Index Theory and the CPI

My previous post regarding government statistics elicited a lot of commentary, with a tremendous amount of vitriolic commentary directed at the current approach to calculating the CPI. Rather than provide more of my own thoughts on what constitutes an appropriate mix of theory and pragmatism, I will quote from the author whose work I had to read in graduate school, W. Erwin Diewert. From his entry in the 1998 Journal of Economic Perspectives which had a symposium on the Boskin commission report:

Defining a true cost of living index must begin on the household level, and then move to the social level. The Konuis (1939) true cost of living index for a single household is defined as the ratio of the minimum costs of achieving a certain reference utility level in a base period, given the prices prevailing at that time, and at a later “current” period, given whatever changes in prices had occurred in the interval. An appropriate generalization of the Konuis cost of living concept to the case of many households is Pollak’s (1981, p. 328) social cost of living index, which is the ratio of the total minimum cost or expenditure required to enable each of the households present in the two periods to attain their reference utility levels in both time periods.


As economists have long known, a Laspeyres index, which finds the cost of purchasing a fixed basket of goods representing the base period and then the cost of buying the same basket in the present, tends to overstate the rise in the cost of living by not allowing any substitution between goods to occur. Conversely, a Paasche index, which finds the cost of purchasing a fixed basket of goods representing the present and then the cost of buying that same basket in the past, tends to understate the rise in the cost of living. Diewert (1983, p. 191) showed that the (unobservable) Pollak-Konuis true cost of living index was between the (observable) Paasche and Laspeyres price indexes. An implication of this result is that some average of the Paasche and Laspeyres aggregate price indexes should provide a reasonably close approximation to the underlying true cost of living. Note that this argument does not rely on any particular assumption about the form of the house- hold preferences; in particular, it does not assume that indifference curves are homothetic (that is, shaped so that the slope of the indifference curves will be the same along the path of a ray extending out from the origin).


One strong candidate for an average of the Laspeyres and Paasche indexes is the Fisher (1922) ideal price index, which is the geometric average of the Laspeyres and Paasche indexes (that is, the square root of their product). This choice can be defended from at least four different perspectives. First, it is evident that the base period basket used in the Laspeyres index is just as valid as the current period basket used in the Paasche index. Hence it makes sense to take an even-handed average of the two. The geometric mean is more desirable than other simple averages, like the arithmetic mean, because it has a time reversibility property: using the Fisher formula, price change going from the current period to the base period is the reciprocal of the original price change (Diewert, 1997). Note that the Paasche and Laspeyres indexes also do not satisfy this time reversal test. This leads to a second justification for the Fisher formula: it satisfies more reasonable “tests” or “axioms” than any of its competitors (Diewert, 1992). The test approach to index number theory, initiated by Walsh (1901) and Fisher (1922), looks at an index number formula from the viewpoint of its mathematical properties. For example, if current period prices increase, does the price index increase? Does the price index lie between the Paasche and Laspeyres indexes? If current period prices increase by a common factor of proportionality, does the price index increase by that same factor of proportionality? These reasonable tests are all satisfied by the Fisher formula.’ A third justification for the use of the Fisher formula is the fact that it is exact for (that is, consistent with) a homothetic preference function that can approximate arbitrary homothetic preferences. Diewert (1976) calls index number formulae that have this property “superlative”. The Toernqvist index which is discussed by the Boskin Commission is an example of another superlative formula. A final justification for the use of the Fisher formula rests on its consistency with revealed preference theory (Diewert, 1976, p. 137).

Of course, in this article directed toward generalists, the specific rationales and arguments and proofs are omitted, so one might feel that one is taking too much on faith. Fortunately, Diewert has written a comprehensive review recently published in the New Palgrave Dictionary of Economics (co-edited by UW professor Steven Durlauf). This article is available in its pre-publication form as UBC Discussion Paper 07-02. In this review, Diewert lays out the criteria by which one might prefer one index over another, and what is true is that the Laspeyres (fixed base period weight) approach is not one of the preferred methods.

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44 thoughts on “Index Theory and the CPI

  1. jg

    Glad to hear that you economists agree that the L- index is NOT one of the preferred methods.
    We, hoi polloi, prefer filet mignon once or twice per month, and when we must substitute away from it because it is too expensive, we get irritated, whether you economists agree with us or not. Same thing when we must substitute a ‘staycation’ for a proper ‘vacation.’
    I know, I know, we should understand that our past basket containing filet mignon and a proper vacation is subject to change, and we should feel comforted that less expensive chicken and a ‘NetFlix’ night are substituted at no extra cost, and even some savings.
    But we do not understand, no matter how much you tell us that we should.
    Fixed baskets may not be the preferred method for you economists. But, they make eminent sense over 10-15-20 year periods for us, the masses, because our preferences do not change that much over that period of time.

