nach oben

Erschienen in:

2022 | OriginalPaper | Buchkapitel

10. Empirical Methods: Frequentist Estimation

verfasst von : Alfonso Novales, Esther Fernández, Jesús Ruiz

Erschienen in: Economic Growth

Verlag: Springer Berlin Heidelberg

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

The chapter starts with the Generalized Method of Moments estimator, describing its main properties, and applying it to the estimation of an equilibrium asset pricing model. After that, we explain the implementation of the Maximum Likelihood estimator. The Kalman filter, the main tool for the numerical evaluation of the likelihood on the state-space representation of the model, is discussed in detail. We estimate cyclical and trend components in US GDP and the unemployment rate. Finally, we compute the ML estimator to the Hansen (Journal of Monetary Economics 16:309–327, 1985) model of indivisible labor. We explain MATLAB programs provided to estimate structural parameters and generate some interesting properties of Growth models, as impulse responses to supply and demand shocks, and the decomposition of the variance of forecast errors.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Transitional Dynamics in Monetary Economies: Numerical Solutions

Nächstes Kapitel Empirical Methods: Bayesian Estimation

Evidently, E _t − 1[f(Θ₀, y _t)] = 0 and E _t[f(Θ₀, y _t + 1)] = 0 are the same set of conditions.

This is a modified versión of “gmmestimation.m”, which was written by Cao Zhiguang (see https://www.mathworks.com/matlabcentral/fileexchange/12114-gmm).

The reader may want to change the estimation code to use as instruments a constant and lagged consumption growth.

It is well known that if the order of the dynamic system is higher than 1, it can be rewritten as a first order system by taking some lags as additional state variables.

For a more detailed description, see Hamilton [2], Chapter 13. We use the same notation as in that chapter.

The updating formula for a linear projection is based on the following: Let us assume that, conditional on the information set \( {\mathscr{Y}}_{t-1} \), the vector (Z ₁, Z ₂) follows a multivariate normal distribution: \( \left(\begin{array}{c}{Z}_1\\ {}{Z}_2\end{array}\right)\left|{\mathscr{Y}}_{t-1}\right.\sim N\left(\left(\begin{array}{c}{\mu}_1\\ {}{\mu}_2\end{array}\right),\left(\begin{array}{cc}{\Sigma}_{11}& {\Sigma}_{12}\\ {}{\Sigma}_{21}& {\Sigma}_{22}\end{array}\right)\right). \) Then, the probability distribution of Z ₁ conditional on Z ₂, as well as on the information set \( {\mathscr{Y}}_{t-1} \), is given by Z ₁|Z ₂, _t − 1 ∼ N(μ _1 ∣ 2, Σ_1 ∣ 2), where \( {\mu}_{1\mid 2}={\mu}_1+{\Sigma}_{12}{\Sigma}_{22}^{-1}\left({Z}_2-{\mu}_2\right) \), and \( {\Sigma}_{1\mid 2}={\Sigma}_{11}-{\Sigma}_{12}{\Sigma}_{22}^{-1}{\Sigma}_{21} \). Thus, denoting \( {Z}_1\equiv {\xi}_t,{Z}_2\equiv {y}_t-{\hat{y}}_{t\mid t-1}={H}^{\prime}\left({\xi}_t-{\hat{\xi}}_{t\mid t-1}\right)+{w}_t, \) we have, \( {\mu}_1\equiv {\hat{\xi}}_{t\mid t-1},{\mu}_2=0, \) Σ₁₁ = P _{t ∣ t − 1}, Σ₂₂ = H ^′ P _{t ∣ t − 1} H + R, Σ₁₂ = P _{t ∣ t − 1} H. Thus, \( {\mu}_{1\mid 2}={\hat{\xi}}_{t\mid t},{\Sigma}_{11\mid 2}={P}_{t\mid t}. \)

This definition applies here because we are analyzing an economy without endogenous growth.

As an exercise, the reader could estimate the parameters of the model using GDP and hours worked as observable variables.

The structure of these MATLAB files is inspired by those that Professor Peter Ireland has on his website (http://irelandp.com/programs.html). Of course, we encourage the reader to visit such a page to analyze the files that Professor Ireland has used for the frequentist estimation of different DSGE models in his research.

Clark, P. K. (1987). The cyclical component of U.S. economic activity. Quarterly Journal of Economics, 102, 797–814.CrossRef

Hamilton, J. D. (1994). Time series analysis. Princeton University Press.CrossRef

Hansen, G. D. (1985). Indivisible labour and the business cycle. Journal of Monetary Economics, 16, 309–327.CrossRef

Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica, 50(4), 1029–1054.CrossRef

Hansen, L. P., & Singleton, K. (1982). Generalized instrumental variable estimation of nonlinear rational expectations models. Econometrica, 50(1982), 1269–1286.CrossRef

Newey, W. K., West, K. D. (1987). A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix. Econometrica, 55(3), 703–708.

Titel: Empirical Methods: Frequentist Estimation
verfasst von: Alfonso Novales
Esther Fernández
Jesús Ruiz
Verlag: Springer Berlin Heidelberg
Buch: Economic Growth
Print ISBN: 978-3-662-63981-8

Electronic ISBN: 978-3-662-63982-5

Copyright-Jahr: 2022
DOI: https://doi.org/10.1007/978-3-662-63982-5_10

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner