Relative price shocks, price-level shocks, and who moves first

Suppose a real shock hits the economy. It affects relative prices. The prices of the green firms must rise relative to the prices of the red firms. The prices of the red firms must fall relative to the prices of the green firms. Same thing. But which happens? Do the green prices rise, or do the red prices fall, or is it a bit of both?

It might depend on the central bank's target. Is it targeting the green price level, or the red price level, or a bit of both?

Here's another thing it might depend on: which firms hear about the shock first? If the green firms hear about it first, they will raise their prices. If the red firms hear about it first, they will lower their prices. The firms who hear the news first will respond to the news, because they know the other firms won't. It's a mixture of a Hayek/Lucas local knowledge problem, and a Keynes coordination who-moves-first problem.

Even if both green and red firms hear about it at the same time, but the green firms don't know the red firms hear it, and the red firms know the green firms don't know that the red firms hear it, we get the same results: the green firms will raise their prices and the red firms won't cut theirs.

We only get indeterminacy when it is common knowledge that all firms hear about the real shock at the same time. That is unlikely to happen. Real shocks may have general equilibrium effects on all relative prices, but the shocks themselves are nearly always local in origin, and some firms will hear about them first.

If the shock hits the green firms, they will know about it first, and it will be a positive shock to the price level. The SRAS curve shifts up.

If the shock hits the red firms, they will know about it first, and it will be a negative shock to the price level. The SRAS curve shifts down.

If the central bank accommodates these price shocks, it will help all firms coordinate on the new set of relative prices. It lets firms set their prices using local knowledge and partial equilibrium analysis, which most people understand, rather than economy-wide knowledge and monetary general equilibrium analysis, which hardly anybody understands.

Strict NGDP targeting will do a better job of accommodating price shocks than strict price level or strict inflation targeting. Flexible NGDP targeting might do better than strict NGDP targeting, if the central bank has enough information to distinguish between: Aggregate Demand shocks; SRAS shocks; and LRAS shocks. But we don't want to rely too much on central banks' being able to solve the monetary general equilibrium model in real time.

I see this as an alternative to the Ball-Mankiw 1995 (pdf) model. (See my old post on Teaching SRAS shocks.)

I see this as maybe an interpretation of what Bill Woolsey has been saying?

It's an update on my old post on Sticky prices vs sticky coordination.

Comments

[Majromax]

> Do the green prices rise, or do the red prices fall, or is it a bit of both?

Don't they have to do so equally, because of arbitrage possibilities?

Pretend that green firms initially buy and sell widgets for 1$Green, and red firms buy and sell widgets "for" (with) 1$Red. Shock hits and red prices become more negative (I'll use this terminology instead of "fall" to keep my head from hurting), so red firms instead buy and sell widgets for 2$Red.

Now, I have an initial stock of 10$Green. I use that as collateral for a loan from the central or commercial bank for 10$Green+10$Red, and I'll assume that I must remain solvent and liquid at all times (hold $Green >= $Red). After the loan, I have 10$Green, 10$Red, and more 10$Green that I can't touch.

I purchase 5 widgets from green firms for 5$Green, leaving me with 5$Green, 10$Red, 10$G collateral, and 5 widgets. Then, I sell those widgets to red firms at 2$Red per.

That leaves me with 0 widgets, 0$Red, 5$Green liquid, and 10$Green collateral that I can now use again because I have no $Red holdings. I've made a net profit of 5$Green in the arbitrage.

Provided I can deposit $Red and $Green simultaneously to cancel them, I can do the equivalent if green prices go up and red prices remain the same: take on 10$Red and 10 widgets (holding on to my 10$Green as collateral against the $Red), sell the widgets for 20$Green [holding 10$Red, 20$Green free, and 10$Green collateral], then annihilate the offsetting $Red and $Green to profit 10$Green.

[Majromax]

I appear to have had a comment eaten by the spam filter. The short version was that I think prices have to move equally, as otherwise arbitrage possibilities exist between red and green firms.

[Nick Rowe]

Majromax: this post is unrelated to my previous posts on red and green money. I just wanted names for the firms. The firms produce different types of goods, so there are no arbitrage possibilities. Green firms produce food, and red firms produce clothes, and there's some shock that causes the relative price of food to clothes to increase.

[The Market Fiscalist]

"The prices of the green firms must rise relative to the prices of the red firms"

Couldn't the adjustment take place entirely through quantity adjustement? Red firms reduce qty and green increase - no price changes. In this model problems only occur when demand for both red and green goods falls (or rises?).

[Nick Rowe]

TMF: If the real shock is a shift in relative demand between green and red goods, and the two goods are perfect substitutes in supply (straight line PPF) then that is what would happen. But that is not the sort of shock I am assuming here.