  2. Jeff

    JG — A consistent theme of the lay observers is to use extreme examples like chicken and filet mignon.
    That is not really the method used. There are price spikes and near substitutes.
    Essentially, there are three different audiences for work like Menzie’s. The first consists of professionals who understand the theory and read the papers. The second consists of those who have already made up their minds on their own gut feelings. The third, and most important, are those who can look at the evidence and make an informed choice. This last group has a lot at stake in making investment decisions.
    Sadly, comments tend to come from Group 2. These folks are forceful and vocal, conveying a false sense about the merits of the actual work. My sense is that most of them have never actually read any of the papers cited. Why bother, if one thinks one already knows all of the answers?

  3. jg

    Jeff, when you read the methods behind the madness — e.g., that as utility costs increase, rents decrease, because OER is a fixed pie — you become skeptical of all the mental gymnastics involved in these price measures.
    At least I have.

  4. ed

    Thanks for this post. I get very tired of all the uninformed ranting against the CPI, mostly by people who clearly haven’t bothered to even really think about it. (For example Jeff’s first comment, which shows a complete misunderstanding of the issues.)

  5. Nick Rowe

    ed: I think you mean jg’s first comment, not Jeff’s first comment (the author’s name is below the post).
    jg: suppose the price of filet mignon went up, the price of chicken remained the same, and your income went up so that you were able to afford exactly the same amounts of filet mignon and chicken that you had previously chosen. In this scenario, would you be better off, worse off, or just the same as before? Think about it. The answer is not obvious (which is why we need people to teach ECON 101). The correct answer is better off.)
    I was pleasantly surprised to find Erwin Diewert’s piece so comprehensible. The first half was a re-cap of what I already knew; and the second half was a clear exposition of what I needed to learn.

  6. Sonia

    Agree with Nick. Diewert’s piece clarified my understanding. There is a legitimate criticism of the overly extended use for policy purposes of the CPI without food and energy. When the headline CPI is higher than the CPI ex for many months you can bet that inflation in the CPI ex is around the corner.

  7. odograph

    I missed the other thread, and while I find the Laspeyres/Paasche interesting, I also find it unsurprising.
    The very fact that we are checking “baskets” of consumption makes this a definition chasing its tail. If a future basket becomes less good, subjectively, there is no way to capture that. We might, actually, have a better cellphone and a poorer vacation this year …
    The bottom line is probably that there are many ways to live, and many ways to experience price changes. We hope that cost of living adjustments will properly protect the elderly … and we hope the young will zig and zag to find a happy life.
    In a decade with a declining national savings rate I sense that inflation must be high, just because there is no money left over for so many people! Did they just choose their baskets wrong? That’s a possibility, but that’s one of the things that makes the whole basket-based thinking cyclical.
    FWIW, as a middle aged guy, I want the government to show me real positive interest rates on t-bills, then I’ll believe inflation is low.

  8. odograph

    “FWIW, as a middle aged guy, I want the government to show me real positive interest rates on t-bills, then I’ll believe inflation is low.”
    Oh, I suppose I’ll have to get busy with a spreadsheet and calculate my personal inflation rate to really know this. It’s really about my basket, and my future basket (retirement, with medical costs).

  9. MarkS

    Menzi-
    Thank you for your recent discussions on inflation and price indexes. My perspectives are:

    1. The recent steep rise in commodity prices will disproportionately hurt lower income consumers. They must expend a far larger share of their resources for food, clothing, utilities and transportation than the general population. This group naturally, will view the government’s CPI values as pure fiction. Conversely, the ultra-rich, (who expend a far lower percentage of their income on these factors), may view the current deflation in luxury items, as proof that inflation is well under control.
    2. Implicit in making the “Computable General Equilibrium Model” of the US economy work, is the notion of factoring preferences and availability of items over time. This is achieved in part, by Utility Functions, which attempt to weight consumer value weightings to similar groups of items: (Chicken (C), Fillet Mignon (F), Ground Beef (G), Dog Food(D)): (40% C, 40%F, 20%G, 0%D) may get a preference rating of 10, while (40%C, 1%F, 30%G, and 29%D) may rate 2. The problem, is that all the permutations of all the food choices and their respective ratings becomes so massive that it can not be effectively surveyed. Consequently, arbitrary simplifications are applied.

