Why Doesn't the CPI Seem More Like Real Life?

Government statistics, particularly the CPI, have been in the news (e.g., [0]). Following up on my previous posts [1], [2], I want to take a stab at the question posed in the title.

This post focuses on issue separate from the mathematics of the index formulation, and has to do with what the typical weights at any given instant in time should pertain to. Should one use the expenditure weights that pertain to all the households aggregated in the economy? Or should one use the expenditure weights that pertain to the "typical" household? Kokoski (2003) summarizes the distinction thus:

In the democratic index, the expenditure pattern of each household counts in equal measure in determining the population index; in essence, it is a case of "one household--one vote". In the plutocratic case, the contribution of each household's expenditure pattern is positively related to the total expenditure of that household relative to other households--in essence, "one dollar, one vote".

Clearly, there's no "right" answer to this question. Just like when asking for the average household income, does one take the income earned in a year, and divide by all the households in the US? Or does one identify all the households in the US, rank them by income from top to bottom, and pick the one in the middle? The former yields the mean, the latter yields the median. Both are measures of central tendency.

Understanding that distinction can be helpful in understanding why any given observer does not feel the CPI represents his or her experiences. Literally, unless the income distribution is concentrated at one level, or all households have the same expenditure patterns regardless of income levels, then almost nobody will feel the CPI is representative of the changing prices facing them. The more unequally income is distributed, or the more expenditure shares vary by income level, the more strongly this perception will held.

The gap between the CPI weighted by expenditures (so that higher income households will naturally get a greater weight) and the CPI weighted by the average over households, irrespective of each household's total expenditures, is sometimes termed the "plutocratic gap". From Eduardo Ley in a 2005 Oxford Economic Papers article. From the abstract:

Prais (1958) showed that the standard CPI computed by most statistical agencies can be interpreted as a weighted average of household price indexes, where the weight of each household is determined by its total expenditures. In this paper, we decompose the CPI plutocratic gap -- i.e. the difference between the standard CPI and a democratically-weighted index, where each household has the same weight -- as the product of expenditure inequality and the sample covariance between the elementary individual price indexes and a term which is a function of the expenditure elasticity of each good. This decomposition allows us to interpret variations in the size and sign of the plutocratic gap, and to discuss issues pertaining to group indexes. 

Note that despite the tendency to associate "democratic" with good, and "plutocratic" with bad (the terminology originates with Prais, I believe), economic theory does not provide a basis for strongly preferring the democratic over the plutocratic, in the absence of some strong conditions. And indeed, it's not clear that either index can be justified under general conditions.

Now, in the commentary on my two previous government statistics posts, a recurring theme is that the CPI is not representative of the particular writers' experiences. And it is true that if one's consumption bundle does not match that of the average consumption bundle, then one will either feel that the CPI understates or overstates the price level.

Another way of tackling this question is to ask what kind of household has a consumption pattern that matches the CPI? The answer is as follows:

It is natural to ask then what is the household better represented by the plutocratic CPI. Muellbauer (1974) searched for the household whose budget shares were closest to the ... aggregate weights in the UK CPI, and found it to be at the 71st percentile in the household expenditures distribution. For the US in 1990, Deaton (1998) estimates that this consumer occupies the 75th percentile. Thus, the 'representative' consumer embedded ... is inclined towards upper-expenditure households. 

Ley cites a 1987 study by Kokoski that estimates the plutocratic gap at -0.1 to -0.3 percentage points per year over the 1972-80 period. In words, this means that CPI using democratic weights experienced between 0.1 to 0.3 percentage points greater inflation than the reported CPI inflation rate.

More recently, Kokoski (2003) has updated her analysis (a related version published in Monthly Labor Review in 2000, see here). She summarizes her paper thus:

This paper provides an empirical analysis of the differences between the plutocratic and democratic price indices, using data from the Consumer Expenditure Survey and the CPI for the periods 1987-1997, and for simulated price change scenarios. The results show that there is very little difference between the two types of index, and that one index need not always exceed the other. In the simulated scenarios, even the extreme cases where prices changed only for expenditure-inelastic goods and services, the difference between the democratic and plutocratic indices was only about one point for every ten percent increase in the relative prices of these goods.

Can we extend these results to the present time? It's not clear. There is the conjecture that, with lower income households having a basket skewed toward food and gasoline, the plutocratic gap would be wide, particularly over the last couple years. While that conjecture makes sense to me, I'd say that answer is actually not clear.

The reason I say that is because of a recent paper by Broda and Romalis, who note that because of Chinese imports, lower income households have actually benefitted from globalization to a much greater degree than typically thought exactly because they have consumption patters skewed toward goods that have decreased in price over the past decade. From Broda and Romalis's paper:

We find that inflation for households in the lowest tenth percentile of income has been 6 percentage points smaller than inflation for the upper tenth percentile over this period. The lower inflation at low income levels can be explained by three factors: 1) The poor consume a higher share of non-durable goods -- whose prices have fallen relative to services over this period; 2) the prices of the set of non-durable goods consumed by the poor has fallen relative to that of the rich; and 3) a higher proportion of the new goods are purchased by the poor. We examine the role played by Chinese exports in explaining the lower inflation of the poor. Since Chinese exports are concentrated in low-quality non-durable products that are heavily purchased by poorer Americans, we find that about one third of the relative price drops faced by the poor are associated with rising Chinese imports.

