Sunday, June 13, 2004

Economic Theory: It's not cheaper if it's better

Suppose I were to offer you a product like fried chicken for $10. I think we could agree that if next year I were to offer you twice as much for $10 that you would be getting more for your money. If next year I were to offer twice as much for $20 then the unit price would have effectively stayed the same.

This sort of reasoning undermines the "quality-adjustments" that underlie the corrections being made to inflation measures such as the CPI.(The Economist)

In the same way, booming house prices hurt first-time buyers much more than those already on the property ladder. More troubling is the thought that official consumer-price indices might overstate or understate inflation across the board. One line of economic research over the past decade has focused on whether official indices overstate inflation. The consensus is that they do, by failing to adjust sufficiently for improvements in the quality of goods and services, or the availability of newer, more innovative ones. In other words, because a $500 television today is much better than a $500 set of a few years ago it is, in effect, cheaper. This means that inflation is actually lower, for all consumers, than a simple price index would suggest.

America has made more progress than most other countries in adjusting its main index, the CPI, for such changes. The effect of this is likely to be to save the government money, by reducing the rate at which pensions and benefits increase.

However the problem is three fold. First the underlying theory of these quality adjustments is to assume a linear-regression of price to quality. The problem is that in the physical sciences it is well known that for many classes of problems that linear-regressions are only valid as a perbutative method - only very near the initial sampling. The further one get's away the initial sampling the less likely that a linear interpolation will produce a correct alignment.

To demonstrate this let us consider computing power. It is convenient to consider computing power because it follows Moore's law. Moore's law asserts that every eighteen months that computing power will double. Thus every three years (12x3=36=2x18) the computing power will quadruple. Suppose then we were to go to the store Best Buy and buy a Dell laptop. Suppose for the sake of argument that the cost was $1000 in today's money which is a reasonable assumption given the prices listed on the website.

Conveniently as it turns out, according to this Inflation calculator that the US CPI calculates that from January 1944 to January 2004 that the inflate change was 964.37%. Let's say for the sake of argument that in the past sixty years it was 1000% inflation. This means that something that cost $1 in 1944 would cost $10 in 2004 terms. Reversing that it would have taken $100 1944 dollars to match the purchasing power expenditure from everyday budgets that it now takes to buy a $1000 Dell Computer.

Well obviously if we consider a change of only a few years - say from 2001 to 2004 - then the shift in inflation will be smaller: 5.77% in fact. If you could buy the Dell computer available today but only three years ago for a $1000 it would cost practically the same as if you bought it today. However you would be purchasing today's computer so you would be purchasing four times the computing power at practically the same cost. What a bargain! Clearly in computing terms we're much better off. Okay so far so good for these "quality adjustments".

However what if you tried to buy the same computer available today for a $100 in 1944 money? Well according to Moore's law 60 years ago the computing power available would have been 1,000,000,000,000 or one trillion times less! (60/3 = 20, 4^20 = 1,099,511,627,776) times less. What kind of difference would that have made?

In WWII a brilliant British mathematical genius named Alan Turing found a way to break the cryptological code the Germans used: Enigma. Well if the Germans had possessed a Dell laptop they could have made an unbreakable code. Conversely if the Allies had possessed a Dell laptop they could have trivially read every German message in existence, perhaps ending the war years earlier. It is not too much to say that wars could have been fought over a single Dell laptop and that it's value would be in 1944 terms priceless. Whomever owned such a technological advantage would leap decades ahead of other nations and perhaps come to dominate the entire world. You could not put a price on such a technological advantage.

This is an example of a perbutation deviation from a linear regression. Comparing a Dell computer in price and computing terms works alright for a three year gap. Compare it to a sixty year gap and the comparison falls apart entirely.

Another fundamental problem is that the quality adjustments typically don't take into account reverse purchasing power and economic substitution.
The substitution effect is basically a price change that changes the slope of the budget constraint, but leaves the consumer on the same indifference curve. This effect will always cause the consumer to substitute away from the good that is becoming comparatively more expensive. If the good in question is a normal good, than the income effect will re-enforce the substitution effect. If the good is inferior, then the income effect will lessen the substitution effect.

Okay suppose we talk about this Dell laptop again. Would a laptop that cost $942.30 in 2001 dollars sell on the market now for a $1000 now? No!!! A person today would not agree to buy for a mere $57.70 price break a computer four times less powerful than the Dell laptop commonly available now. I'm guessing that this is not enough of a price incentive to make that substitution work.

