Nonlinear VAR: Some Theory and an Application to US GNP and Unemployment
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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- Potter, Simon M., 2000.
"Nonlinear impulse response functions,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 24(10), pages 1425-1446, September.
- Simon M. Potter, 1999. "Nonlinear impulse response functions," Staff Reports 65, Federal Reserve Bank of New York.
- 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.
- Falk, Barry L., 1986. "Further Evidence on the Asymmetric Behavior of Economic Time Series over the Business Cycle," Staff General Research Papers Archive 11097, Iowa State University, Department of Economics.
- Brunner, Allan D, 1992. "Conditional Asymmetries in Real GNP: A Seminonparametric Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(1), pages 65-72, January.
- 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.).
- Pesaran, M. Hashem & Potter, Simon M., 1997. "A floor and ceiling model of US output," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 661-695, May.
- Pesaran, H.M. & Potter, S.M., 1995. "A Floor and Ceiling Model of U.S. Output," Cambridge Working Papers in Economics 9407, Faculty of Economics, University of Cambridge.
- Potter, Simon M, 1995. "A Nonlinear Approach to US GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 109-125, April-Jun.
- Simon M. Potter, 1993. "A Nonlinear Approach to U.S. GNP," UCLA Economics Working Papers 693, UCLA Department of Economics.
- 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.
- Gourieroux, Christian & Monfort, Alain, 1992. "Qualitative threshold ARCH models," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 159-199.
- Gourieroux Christian & Monfort Alain, 1991. "Qualitative threshold arch models," CEPREMAP Working Papers (Couverture Orange) 9109, CEPREMAP.
- 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.
- 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. Full references (including those not matched with items on IDEAS)
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