Worthwhile Canadian Initiative

Bicycle Disequilibrium Theory

Suppose you need a bicycle to get to work. Suppose bicycles are a common property resource, because bike locks don't work. Every night the workers deposit their bicycles in the bike bank, and in the morning it's first come first served. And suppose that sometimes there aren't enough bicycles to go around. So sometimes the level of employment is determined by the number of bicycles, and not by all the usual stuff.

Any individual can always get a bicycle in the morning, simply by getting up early enough. But in aggregate they can't. Fallacy of composition. A theory of when workers wake up might be interesting, and useful for microeconomists wanting to understand the distribution of employment, but it won't help us understand what determines the aggregate level of employment.

Bicycle disequilibrium theory helps us understand what determines the level of employment and output. It also helps us understand other puzzling phenomena, like why workers sometimes wake up and go to work so ridiculously early.

The Meaning of Life, Labour Supply, and all that

Here are the results of my Twitter poll:

This post is my interpretation of those results.

I recognise all the usual caveats. I am more concerned about bias in the sampling method than in the small size of the sample (because it's not that small). The people who follow me on Twitter (or who follow those who follow me and reTweeted it) are probably richer than average, so less in need of the extra $50, so more likely to choose B. But they are also more likely to be economists, or to "think like economists", and maybe think it might be a trick question, because why would anyone leave $50 on the sidewalk, and if there's no trick then A is the obvious answer. Plus the normal caveat that how people answer any survey might not be the same as their revealed preference in any real choice. (But it's an anonymous survey, so there's no point in signalling a socially-approved answer.)

I would have answered "B" myself. And I wanted to find out how many people thought the same way, and how strongly they felt about it. (I would have switched to "A" if I had been poorer and needed the money more, but I would still have switched back to "B" if the $50 had been raised closer to but still less than $100.)

It's not easy explaining my choice in terms of economists' standard means-end dichotomy. And it wasn't easy constructing a poll question that would get at what I was trying to get at (and I'm not satisfied I've got it right). I find doing something more satisfying when I think it has a purpose than doing the exact same activity when it doesn't have a purpose and so isn't a "real job". And it's not (just) about altruism vs egoism; I get satisfaction out of chopping wood for my fireplace, or my Mother's fireplace, that I don't get out of chopping wood for no reason at all (except exercise), that is separate from any satisfaction I get later from the firewood itself. And I think most people think like me, at least to some extent. And my little poll was intended to try to find out how many people and to what extent.

If I'm right about this, it will matter for labour supply curves. People (or some people) will choose jobs they think need doing over otherwise identical jobs they think don't need doing, unless there's an offsetting wage difference. It will also matter for comparing programs like Basic Income (Negative Income Tax) vs wage subsidies vs job guarantee.

[A few years back I installed a heat pump in my home. The salesman said I would get a subsidy from the Quebec government as an incentive to install a heat pump to reduce electricity consumption. Filling out the forms to collect that subsidy got stuck on my "To Do" list, because it was a pointless job I would get no satisfaction from doing, just to transfer some money.

And I'm recently retired, so I'm still adjusting to a life where I don't really need to do a lot of the things I used to need to do.]

But how could I have asked my question better, to measure what I am trying to measure?

The 1 vs 3 Model of Quick Recessions vs Slow Recoveries

Business cycles are not symmetric; if you flipped the time-series data upside-down the fluctuations would look different. Recessions are usually quick; recoveries are usually slow. And Milton Friedman's "Plucking Model" seems to fit the data: big falls in economic activity are usually followed by big increases; but big increases are not usually followed by big falls. It's as if there were some "normal" level of economic activity, and the economy sometimes falls below "normal" temporarily, by greater or lesser amounts, but rarely rises much above "normal". Recessions are bigger than booms. Big news is usually bad news: it's an illness, and not a burst of super-normal health. So on average it's less than "normal" (which is why I put "normal" in "scare quotes"). And it suggests (but does not prove) that if you could reduce the fluctuations, you could maybe increase the average level of economic activity towards "normal".

Why? Here's a story (I think it makes sense):

A simple model of a monetary exchange economy is the Wicksellian Triangle. The apple producer wants to consume bananas; the banana producer wants to consume cherries; the cherry producer wants to consume apples. But it's hard to coordinate 3 people meeting in the same place at the same time so they can do a 3-way swap in the central Walrasian market. They can only meet pairwise, so they have to use money. And let's suppose they use some 4th good as money (because my story is simpler that way). So we have a circular flow of money clockwise around the Wicksellian triangle; and a flow of fruit counterclockwise.

It only takes 1 person to reduce the circular flow of money. If the apple producer decides he wants to hold more money, he can unilaterally decide to slow down or stop spending his money. He does not need anyone else's consent to do this; because exchange requires mutual consent. Quantity traded is whichever is less: quantity demanded; or quantity supplied. The change in his stock of money equals the flow in minus the flow out; he needs the cherry producer's consent to increase his flow in, but can reduce his flow out to the banana producer unilaterally. And if the apple producer decides to slow down or stop his spending, the whole circular flow of money and fruit slows down or stops too.

The circular flow of money is like an "O-ring" model; a chain is only as strong as it's weakest link.

It takes all 3 people to increase the circular flow of money. The apple producer needs to spend more quickly, the banana producer needs to spend more quickly, the cherry producer needs to spend more quickly. (And each of those 3 decisions requires the mutual consent of both parties to the trade of money for fruit, because the apple producer cannot buy more bananas unless the banana producer agrees to sell more bananas. And only if all 3 have an excess supply of fruit matched by an excess demand for money will that consent be readily forthcoming. [Update: But I put that bit in brackets because I'm thinking of a demand-side model here, and the supply-side will usually not be a constraint in a recession, or if the economy is monopolistically competitive, which it mostly is.])

