Elsevier

Economics Letters

Volume 176, March 2019, Pages 55-59
Economics Letters

Structural changes in large economic datasets: A nonparametric homogeneity test

https://doi.org/10.1016/j.econlet.2018.12.020Get rights and content

Highlights

  • We propose a Bayesian nonparametric homogeneity test for distributional changes.

  • We demonstrate that the test is related to Shannon’s entropy.

  • The homogeneity test is appealing to use with large dataset applications.

  • Findings show that it can detect structural changes in the US economy.

Abstract

This paper proposes a Bayesian nonparametric homogeneity test for distributional changes. We provide an asymptotic approximation of the Bayes factor and show that it is related to the Shannon entropy. The proposed test is suitable for large high-dimensional datasets which otherwise require time-consuming computation for posterior approximation. An analysis on the FRED-QD macroeconomic dataset shows the ability of the test to detect relevant structural changes in the US economy.

Introduction

There exists an established literature on the investigation of structural changes in large panel data for economic and financial time series, encompassing the identification of turning points in business cycles, or financial stress periods in stock markets. Examples of empirical application focusing on the changes in the cross section of macroeconomic variables are the studies by Canova (2004) and Stock and Watson (2014). The former proposes a joint testing procedure to identify convergence clubs in income per capita of the OECD countries while the latter studies the cross section of a large set of macroeconomic series to detect turning points in the US economy. Detecting those structural changes allows policy makers to intervene in a timely way to ensure economic and financial stability, and investors to efficiently manage their portfolios and risk exposition.

The paper attempts to contribute to this stream of literature by proposing a Bayesian nonparametric homogeneity test for distributional changes in large economic datasets. The proposed approach abstracts the distributional assumption and relies onPitman–Yor and Dirichlet process priors (Ferguson, 1973, Lo, 1984, Sethuraman, 1994), which are widely used in statistics and econometrics (Hirano, 2002, Griffin and Steel, 2011, Bassetti et al., 2014, Bassetti et al., 2018). Since simulation methods for posterior approximation can be heavily time consuming when dealing with high dimensional panels, we propose an asymptotic approximation of the Bayes factor (BF) to overcome this issue. We show that the approximated BF has an appealing representation which allows relating the homogeneity test to Shannon’s entropy of empirical distributions. Entropy is a measure of complexity which has been applied successfully in many economic and financial studies (Maasoumi and Racine, 2002, Billio et al., 2016, Gradojevic and Caric, 2017).

We provide an application on the FRED-QD macroeconomic dataset and show the ability of the homogeneity test to detect relevant structural changes in the US economy.

Section snippets

A nonparametric homogeneity test

Let x={xi}i=1n be an i.i.d. sequence of real-valued samples, i.e. xiXR from the sequence of discrete distribution p(x|π)=j=1mπjIAj(x)with m{0,1,2,,}, where π={πj}j=1m is a sequence of probability parameters such that πj0 and j=1mπj=1, {Aj}j=1m is a partition of the support X such that AiAj=, ij and j=1mAj=X. IA(x) is the indicator function, which takes value 1 if xA and 0, otherwise. The likelihood of the data is a product of multinomial distribution and can be written as p(x|π)=i

An application to the FRED-QD dataset

We apply the homogeneity test to detect structural breaks in the FRED-QD dataset (McCracken and Ng, 2016) which is a large US macroeconomic database containing 248 economic variables specifically designed for the empirical analysis of big data.1

Conclusions

This paper proposes a Bayesian nonparametric homogeneity test for distributional changes and provides an asymptotic approximation of the Bayes factor related to the Shannon entropy. The testing procedure is well suited for large datasets which usually require time-consuming posterior computation methods. In the application on the FRED-QD macroeconomic database, the homogeneity test detects distributional changes in correspondence with the most severe US economic turning points. We believe that

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    The authors would like to thank the Editor and an anonymous referee for useful comments and suggestions. Michele Costola acknowledges financial support from the Research Center SAFE, funded by the State of Hessen initiative for research LOEWE. Roberto Casarin acknowledges financial support from the Venice center in Economic and Risk Analytics for public policies (VERA) at University Ca’ Foscari of Venice, funded by Italian Ministry of Education, Universities and Research (MIUR).

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