Winner of the New Statesman SPERI Prize in Political Economy 2016

Tuesday, 15 July 2014

Aggregate demand and the labour market

I’m surprised I do not see a diagram like this more often:

The black lines are familiar from any introductory macro textbook. There is a labour supply curve. It is drawn such that a higher real wage encourages more labour supply, but I will consider what happens if it is vertical later. What I call the ‘unconstrained labour demand’ curve is what firms would choose to do if (a) labour gets less productive as output increases (which is why the curve slopes downward), and (b) firms can sell whatever they like. This is the classical model, and you will find this diagram in nearly every introductory textbook. With flexible wages the level of employment is determined at the intersection of the two curves, and we could call it the ‘natural’ employment level.

However (b) is a fiction. No (surviving) firm produces what it wants to, irrespective of whether people want to buy its product. Aggregate demand can diverge from the level of output implied by the intersection of the two black curves for all kinds of reasons: Says Law does not hold. For simplicity, suppose the aggregate demand for goods in the economy is independent of the real wage, and there is no factor substitution. In that case employment is determined by my red line - it is determined only by aggregate demand. This is pretty clear in the case that I have drawn, where we have deficient aggregate demand. Firms produce what they can sell: they would like to sell more, but there is no point producing more if no one wants to buy more.

It is less clear what happens if the red line shifts right until we have excess aggregate demand. If the number of firms is fixed, why would they produce more than they want to - i.e. at a level where they are losing money on the extra products they are producing? In New Keynesian models where firms are monopolistic and prices are sticky they will produce more if excess demand is modest, because for given prices it is profitable to produce more up to some limit. But will firms be prepared to pay higher (e.g. overtime) wages to workers for long, or will workers be prepared to work more for unchanged wages for long? I will come back to this at the end.

If there is deficient demand, is there anything that makes the red line move right to achieve the natural employment level? With deficient demand, prices may tend to fall, but that alone is unlikely to shift the red line to the right: few people talk about Pigou effects anymore, and the general concern is that deflation is deflationary because the real value of debt has increased. It is monetary policy that shifts the red line in the required direction, either because it responds to falling prices or because it wants to reduce the output gap. Ironically, Real Business Cycle models, which assume the red line is always at the natural employment level, only make sense in a world where monetary policy is very efficient. However, monetary policy does normally work over the medium term, which is why the classical or RBC model makes sense if we are just doing medium/long term analysis.

What happens to the real wage? In the most basic of New Keynesian models, the labour market clears, which means real wages fall until the labour supply curve intersects the red line. (Here a vertical supply curve would be a problem.) If, in contrast, real wages were sticky, we would get involuntary unemployment - rationing in the labour market. Which is true matters a great deal to those unemployed, but it terms of modelling deviations from the natural rate the difference is not that great. Real wages have no direct impact on aggregate demand, and so all that might happen is that monetary policy could be influenced one way or the other. If it is not, what happens to real wages is irrelevant to the basic problem, which is deficient aggregate demand. This is one reason why New Keynesian economists may be happy to work with a model where the labour market clears, but there may be other reasons.

The vertical red line assumes no factor substitution. With factor substitution it can become downward sloping: falling real wages lead firms to substitute labour for capital, which can increase employment even if output is unchanged because aggregate demand is unchanged. As I speculate in this post, based on the work of Pessoa and Van Reenen, something like this could help explain the current UK productivity puzzle. If this speculation is correct, at some point as aggregate demand and investment expands real wages will rise, and labour productivity will increase as factor substitution is reversed.

I was prompted to write this post by this from Noah Smith, which in turn comments on a post by John Quiggin. (See also Mike Konczal and Nick Rowe.) They talk about models of labour market matching, which I have not mentioned, but similar considerations apply with matching models taking the place of the classical model (although there are key differences between the two). This gives me another chance to plug an AER paper by Pascal Michaillat, which addresses the possible asymmetry that may occur when we have excess demand. Michaillat’s model is a matching model when aggregate demand is strong, but a rationing model (with Keynesian involuntary unemployment) when aggregate demand is low. This is one, rather interesting, answer to the question I asked above about possible asymmetry. Putting matching together with Keynesian rationing is complicated, but if Michaillat’s paper is ignored just for this reason, that says something rather sad about current macro methodology.

1. Yes! That diagram is just like the one in Barro Grossman 1971. (And was it in Patinkin 68??)

The black curve is the notional labour demand curve, and the red line the constrained labour demand curve. It all goes back to Clower.

Sometimes I use it to teach my students. I draw the classical labour market diagram, and the ISLM diagram. Start with both at full employment. Then hold both W and P fixed, so W/P stays fixed, and then shift the LM (or IS) to the left. What happens to L and Y?

The students keep wanting to say that L stays the same, and Y falls. But if you then add a production function diagram, Y=F(L), they can't figure out why we should be below the curve.