The circular flow of money is like 3 cars circling a one-lane roundabout, they all need to go faster for any one of them to go faster.

So far I've been talking about the velocity of the circular flow of money; but the same thing applies if we take the derivative with respect to time and talk about the rate of acceleration. It's the rate of deceleration that represents how quickly the economy goes into recession; it's the rate of acceleration that represents how quickly the economy recovers.

The rate of deceleration of cars on the Wicksellian roundabout is determined by the rate of deceleration of the car whose driver wants to decelerate the most; the rate of acceleration of cars on the Wicksellian roundabout is determined by the rate of acceleration of the car whose driver wants to accelerate the least. (That's not exactly true of course, because drivers leave an adjustable buffer zone of space between themselves and the car in front; just like they hold an adjustable buffer stock inventory of money so their flows in and out don't have to match exactly. But it's good enough for this post.) If we take two sets of 3 random numbers, the biggest number in the first set will usually be bigger than the smallest number in the second set. So recessions are usually quicker than recoveries.

And you get Friedman's "Plucking Model" because something going wrong and performing worse than normal has bigger effects than something going right (unless it's the same thing that had previously gone wrong, which it probably won't be).

The Wicksellian triangle is really a many-sided Wicksellian polygon, in any modern highly interdependent economy. So it will be 1 vs n rather than 1 vs 3. But there is usually more than one person producing apples, or bananas, or cherries, so each corner of the Wicksellian triangle is an average of several people, not just one person. And there's usually some degree of substitutability between different goods when relative prices change. And maybe those modifications to the model would roughly cancel out, or maybe not. And we aren't just talking about trade in newly-produced final goods and services (GDP); because (almost) everything gets traded for money, including labour, intermediate goods, real assets, financial assets, etc.

Sure, it's just a story, and not a real "model" with math. But I think you get the drift.

The Blind Target Shooter

This is an attempt by someone who is not very good at math to understand the alleged "indeterminacy problem" of central banks using market signals of expected inflation to help them target inflation (or whatever).

[I used to do rifle shooting at school. "If you can't group you can't shoot". But if you could group, and you had a spotter to tell you where your shots were hitting, and you adjusted the sights accordingly, you could hit the bull. Except for changing winds etc. So here's a parable:]

Let the deviation from target at time t, Y(t), depend on the instrument setting X(t), and an exogenous random variable S(t), according to Y(t) = X(t) + S(t).

If the target shooter can see the wind S(t), and adjust his aim X(t) according to a reaction function X(t) = -S(t), he can hit the target perfectly, so his misses Y(t)=0 for all t.

Suppose he cannot see the wind S(t), but he can see where his shots hit (or miss) Y(t).

If he is firing continuously (it's a machine gun), and his shots hit instantly, and he sees his misses instantly, and he can adjust his aim instantly, and if the windspeed never jumps discontinuously, then by adjusting his aim in response to his misses, he can make his misses arbitrarily small, but not always precisely zero.

[Mathematicians tell me that what happens "in the limit" isn't always the same as what happens "at the limit".]

To see this, suppose he has a reaction function X(t) = -bY(t), so his misses are Y(t) = -bY(t) + S(t) = [1/(1+b)]S(t). By making the adjustment parameter b arbitrarily large, he can make his misses arbitrarily small.

But he cannot make his misses precisely zero (unless the wind never changes [edit: I should have said "never changes unpredictably"]). Proof is by contradiction: if he never misses, then he never adjusts his sights (because misses are the only information he can respond to), so if the wind changes he will miss. Which is a contradiction.

It makes no difference if the target shooter cannot see his misses, but uses a second person, a spotter with a telescope, to tell him where his shots hit (if there are no communication lags between spotter and shooter). The misses can be made arbitrarily small, but not always precisely zero.

It makes no difference if the spotter can also see the wind S(t), and the shooter's aim X(t), and so knows exactly what the miss will be, but can only communicate the misses Y(t) and cannot communicate the wind S(t). The misses can be made arbitrarily small, but not always precisely zero.

Now let us make a small change in the assumptions. Assume the misses Y(t) can only be observed with a 2-year lag. But everything else happens instantly, and the model is still a continuous time machine gun. There is now a big difference between a spotter who can see the wind, and can communicate his continuous forecast of what the 2-year ahead observations of the misses Y(t) will be, vs a different spotter who cannot see the wind. By listening to the forecasts of the spotter who can see the wind, and adjusting his aim accordingly, the target shooter can make his misses arbitrarily small, but not always precisely zero.

If the spotter can see the wind only imperfectly, the misses cannot be made arbitrarily small of course. But if the target shooter cannot see the wind, and the spotter can see the wind imperfectly, the target shooter should still respond to the spotter's forecasts. And the difference between the misses when the spotter communicates only his forecasts, vs the misses when the spotter communicates his imperfect observation of the wind, can be made arbitrarily small, but not always precisely zero.

The target shooter is a central bank trying to hit in inflation (or whatever) target at a 2-year ahead horizon with variable "headwinds". (It won't observe the misses until 2 years later.) The spotter is a market forecast of 2-year ahead inflation. Set aside the question of whether the market forecast is better or worse than the central bank's own internal forecast (who can see the wind better), which depends on market participant's incentives to collect and process information on headwinds, and the fact that that incentive will be reduced if the central bank is targeting inflation. Those are good and relevant questions, but not what I'm trying to get my head straight on in this post.

