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Nonlinear VAR: Some Theory and an Application to US GNP and Unemployment

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  • Filippo Altissimo

    (Banca d'Italia)

  • Giovanni Luca VIolante

    ()
    (University College of London)

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    Abstract

    A generalization of the endogenous threshold model is developed by extending this class to a multivariate framework and to cases where the feedback acts at multiple lags. The feedback is specified, following Beaudry and Koop, by a variable which measures the depth of recessions. We give conditions for the ergodicity of the model and prove strong consistency of the maximum likelihood estimator, although the objective function is discontinuous in the threshold parameter. The model is applied to a bivariate VAR of output growth and changes in the unemployment rate for the US economy. The nonlinearity is found to be statistically significant only in the unemployment equation and it transmits to GNP through the cross-correlation between the series. We also find that, owing to the nonlinear structure, shocks hitting the economy in downturns have lower persistence than those occurring during expansions. Since this dampening effect is stronger for negative than for positive shocks, the feedback from recessions is found to contribute positively to the long-run growth of the economy and we estimate this contribution to be about 1/6 of the total growth over the sample period. We interpret this result as an empirical validation of those economic theories that model recessions as cleansing times. Finally, we suggest that the state-dependence in persistence is a possible key to interpret the divergence in the measures of persistence existing in the literature.

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    Bibliographic Info

    Paper provided by Bank of Italy, Economic Research and International Relations Area in its series Temi di discussione (Economic working papers) with number 338.

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    Date of creation: Oct 1998
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    Handle: RePEc:bdi:wptemi:td_338_98

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    Web page: http://www.bancaditalia.it
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    Related research

    Keywords: mathematical analysis; stochastic models; United States; unemployment; production; econometric models; estimation of parameters;

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    1. Falk, Barry, 1986. "Further Evidence on the Asymmetric Behavior of Economic Time Series over the Business Cycle," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1096-1109, October.
    2. Allan D. Brunner, 1990. "Conditional asymmetries in real GNP: a semi-nonparametric approach," Finance and Economics Discussion Series 140, Board of Governors of the Federal Reserve System (U.S.).
    3. Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, vol. 74(1), pages 119-147, September.
    4. Gourieroux Christian & Monfort Alain, 1991. "Qualitative threshold arch models," CEPREMAP Working Papers (Couverture Orange) 9109, CEPREMAP.
    5. Braun, Phillip A. & Mittnik, Stefan, 1993. "Misspecifications in vector autoregressions and their effects on impulse responses and variance decompositions," Journal of Econometrics, Elsevier, vol. 59(3), pages 319-341, October.
    6. Cipollone Piero & Marchetti Domenico J., 1998. "Strozzature settoriali, limiti alla crescita e pressioni inflazionistiche," Rivista italiana degli economisti, Società editrice il Mulino, issue 1, pages 27-54.
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