VAR for VaR: measuring systemic risk using multivariate regression quantiles.

White, Halbert and Kim, Tae-Hwan and Manganelli, Simone (2010): VAR for VaR: measuring systemic risk using multivariate regression quantiles.

Abstract

This paper proposes methods for estimation and inference in multivariate, multi-quantile models. The theory can simultaneously accommodate models with multiple random variables, multiple confidence levels, and multiple lags of the associated quantiles. The proposed framework can be conveniently thought of as a vector autoregressive (VAR) extension to quantile models. We estimate a simple version of the model using market returns data to analyse spillovers in the values at risk (VaR) of different financial institutions. We construct impulse-response functions for the quantile processes of a sample of 230 financial institutions around the world and study how financial institution-specific and system-wide shocks are absorbed by the system.

• Item Type: MPRA Paper
• Language: English
• Keywords: Quantile impulse-responses; spillover; codependence; CAViaR
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General

References

Acharya, V., Pedersen, L., Philippe, T., and Richardson, M. (2010). Measuring systemic risk. Technical report, Department of Finance, NYU.

Adrian, T. and Brunnermeier, M. (2009). CoVaR. Manuscript, Princeton University.

Andersen, T. G., Bollerslev, T., Diebold, F. X. and Labys, P. (2003). Modeling and Forecasting Realized Volatility. Econometrica 71: 579--625.

Andrews, D.W.K. (1988). Laws of large numbers for dependent non-identically distributed random variables. Econometric Theory 4, 458-467.

Bartle, R. (1966). The Elements of Integration. New York: Wiley.

Engle, R.F. and C.T. Brownlees (2010). Volatility, Correlation and Tails for Systemic Risk Measurement. Manuscript, Stern School of Business, New York University.

Engle, R.F. and Manganelli, S. (2004). CAViaR: Conditional autoregressive value at risk by regression quantiles. Journal of Business & Economic Statistics 22, 367-381.

Huber, P.J. (1967). The behavior of maximum likelihood estimates under nonstandard conditions. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability. Berkeley: University of California Press, pp. 221--233.

Kim, T.-H. and White, H. (2003). Estimation, inference, and specification testing for possibly misspecified quantile regression. In T. Fomby and C. Hill, eds., Maximum Likelihood Estimation of Misspecified Models: Twenty Years Later. New York: Elsevier, pp. 107-132.

Koenker, R. and Bassett, G. (1978). Regression quantiles. Econometrica 46, 33--50.

Komunjer, I. (2005). Quasi-maximum likelihood estimation for conditional quantiles. Journal of Econometrics 128, 127-164.

Komunjer, I. and Vuong, Q. (2006). Efficient conditional quantile estimation: the time series case. University of California, San Diego Department of Economics Discussion Paper 2006-10.

Komunjer, I. and Vuong, Q. (2007a). Semiparametric efficiency bound and M-estimation in time-series models for conditional quantiles. University of California, San Diego Department of Economics Discussion Paper

Komunjer, I. and Vuong, Q. (2007b). Efficient estimation in dynamic conditional quantile models. University of California, San Diego Department of Economics Discussion Paper.

Newey, W.K. and Powell, J.L. (1990). Efficient estimation of linear and type I censored regression models under conditional quantile restrictions. Econometric Theory 6, 295-317.

Otsu, T. (2003). Empirical likelihood for quantile regression. University of Wisconsin, Madison Department of Economics Discussion Paper.

Powell, J. (1984). Least absolute deviations estimators for the censored regression model. Journal of Econometrics 25, 303-325.

Stinchcombe, M. and White, H. (1998). Consistent specification testing with nuisance parameters present only under the alternative. Econometric Theory 14, 295-324.

Weiss, A. (1991). Estimating nonlinear dynamic models using least absolute error estimation. Econometric Theory 7, 46-68.

White, H. (1994). Estimation, Inference and Specification Analysis. New York: Cambridge University Press.

White, H. (2001). Asymptotic Theory for Econometricians. San Diego: Academic Press.

White, H. (2006). Approximate nonlinear forecasting methods. In G. Elliott, C.W.J. Granger, and A. Timmermann, eds., Handbook of Economic Forecasting. New York: Elsevier, pp. 460-512.

White, H., Kim, T.-H., and Manganelli, S. (2008). Modeling autoregressive conditional skewness and kurtosis with multi-quantile CAViaR. In J. Russell and M. Watson, eds., Volatility and Time Series Econometrics: A Festschrift in Honor of Robert F. Engle, forthcoming.