Unitary Model

First it was assumed that the unitary model holds for all households. The parameters of the system given in (5) without the Θmatrix were estimated. Prices included food prices, which were numeraire, utility prices, clothing prices, transportation fees, and communication prices. For the single-person households, there were seven preference variables in the a(⋅) index. These were dummies for car ownership, house ownership, living in a city, the female having more than high school education, the female having a white collar job, age and age squared. Also, two variables were included in b(⋅) index; car ownership and house ownership. The absolute price of the numeraire good was excluded from the demand system since homogeneity was maintained and it was also correlated with total expenditure since agents were not at all sensitive to real interest rates. As to the income variables, in a unitary model income should not affect demand once we condition on total expenditure but it was obviously correlated with total expenditure. One objection to this is that preferences may be correlated with demand if, for example, higher paid jobs require more expensive clothing. In this case we would expect to see that higher paid individuals had a higher budget share for clothing than lower paid individuals with the same total expenditure. This was entirely plausible, but it was rejected in our case.

For couples, in addition to the five goods prices, the prices of men’s clothing were introduced. Eight preference factors were included in the a(⋅)

index. Six dummy variables and three continuous variables were also added. The selection of these variables was based on the end result of some preliminary analysis which excluded some other variables (such as the wife's education) which were found to be wholly insignificant. The dummies were

home ownership, living in a city, car ownership, the husband having more than a high school education, the husband having a white collar job, and the wife- management dummy. The wife-management dummy variable took the value one if the income management types were categorized into A-H. Otherwise, the variable took zero. The three continuous variables were the age and age squared of the husband and the age of wife. For the preference factors in the b( ) index, the same variables were included as for singles, that is, dummy variables for car and home ownership.

Table 3.10 and Table 3.11 show the estimated parameters of single- person households and two-person households respectively. Among single- person households, city-dweller spent more on transportation and communication. In general, in cities, people commute by public transportation every day and have more chances to use communication devices, so the signs of the parameters make sense. Home owners spent less on transportation and communication. This might be because their houses were built near their offices and the commute fees could be reduced. Although the reason for lower expenditure on communication is hard to define, it might be that home owners took advantage of obtaining special discount when making contract with communication companies such as a combined telephone, TV, internet package. The expenditure on transportation and communication of higher educated people and white collars was also lower. Maybe they could afford to have or rent houses near their offices to save on transportation and communication fees. In the case of two-person households, city-dwellers spent more on utilities, whose charges are higher in the city areas. Household owners also spent more money for utilities. In general, privately owned houses are larger than rented houses, so they need more utilities. What is interesting

is that higher educated people or white collars spent more money on their clothing. This might represent that higher educated people or white collars were required to wear a variety of clothes or higher quality clothing. Wife- management dummy represents that the households where wives managed their incomes saved more on the expenditure on utilities. On the other hand, those households purchased more clothes for both men and women. According to this model, wives might know more about how to reduce the utility cost. Instead, they tended to spend more on their personal items.

In Table 3.13, the tests for symmetry for our two strata are presented. It seems that the singles data were consistent with the unitary model (or at least the implications of symmetry and the exclusion of income). The results for couples are representative of the results usually presented in the literature on demand analysis on micro data: the symmetry restrictions were rejected at conventional sizes. One reaction to this is to adjust significance levels so that these test statistics are not interpreted as indicating rejection. For example, if a Schwarz critical level of (degrees of freedom * log (sample size)) for both of the tests given here are used, then it would be concluded that the unitary model was, a posteriori, the more likely. Under this interpretation there are no problems with the application of the unitary model to household data. The converse view is that the restrictions are suspect and that we cannot necessarily apply the unitary model to two-person households. Now testing the implications of our proposed alternative for couples, the collective model is investigated.