# 10

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I've always found that learning new areas always goes a lot better if you start with a key insight of what the field is about. Often this is not presented or explained at the beginning of the course, and you have to deduce it later on.

For instance, I would have better grasped the epsilon-delta definition of a limit if the instructor had started with something like:

• Our intuitive definition of a limit is that as we get closer to this point, the function gets closer to this value. It has turned out to be very tricky to formalise this intuition, however. Early mathematicians used calculus without a good definition of limit, and their informal definitions led to a lot of paradoxes. The epsilon-delta definition is a bit clunky and may seem counter-intuitive, but it actually manages to capture our intuitive definition without paradoxes and problems - that's why we choose it, not for its elegance (though you will come to appreciate it). With that in mind, let's have a look at it...

Similarly, I would have made more rapid progress with Gödel's theorems if, before giving the formal definition of Gödel numbering and of the provability symbol □, someone had clarified that direct and indirect self-reference was a problem. If a formal system of a certain complexity can talk about its own structure, even without "realising" that it's doing so, problems will arise. Some of my other key insights in the field can be found in my post here.

So when I do stumble upon a key insight, I want to share it. I've found some recently in Keynesian economics, giving me a much better grasp of what makes that economic theory tick, and which would be my point of entry should I ever study the subject in detail. The two key insights are:

1. Keynesian models do not require irrationality. Unemployment can persist (in the model) even if every agent is completely rational.
2. Hence theoretical macroeconomics really is different from theoretical microeconomics.

Of course, Keynesianism makes great use of irrationality or partial rationality of the agents (such as the stickiness of wages or the irrationality of bubbles), but it was a revelation that rational models, full of Homo Economicus, could still produce excess unemployment.

This seemed intuitively very odd. After all, if there is unemployment, wages should fall, making it more attractive to hire workers. Therefore the equilibrium should be that everyone who wanted to work at the wages available should work. And this is not only an equilibrium, but an attractor: free-floating wages should move the economy towards the equilibrium.

But this lecture presented the rest of the argument. In a closed economy, investment (by firms) plus consumption (by individuals) must be equal to the total production of the economy - you can't sell stuff to thin air. Similarly, the amounts sold by firms translate into income for firms, shareholders and workers - you can't generate income without selling to someone. Over the short term, things can move out of equilibrium (people can increase or cash in their savings), but over the long term it has to balance.

That equilibrium is also an attractor. So we have two equilibrium processes - the wage changes, and the consumptions plus investment equality. Notice, though, that they interact! As wages rise and fall, people's incomes rise and fall, and hence their consumption, which feeds through to the incomes of firms and hence to their own levels of investment and salaries...

The question then, is whether there exists a joint equilibrium for both processes at once (more properly, since consumption consists of many markets, a general equilibrium for the whole economy). We'd want an equilibrium that was also an attractor, since we'd want to move to that state. In some circumstances, such attracting joint equilibriums exist - but in others, they don't.

So, at least in the model, excess unemployment can persist in the presence of fully rational agents.

# 10

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[-][anonymous]9y 11

For me the key Keynesian insights are:

1. The economy can be in equilibrium at a high level of unemployment.

2. People can choose more goods and less money, or more money and less goods. If they choose the in a sufficiently dramatic and surprising way, then you can end up with a general glut.

Of course both these arguments predate Keynes and Keynesian economics but nevertheless.

Microeconomics has its own ways of explaining persistent unemployment beyond the "natural rate" without invoking irrationality. These explanations have to do with a lack of information. They aren't particularly new, either. Armen Alchian pioneered these models half a century ago.

Here's an example of how things could go.

Aggregate demand drops, and so the employer, whose demand has also gone down, tries to lower the wages of his employees, who do not know that aggregate demand has dropped. They only see that their employer's demand has dropped. They can rationally decide that it is worth quitting their job rather than taking they pay cut and looking for a job that will pay them what they think they are worth elsewhere. If this is happening in businesses all over the country, unemployment could get large quickly for entirely rational reasons.

Now, workers might realize their mistake and try to ask for lower wages. But this won't get them hired either, because stepping out of the crowd to ask for a lower wage just sends a signal that you're not worth very much and also that you're unusual in some way. Employers won't be interested in hiring a high-risk low-productivity worker. And furthermore, the workers know that employers will react in this way, so no individual will even bother trying.

Employers will see that people aren't willing to work at the wage necessary to make it profitable to hire them and that they're not budging on this. So they'll start restructuring their business, substituting capital for the labor that has gone. Now you have a skills mismatch where the workers can't do the sorts of things people are willing to pay them to do because the jobs they were trained for are now done by machines. And that can give you pretty persistent unemployment just with rational imperfect information microeconomics.