A well-deserved tribute to Nick Rowe

As you may know, Nick has retired from teaching. His career as a teacher and blogger has earned him this very nice tribute in the pages of The Economist:

Learning macro is a source of anxiety for many students. Teaching it can give their professors the jitters, too. The subject is notoriously difficult to explain well. During his 37 years at Carleton Mr Rowe remained, by his own admission, “fairly low down the totem pole” as a researcher. But he became a thunderbird at conveying macroeconomic intuition. In the past decade this served him well in his second intellectual career, contributing to Worthwhile Canadian Initiative, an economics blog. Many a controversy has benefited from one of his ingenious analogies or numerical parables, usually involving some kind of fruit.

 

 

Micro Profs teaching Intro Macro

My crappy little Twitter poll isn't conclusive of course, but it mostly agrees with my priors based on anecdotal evidence, so I think it's probably mostly right.

I think this points to a problem, in two senses:

1. Finding profs willing and able to teach Intro well is not easy. It's low status (and economists dumping on "Econ101" doesn't help); it doesn't help with your research (which is what gives most status and career advancement); and some profs are not good at teaching large classes and explaining things simply and clearly to students who might not be natural economists and who don't know much math. And if more than half the profs in a department (Macro profs are a minority) aren't comfortable teaching the Macro half of Intro, this makes it harder. (This can be ameliorated only partly by having Micro profs teach only Intro Micro and not Intro Macro).
2. As K D said in reply to my Twitter poll: "How in the heck can a person have an econ phd and not understand the basics of both? We all passed qualifying exams. An Econ PhD should be capable of teaching intermediate in both, IMO." He's got a point. Something's not right. It is a puzzle that needs to be explained. But the puzzle is the asymmetry.

I think this problem has always been there (at least in the 40 years I have been teaching Intro), but suspect it's been getting worse over time as the content of graduate Macro has become more different from the content of Intro Macro.

This is what I think is going on:

All teaching benefits from having an intuitive feel for the subject you're teaching. But this is more true for Intro than for more advanced courses in economics. Because the students themselves, being (mostly) new to economics (some have taken it in high school), don't yet have an intuitive feel for the economic perspective, and it's your job to teach it to them. When you are teaching Intro you are going to get all sorts of questions coming out of left field, and you have to do your best to answer them; you can't just crank through the model and point to the equations. Teaching Intro is not like passing a PhD comprehensive exam (though that might say something about PhD comp exams).

Macro profs "get" Micro; Micro profs don't "get" Macro. Macro just feels weird to them.

Yes of course this is a gross generalisation, to which there are many exceptions. But I think there is a real asymmetry here.

If I'm right about that (and Microeconomists can tell me whether they think I'm right), we need to ask why that is. (And it's obviously not because Micro profs are less smart than Macro profs.) Here is my hypothesis:

Macro feels weird to Micro profs because Macro is weird. And Macro is weird because Macro (often implicitly) assumes monetary exchange and Micro doesn't. (Yes I'm back on my hobbyhorse again.)

It's got nothing to do with Macro being about "the economy as a whole" and Micro being about parts of the whole (which we sometimes misleadingly tell our Intro students when trying to explain the difference between Micro and Macro). Yes Macro is (mostly) about "the economy as a whole", but a lot of Micro is too. And Micro profs are comfortable thinking about General Equilibrium as well as Partial Equilibrium.

It's got nothing to do with Money as Unit of Account. Microeconomists are perfectly comfortable treating any good as numeraire, so if you tell them the numeraire is money, because that's what real people use as numeraire, they're fine with that.

I think it's about the role of Money as Medium of Exchange. Which makes general equilibrium, and general disequilibrium when some prices are "sticky", very different from a barter economy or one with a central Walrasian market where any combination of goods can be swapped with any other combination of goods by all agents meeting simultaneously in one big market.

If my hunch is right, then Micro profs should feel more comfortable teaching the Long Run Growth theory part of Intro Macro, because Long Run Growth theory ignores monetary exchange. It's the other part of Intro Macro -- Short Run Macro -- that they won't feel comfortable with. Microeconomists: do you think I'm right about that?

Suppose we introduced Short Run Macro like this:

"Micro starts out with Scarcity and Choice. Then it talks about how people Gain From Trade (exchange), and Markets and Supply and Demand. And you can get Gains From Trade even in a pure endowment economy with no production. But if you add Comparative Advantage (Ricardo) and Economies of Scale (Adam Smith) you motivate Division of Labour in production and the Gains From Trade get even bigger. And what Micro says about all that is important. But Macro adds that trade is very difficult if you don't use money to buy and sell goods. And if something goes wrong with the supply or demand for money, this can make trade more difficult in all markets in which money is used. So some of the potential Gains From Trade are lost, which makes people worse off, and reduces the amount of goods produced. A shortage (excess demand) of money, for example, can reduce demand in all markets where money is used to buy whatever is being sold in that market. And that's a big economic problem."

So I'm asking Microeconomists in particular: if we introduced Short Run Macro that way, would it make more sense to you than Y=C+I+G+NX and Saving and Investment and Income and Expenditure and Aggregate Demand and Aggregate Supply?

[Today (tomorrow if you count Saturdays) is my last day at "work". I'm vaguely thinking about retirement projects.]

Hydraulic Monetarism

There are two ways to increase your stock of money: 1. increase the flow in; 2. reduce the flow out.

There is only one way to increase your stock of any other asset: 1. increase the flow in.

(Unless you are a producer of that other asset. Or unless you are a dealer in that other asset, who both buys and sells and holds a buffer stock of inventory. But we are all dealers in money.)

Money is different because it circulates. That difference matters. If I want to increase my flow in, I must find some other individual who is willing to increase his flow out. Because trade is by mutual consent. And if everybody else is trying to do the same thing as me, I won't be able to find some other individual who wants to increase his flow out. But if I want to decrease my flow out, I can do it unilaterally. Quantity traded is whichever is less: the quantity buyers want to buy; the quantity sellers want to sell.

