This paper aims at estimating a system of demand equations under the restrictions suggested by the traditional theory of consumer demand: The homogeneity condition, the symmetry condition and negativity condition, ie., the negative semidefiniteness of the substitution matrix. The three conditions are tested by estimating the Rotterdam model on Italian data, both in the restricted and the unrestricted forms. The maximum likelihood principle is used to estimate the model. In particular, the negativity condition is imposed by using the Cholesky decomposition, hence introducing non-linear combinations of the parameters. Following some recent theoretical works, we can calculate the exact distribution of the tests and propose some correction factors for tests which fail to attain the asymptotic conditions. Our results show that the restrictions suggested by economic theory are not unrealistic in the Italian case. This is in contrast with the results of previous research aimed at testing the homogeneity and symmetry properties. Furthermore, these results, obtained for Italy and other countries may be misleading, since they are based on tests with approximated asymptotic distribution. Montecarlo simulations have indeed shown that these tests are severely biased towards rejection of the null hypothesis (the restricted model) when the number of commodity groups in the demand system is large.

### An Empirical Assessment of the Neoclassical Theory of Demand: The Italian Case 1960-1983 (in Italian)

#### Abstract

This paper aims at estimating a system of demand equations under the restrictions suggested by the traditional theory of consumer demand: The homogeneity condition, the symmetry condition and negativity condition, ie., the negative semidefiniteness of the substitution matrix. The three conditions are tested by estimating the Rotterdam model on Italian data, both in the restricted and the unrestricted forms. The maximum likelihood principle is used to estimate the model. In particular, the negativity condition is imposed by using the Cholesky decomposition, hence introducing non-linear combinations of the parameters. Following some recent theoretical works, we can calculate the exact distribution of the tests and propose some correction factors for tests which fail to attain the asymptotic conditions. Our results show that the restrictions suggested by economic theory are not unrealistic in the Italian case. This is in contrast with the results of previous research aimed at testing the homogeneity and symmetry properties. Furthermore, these results, obtained for Italy and other countries may be misleading, since they are based on tests with approximated asymptotic distribution. Montecarlo simulations have indeed shown that these tests are severely biased towards rejection of the null hypothesis (the restricted model) when the number of commodity groups in the demand system is large.
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1988
35
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10278/3687857`