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Wait, what?

In the scenario you describe, the only reason workers "aren't budging" is that they (correctly, it says here) anticipate that employers will fail to hire them at a profitable wage, due to the signalling effects of their reduced offer. Given that the employers are willing to restructure their businesses anyway, why don't any of them restructure their hiring methods to make use of that cheaper labor pool?

[-][anonymous]9y 2

Employers can do that, and they might. That would still take a while, however, and unemployment would persist in the meantime. This model isn't a model of how unemployment would last forever, but only a way of showing that microeconomics has models that can produce a high level of unemployment without invoking irrationality.

But of course, employers might not do that as well. It depends: is it cheaper to restructure my business so that I don't need those laborers, or is it cheaper to try to find out how to get those workers back indoors at a price I'm willing to pay? They've given me a pretty strong signal that the latter is going to be difficult. True, that signal was a result first of imperfect information and then a coordination problem, but that's only obvious to the modeler. All the employer sees is that people walked out rather than take a pay cut and they're not coming back even after learning that the economy in general is depressed.

Restructuring a business so that less labor is necessary seems like a more common activity than changing hiring practices so as to successfully lure workers back in. I hear about the former all the time, and I can't recall a single instance of hearing about the latter, have you?

Not that this model is intended to actually explain anything that happens in reality, although it very well might. I don't know. But it does show that rational microeconomic models can produce persistent high unemployment. This model can even lead to a fun Spiral of Doom where employees can't get jobs because their old jobs are done by machines, so they need to go to school to learn new skills, but they can't afford to go to school because they don't have jobs, but they can't get jobs because they don't have any skills, but they can't go to school...ad infinitum. Let's hope there's something about that model that's very different from reality.

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Restructuring a business so that less labor is necessary seems like a more common activity than changing hiring practices so as to successfully lure workers back in. I hear about the former all the time, and I can't recall a single instance of hearing about the latter, have you?

If companies hiring employees at a lower wage than they used to pay is an example of this, then yes.
If not, then I'm very confused.

In any case, I think I misunderstood your initial point and my confusion is entirely tangential to your actual point.

[-][anonymous]9y 0

Yeah, no problem. Let me just add that lowering the wage they pay to workers is what employers tried in the first part of the model, and they received a very strong NO in response.

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How can an argument which invokes 'Aggregate demand' be a micro-economic model?

[-][anonymous]9y 4

First of all, the division between micro- and macroeconomic models is essentially arbitrary. It's not as if the economy itself cares about whether a phenomenon is micro- or macroeconomic. So even though I invoked aggregate demand, this model still seems microeconomic to me. There's no money--the wages could be in coconuts for all the difference it would make. While what's happening is economy-wide, that's not relevant. When we talk about a simple kind of perfectly competitive economy, the slightest change in the cost of producing whatever the output is instantly has economy-wide effects, and yet that is certainly a microeconomic model. There's no national accounting figures or any individual step in the argument that would make a 19th-century economist look at you funny.

If you don't buy that then just substitute "the demand of a bunch of firms all fall at the same time" rather than "aggregate demand falls." Now it's microeconomics and totally unchanged.

Anyway, there are simpler ways of showing that rational microeconomics can produce high persistent unemployment. You can just ask why you expect the equilibrium level of price and quantity demanded of labor will be just happen to leave us with ~%5 unemployment. Then you might introduce a factor in addition to price and quantity that interferes with the operation of that simpler model. Information is an obvious candidate. Then you might read "The Market for Lemons" by George Akerloff and notice that there's no reason that kind of model can't apply to the labor market.

Basically, Joe Stiglitz would be surprised to learn that rational microeconomics doesn't have models that can explain high persistent unemployment.

There could also be structural things going on in the economy. It's easy to understand a model of the economy where what workers are capable of doing isn't what anyone wants them to do, so they can't get jobs. Their value to the economy might actually be zero, or information and signaling problems might make it impossible for workers to convince employers to hire them at a wage low enough to be worth it.

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Now, workers might realize their mistake and try to ask for lower wages. But this won't get them hired either, because stepping out of the crowd to ask for a lower wage just sends a signal that you're not worth very much and also that you're unusual in some way.

The fellow could be unusual in accurately assessing likely wage rates faster than his fellows. You're making huge assumptions about the priors of the attitudes of employers.

Keynesian models virtually always involve two key elements: (1) a monetary exchange economy, and (2) some kind of nominal price stickiness. (The simple income/expenditure model assumes no price adjustments at all; the full implications of imperfect price adjustment are only seen in AS/AD type models.) From a micro-economic perspective, there is no mystery: price stickiness is just like a binding price control, where the short side of the market determines quantity traded.

