Measuring the substitution bias in Japan: the demand system approach and a superlative index

Abstract

This study estimates the demand system using Japanese micro data and calculates the cost of living index (COLI) to assess the substitution bias in the Consumer Price Index. The estimated bias during the sample period of 1982–2000 is about 0.06 percentage points, which is larger than the estimates calculated from a superlative index. The difference between the COLI and a superlative index can be explained with the upward movements of the average utility level in Japan, since the cost of living for the rich has grown more rapidly than that for the poor.

Notes

¹ For example, Lebow and Rudd (2003) compares the CPI with the chained Laspeyres index, and Shiratsuka (1997, 1999) uses the chained Tornqvist index and the chained Fisher index as the ‘true index’.

² Braithwait (1980) and Manser and McDonald (1988) estimated the substitution bias with estimating consumer demand for the United States.

³ Unayama (2004) basically uses the same data and methodology, while this article provides further results and adequate interpretations.

⁴ This problem can be consistent with the dynamic optimization if preferences are time separable, while Karagiannis and Velentzas (2004) explicitly consider the habit effect with the QUAIDS.

⁵ Ruiz-Castillo et al. (2002) pointed out that actual survey period of q ₀ or w ₀ may be prior to the reference period, but this article does not address this issue.

⁶ If the utility function is of the Leontief form, the two are equal.

⁷ Although Leybourne (1993) showed that data would be more compatible with time-varying coefficients, the coefficients here are assumed to be constant over time.

⁸ One-person households are also being included in the JFIES since January 2002; however, they have been excluded from the period under consideration.

⁹ To preserve enough sample size, the first percentile has not been excluded since many households in the sample reported zero expenditure as shown in Table 1. This treatment would cause biased estimates. See, e.g., Keen (1986).

¹⁰ The northern region includes Hokkaido and Tohoku, and the southern region includes Kyusyu and Shikoku.

¹¹ Instrument variables are age of household head, number of working members, 10 regional dummies, yearly income, interest rates, wage, prices, trend and higher-order interactions of these variables.

¹² The process converges within two to eight iterations in the application subsequently.

¹³ Browning and Meghir (1991) and Banks et al. (1997) adopted another two-stage estimation procedure.

¹⁴ The results for the partly and fully unrestricted estimation are not shown here.

¹⁵ Lau (1978) developed a method for imposing concavity using the Cholesky decomposition. See Abdulkadri et al. (2006) for a summary of its implementation.

¹⁶ The eigenvalues for the QUAIDS are (−1.86, −1.31, −0.69, 0, 0.08, 0.55) and for the AIDS (−1.95, −1.56, −0.73, 0, 0.05, 0.56).

¹⁷ Manser and McDonald (1988), Blow and Crawford (2001) and Blundell et al. (2003) presents the nonparametric methods for checking the law of demand.

¹⁸ Unayama (2004) set the utility level, u, to unity, or log u = 0.

¹⁹ The estimates of the bias for the US CPI range from 0.1 to 0.3 percent. See Lebow and Rudd (2003).