I then draw the vertical constrained labour demand curve.

I hadn't heard of Michaillat's paper, but from your description it makes perfect sense. Search matching models need a labour demand curve. Replace the classical curve with the kinked black-then-red curve.

1. Yes indeed! But the problem with Barro Grossman and all that was that this was set in a framework where W and P were fixed, so it seemed to imply that the problem was nominal price rigidity. Being the good New Keynesian that I am, I see the problem as the wrong real interest rate.

2. And notice, by the way, that monetary exchange really really matters in this sort of model. If firms and workers were able to barter apples for labour, as opposed to exchanging labour for money, and then money for apples, the level of output and employment would go straight back to the intersection of the black classical labour demand and supply curves (provided the relative price W/P was correct), even if aggregate demand was too low. The fact that both would prefer to swap apples for money, and labour for money, but can't, wouldn't prevent them swapping apples for labour optimally. It's a shortage of money that causes the problem, plus the difficulty of using barter. Interest rates don't matter.

3. Simon: "But the problem with Barro Grossman and all that was that this was set in a framework where W and P were fixed, so it seemed to imply that the problem was nominal price rigidity."

True. It did seem to imply that.

"Being the good New Keynesian that I am, I see the problem as the wrong real interest rate."

And being the good monetarist and disciple of Clower that I am, I see the problem as a shortage of money. Because there were no interest rates in Barro-Grossman 1971. And if barter were easy, a too high real interest rate would not cause unemployment.

4. I'm happy to agree that the existence of money is important in allowing this problem to emerge, but not that interest rates are unimportant. But there is an equivalence here, so I'm not sure we really disagree. Imagine nominal rates are at zero. For you (I guess) falling prices will do the trick, because you assume that the monetary authority would not reduce the nominal money stock pari passu, which implies higher future inflation. In other words, it would not have an inflation target. I would describe that as monetary policy ensuring real interest rates fall. Its the same thing - we just talk about it in different ways.

5. Simon: "Imagine nominal rates are at zero. For you (I guess) falling prices will do the trick, because you assume that the monetary authority would not reduce the nominal money stock pari passu, which implies higher future inflation."

Well, falling prices *might* do the trick, but I wouldn't want to rely on it. Like you, I would much rather have the central bank do something more sensible than simply not let M fall pari passu. Letting M fall pari passu would be the worst. Increasing M, and announcing you were going to do it, would be best.

"But there is an equivalence here, so I'm not sure we really disagree."

That's the tricky bit. I keep trying different ways to explain my views on this clearly. Let me try it this way:

It's a one-way equivalence. If you specify the time-path for M(t) you can solve for the time-path of i(t). But you can't do it the other way around. And this really matters at the ZLB, because you can loosen monetary policy by communicating a faster-growing time-path of M(t) (which would result in i increasing, because expected inflation and/or expected real growth would increase), but you can't loosen monetary policy by communicating a lower time-path of i(t), because of the ZLB.

The world would be a better place if central banks, and people, treated interest rates as a symptom rather than a cause. Central banks would be able to say things that they cannot say now.

6. What central banks do is set an inflation target. So they can communicate a lower real interest rate at the ZLB by announcing a higher inflation target. I think that is much more effective than announcing a higher M. Look at Japan.

7. I would not say money is needed for aggregate demand shortages. The NK model is cashless and Mike woodford showed that all is needed is that the dollar is the unit of account. Without sticky prices the price level moves in such a way to get the Real rate right, bit this msy not be the case of the model is modified along the Lines of eggertson krugman

8. Simon: Yep. Announcing a higher inflation target would be better than announcing a higher M. Announcing a higher price level path target would be better still. Announcing a higher NGDP level path target even better! (But the people of the concrete steppes would complain "But what concrete steps does the Bank actually take to hit that target, if it can't cut interest rates at the ZLB??")

9. LM: and Mike Woodford was wrong.

Simple representative agent producer/consumer model, where people like a variety of goods but only produce one good themselves. Start in equilibrium, where all relative prices are one. Assume the Calvo fairy is very slow, just to keep it simple, so all nominal prices are fixed forever. Then have the central bank set a stupidly high rate of interest (indexed for inflation if you like, so it's a stupidly high real rate of interest). Woodford say you get a drop in real output. But people would just barter their way back to full-employment output. "I will buy 100 of your apples if and only if you agree to buy 100 of my bananas in exchange.". That's a mutually beneficial (barter) exchange. Rational agents would do those exchanges.

