10. Empirical Methodologies and Software Tools

An interesting explanation of the differences between these two methodologies is provided by Canova [1], who claims that the differences between estimation and calibration methods arise because of the different questions these two methodologies try to measure. Calibration methods try to answer the question of ‘Given that the model is false, how true is it?’(p. 2) while in the case of estimation ‘Given that the model is true, how false is it?’(p. 1).

For more information on estimation methodologies used in DSGE modelling and their dominant position in DSGE parameterizations, see the econometrics summary conducted by Fern\(\acute{a}\)ndez-Villaverde [8].

For detailed discussion on calibration, see its application in DSGE modelling exercises undertaken by Kydland and Prescott [2] and Canova and Ortega [9]. Canova [1] made a very important contribution in evaluating the calibrated models. His work also discusses the differences between estimation and calibration methods. As summarized in his work, theoretical jurisdiction of calibration could be found in the macro-level economic models, where the structural parameters are directly identified according to subjective judgements rather than statistical inference (although they admitted statistical methods might be applied to provide more accurate information than purely guessing the numerical values of the structural parameters). Early attempts to apply statistical approaches in model identification include the contribution proposed by Haavelmo [10], who systematically introduces the modern theory of probability and statistical inference as the basis of economic analysis to find the interactions among economic variables. Based on these contributions, calibration and estimation find their fruitful application in DSGE model identification exercises.

For more details of the mathematics behind ML and QMLE methods, one can find them in the work conducted by Fisher [16], who is among the pioneer advocates of the ML methods in econometrics; and White [17], who analyses the consequences and detection of model misspecification in the studies using ML and QMLE approaches.

Gal\(\acute{i}\) and Gertler [18] make a very influential analysis using the GMM method. In this paper, they use data of the period 1960:Q1–1997:Q4 to estimate the structural parameter \(\theta \) in the Phillips curve via GMM methods. Another important DSGE paper using the GMM method is the work of Gal\(\acute{i}\) et al. [19]. In this work, based on data of the time period from 1970 to 1998, a DSGE model with parameter values determined by GMM method is developed. It provides evidence that supports empirically a New Phillips Curve (NPC) for the Euro area.

The SMM method can be viewed as an extension of the original GMM method in that it substitutes the response probabilities of the GMM method with estimators given by the Monte Carlo simulation. In McFadden’s work [20], the mathematical framework of the SMM method is thoroughly discussed.

For more details of Bayes’ Theorem and its wide applications, see the summary demonstrated by Vapnik [22].

For more details of the Kalman Filter and its application, see the works conducted by Harvey [23], Swerling [24] and Kalman [25].

For more details, see the discussion of Blanchard–Kahn condition in the previous chapter.

Due to the limited space, we can not provide a full discussion of all the details of Metropolis–Hastings algorithm; more details can be found in the works of Roberts et al. [26] and Chib and Greenberg [27].

For simplicity, some of the details of the MCMC have been omitted in this thesis; otherwise they would require hundreds of pages. Chib and Greenberg [27] and Gasparini [28] give us a wider reach in MCMC methods with greater details.

In the work of Zellner [29], Bayes’ Theorem is considered as the optimal information processing rule since it makes full use of all the information embodied in the data in a very effective way, and it adds no extraneous information. For a more complete discussion of Bayesian theory, see Bernardo and Smith’s contribution [30].

For a full description of MATLAB, see the official website of Mathworks at http://​uk.​mathworks.​com/​products/​matlab/​index.​html?​s_​tid=​gn_​loc_​drop.

The full description of Dynare is available at http://​www.​dynare.​org.

In order to better demonstrate the application of MATLAB Dynare, we demonstrate the full Dynare code for a simple DSGE model in Appendix.

Interested readers may refer to http://​www.​originlab.​com/​.

Interested readers may refer to http://​www.​eviews.​com/​home.​html.