[The Market Fiscalist]

"that is not the sort of shock I am assuming"

Suppose total spending remains the same but with more spending on green goods and less on red. If red prices are sticky (qty produced declines , prices stays the same) but green flexible (price changes , qty produced is fixed) then you will get a recession even though NGDP remains constant. IT would in theory prevent the recession but only if it could exactly adapt the index used to the change in relative demand. In this case (assuming wages are sticky) targeting nominal spending on wages might be better. But if wages in the red and green industries are differently sticky then this might not work either.

[The Market Fiscalist]

Oh, IT would make things worse in that scenario - no matter how the index was calculated.

[Tom Brown]

"Majromax: this post is unrelated to my previous posts on red and green money. I just wanted names for the firms." Good to know, I was confused by that too.

BTW Nick, you should be happy that when you type "Nick Rowe" into Google, the first thing on the list it wants to complete that with is "Nick Rowe Worthwhile." You've got to be feeling better than (Rick) Santorum in that regard!

[notsneaky]

I'm not sure if the link to the Ball and Mankiw paper is current (I can't get it). Here is the NBER WP version:
http://www.nber.org/papers/w4168.pdf

[Bill Woolsey]

Oddly enough, I thought the Market Fiscalist was on point.

If there is a shift in relative demands, so that people demand less of one good and more or the other, then the appropriate response is for the price of one good to fall and the price of the other good to rise.

I realize that we can imagine some scenario where there is a shift in supply, where firms decide the want to produce less of one good and more of another, then the situation is similar. The price of one good should rise and the other fall. However, that almost sounds like some change in the preferences of nonpecuniary preferences of producers. It is cool to run a tony restaurant. No, now it is more fashionable to run an art gallery.

Anyway, I am more interested in a scenario where the supply of one good decreases. War in the Persean Gulf. Bad weather in in corn belt.

It isn't all shifts in relative prices that concern me, just a change in supply of one (or some) goods.

In a one product economy, this issue makes no sense.

Now, like many naïve Market Monetaists (Sumner,) I am using simply principles level economics. But this time, I am using micro. How do we do simple indifference curves? Usually, with constant income. What is the macro framework implicit in that? Nominal GDP level targeting.

Yes, it is not general equilibrium Walrasian auctioneer the numeraire is arbitrary.

Anyway, if the simple micro approach, if the supply of a single good changes, both spending on the good and the income generated for producers depends on the elasticity of demand for the good. If total spending is held constant, then it is the change in spending on the good with a shift in supply that has an equal and opposite effect on total spending in the rest of the economy. Is no effect on the rest of the economy perfect? Not likely. Will nominal GDP targeting lead to no effect on the rest of the economy? Only under very special conditions.

But is this result better than trying to stabilize some index of prices? Almost certainly.

I think the long run and short run aggregate supply curve approach smuggles in an implicit assumption that we have a one good economy.

obviously, the green and red goods helps that problem. But real shocks that impact relative prices fails to emphasize that the problem isn't a shift in the composition of demand, but rather a shift in the supply of a particular good. Also, if there are just two goods, you can't get the point that there is a shift in supply of one good, and price level targeting requires adjustments in thousands of other prices.

[mb]

In Irving Fisher's "The So-Called Business Cycle is a Dance of the Dollar" output prices rise in advance of sticky input prices and, by changing profits, firms either expand or contract output. Is your thinking here in any way related to what Fisher had in mind?

[The Market Fiscalist]

I think Market Monetarists don't so much assume a one-good economy as that recessions are caused by a change in the demand for money and the relative demand for all other goods stays the same (or at least that changes in relative demand take place painlessly ). Is there also an assumption that price-stickiness is the same in all industries?

What happens in a supply shock ?

In Nick's model he doesn't mention price stickiness. Assuming all industries have flexible prices then (I think) the knowledge problem will affect the price level differently in the different scenarios but not relative prices. (Of course you need to distinguish between prices stickiness as a result of changing demand and price stickiness as a result of changing input costs.)

If red and green prices are equally sticky but the knowledge problem means you don't know which direction prices will move then both NGDP and IT may move the economy in the wrong direction.

In addition: if a supply shock reduces optimal RGDP levels then isn't it also likely that this will cause demand for money to change relative to other goods ? This would render NGDPT sub-optimal even under flexible pricing. (NGDP might rise endogenously but be suppressed by NGDPT). Introduce different industries reacting differently to the supply shock and things get very complicated very quickly.

In a world where localized and generalized supply and demand shocks of various magnitudes are constantly affecting the economy, and depending upon the shape of the various demand and supply curves the economy will react with different combinations of price and qty level changes in different industries , and (as in the post) knowledge problems add additional level of indeterminacy then the effectiveness of various forms of targeting start to dance before your very eyes.

