A Test of Normality in Nonlinear Systems of Consumer Demand Equations
Largely because of its increasingly heavy use in the consumer demand systems literature, the class of nonlinear systems of simultaneous (or joint) equation systems has become important in applied econometrics.1 The FIML (full information maximum likelihood) estimator is the most commonly used estimator for those models. Yet hypothesis tests based upon FIML estimation of simultaneous equation systems commonly condition upon an untested maintained hypothesis of normality of the error structure. In addition, when the system is nonlinear in its parameters, many of the asymptotic properties of widely used parameter estimators are known only subject to a normality assumption.2 Furthermore, a fully developed theory of quasi-maximum likelihood estimation does not yet exist in the nonlinear case.3 Hence the assumption of normally distributed disturbances inherently plays a central role in statistical inference with nonlinear simultaneous equation systems. Nevertheless, that normality assumption, unlike other assumptions on the error structure, appears never to have been tested in the relevant applied consumer demand systems literature.4 We shall present and apply a test for error structure normality.
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- Ash, R.B. (1972) Real Analysis and Probability (New York: Academic Press).Google Scholar
- Barnett, W. A. (1981) Consumer Demand and Labor Supply: Goods, Monetary Assets, and Time (Amsterdam: North-Holland).Google Scholar
- Billingsley, P. (1968) Convergence of Probability Measures (New York: Wiley).Google Scholar
- Bowman, K.O. and Shenton, L.R. (1975) Biometrika, 62, 243–50.Google Scholar
- Chung, Kai Lai (1968) A Course in Probability Theory (New York: Harcourt, Brace & World).Google Scholar
- Feller, W. (1966) An Introduction to Probability Theory and Its Applications, Vol. 2 (New York: Wiley).Google Scholar
- Koopmans, T.C., Rubin, H. and Leipnik, R.B. (1950) ‘Measuring the Equation Systems of Dynamic Economics’, in T.C. Koopmans (ed), Statistical Inference in Dynamic Economic Models, Cowles Commission Monograph 10, (New York: Wiley) 53–237.Google Scholar
- Loeve, M. (1963) Probability Theory (Princeton: Van Nostrand).Google Scholar
- Rao, C.R. (1965) Linear Statistical Inference and its Applications (New York: Wiley).Google Scholar
- Selvanathan, E. Antony (1989) ‘Further Results on Aggregation of Differential Demand Equations’, Review of Economic Studies, 56, 799–805.Google Scholar
- Theil, H. (1975) Theory and Measurement of Consumer Demand, Vol. 1 (New York: North-Holland).Google Scholar
- Tucker, H.G. (1967) A Graduate Course in Probability (New York: Academic Press).Google Scholar