    My opinion, is that the economic classes with the most control over the US government, will use their influence to assign arbitrary simplifications to utility rankings most likely to result in lower positive change in the price index. Their motive for doing so, is to make normalized government statistics relative to GNP look better, buoying financial markets, and minimizing future expenditures on CPI indexed entitlements.

  10. PaulS

    Nick Rowe – and Menzie Chinn:
    “suppose the price of filet mignon went up, the price of chicken remained the same, and your income went up so that you were able to afford exactly the same amounts of filet mignon and chicken that you had previously chosen. In this scenario…the correct answer is [you would be] better off.”
    This answer makes no mathematical sense to me. Consider:
    Suppose, now, there are more iterations, as usually happens in the real world. Now the price of chicken goes up and so does my income until I can afford the same basket again. According to your analysis, I’m again better off. Then, in the same manner, the price of plasma TVs goes up and again I’m better off. And so on…
    Eventually, everything has gone up, my income has gone up so that I can afford exactly the same basket as before it all started, relative prices are the same as before it all started, my budget is the same as before it all started excepting only that the unit of account, and my savings, have both shrunk…and according to your analysis I’m umpteen times better off, where umpteen is the the number of items in my basket…?
    Now I’m really confused.

  11. Don Briggs

    I didn’t read through all of the comments BUT, why are we interested in a CPI. I think it’s because government funding programs depend on it. If it is, as I suspect, to give an average citizen a chance to keep some kind of life style, I don’t have any trouble with it when he or she has to substitute chicken for filet mignon. If the CPI is being applied in a governmental program, I want maximum survival, not luxury.

  12. ed

    Now the price of chicken goes up and so does my income until I can afford the same basket again. According to your analysis, I’m again better off.
    Paul, I think you are making a slight error here. Nick is saying that if prices go up from time 1 to time 2, and income goes up so that you can afford time 1’s basket in time 2, then you are at least as well off in time 2 as in time 1. The proof is simple: you can afford the same basket, so you can’t be worse off, and you have the opportunity to switch towards the cheaper goods, which might make you better off. (And if we observe that you DO prefer to change baskets, we can say that you must be strictly better off.)
    Now if prices and incomes go up again, so that we can still afford basket 2, then we are again at least as well off. (But note you have to use basket 2 this time, not go back to basket 1. It sounds like you are trying to use basket 1 for both steps, and that is why you are getting confused.) In fact we can prove mathematically that we will still be able to afford basket 1 under this scenario and still have money left over, so that is why we are better off.
    Here’s an example with numbers….
    Period 1: chicken $1, beef $1, income $10; I choose 5 beef and 5 chicken.
    Period 2: chicken $1, beef $2, income $15; I choose 4 beef and 7 chicken.
    Period 3: chicken $2, beef $2, income $22; I choose 5.5 beef and 5.5 chicken
    You can tell that I prefer my period 2 basket to my period 1 basket, because otherwise I would have chosen to buy my period 1 basket again in period 2. You can tell that I’m better off in period 3 than in period 2 using similar reasoning. Finally, I’m clearly better off in period 3 than in period 1 because I get more of both beef AND chicken.
    Note that if you had used a Laspeyres index in both periods, you would have found zero real wage growth over time.

  13. Nick Rowe

    Good clarifying example ed.
    I can’t help thinking though, that the substitution bias is dwarfed by the new goods/quality bias, and we are arguing about trivial things while missing the big things. I can’t remember who first came up with the following thought experiment, but consider this:
    Has there really been any inflation at all over the last 100 years? Suppose I lived in 1908, but had my current 2008 income. I would be one of the super-rich in 1908, but would I be better off than I am now, in terms of material goods and services? The answer is not obvious. Let’s consider various expenditure categories:
    Transportation. My current car is nothing special, but has a top speed that would match the speed record in 1908, can corner better than the best 1908 race car, is more comfortable than any 1908 car, and more reliable, and safer, etc. I can visit my mother in Europe in about 12 hours door to door, while this would have taken several days in 1908. I am much better off today than the richest person in 1908.
    Food. OK, I could have my own personal chef in 1908, but could my chef do Chinese, Thai, Indian, etc. cooking; were the ingredients available? When you consider the variety available now, I think I’m better off today.
    Housing. OK, I would probably be better off in 1908, living in a mansion (interesting the relative lack of technical advance in construction, which no doubt explains part of rising real house prices over time). But then the mansions of even the very rich often had very primitive heating and plumbing in 1908.
    Servants. I could afford lots in 1908, and none now, but then with modern household appliances, heating and plumbing I don’t really need any. It would probably take me more time to manage the servants than it does to do my housework! Call it a draw.
    Arts/entertainment. No contest, when you consider the massive variety of music, books, films, TV, radio, etc. cheaply and easily available today, I can afford more and better than the richest person in 1908.
    Communication. No contest (phone, email, etc.). I am better off in 2008.
    Clothing. Probably better off in 1908 I think.
    Health care: No contest. Anyone who has needed basic health care like an appendix removal or antibiotics might argue that for them the cost of living (understood literally) was infinitely higher in the past.
    What important categories have I left out?
    So, for someone with an average 2008 nominal income, I think you can argue reasonably that there has been deflation over the last 100 years. That means there must be a massive upward bias in the CPI.
    (Of course, for someone with an average 1908 nominal income, the results would be very different, but what is the relevant comparison, since nominal incomes have in fact risen?)