There is no circular flow of income; there is a circular flow of money. People in a barter economy still have income, when they trade the apples they produce for the bananas they consume, but nothing flows in a circle. And when money flows one way, something else flows the other way. That something else could be anything: newly-produced final goods; inputs like labour land and machine services; intermediate goods; or non-money real and financial assets. And if barter is too difficult, nothing else can flow unless money flows in the opposite direction.

If we observe a buyers' market for one good, it makes sense to ask what has happened to increase the supply or reduce the demand for that particular good. If we observe a buyers' market for lots of goods, it makes sense to ask what has happened to reduce the supply or increase the demand for money. Because every market is a money market: the demand for apples is a supply of money; the supply of apples is a demand for money.

If everyone wants to increase their stock of land, and the aggregate stock of land does not increase to satisfy their desire, there is nothing they can do in aggregate, and there is nothing they can do as individuals. They cannot buy more land (increase the flow in) because nobody is willing to take the other side of the trade.

If everyone wants to increase their stock of money, and the aggregate stock of money does not increase to satisfy their desire, there is nothing they can do in aggregate, but there is something they can do as individuals. They cannot buy more money (increase the flow in); but they can sell less money (decrease the flow out). And as individuals they will do what is individually rational, even though the outcome, like Prisoners' Dilemma, is collectively irrational. So the circular flow of money falls, and the flow of everything else in the opposite direction falls too. And since exchange makes people better off, that reduction in the volume of exchange makes people worse off. We call that a recession.

I've said all this before (and it's all in Yeager and Clower and others). But maybe I've said it clearer this time.

The Parable of the Fruit Trees

The apple producer produces apples. The banana producer produces bananas. The cherry producer produces cherries. Every year they always work exactly the same number of hours and produce exactly the same quantity of fruit.

If you define "recessions" as a decline in output and employment, there cannot be a recession in this economy. By assumption.

But suppose the apple producer prefers eating bananas; the banana producer prefers eating cherries; and the cherry producer prefers eating apples. And the Wicksellian triangle (lack of coincidence of wants) means they use money to buy and sell fruit, because it is difficult for all three agents to meet at the same time at a central Walrasian market and trade all three fruits simultaneously. Then a shortage of money (an excess demand for the medium of exchange) would cause a decline in the volume of trade. Unable to sell as many apples as he wants to sell, the apple producer buys fewer bananas than he normally would. So the banana producer is unable to sell as many bananas as he wants to sell, and buys fewer cherries than he normally would. So the cherry producer is unable to sell as many cherries as he wants to sell, and buys fewer apples than he normally would. Each is stuck consuming too much of his own fruit, and too little of the fruit he prefers to eat.

I would call that a "recession", even though (by assumption) output, employment, and (aggregate) consumption are unchanged. People are worse off, because of a reduction in the volume of exchange, due to a reduction in the circular flow of money around the Wicksellian triangle. (A triangle is just a very small pointy circle.) It wouldn't make much difference to this story if they all decided to work fewer hours and produce less fruit because they couldn't sell it to earn the money to buy the fruit they wanted to eat.

Now let's change the parable slightly.  Each individual's tastes change over time, in a regular circular way. After a year of eating apples, they want to switch to eating bananas. And after a year of eating bananas, they want to switch to eating cherries. After a year of eating cherries, they want to switch to eating apples. But people only eat the fruit they themselves have picked from the trees they own (it tastes better that way). So there is a triangular trade in fruit trees, instead of the original triangular trade in fruit. The owners of apple trees sell their trees and buy banana trees. The owners of banana trees sell their trees and buy cherry trees. The owners of cherry trees sell their trees and buy apple trees. (Like a 3-crop rotation.)

In the new version of the parable, just like in the original version, a shortage of money (an excess demand for the medium of exchange) would cause a decline in the volume of trade. Unable to sell as many apple trees as they want, the owners of apple trees buy fewer banana trees than they normally would. And so on around the triangle.

I would call that a "recession". It looks exactly like the recession in the original version of the parable. The only difference is that in the new version there is no trade in newly-produced goods and services (by assumption); the only trade is in assets -- people exchange fruit trees for money.

And in the new version of the parable it cannot be said that recessions are caused by an excess of (desired/planned/ex ante) saving. Nobody ever saves or wants to save part of their income in this parable (by assumption). They don't even have any "income", in the sense of "monetary income". It is not an excessive desire to accumulate assets that causes recessions; it is an excessive demand for one particular asset (the medium of exchange) relative to other assets. It's about the composition of their portfolios of assets, not about the total size of that portfolio.

Recessions are not about saving and investment. Recessions are about the supply and demand for the medium of exchange. A shortage of money causes a decline in the volume of monetary exchange. The volume of monetary exchange of flows of newly-produced final goods and services is just one part of the story, because those are not the only things that are traded. It's not all about GDP and its components. It's about gains from trade, where trade requires the use of money.

A very simple model of too much city

100 identical individuals choose to live in one of two identical locations. The only thing they care about is how many people live in the same location. Let W individuals choose to live in the West, so 100-W choose to live in the East. The Utility of living in the West is U(W), and the Utility of living in the East is U(100-W), but it's the same U(.) function for both locations. Individuals have zero moving costs, and choose the location with the highest Utility.

Draw a curve for U(W). Then take the mirror-image of that curve (so East and West are transposed) and superimpose it on the first curve. Any point at which the two curves cross is an equilibrium, with the same Utility of living in each of the 2 locations, so no individual has an incentive to move. There is always an equilibrium at W=50, but it may be a stable or unstable equilibrium, and there may be other equilibria.

