Note: The following blog post originally appeared as two blogs on February 16, 2010 ("Oh, (Yeah!) Canada!") and August 17, 2010 ("The 'Real-Feel' Inflation Rate"). I have combined them because they speak to the same topic, and given the resulting dual-article a more representative name. I have removed some of the references to then-current market movements and otherwise cut the article down to the interesting bits. You can read the original posts here and here.

Re-Blog of "Oh, (Yeah!) Canada!":

On Friday the BLS will release the Consumer Price Index, which is a very important release and one of the most maligned even though CPI is one of the more carefully-designed and researched numbers in the entire list of government releases. This is partly because so much is riding on it, between securities linked to non-seasonally-adjusted CPI (such as TIPS) and contracts such as Social Security and others. To some people, this just opens the door for more government shenanigans, since arguably the government stands to gain the most from monkeying with CPI.

But if people with lots of money on CPI didn't fundamentally believe in the veracity of the number, then the $500billion-plus TIPS market would be in real trouble. Indeed, in some countries where there is better reason to doubt the government's accountability on such matters, there are private as well as public inflation indices and there are securities are linked to each index. (Brazil is one example.)

That doesn't mean that these investors are right, of course, but you can believe that they've looked pretty hard at the number. Sure, investors have also looked very hard at equities and concluded that they are entitled to a very lofty multiple right now, so we can't just rely on that. I will tell you, though, why inflation cannot possibly be as high as some folks believe it is, and why you very likely feel that inflation is higher than is being reported by the government.

What follows is an enumeration of some of the cognitive errors that people make with respect to CPI. The list isn't complete, but I think I've hit on the biggest of them.

As a first point: CPI does what it is supposed to do very well, but that might not be what you want it to do. CPI is a cost-of-living index, which means that if your standard of living improves then the price you pay for that standard of living should also increase (that is, your outlays should increase faster than general inflation); if your standard of living is static then your outlays should increase with inflation. CPI measures, in other words, the cost of an unchanged standard of living.

This important point gives rise to the concept of hedonic adjustments, which adjust the price recorded by the BLS for a particular good to account for changes in the quality of those goods. This is a crucial adjustment for certain goods that change significantly in quality, such as cars, computers, and medical care. But this is one source of complaints of people who don't bother to understand the CPI: people don't mentally record hedonic adjustments; people measure cash out of their pockets. So when you buy a new computer and it's lots better than the last one but costs the same, you experienced deflation in the sense that the cost of your old lifestyle...which you no longer have...costs less. Since you spent the same amount, it doesn't feel like deflation to you, but since your standard of living improved while the costs were unchanged, that's deflation in a cost-of-living-index sense.

Second, your consumption basket may vary. For most people, the broad CPI index is a reasonable measure, but each person's consumption is different. Some people spend more on Apparel and less on Recreation; others are the opposite. CPI is supposed to measure the average experience, and no one is exactly average.

Third, CPI excludes taxes that don't have anything to do with consumption, since CPI is only supposed to measure changes in the costs of things you consume. But taxes definitely affect our standard of living, so if income taxes rise and that causes a decline in your standard of living, that sucks but it's not inflation. Don't blame CPI - blame the dudes who are taxing you!

Fourth, people tend to remember price changes of small, frequently-purchased goods rather than large, infrequently-purchased goods even though the latter are more important to your cost of living. For example, your house is typically no more than a once-a-year negotiation (if you rent) or even less frequent if you own. But it is a huge part of your cost of living. When milk doubles in price, or gasoline spikes, you notice it a lot but it's a much smaller portion of your consumption and matters less.

Fifth, you may be the victim of classic attribution bias. When you go to the store and you come home with a bunch of stuff at higher prices, you say it's inflation; when you come back with a bunch of stuff at lower prices, it's "good shopping." Combined with the prior effect, the rapid oscillations in food and energy prices seem to us to be lots of inflation interspersed with lots of good shopping.

These are the predominant cognitive and comprehension errors that most people make when they think about inflation. But some complaints about CPI go way beyond these innocent and entirely normal perceptual biases.

