Testing demand homogeneity when error terms have an elliptically symmetric distribution

Abstract

In this article, we show that the exact test for the homogeneity restriction developed by Laitinen (1978) is robust when the error terms have an elliptically symmetric distribution. The power performance of the test is also examined, assuming that the error terms have a multivariate t distribution. Our empirical example shows that the homogeneity restriction is not rejected at the 5% level by the exact test though it is rejected by the asymptotic Wald test.

Notes

¹ The data is a year average of monthly receipts and disbursements per household in all household.

² The income elasticities and price elasticities are: η _i  = 1 + β _i /w_i , ϵ _ij  = −δ _ij  + γ _ij /w_i  − β _iw_j /w_i , where, δ _ij  = 1 when i = j and δ _ij  = 0 when i ≠ j.

³ Only the estimation results of five goods are represented in Table 2. The income elasticities for 10 goods reveal that (1) food, (2) housing, (3) fuel etc. and (8) education are inelastic and necessities and the rest of (4) furniture, (5) clothing, (6) medical care, (7) transportion, (9) recreation and (10) other expenditure are luxurious goods. The own-price elasticities of (1) food, (3) fuel, (4) furniture, (6) medical care, (7) transportion and (10) other expenditure satisfy the negative condition.

⁴ We also conduct the normality test for the case of m = 9. The residual normality is rejected in the three error terms of nine equations. Compared with m = 4, we find that the possibility of rejecting the normality is higher than m = 4.