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Tuesday, February 22, 2011


Wallyver offers a very interesting and useful reply to my comment on his comment, and I should like to keep the exchange going a bit longer, but I need to warn the young and impressionable that this will get a trifle gnarly, so if you do not feel a faint fluttering of your heart at the prospect of a little mathematics, it might be best to pass by this post and wait for the next snark.

The subject is index numbers, and their difficulties. Wallyver references Paasche and Laspeyres index numbers, which, as he says, are the industry standard, though by no means the only measures out there. There are two problems with price indices, only the second of which is addressed by the efforts of Paasche and Laspeyres [two old-time economists, needless to say.] Both problems arise when one is trying to measure the rate of inflation. As I explained a while back in an earlier post [part of my How to Study Society series], the first problem is that different households spend their available income in different ways -- one household spends a huge proportion on housing, and almost nothing on education; a second spends relatively little on housing, a great deal on education, and in addition buys lots of clothes. And so forth. Since prices change from year to year in a wide assortment of ways, some rising a lot, some a little, and some falling, whether a household experiences a high or low rate of inflation will in part depend on how it spends its money. It would, of course, be possible, although absurd, to construct an inflation index for each separate household, but once having done that, how on earth would you aggregate them to arrive at something identifiable as the economy-wide inflation rate? The simple answer is that it cannot be done, which means that the Consumer Price Index [or Producer Price Index, or any other similar price index] is a fiction. It is not an approximation -- that suggests there is a real or true number that in practice we can only approximate. But that is false. There is no such number. Wallyver refers to attempts to craft price indices that are deliberately weighted to reflect the experiences of ordinary low or middle income households rather than rich households. This attempt, of which I was quite unaware [like so much else, alas], is one of many interesting attempts that have been made to formulate economic measures that are designed to express a progressive ideological perspective [such as, for example, revisions to the Gross Domestic Product that take account of unpaid household labor by women.]

The second problem, which Paasche and Laspeyres address, is that households, in response to price changes or other considerations, typically alter the mix of goods and services that they consume. One household may decide to eat less fish and more meat, because fish these days is a good deal more expensive at the market than fish. [Example: I have to pay upwards of $20 a pound at Whole Foods for tuna or swordfish, but yesterday I got really nice bone-in pork loin chops for half that price. When I was a young Instructor, fifty plus years ago, the situation was precisely reversed -- fish was cheap, meat was expensive.] Another household may cut back on its recreational budget because it is putting a daughter through a pricey college.

In general, from one year to the next, both the quantities and the prices of the goods in the typical market basket [assuming there is such a thing] will change, and not all in the same direction either. So, how to compare the price of the market basket of goods and services purchased in the base year with the price of the market basket of goods purchased in the current year? [The universal practice is to choose some year as the year against which every later situation is being measured -- the so-called base year. The index for that year is arbitrarily put at 100. Then, each subsequent year can be seen easily as some percentage increase or decrease of the base. So a price index of 112 means a 12% rise over the base year.]

Paasche and Laspeyres each offered a proposal, and as will become clear, they are two different, equally plausible, and totally arbitrary ways of trying to square the circle. Paasche said: Let's compare what it costs a household to buy its current market basket of goods and services at current prices with what it would cost that household to buy the same market basket of goods at the prices that reigned in the base year. Laspeyres said: Let's compare what it would cost, at today's prices, for a household to buy the market basket of goods and services that they bought in the base year, with what it actually cost them to buy that same market basket of goods at the prices in the base year.

Hmm. How does either one of those measures help us? Not a lot, I am afraid, since both involve counterfactual assumptions. To Paasche, we must say: But the household didn't buy the current market basket of goods and services back then in the base year. That is just the problem. The shape of their purchases has changed. To Laspeyres, we object: But the household is not buying, this year, the market basket of goods and services they bought in the base year. Now Paasche and Laspeyres knew that, of course, as did everyone else who contributed to this literature [including the late, great Irving Fischer].

Wallyver notes that the difference between the two numbers, over a single year, is likely to be very small. That would be a heartening fact if there were some objective number that we were trying, experimentally, to approximate. After all, in real science, where margins of error are a universal fact of life, a very small margin of error is cause for elation. BUT THERE IS NO OBJECTIVE QUANTITY THAT THESE VARIOUS MEASURES ARE TRYING TO APPROXIMATE. In the immortal words of Gertrude Stein [who was, I believe, talking about Oakland, California], "there is no there there."

Since I have started this riff, let me mention two problems with price indices before I knock it off and invite Wallyver to respond, should he wish to. The first problem is that in addition to changes in the contents of the market basket purchased by the hypothetical typical household, there also occur changes over time in the range of goods and services available to be purchased. IPads did not exist ten years ago [I think.] If a household buys an IPad, neither Paasche nor Laspeyres nor any other index designer has a way of factoring that into an index. [This is, in odd ways, akin to the problem of describing the rational choices of agents whose utility functions themselves change over time -- see my comments on military strategy and Game Theory in my Formal Methods blog.]

The second problem concerns changes in the efficiency or performance of goods customarily considered members of the same category. We are all aware of the dramatic improvements in memory, speed, and general performance of computers oer the last thirty years or so. How does one take that into account when trying to answer the Paasche or Laspeyres question, "What would the computer I bought this year have cost in the base year?" [or alternatively, "What would the computer I bought in the base year have cost this year?"] "The" computer? Are we comparing an Apple IIE [my very first computer] with an iMac?

Well, enough said, I think. I invite the fellow nerds out there to respond.

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