SRAS/SRPC; levels vs rates of change

Something's been puzzling me about the data for the last couple of years. (This post isn't very clear, sorry. I can't even get my head clear enough to explain clearly what's unclear to me.)

There are two curves in short run macroeconomics: the AD curve, and the "other" curve. This post is not about the AD curve. It's about that other curve. The other curve is the one that tells us what happens when the AD curve shifts exogenously. The other curve tells us whether a shift in the AD curve will affect real variables or nominal variables or both. Theory tells us that the other curve should be close to vertical in the long run, when AD affects only nominal variables. I'm more interested in that other curve in the short run.

In particular, if we put the levels of real variables on the horizontal axis, what belongs on the vertical axis of the other curve? Is it levels, or rates of change? Is it the price level, or the inflation rate? Does it matter?

We don't normally observe that other curve. We would only observe that other curve if the AD curve shifted around at random, tracing out a path along that other curve. But the whole point of having good monetary policy is to ensure that the AD curve doesn't shift around at random. We can't normally econometrically identify that other curve, because the job of a good central bank is to make life impossible for econometricians by making damn sure there aren't any monetary policy shocks.

But the last three years have given us a natural experiment. Monetary policy failed to do its job right. (Or was unable to do its job right, if you insist, because I don't want to argue it here). So we actually get to see what that other curve looks like.

Here's my take on the data. (Here's Canada, for example). For most countries, real output is currently below trend and unemployment is currently above trend. There is not yet a full recovery from the recession. The price level is below trend, but the inflation rate is back on trend. The data suggest, to me, that we need to put the price level, and not the inflation rate, on the vertical axis of the other curve.

And I find that puzzling.

(I'm not saying there's a good relationship between the depth of the recession and the deviation of the price level from trend. I'm just saying I think it's better than the relationship between the depth of the recession and the deviation of the inflation rate from trend.)

We have two names for the short run version of that "other" curve: the Short Run Aggregate Supply Curve; and the Short Run Phillips Curve. They are sort of the same thing. Both are supposed to show us what happens, in the short run, when there's an exogenous unexpected shift in the AD curve. When teaching macro, we normally switch from one to the other by just waving our hands.

The names sure sound different. But these are just names. The SRAS curve isn't necessarily a supply curve, because it needn't show what firms want to sell in a recession; it shows what they do in fact sell. We could think of it as a price-setting curve instead. We might read a SRAS curve from right to left, with output as a function of price, but we could equally read it from left to right, with price as a function of output.

The SRAS curve has real output on the horizontal axis, and the SRPC has the unemployment rate on the horizontal axis, but that's no big deal. If there's a sudden leftward shift in the AD curve, unemployment rises and output falls. So SRAS slopes up, and SRPC slopes down, but it's the same thing.

It's the vertical axis I'm talking about here. The SRAS curve has the price level on the vertical axis, and the SRPC has the inflation rate on the vertical axis. Does that matter?

Until a couple of years ago, I would have said that it didn't matter.

Start with: Y(t)-Yn = B[P(t)-E(P(t))]

Do some trivial arithmetic and get: P(t)-P(t-1)=E(P(t))-P(t-1) + (1/B)[Y(t)-Yn]

The first one says that the output gap depends on the gap between the price level and the expected price level. Sounds like an Expectations-Augmented Aggregate Supply Curve.

The second one says that actual inflation equals expected inflation plus some function of the output gap. Sounds like an Expectations-Augmented Phillips Curve.

But they are the same equation. And it shouldn't matter if we use one or the other.

Yet when I look at the data for the last three years, my brain wants to tell a story in levels, not rates of change. Does it take three years for expectations of the price level to adjust?

Someone [Milton Friedman, thanks Gregor] said that the only advance in macroeconomics in the 200 years since David Hume was to slip one derivative. I'm not sure if that was an advance.

Comments

[Gregor Bush]

Nice post Nick. It was Friedman who said it. Although I'm sure you knew that.

Bernanke talked quite a bit about the "price-level gap" in Japan in the 1990s. I haven't heard him or anyone at the Fed mention it lately though. Curious.

I'm not mistaken, you wrote a post back in September of 2010 responding to Sumner in which you argued that inflation-targeting was superior to price level targeting becasue inflation is stickier than the price level. Have you changed your view? Here's what you wrote last fall:

"The primary reason why monetary policy matters is sticky prices. And it's not really the price level that is sticky; it's the inflation rate."

[Nick Rowe]

Thanks Gregor. Post updated. My memory is bad, I had forgotten it was Friedman.

"Bernanke talked quite a bit about the "price-level gap" in Japan in the 1990s. I haven't heard him or anyone at the Fed mention it lately though. Curious."

I haven't heard it mentioned either.

I did use to think it was inflation, not the price level, that was sticky. Now I'm just confused. I blame the data. The facts seem to keep changing. They won't make up their minds.

[Gregor Bush]

Nick,

"I did use to think it was inflation, not the price level, that was sticky. Now I'm just confused. I blame the data. The facts seem to keep changing."

Well, if you look at the US data, wages (average hourly earnings) are behaving exactly as one would expect given the massive excess supply in the labour market. Wage growth is continuing to slow and is now down in the 1.5% y/y range. Over the last 24 months, wage growth has been below 2% - the weakest stretch since the beginning of the series. If the Fed had a 2% inflation target, wage growth would need to stay in the 3.7%-4.0% range over the medium term.

If I'm not mistaken, Mankiw argued that wage growth was actually the "stickiest price" and should be considered as the policy target variable.