What the income/expenditure model adds is that, in the very short run, feedback loops can drive effective income/expenditure very far below their "notional" values (the values that would prevail in the absence of frictions), due to how desired expenditure depends on realized income.

Note that here, wage flexibility does not remove all frictions, because price stickiness also matters a lot. To a first approximation, adding wage flexibility would merely result in making wages sharply pro-cyclical (because labor demand also depends on realized income).

I don't think this captures the essence of macro economic theories. In my view, the key insight is that you must think about the money balances people hold (carefully distinguishing money from wealth here), how trade affects that balance and how they attempt to optimize it.

In particular with sticky prices, the 'hot potato effect' becomes important. You might also hear it called, 'monetary disequilibrium', 'excess cash balances mechanism' and probably some other things as well. The Keynesian concept of the “Paradox Of Thrift” is related, though less well developed. I've written more about it here.

consider an economy initially at equilibrium with a fixed quantity of money and prices that adjust to changes only after some time (sticky prices). Some people in the economy decide they want to hold higher money balances than they had in the past:

When people hold less money than they would like, they try to increase their holdings of money in two ways: 1) try to reduce their spending 2) try to increase their income. The quantity of money is fixed, so if one person holds a higher nominal quantity of money than before, all others must hold a lower quantity of money than before in aggregate. Prices are fixed, so this is also true for the real quantity of money. When one person reduces their spending, they reduce the income of others in the economy. Unless those others desire to hold less money than before, they now hold less money than they would like. Now those others also try to increase their money holdings by the same means. This is a vicious circle and aggregate spending and incomes decline. The circle ends when people no longer want to reduce their their spending to achieve higher money balances.

There are two effects which determine how far this process proceeds. 1) The quantity that people want to hold is positively related to the quantity people expect to spend, so as people expect to spend less they will need to hold somewhat less money. 2) As people reduce their spending, those reductions become more painful, so will be more reluctant to trade off consumption for increased money balances.

Do you know of a good explanation for why the Federal Reserve's efforts to inject more money into the US economy since 2008 has not quickly brought it back to near full employment?

Yes, there are two big reasons:

1) The Fed has made it clear that the injections are temporary and will be removed if the economy improves. Standard theory says that increases in the money supply expected to be temporary basically have no effect on inflation or (they lead people to want to hold more money). If you double the money supply but promise to reverse this in a year, the result is not huge inflation now till a year from now and then huge deflation, but no inflation (lots of people think about inflation as a differential equation, but this will lead you astray).

2) Near the start of the crisis in 2008, the Fed started paying interest on reserves which encourages banks to hold excess reserves, of which they hold a huuuuuuuuuuge amount. The interest rate is quite small, but this can have a huge effect this rate is above what banks can get elsewhere (risk adjusted). The appropriate interest on reserves could also easily be negative.

Also, the uncertainty about when the injections will be removed keep investors on the sidelines. People don't like uncertainty, and will often wait it out.

Why would anyone assume that everyone (in the US and other wealthy nations in particular) is economically viable as an employee at prevailing wage rates?

Add in increasing regulatory and financial burdens to employers. Add in an economy increasingly based on information, where information coordination is more and more a relevant and limiting factor. Add in technology rapidly making people with meager skills obsolete.

Even without the add ins, management and coordination have financial costs and opportunity costs that a worker's productivity may not overcome.

Thanks! That helps.

In case you're interested, I have a short mathematical model of monetary disequilibrium, which is something I haven't been able to find anywhere else. The people who seem to understand this aspect of macroeconomics clearly tend to incorrectly think that math is useless.

1. Keynesian models do not require irrationality. Unemployment can persist (in the model) even if every agent is completely rational.
2. Hence theoretical macroeconomics really is different from theoretical microeconomics.

Asking from ignorance here -- how does the second point follow from the first? Does theoretical microeconomics require irrationality?

The theoretical microeconomics view is the one that claims:

After all, if there is unemployment, wages should fall, making it more attractive to hire workers. Therefore the equilibrium should be that everyone who wanted to work at the wages available should work. And this is not only an equilibrium, but an attractor: free-floating wages should move the economy towards the equilibrium.

Ah, thanks!

No, it's simply that unemployment cannot persist in rational microeconomic models.

Ah, that makes sense (and seems obviously to have been your meaning in retrospect). Thanks!

No, it's simply that unemployment cannot persist in rational microeconomic models.

