Using multiple price indexes to measure changes in inequality is not a good idea
Although I often disagree with him, I very much enjoy Will Wilkinson as a writer. But I really have to object when he claims in desperate italics that
the use of multiple price indexes to measure trends in inequality…is the correct thing to do.
It is not at all the correct thing to do.
Wilkinson’s post is called “The Indeterminacy of Income Growth”. Putting aside measurement error in tracking nominal income (not Wilkinson’s point), the current distribution of income and its relative growth in different quantiles is not at all indeterminate. Many consequences of inequality follow from nominal disparities in income, independently of how changes alter consumption. Kevin Drum makes this point very well.
“Consumption inequality” is in general the wrong way to think about the consequences of inequality. As Mark Thoma recently pointed out, wealth is largely not about what one consumes, but about the time and freedom one has to sacrifice to sustain “normal” consumption. The price of freedom is nowhere in ones “consumption basket”. It is related to the gap between income and ordinary consumption, and also to the price of what one does not ordinarily consume, the cost of deviation. Indebtedness also entails a cost in freedom that we miss if we focus on consumption. In my view, freedom, not consumption, is the central distinction between rich and poor. It is odd that I should argue this point with libertarian Wilkinson.
But, let’s put that question aside and focus on consumption inequality. Here’s a thought experiment that I think captures Wilkinson’s view of why we should “use multiple price indexes” when thinking about changes in inequality.
Suppose that two gentleman, Richie Rich and Peter Poor have incomes respectively of $1,000,000 and $10,000 in the year 2000. There are four goods in our economy, caviar, opera, hot dogs, and sit-coms. Each month, Rich purchases 73 servings of caviar, 24 operas, two hot dogs, and a sit-com. Poor purchases 38 hot dogs and 15 sit-coms. Since we are focusing in consumption inequality alone, we’ll say both Rich and Poor spend their entire incomes each month on these goods. They are both budget constrained: they would consume more if they had more cash.
Now suppose that, between 2000 and 2010 Rich’s income doubles while Poor’s income increases by 10%. Further, suppose that the price of caviar and opera both double, while the price of hot dogs and soap operas increase by 10%. What Wilkinson wants us to conclude from this experiment is that inequality has not, in fact increased. Ignoring rounding errors, Rich can still consume basically what he could consume in 2000, as can Poor. They are both in the same situation they were in 2000, no?
No, they are not. Wilkinson is ignoring substitution effects. As the price difference between caviar and hot dogs expands, Rich will shift his consumption basket, foregoing some caviar for hot dogs. Doing so will make Rich strictly better off than he was in 2000: he could have maintained his old consumption basket, but the opportunity presented by cheap hot dogs gave him a better deal. Poor, on the other hand, will not shift any of his consumption towards caviar and opera, and he cannot shift away, since he was already consuming none of the now more expensive luxuries. Poor’s consumption basket will have gone nowhere over the aughts, while Rich’s will have improved. If we use multiple price indices to claim that the two groups’ “real incomes” stayed the same over the period, we will have missed this change. It is an error of elementary microeconomics.
It would be an error to claim that consumption inequality does not change with a changing price level even if incomes are fixed and prices move uniformly. This is easy to see when inflation outpaces income. Suppose there is no income growth in our economy, but the price of all goods double. Using price indices to measure “real income”, there will appear to have been no change in inequality. But Poor would have been forced to cut his consumption of sit-coms entirely and to carefully ration hot dog calories. Rich will have partially substituted from caviar to hot dogs and from opera to sit-coms, but his nutritional needs will remain met. In “utility” terms, the change in the price level will have impacted Poor far more than Rich, both because the marginal utility of consumption diminishes with wealth and because Rich can cushion the loss of real income with substitutions unavailable to Poor.
For a reductio ad absurdam, assume that incomes remain constant while the price of rich goods increases 100 fold, but that of poor goods increases only 50 fold. “Real income inequality” will appear to have fallen by half, but Poor will have starved to death while Rich gorges on hot dogs. I’d say inequality had in fact increased.
In his initial piece, Wilkinson frequently alludes to the conventional inflation rate, suggesting by analogy that if using a consumption-basket-based price index is sensible at a national level, it ought to be sensible for smaller groups too, and perhaps we should even imagine different inflation rates for each individual. But the basic problem with price indices, that they ignore substitution, gets more pronounced the more finely you slice and dice the population. Patterns of national consumption over the short-term are much less sensitive to changes in relative price than an individual’s or a subgroup’s consumption. An individual will switch to hot dogs when caviar prices skyrocket, but the economy as a whole will consume what the economy produces, while prices adjust to ensure equilibrium. Over longer terms, national consumption baskets change, and BLS has to account for shifts in the overall consumption basket with unempirical estimates of changes in value (“hedonics”). These questionable fudges would have to be used at a very high frequency for subgroup CPIs to track lived experience.
