Talk:Price index

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Contents 1 formula 2 Formula representation 3 is there no asset price index ? 4 Perfect index 5 Going for FA 6 Diewert 7 GDP deflator and GDP price index 8 Marshall-Edgeworth index 9 Two ways to evaluate price indexes? 10 Standardizing time subscripts 11 Article organization 12 Why price indexes? 13 Refugees from my big edit 14 Feedback on my big edit? 14.1 Things I wanted to address in my changes 14.2 Things that didn't go as well as I'd hoped 15 Un-Encyclopedic language

[edit] formula

The formula for the index should be this: http://mathworld.wolfram.com/LaspeyresIndex.html

Note the use of a "n" or "t" subindex instead of 1 and 2 (which may lead to the belief that the index is chained as it only mentions two years).

This also applies for Paasche.

About the base year: http://eaindustry.nic.in/report/fin4.htm I think we should have an article about this :-)

[edit] Formula representation

Being new to this subject, I am a bit confused by the representation of the indexes given. I assume that the values p₀ and q₀ are constants since they are the values in the base year. Why then have they not been taken out as a factor, i.e. moved to the left of the sigma. Not doing so gives the impression that they are not constant. Indeed, q₀ can be completely removed from the Laspeyres index since it cancels out. I think these formulas should be modified or at least an explanation added as to the reasons for the curious representation.

I cleaned-up that notational mess a few days ago. —SlamDiego 05:15, 21 February 2007 (UTC)

[edit] is there no asset price index ?

This is a problem because the deflation item relates to here and deflation could also mean falling asset prices. So again is there an asset price index ? (housing + stocks + value of small companies etc.) —Preceding unsigned comment added by 82.232.235.239 (talk • contribs)

If we consider decrease of asset prices as deflation, then we would need to consider increase of asset prices as inflation. Therefore, we would be confusing asset bubbles (in houses or stocks) with the "cost of living", which is just what inflation/deflation tries to capture.

However, I do agree that an index that measures the wealth of the avg. consumer is a long overdue task.

--200.11.34.59 23:01, 9 October 2006 (UTC)

[edit] Perfect index

The sentence: "While these indices were introduced to provide overall measurement of relative prices, there is ultimately no way of measuring the imperfections of any of these indices (Paasche, Laspeyres, Fisher, or Marshall-Edgeworth) against reality."

is incorrect IMHO. There ultimately is no (way of calculating a) perfect index in a multiproduct market. This is due to the fact that there exist multiple kinds of mean (weighted, harmonic, geometric), and for building an index that aggregates changes in multiple products into one value index, choices are necessary. I'm not a mathematician but i would guess Arrow's_impossibility_theorem comes close to explaining why there exists no perfect index. —Preceding unsigned comment added by 62.59.33.94 (talk • contribs)

To measure the imperfections of any or all of these indices, one would have to quantify their failures. Proving their imperfections (in some manner analogous to the Arrow Impossibility Theorem) would not do this. —SlamDiego_←T 15:35, 26 June 2007 (UTC)

[edit] Going for FA

I'd like to try to get this article to FA status. It'll probably be a slow process. Here's a rough layout. Let me know what you think.

1. Intro
2. History
3. Criteria for a price index: a. axiomatic b. cost of living theory
4. Price index formulas and comparisons
5. Price index uses/examples
6. Hedonic price indices

--Bkwillwm 02:10, 11 July 2007 (UTC)

Well, first, before you you begin extensively editting any technical article, you should develop a better facility with wiki mark-up. Second, this article is presently written to provide the reader with an accessible treatment, and a framework within which the fundamental deficiency of any price index can be discussed (though such discussion is not provided). That accessibility should not be diminished, nor should the framework cripple the reader's ability to think critically. (I feel compelled to make that last point because so many treatments condition the reader so that he or she will find it difficult to grasp the problem.) —SlamDiego_←T 03:46, 11 July 2007 (UTC)

[edit] Diewert

A reference should be provided for Diewert. —SlamDiego_←T 06:33, 12 July 2007 (UTC)

[edit] GDP deflator and GDP price index

The article says that "the GDP deflator does not assume a fixed market basket of goods and services". In context, this seems to imply that the GDP deflator does not count as a price index. Can someone make it explicit in the article whether or not this is true? In addition, I've noticed that economic sources sometimes speak of the "GDP price index". (See, for instance, http://bea.gov/bea/glossary/glossary.cfm?key_word=GDP_price_index&letter=G.) Is this an important price index, worthy of mention in the article? Is it related to the GDP deflator at all? --Ryguasu 15:16, 1 August 2007 (UTC)

