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Journal Article•DOI•

An estimated dynamic stochastic general equilibrium model of the euro area

Frank Smets1, Raf Wouters2•
European Central Bank1, National Bank of Belgium2
01 Sep 2003-Journal of the European Economic Association (Journal of the European Economic Association)-Vol. 1, Iss: 5, pp 1123-1175
TL;DR: In this paper, a dynamic stochastic general equilibrium (DSGE) model with sticky prices and wages for the euro area was developed and estimated with Bayesian techniques using seven key macroeconomic variables: GDP, consumption, investment, prices, real wages, employment, and the nominal interest rate.
Abstract: This paper develops and estimates a dynamic stochastic general equilibrium (DSGE) model with sticky prices and wages for the euro area. The model incorporates various other features such as habit formation, costs of adjustment in capital accumulation and variable capacity utilization. It is estimated with Bayesian techniques using seven key macroeconomic variables: GDP, consumption, investment, prices, real wages, employment, and the nominal interest rate. The introduction of ten orthogonal structural shocks (including productivity, labor supply, investment, preference, cost-push, and monetary policy shocks) allows for an empirical investigation of the effects of such shocks and of their contribution to business cycle e uctuations in the euro area. Using the estimated model, we also analyze the output (real interest rate) gap, dee ned as the difference between the actual and model-based potential output (real interest rate). (JEL: E4, E5)

Summary (5 min read)

Jump to: [1. Introduction] – [2. A DSGE model for the euro area] – [2.1 The household sector] – [2.1.2 Labour supply decisions and the wage setting equation] – [2.1.3 Investment and capital accumulation] – [2.2 Technologies and firms] – [2.2.1 Final-good sector] – [2.2.2 Intermediate goods producers] – [2.3 Market equilibrium] – [2.4 The linearised model] – [3 Estimation results] – [3.1 Estimation methodology] – [3.2 Parameter estimates] – [3.3.1 Comparing the estimated DSGE model with VARs] – [3.3.2 Comparison of empirical and model-based cross-covariances] – [4.1 Impulse response analysis] – [4.2 Variance decomposition] – [4.3 Historical decomposition] – [5 Output and interest rate gaps: an application] and [6 Conclusions]

1. Introduction

  • In this paper the authors present and estimate a stochastic dynamic general equilibrium (DSGE) model for the euro area.
  • 2 Several results of their analysis are worth highlighting.
  • Fourth, regarding the relative contribution of the various shocks to the empirical dynamics of the macro economic time series in the euro area, the authors find that the labour supply and the monetary policy shock are the two most important structural shocks driving variations in euro area output.
  • In Section 3, we, first, discuss the estimation methodology, then, present the main results and, finally, compare the empirical performance of the estimated DSGE model with that of various VARs.

2. A DSGE model for the euro area

  • In this section the authors derive and present the linearised DSGE model that they will estimate in Section 3.
  • Households maximise a utility function with two arguments (goods and leisure (or labour)) over an infinite life horizon.
  • This model is a version of the model considered in Kollmann (1997) and features monopolistic competition in both the goods and labour markets.
  • In addition, several features of CEE (2001) are introduced.
  • The marginal costs depend on wages and the rental rate of capital.

2.1 The household sector

  • Households differ in that they supply a differentiated type of labour.
  • So, each household has a monopoly power over the supply of its labour.
  • Equation (2) above also contains two preference shocks: ε.
  • The external habit stock is assumed to be proportional to aggregate past consumption: (3) ChH tt 1−= 5 Habit depends on lagged aggregate consumption which is unaffected by any one agent's decisions.

2.1.2 Labour supply decisions and the wage setting equation

  • Households act as price-setters in the labour market.
  • Following Kollmann (1997) and Erceg, Henderson and Levin (2000), the authors assume that wages can only be optimally adjusted after some random “wage-change signal” is received.
  • The probability that a particular household can change its nominal wage in period t is constant and equal to wξ−1 .
  • When 0=wγ , there is no indexation and the wages that can not be re-optimised remain constant.

