Financial Autarky and International Business Cycles (JME 2002)

Transcription

1 Financial Autarky and International Business Cycles (JME 2002) Jonathan Heathcote and Fabrizio Perri 9/9/2014 Sargent Reading Group Joseba Martinez Jonathan Heathcote and Fabrizio Perri Financial Autarky and International Business Cycles (JME 2002) 9/9/ / 15

2 Introduction International macro is beset by puzzles Quest continues for a model that generates cross-country correlations between quantities (not to mention prices) similar to those observed in data This paper: Examine effect of different (exogenously specified) risk-sharing arrangements on model moments Compare to data Study effect of alternative calibrations Conclusion: For plausible parametrization of productivity shocks, bond and complete markets economies very similar. Autarky economy is very different, and closer to data in most dimensions. Problem: countries definitely do not live in financial autarky! Jonathan Heathcote and Fabrizio Perri Financial Autarky and International Business Cycles (JME 2002) 9/9/ / 15

3 Discrepancies between complete markets IRBC and data Empirical cross-country consumption and output correlations are similar (models predict much higher consumption correlation) Investment and employment positively correlated across countries (model predict negative) Models generate far less volatility in terms of trade and real exchange rate than in data Jonathan Heathcote and Fabrizio Perri Financial Autarky and International Business Cycles (JME 2002) 9/9/ / 15

4 Model Two countries (i = 1, 2) Each produces a different intermediate good (a and b) Intermediate goods packaged into final goods in each country Intermediate goods market is frictionless (implies law of one price holds) Capital and labor are not internationally mobile Jonathan Heathcote and Fabrizio Perri Financial Autarky and International Business Cycles (JME 2002) 9/9/ / 15

5 Model Objective function t=0 s t π(s t )β t U(c i (s t ), 1 n i (s t )) Subject to budget constraint, where U(c i (s t ), 1 n i (s t )) = 1 γ [cµ i (s t )(1 n i (s t )) 1 µ ] γ c i is consumption of country i final good Jonathan Heathcote and Fabrizio Perri Financial Autarky and International Business Cycles (JME 2002) 9/9/ / 15

6 Model Production of intermediates max {F (z i(s t ), k i (s t ), n i (s t )) w i (s t )n i (s t ) r i (s t )k i (s t )} k i (s t ),n i (s t ) Where F (z i (s t ), k i (s t ), n i (s t ) 1 θ ) = e z i (s t) k θ i (s t )n 1 θ i (s t ) z(s t ) = [z 1 (s t ), z 2 (s t )] z(s t ) = Az(s t 1 ) + ɛ(s t ) k i (s t+1 ) = (1 δ)k i (s t ) + x i (s t ) Jonathan Heathcote and Fabrizio Perri Financial Autarky and International Business Cycles (JME 2002) 9/9/ / 15

7 Model Final Goods max {G i(a i (s t ), b i (s t )) q a i (s t ),b i (s t i a (s t )a i (s t ) qi b (s t )b i (s t )} ) Where { G i (a i (s t ), b i (s t [ωai (s )) = t ) (σ 1)/σ + (1 ω)b i (s t ) (σ 1)/σ ] σ/(σ 1) [(1 ω)a i (s t ) (σ 1)/σ + ωb i (s t ) (σ 1)/σ ] σ/(σ 1), σ: elasticity of substitution between a and b ω 1 > 0.5: home bias in consumption q j i denominated in units of the country i final good Jonathan Heathcote and Fabrizio Perri Financial Autarky and International Business Cycles (JME 2002) 9/9/ / 15

8 Budget Constraint Complete Markets c 1 (s t ) + x 1 (s t ) + q1(s a t ) Q(s t, s t+1 )B 1 (s t, s t+1 ) s t+1 = q1(s a t )(r 1 (s t )k 1 (s t ) + w 1 (s t )n 1 (s t )) + q1(s a t )B 1 (s t 1, s t ) Bond economy c 1 (s t ) + x 1 (s t ) + q1(s a t )Q(s t )B 1 (s t ) = q1(s a t )(r 1 (s t )k 1 (s t ) + w 1 (s t )n 1 (s t )) + q1(s a t )B 1 (s t 1 ) Autarky c 1 (s t ) + x 1 (s t ) = q1(s a t )(r 1 (s t )k 1 (s t ) + w 1 (s t )n 1 (s t )) Jonathan Heathcote and Fabrizio Perri Financial Autarky and International Business Cycles (JME 2002) 9/9/ / 15

9 Equilibrium - Market Clearing Intermediates market clearing a 1 (s t ) + a 2 (s t ) = F (z 1 (s t ), k 1 (s t ), n 1 (s t )) Finals market clearing b 1 (s t ) + b 2 (s t ) = F (z 2 (s t ), k 2 (s t ), n 2 (s t )) c i (s t ) + x i (s t ) = G i (a i (s t ), b i (s t )), i = 1, 2 Bonds or B 1 (s t, s t+1 ) + B 2 (s t, s t+1 ) = 0, s t+1 S B 1 (s t ) = B 2 (s t ) Jonathan Heathcote and Fabrizio Perri Financial Autarky and International Business Cycles (JME 2002) 9/9/ / 15

10 Some definitions GDP (numeraire is domestic final consumption) y i (s t ) = q a i (s t )F (z i (s t ), k i (s t ), n i (s t )) Terms of trade Real exchange rate p(s t ) = qb i (st ) q a i (st ) i = 1, 2 rx(s t ) = qa 1 (st ) q a 2 (st ) = qb 1 (st ) q b 2 (st ) Jonathan Heathcote and Fabrizio Perri Financial Autarky and International Business Cycles (JME 2002) 9/9/ / 15

11 Calibration Jonathan Heathcote and Fabrizio Perri Financial Autarky and International Business Cycles (JME 2002) 9/9/ / 15

12 Results Jonathan Heathcote and Fabrizio Perri Financial Autarky and International Business Cycles (JME 2002) 9/9/ / 15

13 Results Jonathan Heathcote and Fabrizio Perri Financial Autarky and International Business Cycles (JME 2002) 9/9/ / 15

14 Results Jonathan Heathcote and Fabrizio Perri Financial Autarky and International Business Cycles (JME 2002) 9/9/ / 15

15 Results Jonathan Heathcote and Fabrizio Perri Financial Autarky and International Business Cycles (JME 2002) 9/9/ / 15