  14. vorpal

    when I think of inflation, I think of WalMart. Walmart sells mostly the same goods from month to month. Each month, a few goods are introduced, and a few are dropped. Why not just do an average price increase of all of the goods sold, weighted by the total sales in dollars? An everchanging basket, as it were. Even though every product could change over a decade, from month to month the change would be small and we be able to calibrate the value of new products as they are introduced against the value of a reservoir of old products.

  15. DickF

    How many angels can dance on the head of a pin?
    CPI is not a measure of the basket of goods. CPI is a measure of the change in the value of money. You use a basket of goods to get as close to a consistent commodity mix as possible so that you can tell if the money is appreciating (unusual) or depreciating (in today’s world expected and legislated).
    As can be seen the determination of the basket of goods is not an easy thing. There are changes in taste, quality, performance, on and on. So let’s say that we have a basket of goods representative of everything we quickly recognize that some items are very volatile and so distort our basket of goods. So we begin to remove items one by one with the intent of reaching the optimal basket of goods. Interesting is that we find that the commodity that has a very limited use, with a consistent supply, is nearly indestructible and has all the attributes of a near perfect commodity for this kind of monetary measure, and is actually distorted if any other commodity with less stability is averaged with it, is the best measuring rod. What we find is that the price of gold is the best “basket” of goods with the least arbitrary variation we can use.
    But then the politicians become nauseous because they realize that if everyone realizes this they will lose their power to manipulate the illusion of constant money value but changing commodity values.

  16. Josh Stern

    If this question was of national urgency, it would be possible to conduct controlled interviews (i.e. what psychologists call experiments) with people, asking them about their preferences and how they would choose to spend money among a set of choices, and by including old and new goods the actual change in cost of living could be accurately regressed from the noisy preference data.

  17. Sebastian

    PaulS said: “Now I’m really confused.”
    Hey, out in the real world it’s even more complex.:)
    Ex.: My wife and I love to grill on our Weber, been doing it since shortly after we got married. Back then, in our 20’s, we’d grill large rib-eyes with lots of marbling, and only two at a time, enough for one dinner apiece.
    Today, though, with our income nearly quadruple what it was back then, what do we grill? Chicken, for reasons having to do with our health and nothing whatsoever to do with the cost of steak relative to chicken. (It might even be a major “thing” with baby-boomers because we’ve *all* got that same risk-factor problem for heart disease and cancer.)
    Also, we buy chicken in a “value pak” with several boneless breasts and cook them all up at the same time, enough to make 4-6 meals.
    So what happened here? Well, we *permanently* substituted for a cheaper product, and probably wouldn’t go back even if steak was cheaper. We’re also more economical about the way we buy and cook the chicken than we were with the steak.
    Not sure if God himself could come up with a good inflation measure, given all the variables, known and unknown.:)))
    Sebastian

  18. Anonymous

    w: I was trying to follow Paul’s question, and make an illustrative example. Of course, you could let chicken and beef prices go to anything you want in period 3…the important thing for the example is that income also rises in period 3 exactly to the point where you could still buy the period 2 basket at the new prices.
    The example shows that if you use a Laspeyres index in each period, with non-constant relative prices and substitutions between goods, you won’t think standards of living are rising, when in fact they are.

