Keynesian Beauty Contest SRAS shocks

[I'm not fully happy with this post. I think it does an OK job of explaining SRAS shocks that the central bank accommodates. But it doesn't say what happens when the central bank does not accommodate SRAS shocks. And I would like to integrate George Selgin's analysis of SRAS shocks in Less Than Zero, which I haven't yet done. But I'm posting it anyway.]

When we teach Intro Macro we usually draw a diagram something like this:

 

Sometimes we draw the SRAS (Short Run Aggregate Supply) curve as horizontal, but that doesn't matter for this post. Sometimes we put the inflation rate rather than the price level on the vertical axis, and call the SRAS curve the Short Run Phillips Curve, but that doesn't matter for this post. And the SRAS curve is not, strictly, a supply curve, but that doesn't matter for this post.

The SRAS curve incorporates the fact that the average price level seems to be sticky, so that (sudden, unexpected) shifts in the AD (Aggregate Demand) curve cause real output Y to change. The LRAS (Long Run Aggregate Supply) curve allows the average price level to adjust (though relative prices may still be sticky). A (sudden) leftward shift in the AD curve would cause a recession, like the one shown in the diagram. Optimal policy tries to prevent any (sudden) shifts in the AD curve, so the economy is always where the SRAS and LRAS curves intersect, at potential output Y*.

But the SRAS and LRAS curves may also shift.

If the SRAS and LRAS curves always shift left (or right) by exactly the same amount, then optimal AD policy is to ensure that the price level (or inflation rate) is unaffected by those "supply shocks". You can think of this as shifting the AD curve left by that exact same amount, or think of it as making the AD curve horizontal. Targeting inflation, or the price level, is optimal. There's a "divine coincidence" between preventing fluctuations in the price level (or inflation) and preventing output gaps between actual Y and potential Y*.

But sometimes the SRAS curve seems to shift left (or right) by more than the LRAS curve. Or, if the SRAS curve is horizontal, you can think of the SRAS curve as sometimes shifting vertically up (or down). So the AD curve needs to allow the price level to rise (or the inflation rate to rise temporarily) if you wanted to keep the economy where SRAS and LRAS curves intersect, so Y=Y*. Shifting the AD curve left by a large enough amount to keep the price level unchanged (or making the AD curve horizontal) is bad policy. Divine coincidence fails. Strict inflation targeting is bad policy. We call these "SRAS shocks", or "price level shocks".

And those SRAS shocks are what is very hard to teach. (It's very easy to teach "If it's a short shock to supply it shifts SRAS, and if it's a long shock to supply it shifts LRAS", but that's wrong.) And what makes it especially hard to teach is that us teachers don't really understand them either.

Here is a story of SRAS shocks:

I tell 100 people they each have to pick a number that is as close as possible to the average number they pick. I will reward them for picking a number close to the average (or punish them for picking a number distant from the average). They are not allowed to collude by talking to each other.

If they all pick 7 (because 7 is a lucky number) that is a Nash Equilibrium. (If you think that all the other players will pick 7, then you have an incentive to pick 7 too.) But if they all pick 8 that's a Nash Equilibrium too. So is any number, if they all pick it.

I don't know what number they will pick. And if the game is played only once, it is unlikely they will all pick the same number. Unless they all share a culture where everyone knows that everyone knows, etc., that 7 is the luckiest number to pick. But if the game is repeated, and the players all hear what the average was in the last round, I think they will eventually all converge to one of the Nash Equilibria, where they all pick the same number, whatever it is. The average in the last round of the game becomes a Schelling Focal Point, rather like a culture where they all know that the last number they picked becomes the luckiest number, because of custom.

(This game is actually very similar to the real world game where I'm the central bank which targets inflation, and the players are firms choosing prices. If the average firm has an incentive to pick a price that is higher than the average price, there is no Nash Equilibrium, and inflation will accelerate. If the average firm has an incentive to pick a price that is lower than the average price, there is no Nash Equilibrium, and deflation will accelerate. So to keep inflation on target, the central bank adjusts the interest rate to adjust AD to try to ensure that the average firm has an incentive to pick a price equal to the average price. Only if actual and expected inflation gets above/below target (expected inflation becomes "unanchored") does the central bank try to give firms an incentive to pick a price below/above the average price. But if some shock (or mistake by the central bank) does cause the price level to jump up (or down), the central bank does not try to make it jump back down (or up) again; it lets bygones be bygones and tries to keep the price level growing at the target inflation rate thereafter. But let's suppose the target inflation rate is 0%, because it makes the story simpler for me to tell. The "shock" that makes the price level jump up (or down) might be nothing more than a new popular song that says "8 (or 6) is actually the luckiest number, not 7".)