Some complaints of CPI are just silly. Shadow Government Statistics, which has made quite a great business catering bad data to conspiracy theorists - and I won't link to the site; if you need to find it for some reason I am sure you can - has a chart of what inflation would be if the BLS used 1980 methods, with the implication being that the guvmint is trying to hide the 9% rate of inflation (the site says inflation is understated by about 7%). The choice of 1980 is very adept, since it was in 1982 that the BLS changed the method of computing the cost of housing to remove investment-value-of-the-home considerations (such as the mortgage rate) and focus on the consumption-value-of-the-home (which is best represented by what it would cost to rent). This was done after much research, many public papers and debate, and is absolutely the right way to measure inflation in the cost of housing consumption as distinct from changes in the value of the home as an asset. There are lots of other improvements that have been made to CPI, and they really are improvements. Not everything from 1980 is better than the 2010 version. Computers, cars, medicine. I'll concede music.

But we can rely on a very simple argument to prove that true inflation cannot be at 9% (but it involves math). I presume that most readers can recall what they were paid ten years ago, or at least can very easily figure out what their income was back then. Government statistics say that the average increase in wages and salaries (in the Employment Cost Index) has been about 36% over 1998-2008 (for some reason I am having trouble finding 2009 data, perhaps because it is subject to revision). I assume that we don't think the government is exaggerating that number on the low side for some sinister reason. Now, if inflation is really running at the 9% or so that Shadow Government Statistics says it has for the last decade, then while your wages have grown 36%, cost of living has risen 136% (the government says inflation has been more like 29%).

More concretely: suppose you made $60,000 in 1998, took home $40,000 after tax and were just breaking even with your cost of living at $40,000. According to the government, you ought to be making about $81,500, and if taxes were the same your take home pay of $54,333 would leave you about $3,000 better off, with your cost of living about $51,500. If, however, inflation was really at 9%, then your cost of living is now $94,700, and you declared bankruptcy several years ago. You don't have to be able to track your receipts to see that 9% is not the right rate of inflation - you just need to look at the compounded outcome.

Consider a longer period of time for a more-poignant comparison. The person making $30,000 and taking home $20,000 in 1980 is now making $89,000 and the $59,300 take-home pay (2/3, assuming improbably that taxes were unchanged) has improved his/her standard of living somewhat as the old standard of living now costs $52,800 using CPI. Using a 7% higher rate of inflation, the same standard of living this person enjoyed in 1980 for $20,000 now costs $353,000.

That is nonsense. And by the way, it also means that housing over the last decade not only wasn't in a bubble, it didn't even come close to keeping up with inflation, and neither did any other asset in the world. That's worse than nonsense; it is an offensive ignorance of mathematics.

CPI is not a perfect number, and moreover it may not be a perfect number for what you want it to do. But it does what it is supposed to do, and it does it very well. I am certainly no apologist for the government and the way it is run, but on the occasions that the bureaucrats get something basically right, I think it's okay to say so.

Re-Blog of "The Real-Feel" Inflation Rate:

In today's comment, I would like to talk about inflation as it is measured, inflation as it is perceived, the difference between the two, and the implications of that difference. First, I want to thank the readers of this column for helping me by taking the poll on my website; the poll supported certain hypotheses of mine (or, more technically, it failed to reject them) that I will discuss here. Read on for poll results!

But first, let me discuss CPI (inflation as it is measured). The vitriolic rants that occur against this measure were one of the motivations for my research. As an inflation trader, I have had to become intimately familiar with the CPI and its quirks, and also have had to explain it many times. Since I believe that CPI does what it is supposed to do very well, I have occasionally become a target of the ranter and called a government stooge, conspirator, or worse. And so I have always wanted to figure out the difference between inflation as it is calculated and inflation as it is perceived, since it is this difference that leads to the vitriol.

Let me get this out of the way: yes, I think CPI accomplishes its mission. But its mission may not be what the ranter thinks its mission should be. It is not supposed to measure (nor could it ever measure) the change in prices that any individual faces. It is an aggregate, meant to reflect the average experience of consumers. You are not average. And you are not an average consumer. And so your experience may vary.

Moreover, it is not supposed to measure the average change of prices in the economy. It is closer to a cost-of-living index, which means that it is meant to answer the question "what is the cost of achieving today the standard of living actually achieved in the base period?" This is a difficult goal, since your "standard of living" must necessarily incorporate your preferences about how different goods and services are better or worse than others and we can't directly test your preferences. All that the Bureau of Labor Statistics can do is to survey prices and quantities consumed, to draw inferences about consumption patterns, and to calculate the change in prices of the consumption basket that keeps the average consumer's standard of living approximately unchanged. That's difficult, and they do it remarkably well at that. The fact that they do it pretty well is evidenced by the observation that, if the BLS were appreciably wrong about the rise in prices for a given standard of living, over long periods of time we would see a substantial difference in standards of living compared to what we expect. The difference between 2% and 5%, compounded over 40 years, is huge. If prices rise 2% over 40 years, the same standard of living now costs 2.2 times what it did back then. If the compounding rate is 5%, the same standard of living costs 7 times as much. So while it is reasonable to ask whether the BLS is off 0.2% or 0.5% here or there, it is very unlikely to be meaningfully biased over long periods of time.

