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Thank you for this. It was bothering me that both of your previous upward sloping IS line posts assume that the capital stock is kept constant. Your discussion here about what would happen under sticky wages vs prices is therefore very enlightening for me.

I may well be wrong but it looks like you may have left something out though. All capital depreciates at the end of the period and this makes it unclear what happens to the quota-induced interest rate reduction. Sure, the still-employed workers get a larger share of total income (and save it all) but some of them are now unemployed and can’t save anything. Keep in mind that the economy’s output is now only 90. Whether or not the interest reduction persists depends on what the quota does to the relative net capital/labour shares of income. If the relative shares remain constant, the Capital/Labour ratio (as well as the MRTS) reverts to its pre-quota level. If savings were 50 and consumption 50 when Y was 100, both have now changed to 45.

If I’m right, your paragraph about what happens in the next period is a bit wrong in places. Am I missing something?

That was sloppy of me. Of course I should have written that if relative income shares remain the same, the savings/consumption ratio returns to it's pre-quota level, BUT NOT 45 EACH since some of the income goes to the owners of the quota (whoever they are).

Thanks Hugo Andre. Yep, in the back of my mind I always tend to assume that recessions are short enough that both gross investment and depreciation over the duration of the recession are small relative to the existing stock of capital, so we can treat K as approximately fixed. But in David's model, with 100% depreciation per "period", we are forced to think what happens next period.

Yep. In my version of David's model income shares of both labour and capital fall in a recession, and capital's share falls more than labour's share, because quota owners' share increases.

(Watch the crazy conspiracy theorists come on here wildly speculating about who those mysterious quota owners are!)

Depends on capital depreciating through use or through time doesn't it?

Lord: yes. David assumes rust, not wear. Assuming wear would change the results a little, because the supply curve of capital services would not be perfectly inelastic.

I think this is right, but the political economy needs to be brought in. I suspect that the Fed (after a few months of distraction) knew in 2008-2015 that the economy needed more monetary stimulation. They were, however, politically (more than intellectually) constrained not to reduce interest rates below 0, not to buy "too many" LT assets (buying foreign exchange was just not in the cards), and not to allow the inflation rate to approach, much less exceed, 2%. These political constraints explains the Fed's tight money policy 2008-15 and looks like it (plus some independent yen for "normal" interest rates) will continue to explain it going forward. If you would work those constraints "They are funny like that" into your model, it would explain a lot more.

I think only (some) North American economists think what you express in the first two sentences of your final paragraph, and I'm damned if I know why.

Back to the books, I guess.

Luc: the books may not help you much on that one. A metaphor may help. You are balancing a broomstick upright on the palm of your hand. If you first move your hand North, so the broomstick starts to lean South, you must subsequently move your hand even further South than you started, to keep the broomstick upright. (Except broomsticks don't have expectations.)

I must say, I don't think much of David's model:

(1) No money or price stickiness, so how is the central bank setting r? Not by changing the real money supply, that's for sure.

(2) He has the central bank fixing the *rental rate of capital* not the interest rate. That means that not only is the interest rate (going forward) set too low, but the contemporaneous rental rate can't rise when capital is destroyed. Nobody thinks the central bank can set the current rental rate. Essentially he's assuming a price control.

(3) He doesn't discuss how rationing occurs following this price control. He says that because r can't rise, w doesn't change either. But if K is rationed, it will no longer be the case that r = MPK, and thus it will no longer be the case that r fixed implies K/N fixed, and therefore w fixed.

I'm sorry, but I just can't take this model seriously. When I try to understand what's making this model tick, my head hurts.

jonathan: I was fine with David's model until he had the central bank fix r. Like you, I wondered how it would do that, and if it did it, how the rationing would play out. Which is why I wanted to start with an explicit quota on output. Assuming an explicit price control on capital rentals would be another way to go, but I can't see how it would cause unemployment of labour, simply an excess demand for capital services.


I was "fine" with the model up to that point, meaning I understood what the model was doing and thought it was reasonable, but I didn't like that he called it an "IS curve".

In his basic model, there's a negative relationship between (r,Y) because investment is a fixed fraction of income:

K' = I = a*Y

Thus higher Y => higher K' => lower MPK' => lower R'

This is already quite different from the Keynesian IS curve, where lower R' implies higher Y because lower R' raises demand, and output is demand-determined. Basically the causality is reversed: in his model, causality flows from Y to I to R', whereas in the Keynesian model it flows from R to I/C to Y.

Jonathan: agreed that it's different from the Keynes/Hicks IS curve. But I disagree a bit on causality flowing from R to I (and/or C) to Y. Causality could flow either or both ways (though Keynes, and many Keynesians, seem to talk about it flowing from R to Y). I see the big difference as being that the Keynes/Hicks IS curve tells us about the relationship between R and Y holding Y* constant, while David is talking about the relation between R and Y* assuming Y=Y*. (Y* = "potential").