If the curve always slopes down, U'(W) < 0, the W=50 equilibrium is unique and stable. People dislike crowding, so move away from the more crowded location, until both locations are equally crowded. But that equilibrium does not fit the fact that cities exist.

If the curve always slopes up, U'(W) > 0, the W=50 equilibrium is unstable. People like crowding (there's some sort of Increasing Returns for jobs or amenities), so move towards the more crowded location, until everyone lives in the same location. There are two "corner solution" equilibria: one where everyone lives in the West; a second where everyone lives in the East. But those equilibria do not fit the facts either, because not everyone lives in the city.

So assume the curve initially slopes down, then slopes up, and is upward-sloping when W=50, and then eventually slopes down again, as W gets bigger. We get 3 equilibria: one unstable equilibrium where W=50; and two stable equilibria -- one in which most people live in the West, and one in which most people live in the East. Those two stable equilibria fit the facts; a city exists, but not everyone lives there. So that is the version of the model I will stick to.

The two stable equilibria are identical, except that East and West are transposed. They have the same level of Utility.

Here is the important question: Does the stable equilibrium (where the city exists) have a higher or lower level of Utility than the unstable equilibrium (where half the individuals live in each location)? It could go either way. It all depends on how you draw the curve.

Here is an example where cities are Bad Things, even though most people choose to live in the city:

Here is the intuition: Start in the unstable equilibrium where W=50. Now suppose that one individual randomly moves from East to West. That creates a positive externality for those already living in the West, and a negative externality for those remaining in the East. So that encourages a second individual to move West.

It is the (positive) sign of the difference between those two externalities that determines whether or not there is strategic complementarity (so the second individual wants to follow the first). Which depends on the sign of U'(W). But it is the (positive or negative) sign of the sum of those two externalities (weighted by populations in West and East) that determines whether it is a Good Thing or a Bad Thing for individuals to move West. Which depends on the sign of U''(W).

"Network externality" is a term that fudges that important distinction: the kid who gets a cellphone may create a positive externality for other kids who have cellphones, but a negative externality for other kids who don't have cellphones. Following the herd might be individually rational but collectively irrational. And following the herd might even create a negative externality for those in the herd, but an even bigger negative externality for those not in the herd, which induces others to join the herd but makes everyone worse off. It depends.

The biggest flaw in my very simple model is not that everyone is identical and the locations are identical; it's that I have ignored land rents. Land rents are a way to transfer utility from those who live in the city to those who live outside the city (because you don't need to live in the city to own land in the city).

Thanks to Robert Waldmann on Twitter for fixing my mathos. Robert has a related but more complicated post, but Photobucket has lost his pictures. Alex Tabarrok on Twitter notes that my model is related to one used to allocate cars between two roads. The difference is that drivers always prefer the road to be less crowded (U' < 0), and so the two roads problem is only interesting if the roads are not identical (one road is longer than the other). I don't know how original my model is; because as I keep telling myself, I don't do Urban economics.

"Trickle Down", "Magic Dirt", memes and deep parameters

"Trickle Down Theory" is a meme used (mostly by non-economists) to ridicule certain economic policies and the theories on which those policies are supposedly based. My first year students sometimes ask me to explain it to them, not understanding that it's a meme and not a theory.

"Magic Dirt Theory" is a similar meme, of more recent (and "deplorable") origin (a quick search tells me it's from Vox Day/Supreme Dark Lord). But ideas, including memes, should be evaluated on their merits. Here is a critique of that meme, from a nationalist/conservative perspective.

You have probably heard of "Trickle Down Theory". But only 16% of the (probably unrepresentative) 127 people who answered my Twitter poll (thanks!) had heard of "Magic Dirt Theory". And the percentage was smaller for economists than for non-economists. This is a smaller percentage than I thought it would be, but not trivially small. I don't know whether in the long run it is memes that are powerful for good or evil.

Monetary and Fiscal Federalism, Debt, Canada, and the Eurozone.

A government that undertakes a commitment to target 2% CPI inflation does not, strictly speaking, "borrow in its own currency". Its bonds are an indirect promise to pay, via transversality transitivity (damn!), a specified quantity of CPI baskets of goods and services. In much the same way that bonds under the gold standard were an indirect promise to pay a specified quantity of gold. See my old post.

It is true nevertheless that a government whose bonds are promises to pay money that it itself prints, even if it targets 2% CPI inflation, cannot suffer a liquidity crisis. If there were a run on those bonds, where bondholders wanted to sell and hold money instead, the central bank could and would (to keep inflation on target) simply print as much extra money as people wanted to hold and use it to buy back the bonds they did not want to hold.

It cannot suffer a liquidity crisis, but it can nevertheless suffer a solvency crisis. The Magic Money Tree is real, but not very big. If we assume a currency/NGDP ratio of 5%, and Nominal GDP growing on average at 4% (2% Real GDP growth plus 2% inflation), the Magic Money Tree gives the government that owns the printing press profits worth 0.2% (=5%x4%) of GDP per year. Which isn't very big, and is already built into the government's budget anyway, as the profits from the central bank. In a solvency crisis the government would face a choice between defaulting on its bonds and defaulting on its commitment to not let inflation rise above 2%. Much like a government under the gold standard would face a choice between defaulting on its bonds and defaulting on its commitment to making its money worth a specified quantity of gold. But a solvency crisis like that could not coincide with a deficiency of Aggregate Demand where inflation threatens to fall below the 2% target. Instead it could coincide with an excess of Aggregate Demand, where inflation threatens to rise above the 2% target.

The above describes the Canadian Federal government.

Canadian Provincial governments are different. They do not "borrow in their own currency"; they can't pay their debts by printing money. They can suffer a liquidity crisis and/or a solvency crisis.