Still, the Broda-Romalis paper does not directly address what has happened in the very recent past (say the last two and half years), as prices of goods imported from China have started to rise, and oil and food prices have risen relative to other prices. Some ideas can be gleaned from the data provided in Kokoski (2003), who provides 1987 expenditure shares for the various income quintiles. I present for illustration the distributions for the bottom first and top fifth quintiles.

 

Figure 1: 1987 expenditure shares for bottom income quintile, according to Consumer Expenditure Survey. Source: Kokoski (2003), Table 5.
Figure 2: 1987 expenditure shares for top income quintile, according to Consumer Expenditure Survey. Source: Kokoski (2003), Table 5.

With this information, one can make a back of the envelope calculation (and I stress this is only a back of the envelope calculation), based upon these shares and the indices reported for the components. This yields the following figure:

Figure 3: Year-on-year inflation calculated using annual CPI (not seasonally adjusted), (black), and guesstimated CPI for first quantile (blue) and fifth quantile (red). Inflation calculated as first log difference of annual CPI. Guesstimated CPIs calculated as geometric averages of component indices. Source: BLS, and author's calculations based on weights in Kokoski (2003), Table 5.

Here are several caveats. First, these are calculations that take into account differential expenditures at a very high level of aggregation, so they ignore differential shares at much finer levels of disaggregation. Second, relative prices may have moved even more dramatically in 2008, and the impact of that effect will be missed in this calculation. Third, these are a calculation based upon annual data; calculation of year to year changes will then allow for minimal influence of what has happened to food prices in the last half of 2007.

Those caveats in mind, these guesstimates imply that the differential between the actual CPI inflation and the inflation rate for the first quintile is only about 0.3 ppts in 2007.

A final caveat to keep in mind (from Kokoski (2003)):

...For most a priori definitions of demographic groups, there is generally more variation across households within each group than there is across groups. Since the statistical significance of any differences observed here between quintile indices is unknown, one should not draw quantitative conclusions from these results.

So one's experience should deviate from that represented by the CPI, even if one were at the 75 thquintile, exactly because of the highly individual nature of consumption bundles. But it is not clear that the income distributional aspects are driving people's differential experiences.

 

Comments

[AmesTiedeman]

People have been suggesting what you are stating for years and years. I have always viewed the inflation numbers and the CPI with skepticism.

[notsosmart]

its not that hard or complicated.take the 5 daily needs of all households(gasoline,ut... housing.) & just figure the inflation rate on these(currently @ app.16%) & you have a pretty good idea of what is happening to the family be they rich,poor or middleclass.based on the increase in price(include shinkage of weight & size & amount)& it becomes simple.but that would be too simple.at some point the americans might be able tu figure this out .

[notsosmart]

re above-5 daily needs-gasoline,utiliti... price of house,just maintaining the roof over your head.

[trader717]

It was interesting to see the quantitative differences between the democratic and plutocratic price indices. However, I still believe the CPI will always be skewed because it must use a 'hypothetical' base year and because it can be debated for reasons such as yours. It is a great article and goes to show you that if problems such as these exist with a particular measure, it may not be the best measure to use. It is also difficult to use data prior from 2000, as the economic environment has changed considerably since then.

[notsosmart]

sorry re above. 5 daily needs. gasoline,utulities,foo... your shelter.

[notsosmart]

not publishing correctly.add health.

[notsosmart]

thanx-got them all now

[BrunoT]

Anything else you'd like to add, Notsosmart? LOL

I want to say that I hope the author is paid for his time doing this, because he took the long way around on this one. The CPI is distorted. To sum it up, inflation is higher for you if you happen to buy more of the things that are going up in price and have already bought (or rarely/never buy) the things that are going down in price.

For example. Already own a house with a fixed mortgage? That is your biggest expenditure likely and the price is fixed on that. Work from home/don't drive much? You'll be hit less hard by energy. Live in a smaller home? Ditto. But if you commute a long way, are shopping for a McMansion, and have 4 kids to feed, you'll see more effect. But since you are presumedly well off, you'll feel the pain less than someone who makes less and has less cushion in the budget.

[bearfund]

There are also tremendous regional and even local gaps in the CPI. If one takes notsosmart's "5 essentials" and applies them to, say, San Francisco and Memphis, one will get wildly different results. Most San Franciscans don't use any gasoline at all, but shelter often consumes 75% of one's after-tax earnings. An opposite pattern would be found in Memphis, and while prices of food, health care, and utilities would be similar in both places, the enormous difference in the price of shelter makes constructing an index suitable for both locales impossible.