2.1.3 Investment and capital accumulation

  • Finally, households own the capital stock, a homogenous factor of production, which they rent out to the firm-producers of intermediate goods at a given rental rate of ktr .
  • An infinite supply elasticity limits the increase in marginal costs and prices following an expansion of output in a model with sticky prices, which helps to generate real persistence of monetary shocks.
  • 11 This specification of the costs is preferable above a specification with costs in terms of a higher depreciation rate (see King and Rebelo, 2000; or Greenwood, Hercowitz, and Huffman, 1988; Dejong, Ingram and Whiteman, 2000) because the costs are expressed in terms of consumption goods and not in terms of capital goods.
  • 8 NBB WORKING PAPER No.35 - October 2002 Equation (16) describes the optimal dynamic behaviour of investment.
  • As the rental rate increases it becomes more profitable to use the capital stock more intensively up to the point were the extra gains match the extra output costs.

2.2 Technologies and firms

  • The final good is used for consumption and investment by the households.
  • There is monopolistic competition in the markets for intermediate goods: each intermediate good is produced by a single firm.

2.2.1 Final-good sector

  • Recently, Woodford (2000) has illustrated how this assumption can be relaxed in a model with sticky prices and adjustment costs in investment.
  • The hypothesis has important consequences for the estimation of the degree of price stickiness.
  • With capital specific to the firm, firms will be more reluctant to change the price of their good as the resulting demand response will have a much stronger impact on the marginal cost of production.
  • The assumption of capital mobility across firms therefore biases the estimated degree of price stickiness upwards.
  • NBB WORKING PAPER No. 35 - October 2002 9 where jty denotes the quantity of domestic intermediate good of type j that is used in final goods production, at date t. tp,λ is a stochastic parameter which determines the time-varying mark-up in the goods market.

2.2.2 Intermediate goods producers

  • (22) α α− = 1 ~ , , tj k t tjt Kr LW Equation (22) implies that the capital-labour ratio will be identical across intermediate goods producers and equal to the aggregate capital-labour ratio, also known as Cost minimisation implies.
  • This implies that the marginal cost, too, is independent of the intermediate good produced.
  • As in Calvo (1983), firms are not allowed to change their prices unless they receive a random “price-change signal”.
  • With sticky prices the mark-up becomes variable over time when the economy is hit by exogenous shocks.

2.3 Market equilibrium

  • The final goods market is in equilibrium if production equals demand by households for consumption and investment and by the government: 15 Erceg, Henderson and Levin (2000) use indexation to the average steady state inflation rate.
  • The capital rental market is in equilibrium when the demand for capital by the intermediate goods producers equals the supply by the households.
  • The interest rate is determined by a reaction function that describes monetary policy decisions.

2.4 The linearised model

  • For the empirical analysis of section 3 the authors linearise the model equations described above around the non-stochastic steady state.
  • Note that in this case the interest elasticity of consumption depends not only on the intertemporal elasticity of substitution, but also on the habit persistence parameter.
  • Similarly, partial indexation of nominal wages results in the following real wage equation: 16 This is the only shock that is not directly related to the structure of the economy.
  • For such alternative interpretations of this equity premium shock and an analysis of optimal monetary policy in the presence of such shocks, see Dupor (2001).
  • Finally, the model is closed by adding the following empirical monetary policy reaction function: (36) R t p 1t1t p tty1tt p 1t1tYt1tt1tt )).

3 Estimation results

  • First, discuss how the authors estimate the structural parameters and the processes governing the ten structural shocks.
  • Next, the authors present the main estimation results.
  • Finally, the authors compare the empirical performance of the estimated DSGE model with a number of a-theoretical VARs.

3.1 Estimation methodology

  • There are various ways of estimating or calibrating the parameters of a linearised DSGE model.
  • In the final step, the parameters are estimated by maximising the likelihood function.
  • 16 NBB WORKING PAPER No.35 - October 2002 econometric interpretation of DSGE models is not necessarily less stringent than the strong interpretation: in spite of the focus on a restricted set of moments, the model is assumed to account for all aspects of the observed data series and these aspects are used in calculating the moments of interest.
  • The standard errors were set so that the domain covers a reasonable range of parameter values.
  • A wide range of calibrations has been used for the inverse elasticity of labour supply.