It is a very separate question, though, what inflation feels like. Moreover, it is very relevant. Modern monetary policy considers inflation expectations a metric of signal importance in the formulation of monetary policy. While the Taylor Rule provides a well-known heuristic for monetary policymakers that relies on actual, not expected inflation, policy discussions rely very heavily on the question of whether inflation expectations are, and will continue to be, "contained." Current Federal Reserve Chairman Ben Bernanke himself described the importance and significance of inflation expectations in a speech in 2007 by saying "Undoubtedly, the state of inflation expectations greatly influences actual inflation and thus the central bank's ability to achieve price stability."

So how does the Fed measure inflation expectations? Generally, with surveys - including the Livingston survey, the Survey of Professional Forecasters (SPF), and the Michigan Survey of Consumer Attitudes and Behavior. Some of these measure the expectations of economists about CPI, which isn't really helpful - the Fed already has their staff economist forecasts, so checking a survey essentially of the people they hang out at the club with would give a false sense of security.

The Michigan survey asks consumers for their views about "the expected change in prices." But here's the problem, as illustrated by the survey I took on my website recently: normal humans are not capable of conducting in their heads the monumental tasks of cataloging all of the year's purchases and calculating the differences from the same basket from the year before. Price changes are not homogeneous, and this leads to seat-of-the-pants adjustments. Consider this very thorough explanation from one person who answered my survey and then wrote to explain her vote:

"My personal experience has been that big ticket items have gone down, but small ticket items have gone up (example fast food ice tea prices or Frontline for my dog). It is crazy that I spend almost $2 for a glass of ice tea that is just water and a tea bag with some ice. But the cost has gone up around 20 cents at most places in the past two years. Conversely, grocery store prices are very mixed with some real bargains, but I do see vast differences between the same good at Wal-Mart and at Krogers. Sometimes Kroger prices are 25% higher for the identical item. I stopped drinking Coke over six years ago. A bargain then was three cases for $10. I saw a display at Wal-Mart the other day of one case for $5.25. It may have had 18 cans instead of the 12 of old. It looked bigger, if so, that would indicate not much price pressure. I recently bought a fan to replace one that died. The new one was by the same company and almost identical, but cost the same after 3-4 years. Of course I bought the first one at a department store and the second one at Wal-Mart. (FYI Walmart is about the only store less than an hour and fifteen minutes from my house other than dollar stores or local hardware stores. Did you know that each Wal-Mart sets its own pricing? There can be noticable price differences sometimes on the same item at my two nearest Wal-Marts. The slightly closer one has less competition and they told me that lets them price some goods higher than the other store.) But, TVs and computers are a lot cheaper, so much so that it has induced me to buy. My telephone and cable bills haven't changed in years. These conflicting observations made it very hard for me to answer your question."

Yes, exactly !!

Clearly, the FOMC would like to sample the perceptions of the people who are involved in price-setting and wage-setting behavior. But consumer surveys are not ideal instruments for at least two reasons. First, as some researchers have pointed out, taking the "median" expectation obscures a lot of information and it isn't exactly clear what role the variation in expectations should play. Second, and more importantly, surveys of inflation don't work well because consumers do not discern inflation properly. Perceptions of inflation are muddied by a myriad of practical problems (such as those described so clearly by my correspondent above!) and behavioral biases that tend to impair accurate assessment of price changes. For example:

1. Quality change and substitution adjustments are not recognized viscerally by consumers, although they are a necessary part of a cost-of-living index. It might also be the case that people notice downward quality adjustments ("my insurance coverage is shrinking") more than upward quality adjustments.

2. Consumers have an asymmetric perception of inflation as a whole, as well, so that they tend to notice goods that are inflating faster than the overall market basket, but to notice less the goods that are not inflating as fast. This sense is enhanced by classic attribution bias: higher prices is inflation, lower prices are "good shopping."

3. Items whose prices are volatile tend to draw more attention, and give more opportunities for these asymmetries to compound, so they tend to factor more heavily into our sensation of inflation.

