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surely we want a real shock to not be purely real, that is wouldn't we want to offset a real negative shock with some monetary stimulus?

c8to: just suppose, that everyone wanted to take August off work, so that RGDP would be lower in August. And everyone wanted to work twice as hard in September, so that RGDP would be higher in September. Because of the weather, or because they all like to take time off at the same time, to party. Why should the central bank even try to stop that happening? Or, suppose it's odd and even years. Or, suppose it's days and nights.

Even if the underlying model in the link is incorrect, a function P(MB, NGDP) fit to the empirical data (inflation, ngdp, monetary aggregate of your choice, e.g. mb) should allow one to begin to get a handle on resolving the components:

http://informationtransfereconomics.blogspot.com/2013/07/extracting-nominal-shocks.html

The functional form of the fit will determine e.g. how much is nominal vs real, but then you have a test of that functional form ... the fit to the 3D surface P(MB, NGDP):

http://informationtransfereconomics.blogspot.com/2014/01/it-really-does-seem-to-be-about-size-of.html

Perhaps we need to understand nominal rigidities better? Essentially what we want is a monetary policy regime that never induces distortions in the economy as a result of nominal rigidities. But until we understand those rigidities, designing such a system is going to be very hard to do. Are the main rigidities sticky wages, sticky prices, nominal debt contracts, or something else?

Okay, here is my take on your question. Inflation targeting tends to fail in two circumstances: (1) when supply shocks arrive and (2) when there are large demand shocks. Supply shocks make it difficult to properly respond to changes in inflation (e.g. oil shock that weakens economy and temporarily raises inflation). The latter shocks cause problems because it is difficult for central bankers (who value their inflation-fighting credibility) to allow temporary burst of higher inflation that may be needed to offset large demand shocks. Inflation targeting, in short, only works when there are small demand shocks. There are several surveys of inflation targeting that in some fashion point out the success of inflation targeting may simply be do to with luck. The Great Moderation period, when inflation targeting became the norm, was a lucky period with mostly smaller demand shocks.

Nick, a second thought. Your and Scott's discussion takes me back to the post you did on Milton Friedman's thermostat. It seems that should be the benchmark of an ideal monetary policy, no?

Matt: that's how I think about it too. For example, if there are shocks to labour productivity, the best monetary policy when nominal wages are sticky won't be the best monetary policy when prices are sticky, because real wages may need to change.

David: I think it depends on the nature of the supply shock, and on the nature of the nominal rigidity.

Why should temporary bursts of higher inflation be needed to offset demand shocks? Why not have monetary policy prevent demand shocks? ZLB?

I'm not sure how my MF Thermostat post helps tell us what an ideal monetary policy would look like. It tells us whether the central bank is ideally (given its information) hitting its nominal target, but it doesn't tell us what that nominal target should be.

"Under inflation targeting it might still also be a nominal shock (is the price of gold jewelry part of the CPI?) but it would be a much smaller nominal shock than under the gold standard. Inflation targeting does better than the gold standard at separating nominal shocks from real shocks to gold mining technology."

Does that depend on the size of the gold mining industry?

I've sometimes wondered, if the U.S. had been on an agricultural commodity (wheat/corn/etc) standard in 1930 (at the time 50% of the economy) instead of the gold standard (gold mining being a tiny part of the economy), would the Great Depression have been possible?

Max: "Does that depend on the size of the gold mining industry?"

I think it does. If a country was little more than one big gold mine, a gold standard might be a quite sensible monetary policy.

Hmmm. I think that if the US (or Canada) had targeted the price of wheat, the Great Depression would have been a lot less bad than it was.

We we going to have great bonfires of wheat on the prairies, as there was an agricultural glut with low prices?

Or semi-seriously, the wheat price was targeted, by the Dust Bowl, which was the result of poor agricultural practice in previous decades.

Inflation targeting does not do as good a job as needed in separating real shocks from nominal shocks because it does not manage income expectations. That is, it is only managing the nominal a bit. Inflation targeting provides a pretty good implicit/explicit guarantee about the rate of change of P but none about Py -- i.e. under inflation targeting, monetary policy worries about dP but not d(Py) and they are not the same.

(Unless, of course, you are in Australia and the central bank does worry about d(Py) because it targets an average inflation rate over the business cycle.)

So, under "narrow" inflation targeting, folk are confident that their money will retain value but not that their income will stay on trend. So money is a safe asset and thus hedge against income uncertainty. Great way to have nominal and real shocks magnify each other.

After all, how can nominal shocks be separated from real shocks if the manager of the nominal is only half managing it; is only managing a bit of it and leaving the rest to flap about transmitting/magnifying any shock that comes along?

Nick,

"It is much harder to use our imaginations to think up an example of a purely real shock. Any real world example of a shock will nearly always be a mixture of both a real shock and a nominal shock."

I will treat the first order case (shocks to Real GDP / Nominal GDP level). The second order case would be shocks to Real GDP / Nominal GDP growth rate.