  19. Blissex

    The Konuis (1939) true cost of living index for a single household is defined as the ratio of the minimum costs of achieving a certain reference utility level in a base period,
    But this is where the intellectual shysterism lies: “a certain utility level”, a phrase which is entirely devoid of meaning except in the talk of political propagandists.
    What one can measure is a constant basket of goods and how money moves against it.
    Attempting to define a utility level, never mind a constant one across changes in relative prices, is pure intellectual dishonesty, and leads to absurdities such as assigning imaginary prices to non existent goods; and the latter absurdity is implicitly justified by the idea that if we can given a good say what utility it has, then given a utility we can define the good that would produce it.
    Hedonics is just convoluted propaganda based on laughable Economics.
    What matters to people is how much it costs to maintain a certain level of consumption defined by a basket of goods, and the utility of that basket is entirely in the eye of the shyster. It is hard enough to define a semi-representative basket.

  20. ed

    Blissex, my example with chicken and beef never used the phrase “utility” at all. What is it about the example that you don’t agree with?

  21. Blissex

    Period 1: chicken $1, beef $1, income $10; I choose 5 beef and 5 chicken.
    Period 2: chicken $1, beef $2, income $15; I choose 4 beef and 7 chicken.
    Period 3: chicken $2, beef $2, income $22; I choose 5.5 beef and 5.5 chicken
    The shysterism here is in the “I choose” bit, where the intellectual dishonesty is that the quantities both absolute and relative in the basket of goods changes over time.
    The second bit of shysterism is to measure inflation in terms of salary instead of prices.
    Prices indices are measure in units of money (how much one dollar buys), not units of time (how much one period of wages buys).
    The basket is 5 beef and 5 chicken. In period one it costs $10, in period 2 it costs $15, in period 3 it costs $20.
    So between period 1 and 2 inflation is 50%, and between period 1 and 3 it is 100%.
    Finally, I’m clearly better off in period 3 than in period 1 because I get more of both beef AND chicken.
    That’s a welfare argument, not a price index argument.
    Note that if you had used a Laspeyres index in both periods, you would have found zero real wage growth over time.
    And indeed a properly constructed, not dishonestly constructed, basket-of-goods index arrives at the same conclusion: good price inflation between period 1 and 3 is 100%, wage price inflation is 110%, purchasing power has improved.
    Do you really think people are morons that don’t see that your arguments are based on switching subjects and on begging the question, some of the coarsest and oldest tricks shysters use?

  22. Blissex

    Blissex, my example with chicken and beef never used the phrase “utility” at all.
    This is a classic shyster claim: “I choose” implies that differently composed baskets have the same utility, or else one is just using a different metric for inflation every period.
    Sure you did not use the word “utility”, and as half truths can be great lies, that’s true, but the argument is entirely based on the concept of utility.

  23. Menzie Chinn

    Blissex: Since your worldview and mainstream neoclassical microeconomic theory apparently have no overlap, perhaps it would be best to just conclude that you do not agree with the framework at hand, and forego further use of the shyster term, which does not seem to add to the debate in a substantive fashion.

  24. MikeekiM

    Who’s this guy?
    How did someone with common sense trip into this web site?

    The recent steep rise in commodity prices will disproportionately hurt lower income consumers. They must expend a far larger share of their resources for food, clothing, utilities and transportation than the general population. This group naturally, will view the government’s CPI values as pure fiction.

    Conversely, the ultra-rich, (who expend a far lower percentage of their income on these factors), may view the current deflation in luxury items, as proof that inflation is well under control.

    Phil Gramm, I’m guessing, is in that top 1% that’s currently blind to the working-class Inflation rate.
    For example last year I’d send $370 to get 150 gallons of home heating oil. Thanks to Wall Street this winter I’ll now spend $645. My calculator say’s this is a 74% price increase. You’re CPI inflation rate of 4% is a JOKE.


    Economists are Prostitutes.

  25. Marcus

    Sonia: You wrote:”When the headline CPI is higher than the CPI ex for many months you can bet that inflation in the CPI ex is around the corner”.
    Long ago that used to be true. Over the last 24 years it has diminished and essentially dissapeared since 1991.