Let's suppose they eventually all pick 100 (because it makes the math simpler for me).

1. After the players have all settled down to picking 100 for a few rounds of the game, I change the rules slightly. I tell half the players to pick a number 10% higher than the average pick, and tell the other half to pick a number 10% less than the average pick. (And I change the rewards accordingly, and they all get to hear me tell them all this.) What happens next? I don't know. But my guess is that half of them will pick 110, and the other half will pick 90, so the average stays at 100. Dear reader: what is your guess? Because in this game, your guess is as good as mine, and the players' guesses are the only things that matter.

(That was a symmetric relative price shock. The SRAS curve does not shift.)

2. Now let me change the rules a second time. I tell 10% of the players to pick a number 10% higher than the average pick, and tell the other 90% to pick a number 1.111...% lower than the average pick [did I get the math right?] (And again, I change the rewards accordingly, and they all get to hear me tell them all this). What happens? Again, your guess is as good as mine, and only the players' guesses matter. My guess is that the 10% minority will pick 110, and the 90% majority will stick with 100, so the average rises to 101.

(That was an asymmetric relative price shock that is accommodated by the central bank. The SRAS curve shifts up by 1%.)

I would be more confident my guess is right if I told the players that that was my guess.

(Central bank communication matters, even when it's just talk.)

I would be even more confident that my guess is right if I told the 10% minority that I had changed their rewards but did not tell the 90% majority that I had changed their rewards, until after they had picked a number.

(The minority of firms most affected by the relative price shock are the most likely to hear about it and take it into account when setting prices.)

3. Now let me change the rules a third time. I tell all the players I will raise the numbers they pick by 1%, and then apply the rewards to the new numbers. Again, your guess is as good as mine, but my guess is they will all stick with 100, so the new numbers all rise to 101. I would be more confident my guess is right if I told them my guess, or if the ones that listened to the new rules knew that some of them might not be listening.

(A 1% sales tax increase shifts the SRAS curve up by 1%.)

There are no costs to changing prices in this "model". There is no price stickiness at the level of the individual firm; sticky prices are an aggregate phenomenon that represent the difficulty of coordinating on a Nash Equilibrium. Menu costs, or lags in changing prices while you wait for Calvo's fairy, might matter as well, but I don't think they are key. Inflation targeting makes inflation stickier, and the Short Run Phillips Curve flatter, because the inflation target is a lucky number. Inflation targeting makes SRAS shocks (aka "price shocks") bigger, because it validates those one-time price shocks.

That's my best guess about what's going on in an inflation-targeting economy when it's hit by SRAS shocks that the central bank accommodates. But I don't think I could teach it so that more than a few percent of first year students could understand it. Just as well I'm retired. Did you understand it?

Comments

[George Selgin]

Nick, here is a capsule version of my "productivity norm" argument, starting with some of your own observations.

"If the SRAS and LRAS curves always shift left (or right) by exactly the same amount, then optimal AD policy is to ensure that the price level (or inflation rate) is unaffected by those "supply shocks". You can think of this as shifting the AD curve left by that exact same amount, or think of it as making the AD curve horizontal. ...But sometimes the SRAS curve seems to shift left (or right) by more than the LRAS curve. Or, if the SRAS curve is horizontal, you can think of the SRAS curve as sometimes shifting vertically up (or down). So the AD curve needs to allow the price level to rise (or the inflation rate to rise temporarily) if you wanted to keep the economy where SRAS and LRAS curves intersect, so Y=Y*."

Productivity shocks all fit the second case. Those shocks consist of two elements: first, a change in goods' average unit costs of production and, second, a corresponding change in the *actual* quantity of goods offered for sale during the relevant period of analysis. The first of these is represented by shifting the LRAS and SRAS schedules vertically; the second by shifting them horizontally. The argument applies, mutatis mutandis, to both one-time (level) shocks and ongoing (growth rate) shocks. Because the horizontal and vertical shifts are proportional, together they move the AS curves along a 45-degree vector. Allowing for a rectangular-hyperbola AD (constant NGDP) schedule, the optimal (natural output preserving) monetary policy response is that of leaving that schedule unaltered, that is, it is for the central bank to stabilize NGDP rather than P.

I'm pretty sure one can come up with exceptions to these arguments. But I believe the burden in the case of productivity shocks should fall on those who imagine that those shocks only shift AS schedules horizontally.

[Nick Rowe]

George: I was hoping you might comment!

First, thanks for your book. I enjoyed reading it, but don't think I understand it fully. This might help me understand your argument.

"Productivity shocks all fit the second case." Yes. I got that from your book. Most productivity increases affect only a small percentage of firms, so it's like my second case (except you are considering a fall in costs rather than a rise like in my example). But it's what you say after that where I'm not sure I follow.

