Computer Automation of General-to-Specific Model Selection Procedures

That econometric methodology remains in dispute partly reflects the lack of clear evidence on alternative approaches. This paper reconsiders econometric model selection from a computer-automation perspective, focusing on general-to-specific reduction approaches, as embodied in the program PcGets (general-to-specific). Starting from a general linear, dynamic statistical model, which captures the essential data characteristics, standard testing procedures are applied to eliminate statistically-insignificant variables, using diagnostic tests to check the validity of the reductions, ensuring a congruent final model. As the joint issue of variable selection and diagnostic testing eludes most attempts at theoretical analysis, a simulation-based analysis of modelling strategies is presented. The results of the Monte Carlo experiments cohere with the established theory: PcGets recovers the DGP specification with remarkable accuracy. Empirical size and power of PcGets are close to what one would expect if the DGP were known.

General-to-Specific Model Selection Procedures for Structural Vector Autoregressions

Structural vector autoregressive (SVAR) models have emerged as a dominant research strategy in empirical macroeconomics, but suffer from the large number of parameters employed and the resulting estimation uncertainty associated with their impulse responses. In this paper we propose general-to-specific model selection procedures to overcome these limitations. After showing that single-equation procedures are efficient for the reduction of the SVAR, but generally not for the reduction of its reduced form, the proposed reduction procedure is computer-automated using PcGets and its small-sample properties are evaluated in a realistic Monte Carlo experiment. The model selection procedure is shown to recover the DGP specification from a large unrestricted SVAR model with controlled size and power. The impulse responses generated by the selected SVAR are compared to those of the unrestricted and reduced VAR and found to be more precise and accurate. The proposed reduction strategy is then applied to the US monetary system considered by Christiano, Eichenbaum and Evans (1996). Although the selection process is hampered by the misspecification of the unrestricted VAR, the results are consistent with the Monte Carlo and question the validity of the impulses responses generated by the full system.Model selection, Impulse responses, Vector autoregression, Structural VAR, Causal order, Data mining

General--to--Specific Reductions of Vector Autoregressive Processes

Unrestricted reduced form vector autoregressive (VAR) models have become a dominant research strategy in empirical macroeconomics since Sims (1980) critique of traditional macroeconometric modeling. They are however subjected to the curse of dimensionality. In this paper we propose general-to-specific reductions of VAR models and consider computer-automated model selection algorithms embodied in PcGets (see Krolzig and Hendry, 2000) for doing so. Starting from the unrestricted VAR, standard testing procedures eliminate statistically-insignificant variables, with diagnostic tests checking the validity of reductions, ensuring a congruent final selection. Since jointly selecting and diagnostic testing eludes theoretical analysis, we evaluate the proposed strategy by simulation. The Monte Carlo experiments show that PcGets recovers the DGP specification from a large unrestricted VAR model with size and power close to commencing from the DGP itself. The application of the proposed reduction strategy to a US monetary system demonstrates the feasibility of PcGets for the analysis of large macroeconomic data sets.Econometric methodology, Model selection, Vector autoregression, Data mining.

Classical and Modern Business Cycle Measurement: The European Case

This paper intends to harmonize two different approaches to the analysis of the business cycle and in doing so it retrieves the stylized facts of the business cycle in Europe. We start with the “classical” approach proposed in Burns and Mitchell (1946) of dating and analyzing the business cycle; we then adopt the “modern” alternative: the Markov-switching vector autoregression (MS-VAR). The model's regime probabilities provide an optimal statistical inference of the turning point of the European business cycle. For assessing the capacity of the parametric approach to generate the stylized facts of the classical cycle in Europe, the stylized facts of the original data are compared to those of simulated data. The MS-VAR model is shown to be a good candidate for use as an statistical instrument to improve the understanding of the business cycle.International business cycles, European Union, Markov Switching, Structural breaks, Time series analysis.

Wage and Price Phillips Curves

In this paper we introduce a small Keynesian model of economic growth which is centered around two advanced types of Phillips curves, one for money wages and one for prices, both being augmented by perfect myopic foresight and supplemented by a measure of the medium-term inflationary climate updated in an adaptive fashion. The model contains two potentially destabilizing feedback chains, the so-called Mundell and Rose-effects. We estimate parsimonious and congruent Phillips curves for money wages and prices in the US over the past five decades. Using the parameters of the empirical Phillips curves, we show that the growth path of the private sector of the model economy is likely to be surrounded by centrifugal forces. Convergence to this growth path can be generated in two ways: a Blanchard-Katz-type error-correction mechanism in the money-wage Phillips curve or a modified Taylor rule that is augmented by a term, which transmits increases in the wage share (real unit labor costs) to increases in the nominal rate of interest. Thus the model is characterized by local instability of the wage-price spiral, which however can be tamed by appropriate wage or monetary policies. Our empirical analysis finds the error-correction mechanism being ineffective in both Phillips curves suggesting that the stability of the post-war US macroeconomy originates from the stabilizing role of monetary policy.Phillips curves, Mundell effect, Rose effect, monetary policy, Taylor rule, inflation, unemployment, instability

