Abstract
To estimate the model \({{\text{y}}_{\text{t}}} = \sum\nolimits_{{\text{i}} = 1}^{\text{k}} {{\beta _{\text{i}}}} {{\text{x}}_{{\text{ti}}}} + {\varepsilon _{\text{t}}}\) (t = 1,...T observations) by least squares, the T × k matrix of independent variables [xti] must be of full column rank. This requires that the number of observations T exceeds k, the number of independent variables. If this condition is not satisfied, the sample is said to be undersized.
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References
Barnard, G.A. (1963). ‘In discussion,’ Journal of the Royal Statistical Society,Series B, 25: 294.
Barten, A.P. and H. Theil (1964). ‘Simultaneous Estimation of a Complete System of Demand Equations,’ Netherlands School of Economics, Econometric Institute, Report 6405.
Brown, B.W. (1981). ‘Sample Size Requirements in Full Information Maximum likelihood Estimation,’ International Economic Review 22: 443–459.
Deaton, A. (1975). Models and Projections of Demand in Post-War Britain. London: Chapman and Hall.
de Boer, P.M.C. and R. Harkema (1986a). ‘Maximum Likelihood Estimation of Sum-Constrained Linear Models with Insufficient Observations,’ Economics Letters 20: 325–329.
de Boer, P.M.C. and R. Harkema (1986b). ‘An Algorithm for Maximum Likelihood Estimation of A New Covariance Matrix Specification for Sum-Constrained Models,’ Report 8639, Econometric Institute, Erasmus University, Rotterdam.
de Boer, P.M.C. and R. Harkema (1990). ‘Estimating the Consumption Block of the HERMES Models: An Application to the Netherlands,’ Applied Economics 22: 1149 1165.
Fiebig, D.G. and H. Theil (1983). ‘The Two Perils of Symmetry-Constrained Estimation of Demand Systems,’ Economics Letters 13: 105–111.
Italianer, A. (1985). ‘A Small-Sample Correction for the Likelihood Ratio Test,’ Economics Letters 19: 315–317.
Klein, L.R. (1971). ‘Forecasting and Policy Evaluation Using Large Scale Econometric Models: The State of the Art,’ In M.D. Intriligator (ed), Frontiers of Quantitative Economics. Amsterdam: North Holland Publishing Company,133 177.
Laitinen, K. (1978). ‘Why Is Demand Homogeneity So Often Rejected?’ Economics Letters 1: 187–191.
Lluch, C., A.A. Powell and R.A. Williams (1977). Patterns in Household Demand and Saving. Oxford: Oxford University Press.
Maddala, G.S. (1981). ‘Statistical Inference in Relation to the Size of the Model,’In J. Kmenta and J.B. Ramsey (eds)Large—Scale Macro Econometric Models. Amsterdam: North—Holland Publishing Company, 191–218
Meisner, J.F. (1979). ‘The Sad Fate of the Asymptotic Slutsky Symmetry Tests for Large Systems,’ Economics Letters 2: 231–233.
Sargan, J.D. (1975). ‘Asymptotic Theory and Large Models,’ International Economic Review16: 75–91.
Selvanathan, S. 1987). ‘A Monte Carlo Test of Preference Independence,’Economics Letters 25: 259–261.
Selvanathan, S. (1991), The Reliability of ML Estimators of Systems of Demand Equations: Evidence from 18 CountriesReview of Economics and Statistics LXXIII: 338–346.
Selvanathan, S. (1993), ASystem-Wide Analysis of International Consumption PatternsAdvanced Econometric Series, Boston: Kluwer Academic Publishers.
Swamy,P.A.V.B.and J. Holmes (1971). ‘The Use of Undersized Samples in the Estimation of Simultaneous Equation Systems,’Econometrica 39: 455–459.
Theil, H. (1987). ‘The Econometrics of Demand Systems,’ Chapter 3 in H. Theil and K.W. Clements,Applied Demand Analysis: Results from System—Wide Approaches. Cambridge, Mass.: Ballinger Publishing Company, 101 162.
Theil, H. and K. Laitinen (1980). ‘Singular Moments Matrices in Applied Econometrics,’In P.R. Krishnaiah (ed), Multivariate Analysis—V. Amsterdam: North—Holland Publishing Company, 629–649.
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Dongling, C. (1995). Undersized Samples and Demand Analysis. In: Recent Developments in Applied Demand Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85205-3_5
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