One True Price Index?

by Will Wilkinson on May 20, 2008

Lane Kenworthy writes:

I’m not sure why Broda and Romalis, or Levitt and Wilkinson, think this should alter our assessment of the trend in inequality. Do they mean to suggest that the revealed preference of the poor for cheap goods is exogenous to their income? In other words, people with low incomes simply like buying inexpensive lower-quality goods, and they would continue to do so even if they had the same income as the rich. Likewise, the rich simply have a taste for better-quality but pricier goods, and they would continue to purchase them even if they suddenly became income-poor. If this is the assumption, I guess the conclusion follows. But I can’t imagine the authors, or anyone else, really believe that.

Maybe I’m missing something, but it seems as though Kenworthy’s response might be based on some kind of conceptual misunderstanding. I’m not sure that this is it, but is the idea here that there is a single, standard, uniform price index, perhaps kept in a vault in Paris next to that famous platinum-iridium bar, the standard meter? But there is no standard index with which to determine the one true rate of inflation, or one true rate of change in real wages, because there is no one true standard consumption basket.

It seems that Kenworthy thinks there is something suspect about looking at the typical consumption basket of people at one part of the income distribution, looking at the typical consumption basket of people at another part of the income distribution, and then determining separately the change in rate of actually experienced inflation for people at those points in the distribution. I don’t see how this requires any weird assumptions about the exogeneity of preferences to income. All it requires is that we take seriously what different kinds of people tend to buy.

Think about it this way. Suppose you’ve got a country with only poor people and a country with only rich people. In each country, their version of the BLS creates something like the CPI. We find that price inflation is lower in the poor country. Then the rich country annexes the poor country. Does calculating separate CPIs suddenly become a kind of mistake?

As I noted in my first post on this paper, when I talked very, very briefly to Sachs about my paper on inequality, looking at the change in price of the typical consumption baskets of the rich and poor was the one thing he suggested one might try to do to get a better sense of what’s happening in terms of the trend in real consumption inequality. I said I didn’t have the technical wherewithal to do that. But Broda and Romalis do. I’m not convinced that they or Sachs or Levitt is confused.

Viewing 12 Comments

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    I think this is an instance of a common mistake made when thinking about income groups. When we're talking about groups of "rich" and "poor" people we're not talking about individuals. Individuals can move in and out of those groups over time (taking their changing consumption patterns with them).

    The revealed preferences of a group (if there even are such things) aren't the same as the revealed preferences of the individuals in those groups. In other words, its logically consistent to have individuals' consumption patterns change as their wealth increases, but to have the average consumption pattern of a group stay the same, especially given the group is defined by income level. Some "poor" are becoming rich, and thus changing their consumption patterns to be more like the "rich", but they are leaving the "poor" group and entering the "rich" group. Similarly for the rich becoming poor.
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    I also think the quoted reply may be based on a misunderstanding. I think Lane is suggesting that the "poor bundle" of goods sucks, while the "rich bundle" is awesome, and thus there is a big hidden gap in well-being.

    Yes, that is true. But is the rich bundle getting more awesome with time? Or is the poor bundle getting more sucky? I think neither of those is true-- in order to have a valid price index, I think you have to fix the awesomeness of the bundle to some constant value (even if you have to change the bundle occasionally when there are new products, etc. -- the total awesomeness of the bundle stays constant, no?)

    If bundle-awesomeness within one index is indeed constant across the years, then relative awesomeness among two different indices is also constant. Therefore, there is no problem with Broda/Romalis' analysis.

    Any economists out there? :)
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    MK, I think, has got it. However I also think that most people, when considering equality, are actually thinking of some putative "base bundle". People are measured based on their distance from this base bundle in either direction. It's considered unethical for the rich to exceed this base bundle by too much if the poor fail to meet this bundle by too much.

    I think this kind of thinking is inherent in the idea of the "living wage" or "dignity wage" that is so often bandied about- also consider "it's obscene for Tiger Woods to spend X when there are people in this country without Y." People aren't upset about the yacht per se (not many people pine over not having a yacht) but they DO see the yacht as representing a multiple of what consider to be "basic needs".

    If this is the attitude you take, which is fundamentally different from strictly caring about inequality in the abstract, then finding out that prices rise steeply beyond the base bundle won't satisfy you very much.

    The hard-core egalitarians are picking a bundle X and measuring inequality relative to the cost of X over time. They're indexing to one bundle. I think that this is essentially the emotional logic behind egalitarianism- a rich man can afford 10,000 bundles of X while the poor man can't even afford .7X. Never mind that no one wants 10,000X or .7X, rather they prefer Y and Z.

    The egalitarians seem to think that there's a set consumption bundle that is the moral minimum level of consumption in a society. If someone falls below the base bundle X, then the needed amount can be transfered, you can't use 10,000X anyway. I'm not sure what the bundle X is, but it would probably make for an excellent paper.

    This little fact means that inflation in the top consumption baskets is (emotionally at least) irrelevant to the egalitarians. That's what I suspect anyway.
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    Ones personal inflation level is always going to be different then the basket used by the BLS. But just because caviar has gotten more expensive relative to bread doesn't mean rich people are poorer. The more money you have, the more options are open to you. The rich could shop at Wal-Mart if they wanted to, the homeless couldn't buy anything on 5th Avenue.

    This measure of inequality, using separate CPIs for different income groups, is certainly worthwhile. It might explain why rich people consistently are greedy, even though it seems like they should have enough. But it's not correct to say that inequality is the same now as it was 30 years ago, when the dollar value disparity in income and wealth is so much larger.