Nick and jonathan, I think part of what you're getting at is that there's no reason in David's model why the disequilibrium must occur in the labor market, with excess labor supply. It could just as easily occur in the capital-rental market, where firms simply wish to rent more capital then exists, and tough noogies to them. In the latter case, the "IS curve" (if I'm understanding what is meant by that correctly) would be vertical.

(I take the "IS curve" to be a relationship between the departure of the central bank fixed rental rate from it's equilibrium level and output)

I think I'm right.

In particular there could be a continuum of valid disequilibria, depending on the rationing and quota rents. You could have a little bit of a disequilibrium in one market and a whole bunch of disequilibrium in another. What you wind up with depends on the way the quotas are rationed and how "sticky" the real wage is (I know David says it's flexible, but he actually assumes it's fixed).

notsneaky @9.57: I *think* that's right. If there's a binding price ceiling on capital rental rates, I think that would simply cause an excess demand to rent capital, with owners of firms collecting profits that should have gone to owners of capital. Real wages and employment and output would stay the same. So the "IS curve" is vertical at Y* in that thought experiment.

But I don't agree (or understand) with your @12.24. I *think* the only way David gets employment to fall is that he insists on R=MPK despite binding rent controls, so a fall in N is the only way to get that, and a rise in W is the only way to keep W=MPL.

Thinking about it a little more, maybe David is thinking about firms as they are in the New Keynesian model.

In the New Keynesian model, firms that can't adjust their prices are forced to produce exactly enough to meet the demand they face. Suppose all firms are in this position, with fixed prices p=1.

Now this doesn't mean the firm problem is trivial -- firms still optimally choose between capital and labor, subject to the constraint that they produce enough output to meet demand (cost minimization problem). What changes is that firms' real marginal cost of production need not equal 1.

In this case, we're one condition short of specifying equilibrium. Then we just follow the New Keynesian practice of letting the Fed pick the equilibrium, which corresponds to a particular R.

Now in the NK model, there's an obvious "story" behind this policy: in the background, there's money demand, and the Fed adjusts the money supply to change interest rates, which then affect demand through the incentives for consumption and investment.

But that doesn't happen in David's model, because C and I (the two components of demand) are entirely determined by income in his model. The young save/invest all their income, and the old consume all the income. So the Fed can't change demand by adjusting interest rates.

So what is the Fed doing in David's model? Effectively, it's picking the level of output, and then R (and w) adjust so that firms produce the desired amount. In this case, a low R(t) corresponds to *low* demand in period t. (By contrast, in the NK model the Fed picks R(t+1), not R(t)).

How does the Fed set the level of demand in this model? It's not really clear -- it just picks the level of output (setting NGDP expectations?). What matters is that there are many paths of output possible, and he assumes that the Fed is able to pick one. A low level of R corresponds to the Fed picking a low path of output.

If you want to call that "monetary policy", it sounds more like contractionary monetary policy to me! But then, this is essentially my whole complaint with Neo-Fisherians in the first place: They observe that if the Fed magically sets high growth expectations the interest rate goes up, and then conclude that the Fed should raise interest rates to raise growth!

jonathan: I think that's right.

"(By contrast, in the NK model the Fed picks R(t+1), not R(t))."

Hmmm. I missed seeing that.

Actually, the model I described above would cause w to fall under his thought experiment, so it doesn't exactly coincide to what he's describing.

He seems to be assuming that the Fed gets to pick labor supply.

"(By contrast, in the NK model the Fed picks R(t+1), not R(t))."

Actually, I reread David's post (after writing my long comment above), and he might have used R(t) a little inconsistently. At one point he defines R(t) as the rental rate in period t+1, and thus the interest rate on savings in period t, but then later talks about R(t) as the rental rate in period t (I think).

In any event, he's assuming the Fed picks the path of output y(t), which then determines the rental rate in every period.

The way I was thinking about it, and it might not be right, is that the interest rate is given by the (too low, since the shock is a fall in capital) steady state and "the entity" sets the price of a quota (right to rent a unit of capital), q. Of course that sort of begs the question - why not just set a different interest rate to begin with? But if it is done that way (and assuming quota revenue is redistributed lump sum to somebody) then the usual r=MPK condition becomes q=MPK-r, or another words, the demand for quotas. K is given, so q is a function of L (employment). We still have w=MPL, which is also a function of L. So we have three unknowns; q, L and w and two equations so you have an indeterminacy - a continuum of disequilibria. If "the entity" also picked the quota price q (again, why not just set a different r), we can then solve for L and w.

The problem with that is that if there is excess labor supply any worker could go to a firm and propose working at a real wage and there's still nothing stopping the wage rate from falling. But letting that happen amounts to assuming there's always full employment and no change in output.

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