Empirical issues in the computation of Stone–Lewbel price indexes in censored micro-level demand systems

ABSTRACT

In this article, we propose an empirical method for the computation of the Stone–Lewbel (SL) price index for product aggregates, when censored samples with zero expenditures are available from household budget surveys. The proposed technique is based on a regression imputation method that takes into account the price dynamics, therefore, allowing to disentangle the role of demographics from the role of prices in computing the SL index. Our simulations seem to indicate that our method is a valuable alternative.

KEYWORDS:

• Stone–Lewbel price indexes
• censored data
• household budget survey
• demand estimation

JEL CLASSIFICATION:

• C24
• D11
• D12

Acknowledgement

This work was supported by the Daniel & Nina Carasso Foundation through the [FP7 SUSFOOD ERA-Net Research Project ‘SUSDIET] – Implementing sustainable diets in Europe’ (Scientific Coordinator: Louis-George Soler).

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ In their article, Castellón et al. (2015) found that different specifications of the SL index do not have a significant impact on demand estimation. Although limited to the data set used in their paper, this finding suggests that demand estimation may not suffer from the absence of any price information.

² Note that this is somewhat similar to the ‘no price’ case in Castellón et al. (2015), where individual price differences are only due to demographic heterogeneity (see Lewbel 1989); however, to account for price dynamics, we introduce the Cobb–Douglas index in Equation (1a).

³ As pointed out by a Referee, being (1a) an empirical approximation to the true index in Equation (1), alternative formulations for the Cobb–Douglas price index in Equation (1a) could be adopted, such as time-specific average budget shares. We have chosen to resort to this formulation because it uses constant budget shares, and therefore, the dynamics of the Cobb–Douglas price index is only due do the dynamics of prices within the group.

Additional information

Funding

This work was supported by the Daniel & Nina Carasso Foundation through the [FP7 SUSFOOD ERA-Net Research Project ‘SUSDIET] – Implementing sustainable diets in Europe’ (Scientific Coordinator: Louis-George Soler).