Such models must include the assumption such as "all potential workers are able to provide a net positive value to an employer".

The two key insights are:

Keynesian models do not require irrationality. Unemployment can persist (in the model) even if every agent is completely rational.
Hence theoretical macroeconomics really is different from theoretical microeconomics.

Could you elaborate and clarify the first insight? The insight can't be that people can be unemployed even when people are acting rationally, yet that is the way I read what you wrote.

The insight can't be that people can be unemployed even when people are acting rationally, yet that is the way I read what you wrote.

The insight is that! Microeconomics says that wages demanded and supplied will adjust to reach full employment. Macroeconomics points out that adjusting wages will change consumption and gdp and change demand, and hence company profits, and hence more jobs will be created, destroyed, or repriced.

Full employment is only possible if both these things balance simultaneously. Usual Keynsian approaches posit some friction or irrationality that prevents them balancing (or at least balancing fast enough). But in some cases, it might just be because there is no convergent simultaneous balancing for both processes.

In that case, even if frictionless and rational, unemployment will persist (probably going through wild gyrations) because there's no way of getting to zero unemployment, and it wouldn't be stable even if you reached there. If we're really unlucky, we could get a strange attractor (http://en.wikipedia.org/wiki/Attractor#Strange_attractor).

Microeconomics says that wages demanded and supplied will adjust to reach full employment.

Next time you meet Mr. Microeconomics, tell him he's an idiot. Fortunately for me, I don't know anyone so stupid.

Everyone is employable! Everyone will be employed! What grown up with an intact brain thinks that?

Full employment meaning that everyone that desires to work at the wages that they would be offered to do so, would indeed be working.

"Would be offered" in what counterfactual universe?

Without counterfactuals: assume Mr X is willing to do job Y at wage Z, and has as much skills as Mr A. Then if Mr A has job Y at wages above Z, and Mr X is unemployed, we do not have full employment.

Next time you meet Mr. Microeconomics, tell him he's an idiot. Fortunately for me, I don't know anyone so stupid.

Everyone is employable! Everyone will be employed! What grown up with an intact brain thinks that?

I expect "Mr. Microeconomics" to glance behind him at "Mr. Straw-man Microeconomics", to whom I would addressing my gratuitous insult.

Isn't income to shareholders also a source of money spent on goods? How is it possible for the system to move all of the money and all of the goods to the shareholders?

There's one expression of this idea I like because it uses the partial equilibrium supply & demand model that introductory microeconomics classes always use, and it's a reasonably easy formulation to follow if one knows that model. (It also illustrates a danger of doing back-of-a-napkin partial equilibrium analysis for a single market when that market's big enough to have a big knock-on effect on another market.)

I'm lifting this from Robin Hahnel (Journal of Economic Issues, 41(4), pp. 1139-1159), although he says he got it from Axel Leijonhufvud:

Consider a labor market and a goods market. Assume that if either market is out of equilibrium the excess supply or excess demand in that market will eventually lead to wage or price adjustments leading that market to its equilibrium. Now assume that while the goods market is initially in equilibrium, the labor market is not because the wage rate is temporarily higher than the equilibrium wage. While the excess supply in the labor market will generate equilibrating forces pushing the wage rate down toward its equilibrium, suppose it does not reach its equilibrium immediately, and in the meantime labor contracts are struck at a wage rate that is still higher than the equilibrium wage. If the labor demand curve is elastic this will result in lower labor income than would have been the case if the wage rate had reached its equilibrium. But the demand curve in the goods market was premised on the (implicit) assumption that the labor market was in equilibrium, and therefore that labor income was higher than it actually will be. When we reconstruct the demand curve in the goods market based on the actual outcome in the labor market, where labor income is lower than it would have been had the labor market been in equilibrium, we get an actual goods demand curve to the left of the one anticipated. No matter how quickly or slowly the price in the goods market adjusts to the resulting excess supply, we will get a drop in sales and revenues in the goods market.

But lower sales and revenues in the goods market will decrease the demand for labor in the labor market. The demand curve we originally drew in the labor market was premised on the (implicit) assumption that we had reached the equilibrium outcome in the goods market. Now that sales and revenues are lower in the goods market, when we reconstruct the demand for labor curve based on the new, actual outcome in the goods market, we get a new demand for labor curve to the left of the initial one. No matter how quickly or slowly the wage rate adjusts to the new excess supply, employment and labor income will drop, further depressing the actual demand for goods in the goods market. Instead of remaining in equilibrium in the goods market and moving toward the higher, equilibrium level of employment in the labor market, we move out of equilibrium in the goods market and even farther away from equilibrium levels of employment in the labor market.