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You say that the economy produces two goods. One might wonder why it matters which one is chosen as numeraire. I think the key is to explain how this choice affects factor prices - land and labour, which are contracted with long-term agreements that are mostly fixed in nominal terms. Whereas most of us buy apples on the spot market.

Deepwatr: well, there's two goods, plus money, which is the unit of account. And implicitly labour too. But which ones get set in long term agreements might itself depend on what the central bank targets.

If you said they produced olives and haircuts you would be describing the Greek economy.

http://blogs.wsj.com/canadarealtime/2014/08/13/slow-moving-money-a-big-challenge-for-bank-of-canada/

The Bank of Canada was successful in stabilizing inflation around its 2% target in the decade from 1997 to 2008, the report says. But inflation has been below target since 2012, except for a shift higher in May and June, which the Bank of Canada believes will prove transitory.

The difficulty the central bank has encountered with inflation in the last few years echoes the decade before 1997, the study says.

What the two periods have in common–and what’s different from the decade of success–is a breakdown in the connection between inflation and the amount of money in the economy, C.D. Howe says.

“The association between money growth and inflation has been weak since 2008, as it was in the decade before 1997,” the report says. “This is likely due to unpredictable changes in the velocity of money in Canada during the 1980s, and since the recent recession.”

Canadians order apples via internet, order haircuts with a visit. Underneath, the internet delivery services isn't exchanging as much, they buy huge fleets and fuel by the tanker. But on your personal visit to the hairdresser, you might buy gas, making an extra transaction. As transactions over slows, inflation over time is volatile, smaller N.

I'm thinking that if we want to maintain labour market equilibrium (full employment) it is better to stabilize the price of the labour-intensive good, which in this case is probably the haircut. But it is somewhat difficult to discuss this without a more complete picture of how workers spend their incomes (with a large fraction going to rent on land).

Nick,

"It might be better to ask which particular measure of inflation correlates most closely with the unemployment rate, if you insist on targeting some measure of inflation."

So you have doubled your problem? Instead of just finding the correct measure of inflation, now you must find the correct measure of both inflation and the unemployment rate?

Frank it would be interesting to find that the price of haircuts is correlated with some measures of unemployment and not with others. I think that Nick is simply pointing out that the price of haircuts matters much more for macroeconomic stabilization than the price of apples does, because haircuts are a very labour-intensive product.

Deepwatrcreatur,

"...because haircuts are a very labour-intensive product..."

They were until I built my hair cutting robot :-)

Perhaps the deeper question is - how should a central bank act in response to technological improvements as opposed to changes in aggregate demand? Both will influence the price level (or inflation rate), but surely the central bank reaction function should distinguish between the two.

I think the central bank should decide how the technological innovation affects the marginal product of labour, and adjust its target for the real wage accordingly. I think that George Selgin nails it, though he seems to be regarded as a market monetarist. Indeed he writes about NGDP targeting.

First, I appreciate the pun in the title.

Second, while your thought experiment is appealing, I think it's an artifact of your two-goods model economy. If we had three goods – apples, haircuts, and tax preparation services – we'd find that the prices of haircuts and tax preparation were highly correlated even as the central bank targets the price of apples.

This would provide independent evidence that the central bank was (successfully) targeting the "wrong" price index. By instead targeting the prices of haircuts (or even better a weighted average of haircuts and tax preparation), we'd instead find less correlation between de-trended prices in the economy.

Additionally (although this is getting beyond statistics), you've made a strong assumption that the central bank perfectly controls the price of apples. Part of the reason for a 'core' inflation guide is that central banks believe (rightly or wrongly) that they can't so-strongly control inflation in the very short term. If they tried to fix apple price growth at 2% per year, they'd fail and introduce higher de-trended variance for the effort.

To expand a little bit with reference to the Bank of Canada talk, your post looks at the pitfalls of point (i) (that a core index of CPI be unbiased) and argues for stronger consideration of point (iii) (relation to underlying economic trends), when the biggest advantage of a core CPI index is really point (ii) (that it is less volatile than broad CPI).

This reduced volatility is important. Your post as-written would reach the same conclusion if the central bank targeted not the price of apples, but the price of apples plus or minus one percent based on a quarterly coin-flip. That would obviously be a stupid measure of core inflation, but the same argument, that single-good price deviation is transitory and reverts to the mean, holds.

"I think that George Selgin nails it, though he seems to be regarded as a market monetarist. Indeed he writes about NGDP targeting."

Writing about the importance of a stable effective money stream does not make one a Market Monetarist. The "market" in "Market Monetarism" refers to the notion that the appropriate target is the market forecast of the level/growth rate of nominal spending.

Thanks! I guess I've been wrongly labeling Nick a market monetarist as well! I'm glad someone finally pointed it out.

I think this model is missing something essential when trying to compare it to the behavior of actual central banks.

For example, a real central bank can't instantly control the price level however it wants. It must observe the price level like everyone else and then set rates which have lags. Those lags are dependent on both the direction and size of the rate adjustment. E.g. Hiking rates from 3% to 20% will immediately effect the economy and prices. Lowering rates from 3% to 2% will have a much more muted effect that can take years. And the cost, in terms of loss of real output, as a result of hiking rates like this is much higher when the rate hikes are large. E.g. marginal firms go out of business when they can't roll over short term debt, and many more firms will go out of business when the rate hike is large. Volcker's large hike drove the money center banks in NY to insolvency and created the Latin American debt crises, which affected the real economy for over a decade. Many blame rate hike as one of the causes of the crash of 29' and the ensuing depression.

So I would say in this model, because the CB can only observe the random apple prices, it will be unable to to keep them constant. It will see a +1% divergence, take action which will filter down to prices only in future periods, but since these deviations are uncorreleted, taking action based on apple prices today will have no effect on stabilizing apple prices.

A second point is that if there are two series that move together, but one has deviations of 1% whereas the other has deviations of 3%, then you want to target the one with smaller deviation in order to minimize the economic cost of the rate hikes necessary to stabilize the time series.

A third point is that the rate hikes affect different prices differently. E.g. the effect on land prices is larger than the effect on durables, which is larger than the effect on non-durables. Going by Industry, highly levered industries like Finance are much more sensitive to rate hikes the industries such as construction which are themselves much less sensitive than retail.

Ideally, you would find the smoothest moving series that is also the slowest moving and target that. This is the point of looking at core. But I agree that if you create a model that assumes all these issues away, then there is no particular reason to look at core.

^^^The above should say "more sensitive" than retail, not less sensitive.

Dear all: thanks for the comments. Just one response comes to my mind:

This post is making a narrow point, and using an example to illustrate that point. If a central bank has been targeting any subset of prices to 2% inflation, then it is not at all surprising that prices outside that subset should show more variable inflation that reverses itself. So using reversibility as a way to distinguish core from non-core inflation may not be very useful. All it tells us is what the Bank has in fact been targeting.

Whether there is some more useful way of empirically defining "core", and whether it would be good policy to target "core" as thus defined, is left open.

Nick,

OK, but my point is that this isn't a generally valid principle. If the price of A is set by the price of B plus a white noise term, then you are always only targeting B, except that in some cases you target it badly.

If you try to target A, you are not going to succeed in reducing the volatility of A. It will remain white noise, except now B will also be white noise.

Non-god like CBs can't take action today to account for a roll of the dice tomorrow, nor does the effect of their decision today take effect today, it takes effect tomorrow.

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