David,
You certainly have.
I think I see where we’re differing here. I’m looking at measuring inflation once an injection of money has worked its way through the system where it will eventually raise all prices by the same proportion. Ie, the injection of money will only end up creating an income effect. It won’t distort relative prices, and so any relative price distortion that occurs because of non-monetary factors (supply shocks) should be removed from the measure, because they aren’t representative of underlying inflation.
If I understand correctly, you’re saying that in the short run an injection of money won’t raise all prices in the same proportion. There will be some relative price distortions until the money works its way through the system. In which case, removing the substitution effects will be removing price rises that the increase in the money supply has caused, which means that the index will under-estimate the effects of a monetary injection.
And that’s completely true. However, I’m not saying that making weekly or monthly adjustments for substitution is going to accurately measure inflation. I’m saying that adjustments to at least quarterly, but especially 6 monthly to yearly measures will have allowed enough time to pass for all prices to be raised in proportion. So compensating for substitution in these longer periods won’t create a downward bias.
Now on your supply side price change point, that doesn’t constitute inflation pecisely because it’s a change in relative price due to supply shocks, not the general price due to an increase in the money supply. We only want to compensate people for changes in prices that occur due to monetary inflation. If there’s a cyclone that destroys a large part of a banana crop, the price of bananas will skyrocket. The relative price has been changed and people will naturally begin substituting apples for bananas. We don’t compensate a retiree for the increase in the price of bananas, despite that bananas are in the basket of goods, because everybody is rationally substituting away from them because of real factors. We only want to compensate them for price increases that are the result of the increased money supply, not for real shocks.
Headline CPI is not adjusted for the substitution effect by the way (I probably should have said that earlier). Chained CPI is. So the monthly CPI measure you see in the news doesn’t do this stuff. Social Security isn’t actually adjusted with chained CPI, it’s adjusted with CPI-W, which is a wage index (so increases in the general level of wages means that retirees get an increase in social security payments). Now TIPS, the thing that started this conversation, are index to CPI-U (headline CPI). Since coupons are paid every 6 months (which is a reasonable amount of time for the chained CPI to be accurate), they’re actually getting paid slightly more than “real” inflation since the measure also includes supply shocks, not just the inflation caused by the increase in money.