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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)

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.

Suggested Citation

  • Filippo Altissimo & Giovanni Luca VIolante, 1998. "Nonlinear VAR: Some Theory and an Application to US GNP and Unemployment," Temi di discussione (Economic working papers) 338, Bank of Italy, Economic Research and International Relations Area.
    • Handle: RePEc:bdi:wptemi:td_338_98
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    1. Filippo Altissimo & Giovanni L. Violante, 2001. "The non-linear dynamics of output and unemployment in the U.S," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(4), pages 461-486.
    2. Dapontas Dimitrios & Evangelopoulos Panagiotis, 2013. "Has the NAFTA Foundation Affected Business Cycles Length? An Introduction," Scientific Annals of Economics and Business, Sciendo, vol. 60(1), pages 145-153, July.
    3. Siviero, S. & Terlizzese, D. & Visco, I., 1999. "Are Model-Based Inflation Forecasts Used in Monetary Policymaking? A Case Study," Papers 357, Banca Italia - Servizio di Studi.
    4. Sella Lisa, 2008. "Old and New Spectral Techniques for Economic Time Series," Department of Economics and Statistics Cognetti de Martiis. Working Papers 200809, University of Turin.

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    More about this item

    Keywords

    mathematical analysis; stochastic models; United States; unemployment; production; econometric models; estimation of parameters;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production
    • E24 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Employment; Unemployment; Wages; Intergenerational Income Distribution; Aggregate Human Capital; Aggregate Labor Productivity

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