  26. gmc

    Agree w/Menzie.
    Attacking the CPI as “understating” inflation has become a fun pastime for left leaning academics and activists of all stripes. Unfortunately, it makes very little sense – the only thing that makes less sense is the CPI itself.
    Substitution bias is only included in the CPI between similarly preferred goods; that is, goods that are relatively similar in cost and function. Chicken and Filet Mignon are not good substitutes, but frozen boneless chicken breasts might be a good substitute for bratwurst (at least during grilling season!).
    I think that last paragraph illustrates the points both in favor and against including substitution. On the one hand, you can have a perfectly adequate barbecue with either chicken or bratwurst; buying more bratwurst when it is less expensive is just sensible (I do it myself!). Adjusting the CPI to mimic actual choices does make it more accurate.
    On the other hand, changing the basket in this way means you aren’t measuring the same thing; which means that the CPI isn’t really an index of anything year to year, which is pretty much the point. (Although I note that WalMart is in the DJIA now).
    What really ought to be done is to use the GDP deflator, which is the price index for all goods and services in the economy; but it doesn’t come out until well after the CPI does for a given period, and isn’t particularly consumer focused.
    Now, energy prices are a different matter. Saying that “If the CPI-E rises, inflation in the broader index is sure to follow” is one thing. It may even be true. But from a monetary policy perspective, it is meaningless. Certainly energy prices feed back into the broader economy. But commodity price shocks are not monetary inflation; it’s not that we’re raising the price of everything, but that we’re really that much poorer. The fact that oil “goes into” most goods and services and makes them more expensive doesn’t change an external price shock into a monetary (or monetary-policy relevant) phenomenon.
    The danger is not that inflation will occur because of lax monetary policy (that isn’t what happened in the 70’s either), but that inflationary expectations will begin, and cause a wage/price spiral. People need to know that they really are worse off, and it’s probably going to stay that way until we grow national income back up.
    But that’s a hard thing for a politician to say. It’s easier to blame Ben Bernanke, Alan Greenspan, or someone on Wall Street.

  27. Anonymous

    MikeekiM, you’re absolutely correct that price changes will have different impacts on different consumers.
    That’s one of the reasons a meaningful price index is inherently difficult to define. One approach would be to give up on producing price indexes altogether…is that what you’re advocating?

  28. Josh Stern

    “The danger is not that inflation will occur because of lax monetary policy (that isn’t what happened in the 70’s either), but that inflationary expectations will begin, and cause a wage/price spiral. People need to know that they really are worse off, and it’s probably going to stay that way until we grow national income back up.
    But that’s a hard thing for a politician to say. It’s easier to blame Ben Bernanke, Alan
    Greenspan, or someone on Wall Street.”

    Surprise! What people actually care about is being richer or poorer and having the policies that lead to the desired outcome. The Theory of Comparative Advantage is basically a theorem, but if the theory, as applied, only has a 50-50 chance of leading to desired outcome, then economists’ salaries probably go down.

    Seriously, claiming that theoretically things would have been worse if someone hadn’t followed one’s advice, or that the advice would have been good except for more important factors that one neglected to consider is, and should be, a tough sell.

  29. Nick Rowe

    But Blissex, if you define inflation as the rate of increase in the price of a fixed basket of goods, which particular basket do you use? Is it the basket we consume this year? Or the basket we consumed last year? The former gives us Paasche, the latter gives us Laspeyres, and we (almost always) get two different answers for inflation. Which is where Diewert came in…
    Or, you could use the basket we consumed 100 years ago, which would give you a very different answer; indeed it would give you an infinite inflation rate if some of those goods were totally unavailable today!
    Defining inflation as the % increase in income that would leave you indifferent between old prices/old income and new prices/new income resolves the ambiguity about which basket to use, and provides a much more useful definition of inflation. But it does make it harder to measure, which again, is where Diewert comes in….
    You can interpret “indifferent” as “same utility” if you like, or as “no revealed preference” (as ed might prefer ;)).

  30. MikeekiM

    What I’m saying is, looking at you folk “debate” the basket of goods is irrelevant when you’re comparing year to year. Unless, you need to “fix the books” for political reasons.

    >> “The former gives us Paasche, the latter gives us Laspeyres” Not for year to year comparisons they don’t. The only meaningful way they make sense is if the basket doesn’t change, but, I only hold that opinion because I’m not an economist I guess.

    You are understating inflation. We, the general public, know it. We actually laugh at your “CPI” numbers.

    Also, the unemployment numbers are obviously being understated, but, those numbers aren’t funny.

  31. Edgewater Rat

    Nick Rowe – thanks.
    That was a great example on inflation and quality adjustments. Never thought of it that way.

  32. jg

    Professor, the BLS has killed its credibility IRT CPI; looking back, that the CPI registered only modest increases given the huge run up in housing prices is the elephant sitting in the corner, IMO.
    The biggest bubble in history, when folks spent ever larger chunks of their income on house payments, sneaked by the folks at BLS.
    Appalling.

