Demand estimation when some prices are unobserved: an application to fresh lettuce

Abstract

This study proposes a linear two-stage approach to derive prices of observations when reported consumption is zero. In the first stage, demand equations are estimated using an ad hoc filling of unobserved prices. Then, each estimated demand equation is solved for price and a numerical estimate of the price, which drives consumption to zero, referred to as the choke price, is calculated. The demand equations are re-estimated with the choke-price series replacing the initial ad hoc prices. Although differing claims can be made on the appropriateness of the chosen method for filling prices, we demonstrate significant differences in statistical fit of the demand model and own-price demand elasticities among alternative approaches.

Notes

¹Dong et al., (1998) use a maximum-likelihood approach to jointly estimate demand and price (unit value) equations. They focus on quality of products, and hence, the unit values are set to be functions of household characteristics. Our approach considers the zero-price realization as economic in nature.

²The data series began in September 1999 and ended in January 2004.

³Demand estimation by finer brands was not considered because the proportion of nonzero observations was less than 2% for several brands. Our definition of local brands is the electronic board category listed in the AC Nielsen Homescan Surveys. Prices in each category represent unit values, that is, expenditures on all brands within a category is divided by total quantity.

⁴We do not report long-run elasticities because they are computationally tedious given the multiple lags on ln Q and the recovery of parameters of new brand equations from the two estimated equations.

⁵The bias in expenditure elasticities between the two methods does not appear to follow a pattern.