10. I think your view and that of Woodford are closer than you think. What he meant (at least as I understood it) is that in order for monetary policy to be effective you need two things: 1) people cannot use barter, 2) people must either use dollars or promise dollars to pay for things. So it is enough that the central bank has the power to issue dollars, even if in equilibrium nobody will use dollars and the economy will be cashless. Indeed, consider again the economy you were talking about, and assume people cannot coordinate to use barter. So if agent A wants to buy oranges from agent B he must either borrow dollars from the central bank to pay spot, or promise to pay with dollar at the end of the period. In the latter case, a clearing house will open a debt position for agent A and a credit for agent B. The two payment possibilities must be equivalent. If A borrows money from the central bank, he has to pay the interest rate decided by the central bank. If A uses the clearing house system nothing changes, as B could always demand him to pay with money, lend the money to the central bank and get the interest rate. So B will ask A to pay the interest rate decided by the central bank even if the clearing house system is used and no money is issued by the CB. So we can assume no money will be issued, as at the end of the period all positions at the clearing house cancel out. Still a higher interest rate will be effective in chocking off demand.

11. LM: start with an economy where people must use green bits of paper to buy and sell things. When you buy 100 apples from the apple producer, at a price of \$1 each, you must give 100 green notes to the seller of apples.

Now assume, to avoid the risk of muggers, people store their notes, not in their pockets, but in little boxes at the central bank, with their names on the boxes. When you buy 100 apples, you notify the central bank, with a form letter, and the central bank takes 100 green notes out of your box and puts them in the seller's box.

It's exactly the same. We call that form letter a "cheque". And if you send that form letter by email, we call it "e-money". And if the boxes and bits of green paper were destroyed in a fire, but the central bank had perfect computer records as a backup, it still wouldn't make any difference.

Now take a second economy, exactly like the first, except people use red bits of paper to buy and sell things. And each red note has negative value, so when you buy 100 apples at \$1 each the seller gives you 100 red notes. And those red notes are kept in a little box in the central bank with your name on it, to stop people throwing them away.

Now merge the first and second economies into a third economy, that has both green notes and red notes.

Now suppose the central bank pays interest on those notes. If you have 100 green notes in your box, the central bank prints 100r extra green notes per year and puts them in your box. And if you have 100 red notes in your box, the central bank prints 100r extra red notes per year and puts them in your box. The central bank sets r.

Now suppose that, if you ask, the central bank will always print and add one extra green note plus one extra red note to your box. Or burn one green note plus one red note.

Finally (sorry) now take the limit of that economy, where the central bank decides that the aggregate number of green notes across all agents must equal the aggregate number of red notes.

We now have Woodford's "cashless" economy.

But it is certainly not a cashless economy. The fact that we keep the cash in little boxes at the central bank and not in our pockets makes no difference. The fact that the cardboard boxes and paper notes were destroyed in a fire, which the Bank kept a secret, because it kept perfect records on a ledger or computer, makes no difference.

The physical form of cash does not matter (except for convenience, and muggers). Those positive and negative balances at the central bank are cash. It is a monetary exchange economy. People must use that cash as a medium of exchange.

12. In my above comment, I should have merged these two paragraphs together:

"Now merge the first and second economies into a third economy, that has both green notes and red notes.

Now suppose that, if you ask, the central bank will always print and add one extra green note plus one extra red note to your box. Or burn one green note plus one red note."

Because it is that second paragraph that explains why one red note will always be worth minus one green note. Otherwise, red and green notes would have a floating exchange rate.

BTW: it's good arguing with you, LM! You know your stuff.

13. @Nick Rowe: thank you very! Your explanations manage to make difficult concepts simple and are illuminating. So, I think we agree on the point and the difference was simply semantic. Actually, I think you are right: I would not call this economy cashless.

14. Sorry, that was a thank you very much. I forgot "much".

15. Thanks LM!

And in the limit, as each agent's purchases and sales of fruit become perfectly synchronised, because they are buying and selling continuously in continuous time, and if all agents are identical (except for the variety of fruit they produce) the quantity of cash demanded (green notes plus red notes) would also approach zero in the limit.

You might, I think, legitimately call that a "cashless" economy. Even though you buy and sell everything for cash, the stock of cash would approach zero in the limit.

But that's not the real world, because it is very costly to synchronise our purchases and sales of goods perfectly. Which is why there is a demand for money. And why monetarism exists!

2. It would be great if somebody could help me out in thinking about what happens at the margin of employment. By that, consider the following thought experiment:

A firm, even though it is currently producing exactly at the aggregate demand constraint, decides to higher another worker and pay that worker his marginal product. This worker now has more wealth than he had before, yet he cannot consume out of this wealth without violating the aggregate demand constraint. Thus he must save it. This, then, leads either to investment (another contradiction of the aggregate demand constraint) or a divorce of savings from investment.

With interest rates as low as they currently are I could believe a liquidity trap story, where savings are greater than investment. Short of a liquidity trap story, however, what could happen for this marginal employee so that the aggregate demand constraint holds?