Canada is not like other countries. Canadian provinces play a big role fiscally, in taxing, spending, and borrowing. [Can anybody find that lovely graph I saw a few months ago showing Canada at the extreme end of the fiscal federalism measure?] Update: Thanks to Jim Sentance for pointing me to Kevin Milligan's post.

If you drew a line, with a unitary state at one end, and the Eurozone at the other end, Canada is halfway along that line. If you abolish the Federal government, leaving only the Bank of Canada, you get the Eurozone. Eurozone national governments are like Canadian provincial governments.

So what happened in the Eurozone could happen here, at the provincial level, even though it wouldn't be exactly the same. The biggest difference is that someone is in charge who can ultimately control both monetary and fiscal policy at the Federal level and decide who gets bailed out under what conditions.

I am not aware of any problems in the near and foreseeable future. But then I don't trust my foresight. And it may be a good idea to think through how we should respond to problems before they happen, and how we might reduce the probability that they do happen. Under what conditions should the Bank of Canada do a Draghi whatever it takes buying provincial government bonds?

Price Level Targeting targets the Stickiest Prices; Inflation Targeting targets the more Flexible Prices

And it's good to target the stickiest prices; and bad to target the more flexible prices.

It means that recessions under inflation targeting can last as long as it takes for the stickiest prices to change. Which is bad. And it's especially bad for us old macroeconomists, who remember that the whole point of New Keynesian macroeconomics, when it began in the 1970's, was to show that a good feedback rule for monetary policy, unlike a k% money growth rule, meant that recessions did not have to last as long as it took firms to change prices.

Some prices are stickier than others. Here's a simple extreme example to illustrate my point:

Half the firms change their prices every n periods; so a fraction 1/n of them change their price each period. Think of n as a big number, so 1/n is a small number. And they have to announce any price changes one period in advance, to warn their customers (this assumption doesn't matter much). The other half the firms change their prices every period, (without advance warning).

The economy is humming along normally, with all prices constant. Then a negative shock hits aggregate demand. The central bank does not have a crystal ball, so does not see the shock coming. It only learns of the shock when it sees all the flexible price firms cut their prices 10%. How does the central bank respond in the following period?

Constant Price Level Target. The central bank wants the price level to go back to where it was before the shock. So it loosens monetary policy just enough to offset the shock fully, so the flexible price firms raise their prices back to where they were before. The sticky price firms, since they know the central bank will do this, don't change their prices at all. The recession is over after one period (as long as it takes for the central bank to recognise the shock and respond to it).

0% Inflation Target. Since half the firms have cut their prices by 10%, the average price level has fallen by 5%. The central bank lets bygones be bygones, and wants the price level to remain at its new lower level, so inflation stays at 0% thereafter. The central bank knows that every period a fraction 1/n of the sticky price firms will cut their prices by 5%, and to offset this it loosens monetary policy just a little so that the flexible price firms raise their prices by (5/n)%. After n periods all firms have prices that are 5% lower than originally. The economy slowly recovers from the recession, but does not fully recover until all firms have adjusted their price to the new level of aggregate demand. Which means the recession lasts for n periods. After n/2 periods, for example, 3/4 of firms's prices are where they want them to be, but 1/4 of firms still have prices that are too high, so their sales and output is too low.

Intuition. Inflation targeting ignores the levels of prices. It only looks at changes in prices. It wants all price changes to average out to 0% (for a 0% inflation target). So firms that change their prices twice as frequently get twice the weight in the average that the central bank targets. But firms who change their prices twice as frequently should only get half the weight; because they can adjust to aggregate demand shocks twice as easily, and have only half the need for the central bank to adjust aggregate demand so they don't have to change prices.

Other off-topic stuff: A Price Level Target also acts as an automatic stabiliser (for a central bank that sets a nominal interest rate). Because the expected inflation in the second period means the real interest rate falls in the first period. So the shock to aggregate demand is partly offset even if the central bank doesn't see it. And an NGDP level path target would be better still, if there are supply shocks, especially if the Short-Run Phillips Curve is flattish. But all that other stuff is beyond this post.

The Tale of the Two Cobblers (collusive price cuts)

Mostly for fun, and teaching. But I think it might matter.

A village had two cobblers. The right-handed cobbler was best at making right shoes. The left-handed cobbler was best at making left shoes. So the villagers would buy one shoe from each cobbler.

Other villages were some distance away, so the cobblers had monopoly power and faced downward-sloping demand curves for their shoes. Each cobbler set a price to maximise individual profits, taking the other cobbler's price as given. The cobblers were in a Bertrand equilibrium, except the two goods are strict complements, rather than substitutes as is normally assumed.

Then one day the two cobblers fell in love, got married, and set the price for a pair of shoes to maximise their joint profits. They set a price that was lower than the price of a pair of shoes when they were single. The cobblers were happy because their profits were higher. And the other villagers were happy too, because the price of shoes was lower.

Is this (one reason) why firms exist?

Math appendix:

Marginal Revenue is (1-(1/E))P where E is Elasticity of demand and P is Price. A profit-maximising firm wants Quantity sold where Marginal Revenue equals Marginal Cost, and so sets price at P = [1/(1-(1/E))]MC.

The demand function for shoes is Q_R = Q_L = D(P_R+P_L), where (P_R+P_L) is the price of a pair of shoes. If P_R=P_L initially, a 1% cut in P_R, holding P_L constant, will cause only a 0.5% cut in (P_R+P_L), so the elasticity of demand for right shoes (or left shoes) is half the elasticity of demand for pairs of shoes. So when the two cobblers merge, elasticity doubles, and they set Price as a smaller markup over Marginal Cost.

