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Evaluating an estimated new Keynesian small open economy model Malin Adolfson, Stefan Laséen, Jesper Lindé, Mattias Villani Marc Goñi – 19 th April

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Motivation During the last years, the use of DSGE models for forecasting and policy recommendations has grown. However, key macroeconomic series arent still fitted: -Persistence and volatility of real exchange rate -International transmission of business cycles This paper estimates a NK small open economy for Sweden using Bayesian techniques and accounting for the Swedish monetary policy regime shift. By modifying the UIP condition the model is able to account for realistic persistence and volatility of the exchange rate. Introduction Model Methodology Results Conclusion

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Literature Review Christiano et al (2005) Nominal rigidities and the dynamic effects of a shock to monetary policy Smets and Wouters (2003) An estimated DSGE for the Euro Area Smets and Wouters (2004) Forecasting with a BDSGE model. An application to the Euro area Adolfson et al (2007) Forecasting performance of an open economy DSGE model with incomplete pass through Introduction Model Methodology Results Conclusion

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Outline 1. Model Modified UIP Monetary Policy regime shift 2. Methodology Estimate the DSGE model using Bayesian techniques Use Del Negro, Schorfheide (2004), Del Negro (2007) for misspecification evaluation 3. Results Posterior probabilities and Impulse Responses Forecasting ability Misspecification Introduction Model Methodology Results Conclusion

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Firms 1.Domestic Goods Firms The domestic final good is a composite of intermediate goods produced using capital K and labor H subject to price stickyness and an externally financed wage bill. Moreover, it is exposed to technology shock. Introduction Model Methodology Results Conclusion

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Firms Final Domestic Good Intermediate Domestic Good Demand Introduction Model Methodology Results Conclusion

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Firms Production Function Marginal Cost Introduction Model Methodology Results Conclusion

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Firms Optimization problem Phillips Curve for the domestic Goods Sector Introduction Model Methodology Results Conclusion

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Firms 2. Import and Export Sector The are import consumption and investment firms and export firms Each firm buys the homogeneous foreign (home) good at price P* (P d ) and converts it to a differentiated good through brand naming technology Nominal rigidities in the local currency price imply short run incomplete pass-through Introduction Model Methodology Results Conclusion

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Firms Final Import (Export) Good Intermediate Good Demand Production function Introduction Model Methodology Results Conclusion

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Firms Marginal Cost for the importing firms for the exporting firm Optimization problem Phillips curves for Consumption and Investment Imports and Exports Introduction Model Methodology Results Conclusion

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Households The economy is populated with a continuum of Households which attain utility from consumption, leisure and real cash balances. To purchase these commodities they invest in physical capital and supply capital and labor to firms Introduction Model Methodology Results Conclusion

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Households Preferences where, Introduction Model Methodology Results Conclusion

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Households Capital Accumulation where, Introduction Model Methodology Results Conclusion

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Households Labor Decision Introduction Model Methodology Results Conclusion

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Households Bond Holdings The choice between domestic and Foreign bonds balances into a no arbitrage condition (UIP). -Nominal interest rate difference equals expected change in exchange rate Not much empirical support for UIP: -Persistent hump-shaped response of the exchange rate to monetary shock Introduce negative correlation between expected change in exchange rate and risk premium to get this persistence (forward premium puzzle) Introduction Model Methodology Results Conclusion

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Households Bond Holdings – Risk Premium – MUIP Introduction Model Methodology Results Conclusion

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Central Bank As Sweden went from a fixed to a floating exchange rate in 1992 we need to account for this break Pre 1992 Generalized Taylor Rule Introduction Model Methodology Results Conclusion

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Central Bank Post 1992 Allow for three different policy specifications and let the data tell the most appropriate. – Fixed exchange rate rule – Semi-Fixed exchange rate rule Introduction Model Methodology Results Conclusion

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Central Bank – Inflation Targeting with parameters that is, no break in the monetary policy. Introduction Model Methodology Results Conclusion

