Estimation of continuous-time linear DSGE models from discrete-time measurements

Bent Jesper Christensen; Luca Neri; Juan Carlos Parra-Alvarez

doi:10.1016/j.jeconom.2024.105871

Estimation of continuous-time linear DSGE models from discrete-time measurements

Bent Jesper Christensen^*
, Luca Neri
, Juan Carlos Parra-Alvarez

^*Corresponding author for this work

Department of Economics and Business Economics

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

1 Citation (Scopus)

9 Downloads (Pure)

Abstract

We provide a general state space framework for estimation of the parameters of continuous-time linear DSGE models from discrete-time data. Our approach relies on the exact discrete-time representation of the equilibrium dynamics, hence avoiding discretization errors. We construct the exact likelihood for data sampled either as stocks or flows, based on the Kalman filter, and provide necessary and sufficient conditions for local identification of the frequency-invariant structural parameters of the underlying continuous-time model. We recover the unobserved structural shocks at measurement times from the reduced-form residuals in the state space representation by exploiting the underlying causal links implied by the economic model. We illustrate our approach using an off-the-shelf real business cycle model. Extensive Monte Carlo experiments show that the finite sample properties of our estimator are superior to those of an estimator relying on a naive Euler–Maruyama discretization of the economic model. In an application to postwar U.S. macroeconomic data, we estimate the model using series sampled at mixed frequencies, and combinations of series sampled as stocks and flows, and we provide a historical decomposition of the effects of shocks on observables into those stemming from structural supply and demand shocks.

Original language	English
Article number	105871
Journal	Journal of Econometrics
Volume	244
Issue	2
ISSN	0304-4076
DOIs	https://doi.org/10.1016/j.jeconom.2024.105871
Publication status	Published - Sept 2024

Keywords

Continuous time
DSGE models
Exact discrete-time state space representation
Local identification
Mixed frequency data
Stock and flow variables
Structural shocks

Access to Document

10.1016/j.jeconom.2024.105871Licence: CC BY

1-s2.0-S0304407624002161-mainFinal published version, 1.47 MBLicence: CC BY

Library access?

Check availability with the Royal Danish Library

Cite this

@article{4c0aa19220d342dbb76789822412ba0f,

title = "Estimation of continuous-time linear DSGE models from discrete-time measurements",

abstract = "We provide a general state space framework for estimation of the parameters of continuous-time linear DSGE models from discrete-time data. Our approach relies on the exact discrete-time representation of the equilibrium dynamics, hence avoiding discretization errors. We construct the exact likelihood for data sampled either as stocks or flows, based on the Kalman filter, and provide necessary and sufficient conditions for local identification of the frequency-invariant structural parameters of the underlying continuous-time model. We recover the unobserved structural shocks at measurement times from the reduced-form residuals in the state space representation by exploiting the underlying causal links implied by the economic model. We illustrate our approach using an off-the-shelf real business cycle model. Extensive Monte Carlo experiments show that the finite sample properties of our estimator are superior to those of an estimator relying on a naive Euler–Maruyama discretization of the economic model. In an application to postwar U.S. macroeconomic data, we estimate the model using series sampled at mixed frequencies, and combinations of series sampled as stocks and flows, and we provide a historical decomposition of the effects of shocks on observables into those stemming from structural supply and demand shocks.",

keywords = "Continuous time, DSGE models, Exact discrete-time state space representation, Local identification, Mixed frequency data, Stock and flow variables, Structural shocks",

author = "Christensen, \{Bent Jesper\} and Luca Neri and Parra-Alvarez, \{Juan Carlos\}",

note = "Publisher Copyright: {\textcopyright} 2024 The Author(s)",

year = "2024",

month = sep,

doi = "10.1016/j.jeconom.2024.105871",

language = "English",

volume = "244",

journal = "Journal of Econometrics",

issn = "0304-4076",

publisher = "Elsevier B.V.",

number = "2",

}

TY - JOUR

T1 - Estimation of continuous-time linear DSGE models from discrete-time measurements

AU - Christensen, Bent Jesper

AU - Neri, Luca

AU - Parra-Alvarez, Juan Carlos

PY - 2024/9

Y1 - 2024/9

N2 - We provide a general state space framework for estimation of the parameters of continuous-time linear DSGE models from discrete-time data. Our approach relies on the exact discrete-time representation of the equilibrium dynamics, hence avoiding discretization errors. We construct the exact likelihood for data sampled either as stocks or flows, based on the Kalman filter, and provide necessary and sufficient conditions for local identification of the frequency-invariant structural parameters of the underlying continuous-time model. We recover the unobserved structural shocks at measurement times from the reduced-form residuals in the state space representation by exploiting the underlying causal links implied by the economic model. We illustrate our approach using an off-the-shelf real business cycle model. Extensive Monte Carlo experiments show that the finite sample properties of our estimator are superior to those of an estimator relying on a naive Euler–Maruyama discretization of the economic model. In an application to postwar U.S. macroeconomic data, we estimate the model using series sampled at mixed frequencies, and combinations of series sampled as stocks and flows, and we provide a historical decomposition of the effects of shocks on observables into those stemming from structural supply and demand shocks.

AB - We provide a general state space framework for estimation of the parameters of continuous-time linear DSGE models from discrete-time data. Our approach relies on the exact discrete-time representation of the equilibrium dynamics, hence avoiding discretization errors. We construct the exact likelihood for data sampled either as stocks or flows, based on the Kalman filter, and provide necessary and sufficient conditions for local identification of the frequency-invariant structural parameters of the underlying continuous-time model. We recover the unobserved structural shocks at measurement times from the reduced-form residuals in the state space representation by exploiting the underlying causal links implied by the economic model. We illustrate our approach using an off-the-shelf real business cycle model. Extensive Monte Carlo experiments show that the finite sample properties of our estimator are superior to those of an estimator relying on a naive Euler–Maruyama discretization of the economic model. In an application to postwar U.S. macroeconomic data, we estimate the model using series sampled at mixed frequencies, and combinations of series sampled as stocks and flows, and we provide a historical decomposition of the effects of shocks on observables into those stemming from structural supply and demand shocks.

KW - Continuous time

KW - DSGE models

KW - Exact discrete-time state space representation

KW - Local identification

KW - Mixed frequency data

KW - Stock and flow variables

KW - Structural shocks

UR - https://www.scopus.com/pages/publications/85208178545

U2 - 10.1016/j.jeconom.2024.105871

DO - 10.1016/j.jeconom.2024.105871

M3 - Journal article

AN - SCOPUS:85208178545

SN - 0304-4076

VL - 244

JO - Journal of Econometrics

JF - Journal of Econometrics

IS - 2

M1 - 105871

ER -

Estimation of continuous-time linear DSGE models from discrete-time measurements

Abstract

Keywords

Access to Document

Library access?

Other files and links

Fingerprint

Cite this