Back to the sweet sweet bog

For the past several years, the public health crowd has brushed off John Gibson's work on sugar taxes by saying that they don't worry about things that aren't in refereed journals.

It takes a lot longer to get things published in economics journals than in public health. Inaccuracies in public health work can then go around the world's newspapers several times before economics starts testing the more robust work in series of departmental seminars before sending the revised and improved draft off to a journal.

Gibson's paper with Bonggeun Kim is now up in the Journal of Development Economics and is ungated for the next month via this link. 

Here's the abstract, which won't be unfamiliar to those who've here been following the debate.

Estimating potential effects of price reforms is a key issue for many developing countries. Demand studies increasingly use household survey data on budget shares, which vary with quantity, price, and quality. If quality response to price is ignored, estimated price elasticities of quantity demand conflate responses on quantity and quality margins. Our review finds over 80% of published studies using budget shares from household survey data have this error. We use survey data from Vietnam, with prices and qualities observed over space, to directly estimate the price elasticity of quality. This is much larger than what is derived from the income elasticity of quality, based on the Deaton (1988) separability restrictions. Across the 45 items we study, the own-price elasticity of quantity demand is overstated by a factor of four, on average, if the response of quality to price is ignored.

The paper covers complicated technical issues in simple language. Economists are sometimes stuck with household expenditure data that only says how much a household spent in total on a product category over the past week, fortnight or month. If they want to know how demand responds to price changes, they have a problem because that data does not say how much was purchased or the price at which things were purchased. The data only says what total expenditure was. Total spending could change because quantities changed, or because

These issues were recognized, and potentially solved, thirty years ago in a set of papers by Angus Deaton (1987, 1988, 1990). Deaton derived the response of quality to price so as to isolate quantity demand elasticities, without needing price data. He assumed weakly separable preferences so that unobserved effects of price on quality could be derived from income elasticities of quality and quantity. Intuitively, by forcing the effect of price on quality to operate as an income effect, Deaton leveraged off what household surveys are good at – measuring incomes or expenditures – to get at what they are bad at or rarely do, which is measuring local prices.1 If one had a household survey with good measures of local prices, and with the usual data on food group expenditures and quantities, one could directly estimate the effect of price on quality by using unit values to indicate consumer quality choice (because the unit value is the product of price and quality). Indeed, Deaton (1990, p.302) concluded that it “would be extremely desirable to have direct measures of market prices against which this method could be tested.”

Gibson and Kim have data allowing this testing. And the testing shows us that weak separability fails, so back to the bog:

Our main title deliberately copies Deaton (1988) because in our view unidentified quality responses are still biasing price elasticities of quantity demand estimated from survey data. Our sub-title is from Gordon Tullock (1985, p.262) describing his role in an intellectual debate:

“… my role in this controversy is to watch people trying to get out of the swamp and then push them back in. Clearly, my role is not a constructive one, but nevertheless, I feel it necessary.”

Our contribution may be viewed similarly; before Deaton, economists used unit values as if they were prices when estimating elasticities of quantity demand. They were in a bog where quality and quantity effects intermixed. Deaton found a way out, pulling himself up just by the bootstraps of separability restrictions, with no firm ground (good price data) in sight.7Standing on firm ground now, with good data on local prices and on consumer's choice of quality, we are pushing people back into the bog by showing that these separability restrictions do not hold. More generally, any model that assumes that the price and income elasticity of quality are closely related is unlikely to hold. The necessary role we play, even if not a constructive one, is to show that we are still bogged down; many estimates of the effect of price on quantity are instead some murky mix of quality and quantity responses. Our defence for our role is that it is only by realizing that we are still bogged that the value of firm ground (good data on local prices and on quality) becomes clear. In our opinion, there will be little headway in using household survey data to accurately estimate quantity responses to spatial price variation until better data on local prices and qualities are collected, so that responses on both the quantity and quality margins can be directly estimated.

I love Tullock references - this one's to Tullock's pushing people back into the bog by showing that explanations around the 'why so little rent-seeking' problem were wanting. Gibson and Kim show that Deaton's path out of the problem doesn't work.

Public Health critiques around hierarchies of evidence and that this is just one paper compared to dozens of other papers so we should look to metastudies - they completely misunderstand the nature of Gibson's contribution here, whether through ignorance or stubbornness, I don't know. Gibson and Kim show that the dozens of other papers that use the Deaton method for estimating price elasticities out of household survey measures are systematically incorrect. Doing a metastudy of papers that have a systematic error in method will not get you a correct answer.

These large biases, from either ignoring quality response to price, or from restricting that response to be what weak separability allows, are in line with the few prior studies on the quality response issue. In the first of these, quantity demand elasticities were inflated to an average of 250% of their unrestricted value, if quality response is ignored (McKelvey, 2011). While that evidence was just for six broad food groups, our results are much the same if based on broad consumption groups or narrower price survey items, so this magnitude of bias may hold more widely. A similar level of bias is seen in studies of soft drinks demand using the unrestricted method and the standard price method. In Melanesia, where spatial price variation is high and product differentiation of soft drinks more limited, the quantity demand elasticities are overstated two-to three-fold if quality response to price is ignored (Gibson and Romeo, 2017). In Mexico, where there is less spatial price variation and more quality variation the bias is four-fold (Andalón and Gibson, 2017).

These quality responses may undermine price policies that aim to reduce consumption of unhealthy items. For example, quantity demand elasticities that ignore the quality response to price are used by Grogger (2017), to forecast that Mexico's peso per liter tax on soft drinks will reduce steady state body-mass index (BMI) of Mexicans by up to 1.8%, which is enough to provide some health benefit. However, if quality downgrading in response to tax-induced price rises is accounted for, the average BMI will fall by just 1/200th (Andalón and Gibson, 2017). This is salient to Vietnam, where a special consumption tax of 10% on soft drinks, instant tea and flavored milk has been proposed by the finance ministry as a way to reduce the health burden of high sugar intakes. However, if adjustment to higher prices is on the quality margin and quantity consumed falls only a little, as in Mexico, this proposed tax will be largely ineffective in achieving health objectives.

The implications are rather broader than sugar tax.

Extrapolating from income effects to price effects may be unwise, as seen with failure of the weak separability assumptions, but a prior debate in development economics about effects of income on nutrition is germane to this discussion. Early studies derived indirect estimates of the income elasticity of calories from food expenditure data, assuming that higher spending on a food group meant proportionately more nutrients. This ignored within-group quality substitution, and later studies showed that extra spending on food as incomes rose went on attributes other than food quantity. Writing about poor people with rising income, Behrman et al. (1988, p.308) noted that:

“… at the margin they concentrate on food attributes other than nutrients – taste, appearance, odor, degree of processing, variety, status – that are not necessarily highly positively correlated with nutritive value.”

In perhaps the same way that policy makers learnt that effects of income changes on nutrients are mediated by within-group quality substitution, so too may they need to learn that effects of price changes on quantities can likewise be mediated by responses on the quality margin.

While Gibson and Kim don't cover it here, because it is obvious, the analysis applies whether a soda tax or sugar tax is ad valorem or a per-unit excise. Whatever you thought the demand response to your price increase was going to be, it'll be smaller to the extent that your elasticity estimates conflate quantity and quality adjustments.

The only case where this won't be true is for people who are already only consuming product that is at the lowest quality point - and you'd probably then want to have an elasticity estimate for that specific cohort anyway rather than assuming that the estimates that apply elsewhere also apply to that cohort.