3.2 Parameter estimates

  • In addition to the prior distribution, Table 1 reports two sets of results regarding the parameter estimates.
  • The second set reports the 5, 50 and 95 percentile of the posterior distribution of the parameters obtained through the MetropolisHastings sampling algorithm.
  • The persistent shocks are estimated to have an autoregressive parameter which lies between 0.82 (for the productivity shock) and 0.95 for the government spending shock.
  • Only when they assume decreasing returns to scale and an upward-sloping marginal cost curve, Gali, Gertler and LopezSalido (2000) estimate a more reasonable degree of price stickiness that is comparable with what the authors estimate for wages.
  • One needs to be careful when making such comparisons, as their model features external habit formation which turns out to be significant.

3.3.1 Comparing the estimated DSGE model with VARs

  • The discussion in the previous section shows that the model is able to deliver reasonable and significant estimates of the model parameters.
  • The authors analyse how well their estimated model does compared to a-theoretical VAR models estimated on the same data set.
  • Given these samples of the posterior distribution, Geweke (1998) also proposes different methods to calculate the marginal likelihood necessary for model comparison (a method for importance sampling and for MH algorithm, a method for the Gibbs sampler, and the modified harmonic mean that works for all sampling methods).
  • This method applies a standard correction to the posterior evaluation at the posterior mode to approximate the marginal likelihood.
  • The marginal likelihood of the DSGE model is larger than that of the VAR(2) and VAR(3) model and very close to that of the VAR(1) model.

3.3.2 Comparison of empirical and model-based cross-covariances

  • Traditionally DSGE models are validated by comparing the model-based variances and covariances with those in the data.
  • Graph 2 summarises the results of this exercise.
  • The error bands are quite large, indicating that there is a large amount of uncertainty surrounding the model-based crosscovariances.
  • In particular, the crosscorrelations with the interest rate do not seem to be fully satisfactory.

4.1 Impulse response analysis

  • Note that these impulse responses are obtained with the estimated monetary policy reaction function.
  • The real interest rate rises reflecting the fact that the wage mark-up shock creates a trade-off between inflation and output gap stabilisation.
  • Qualitatively similar impulse responses are derived following a temporary negative equity premium shock (Graph 9), but in this case the effects on output, employment and investment are much more short-lived and the resulting effects on real wages, the marginal cost and prices much more limited.
  • This leads to a hump-shaped fall in output, consumption and investment.

4.2 Variance decomposition

  • The contribution of each of the structural shocks to the forecast error variance of the endogenous variables at various horizons (short run: 1 year; medium run: 2.5 years and long run: 25 years) is reported in Table 3.
  • Beyond the very short-term horizon, output variations are driven primarily by the labour supply and the monetary policy shocks.
  • The price and wage mark-up shocks do not seem to matter for output variability.
  • Empirically inflation is a quite volatile process.
  • Somewhat surprisingly, other shocks together typically account for less than 15% of the variance in inflation.

4.3 Historical decomposition

  • Graphs 13 and 14 summarise the historical contribution of the various structural shocks to output and inflation developments in the euro area.
  • This decomposition is based on their best estimates of the various shocks.
  • While obviously such a decomposition must be treated with caution, it helps in understanding how the estimated model interprets specific movements in the observed data and therefore can shed some light on its plausibility.
  • Finally, the run-up in inflation in the late 1980s and early 1990s is attributed to the various “supply” and “demand” shocks.
  • While loose monetary policy contributed to offsetting the fall in output due to negative supply and demand shocks in the 1970s, it contributed very little to output variations in the 1980s and 1990s.

5 Output and interest rate gaps: an application

  • In a simple benchmark New-Keynesian model with only nominal price rigidities and no “mark-up” shocks, Woodford (2002) has pointed out that optimal monetary policy will be able to replicate the flexible price equilibrium, thereby restoring the first best.
  • As these shocks give rise to inefficient variations in the flexible-price-and-wage level of output, one can argue that monetary authorities should not accommodate such variations and instead try to keep output at its efficient level.
  • A positive labour supply shock has very similar effects on output and the natural real interest rate (Graph 16).
  • From 1982 onward potential output has gradually risen to a higher level with a dip in the early 1990s.
  • 42 The authors gap differs from the gap that is calculated in Gali, Gertler and Lopez-Salido (2002) and Neiss and Nelson (2001) in the sense that those papers implicitly assume that there are no mark-up shocks.

