Variable Selection in Panel Models with Breaks

We develop a Bayesian approach that performs variable selection in panel regression models affected by breaks. Our approach enables deactivation of pervasive regressors and activation of weak regressors for short periods (regimes). We establish theoretical results on the concentration properties of the posterior as well as the rate of convergence for estimating the break dates. Our methodology is demonstrated in simulations and in an empirical application to firms’ choice of capital structure. We find that ignoring breaks can lead to overestimating the number of relevant regressors, but also a failure to activate regressors that are informative only in short-lived regimes.

[1]  Domenico Giannone,et al.  Economic Predictions with Big Data: The Illusion of Sparsity , 2017, Econometrica.

[2]  Frank Schorfheide,et al.  Forecasting with Dynamic Panel Data Models , 2016, Econometrica.

[3]  M. Pesaran.  General diagnostic tests for cross-sectional dependence in panels , 2004, Empirical Economics.

[4]  Soumendu Sundar Mukherjee,et al.  Weak convergence and empirical processes , 2019 .

[5]  Allan Timmermann,et al.  Detecting Breaks in Real Time: A Panel Forecasting Approach , 2018 .

[6]  Matias D. Cattaneo,et al.  Inference in Linear Regression Models with Many Covariates and Heteroscedasticity , 2015, Journal of the American Statistical Association.

[7]  Badi H. Baltagi,et al.  Estimation and identification of change points in panel models with nonstationary or stationary regressors and error term , 2017 .

[8]  Martin Weidner,et al.  DYNAMIC LINEAR PANEL REGRESSION MODELS WITH INTERACTIVE FIXED EFFECTS , 2014, Econometric Theory.

[9]  Pierre Perron,et al.  Testing for Common Breaks in a Multiple Equations System , 2016, 1606.00092.

[10]  Gerdie Everaert,et al.  Common Correlated Effects Estimation of Dynamic Panels with Cross-Sectional Dependence , 2016 .

[11]  Badi H. Baltagi,et al.  Estimation of Heterogeneous Panels with Structural Breaks , 2016 .

[12]  Matias D. Cattaneo,et al.  ALTERNATIVE ASYMPTOTICS AND THE PARTIALLY LINEAR MODEL WITH MANY REGRESSORS , 2015, Econometric Theory.

[13]  Pier Giovanni Bissiri,et al.  A general framework for updating belief distributions , 2013, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[14]  Sandra Lowe,et al.  Probability A Graduate Course , 2016 .

[15]  Allan Timmermann,et al.  Complete subset regressions with large-dimensional sets of predictors , 2015 .

[16]  Elena Manresa,et al.  Grouped Patterns of Heterogeneity in Panel Data , 2015 .

[17]  Jeffrey Pontiff,et al.  Does Academic Research Destroy Stock Return Predictability? , 2015 .

[18]  Geert Dhaene,et al.  Split-Panel Jackknife Estimation of Fixed-Effect Models , 2015 .

[19]  M. Weidner,et al.  Linear Regression for Panel with Unknown Number of Factors as Interactive Fixed Effects , 2014 .

[20]  Mark T. Leary,et al.  A Century of Capital Structure: The Leveraging of Corporate America , 2014 .

[21]  Frank Schorfheide,et al.  Shrinkage Estimation of High-Dimensional Factor Models with Structural Instabilities , 2013 .

[22]  Ulrich K. Müller.  RISK OF BAYESIAN INFERENCE IN MISSPECIFIED MODELS, AND THE SANDWICH COVARIANCE MATRIX , 2013 .

[23]  P. Phillips,et al.  X-DIFFERENCING AND DYNAMIC PANEL MODEL ESTIMATION , 2013, Econometric Theory.

[24]  Shuheng Zhou,et al.  25th Annual Conference on Learning Theory Reconstruction from Anisotropic Random Measurements , 2022 .

[25]  M. Hashem Pesaran,et al.  Common Correlated Effects Estimation of Heterogenous Dynamic Panel Data Models with Weakly Exogenous Regressors , 2013, SSRN Electronic Journal.

[26]  Barbara Rossi,et al.  Advances in Forecasting Under Instability , 2012 .