4. People notice price changes of small, frequently-purchased items more than they notice large, infrequently-purchased items even though the latter are a bigger part of consumption basket. Gasoline is hugely important even though it's not a huge part of the basket because (a) it is purchased frequently and (b) it is volatile, which means attribution bias acts constantly.

5. Consumers do not viscerally record imputed costs, such as owners'-equivalent rent as distinct from what they see as their costs (principal plus interest, taxes, and insurance). Even though the former is better for CPI, the latter (which is the pre-1983 method, basically) affects perception more directly.

6. People perceive increased changes in income taxes as inflation.

So what is the result of this complex problem? Well, here are the results from the poll I conducted. The question was "Consider your personal experience of inflation over the last year. Would you say that the prices you pay have generally (choose the best answer): " There were 355 votes, 22 of which (6%) were "I don't know." Here are the percentages of respondents who perceived different price increases.

Two immediate observations, both of which support my general contention: first, the average response (coarsely, if we take the first category mid to be 0.50%, the second to be 2.5%, the third to be 4.5%, and the fourth to be 6.5%) is 3.45%, obviously much higher than the official CPI (1.2%). Clearly, consumers perceive higher inflation than what is calculated, which is the direction in which I would expect the behavioral biases to operate. Second, there is no general agreement about whether inflation is low or high, much less how low or high it is. A small plurality prefers the "4-5%" answer. The sample size is small, but not that small...we should have expected, if humans were coldly rational calculating machines who have generally similar consumption baskets, to see at least something of a bell curve developing. The difference in experienced price increases is probably not this wide; at least some of this is because while consumption baskets are in fact more similar than you might think, we have wildly different heuristics and biases that we use when answering this question.

In my paper, I attempt to correct for a few of these biases. If we can model inflation perceptions this way then we might not only be able to identify changes in inflation perceptions but to also understand the drivers of those changes in any particular episode. The monetary policy prescription might vary if, for example, elevated perceptions of inflation were driven because of an increase in taxes than because of an increase in the volatility of price changes in the consumption basket.

I don't attempt to correct for every bias here, but for some of the more important ones. I correct for the misperception of quality and substitution effects (specifically, I remove all of the quality adjustments that tend to decrease CPI while retaining all of those that tend to increase it), for the asymmetric perception of price changes, and for the perception of volatility (big changes in prices) as inflation. You probably don't want to see the math, and if you do then you should wait for the paper itself, but as an example here is the adjustment I make for the perception of volatility as inflation:

where lambda is a coefficient of loss aversion per Kahneman and Tversky; w is the weight of an item in the CPI basket; and σ is the standard deviation of the item's price over the past year. This adjustment is derived from a result that tells us the expected future value of a one-period, at-the-money option.

The details, as I say, are probably not of much interest to most readers of this column. But the charts will be. The tricky part is calibrating the lambdas, and this can and should be done more diligently in a behavioral economics laboratory. But with the choice of lambda that I thought to be "about right," here is the aggregate upward adjustment that should be made to CPI to get to perceived inflation.

And, combining this with year-on-year CPI, the chart below shows the difference between the official CPI and the perceived CPI, incorporating my adjustments.

This chart suggests that one reason that 6%+ may have been so prevalent as a poll answer is that until a few months ago, that is how it actually felt . The most-recent point, incidentally, is 3.4%, so thanks again to everyone who took the poll - I couldn't have hoped for a nicer match!

Let me return one more time to the reason for this exercise, this time with a simple analogy. There is clearly a reason that we need to measure the CPI with as much exacting, mechanical precision as we can muster. Knowing how prices are actually changing in the economy is important for consumers, wage-earners, and investors. Similarly, it is very important to have a good thermometer that can tell you just how cold it actually is outside in Chicago in January. But before venturing outside in Chicago in January, you ought to also consider the "wind chill" or "real feel" temperature, because it has great relevance for your real-life behaviors. The "true" temperature is given by the thermometer, but in many situations the wind chill is what actually matters (it is connected more directly, in this case, to your survival chances if you under-dress).

In the same way, policymakers need to know not only what prices are actually doing, but what the "real feel" inflation rate is, because it is relevant for many consumer decisions. My research here is a first step, I hope, to developing such a tool.

Editor's Note: The paper referred to here was eventually published in the journal Business Economics; you can find a link to the full published article here.

You can follow me @inflation_guy!

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