Arbitrage pricing theory as a restricted nonlinear multivariate regression model: Iterated nonlinear seemingly unrelated regression estimates

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By replacing the unknown random factors of factor analysis with observed macroeconomic variables, the arbitrage pricing theory (APT) is recast as a multivariate nonlinear regression model with across-equation restrictions. An explicit theoretical justification for the inclusion of an arbitrary, well-diversified market index is given. Using monthly returns on 70 stocks, iterated nonlinear seemingly unrelated regression techniques are employed to obtain joint estimates of asset sensitivities and their associated APT risk “prices.” Without the assumption oi normally distributed errors, these estimators are strongly consistent and asymptotically normal. With the additional assumption of normal errors, they are also full-information maximum likelihood estimators. Classical asymptotic nonlinear nested hypothesis tests are supportive of the APT with measured macroeconomic factors. © 1988 American Statistical Association.






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McElroy, MB, and E Burmeister (1988). Arbitrage pricing theory as a restricted nonlinear multivariate regression model: Iterated nonlinear seemingly unrelated regression estimates. Journal of Business and Economic Statistics, 6(1). pp. 29–42. 10.1080/07350015.1988.10509634 Retrieved from

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Marjorie B. McElroy

Professor of Economics

Professor McElroy focuses her research on the subjects of labor, demand systems, and financial economics. She has completed several of her research projects under the funding provided by National Science Foundation grants, including her latest work on the economics of the family in relation to bargain decision-making and marriage markets. She is also currently investigating altruism in marriage markets and bargaining on the core in marriage markets. She has also completed studies involving the investigation of international populations, such as her work with D. Yang on, “Carrots and Sticks: Fertility Effects on China’s Population Policies.” She has collaborated with her contemporaries on several projects, including her earlier work with Hwei-ju Chen, R. Gnanadesikan, and J.R. Kettenring entitled, “A Statistical Study of Groupings of Corporations,” and her project with T.J. Kniesner and Stephen Wilcox on, “Family Structure, Race, and the Feminization of Poverty.” One of her recent published studies, which she completed independently, is entitled, “What’s New with Nash-Bargained Household Demands?”


Edwin Burmeister

Research Professor Emeritus of Economics

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