This substitution effect works both ways. First consider if a person in 2001 would have chosen to buy a computer available today for a $1000 dollars. No what was available then was a computer four times less powerful. A computer four times more powerful than what was available in 2001 surely would not have had a premium of merely 5.77%! It would have been a very high end luxury item at best, and perhaps even the subject of corporate espionage ("reverse engineering") - the same process that brought us IBM "clone" computers or knockoffs functionally exchangable from the original brand.

A person in 2001 is going to use their purchasing power to buy on their own price scale of what is available. If you were able to buy the top of the line in 2001, then you would have bought the top of line. In no way was there an available choice to buy for a mere 5.77% more four times the then available computing power. If in 2004 you are able to buy the top of the line you're going to buy the top of the line. You're not going to agree to buy a three year old outdated computer with four times less the computing power for a mere 5.77% price break.

Purchasing power applies itself to presently available market choices. Historical comparisons of purchasing power require one to compare apples and apples, that is choices that are static in time. Therefore if we assume that fried chicken is a historical constant then it is fair to compare it from 2001 terms to present day 2004 terms. However if there is no predictability and constancy then you can't compare purchasing power decisions. A Dell laptop in the year 60 CE is going to be useless - because the most advanced civilization on the planet are the Romans and they're grappling with the cutting edge scientific breakthrough of metallic chemistry and steampower and Europeans won't master those for another 1700 years.

The third significant problem with these quality adjustments to price increases for inflation gauges is that they don't factor in purchasing power decision making. Suppose we tried to buy a car in 1984. The cost of a car in 1984 on average twenty years ago was 76% of what it was available today. The cost of an average house was 50% less. Suppose a house you could buy a house or car that was because of quality improvements "twice" as good as it was then. Would someone buying houses pay twice as much then in order to get the present day twice as good model? Would someone buying a car pay half again (75%x2=150%=3/2) what they would have paid to get the present day twice as good model? No. Because of economic substitution effects, people would switch to a model that cost less but was 1984 good "enough" for them rather than paying double for the extra-good present day model even if it were available. People buy what's within their budget and not generally according to absolute quality standards. Certainly this is true for a historical comparison.

So maybe houses are twice as good today as they are in 1984, but if you're paying a $300k for a home today and you would have paid $150k for a home in 1984 even if all other things considered the present day home is twice as good as the 1984 home you did not "get twice as much for the same money". You paid $300k 2004 dollars and your parents paid $150k 1984 dollars but even if your home is twice as "nice" with new quality features you aren't paying less than they did.

Which is what the Economists would like you to believe. That if you pay for something and it's twice as nice as what you could have gotten for the inflation adjusted price twenty years ago that you're actually paying less than you paid twenty years ago. It just doesn't add up.

Price increases are price increases. What matters is the effect of price increases on purchasing power. If price increases are neutral to purchasing power there is no inflation. If price increases occur but purchasing power increases then you are indeed more wealthy. If prices increase and purchasing power declines or fails to keep up then you have inflation. Purchasing power is always relative to consumer habits and human needs. If you can buy as much gold as you want but can't buy food, your puchasing power has declined to zero. That's because human beings have an absolute need for food.

There are a lot of other shenanigans that go on in the inflation indices. If GDP is growing at 4% annualized and money supply at 12% annualized that means we have 8-9% real inflation. Yet the claims for inflation are much lower than this. The only way that could be happening is if the dollar-sphere was expanding. However it's not. If we print money and other people use it, then as long as it stays away from home we have a license to print money cheaply without raising inflation.

Unlike some goons may think, every dollar we spend overseas doesn't necessarily come back. It could not while we have extraordinarily historically low interest rates while having excessively lubriguous monetary policy. We're printing money to buy overseas goods, and they're accepting our dollars because in turn they use them to trade amongst themselves since the dollar hegemony means they often prefer the dollar to their own currency. They all accept it amongst themselves and moreover can use it to buy commodities such as metals, precious metals, oil, etc.

However the dollar sphere is not appreciably expanding. It's reached a high-water mark and indeed has retrenched somewhat. This is why the value of the dollar has fallen against the Euro. The world is signaling that their appetite for dollars is finite. The license to print money has reached its limit.

Given that there is no license to print money the only conclusion from the expansion of monetary supply is that the official inflation measures are seriously out of whack. Why would the government systematically lowball inflation? For reasons of social stability and to lower their own social spending costs. We'll explore that tomorrow.


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