Usually the substitution problem leads to overstatements of inflation or understatements of real income growth. Rich people and poor people have different abilities to make substitutions in their consumption basket. Suppose I’m rich and I work in New York, so I commute by taxi. If taxi fares rise, I can substitute subway commutes. But if I’m poor, my “consumption basket” was already all subway for the trip to work. I can’t substitute when the cost of my cheapest feasible option rises. This asymmetry means that a rich-person CPI will be overstated due to neglected substitutions much more than the poor person’s CPI. Measurement error will bias us against perceiving inequality.
In general, trying to capture changes in “real income inequality” via price indices, single or multiple, will fail to track a big source of inequality, the differential ability of the wealthy to respond to price and income changes via substitution. This mismeasurement can go both ways: the approach can understate the relative gains of the poor as their incomes increase relative to the price of “rich goods”, creating new substitution options for the poor without much changing the consumption options of the rich. (Note that the poor are harmed, always in absolute terms and sometimes in relative terms, when the price of “rich goods” increases, unless we take their income as permanently fixed. The multiple price index approach assumes the poor should be indifferent to the price of goods outside their typical basket.)
It is basically a bad idea to try to measure “real income inequality” with price indices, because the consumption-related welfare of the poor is so much more sensitive to changes in income than that of the rich. Variations in consumption or spending that generate small changes in quality of life among the wealthy generate large variations in nutrition, health, education, and shelter among the poor. If you think consumption inequality is all that matters, you should just not pay any attention to what’s going on with the rich and focus on increasing real consumption among the poor. If that’s what you think, then the multiple price index stuff is just a fancy way of persuading us to ignore the burgeoning nominal incomes of the rich. But it’s not “correct”, and not helpful except as smart-sounding obfuscation. If we should concentrate on the absolute consumption of the poor, just make a simple case based on decreasing marginal utility. I won’t be persuaded, because I think the benefits of relative wealth are much larger than what is visible in consumption. But messing around with price indexes won’t help us resolve that argument.
Wilkinson’s bottom line, I think, is this:
[T]here is no fact of the matter about real income growth. And this means that there is no fact of the matter about the trend in income inequality.
I’ve ultimately supported Wilkinson’s case, in a sense. He talks up multiple price indices as the “correct” tool to measure inequality ultimately to persuade us that it is too hard to do properly. I agree that it is hard to do properly, and think claims based on income-level specific price-indices should be taken with boulders of salt. Wilkinson then continues
[I]f you’re committed to a story about American political economy that requires a great deal of confidence about how much median income or income inequality has or hasn’t risen since the 1970s, you should know that no such confidence is warranted.
That’s a step too far. Most social phenomena lack precise measures. We build social theories on differences along dimensions of freedom, individualism, racism, “happiness”, quality of institutions, trust, relationship-strength, formal versus familial affiliations, etc. etc. etc. We’ve made up measures for all of these things, but they are all poor. We do empirical work with our measures anyway. Smart readers aren’t snowed by the false precision of a regression and a t-statistic. We should require a lot of evidence to take seriously results whose fancy math obscures messy data. Nevertheless, I’m pretty sure that “quality of institutions” has had something to do with economic growth and that cross-sectional differences in freedom have important implications for welfare.
We always observe qualitative differences first, and then try to quantify those with our measures. (If you don’t believe me, look at the tendentious manner by which measures of social phenomena are actually constructed). Qualitatively, I’m as certain that income inequality has increased in meaningful ways as I am certain that the United States has better institutions than post-Communist Eastern Europe or that the character of racism in America has changed since the 1970s. I can come up with quantitative measures that would capture some aspects of those changes. (If I couldn’t come up with anything, I might revisit my qualitative certainty.) But I can’t come up with a definitive measure, something objective that I can use as uncontroversially as a chemist uses temperature. Wilkinson tries simultaneously to anoint one true measure and then trash it as too noisy to be reliable. He is right that his measure is bad. We have better measures, and our evidence that inequality has consequentially increased in America is at least as good as our evidence for many other social phenomena that we widely assume are real.
Note: See Karl Smith for an excellent discussion of the ambiguous line between price inflation and quality distinctions, and how that can contributes to mismeasurements of inflation even using conventional, national price indexes. If rich people are paying more and getting more value for their money, then an inflation measure that saw the price change but ignored the increase value would understate rich-person income growth.
- 28-September-2010, 12:15 p.m. EDT: Cleaned up some embarrassing repeated phrases and grammatical mistakes. No substantive changes.
- 28-September-2010, 2:50 p.m. EDT: Fixed a couple of typos pointed out by gappy in the comments. Thanks gappy!