6 Conclusions

  • Recently a new generation of small-scale monetary business cycle models generally referred to as New-Keynesian or New Neoclassical Synthesis models have been developed (Goodfriend and King (1997), Rotemberg and Woodford (1997) and Clarida, Gali and Gertler (1999)).
  • Clearly, all “non-monetary” shocks will potentially affect output and the real rate in a flexible price and wage economy.
  • Overall, the results presented in this paper show that an estimated version of the DSGE model with sticky prices and wages can be used for monetary policy analysis in an empirically plausible set-up.
  • Also a further examination and identification of the various structural shocks would be interesting.

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Smets, Frank; Wouters, Raf
Working Paper
An estimated dynamic stochastic general equilibrium
model of the euro area
NBB Working Paper, No. 35
Provided in Cooperation with:
National Bank of Belgium, Brussels
Suggested Citation: Smets, Frank; Wouters, Raf (2002) : An estimated dynamic stochastic
general equilibrium model of the euro area, NBB Working Paper, No. 35, National Bank of
Belgium, Brussels
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NBB WORKING PAPER No. 35 - October 2002 1
NATIONAL BANK OF BELGIUM
WORKING PAPERS - RESEARCH SERIES
AN ESTIMATED DYNAMIC STOCHASTIC GENERAL EQUILIBRIUM MODEL
OF THE EURO AREA
_______________________________
Frank Smets
(*)
& Raf Wouters
(**)
We thank participants in the ECB Workshop on “DSGE models and their use in monetary
policy”, the San Francisco Fed/SIEPR Conference on “Macroeconomic models for
monetary policy” and the NBER/EEA International Seminar on Macroeconomics (ISOM)
and in particular our discussants, Harris Dellas, Stefano Siviero, Peter Ireland, Lars
Svensson, Jordi Gali and Noah Williams for very useful comments. We thank Larry
Christiano, Chris Sims, Fabio Canova and Frank Schorfheide for very insightful
discussions. We are also grateful to Frank Schorfheide for making his code available.
Finally, thanks are also due to Jim Stock (editor) and three anonymous referees of the
Journal of the European Economic Association. A previous version of the paper was
published at the occasion of the ISOM-conference as ECB-WP No. 171. The views
expressed are solely our own and do not necessarily reflect those of the European Central
Bank or the National Bank of Belgium. All remaining errors are the author’s.
(*)
Frank Smets: European Central Bank and CEPR, e-mail: Frank.Smets@ecb.int.
(**)
NBB, Research Department, (e-mail: Rafael.Wouters@nbb.be).
2 NBB WORKING PAPER No.35 - October 2002
Editorial Director
Jan Smets, Member of the Board of Directors of the National Bank of Belgium
Statement of purpose:
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studies (Documents Series) made within the National Bank of Belgium or presented by outside economists in seminars,
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NATIONAL BANK OF BELGIUM
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Imprint: Responsibility according to the Belgian law: Jean Hilgers, Member of the Board of Directors, National Bank of Belgium.
Copyright © National Bank of Belgium
Reproduction for educational and non-commercial purposes is permitted provided that the source is acknowledged.
ISSN: 1375-680X
NBB WORKING PAPER No. 35 - October 2002 1
Abstract
This paper develops and estimates a dynamic stochastic general equilibrium
(DSGE) model with sticky prices and wages for the euro area. The model incorporates
various other features such as habit formation, costs of adjustment in capital accumulation
and variable capacity utilisation. It is estimated with Bayesian techniques using seven key
macro-economic variables: GDP, consumption, investment, prices, real wages,
employment and the nominal interest rate. The introduction of ten orthogonal structural
shocks (including productivity, labour supply, investment, preference, cost-push and
monetary policy shocks) allows for an empirical investigation of the effects of such shocks
and of their contribution to business cycle fluctuations in the euro area. Using the
estimated model, the paper also analyses the output (real interest rate) gap, defined as the
difference between the actual and model-based potential output (real interest rate).
Key words: DSGE models; monetary policy; euro area
JEL-classification: E4-E5
2 NBB WORKING PAPER No.35 - October 2002
Citations
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Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach

