Economics Letters 13 (1983) 105-111 North-Holland 105 THE TWO PERILS OF SYMMETRY-CONSTRAINED ESTIMATION OF DEMAND SYSTEMS * Denzil G. FIEBIG Unioersify of Sydney, Australia Henri THEIL University of Florida, Gainesville, FL 3261 I, USA Received 4 April 1983 When the error covariance matrix B of a demand system is unknown and is estimated, (1) symmetry-constrained estimates based on such a P estimate may have large mean squared errors, and (2) the conventionally computed standard errors may seriously underestimate the variability of these estimates. Several procedures are compared; the conventional one (which uses a P estimate consisting of mean squares and products of LS residuals) performs worst. The work of Laitinen (1978) Meisner (1979) and Bera et al. (198 1) has illustrated the deficiencies of asymptotically valid tests of demand homogeneity and Slutsky symmetry. Meisner (1981) conducted a simula- tion experiment based on data for 15 countries to verify the performance of symmetry-constrained estimators; the objective of this paper is to extend the analysis for other estimators using the same data. The homogeneity-constrained demand model takes the form n-1 YK = a, + PIXOC + c T,(X,c - %,.) + c,cr (1) /=I * Research supported in part by the McKethan-Matherly Eminent Scholar Chair, Univer- sity of Florida. 0165-1765/83/$3.00 0 1983, Elsevier Science Publishers B.V. (North-Holland)