In the initial Bertrand equilibrium, a small cut in P_R, holding P_L constant, will have a negligible effect on profits from right shoes (since we are starting at a point where P_R maximises profits from right shoes). But it will increase the demand for left shoes, and so increase profits from left shoes. So if the two cobblers collude, they would want to collude to cut prices. And each individual cobbler has an incentive to cheat on the collusive agreement by raising price above the joint-profit-maximising price. It's the opposite of the standard case where the two goods are substitutes.

We could relax the assumption of strict complementarity. Results would be similar in any example where the two goods are complements rather than substitutes. Because if one firm cuts price it increases (rather than reduces) the other firm's demand and profits. Mergers and collusion will result in lower rather than higher markups of price over marginal cost.

[I vaguely remember reading about a river in Germany(?) where all the jurisdictions along the river collected a toll on passing boats. And how the sum of the individual revenue-maximising tolls was bigger than the joint revenue-maximising toll. But that's all I can remember. Update: Alex Tabarrok on Twitter tells me it's the "Rhine River Problem", originally from Cournot. In Cournot equilibrium firms set quantities taking other firms' quantities as given (in Bertrand equilibrium firms set prices taking other firms' prices as given). The Cournot equilibrium for the two cobblers is a corner solution where both sell zero shoes (because selling slightly fewer right than left shoes means left shoes have a zero price so the right cobbler gets all the revenue).]

"Profits = Investment - Saving"

Or, "Profits = Expenditure - Income". Those are just alternative ways of saying the same thing, for a closed economy, if investment and saving include government investment and saving.

Most economists will say that's wrong. And it is wrong by standard definitions, where aggregate expenditure and income are the same thing, and investment and saving are also the same thing (for a closed economy, including government investment and saving).

But let me tell you a story:

There are firms and households (ignore government and foreigners). Firms rent land and labour from households, and use it to produce food which they sell to households (ignore capital). There is a fixed stock of currency that is used to buy and sell everything. Food cannot be stored. No other assets.

In any given year, if households spend $100 more buying food than the income they earn from rent and wages, then at the end of the year households own $100 less currency and firms own $100 more currency than at the beginning of the year. Firms have made a profit exactly equal to the $100 difference between households' expenditure and income. Or, firms' $100 profits are equal to households' negative saving (there is no capital and no investment in this story).

But who owns the firms?

If households own the firms, we can say that firms' assets are owned by households, and firms' profits are included in households' income. And if we do that, then we are back at the standard definitions where Expenditure = Income, and Investment = Saving, must always be true.

Or we could adopt an intermediate position: we could say that firms' profits are part of household income only if firms actually distribute those profits to the households that own them. In which case we get: Undistributed Profits = Expenditure - Income = investment - Saving.

There's a number of different ways we could add things up. Which is the best way? It depends.

Suppose firms were like a strange religious cult; they save all their profits for six years, then on the seventh year they blow the lot by spending it all on food which they burn as a sacrifice to the gods. None of the households want firms to do that; it's just what firms do, following some weird internal logic of their organisational structure. If so, you had better build that fact about firms' behaviour into your macroeconomic model. And it would not make sense to include firms' profits as part of households' income, because households know they will never be able to consume firms' profits. (And a corporate profit tax might really be a tax on corporations, and not on the households who own them, work for them, or buy from them.) So Profits = Expenditure - Income = Investment - Saving.

There is no one right way to do the accounting (though there are conventional ways, and it's easier to understand what others are saying if we all follow the same conventions). The accounting can't tell you what the world looks like (though it can help you keep your head straight when you are looking at the world). First decide what the world looks like; then do your accounting accordingly.

[An economist will probably make a comment on this post, and that comment will go automatically into the spam folder. Because Typepad, and history, across this and other macro blogs. But if it's a reasonable comment I will fish it out, after a short delay.]

"Monetary Policy Accommodation" and Upward-sloping IS curves

If you believe that the IS curve slopes up, then what the Bank of Canada says about "monetary policy accommodation" makes sense. If you believe the IS curve slopes down, like in the textbooks, then it doesn't make sense.

This is supposed to be a simple teaching post. My own mind is pretty simple anyway.

The IS equation is D(Y,r)=Y, where D is output demanded (desired expenditure), which depends positively on actual output (=income) Y, and negatively on the real interest rate r.

If we take the total derivative of the IS equation D_ydY+D_rdr=dY, and rearrange, we get the slope of the IS curve as dr/dY= (1-D_y)/D_r. The textbook assumes that 0 < D_y < 1, so the IS curve has a negative slope, because D_r < 0. If instead we assume D_y > 1, we get a positive slope. And if firms don't want to invest when output is low and there is lots of spare capacity, this assumption that D_y > 1, and so the IS curve has a positive slope, may be plausible.

Define the natural rate of interest r* as the solution to D(Y*,r)=Y*, where Y* is "potential output" -- the level of output consistent with inflation staying at the 2% target.

If there is a recession, so Y < Y*, then the Bank of Canada will need to set r below r* just to prevent Y falling even further below Y*, and set r even lower still to get Y to grow back to Y*. The Bank of Canada calls this "monetary policy accommodation".

Here's a picture:

It's more complicated than this of course. It always is. Expectations of future interest rates, output, inflation, and exchange rates, matter too. And it may take time for output and expectations to adjust. The natural rate of interest moves around over time, and a loss of "business confidence" (firms fear demand won't be there to justify investment) may take time to recover. And the IS curve might not slope up everywhere -- it might slope down at very low levels of Y, when gross investment is already zero and can't fall any further. But I think that's the gist of it.

And yes, if the Bank of Canada just sets an interest rate and holds it constant regardless of what happens to output and inflation (so the LM curve is horizontal forever) this is an unstable system (so resist the temptation to say that an upward-sloping IS curve means that if the Bank of Canada cuts the rate of interest this will cause a recession). But the Bank of Canada doesn't do that.