The Properties of Automatic Gets Modelling

We describe some recent developments in PcGets, and consider their impact on its performance across different (unknown) states of nature. We discuss the consistency of its selection procedures, and examine the extent to which model selection is non-distortionary at relevant sample sizes. The problems posed in judging performance on collinear data are noted. We also describe how PcGets has been extended to assist non-experts in model formulation, handle more variables than observations, and tackle non-linear models.Model selection, econometric methodology, PcGets, selection consistency, Monte Carlo

Wage and Price Phillips Curves An empirical analysis of destabilizing wage-price spirals

In this paper we introduce a small Keynesian model of economic growth which is centered around two advanced types of Phillips curves, one for money wages and one for prices, both being augmented by perfect myopic foresight and supplemented by a measure of the medium-term inflationary climate updated in an adaptive fashion. The model contains two potentially destabilizing feedback chains, the so-called Mundell and Rose-effects. We estimate parsimonious and congruent Phillips curves for money wages and prices in the US over the past five decades. Using the parameters of the empirical Phillips curves, we show that the growth path of the private sector of the model economy is likely to be surrounded by centrifugal forces. Convergence to this growth path can be generated in two ways: a Blanchard-Katz-type error-correction mechanism in the money-wage Phillips curve or a modified Taylor rule that is augmented by a term, which transmits increases in the wage share (real unit labor costs) to increases in the nominal rate of interest. Thus the model is characterized by local instability of the wage-price spiral, which however can be tamed by appropriate wage or monetary policies. Our empirical analysis finds the error-correction mechanism being ineffective in both Phillips curves suggesting that the stability of the post-war US macroeconomy originates from the stabilizing role of monetary policy.Phillips curves, Mundell effect, Rose effect, Monetary policy, Taylor Rule, Inflation, Unemployment, Instability

We Ran One Regression

The recent controversy over model selection in the context of `growth regressions' has led to some remarkably numerous `estimation' strategies, including 4 million regressions by Sala-i-Martin (1997b). Only one regression is really needed, namely the general unrestricted model, appropriately reduced to a parsimonious encompassing congruent representation. Such an outcome was achieved in one run on PcGets, within 15 minutes of receiving from Professor Ley the data set in Fernández et al (2001). We reproduce that equation, and corroborate the findings in Hoover and Perez (2004), who also adopt an automatic general-to-simple approach.

Sub-sample Model Selection Procedures in Gets Modelling

When the DGP is nested in the model, PcGets delivers high performance selection across different (unknown) states of nature. One of its steps involves sub-sample post-selection assessment, and here we consider its properties and investigate its practical application. The simulation results show that conditional on retaining a variable, sub-sample information cannot discriminate between substantive and adventitious significance. The Monte Carlo experiments also reveal that the sub-sample selection method suggested by Hoover and Perez (1999) is dominated by procedures selecting only on full-sample evidence, when both approaches are evaluated at a given size. Nevertheless, although the sub-sample procedures do not result in a genuinely beneficial trade-off between size and power, they are particularly successful in controlling the size for selection problems that were previously seemed almost intractable.

Comparison of Model Reduction Methods for VAR Processes

The objective of this study is to compare alternative computerized model-selection strategies in the context of the vector autoregressive (VAR) modeling framework. The focus is on a comparison of subset modeling strategies with the general-to-specific reduction approach automated by PcGets. Different measures of the possible gains of model selection are considered: (i) the chances of finding the `correct' model, that is, a model which contains all necessary right-hand side variables and is as parsimonious as possible, (ii) the accuracy of the implied impulse-responses and (iii) the forecast performance of the models obtained with different specification algorithms. In the Monte Carlo experiments, the procedures recover the DGP specification from a large VAR with anticipated size and power close to commencing from the DGP itself when evaluated at the empirical size. We find that subset strategies and PcGets are close competitors in many respects, with the forecast comparison indicating a clear advantage of the PcGets algorithm.Model selection, Vector autoregression, Subset model, Lag order determination, Data mining