[27]  Alexei Onatski,et al.  Asymptotics of the principal components estimator of large factor models with weakly influential factors , 2012 .

[28]  M. Hashem Pesaran,et al.  Testing Weak Cross-Sectional Dependence in Large Panels , 2012, SSRN Electronic Journal.

[29]  Van Der Vaart,et al.  The Bernstein-Von-Mises theorem under misspecification , 2012 .

[30]  Richard Nickl,et al.  Rates of contraction for posterior distributions in Lr-metrics, 1 ≤ r ≤ ∞ , 2011, 1203.2043.

[31]  Dukpa Kim,et al.  Estimating a common deterministic time trend break in large panels with cross sectional dependence , 2011 .

[32]  Emmanuel J. Candès,et al.  Tight Oracle Inequalities for Low-Rank Matrix Recovery From a Minimal Number of Noisy Random Measurements , 2011, IEEE Transactions on Information Theory.

[33]  J. Bai,et al.  Common breaks in means and variances for panel data , 2010 .

[34]  Rodney W. Strachan,et al.  Bayesian forecasting using stochastic search variable selection in a VAR subject to breaks , 2010 .

[35]  Jörg Breitung,et al.  Testing for Structural Breaks in Dynamic Factor Models , 2011, SSRN Electronic Journal.

[36]  J. Rousseau.  Rates of convergence for the posterior distributions of mixtures of betas and adaptive nonparamatric estimation of the density , 2010, 1001.1615.

[37]  Dimitris Korobilis,et al.  VAR Forecasting Using Bayesian Variable Selection , 2009 .

[38]  J. Bai,et al.  Panel Data Models With Interactive Fixed Effects , 2009 .

[39]  Rodney W. Strachan,et al.  Stochastic search variable selection in vector error correction models with an application to a model of the UK macroeconomy , 2009 .

[40]  H. Lian.  Posterior Convergence and Model Estimation in Bayesian Change-point Problems , 2008, 0808.2700.

[41]  Van Der Vaart,et al.  Rates of contraction of posterior distributions based on Gaussian process priors , 2008 .

[42]  Murray Z. Frank,et al.  Capital Structure Decisions: Which Factors are Reliably Important? , 2007 .

[43]  Simon M. Potter,et al.  Estimation and forecasting in models with multiple breaks , 2007 .

[44]  M. West,et al.  Shotgun Stochastic Search for “Large p” Regression , 2007 .

[45]  P. Perron,et al.  Estimating and Testing Structural Changes in Multivariate Regressions , 2007 .

[46]  A. V. D. Vaart,et al.  Convergence rates of posterior distributions for non-i.i.d. observations , 2007, 0708.0491.

[47]  Graham Elliott,et al.  Efficient Tests for General Persistent Time Variation in Regression Coefficients , 2006 .

[48]  Paul Fearnhead,et al.  Exact and efficient Bayesian inference for multiple changepoint problems , 2006, Stat. Comput..

[49]  Christian Gourieroux,et al.  Indirect Inference for Dynamic Panel Models , 2006 .

[50]  Sveriges Riksbank.  Efficient Bayesian inference for multiple change-point and mixture innovation models , 2006 .

[51]  Frank Kleibergen,et al.  Tests of risk premia in linear factor models , 2009 .

[52]  R. Kohn,et al.  Efficient Bayesian Inference for Multiple Change-Point and Mixture Innovation Models , 2005 .

[53]  Allan Timmermann,et al.  Instability of Return Prediction Models , 2005 .

[54]  J. Stock,et al.  A Comparison of Direct and Iterated Multistep Ar Methods for Forecasting Macroeconomic Time Series , 2005 .

[55]  B. M. Pötscher,et al.  MODEL SELECTION AND INFERENCE: FACTS AND FICTION , 2005, Econometric Theory.

[56]  Gary Koop,et al.  Prior Elicitation in Multiple Change-Point Models , 2004 .

[57]  M. Pesaran.  Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure , 2004, SSRN Electronic Journal.

