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Elias Tzavalis
- 29 July 2026
- WORKING PAPER SERIES - No. 3263Details
- Abstract
- We develop an endogenous threshold VAR that addresses contemporaneous dependence between the threshold variable and reduced-form innovations— a pervasive issue when regime indicators are jointly determined with system dynamics. A regime-specific copula-based control function removes this dependence instrument-free, without parametric assumptions on the threshold’s marginal distribution, while preserving the linear regime-wise least-squares structure. We characterize the resulting misspecification through excess sensitivity and excess propagation errors in impulse responses, clarify structural and proxy-SVAR identification under endogenous regimes, and establish conditions under which Chan-type threshold asymptotics remain valid with generated controls. A Hermite sieve extension accommodates tail-dependent and asymmetric dependence. Monte Carlo evidence documents large distortions from ignoring endogeneity. Applied to monetary transmission, the framework avoids the price and persistence puzzles displayed by the linear VAR, delivers regime-dependent sacrifice ratios, and aligns estimated regimes with historical inflation episodes.
- JEL Code
- C32 : Mathematical and Quantitative Methods→Multiple or Simultaneous Equation Models, Multiple Variables→Time-Series Models, Dynamic Quantile Regressions, Dynamic Treatment Effect Models, Diffusion Processes
C34 : Mathematical and Quantitative Methods→Multiple or Simultaneous Equation Models, Multiple Variables→Truncated and Censored Models, Switching Regression Models
E52 : Macroeconomics and Monetary Economics→Monetary Policy, Central Banking, and the Supply of Money and Credit→Monetary Policy
- 18 December 2019
- WORKING PAPER SERIES - No. 2345Details
- Abstract
- Using a novel methodology, we offer new evidence that a threshold relationship exists for Okun’s law. We use a logistic smoothed transition regression (LSTR) model where possible threshold endogeneity is addressed based on copula theory. We also suggest a new test of the linearity hypothesis against the LSTR model. A combination of structural and policy-related variables accounts for changes (rises) in the Okun’s parameter in the US in recent decades. Accordingly, the unemployment gap is increasingly associated with a smaller output gap. Whilst the Great Recession accelerated that rise, the bulk of the change occurred beforehand.
- JEL Code
- C46 : Mathematical and Quantitative Methods→Econometric and Statistical Methods: Special Topics→Specific Distributions, Specific Statistics
E23 : Macroeconomics and Monetary Economics→Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy→Production
E24 : Macroeconomics and Monetary Economics→Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy→Employment, Unemployment, Wages, Intergenerational Income Distribution, Aggregate Human Capital
C24 : Mathematical and Quantitative Methods→Single Equation Models, Single Variables→Truncated and Censored Models, Switching Regression Models
- 1 March 2018
- WORKING PAPER SERIES - No. 2136Details
- Abstract
- We suggest a new method dealing with the problem of endogeneity of the threshold variable in single regression threshold models and seemingly unrelated systems of them based on copula theory. This theory enables us to relax the assumption that the threshold variable is normally distributed and to capture the dependence between the error term and the threshold variable in each regime of the model independently of the marginal distribution of the threshold variable. This distribution can be estimated non-parametrically conditionally on the value of threshold parameter. To estimate the slope and threshold parameters of the model adjusted for the endogeneity of the threshold variable, we suggest a two-step concentrated least squares estimation method where the threshold parameter is estimated based on a search procedure, in the first step. A Monte Carlo study indicates that the suggested method deals with the endogeneity problem of the threshold variable satisfactorily. As an empirical illustration, we estimate a threshold model of the foreign-trade multiplier conditional on the real exchange rate volatility regime. We suggest a bootstrap procedure to examine if there are significant differences in the foreign-trade multiplier effects across the two regimes of the model, under potential endogeneity of the threshold variable.
- JEL Code
- C12 : Mathematical and Quantitative Methods→Econometric and Statistical Methods and Methodology: General→Hypothesis Testing: General
C13 : Mathematical and Quantitative Methods→Econometric and Statistical Methods and Methodology: General→Estimation: General
C21 : Mathematical and Quantitative Methods→Single Equation Models, Single Variables→Cross-Sectional Models, Spatial Models, Treatment Effect Models, Quantile Regressions
C22 : Mathematical and Quantitative Methods→Single Equation Models, Single Variables→Time-Series Models, Dynamic Quantile Regressions, Dynamic Treatment Effect Models &bull Diffusion Processes