Let's take the simplest case where SRAS is horizontal (and LRAS is vertical). Suppose 10% of the firms (all firms the same size initially) have a 10% improvement in total factor productivity. So the LRAS curve shifts right by 1% (assuming no change in total resource employment or in the allocation of resources between firms in the Short Run), and the SRAS curve shifts down by 1% (assuming other firms hold their prices constant, because that's the Schelling focal point, or because they don't hear about the productivity improvements at other firms, which reinforces that focal point). So an unchanged rectangular hyperbola AD curve (an NGDP target) ensures the new equilibrium is exactly where SRAS crosses LRAS.

Is that your argument? If so, I *think* I get it now. It does rest on some simplifying assumptions, but that's OK, because nothing ever holds exactly in the real world, and we're just trying to get in the right ballpark, because central banks aren't omniscient.

[George Selgin]

Nick, your understanding is close. As I try to argue here and there in the book (see, e.g., pp. 29-40 and 91-98) the argument is actually more robust than the particular assumptions invoked here suggest--that is, those assumptions are sufficient but not necessary. In particular, the argument is not so difficult to generalize to widespread productivity changes; it also goes through for reasonable assumptions of price stickiness. (Calvo pricing is not very reasonable, in part because it completely ignores the fact that firms have no difficulty adjusting prices at once in response to own-productivity innovations--see pp. 36ff.). Making the case that AD must shift in response to productivity-driven AS changes generally requires that one appeal to less realistic assumptions.

[George Selgin]

"Assuming other firms hold their prices constant." Keep in mind that it is only firms that produce identical products that must ultimately reduce their product prices to conform to those charged by their more productive rivals, and that unless those firms also become more productive the price reduction isn't after all a necessary part of the ultimate equilibrium response. For a competitive industry the response will in that case consist of a gain in market share for the more productive firms, with the others abandoning the market.

[Jeremy Fox]

As a population ecologist, I want to learn more about SRAS vs. LRAS curves. Population ecologists use similar sorts of diagrams to analyze the qualitative behavior of the dynamical systems we study (well, we used to; it's not a super-popular approach these days...). We call them isocline diagrams. But I've never seen an isocline diagram in ecology that has different isoclines for the short- and long-run behavior of the system. Offhand, it strikes me as an interesting way to study the behavior of dynamical systems with a separation of timescales. Systems that reach some sort of partial equilibrium quickly, but reach full equilibrium only slowly because some state variable(s) changes slowly.

Now would be the time to tell me that I seem to have badly misunderstood the gist of SRAS vs LRAS curves and it would be a complete waste of my time to read up on them. :-)

[Nick Rowe]

George: I'm still thinking about this.

Jeremy: Hi!

The Short Run vs Long Run distinction in economics is very context-dependent. It's a useful intuitive heuristic that usually helps us understand more complicated systems in a simplified stepwise way.

One example is in micro, where a firm uses 2 inputs (labour L and capital K) to produce 1 output Q. So we have a production function relating 3 variables. Since first year students don't understand multivariate calculus, we normally talk about the "short run", where the firm chooses L (and Q) to maximise profits holding K constant, then we talk about the "long run" where the firms chooses the mix of L and K to minimise costs for a given Q. And to motivate this, we tell the students that L can be adjusted more quickly than K (though this may or may not be true, and the whole procedure is really just a way to explain a 3 variable system looking only at 2 variables at a time).

"Offhand, it strikes me as an interesting way to study the behavior of dynamical systems with a separation of timescales. Systems that reach some sort of partial equilibrium quickly, but reach full equilibrium only slowly because some state variable(s) changes slowly."

What you say there is precisely correct about other examples where we use the SR vs LR distinction. For example, an economist teaching the Malthusian model (the original ecological model??) would almost always talk about a short run equilibrium for wages, births, and deaths, holding population (the state variable) constant, then talk about the long run equilibrium where population has adjusted so wages are at subsistence. And it's exactly the same in the Solow Growth Model, except in this case population is assumed exogenous, and the state variable is the aggregate stock of capital (which only changes slowly with saving and investment).

But the SR vs LR distinction in the example of this post is more complicated and unclear. Imagine there is some stochastic process causing the AD curve to shift back and forth. Like a coin toss. The SRAS curve tells us what happens when the coin lands heads or tails. The LRAS curve tells us what happens when we use a coin that is biased towards heads, or biased towards tails, and people have already learned which way the coin is biased.

[Jeremy Fox]

Perfect Nick, that's just the roadmap I needed. Thanks!

[Scott Sumner]

Nick and George, I have a new post that was inspired by your discussion:

http://www.themoneyillusion.com/should-we-target-total-wages-or-average-hourly-wages/