The (In)efficiency of Perfect Price Discrimination

I have always thought, and taught, that Perfect Price Discrimination leads to an efficient allocation of resources. I now think that is wrong. It only seems to work if we use partial equilibrium reasoning, for a single monopolist that practices PPD, holding constant consumers' income and the monopolist's Marginal Cost curve. It doesn't work in general equilibrium. And the easiest way to see this is to construct a counterexample where all consumption goods are produced by monopolists who practice PPD, while the labour market is perfectly competitive.

A PPD monopolist captures 99.99% of Consumers' Surplus by setting a different price for each apple for each consumer, that is 99.99% of that consumer's Willingness To Pay for that apple, down to where the marginal price equals the Marginal Cost of producing an extra apple. So the consumer buys all the apples up to the point where his marginal Willingness to Pay (Marginal Benefit) equals Marginal Cost, but is almost at the point of walking away from the deal and not buying any apples at all. It looks like it works to get an efficient allocation of resources (where Marginal Benefit equals Marginal Cost) if we think partial equilibrium.

But it doesn't work in general equilibrium. If all producers of consumption goods practice PPD, this is like the government imposing a 99.99% marginal tax rate on labour income. It reduces the marginal incentive to work extra hours to earn extra income to buy extra consumer goods to enjoy extra Consumer Surplus by 99.99%, because the monopolists will raise your individual price schedules in response to your increased income to capture 99.99% of your increased Consumer Surplus.

TLDR: if you make the rich pay more, because they are willing to pay more, nobody will do any work to produce anything.

A Balassa Samuelson theory of negative real interest rates despite productive investment and impatient representative agent

I think this is right (but I can't do the math to work out an example to be sure, though any competent grad student could). The idea is that you can get negative interest rates, despite productive investment and impatient consumers, because the prices of the goods you can invest to produce more of will be falling over time relative to goods you can't invest to produce more of. It might be a theoretical curiosum, but it might also be empirically relevant, with falling prices of manufactured goods and falling share of expenditure on manufactured goods, relative to services. And all that.

[And of course, I figure out this model of negative real rates just as it looks like the Bank of Canada will be raising rates soon. Oh well. They are still not very high.]

Here's a toy model, just to illustrate the basic idea:

Don't even try to "Normalise" interest rates

If you think that the rest of the economy is normalised, so it is time to normalise interest rates too, you are wrong. If the rest of the economy is normalised, then interest rates must already be normalised.

Wicksell said there was some underlying "natural" rate of interest. If the central bank sets a rate of interest below the natural rate this would cause inflation; and if the central bank set an interest rate above the natural rate this would cause deflation. So any central bank that wanted to stabilise the price level should aim to set the actual rate of interest equal to that underlying natural rate of interest. And the actual rate of interest would need to be (roughly) equal to the natural rate on average over any extended period of time if we wanted price stability.

We haven't advanced much since Wicksell. The only important thing a Neo-Wicksellian would add is that it's important to distinguish between nominal and real rates of interest (real = nominal minus inflation), so if we have a 2% inflation target we add 2% to the natural rate to get the "neutral" nominal rate. And the actual nominal rate would need to be (roughly) equal to that neutral nominal rate on average over any extended period of time if we wanted to keep inflation stable at 2%.

You can see how this matches the idea of "normalising" interest rates. We've got "normal" both in the sense of an average over time, and in the sense of a desirable norm that central banks should aim for.

But when I hear the words "The Bank of Canada (or some other central bank) needs to normalise interest rates soon" I reach for my shovel. Let me try to tell you why.

The Sustainable Bond-Finance Laffer Curve

Imagine an economy growing at rate g, with an interest rate on government bonds r, and a constant debt/GDP ratio D/Y. The government gains revenue from issuing new bonds gD each year, and loses revenue from paying interest rD each year. If r<g then the government earns positive net revenue from having and maintaining a positive Debt/GDP ratio, and can run a primary budget deficit forever with the debt/GDP ratio staying constant. But r is an increasing function of the debt/GDP ratio (the interest rate must rise to persuade people to hold a higher stock of government bonds, relative to their annual income), so past a certain point r will exceed g. So there is a Laffer Curve, like the one I've drawn above.

Seeing through Sovereign Wealth Funds?

In the first country, the government imposes a 50% flat tax on each individual's income, and uses the proceeds from that tax to finance an annual $10,000 transfer payment to each individual. The government has zero debt.

In an otherwise identical second country, the government has a sovereign wealth fund that owns a 50% non-voting equity share of each individual's personal business, and each individual owns a government bond that pays an annual $10,000 dividend. The government has zero net debt.

In an otherwise identical third country, the government imposes a 50% flat tax on each individual's income, and each individual owns a government bond that pays an annual $10,000 dividend. The government has positive net debt.

In an otherwise identical fourth country, the government has a sovereign wealth fund that owns a 50% non-voting equity share of each individual's personal business, and uses the proceeds to finance an annual $10,000 transfer payment to each individual. The government has negative net debt.

What is the difference between the four countries?

Remember that each individual can borrow or lend to other individuals. An individual in the second or third country can sell his government bonds, but an individual in the first or fourth country can borrow against his future transfer payments.

And each individual can buy or sell shares to other individuals. But there might be a non-negativity constraint here, that I can't quite get my head around. An individual can always issue more than 50% shares in his own business. But I can't figure out how an individual can issue negative shares to bring the total down to 40% if the government insists on owning a 50% share in his business.

Liquidity and risk of default might make a difference. And I haven't said what happens when individuals die or emigrate and new individuals are born or immigrate (things that might make Ricardian Equivalence false). But distorting "taxes" are already in the "model".