There are many kinds of bias in the CPI. One has to forgive regional and plutocratic biases; they are unavoidable. But there is no forgiving systemic bias toward understating price growth. The CPI has this in spades - when a component of the index improves technologically or provides some incremental benefit that was not present in the past, its effective price is revised downward. When a component becomes "too expensive", however, it is substituted out. In other words, the index does not measure the cost of a fixed standard of living, nor does it measure the cost of a centrally-tending standard of living. Rather, it measures the cost of a declining standard of living - the hypothetical cost of older, less capable and less technologically advanced goods plus the cost of cheaper products when the better ones got too pricey. In other words, in the past year it became 5% more expensive to live less well - and don't forget that a huge chunk of that index is the mysterious "owner's equivalent rent" which does not reflect what *anyone* (wealthy or poor) actually pays for any good or service!

A more meaningful set of indexes would exclude shelter (it is intensely local and must be computed separately for each market). They would also include a "basic necessities" index that includes commodity goods and services of the simplest and least expensive type offered by the market. For example, I need a toothbrush every few months. It does not matter what kind, and better toothbrushes might clean my teeth better but they do not help me balance my budget, so the price used ought to be that of the cheapest ones on the shelves. Other indexes could include luxury and discretionary goods. Items should be removed only when they have become obsolete, not when they have simply become "too expensive". If an item becomes unavailable because it has become so expensive that no one buys it, it should be added to a separate adjustment pool that reflects declining standards of living.

The task of compiling a useful CPI is hard. The troubling thing is not that the index we have is flawed but that those responsible for it have not made an honest effort.

[Bob Gary]

The simple deal is CPI is flat out calculated incorrectly.

[notsosmart]

some have missed my point. you use the increase in the price.the increase in the price of gasoline in one,s own region increases a certain amount wether you work at home or drive 60 mi rt. to work. the increase in the price of the item is the only thing counted.if need be this can be refined to geographical areas.it might not be perfect but its better than the bs the govt.is handing out.

[iThinkBig]

Great comments all! Thank you Mr. Chinn for your time in sharing the analytics. The world needs many more of your kind. On that note, I conducted an economic feasibility study in China in 2004. Consumer Health data is what I do (marketing). Perhaps I can repay the favor and send over the outputs if you are interested. Email me at jrines@primehealthsolu... .

[iThinkBig]

Guess you will have to go through my website to contact me Mr. Chinn.

[yuman]

Is PPI plutocratic then since it is not associated with households?

[notsosmart]

ppi,cpi etc.anything with this govt.is bs & suspect.all you can do is be alert & think for yourself.you cant believe anybody about anything.the same goes for wall st.

[iThinkBig]

Sigh... Your correct NotSo. The thought of the damage control and recovery process required to correct all of this is in itself, tiring.

[Think-About-It]

"We find that inflation for households in the lowest tenth percentile of income has been 6 percentage points smaller than inflation for the upper tenth percentile... "

Lower inflation for the poor... you'll never here that from a politician.

[TinyTim]

Great stuff. Very interesting and well written paper, including references.

The problem I have with the CPI is that it tries to be too broad in application. For Social Security COLA adjustment, this recent data and interpolations seem to indicate that there is a statistically insignificant difference between the highest and lowest quintiles. There is just as much variation within each quintile. But if the aggregations in Kokoski's pie charts (similar to Notsosmart's) and the numbers themselves are representative, the essentials of food, housing, utilities, apparel and medical show major differences between quintiles. The greatest differences are in the discretionary areas of cars and furniture, which are durable goods. I doubt the variation within the lower quintiles is as great as the higher because there is less opportunity for substitution and the individual nature of consumption bundles is less pronounced. I think it follows that the lower the total expenditures, the less are people's differential experiences. It would be interesting to see the same pie charts with the size reflecting the comparative total expenditures. This would better illustrate the difference in the democratic versus plutocratic indices. Assuming the fifth quintile is the same as the bottom quintile, it's good that the interpolations show the CPI most reflects it since this is where many people concerned with COLA probably reside.

Using the CPI for TIPS is the opposite extreme. People investing in TIPS probably are in the 71st percentile or higher and have highly individual consumption bundles. The lack of credibility in the CPI expressed in the comments above is causing a lack of faith in TIPS, in addition to the general feeling of poor bundle representation in these higher percentiles. The St Louis FRB recently published a paper trying to justify the ommission of food and fuel from their inflation metrics. It was quite a bit of hand-waving.

Lastly, this lack of credibility in the CPI has a lot to do with regular manipulation by govenment officials. Substitution and obsolescence are obviously necessary, but there is no clear evidence that they're comparable. I would agree with the comment that they appear to be adjusting down, which I think is a function of the deleterious effects of long term inflation.

[secmaven]

Learned discourse. What chapter of your Phd thesis was this article?