Business Cycles and Exchange Rate Regimes

Transcription

1 Business Cycles and Exchange Rate Regimes Christian Zimmermann Département des sciences économiques, Université du Québec à Montréal (UQAM) Center for Research on Economic Fluctuations and Employment (CREFE) 1

2 RBC model with three countries Steps: 1. Build a model with exchange rate fluctuations 2. Calibrate the model 3. Simulate the model economies 4. Compare the experimental moments with the data Does the model economy replicate the changes observed in the data? 5. If yes, what type of shock was responsible for these change? 2

3 Stylized facts: Volatilities are higher in North America (output, employment, trade balance, terms of trade Japanese aggregates tend to become less volatile European consumption becomes more procyclical, terms of trade more countercyclical Become more procyclical in North America: inverstment, exports, emplyment, imports. Countercyclical: terms of trade In Japan, employment become more procyclical, the terms of trade more countercyclical 3

4 The model Consumer side In each country, infinitely lived consumer, with intertemporal preferences over consumption and leisure: [ ] max E 0 β t U(c it, 1 n it ) {c it,n it } t=0 t=0 S.T. [ E 0 with t=0 w it n it + (r it + δ)k it (1 + r it ) t ] = E 0 [ t=0 c it + x it (1 + r it ) t ] U(c, 1 n) = 1 γ [ c µ (1 n) 1 µ] γ 4

5 For each agent a firm: with max {n it,k it } z itf (k it, n it ) (r it + δ)k it w it n it Use of production: F (k, n) = k 1 θ n θ α i y it = α i y iit + α j y ijt + α k y ikt 5

6 Use of imports: where c it + x it = G(y iit, y jit, y kit ) G(y 1, y 2, y 3 ) = (ω 1 y ρ 1 + ω 2 y ρ 2 + ω 3 y ρ 3 ) 1 ρ Allows to introduce elasticity of substitution, y ijt > 0 and y jit > 0 6

7 Exchange rates: Share π i of imports billed in foreign currency E 0 [ t=0 ( αj (π j p it + (1 π j ) p jt e ijt ) y ijt (1 + r it ) t + + α ) k (π k p it + (1 π k ) p kt e ikt ) y ikt (1 + r it ) t = α i E 0 [ t=0 ( (πi p jt e ijt + (1 π i ) p it ) y jit (1 + r it ) t + + (π ) ip kt e ikt + (1 π i ) p it ) y kit (1 + r it ) t ] ] 7

8 Laws of motion: Capital k i,t+1 = (1 δ)k i,t + x it Investment projects s j,t+1 = s j+1,t j = 1, J 1 Technology innovations z 1,t+1 z 2,t+1 = A z(l) z 1t z 2t + ε z1,t+1 ε z2,t+1 z 3,t+1 z 3t ε z3,t+1 Exchange rates e 21,t+1 e 31,t+1 = A e (L) e 21t e 31t + ε e21,t+1 ε e31,t+1 8

9 Identities: Investment Terms of trade x t = J φ j s jt j=1 p jit = β G(y [ iit, y jit, y kit ) G(yiit ], y jit, y kit ) 1 y jit y iit ( ( 1 π j )e ijt p jt p it +π j )α j y ijt + p it = y jitp jit + y kit p kit y jit + y kit ( α j y ijt +α k y ikt (1 π k )e ikt p kt p it +π k )α k y ikt Trade balance ( π i + (1 π i ) p jt ) αj e ijt y ijt + p it α i ( π i + (1 π i ) p kt p it e ikt ) αk α i y ikt p jit y jit p kit y kit 9

10 The business cycle in this economy: ε zt z t productivity ε et e t p t if shock is persistent: w t n t w t c t r t c t, x t p t, x t, c t y 1t, y 2t z t, n t, x t J y t 10

11 Calibration: Take some parameter values from the literature: Estimate some: z 1,t+1 z 2,t+1 = z 1 z 2 β, δ, ρ, θ, n, c, γ, π + y ji y i a 11 a 12 a 13 a 21 a 22 a 23 z 1t z 2t + ε z1,t+1 ε z2,t+1 z 3,t+1 z 3 a 31 a 32 a 33 z 3t ε z3,t+1 ε z1,t+1 ε z2,t+1 ε z3,t+1 N, 0 0 (σ z1) 2 r z12 σ z1 σ z2 r z13 σ z1 σ z3 r z12 σ z1 σ z2 (σ z2 ) 2 r z23 σ z2 σ z3 0 r z13 σ z1 σ z3 r z23 σ z2 σ z3 (σ z3 ) 2 11

12 ( ) e 21,t+1 e 31,t+1 = ( ) ( ) ( e 21 a e e 31 0 a e31 ) e 21t + e 31t ( ) ε e21,t+1 ε e31,t+1 ( ) ε e21,t+1 ε e31,t+1 N ([ 0 0 ], [ ]) (σ e21 ) 2 r e σ e21 σ e31 r e σ e21 σ e31 (σ e31 ) 2 Determine the others using the first order conditions. 12

13 Solution procedure: Complex problem Pareto Optimum = Market equilibrium Quadratic approximation of the value fonction Linear decision rules Simulation with random numbers 13

14 Replication of stylized facts: Volatilities are higher in North America (output, employment, trade balance, terms of trade Japanese aggregates tend to become less volatile European consumption becomes more procyclical, terms of trade more countercyclical Become more procyclical in North America: inverstment, exports, emplyment, imports. Countercyclical: terms of trade In Japan, employment become more procyclical, the terms of trade more countercyclical 14

15 Are these results stable? σ and π are critical for vol(trade): higher σ, lower π σ influences corr(output, invest) > corr(output, cons): lower σ idem for corr(output, imports) > corr(output, exports), also higher π corr(output, trade balance): lower σ corr(output, tot): lower σ, same π crosscorr(output) > crosscorr(cons): Hopeless? Time-to-ship: prevents to much consumption smoothing 15

16 What now? Find better estimates of σ and π Endogenize the exchange rate movements Cost of exchange rate movements 16