    A fair measure would be to look at the percent of the top quintiles income which would be necessary to maintain the middle, or lowest, quintiles standard of living. That ratio has gotten lower.
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    Say the population consists of two types, rich and poor, with fixed nominal incomes. The poor eat gruel and the rich eat beef wellington. Now say that the price of gruel falls but the proportion of poor people in the population rises. Nothing else changes.

    Should the gruel price decline be presented as something that stops us worrying about the increased proportion of poor people?

    Clearly an increase in the number of poor people accompanied by falling gruel prices is preferable to the same increase but stable prices, which I imagine Lance would agree to, so it may reduce our concerns about increased inequality to some extent. But isn't Lance right that falling gruel prices do not neutralise concerns about rising inequality?

    You'd have to modify my parable to make it reflect the subject in hand more accurately , but I think it captures the issue at stake.
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    Luis, The proportion of the population in the top and bottom decile cannot cannot change. That's the sort of thing we're talking about. And the issue is about WHETHER inequality has increased, not whether to be concerned about it. That prices may rise slower or that quality may increase faster for the goods typically purchased by the poor doesn't neutralize concerns about growing inequality, it may actually stop the inequality -- the kind that matters -- from growing.
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    The quibble with the paper is that to just compare 90th percentile to 10th percentile ignores what's happening between the two-- a huge mass of people could become way more poor, but not enough to move down to the 10th percentile, and nothing in the analysis will suggest higher inequality.

    So, the best variation on this analysis might include more gradations, or or a continuous function, of bundles, rather than 2. But I think this is a quibble.

    A possible non-quibble is that what the authors are doing seems really, really hard. Are they sure they're holding "bundle goodness" constant over the years? That seems to involve a lot of subjectivity. I'd like to understand more about the methodology.

    It's a problem with any price index, though. I trust they followed good standard methodology, and so this is the best guess we have.
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    Will,

    Thanks for the reply. Yes I used an example with changing proportions of rich & poor in an attempt to get at what I thought the issue was in a simple way; this does not mean I think the proportions of the population in each income declines changes!

    When I wrote in terms of neutralising 'concerns' (which may have been a mistake) I was trying to get at whether the 'kind of inequality that matters' (i.e. concerns us) has increased. In my example, I meant to suggest that while increased gruel buying power for the poor may decrease the kind of inequality that matters to some extent, the inequality that matters has more to do with who is eating beef wellington and who is eating gruel.

    I'll try to get closer to reality. Say the top decile eats beef wellington and the bottom eats gruel. Now say the real wage as measured against an economy-wide average price index is unchanged for the poor, but trebles for the rich. At the same time gruel prices fall and beef wellington prices rise by exactly the right amounts so that, when adjusted by their own consumption baskets, the ratio of income between the top and bottom deciles “has risen only 2 percent in this period”. The real income of the rich, measured against the economy average price index, has increased by much more. Perhaps we also need to assume that beef wellington is sufficiently expensive so that the gruel price decline income effect is not large enough for the poor to now choose to purchase a little beef wellington. I'm not sure how well this new story now fits the Broma paper – I haven’t read it closely enough to figure out how they calculate their adjusted change in income ratios - but would you say that in my little revised parable, the sort of inequality that matters has increased?
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    duh - I meant 'decile' not 'declines' in 1st para.
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    Ah. I think I better understand Lane's comment after rereading.


    Suppose there are rich people and poor people. Suppose poor people have flat income growth and flat price growth-- no change. Suppose rich people have high income growth and high price growth -- suppose at the exact same rate -- so that their bundle-adjusted income growth is also flat.

    So, for rich and poor alike, flat growth in bundle-adjusted incomes. Is inequality growing? Maybe!

    The rising cost of rich goods shrinks poor people's consumption possibility frontier (CPF). This is true even if poor people aren't buying rich goods!

    Since in this example, poor people's CPF is weakly shrinking, while rich people's CPF is weakly expanding, poor people are becoming worse off relative to rich people.

    Now, OK. If I have a 25K/year job, and the price of yachts goes up, I probably don't care. But if the price of IPod's goes up, I might care! You can't tell me that I didn't care just because ex post facto, I didn't buy an IPod! That's bad reasoning. Maybe I would have bought one if there was less inflation in the price.

    We cannot examine the counterfactual world where rich people have flat nominal income growth and flat bundle price inflation.

    But I think we have to assume that shrinking someone's CPF is utility-decreasing.
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    mk

    Nicely put. In my parable the rich can now buy much more gruel than they could before (even though they choose not to) and the poor can buy less beef wellington (even though they choose not to) so , while own-consumption adjusted incomes may not have diverged, this still amounts to an increase in inequality. As you have it, changes in feasible consumption sets may be the kind of 'inequality that matters'.
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    Let's step back a bit and look at the forest. All the discussion of inequality as it relates to bundles of goods and movement of people within deciles seems like an attempt to determine whether inequality of utility has increased over time. It seems like the answer is manifestly: NO. In fact, quite the opposite. Gains in utility for those with the least have been far greater than gains for those with the most. I would think redistributionists would be hard pressed to deny this as this is one of the underlying rationales for advocating redsitribution. All the analysis from the subject paper does here is back up this extremely plausible statement. Given this insight, those that are concerned about inequality should probably focus less on inequality of income and more on what makes the least well off better off. Hence the excellent title of the original post "Capitalism to Egalitarians: You’re Welcome!"

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