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Frank Smets1, Frank Smets2, Rafael Wouters3•
Center for Economic Studies1, European Central Bank2, National Bank of Belgium3
01 Feb 2007-Social Science Research Network
TL;DR: Using a Bayesian likelihood approach, the authors estimate a dynamic stochastic general equilibrium model for the US economy using seven macroeconomic time series, incorporating many types of real and nominal frictions and seven types of structural shocks.
Abstract: Using a Bayesian likelihood approach, we estimate a dynamic stochastic general equilibrium model for the US economy using seven macro-economic time series. The model incorporates many types of real and nominal frictions and seven types of structural shocks. We show that this model is able to compete with Bayesian Vector Autoregression models in out-of-sample prediction. We investigate the relative empirical importance of the various frictions. Finally, using the estimated model we address a number of key issues in business cycle analysis: What are the sources of business cycle fluctuations? Can the model explain the cross-correlation between output and inflation? What are the effects of productivity on hours worked? What are the sources of the "Great Moderation"?

3,155 citations

Journal Article•DOI•
Shocks and frictions in US business cycles: A Bayesian DSGE approach

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Frank Smets1, Rafael Wouters2•
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01 Jan 2007-The American Economic Review
TL;DR: In this paper, a dynamic stochastic general equilibrium (DSGE) model for the US economy is proposed, which incorporates many types of real and nominal frictions: sticky nominal price and wage setting, habit formation in consumption, investment adjustment costs, variable capital utilisation and fixed costs in production.
Abstract: We estimate a dynamic stochastic general equilibrium (DSGE) model for the US economy. The model incorporates many types of real and nominal frictions: sticky nominal price and wage setting, habit formation in consumption, investment adjustment costs, variable capital utilisation and fixed costs in production. It also contains many types of shocks including productivity, labour supply, investment, preference, cost-push and monetary policy shocks. Using Bayesian estimation techniques, the relative importance of the various frictions and shocks in explaining the US business cycle are empirically investigated. We also show that this model is able to outperform standard VAR and BVAR models in out-of-sample prediction.

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Matteo Iacoviello1•
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TL;DR: This paper developed a general equilibrium model with sticky prices, credit constraints, nominal loans and asset prices, and found that monetary policy should not target asset prices as a means of reducing output and inflation volatility.
Abstract: I develop a general equilibrium model with sticky prices, credit constraints, nominal loans and asset prices. Changes in asset prices modify agents’ borrowing capacity through collateral value; changes in nominal prices affect real repayments through debt deflation. Monetary policy shocks move asset and nominal prices in the same direction, and are amplified and propagated over time. The “financial accelerator” is not constant across shocks: nominal debt stabilises supply shocks, making the economy less volatile when the central bank controls the interest rate. I discuss the role of equity, debt indexation and household and firm leverage in the propagation mechanism. Finally, I find that monetary policy should not target asset prices as a means of reducing output and inflation volatility.

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Understanding the Effects of Government Spending on Consumption

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Jordi Galí1, J. David López-Salido2, Javier Vallés•
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Abstract: Recent evidence suggests that consumption rises in response to an increase in government spending. That finding cannot be easily reconciled with existing optimizing business cycle models. We extend the standard new Keynesian model to allow for the presence of rule-of-thumb consumers. We show how the interaction of the latter with sticky prices and deficit financing can account for the existing evidence on the effects of government spending. (JEL: E32, E62)

1,542 citations

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Staggered prices in a utility-maximizing framework