Imagine how different Fed policy would have had to have been 18 month ago (the Spring of 2010, when wage growth was below 2.5%) if the Fed had to undertake action such that it expected to achieve 4% average hourly earnings growth by April of 2012.

The world would look very different, I think.

[Nick Rowe]

Hmm. Stephen's graphs do show real wages rising ( a little bit faster than normal) at the beginning of the recession, then falling a little in the recovery.

http://worthwhile.typepad.com/worthwhile_canadian_initi/2011/11/real-wages-during-the-recession.html

Maybe it's just that wages are slower to adjust than prices? But I don't think you get the same pattern in all recessions.

I'm still confused.

[Jon]

Isn't the problem that the path cannot adjust? I think the relative variable is gap between the present and expectations of the future and the prior expectations of those periods.

So it's not about: why haven't we started to expect the right future so much as why haven't we started to expect the future we used to expect.

A metaquestion would be does the media set our expectations or do they reflect our expectation. As FDR put it: we have nothing to fear but fear itself.

[Nick Rowe]

Jon: you lost me a little there.

[Jon]

I'm asserting that the relevant nominal variable isn't a variable it's a curve. There is the timepath curve we expected and the time path curve we are now experiencing an now expect. It's the difference between those curves that matters.

When the shape of the curves is simple and deviations small, we can discuss differences in the inflation rate. That's a good single number that approximates the difference between what was expected then and what is expected now. You might also attempt to approximate by comparing a single point in time. Thats the price level difference.

Both ways of denoting a single variable in \reals are approximations. The correct vertical axis is R^n if we assume discrete periods n is some time horizon.

[W. Peden]

Isn't the increase in real wages supposed to be a big part of what causes a rise in unemployment in a demand-driven disinflation/deflation? I.e. real wages lag behind the fall in prices?

For example, the US unskilled wage rose by 2% in real terms in 1930, measured by the GDP deflator. The stickiness was relative though: the unskilled wage fell in nominal terms by about 2%, while the GDP deflator fell by about 4%.

One other factor might be that, since big crashes tend to come at the end of prolonged expansions, unemployment is probably around or above the NAURU and so the bargaining position of labour is better.

[Nick Rowe]

Jon: I think I follow you now. But underlying your curves must be a different story from the simple Calvo story. There must be some long-ago past expectations that still matter today.

W Peden: If nominal wages kept on rising at trend, despite the recession, while prices responded quickly, then we would expect to see real wages rise in a recession. But, IIRC, that's always been an empirical problem with Keynes' theory, because real wages don't seem to be countercyclical. But it may be that some prices and wages are sticky, and other prices and wages are flexible, so we see relative wages and relative prices distorted during a recession, even though average real wages don't move much.

[Bill Woolsey]

Nick:

If nominal GDP stays on a stable growth path, then persistent supply shocks will cause the price level to move to a higher growth path and real output to fall to a slower growth path. Moving to those new growth paths combines higher inflation and lower real output growth.

Now, consider a demand side recession. Nominal GDP grows more slowly. Inflation and output growth low. Then nominal GDP grows more quickly, moving us back to the trend growth path. Inflation and real output growth spead back up.

Growth rates work great to explain everything.

Now, suppose we shift to a 14% lower growth path of nominal GDP. Inflation must remain lower for a long, long time before real expenditure rises back to trend. The price is initially 14% too high. In the U.S., anyway, it is 2% lower than trend. So there is a long way to go.

If we assume that as that happens, with inflation being 1% or something, the monetary authority will respond by having the growth rate of nominal GDP rise faster, then it is moving back up to through higher growth paths.

[Joe]

Nick,

Mankiw's textbook has the price level, as do most. The recent Cowen/Tabbarok macro has inflation on the vertical. Therefore, instead of AD and SRAS moving further and further to the right as time goes on, they instead sort of loop around the LRAS for each year. They treat AD as being MGDP, and fiscal policy as affecting the velocity of money, neither of which Mankiw does say.

[Min]

Stupid question:

When you talk about a 2 dimensional curve shifting, as opposed to movement along the curve, I interpret that as a 3-D phenomenon. (At least 3 dimensions. :)) If that is the case, why should we even think that there is another curve? Aren't we talking about a surface?

[W. Peden]

Nick Rowe,

"But it may be that some prices and wages are sticky, and other prices and wages are flexible"

I would have thought that this was uncontroversial. A highly skilled public sector worker's wage is going to be very sticky. A waiter's wages in an area with very seasonal patterns of employment will be very flexible.

For certain skilled workers in the age of inflation (say post WWII) the early period of recessions may be "catch-up" periods, especially if their wages have been suppressed by incomes policies. 2008 wasn't just the beginning of the recession; it was also roughly the peak of inflation in the decade in Britain and the US (and Canada?).

[Nick Rowe]

Bill: But I think the facts contradict your example. Forget the trend. Assume a stationary equilibrium. A one-shot leftward shift in AD curve (NGDP) would cause a jump down in RGDP, then slowly rising RGDP as P is slowly falling. But that is not what I see happening.

Joe: one of these days i must take a look at the Cowen/Tabbarok text.

Min: yep, it's really a 3D (or nD) surface. So, why do we do it in 2D?

1. We only have 2D paper.
2. Our brains can't handle more than 2D at once.
3. Because these 2 dimensions are special. It is P and Q that adjust to equilibrate Supply and Demand.

W Peden: Yes, it's uncontroversial that some wages and some prices are stickier than others, in practice. But how to build that into a macro model to get the right results is less obvious.