PQ = Nominal GDP
dP /dt * Q + dQ / dt * P = dNGDP / dt
( dP * Q + dQ * P ) / PQ = dNGDP / GDP
dP/P + dQ/Q = dNGDP / GDP

Real GDP = P * Q * ( 1 - dP/P ) = Q * ( P - dP )
dRGDP = dP * Q + dQ * P - dQ * dP - Q * d(dP)
dRGDP / RGDP = [ dQ * P - Q * d(dP) ] / [ Q * ( P - dP ) ]

dRGDP / RGDP = [ dQ / Q - d(dP) / P ] / [ 1 - dP / P ]

For a shock that does not affect nominal GDP, dQ / Q must be the negative of dP / P ( dNGDP / NGDP = 0 ).

dRGDP / RGDP = [ -dP / P - d(dP) / P ] / [ 1 - dP / P ]
dRGDP / RGDP = [ dP + d(dP)] / [ dP - P ]

For nonzero changes in real GDP where nominal GDP remains unchanged, dP + d(dP) must be non-zero or dP - P must be equal to zero. This can occur under a couple of different scenarios:

1. Price doubling ( dP = P ) while dQ/Q = - dP / P
2. Accelerating inflation with positive inflation rate ( both dP & d(dP) are positive ) while dQ / Q = - dP / P
3. Decelerating inflation with negative inflation rate ( both dP & d(dP) are negative ) while dQ / Q = - dP / P

Dang math mistake,

dRGDP = dP * Q + dQ * P - dQ * dP - Q * d(dP)
dRGDP / RGDP = [ dP * Q + dQ * P - dQ * dP - Q * d(dP) ] / [ Q * ( P - dP ) ]

dRGDP / RGDP = [ dP / P + dQ / Q - ( dQ / Q ) * ( dP / P ) - d(dP) / P ] / [ 1 - dP / P ]

For a shock that does not affect nominal GDP, dQ / Q must be the negative of dP / P ( dNGDP / NGDP = 0 ).

dRGDP / RGDP = [ ( dP / P )^2 - d(dP) / P ] / [ 1 - dP / P ]
dRGDP / RGDP = [ (dP)^2 / P - d(dP) ] / [ P - dP ]

For nonzero changes in real GDP where nominal GDP remains unchanged, (dP)^2 / P - d(dP) must be non-zero or dP - P must be equal to zero. This can occur under a couple of different scenarios:

1. Price doubling ( dP = P ) while dQ / Q = - dP / P
2. (dP)^2 / P <> d(dP) while dQ / Q = - dP / P

And so back to your problem:

"But finding a monetary policy that separates real shocks from nominal shocks, so that real shocks don't also create nominal shocks, is harder. But that is exactly the sort of monetary policy we want."

A "real only" shock occurs when dP / P = - dQ /Q and (dP)^2 / P <> d(dP). If the central bank is setting dP / P = - dQ / Q (stabilizing nominal GDP level) then it could conceivably be creating a "real only" shock all on its own. If instead the central bank is instead setting (dP)^2 / P to be equal to d(dP), then it is eliminating "real only" shocks.

When the central bank is able to eliminate "real only" shocks, it is able to prevent "real only" shocks from becoming nominal shocks.

Lorenzo: But your argument (I think) just assumes that stabilising nominal income is the right thing to do. I can dream up examples where it isn't: suppose the price of apples is sticky, but all other prices are perfectly flexible. Then targeting the price of apples, so it doesn't need to change, would be the best monetary policy. Now, it does look plausible from the data that targeting NGDP would be good monetary policy. But I would really like to know more about *why*. That explanation must have something to do with the source of nominal rigidities.

Frank: I see one definition: NGDP=P.Y, plus a lot of math. That is not a *theory*. Definitions+maths do not explain the empirical world.

Determinant: we aren't talking about targeting the price of wheat by burning wheat when the price of wheat falls. We are talking about printing money when the price of wheat falls. Big difference.

Nick:

But the Dust Bowl would have been deflationary under a wheat standard. With a nominal GDP level target, the result would be more rapid increases in wheat prices. With a wheat standard, the result would have been drops in nominal income to clear the wheat market at the target price.

Of course, in reality wheat prices fell.

Bill: OK. The wheat standard would not have been perfect. But it would have been better than what actually happened, given that wheat prices fell, despite the dust bowl. Because money would have been looser, to prevent wheat prices falling.

"If new investment and capital formation is a function of saving, then if inequality fosters greater saving, it should also play some role in fostering investment and economic growth."

Natural disasters or wars would seem to be purely real.

" Inflation targeting does not separate real shocks from nominal shocks as well as I thought it would. But I don't really know why inflation targeting failed to separate real from nominal shocks as well as I thought it would."

I thought the reason is supposed to be what Sumner's always saying-because the inflation rate is impacted by both real and nominal variables.

Mike S: see my most recent post.

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