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Shocks where Introduction Model Methodology Results Conclusion

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Government The Government spends resources in consuming the domestic good, collects taxes from households and transfers the surplus/deficit plus the seigniorage to the households via lump sum taxes Introduction Model Methodology Results Conclusion

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Foreign Economy Foreign prices, output and interest rate are exogenously given by a 4-lag VAR estimated using un-informative priors Introduction Model Methodology Results Conclusion

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Model Solution To solve the model consider the market clearing conditions To compute the equilibrium decision rules, -Stationarize all variables -Log linearize around the steady state -Use the AIM algorithm to calculate the numerical reduced form solution Introduction Model Methodology Results Conclusion

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Data Use quarterly Swedish data for the period 1980Q1-2004Q4 For the foreign variables weight Swedens 20 largest trading partners in 1991 according to IMF Introduction Model Methodology Results Conclusion

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Bayesian Estimation Previously, compute the reduced form solution Construct the observed data vector Transform the reduced form solution into a state-space representation mapping the unobserved state variables to the observed data Introduction Model Methodology Results Conclusion

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Bayesian Estimation 1. Prior Distribution Set priors for unobserved state variables using 1980Q1- 1985Q4 a training sample For the majority of the estimated parameters, use Adolfson et al (2007) Set some priors (stickiness and markup shocks) based on micro evidence and on educated guesses Set identical priors for the parameters in the monetary policy rule (allows to compare them disregarding any prior effect) Introduction Model Methodology Results Conclusion

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Bayesian Estimation 2. Likelihood function To compute the Likelihood function apply the Kalman filter to the state space transformation of the reduced form solution The structural shocks and the exogenous fiscal al foreign VAR shocks enter in such a way that there is no singularity of the Likelihood function Introduction Model Methodology Results Conclusion

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Bayesian Estimation 3. Posterior distribution Obtain the joint posterior distribution in two steps: -The posterior mode and the Hessian matrix (evaluated at the mode) is computed by standard numerical routines -This Hessian is used in a Metropolis Hastings algorithm to generate a sample for the posterior distribution Introduction Model Methodology Results Conclusion

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Bayesian Estimation Notes -Calibrate those parameters suspicious of weak identification -Work with a large number of variables to facilitate Identification of parameters and shocks Introduction Model Methodology Results Conclusion

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Misspecification Following Del Negro, Schorfheide (2004), Del Negro (2007) -Estimate a more flexible empirically oriented VAR with a prior centered at the DSGE with tightness -Find the optimal (maximum likelihood) -If the is large, that is the DSGE-prior pushes the VAR towards the implied cross-equation restrictions, then the model is compatible with the data and, thus, the DSGE is well specified Introduction Model Methodology Results Conclusion

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Posterior Distribution Table 1 Monetary policy rules Taylor based rule with a break in parameters gets the best fit Evidence for a break but not for a strong fix exchange rate policy Parameters In general, similar parameter estimation across specification Wage stickiness and lagged inflation response equal the prior Policy rule parameters similar in the two regimes Introduction Model Methodology Results Conclusion

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Posterior Distribution UIP Condition Need to separately identify the risk premium shock from its propagartion Modifying the UIP condition allows to generate the desired exchange rate persistence Introduction Model Methodology Results Conclusion

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Impulse Responses Introduction Model Methodology Results Conclusion

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Forecasting Performance Introduction Model Methodology Results Conclusion

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Forecasting Performance Introduction Model Methodology Results Conclusion

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Forecasting Performance Introduction Model Methodology Results Conclusion

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Model Misspecification Introduction Model Methodology Results Conclusion

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Model Misspecification Introduction Model Methodology Results Conclusion

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Conclusions -Improve the NK small open economy model by modifying the UIP condition -By improving the acknowledgement of the workings of the economy the CB is now able to derive policy implications a part from forecasting -However, it seems that misspecification should be more considered Introduction Model Methodology Results Conclusion

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