1. I'm not sure if I've understood the question, but here is a reply to what the question might be. If the firm does hire an unemployed worker, that worker would be likely to consume more, and so aggregate demand would increase. But unless the worker happened to just buy the output of the firm, the firm would still lose money - and regret hiring the worker. What the firm needs to do is coordinate with all the other firms, such that they all agree to hire one extra worker. But of course firms cannot do that. But the government can!

2. The workers (or someone) could choose to spend all their wages (or income) if they wanted to. But they don't want to. They want to accumulate extra money instead. So demand for goods falls, and output and income falls, until they stop wanting to accumulate extra money, and then income stops falling.

3. Great, thank you for the help! I'm glad to hear it is a coordination problem - that's how I've always imagined Say's Law would fail - so I'm happy my priors aren't totally off base.

4. To Nick - there still needs to be a coordination problem for your story right? By this I mean that savings doesn't inherently imply a lack of demand, as investment is a positive function of savings.

In fact, on the margin it is hard to imagine how somebody could save their wages for the purposes of accumulating extra money yet have those savings not translated into investment, since whoever is offering that person an interest rate must be losing money on the margin.

However, I think that a coordination problem --eg; money saved for intended investment that for some reason does not occur -- is sufficient for savings to not translate into aggregate demand.

5. Anonymous: "To Nick - there still needs to be a coordination problem for your story right?"

Yes. (But there's always a coordination problem if the economy gets into a bad equilibrium).

"By this I mean that savings doesn't inherently imply a lack of demand, as investment is a positive function of savings."

If everyone decides to save \$100 per year more, and also invest \$100 per year more, we don't get a lack of demand.

"In fact, on the margin it is hard to imagine how somebody could save their wages for the purposes of accumulating extra money yet have those savings not translated into investment, since whoever is offering that person an interest rate must be losing money on the margin."

Take a very simple model, where money is currency. Every individual chooses to hold some average stock of currency to make the shopping easier. As individuals, we have a choice between spending money on newly-produced goods, or holding extra currency. If we all decide we want to hold more currency, we spend less. Collectively we fail, if the total stock of currency does not expand in proportion, but each individual can always accumulate money by spending less.

6. Great, I'm very much in agreement with you. If I had one last question, it would be over the mechanism you outlined as to why we hold more currency.

"Every individual chooses to hold some average stock of currency to make the shopping easier."

I was thinking that increased liquidity would be due to a speculative motive (waiting for interest rates to increase) as opposed to a transactions motive (holding more money to make shopping easier).

Especially in this context of an aggregate demand constraint where only a limited number of goods are being demanded, it seems to me that the speculative motive, rather than the transactions motive, would be the cause of the increased liquidity which would then separate savings from investment.

Anyway, it would be great to hear your perspective on this.

7. Anonymous: dunno. It could be almost anything. Like fear of a financial crisis, so you hold more cash because you are afraid that some people you normally sell to might not be able to pay you at the normal time. And if you do that, it means you slow down your own payments, which just makes it worse for everyone else, so the whole thing snowballs, like one car slowing down on a roundabout.

8. Ok that sounds good to me -- thank you again for taking the time!

3. I presume that part of the issue is the ineffectiveness of monetary policy at the ZLB

4. Simon says “labour gets less productive as output increases..”. Quite right. That is, the lower is unemployment, the less suited are the remaining unemployed for vacancies.

Ergo NAIRU can be reduced if those “unsuitable” potential employees are subsidised into work, which is theoretical backing of a sort for schemes like the Work Programme.

5. What a pleasure to see another model to explain Keynes' effective demand constraint on employment and output.
I will add another idea... You have real wage on the y-axis. You can expand it.
Real wage = labor share * productivity
Labor share = real wage/productivity

I use labor share as the determinant of effective demand. You could put labor share on the y-axis. Then you not only reflect real wages but also the inverse relationship to productivity. What would the diagram look like with labor share on the y-axis?
If you hold productivity constant, the demand and supply curves do not change.
However, the data shows that productivity will increase when labor employment falls to the left of the effective demand vertical line that you have drawn. But when labor employment returns to the vertical line, productivity stops increasing.
That makes sense because being more productive at the effective demand limit creates production that may not be sold at a sticky real wage. So we solve a portion of the productivity puzzle there.
If you use labor share on the y-axis, there is a labor share % where the supply and demand curves will cross, like you say that is the natural employment level. Now if labor share falls below this level, we move down the labor supply curve, people drop out of the labor force and there is less employment. Employment will not return to its natural level. Moving up the labor demand curve, firms would be willing to hire that level of labor at a much higher labor share, but they are enjoying greater profits, so why fix something that is not broken.
The solution is to raise labor share back up to the level where we find the natural rate of employment. The key to that is raising real wages as productivity becomes sticky below the natural rate of employment.

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