A Paasche index does not assume a fixed market basket; and, as far as I know, the GDP deflator is actually just a Paasche index. (The article on the GDP deflator begs the whole question.) —SlamDiego_←T 06:04, 2 August 2007 (UTC)

I think the Paasche index is still considered a fixed market basket index. Unlike the Laspeyres, which uses a set basket from a prior period, the Paasche uses a set basket from the current period. I suppose a chained Paasche index would have a new basket each period, so in this sense it's not a "fixed" basket. However, a Paasche index across several time periods is still considered fixed since one basket is used with changes across several time periods. Also, the GDP price indices (at least the PCE price index) produced by the BEA use Fisher price indices.[1]--Bkwillwm 20:01, 19 August 2007 (UTC)

[edit] Marshall-Edgeworth index

The article says that the Marshall-Edgeworth index incorporates the "arithmethic mean of the quantities". This is not, however, how I would choose to summarize the formula as currently given; I would summarize the current formula as involving the "sum of the quantities". For me, "the arithmetic mean" would be better reflected in the formula

(Mathematically, of course, the two formulas are equal.)

My first impulse is either to switch the formula to the one I just gave, or to switch the wording to involve "sum" rather than "arithmetic mean". Both of these moves have disadvantages, though. As to changing the wording, this has the disadvantage of making the rationale for the formula less clear; at least to me, it's more obvious why it would make sense to average the quantities than why it would make sense to sum them. As to changing the formula, this would make the formula more complicated, and some people would be severely tempted to cancel out the one-halves. Any thoughts? --Ryguasu 23:15, 5 August 2007 (UTC)

Referring to the formula as involving the sum loses the intuition. Simply changing the formula leaves an unnecessary calculation in the expression. So I've done something different. :-) —SlamDiego_←T 23:50, 5 August 2007 (UTC)

I think your change is an improvement. Thanks. --Ryguasu 01:19, 6 August 2007 (UTC)

I'd thought about the issue myself. Your comment made me feel licensed to make a change that I'd considered. :-) —SlamDiego_←T 01:33, 6 August 2007 (UTC)

[edit] Two ways to evaluate price indexes?

The "Index number theory" section says that

There are two approaches to evaluating price index formulas. One of the approaches, referred to as either the test or axiomatic approach, evaluates the index numbers based on their mathematical properties.

The article doesn't explicitly say what the second approach is. Is there a sensible answer for what the second approach is, or is this "there are two approaches" business misleading? --Ryguasu 05:14, 6 August 2007 (UTC)

Bkwillwm, the editor who wrote that passage, seems not to have completed his programme of edits. My inclination has been to allow him some time to finish what he is or was attempting, but in the context of your query I note that more than two weeks has passed since the last edit by that account, so perhaps it is time to try to clean things up a bit. :-/ —SlamDiego_←T 08:21, 6 August 2007 (UTC)

[edit] Standardizing time subscripts

Currently the article has three ways of labeling the base period vs the period of interest:

• t and t + 1
• t₁ and t₂
• t₀ and t_n

We should probably pick one way and stick to it. Here are some considerations:

• The first two choices use sequential numbers, which arguably suggests that you can only compare adjacent years/quarters/whatever.
• t₁ and t_n is a potential alternative to the third choice. It has the advantage of labeling the mth time period as t_m rather than as t_{m − 1}. Is this less confusing?
• Perhaps the choice in this article should be synchronized with choices made for other articles?

--Ryguasu 14:06, 6 August 2007 (UTC)

For now, at least, I have brought the notation of the section “Index number theory” into conformity with what had been prior convention within this article.

I favor having the article consistently use “t₀” for the base period, and “t₁”, “t₂”, &c or “t_m”, “t_n”, &c for all periods. I don't greatly object to changing the occurrences of “t₁” and “t₂” to “t_m” and “t_n”, but the idea was to give the reader a slightly more concrete example before talking willy-nilly about “” and “”. However, the section “Index number theory” was not in the article at that time. (I would in fact prefer to see this section moved to after “Formal calculation”, as “Index number theory” is both intrinsically less accessible and less likely to be of use to the vast majority of readers.)

I don't think that we want to write of the m^th period at all. I know of no cases where we need to talk about immediately successive periods, and the indices needn't be presumed to provide an ordering; they can just be names rather than descriptions. I hope to avoid cases of “t_{m − 1}” or “t_{m + 1}” altogether.

