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I see a lot of debate about the right measure to use to determine inflation -- apparently the CPI overstates it, etc. Why not just subtract the GDP growth rate from the money supply growth rate (or to be more accurate, divide 1+R by 1+r)? In the long run, it's supposed to predict inflation perfectly, yes?

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To an extent yes, tracking the money supply is somewhat helpful in determining inflation, but there are other important factors to consider.

Productivity?

Say there was a massive crop failure and the same amount of money. Food prices (and prices in general) would go up, right?

What is money?

Do we just count government money (monetary base)? There are aggregates for that, but if you've accepted a check for services before you know that you also accept bank money which does not have a 1 to 1 relationship with government money. So you have to include bank money to determine how much money is the economy. But what types of bank money? Demand deposits? M1? Interest bearing deposits M2? M3? This is subjective...but it helps to look at many aggregates.

What about foreign trade?

If you count the money supply do you include say dollars in the USA or dollars abroad as well? In some cases dollars are used a medium of exchange abroad and don't really come home, so they don't influence domestic prices like domestic dollars do.

What about foreign exchange

Currencies compete, and because they are fiat there is always the possibility that one currency (especially a smaller one in a weakened state) will suffer a confidence crisis and crash. This can influence prices, yet the amount of money in the economy can stay the same.

So truely, you need to look at many factors to figure out inflation. All that being said though the supply of money is still something very important to keep an eye on.

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If it was impossible to observe prices, we would probably see economists looking at the GDP and the supply and velocity of money to try and back out an estimate of what happened with prices. Essentially,

P = MV/T

Unfortunately, each of these variables is observable only with noise and not particularly quickly (For example, what was the dollar value of all transactions this month? Any answer will be a rough estimate). Moreover, the theory only works in the long run, as you mention. There are plenty of potentially confounding factors, some of which have been mentioned here, that would mess up the computation and introduce error.

I think the short answer is that it is more accurate, cheaper, and more correct to observe price changes directly than to infer them from other, theoretically related, variables.

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The quantity theory of money is a theory. For a variable as important as consumer prices, it is clearly desirable to just measure it directly rather than appeal to a theory, even if the theory had some truth to it.

Besides that, it is also not at all clear what the right measure of money supply would be.

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