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8,580 citations

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Abstract: The equilibrium growth model is modified and used to explain the cyclical variances of a set of economic time series, the covariances between real output and the other series, and the autocovariance of output. The model is fitted to quarterly data for the post-war U.S. economy. Crucial features of the model are the assumption that more than one time period is required for the construction of new productive capital, and the non-time-separable utility function that admits greater intertemporal substitution of leisure. The fit is surprisingly good in light of the model's simplicity and the small number of free parameters. THAT WINE IS NOT MADE in a day has long been recognized by economists (e.g., Bdhm-Bawerk [6]). But, neither are ships nor factories built in a day. A thesis of this essay is that the assumption of multiple-period construction is crucial for explaining aggregate fluctuations. A general equilibrium model is developed and fitted to U.S. quarterly data for the post-war period. The co-movements of the fluctuations for the fitted model are quantitatively consistent with the corresponding co-movements for U.S. data. In addition, the serial correlations of cyclical output for the model match well with those observed. Our approach integrates growth and business cycle theory. Like standard growth theory, a representative infinitely-lived household is assumed. As fluctuations in employment are central to the business cycle, the stand-in consumer values not only consumption but also leisure. One very important modification to the standard growth model is that multiple periods are required to build new capital goods and only finished capital goods are part of the productive capital stock. Each stage of production requires a period and utilizes resources. Halffinished ships and factories are not part of the productive capital stock. Section 2 contains a short critique of the commonly used investment technologies, and presents evidence that single-period production, even with adjustment costs, is inadequate. The preference-technology-information structure of the model is presented in Section 3. A crucial feature of preferences is the non-time-separable utility function that admits greater intertemporal substitution of leisure. The exogenous stochastic components in the model are shocks to technology and imperfect indicators of productivity. The two technology shocks differ in their persistence.

5,728 citations

Journal Article•DOI•
The Science of Monetary Policy: A New Keynesian Perspective

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Columbia University1, Center for Economic and Policy Research2
01 May 1999-Journal of Economic Literature
TL;DR: In contrast to conventional wisdom, this paper showed that gains from commitment may emerge even if the central bank is not trying to inadvisedly push output above its natural level, and also considered the implications of frictions such as imperfect information.
Abstract: The paper reviews the recent literature on monetary policy rules. We exposit the monetary policy design problem within a simple baseline theoretical framework. We then consider the implications of adding various real world complications. Among other things, we show that the optimal policy implicitly incorporates inflation targeting. We also characterize the gains from making a credible commitment to fight inflation. In contrast to conventional wisdom, we show that gains from commitment may emerge even if the central bank is not trying to inadvisedly push output above its natural level. We also consider the implications of frictions such as imperfect information.

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The Dynamic Effects of Aggregate Demand and Supply Disturbances

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Olivier Blanchard, Danny Quah
01 Jun 1993-The American Economic Review
TL;DR: In this article, the authors interpret fluctuations in GNP and unemployment as due to two types of disturbances: disturbances that have a permanent effect on output and disturbances that do not, and they interpret the first as supply disturbances, the second as demand disturbances.
Abstract: We interpret fluctuations in GNP and unemployment as due to two types of disturbances: disturbances that have a permanent effect on output and disturbances that do not. We interpret the first as supply disturbances, the second as demand disturbances. Demand disturbances have a hump-shaped mirror-image effect on output and unemployment. The effect of supply disturbances on output increases steadily over time, peaking after two years and reaching a plateau after five years.

2,711 citations

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Frequently Asked Questions (5)
Q1. What are the contributions in "An estimated dynamic stochastic general equilibrium model of the euro area" ?

In this paper, the authors present and estimate a stochastic dynamic general equilibrium ( DSGE ) model for the euro area. 

Graph 7 shows that a positive preference shock, while increasing consumption and output significantly, has a significant negative crowding-out effect on investment. 

As these shocks give rise to inefficient variations in the flexible-price-and-wage level of output, one can argue that monetary authorities should not accommodate such variations and instead try to keep output at its efficient level. 

Most of these parameters can be directly related to the steady-state values of the state variables and could therefore be estimated from the means of the observable variables (or linear combinations of them). 

Only when they assume decreasing returns to scale and an upward-sloping marginal cost curve, Gali, Gertler and LopezSalido (2000) estimate a more reasonable degree of price stickiness that is comparable with what the authors estimate for wages.