—SlamDiego_←T 20:00, 6 August 2007 (UTC)

I just remembered something that may or may not be significant here: People will often draw graphs of price indexes where the base period is not the leftmost time period but rather somewhere in the middle of the graph. Here

the author is taking the base period to be 1982-84, rather than 1910 or whatever. So far we've agreed that t₀ should be the case period, so t₀ = 1982. This makes me want to call the leftmost spot on the graph t _{− 200} or something, and the negative number bothers me a little. Maybe it shouldn't, though; negative numbers are, in fact, wonderful things. --Ryguasu 21:11, 6 August 2007 (UTC)

But if treat the indices on t as just names, then it's quite acceptable for t₀ = 1982 and t₁ = 1905 and t₂ = 2007. I'm not saying that it would be a fine thing for such labelling to occur (especially were it to occur explicitly), but there's nothing illogical about it. (And you are of course quite right that we could instead say 1905 = t _{− 200}.) —SlamDiego_←T 22:34, 6 August 2007 (UTC)

[edit] Article organization

SlamDiego,

Above you say

I would in fact prefer to see this section moved to after “Formal calculation”, as “Index number theory” is both intrinsically less accessible and less likely to be of use to the vast majority of readers.

My temptation is to make this move, and also to make it a subsection under a new heading, "evaluating index number formulas" or something. (The point of index number theory, after all, seems to be to evaluate indexes.) I guess this would be part of consolidating all the information about evaluating formulas in one section. (Right now it's scattered across "Formal calcuation", "Index number theory", "Practical considerations", and perhaps elsewhere.) This may or may not be a good idea.

Actually, I'm pretty unsure about how the article should be organized overall. Bkwillwm's proposed ordering is a reasonable one, though I might tweak a few things. (I might put examples earlier on, for instance.) You mention above that making the article accessible is important. I'm not sure whether this proposed order would help or hinder that. (We might, for instance, want to have two sections for evaluating index numbers, each aimed at different levels of reader?) --Ryguasu 20:40, 6 August 2007 (UTC)

I for one am comfortable with what I take to be your instincts:

1. Some consolidation would probably be good.
2. Consolidation should not be pedantic or dogmatic.
3. It's not perfectly clear how best to present the material.

As to the last point, basically I think that we want some balance of two conflicting principles:

• Matters should be presented in logical order.
• Matters should be presented in order of decreasing accessibility.

If we could disregard logical order all together, then the way to present the article would be first stuff that a typical high-school student could grasp, then stuff that brighter kids could grasp, &c, until towards the end the material was at the level of graduate studies. :-) Of course, we cannot disregard logical order, and logical order will not simply match accessibility.

I had a sense that Bkwillwm, in placing “Index number theory” before “Formal calculation”, was seeking logical order to a rather extreme point, and that only advanced undergrads or beyond would follow the article, and most would abandon the article before the more accessible (and “practical”) section on “Formal calculation”. —SlamDiego_←T 22:50, 6 August 2007 (UTC)

[edit] Why price indexes?

I'd like to eventually see some more background on why people are interested in price indexes.

First there is the historical side: What inspired people to start calculating price indexes? Why would the idea even have occurred to anyone?

Then there is a more philosophical side: Does the idea of a "general price level" even make sense? Alternatively, how meaningful can it really be try to to sum up the entire state of prices in a single number? Consider that during a period that the CPI or whatever would lead one to call inflationary, you can still have the prices of a significant number of goods -- even the majority of goods! -- on the decline. There's something a little strange about saying that the general price level is rising in these cases. (It reminds me a little of using the Arithmetic mean as a summary statistic for a bimodal distribution; it's not that the mean is meaningless (haha), but it does seem misleading to use it as the summary of the distribution without also mentioning that it's bimodal.)

--Ryguasu 00:19, 7 August 2007 (UTC)

You can find the idea of price levels aggressively attacked in Human Action by Ludwig v. Mises, and in Man, Economy and State by Murray Newton Rothbard.

I'm unsure that your historical questions can be addressed in the article without forbidden “original research”. The essential answer, though, is that quantification of things proved so wildly successful in so many areas that a presumption of much Western thought has become that quantification is always possible, always useful, and always or almost always demanded for science. Further, money appears to be a measurement if examined superficially and over brief intervals. When it is seen to fail as a measurement over longer periods of time, it is somewhat natural to look for a correction under which it will work as a measurement through time. Given the apparent properties of money, that correction would itself seem to be a scalar adjustment.

(I'm hedging right-and-left above because, ultimately, price levels are not philosophically sound.)

—SlamDiego_←T 01:25, 7 August 2007 (UTC)

[edit] Refugees from my big edit

I removed the following during my big edit, because I couldn't figure out where they would now go. The information here should probably go back in somewhere, but perhaps not in this exact form:

A price index can also be thought of as measuring an average change in prices. In price index formulas price changes are represented by price relatives. A price relative is found by dividing a later period price by a base period price. Different price index formulas use different methods for weighting and average price relatives. A Jevons Index uses the unweighted geometric average of price relatives while other indices use weights and arithmetic averages.

