Abstract
This article examines the theory and empirics of extremal quantiles in economics, in particular value-at-risk. The theory of extremes has gone through remarkable developments and produced valuable empirical findings since the late 1980s. We emphasize conditional extremal quantile models and methods, which have applications in many areas of economic analysis. Examples of applications include the analysis of factors of high risk in finance and risk management, the analysis of socio-economic factors that contribute to extremely low infant birthweights, efficiency analysis in industrial organization, the analysis of reservation rules in economic decisions, and inference in structural auction models.
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Bibliography
Abrevaya, J. 2001. The effect of demographics and maternal behavior on the distribution of birth outcomes. Empirical Economics 26: 247–259.
Aigner, D.J., and S.F. Chu. 1968. On estimating the industry production function. American Economic Review 58: 826–839.
Aigner, D.J., T. Amemiya, and D.J. Poirier. 1976. On the estimation of production frontiers: Maximum likelihood estimation of the parameters of a discontinuous density function. International Economic Review 17: 377–396.
Arrow, K., T. Harris, and J. Marschak. 1951. Optimal inventory policy. Econometrica 19: 205–272.
Bickel, P., and D. Freedman. 1981. Some asymptotic theory for the bootstrap. Annals of Statistics 9: 1196–1217.
Caballero, R., and E. Engel. 1999. Explaining investment dynamics in U.S. manufacturing: A generalized (S,s) approach. Econometrica 67: 783–826.
Chernozhukov, V. 2005. Extremal quantile regression. Annals of Statistics 33: 806–839.
Chernozhukov, V. 2006. Inference for extremal conditional quantile models, with an application to birthweights. Working paper, Department of Economics, Massachusetts Institute of Technology.
Chernozhukov, V., and L. Umantsev. 2001. Conditional value-at-risk: Aspects of modeling and estimation. Empirical Economics 26: 271–293.
de Haan, L. 1970. On regular variation and its applications to the weak convergence, Tract no. 2. Amsterdam: Mathematical Centre.
Dekkers, A., and L. de Haan. 1989. On the estimation of the extreme-value index and large quantile estimation. Annals of Statistics 17: 1795–1832.
Donald, S.G., and H.J. Paarsch. 2002. Superconsistent estimation and inference in structural econometric models using extreme order statistics. Journal of Econometrics 109: 305–340.
Embrechts, P., Klüppelberg, C. and Mikosch, T. 1997. Modelling extremal events, vol. 33 of Applications of mathematics. Berlin: Springer.
Fama, E.F. 1965. The behavior of stock market prices. Journal of Business 38: 34–105.
Fox, M., and H. Rubin. 1964. Admissibility of quantile estimates of a single location parameter. Annals of Mathematics and Statistics 35: 1019–1030.
Gnedenko, B. 1943. Sur la distribution limité du terme d’ une série alétoire. Annals of Mathematics 44: 423–453.
Hill, B.M. 1975. A simple general approach to inference about the tail of a distribution. Annals of Statistics 3: 1163–1174.
Jansen, D.W., and C.G. de Vries. 1991. On the frequency of large stock returns: Putting booms and busts into perspective. Review of Economics and Statistics 73: 18–24.
Knight, K. 2001. Limiting distributions of linear programming estimators. Extremes 4(2): 87–103.
Koenker, R. 2006. Quantreg: Quantile regression. R package version 3.90. Online. Available at http://www.r-project.org. Accessed 23 April 2007.
Koenker, R., and G.S. Bassett. 1978. Regression quantiles. Econometrica 46: 33–50.
Laplace, P.-S. 1818. Théorie analytique des probabilités. Paris: Éditions Jacques Gabay, 1995.
Leadbetter, M.R., G. Lindgren, and H. Rootzén. 1983. Extremes and related properties of random sequences and processes. New York/Berlin: Springer.
Longin, F.M. 1996. The asymptotic distribution of extreme stock market returns. Journal of Business 69: 383–408.
Mandelbrot, M. 1963. The variation of certain speculative prices. Journal of Business 36: 394–419.
Meyer, R.M. 1973. A poisson-type limit theorem for mixing sequences of dependent ‘rare’ events. Annals of Probability 1: 480–483.
Pareto, V. 1964. Cours d’économie politique. Genéve: Droz.
Pickands, J. III. 1975. Statistical inference using extreme order statistics. Annals of Statistics 3: 119–131.
Portnoy, S., and J. Jurečková 1999. On extreme regression quantiles. Extremes 2: 227–243 (2000).
Praetz, V. 1972. The distribution of share price changes. Journal of Business 45: 49–55.
Quetelet, A. 1871. Anthropométrie. Brussels: Muquardt.
Roy, A.D. 1952. Safety first and the holding of assets. Econometrica 20: 431–449.
Sen, A. 1973. On economic inequality. New York: Oxford University Press.
Timmer, C.P. 1971. Using a probabilistic frontier production function to measure technical efficiency. Journal of Political Economy 79: 776–794.
Zipf, G. 1949. Human behavior and the principle of last effort. Cambridge, MA: Addison-Wesley.
Acknowledgment
We thank Emily Gallagher, Greg Fischer and Raymond Guiteras for their help and valuable comments.
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Chernozhukov, V., Du, S. (2018). Extremal Quantiles and Value-at-Risk. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_2431
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DOI: https://doi.org/10.1057/978-1-349-95189-5_2431
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