Evaluating an estimated new Keynesian small open economy model

Malin Adolfson, Stefan Laséen, Jesper Lindé, Mattias Villani

Marc Goñi – 19 th April

Motivation

During the last years, the use of DSGE models for forecasting and policy recommendations has grown.

However, key macroeconomic series aren’t 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

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

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. ResultsPosterior probabilities and Impulse ResponsesForecasting abilityMisspecification

Introduction Model Methodology Results Conclusion

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.

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Firms

• Final Domestic Good

• Intermediate Domestic Good Demand

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Firms

• Production Function

• Marginal Cost

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Firms

• Optimization problem

• Phillips Curve for the domestic Goods Sector

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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* (Pd) and converts it to a differentiated good through brand naming technology

Nominal rigidities in the local currency price imply short run incomplete pass-through

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Firms

• Final Import (Export) Good

• Intermediate Good Demand

• Production function

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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

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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

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Households

• Preferences

where,

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Households

• Capital Accumulation

where,

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Households

• Labor Decision

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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)

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Households

• Bond Holdings

– Risk Premium

– MUIP

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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

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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

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Central Bank

– Inflation Targeting

with parameters

that is, no break in the monetary policy.

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Shocks

where

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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

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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

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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

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Data

Use quarterly Swedish data for the period 1980Q1-2004Q4

For the foreign variables weight Sweden’s 20 largest trading partners in 1991 according to IMF

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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

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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)

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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

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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

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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

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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

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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

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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

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Impulse Responses

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Forecasting Performance

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Forecasting PerformanceIntroduction Model Methodology Results Conclusion

Forecasting Performance

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Model Misspecification

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Model Misspecification

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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