[58]  Josep Lluís Carrion-i-Silvestre,et al.  Structural changes, common stochastic trends and unit roots in panel data , 2004 .

[59]  Davide Pettenuzzo,et al.  Forecasting Time Series Subject to Multiple Structural Breaks , 2004, SSRN Electronic Journal.

[60]  Ivo Welch,et al.  Capital Structure and Stock Returns , 2003, Journal of Political Economy.

[61]  T. Sargent,et al.  Drifts and Volatilities: Monetary Policies and Outcomes in the Post WWII U.S. , 2003 .

[62]  M. Arellano,et al.  The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators , 2003 .

[63]  P. Hansen.  Structural changes in the cointegrated vector autoregressive model , 2003 .

[64]  R. Royall,et al.  Interpreting statistical evidence by using imperfect models: robust adjusted likelihood functions , 2003 .

[65]  J. Bai,et al.  Inferential Theory for Factor Models of Large Dimensions , 2003 .

[66]  Giorgio E. Primiceri,et al.  Time Varying Structural Vector Autoregressions and Monetary Policy , 2002 .

[67]  A. Timmermann,et al.  Market timing and return prediction under model instability , 2002 .

[68]  L. Wasserman,et al.  Rates of convergence of posterior distributions , 2001 .

[69]  Doron Avramov,et al.  Stock Return Predictability and Model Uncertainty , 2001 .

[70]  Jinyong Hahn,et al.  Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects When Both N and T are Large , 2000 .

[71]  K. J. Martijn Cremers,et al.  Stock Return Predictability: A Bayesian Model Selection Perspective , 2000 .

[72]  J. Bai,et al.  Determining the Number of Factors in Approximate Factor Models , 2000 .

[73]  A. V. D. Vaart,et al.  Convergence rates of posterior distributions , 2000 .

[74]  M. Hashem Pesaran,et al.  A Recursive Modelling Approach to Predicting UK Stock Returns , 2000 .

[75]  Campbell R. Harvey,et al.  The Theory and Practice of Corporate Finance: Evidence from the Field , 1999 .

[76]  P. Phillips,et al.  Linear Regression Limit Theory for Nonstationary Panel Data , 1999 .

[77]  S. Chib.  Estimation and comparison of multiple change-point models , 1998 .

[78]  J. Stock,et al.  Testing for and Dating Common Breaks in Multivariate Time Series , 1998 .

[79]  P. Perron,et al.  Computation and Analysis of Multiple Structural-Change Models , 1998 .

[80]  Q. Shao,et al.  Weak convergence for weighted empirical processes of dependent sequences , 1996 .

[81]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[82]  P. Green.  Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[83]  Peter Schmidt,et al.  Efficient estimation of models for dynamic panel data , 1995 .

[84]  P. Perron,et al.  Estimating and testing linear models with multiple structural changes , 1995 .

[85]  R. Rajan,et al.  What Do We Know About Capital Structure? Some Evidence from International Data , 1994 .

[86]  J. Stock,et al.  Evidence on Structural Instability in Macroeconomic Time Series Relations , 1994 .

[87]  D. Andrews.  Tests for Parameter Instability and Structural Change with Unknown Change Point , 1993 .

[88]  Y A Ozcan,et al.  Determinants of capital structure. , 1992, Hospital & health services administration.

[89]  M. Arellano,et al.  Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations , 1991 .

[90]  Artur Raviv,et al.  The Theory of Capital Structure , 1991 .

[91]  D. Pollard.  Empirical Processes: Theory and Applications , 1990 .

[92]  Sheridan Titman,et al.  The Determinants of Capital Structure Choice , 1988 .

[93]  M. King.  The Durbin-Watson test for serial correlation : Bounds for regressions using monthly data , 1983 .

[94]  Cheng Hsiao,et al.  Formulation and estimation of dynamic models using panel data , 1982 .

[95]  Stephen Nickell,et al.  Biases in Dynamic Models with Fixed Effects , 1981 .

[96]  Kenneth J. White,et al.  THE DURBIN-WATSON TEST FOR SERIAL CORRELATION WITH EXTREME SAMPLE SIZES OR MANY REGRESSORS' , 1977 .