Testing the integrability of consumer demand functions: Federal Republic of Germany, 1950–1973

The purpose of this paper is to implement a new econometric methodology for testing the theory of consumer behavior. We begin by fitting systems of indirect and direct demand functions without requiring integrability. We then impose restrictions on the parameters of these functions implied by integrability. We test restrictions corresponding to homogeneity, summability, symmetry, nonnegativity, and monotonicity of systems of demand functions. We formulate tests based on two-sided critical intervals for restrictions that take the form of equalities. We employ tests based on one-sided critical intervals for restrictions that take the form of inequalities. We present empirical results for tests of integrability for German time series data on personal consumption expenditures for the period 1950–1973.