First, let's imagine that Shadow Government Statistics is correct and that the inflation was around 10% in 2006. It would mean that the real interest rate on Treasure Bills would have been of approximately -6%, which is insane. No one would have bought them, if that was the case.
Wikipedia defines real interest rates as follows:
The "real interest rate" is the rate of interest an investor expects to receive after allowing for inflation. ... If, for example, an investor were able to lock in a 5% interest rate for the coming year and anticipated a 2% rise in prices, he would expect to earn a real interest rate of 3%.
If, as Shadow Stats claims, the inflation in the United States was up to 10% and the interest rate on Treasure Bills was of about 4% (source), then the real interest rate would be negative (4%-10% = -6%). Under a negative real interest rate, people lending money to the government would be losing money whereas the US government would be earning money by borrowing. It would make no sense to lend money at such a low rate, yet demand for Treasure Bills remained relatively stable during 2006.
Such a situation would be unsustainable. Eventually, lenders would wise up and stop lending until the real interest rates go back up. It makes no sense for people to invest at a negative rate of return. If inflation was that high, then interest rate would increase as well for to at least positive returns on investment.
That is the most obvious reason Shadow Government Statistics is wrong: if they were right, Treasure Bills would be ways to give money to the US government rather than an investment.
Now, what did Shadow Stats did do to arrive to such values and how is it superior to the Bureau of Labor Statistics' methodology? I can't say. While they have promised to that their methodology will be "published in next month’s 'Reporting Focus'" back in October 2005, I can't find that month's "Reporting Focus" - or any detailed methodology - anywhere on their site.
Based on their criticism of the Bureau of Labor Statistics, we can make a few educated guesses though.
Back in August 2008, the Bureau of Labor Statistics published an article called Common Misconceptions about the Consumer Price Index: Questions and Answers to which Shadow Government Statistics felt need to reply to in ShadowStats.com Response to BLS Article on CPI Misconceptions.
In the response SGS goes into details into why he believes the BLS is biased and underestimates inflation. He blames three factors, which are well summarized in this Forbes article:
Substitution. If steak becomes more expensive, and you buy hamburger instead, then the Bureau of Labor Statistics reasons your cost of beef has stayed the same – no inflation!
Hedonics. If the 2011 model of a car costs more than the 2010 model, but it also comes with more standard equipment, the BLS reasons you’re still getting the same value for your money – no inflation!
Geometric weighting. Nothing fancy here: If the price of something goes up, the BLS simply makes it count for less in the CPI relative to everything else. If the price comes down, it counts for more. Voila!
The idea that the CPI is biased is hardly new or controversial.
In fact, such is taught in economic textbooks (Introduction à la macroéconomie moderne, p. 148-149) and the Bank of Canada even has a section of its website dedicated to explaining its shortcomings:
One reason is that the change in the CPI measures the cost to the consumer of buying a fixed basket of goods and services, the contents of which are updated only once every four years. In reality, consumers can and do substitute cheaper items for those that become more expensive when the relative prices of different products change between basket updates. For example, if the price of beef rises sharply, consumers may buy pork or chicken instead, if they are cheaper. Because of this shift in spending patterns, the actual increase in the overall cost of living is less than the increase in the cost of buying the original fixed basket. So, the true cost of living can be overstated if there is a commodity-substitution bias.
New products (e.g., high-definition TVs, digital cameras) that come onto the market between updates of the consumer basket can also be a source of measurement bias. Typically, the relative prices of some of these new products (notably home electronics) drop considerably following their introduction. If those price decreases happen before the basket is updated to include the new goods, the overall CPI will overstate the true cost of living (by an amount that depends on the share of the new goods in total spending).
The CPI aims to measure the pure price change of a basket of consumer goods and services of constant quality by comparing their prices at two points in time. In fact, quality improvements may decrease the prices of certain items. For example, rapid technological advances have resulted in lower prices for personal computers, as well as an increase in computing capacity. Although Statistics Canada uses various methods to correct prices for quality changes, such adjustments may not fully remove the bias, leaving the overall CPI overstated if quality improvements occur faster than they are measured.
The entry into Canada of new discount retailers and large warehouse stores has resulted in shifts in market shares from high- to low-price retailers. If the effect of these shifts on the prices paid by consumers is not fully captured, the true cost of living will be overstated.
In other words, the notion that the CPI imperfect or biased is in line with mainstream economics. The critique by SGS overlaps with the admission of bias by the Bank of Canada but this is where the agreement stops. When we go into discussing the size of the bias or its possible solutions, mainstream economics and Shadow Government Statistics disagrees.
First, when economists try to measure the bias of the CPI, they arrive at under 1%, which is obviously quite far from the seven or eight percentage point bias that SGS's figures entail. For example, in Measurement Error in the Consumer Price Index: Where Do We Stand?, the authors conclude that:
In total, we estimate that the CPI overstates the change in the cost of living by about 0.6 percentage point per year, with a confidence interval that ranges from 0.1 to 1.2 percentage points. Roughly half of this bias is accounted for by the CPI's inability to fully capture the welfare improvement from quality change and the introduction of new items. Our bias estimate is smaller than that found in several earlier studies, in part because the BLS has recently made a variety of improvements to its procedures; our study highlights several potential areas for further improvement.
Secondly, many times on its website, Shadow Government Statistics says its inflation estimates are "based on methodologies in place as of 1980 and as of 1990." If that's the case, previous studies into the measurement error of the CPI during that time period will be enough to validate or debunk the SGS's numbers.
Well, according to The Consumer Price Index as a Measure of Inflation which analyzes the bias of the CPI between 1967 and 1992, the bias is in the order of 0.5% at the highest. That's within the margin of error of the previous results. (Note: If we look into the bias prior to 1982, however, the bias is greater.)
The claim that the Bureau of Labor Statistics underestimate inflation by seven or eight percentage points is extraordinary, as it would imply that most investors are losing money by lending at a negative real interest rate. As their methodology is not published on their website, as their critique of the current way CPI is calculated is mostly congruent with mainstream economics and as economic analysis only measure a bias of 1%, it is unlikely that Shadow Government Statistics is correct in its belief that inflation is still around 10%.