  33. Terry

    I believe that to argue that national policy decisions concerning what the various inflation indices measure is based on this kind of theoretical analysis–despite its merits–is out of synch with reality.
    The fact of the matter is that administrations of both parties have sought to lower the rate of growth of cost of living allowances and other inflation-driven cost growth while giving the appearance of meeting the needs of beneficiaries–the old, the infirmed, the very young, etc. Forget the economics. This permits politicians to get re-elected, which is always their primary goal.
    The effect of having your cake and eating it too has led to declines in inflation measures for several decades, resulting in a continuing shift in wealth from the less to more fortunate (in addition to the advantages the wealthy have accrued from tax cuts).
    To give these policy decisions the cover of economic thought is an injustice to economics.

  34. DickF

    Terry,
    You are right but who is really on a fixed income, the old, the infirmed, the very young? When inflation eats away at the production of the country and forces the labor force into lower paying jobs, but government handouts are indexed to inflation, who is really on a fixed income?

  35. Charles

    An interesting debate. There are three points I would make: (1) in judging what measure of inflation is correct, one should look at broader patterns. For example, American savings rates over the last 30 years have been falling while we are told that median family incomes have been steady or rising. (2) small systematic errors lead to large errors over time. Therefore, economists may think they are doing a great job by measuring inflation accurately to within a quarter of a percent. But over 30 years, that could represent a substantial drop in standards of living. (3) there are many things that cannot be measured by economic statistics but strongly impact the perceived standard of living that we need to take the statistics with a grain of salt. As long as they are applied honestly and consistently, they will give us a sense of trends.

  36. GNP

    Great choice Menzie!

    I must have spent weeks reading Diewert during my M.A. program prior to constructing original multi-factor productivity indices for defensive-intensive Canadian industries.

    Blog readers may be interested to know that Statistics Canada by the early 1990s had calculated every price, quantity, and multi-factor productivity index series that Diewert suggested. I believe that they are all still available, at least as special orders.

    Blog readers should be aware that Canada has successfully implemented price stability/inflation targeting; the popular whining and moaning about inflation indices is relatively subdued by comparison to the USA.

    I’m impressed with some of the patient, clear explanations offered by posters like ed. It took me a considerable amount of effort to fully grasp the neoclassical economics theory that underpins this measurement theory.

    Best wishes

  37. odograph

    I’m put off by the false argument: any claim against CPI is extreme, fringe, crazed, and so therefore the CPI is a good and valid measure of monetary management.
    I could probably look up the formal name for that fallacy if my tour wasn’t leaving.

  38. RebelEconomist

    I have been thinking about this issue since your first post. Thanks for the reference to Diewerts Palgrave article which is especially helpful. It seems to me that much of the controversy about methods stems from the fact that people have different ideas of what the price index is supposed to do.
    A cost of living (COL) index is not the most relevant price index for a central bank to target. Assuming that the primary purpose of monetary policy is to provide the right amount of money to facilitate transactions without disturbing relative prices, the targeted meausure of inflation ought to be based on transactions prices. It seems obvious that the weighting given to price changes should not depend on the price change itself, which suggests that a Laspeyres index is most appropriate for monetary policy purposes.
    I can see that a COL index can serve as at least a useful starting point for indexation purposes, but it should not be forgotten how subjective the concept of the cost of living is. For a start, the idea that consumers welfare depends on their own current consumption is debateable – we know from behavioural economics that previous and other peoples consumption matter. Some methodological choices seem to derive from stylised microeconomic assumptions, such as a unit elasticity of substitution justifying geometric averaging of price changes. There is a reasonable argument for quality adjustments in a COL index, but they do seem to be applied mainly to technological goods which are proactively upgraded, and since they have been applied to more items over time, the nature of reported cost of living is not what it was. Because consumers are clearly able to substitute consumption inter-temporally by saving and borrowing, asset prices ought to be included in a COL measure. It is hard to avoid concluding that the subjectivity of COL measurement has been used to pick methodological choices that have lowered the reported measure.