[The Market Fiscalist]

I think Market Monetarists don't so much assume a one-good economy as that recessions are caused by a change in the demand for money and the relative demand for all other goods stays the same (or at least that changes in relative demand take place painlessly ). Is there also an assumption that price-stickiness is the same in all industries?

What happens in a supply shock ?

In Nick's model he doesn't mention price stickiness. Assuming all industries have flexible prices then (I think) the knowledge problem will affect the price level differently in the different scenarios but not relative prices. (Of course you need to distinguish between prices stickiness as a result of changing demand and price stickiness as a result of changing input costs.)

If red and green prices are equally sticky but the knowledge problem means you don't know which direction prices will move then both NGDP and IT may move the economy in the wrong direction.

In addition: if a supply shock reduces optimal RGDP levels then isn't it also likely that this will cause demand for money to change relative to other goods ? This would render NGDPT sub-optimal even under flexible pricing. (NGDP might rise endogenously but be suppressed by NGDPT). Introduce different industries reacting differently to the supply shock and things get very complicated very quickly.

In a world where localized and generalized supply and demand shocks of various magnitudes are constantly affecting the economy, and depending upon the shape of the various demand and supply curves the economy will react with different combinations of price and qty level changes in different industries , and (as in the post) knowledge problems add additional level of indeterminacy then the effectiveness of various forms of targeting start to dance before your very eyes.

[Nick Rowe]

notsneaky: thanks. I have updated the link.

MF and Bill: let me try it this way:

Suppose there is a negative shock to the green firm's technology, that reduces their MPL. In a general equilibrium model, with no money, we see the PPF swivel inwards, and the slope at the new tangency point with the indifference curve would have a higher equilibrium Pg/Pr. Say equilibrium Pg/Pr increases by 1%.

Suppose the central bank had perfect information, and always made the AD curve vertical at the natural rate of output, so the AD curve lies on top of the LRAS curve. This means the price level is indeterminate, and the firms setting prices are playing a pure coordination game. Anything can happen to the average price level. One equilibrium is for the red firms to lower their prices by 1%, and the green firms to hold their prices fixed.

But if the red firms don't know about this shock to the green firms' technology, and the green firms know the red firms don't know about it, this can't happen. The only equilibrium, given the information the firms have, is for the green firms to respond to the news.

Now drop the assumption that the central bank has perfect information. Suppose all it knows is that there will be shocks to both green and red firms technology, and to velocity, but all it observes are prices and outputs, but it cannot distinguish between them. And suppose prices are set for one period, after firms observe their own technology. A horizontal AD curve (IT) would be a bad idea. A vertical AD curve would be a bad idea. A downward-sloping AD curve (like NGDPLT) would be a better idea.

[Nick Rowe]

mb: I don't think what I am saying here is related to what Irving Fisher is saying there.

[The Market Fiscalist]

Nick,

I agree that NGDPLT would be a better idea. My concern is that it would not be a perfect idea. You can think of some combinations of sticky/flexible prices between red and green where NGDPLT either under or over-shoots the requirements to achieve optimal RGDP. I'm not sure how realistic these scenarios are but it does leave you wondering if NGDPLT might (like IT appears to have done) work until it fails when you most need it.

Unrelated question: What shape would the AD curve be under wage-level or wage-pool targeting ?

[Nick Rowe]

TMF: I worry a bit about that too. We can't really be sure unless we know more about the nature of nominal rigidities. All we can do in the meantime is see whether fluctuations in NGDP give us a good empirical signal of recessions, across many different monetary policy regimes.

Under wage level targeting, you would get a horizontal AD curve in {W,anything} space.

Under wage pool (W.L ?) targeting, we would get a rectangular hyperbola AD curve in {W,L} space.

In both cases, the AD curve in {P,Y} space would shift if there were real shocks.

[Patrick]

Mightn't the firms respond by doing something to change the perfect substitutability of their products? A (perhaps) silly example: shampoo. Put it in a pink bottle with pictures of fruit on it vs. putting it in a black bottle with angular lines in primary colours. Same stuff in both bottles, but now the stuff in the pink bottle can be sold for 30% more and doesn't compete with the stuff in the black bottle.

[Nick Rowe]

Patrick: if product differentiation were profitable (because it reduces elasticity of demand), firms would probably have done that anyway, without any shock.

[Tom Brown]

"...but it does leave you wondering if NGDPLT might (like IT appears to have done) work until it fails when you most need it."

I once asked Scott Sumner to identify a likely way that NGDPLT might fail:

http://www.themoneyillusion.com/?p=26025#comment-315014

"Tom, It would be some factor that caused wages to be unstable even as NGDP growth was stable. Perhaps a huge discovery of oil, or something like that."