By Eric Crampton 23/08/2017

I’ve noted John Gibson’s work showing that standard demand estimation techniques overestimate the price elasticity of demand for sugary drinks, and consequently overestimate the effects of soda taxes.

Gibson shows that, because most empirical work uses household expenditure on the product category divided by some measure of average price, that work bunches together consumer shifts along both quality and quantity dimensions. If people mostly respond to price hikes by shifting to cheaper brands or cheaper packaging (big bottles versus cans, for example), then the demand estimates will mistake quality shifts for quantity shifts. Gibson uses Vietnamese data where there is both household expenditure data, and actual consumption data, to show the extent of the bias.

Turns out that the effect is pretty pervasive. John presented on some of this at the NZAE meetings; the paper with Bonggeun Kim is now up at RePEc.* They show that the Cox and Wohlgenant method, fairly commonly used, overstates price elasticities by a factor of three. Here’s their abstract:

Consumers respond to price rises by reducing quantity consumed, but also by cutting quality. Most demand studies in agricultural economics fail to estimate quality responses to price. Instead, following Cox and Wohlgenant (1986), quality choice is dealt with by adjusting unit values rather than by treating quality as a valid consumer response to model. Studying a two-choice problem in this manner cannot identify either the price elasticity of quantity or the price elasticity of quality, and instead will yield some unidentified hybrid of the quality and quantity responses. We review 150 papers that cite Cox and Wohlgenant (1986) to see how widespread is the neglect of quality responses to price in the literature. Almost 90 percent of studies wrongly mix quality responses to price in with their reported quantity demand elasticities, thus, overstating by how much price rises can be expected to moderate the quantity consumed. Our empirical test, for 32 food and drink groups in Vietnam, shows that the Cox and Wohlgenant method exaggerates quantity responses to price by a factor of three, on average, and hardly differs from what naïve approaches with unit values show. These results cast doubt on three decades of reported price elasticities of quantity demand estimated from household survey data.

They have elasticity estimates on demand for beer. They show that, using the unrestricted method that allows for quality and quantity choices, the price elasticity of quantity demand for beer is close to zero and statistically insignificant, but the price elasticity of quality demand for beer is -0.96 and highly significant.

beer in vietnam
Wikimedia / Riza Nugraha

In other words, basically all of the consumer demand response to changes in beer prices in Vietnam is shifts along a quality axis rather than changing the quantity consumed. That suggests that hiking alcohol excise may do rather less to reduce consumption than you might expect, except among those who are already at the lowest per-unit prices. This cuts in a couple directions. Moderate drinkers show up as more price elastic than heavy drinkers in empirical work: heavy drinkers show up as about 60% as price responsive, going from memory in Wagenaar’s survey.

This could be because of measurement error. If more of the heaviest drinkers are also on the lowest price point, then there’s less confounding with the quality dimension because they’re already at the corner. Moderate drinkers could then appear more responsive because they’re cutting back on quality rather than quantity, but consumption drops among moderate drinkers would be less than the demand elasticity estimates suggest. That could mean that the health costs to moderate drinkers of alcohol excise increases are not as large as we might have feared (if moderate drinkers shift to being occasional drinkers, they lose the benefits of being at the bottom of the J-curve), because fewer might be actually shifting. But they would still be losing out on substantial consumer surplus by having to downshift on quality.

This all suggests using consumption survey data rather than price elasticity data for figuring this stuff out – something more feasible in alcohol work because plenty of health surveys will ask people how many drinks they have per week. I’ll just have to remember to make sure to look at studies using reported real consumption rather than guessing at it from demand elasticities. Participation elasticities should be fine; consumption elasticities … be careful where they came from.

I’ll copy below extensively from their conclusion:

Consequently, what many studies report as a price elasticity of quantity demand is some unidentified hybrid of the price elasticity of quality and the price elasticity of quantity. About 90% of studies in our review mix quality responses to price in with quantity demand elasticities. This overstates the rate that quantity demand falls as prices rise, and overstates the likely efficacy of fiscal-food policies that tax and subsidize certain foods so as to induce a switch towards healthier diets. Our empirical example from Vietnam shows that standard approaches used with household survey data overstate the magnitude of quantity demand elasticities by a factor of three, on average. This gross exaggeration is irrespective of whether budget share equations use prices or unit values. A similar degree of overstatement by the standard methods is found in the few existing studies that also use the unrestricted method, where households can freely adjust quality in response to price changes (McKelvey 2011, Gibson and Kim 2016 and Andalón and Gibson 2017).

Notably, there are no studies in agricultural economics that use the unrestricted method, and few even cite the intellectual origins, in Deaton (1990). Instead, Cox and Wohlgenant (1986) is cited by agricultural economists to justify how household survey data are used to get elasticities. Our results show that this method is flawed, in the sense that it grossly overstates the response of quantity to price. Indeed, Cox and Wohlgenant elasticities hardly differ from those of the standard unit value method, where budget shares are directly regressed on unit values without any prior regression to get ‘quality-adjusted prices’. The flaws in the Cox and Wohlgenant method are not just an empirical matter – which would leave open the possibility that it might work somewhere else – they are inherent in the way that quality responses to price are treated. Rather than model a two-choice problem with an equation for quantity (or budget share) and one for quality, a dubious identifying assumption that quality is chosen first is made, and it is further assumed that quality effects can be purged by regressing unit values on household attributes. This method also ignores measurement error in unit values and ignores the community-wide response of quality to price.

Relying on Cox and Wohlgenant (1986) also contributes to the ongoing misuse of unit values as a proxy for price. Unit values should always be expected to be a bad price proxy, due to the Alchian-Allen effect; the relative price of quality will vary over time and space due to storage and shipping costs (Gibson and Kim 2015). With relative prices varying, the composition of demand within a survey group will not be constant. Thus, unit values will not refer to the same quality mix over time and space and therefore cannot consistently indicate the group price level. However, if one has local price data, then, conditional on prices, the unit value can be informative about consumer quality choices. Yet the demand put on statistical agencies to provide local price data is diminished by so many studies opting to use unit values to measure price, and some responsibility for this again falls on Cox and Wohlgenant (1986). Looking backwards, 30 years of price elasticities estimated from household survey data are likely to be wrong because they have mixed together quality and quantity responses to price. Going forward, only once databases have both market prices and unit values are we likely to correctly estimate how price changes lead to demand responses on both the quantity and quality margins.

It’s a pretty broad critique.

* Note that the pdf download link from RePEc wasn’t working for me at time of writing; John kindly emailed me the paper. If you have download problems as well, note in comments and I’ll pass it along.

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