home and foreign goods Θ t = time-varying set of foreign goods available in home country P t = consumer price index Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 / 4

Intermediate-Good Firm: Domestic market Price-adjusting firm with current productivity z c chooses P D,t(z c ): V D,t(z c) = max P D,t (zc) +βe t λ t+ λ t { P,t(z D c) y,t(z D c) w tl D,t(z c) r tk,t(z D c) Pt D ]} n z n z α π c cv,t+(z c) D + ( α ) π c cv,t+ D (z c, z c) [ c= c= α j = probability of price adjustment for firms with j-period old price π c c = probability of moving from z = z c to z = z c Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 2 / 4

Intermediate-Good Firm: Domestic market Value of non-price-adjusting firm of type (z c, j, z s ) V D j,t (z c, z s) = P j,t(z D s) yj,t(z D c, z s) w tl D j,t(z c, z s) r tkj,t(z D c, z s) P D t +βe t λ t+ λ t [ α j+ n z c= π c cv D ] n z,t+(z c) + ( α j+) π c cv j+,t+ D (z c, z s) c= z c = current productivity j = number of periods since the price was last set z s = productivity at the time of last price adjustment Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 3 / 4

Evolution of the distribution of domestic firms θ j,t (z c, z s ) = Number of firms starting date t as type (z c, j, z s ) Evolution for non-price adjusting firms: n z θ j+,t+ (z c, z s ) = ( α j ) π c c θ j,t (z c, z s ) c= Total number of firms starting t + as (z c,, z s ): J n z θ,t+ (z c, z s ) = π s c α j θ j,t (z s, z s ). j= s= Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 4 / 4

Evolution of the distribution of exporters ψ j,t (z c, z s ) = Number of incumbents starting t as type (z c, j, z s ) Evolution for non-price-adjusting incumbents: n z ψ j+,t+(z c, z s) = ( α j) ζ j t (z c, z s) π c c ψ j,t(z c, z s) c= Total number of exporters of type (z c,, z s ): J n z ψ,t+(z c, z s) = π s c ζt (z s) α j ψ j,t(z s, z s) j= s= }{{} adjusting incumbents surviving time t + π s c N E t (z s) }{{} entrants at time t Number of entrants with productivity z c at t: [ J ] n z J n z Nt E (z c) = ζt E (z c) θ j,t(z c, z s) ψ j,t(z c, z s) j= s= j= s= Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 5 / 4 Back

Price Index. Price index for domestically-produced goods [ J n z n z Pt D = α jθ j,t(z c, z s)p,t(z D c) γ j= c= s= ] J n z n z + ( α j)θ j,t(z c, z s)pj,t(z D s) γ j= c= s= 2. Price index for imported goods P X t = [ nz c= Nt E (z c)p,t X (z c) γ + J n z n z j= c= s= γ α j ζt (z c)ψj,t(z c, z s)p,t X (z c) γ ] J n z n z γ + ( α j) ζ j (z c, z s) ψj,t(z c, z s) Pj,t X (z s) γ j= c= s= 3. Price index for all the goods available in home country [ ( ) ρ ( ) ] ρ P t = ω ρ Pt D + ω ρ 2 Pt X ρ t Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 6 / 4

Parameter Values Discount factor β.99 Weight on leisure in utility χ 2.9 s.s. labor =.33 Elasticity of substitution γ 3.8 Ghironi & Melitz (25) Armington elasticity ρ.5 BKK(995) Capital share in production ν.3 Depreciation rate of capital δ.25 % depreciation/year Iceberg trade cost τ.5 # of firm-specific productivity levels n z 2 Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 7 / 4

Calibrated parameters Home bias ω.762 Entry costs U (, η U ) η U 2.8 Continuation costs U (, ξ U ) ξ U.7 Firm-specific productivity: ρ z.8 log z = ρ z log z + ɛ, ɛ N(, σ ɛ ) σ ɛ.85 Price adjustment probability α j [.5,.9,.25,.49,.7,.] Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 8 / 4

Shock processes Productivity (Backus, Kehoe and Kydland, 995) [ ] [ ] [ ] [ At.96.88 At ε A A = t.88.96 A + t t ε A t where var(ε A t ) = var(ε A t ) = (.7) 2, corr ( ε A t, ε A t ] ) =.258 Money growth (Chari, Kehoe and McGrattan, 22) [ ] [ ] [ ] [ µt.68 µt ε µ ] µ = t.68 µ t + t ε µ t where µ =.4 /4 I choose var(ε µ t ) = var(ε µ t ) so that σ Y =.42 in baseline model. Back Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 9 / 4

Steady state Sticky Flexible Data EE No EE EE No EE Entry and exit Mass of exporters.2.2.2.2.2 Continuation rate.97/qtr.87.86 Entry rate.4/qtr.4.4 Exporter productivity.2-.8.3.2 relative to nonexporters Imports/GDP ratio.2.2..2. Mean price duration.43-4.33qtrs 2.66 2.66 Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 / 4

Impulse responses: Flexible-price model 2 output.8 consumption labor.6.4.2.5-5 5 2 5 5 2 -.5 5 5 2 6 investment.5 capital rental rate export price index 4 2.5.5 -.5-2 5 5 2 -.5 5 5 2-5 5 2.6 number of exporters.6 number of new exporters.5 number of exiting exporters.4.2.4.2 -.5 - -.2 5 5 2 -.2 5 5 2 -.5 5 5 2. Home net exports.8 real exchange rate productivity shock % of output.5 -.5.6.4.2.5 -. 5 5 2 5 5 2 5 5 2 Home country Foreign country Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 / 4

Impulse responses: Sticky-price model.5 output.8 consumption labor.5.6.4.2 - -.5 5 5 2 5 investment 5 5 2 2 capital rental rate -2 5 5 2.5 export price index - -.5-5 5 5 2-2 5 5 2-5 5 2.5 number of exporters 2 number of new exporters 5 number of exiting exporters.5-5 -.5 5 5 2-5 5 2-5 5 2.5 Home net exports.4 real exchange rate productivity shock % of output..5.3.2..5 -.5 5 5 2 5 5 2 5 5 2 Home country Foreign country Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 2 / 4 back

Policy, exchange rate and trade % change % change from yr from ago yr ago 2 5 2 5 5 M M 5 985 986 987 988 989 99 985 986 987 Terms of 988 trade989 99 2 Terms of trade 2 8 6 8 4 6 2 4 985 986 987 988 989 99 2 985 986 987 988 989 99 billion billion $ $ 4 2 4 2 US dollar index 8 985 986 987 988 989 99 8 985 986 987 Trade balance 988 989 99 - Trade balance - -2-2 -3 US dollar index -3-4 985 986 987 988 989 99-4 985 986 987 988 989 99 Yuko Imura (Bank of Canada) Endogenous Trade Participation June 23 3 / 4