  39. Blissex

    But Blissex, if you define inflation as the rate of increase in the price of a fixed basket of goods, which particular basket do you use?
    Well, honest statistical agencies use a “representative” basket (not an easy task, and a political one) and keep it unchanged for quite a few years, until it is no longer representative, and then they provide bridging data.
    Or, you could use the basket we consumed 100 years ago, which would give you a very different answer; indeed it would give you an infinite inflation rate if some of those goods were totally unavailable today!
    But that’s as ridiculous as hedonics. and it is just a straw man argument.
    Defining inflation as the % increase in income that would leave you indifferent between old prices/old income and new prices/new income resolves the ambiguity about which basket to use,
    Really? Because inflation measurement eventually is about defining a synthetic commodity and using that to define the changing price of money in terms of goods. Your definition here instead is the fruit of two sophistries:
    * It defines inflation in terms of the purchasing power of incomes instead of numerary/money. Which incomes? Whose indifference?
    * It does so by creating an imaginary commodity which is defined by the equi-utility (indifference) between different baskets at different times at different income levels.
    Now your definition, being based on sophistry and fantasy, offers the great advantages of being a very accurate measurement of something that does not exist and can be very easily manipulated.
    Instead using a mostly-fixed, mostly-representative basket of real goods as the synthetic commodity against which money is measured has a couple of rather more interesting properties:
    * It is easy to measure and calculate without using advanced sophistry like hedonics and substitution and products of the imagination as collective indifference curves.
    * It actually measures the trade rate between money and goods (as imperfectly but meaningfully represented by a synthetic commodity).
    But then I do understand that people who owe their careers and tenure to “mainstream neoclassical economics” are well trained to prefer imaginary and meaningless entities that sound very precise to real, meaningful numbers that are somewhat inaccurate. As one of the potential victims, I prefer the latter.
    and provides a much more useful definition of inflation.
    Useful in what sense? How can you measure:
    the % increase in income that would leave you indifferent between old prices/old income and new prices/new income resolves the ambiguity about which basket to use
    This is just wishful thinking sophistry. Also because it is not “you”, it is about a population each member of which may have very different indifference curves, even if each were in practice measurable or even just capable of estimation.
    However a definition based on imaginary quantities supported by neoclassical mumbo-jumbo is very useful in one way: it allows for simply making up numbers, including fantasy claims about hedonics adjustments and substitution effects. “all is well in the best of all possible worlds” is what the bundle of coarse propaganda known as “mainstream neoclassical theory” delivers, and in this case too.
    For a different opinion, let’s look at BusinessWeek:
    http://www.businessweek.com/bwdaily/dnflash/content/jun2008/db20080613_966843.htm
    http://www.businessweek.com/print/magazine/content/08_25/b4089012839022.htm
    Unfortunately, Goodfriend and others acknowledge, the Federal Reserve can only get away with focusing on the core rate of inflation if it can somehow persuade the general public to do the same. That’s a tall order. If ordinary Americans see high headline inflation because of costly oil, their first instinct is to demand higher pay to compensate for it. In other words, they try to insulate themselves from the pain instead of gritting their teeth and accepting that more expensive oil will necessarily reduce their standard of living.

  40. Blissex

    Certainly energy prices feed back into the broader economy. But commodity price shocks are not monetary inflation; it’s not that we’re raising the price of everything,
    What would be non-monetary inflation? That sounds crazy to me. I cannot also imagine that “raising the price of everything” is in any way related to the concept of “inflation”. Some prices always go down even if most go up, so defining “montary inflation” as “raising the price of everything” sounds quite crazy to me.
    but that we’re really that much poorer. The fact that oil “goes into” most goods and services and makes them more expensive doesn’t change an external price shock into a monetary (or monetary-policy relevant) phenomenon
    But raising the price of everything or most things is another way to say that we’re much poorer — also it is not “we”, because inflation is not uniform and there are strong distributional effects too.
    If inflation has to has some meaning (and it can many definition most of which meaningless) it is something like a change in the terms of trade between numerary/money (whatever Milton fatasized that was like in one of his mental trips) and goods.
    Note also that “a monetary phenomenon” is a ridiculous bit of wishful thinking by a particularly dumb propagandist (someone who had wholly baseless fantasies about imaginary quantities called the quantity and speed of money, as if quantity, speed and money were easy to define except by crooked sophistry).
    So one should not say that since it is not a monetary phenomenon it is not “inflation” or “monetary inflation”; that just begs the question.
    Changes (bad changes I mean) in the terms of trade between numerary/money and commodities can happen either because (some/most) commodities become scarcer or because numerary/money becomes less scarce (or its “speed” goes up).
    Both are “inflation”. Both have distributive effects, and both can cause problems. Making a distinction between the two is not that useful, especially for people paid in a fixed quantity of numerary/money.

  41. Bill

    “Fixed baskets may not be the preferred method for you economists. But, they make eminent sense over 10-15-20 year periods for us, the masses, because our preferences do not change that much over that period of time.”
    Unfortunately, they do. You didn’t pay for cellphone 20 years ago, did you ?
    Everyone should have their own CPI, customized for personal preference. That’s the only way we can all be satisfied. A single CPI for a whole country is just too much compromising.

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