Granger Causality and Dynamic Structural Systems

Using a generally applicable dynamic structural system of equations, we give natural definitions of direct and total structural causality applicable to both structural vector autoregressions (VARs) and recursive structures representing time-series natural experiments. These concepts enable us to forge a previously missing link between Granger (G-)causality and structural causality by showing that, given a corresponding conditional form of exogeneity, G-causality holds if and only if a corresponding form of structural causality holds. We introduce a variety of structurally informative extensions of G-causality and provide their structural characterizations. Of importance for applications is the structural characterization of finite-order G-causality, which forms the basis for most empirical work. We show that conditional exogeneity is necessary for valid structural inference and prove that, in the absence of structural causality, conditional exogeneity is equivalent to G noncausality. These characterizations hold for both structural VARs and natural experiments. We propose practical new G-causality and conditional exogeneity tests and describe their use in testing for structural causality. We illustrate with studies of oil and gasoline prices, monetary policy and industrial production, and stock returns and macroeconomic announcements.

[1]  Jean-Pierre Florens,et al.  Non Causality in Continuous Time , 1996 .

[2]  S. Ross,et al.  Economic Forces and the Stock Market , 1986 .

[3]  M. Shapiro.  Federal Reserve Policy: Cause and Effect , 1993 .

[4]  Frank T. Magiera,et al.  Macroeconomic Factors Do Influence Aggregate Stock Returns , 2002 .

[5]  Halbert White,et al.  Settable Systems: An Extension of Pearl's Causal Model with Optimization, Equilibrium, and Learning , 2009, J. Mach. Learn. Res..

[6]  Halbert White,et al.  Time-series estimation of the effects of natural experiments , 2006 .

[7]  C. Granger.  Some recent development in a concept of causality , 1988 .

[8]  P. Burridge,et al.  A Very Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix , 1991 .

[9]  J. Carlos Escanciano,et al.  ON THE LACK OF POWER OF OMNIBUS SPECIFICATION TESTS , 2009, Econometric Theory.

[10]  Rosa L. Matzkin,et al.  Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors , 2005 .

[11]  Robert M. de Jong,et al.  THE BIERENS TEST UNDER DATA DEPENDENCE , 1996 .

[12]  Clive W. J. Granger,et al.  Some recent developments in a concept of causality , 2001 .

[13]  J. Florens,et al.  A Note on Noncausality , 1982 .

[14]  G. Imbens,et al.  Identification and Estimation of Triangular Simultaneous Equations Models without Additivity , 2002 .

[15]  S. Borenstein,et al.  Do Gasoline Prices Respond Asymmetrically to Crude Oil Price Changes , 1997 .

[16]  Halbert White,et al.  Approximate Nonlinear Forecasting Methods , 2006 .

[17]  H. White,et al.  A NONPARAMETRIC HELLINGER METRIC TEST FOR CONDITIONAL INDEPENDENCE , 2008, Econometric Theory.

[18]  J. Heckman,et al.  Econometric Causality , 2008 .

[19]  Eric M. Leeper,et al.  Narrative and VAR Approaches to Monetary Policy: Common Identification Problems , 1996 .

[20]  Sílvia Gonçalves,et al.  Bootstrap Standard Error Estimates for Linear Regression , 2005 .

[21]  H. White,et al.  Maximum Likelihood and the Bootstrap for Nonlinear Dynamic Models , 2000 .

[22]  C. Granger.  Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[23]  C. Granger.  Testing for causality: a personal viewpoint , 1980 .

[24]  C. Granger,et al.  Handbook of Economic Forecasting , 2006 .

[25]  Y. Hochberg.  A sharper Bonferroni procedure for multiple tests of significance , 1988 .

[26]  A. Dawid.  Conditional Independence in Statistical Theory , 1979 .

[27]  Steven Berry,et al.  On the Nonparametic Identification of Nonlinear Simultaneous Equations Models: Comment on B. Brown (1983) and Roehrig (1988) , 2004 .

[28]  E. Candès.  Ridgelets: estimating with ridge functions , 2003 .

[29]  J. Carlos Escanciano,et al.  Generalized spectral tests for the martingale difference hypothesis , 2006 .

[30]  H. White,et al.  A Consistent Characteristic-Function-Based Test for Conditional Independence , 2003 .

[31]  Wenceslao González Manteiga,et al.  Significance testing in nonparametric regression based on the bootstrap , 2001 .

[32]  O. Penrose.  The Direction of Time , 1962 .

[33]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[34]  G. Chow,et al.  Dynamic Economics: Optimization by the Lagrange Method , 1997 .

[35]  H. White,et al.  Identification with Conditioning Instruments in Causal Systems , 2007 .

[36]  W. Newey,et al.  Nonparametric estimation of triangular simultaneous equations models , 1999 .

[37]  C. Crowe,et al.  Monetary Policy Matters , 2010 .

[38]  Nicholas M. Kiefer,et al.  HETEROSKEDASTICITY-AUTOCORRELATION ROBUST TESTING USING BANDWIDTH EQUAL TO SAMPLE SIZE , 2002, Econometric Theory.

[39]  S. Taylor.  Forecasting Economic Time Series , 1979 .

[40]  Nicholas M. Kiefer,et al.  A NEW ASYMPTOTIC THEORY FOR HETEROSKEDASTICITY-AUTOCORRELATION ROBUST TESTS , 2005, Econometric Theory.

[41]  O. Linton,et al.  Conditional Independence Restrictions: Testing and Estimation , 1996 .

[42]  C. Sims.  Money, Income, and Causality , 1972 .

[43]  F. Fisher.  A Correspondence Principle for Simultaneous Equation Models , 1970 .

[44]  O. Linton,et al.  A kernel method of estimating structured nonparametric regression based on marginal integration , 1995 .

[45]  H. White,et al.  Independence and Conditional Independence in Causal Systems , 2007 .

[46]  M. Flannery,et al.  Macroeconomic Factors Do Influence Aggregate Stock Returns , 2002 .

[47]  H. White,et al.  Testing a conditional form of exogeneity , 2010 .

[48]  Michael R. Kosorok,et al.  Robust semiparametric M-estimation and the weighted bootstrap , 2005 .

[49]  Maxwell B. Stinchcombe,et al.  CONSISTENT SPECIFICATION TESTING WITH NUISANCE PARAMETERS PRESENT ONLY UNDER THE ALTERNATIVE , 1998, Econometric Theory.

[50]  R. H. Strotz,et al.  RECURSIVE VS. NONRECURSIVE SYSTEMS: AN ATTEMPT AT SYNTHESIS (PART I OF A TRIPTYCH ON CAUSAL CHAIN SYSTEMS) , 1960 .

[51]  A. Goldberger.  STRUCTURAL EQUATION METHODS IN THE SOCIAL SCIENCES , 1972 .

[52]  H. White,et al.  An Extended Class of Instrumental Variables for the Estimation of Causal Effects , 2011 .

[53]  D. Romer,et al.  Does Monetary Policy Matter? A New Test in the Spirit of Friedman and Schwartz , 1989, NBER Macroeconomics Annual.

[54]  H. White.  Retrospective Estimation of Causal E¤ects Through Time , 2007 .

[55]  Jean-Pierre Florens,et al.  Noncausality in Continuous Time , 1996 .