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Tuesday, July 19, 2011

The "Chained CPI" Scam

This story was interesting. When calculating the cost-of-living-adjustment (COLA) for Social Security and other payments, State comedians are switching from the CPI to the "chained CPI".

Naturally, this move will lead to a lower inflation calculation. This will lead to lower Social Security payments. Whenever State comedians/economists change the inflation index, it leads to lower inflation. Why don't any formula changes ever lead to a higher inflation calculation?

The CPI matters because it's used to index pensions and Social Security. Also, a dishonest CPI enables politicians to lie and say "Inflation is low!"

Ben Bernanke says "I'm only willing to discuss the CPI. I'm not willing to discuss other measures of inflation." Ben Bernanke is a professional liar.

When I heard of the new "chained CPI", I realized I had to look into the Math behind the new calculation farce.

First, I will review the bias in the old CPI.

The CPI uses the geometric mean instead of the arithmetic mean. According to algebra, the geometric mean is always less than the arithmetic mean, for positive numbers.

Here is an example. Consider {1, 3, 9}. The arithmetic mean is (1+3+9)/3 = 13/4 = 4+1/3. The geometric mean is (1*3*9)^(1/3) = 3. By using the geometric mean instead of the arithmetic mean, inflation is understated.

(The geometric mean of {a_1, ..., a_n} is the product of a_i raised to the 1/n power. A theorem from algebra says that the geometric mean of positive numbers is always less than or equal to the arithmetic mean, with equality when all numbers are identical.)

Also, the CPI is reweighted. State comedians don't pick the weights ahead of time. Instead, they look at the price data, and then choose the weights. Naturally, they pick weights to underestimate inflation.

Here's the joke justifying that lie. When prices rise, people substitute what they buy. Therefore, things rising rapidly in price should be underweighted and things rising slowly should be overweighted.

Here is an example. Suppose that in year 1, chicken rises 30% but beef rises 2%. People switch from chicken to beef. Suppose that in year 2, chicken rises 2% but beef rises 30%. People switch from beef to chicken. In both years, "meat" rose 2% annually, even though actual inflation was much higher. The CPI component of "meat" is 2% annually instead of a more honest 14%, due to the reweighting trick. (sqrt(1.3) = 1.14)

Here is a second example of reweighting bias. The "cash for clunkers" discount was deducted from "price of a car", when calculating the CPI. When the "cash for clunkers" program was in effect, more people bought cars, leading to greater weight for "new car" in the CPI. When the "cash for clunkers" program expired, fewer people bought new cars, and therefore "new car" was given a lower weight in the CPI.

Here is a third example of reweighting bias. When the housing market was booming, State comedians said "A booming housing market is a negative CPI adjustment. It's negative implied rent for homeowners." When the housing market crashed, State comedians said "Housing prices are cheaper now for first-time homebuyers. That's a negative CPI adjustment."

Also, it's the "core" CPI and not the full CPI. The "core" CPI excludes food and energy and things that tend to rise in price quickly. (The supply and demand of energy is relatively inelastic, making it very sensitive to inflation. Similarly, the supply and demand for food is relatively inelastic.)

Also, the CPI is calculated via a multi-stage process. First, an index is calculated for each area and each category. Then, those are aggregated. The rebalancing trick and geometric mean trick is used at each stage, to understate inflation. (For example, prices are rising in California but decreasing in Texas. Therefore, people move from California to Texas. The actual census data is irrelevant.)

So far, I've described the *OLD* biased CPI algorithm. What's the new scam for "chained CPI"?

This is the sort of thing I can do better than anyone else. I'm illustrating exactly the formula that the "chained CPI" uses to lie about inflation.

Instead of using "price at time n", the "chained CPI" uses "average of past prices" (typically a year). How does this lead to bias?

Suppose that, instead of using the price at time n, I use a geometric-mean average of 3 prices.

Consider {1, 2, 4, 2, 4 } as the raw price data. (I.e., price is 1 in first year, 2, in second year, 4 in third year, 2 in fourth year, 4 in fifth year.)

I substitute with "3-chained geometric-mean average".

For each 3 adjacent elements, I replace those three elements with the geometric mean of those 3 elements.

The geometric mean of {1, 2, 4} is (1*2*4)^(1/3) = 2.
The geometric mean of {2, 4, 2} is 16^(1/3) = 2*(2^(1/3)) = 2.52
The geometric mean of {4, 2, 4} is 32^(1/3) = 2*(4^(1/3)) = 3.17.

Summarizing, via geometric mean 3-chaining, the series {1, 2, 4, 2, 4} is replaced with {2, 2.52, 3.17}. This "chaining" process smooths out price volatility when dealing with raw price data.

The "geometric mean" trick smooths out price data in one interval. The "chaining" trick smooths out price data over adjacent time intervals.

Notice how a 300% increase {1, 2, 4} is replaced with a 117% increase {2, 2.52, 3.17}. When this trick is combined with rebalancing and reweighting and multi-stage aggregation, this leads to a lower CPI. This "chaining" trick can be used at each stage of CPI index aggregation.

"Chaining" also leads to bias for arithmetic mean. {1, 2, 3, 2, 3} becomes {2, 7/3, 8/3}, via 3-chaining. It's unclear where the CPI uses geometric mean and where it uses arithmetic mean. I think they use geometric mean everywhere, but the documentation wasn't clear.

Why even bother with the farce? The CPI is a lie backed by really fancy Math. However, that Math has nothing to do with how people actually spend money. When I go to the grocery store, does the clerk say "OK, I'll charge you the average of the price over the last 12 months."? That is what the "chained CPI" means.

Here's my proposed price index. I call it the CPI-0. It has a very simple algorithm.

float get_cpi(BLS_Statistics *data)
return 0;

That's more intellectually honest than the actual CPI algorithm.

The CPI is a biased and manipulated statistic. The new "chaining" trick makes it even worse. The price at time T is replaced with an average of prices over the previous year. This leads to lower inflation, especially when combined with the rebalancing and reweighting trick.

This is a clever trick. Instead of admitting there's an inflation problem, State comedians change the definition of inflation! Each time State comedians change the inflation formula, they add new tricks that let them understate inflation!

This type of Math analysis is something I can perform better than almost anyone else. I've seen articles on the new "chained CPI", but none of them explained the details of the scam like me.


Scott said...

Thanks, very interesting. How do they maintain the fraud long term though, do they keep changing the rules and never use a consistent rule and data set over more than a few years?

FSK said...

The CPI is not "current price" vs. "base year price". If they did it that way, it would even out eventually.

The CPI is calculated as an index, "current month" vs. "previous month". They keep rebalancing. That enables the scam to continue over long time periods.

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