While price index formulas all use price and quantity data, they amalgamate this data in different ways. A simple price index can be constructed using various combinations of base period prices (p₀),later period prices (p_t), base period quantities (q₀, and later period quantities (q_t). Price index formulas can be framed as comparing expenditures (An expenditure is a price times a quantity) or taking a weighted average of price relatives.

The GDP deflator does not assume a fixed market basket of goods and services.

--Ryguasu 07:02, 15 August 2007 (UTC)

[edit] Feedback on my big edit?

I've made a lot of changes lately, and I'm hoping for some feedback. I've probably made some improvements, but I'm starting to feel I was a little too rash.

[edit] Things I wanted to address in my changes

Making a more accessible introduction

Giving "price index" a more particular meaning. I've gathered that, in practice, "price index" can mean all of the following: A) the time series, B) the formula used to calculate the time series, and C) the time series value at some particular point. For the purpose of the article, though, I think it's important not to confuse these ideas. I've tried (though I've still be quite sloppy with it) to use "price index" for A, "price index formula" for B, and "price index value" for C.

From an introductory perspective, the formal definitions of Laspeyres and Paasch price index formulas are a bit confusing in that they take two baskets as inputs, and proceed to ignore one of them. ("So wait, the way to compare two baskets at two prices is to just ignore one of the baskets?") I thought this idea would perhaps become more palatable if I could stress how the formula would be applied across multiple base periods. ("Yes, we ignore the 2001 basket in going from 2000 to 2001, but then we make use of it in going to 2001 to 2002. And yes, we ignore the 2002 basket in going from 2001 to 2002, but we make use of it in going from 2002 to 2003.") In retrospect, I'm not sure this actually clarifies things.

Considering "take the mean of everything in the basket" as a way to build a price index

[edit] Things that didn't go as well as I'd hoped

I've added too many words. Perhaps they need to be pruned significantly. Alternatively, maybe we need to fork the article into introductory and non-introductory versions.

There are too few equations in the text I've added. Some of this stuff is silly to explain without at least simple equations (e.g., ones without sigmas). On the other hand, the equation I did add (for taking the mean of the price of apples) is perhaps too simple to include; if you are reading the article, then perhaps you can be assumed to know how to take an average!

The discussion is tied too closely to the consumer price index. This article should be equally about producer price indexes and commodity price indexes. There should also be a comparison to other sorts of index, such as a stock market index.

As I've learned more about price indexes, I've started to think that a discussion of them should also focus on quantity indexes. After all (as Diewert says somewhere), the real goal of many price indexes is to break apart a change into price components and quantity components. (Of course, maybe this isn't always true. If your price index is "the price of a liter of gasoline", then there's not really a quantity component.)

I've not been especially clear in the wording of many things. (This I'm actually less worried about, because it's relatively straightforward to fix. The question of how to organize the article and such are more complicated.)

--Ryguasu 18:37, 19 August 2007 (UTC)

I think we may need to fork the article, perhaps into several individual articles and then recreate this article as an organizer to link to the other articles. I think there is enough in "Index Number Theory" to make an article. We already have individual Producer price index and consumer price index articles. I'm not sure if we should go so far as make articles for individual price indexes, but I think we should make a List of price index formulas, which can help us avoid cluttering the article with formulas.

Regarding your recent edits, I still would like to get this article up to featured status, so I think that requires having a fairly high standard. Additions to the article should have citations. Also, Wikipedia does not use first or second person pronouns in the article (Look at WP:Style). I don't think forking this article into "advanced" and "beginner" versions will fit with usual Wikipedia practice either, but having detailed articles on the more obscure subject matter with lower level summaries in an overview article will accomplish pretty much the same thing.--Bkwillwm 02:55, 5 September 2007 (UTC)

[edit] Un-Encyclopedic language

For example: "Now if we're only comparing two time periods, this is silly; we've forgotten about the second basket!". It's great that someone's having fun writing this but this just sounds goofy. —Preceding unsigned comment added by 71.82.130.30 (talk) 03:40, 4 December 2007 (UTC)

I largely agree. I returned to looking at this article, and parts of it read more like the transcript of an educational television show than an encyclopedia article. Also, the chatty stuff largely duplicates content that was already in the article. What we have, in effect, is style forking within a single article. I am certainly not without sympathy for the urge to make this stuff non-threatening and otherwise accessible, but the present state of things isn't satisfactory. —SlamDiego_←T 13:36, 14 February 2008 (UTC)