阈值内生性在向量自回归模型中的研究：重新评估货币状态依赖性

Threshold endogeneity in vectorautoregressions: reassessingmonetary state dependence Dimitris Christopoulos, Peter McAdam,Elias Tzavalis AbstractWedevelopanendogenousthresholdVARthataddressescontemporaneousde- pendencebetweenthethresholdvariableandreduced-forminnovations,aper-vasiveissuewhenregimeindicatorsarejointlydeterminedwithsystemdynam-ics.Aregime-specificcopula-basedcontrolfunctionremovesthisdependencewithoutrequiringexternalinstrumentsorparametricassumptionsonthethresh-old’smarginaldistribution,whilepreservingthelinearregime-wiseleast-squaresstructure.Wedemonstratethatomittingthecontrolgenerates“excesssensiti-vity”and“excesspropagation”errorsinimpulseresponses,clarifystructuralandproxy-SVAR identification under endogenous regimes,and establishconditionsunder which Chan-type threshold asymptotics remain valid withgeneratedcon-trols.AHermitesieveextensionaccommodatestail-dependentandasymmet-ricdependence.MonteCarloexercisesdocumentthesizeofthebiasesfrom ig-noring endogeneity across different designs.Applied to theanalysisof monetary transmission,the framework avoids the price andpersistencepuzzles displayed by a linear VAR,delivers regime-dependentsacrificeratios,andalignsestimatedregimeswithhistoricalinflationepisodes. KEYWORDS.EndogenousThreshold,MonteCarlo,MonetaryPolicy,ImpulseRe-sponse.JELCLASSIFICATION.C32,C34,E52. NON-TECHNICALSUMMARY The paper studies what happens when the “state” that splits the economy into regimesis itself reacting to shocks, and proposes a way to fix this in threshold VARs. In standardthreshold VARs, the sample is divided into regimes using a threshold variable (for exam-ple, an inflation measure). The literature almost always assumes this threshold variableis predetermined: it can depend on past data, but not on the current shocks hitting thesystem. The authors argue that this is unrealistic in many macro settings, where agentsand policymakers react quickly and thresholds such as inflation, credit spreads, or riskindicators move contemporaneously with shocks. In that case, the threshold is endoge-nous to the VAR and traditional methods can misclassify regimes and distort the esti-mated dynamics. The paper develops an “endogenous-threshold” VAR (TVARN) that explicitly cor-rects for this contemporaneous dependence between the threshold variable and the VARinnovations. The key device is a copula-based control function. The joint distribution ofthe threshold and the VAR shocks is modeled via a copula, which captures their depen-dence structure independently of their marginal distributions. The authors show that,by applying a simple Gaussian copula transformation to the threshold and adding theresulting term as an extra regressor in each regime, one can purge the correlation be-tween the threshold and the residuals. This “copula control” orthogonalizes thresholdand innovations without needing instruments or specifying how the threshold itself isdistributed. It preserves the usual linear-within-regime VAR structure and scales wellwith sample size and dimensionality.Neglecting threshold endogeneity leads to two systematic errors in impulse response analysis. First, excess sensitivity: when the threshold and shocks move together, omittingthe copula control makes the reduced-form shocks mechanically too volatile, becausethey incorporate a missing factor linked to the threshold. As a result, the on-impact re-sponses to a given “structural” shock look too large. Second, excess propagation: thesame omission induces omitted-variable bias in the VAR coefficients, so the estimateddynamics exaggerate persistence or even generate spurious oscillations. These prob-lems arise under common identification schemes (recursive, sign restrictions, long-runrestrictions, external instruments) because they all build on the same biased reduced-form moments. The copula-based correction is designed to remove both channels.The authors assess performance in an extensive Monte Carlo study. They generate data from a TVAR with an endogenous threshold and then estimate two models: the cor-rectly specified endogenous-threshold TVARN and a conventional exogenous-thresholdTVAR (TVARX). They vary the strength and sign of dependence between the thresholdand shocks, allow for Gaussian, Student-t and skewed-t innovations, and consider bothlinear and nonlinear (Archimedean) copulas such as Clayton, Joe, and Gumbel. Acrossdesigns and for sample sizes that mimic typical macro applications (T = 200 and 500quarters), ignoring threshold endogeneity produces substantial bias and mean squarederror in the estimated threshold and in regime-specific covariance matrices. In turn, theimpulse responses from the exogenous model display the excess sensitivity and propa-gation predicted by the theory. By contrast, the endogenous-threshold model substan-tially reduces both bias and MSE and closely tracks the true impulse responses, evenwhen the true dependence structure is non-Gaussian and innovations are heavy-tailed. The