Worthwhile Canadian Initiative

Bitcoin as PAYGO Pension Plan. And Land.

Suppose the government starts a Pay As You GO (unfunded) pension plan. What the young pay into the plan today is what the old take out today. The first generation gets lucky; they get a pension paid out, but never put anything in.  And if the plan ever gets wound up, the last generation of old get unlucky; they paid in, but never get anything out.

Bitcoin is the same. What the young pay in to buy Bitcoin today is what the old take out when they sell Bitcoin today. The first generation gets lucky; they sell out at a high price, but bought in at a low price when it was just starting up.  And if the young ever stop buying Bitcoin, so the price collapses to zero, the last generation get unlucky; they paid to buy into Bitcoin, but never get anything out.

The big difference is that Bitcoin is a strictly voluntary PAYGO plan. You don't have to participate in the plan, and if you do choose to participate you can contribute however much you want, and you can pull your money out any time you like.

Now suppose the government starts a fully funded pension plan, that invests in land. If land is the only asset in the economy, and has a perfectly inelastic supply, it's not very different from a PAYGO plan. Or Bitcoin. It doesn't create any new assets for the economy as a whole; it just makes the existing land more valuable. What the young pay into the plan to buy land is what the old take out by selling land. The first generation of landowners gets lucky, because they bought land at a low price and sell it at a high price. And if the plan ever gets wound up, the last generation gets unlucky; they bought land at a high price and sell it at a low price.

At the macroeconomic level, the only difference between funded and unfunded (PAYGO) pension plans is due to the price elasticity of the supply of new assets ("investment"). If it's perfectly elastic, the total physical quantity of assets rises proportionately with a fully funded pension plan. If it's perfectly inelastic, the physical quantity of assets stays the same, but the price of assets rises proportionately with a fully funded pension plan. And you can think of PAYGO pension plans, and Bitcoin, as creating valuable assets ex nihilo, that satisfy the desire to save a stock of assets you can sell later, like a temporary abode of purchasing power.

[Maybe see my old post on the "Junker Fallacy", which isn't a fallacy in an OverLapping Generations model.]

If you wanna run hot you gotta run steady

Canadian economist Richard Lipsey would always insist that the Phillips Curve is a curve, and not a straight line. Maybe because wages and prices are stickier down than up. Or maybe because unemployment can't go below 0%. Or both.

Here's why that matters for macroeconomic policy:

Suppose the central bank wants 2% inflation on average, over the longer term. One way to get that result would be to flip a coin, every year, or every decade, or whatever. If it's heads, the central bank "runs the economy hot", to get 3% inflation. And if it's tails, the central bank "runs the economy cold", to get 1% inflation. If the Phillips Curve were a straight line, you would get exactly the same average unemployment rate, over the longer term, as you would if the central bank kept inflation steady at 2%. But if the Phillips Curve is a curve, and curves the way we normally draw it, you would get higher unemployment on average with that random monetary policy than you would if you kept inflation steady at 2%. And the sharper the curvature of the Phillips Curve, the worse unemployment will be, on average, with a random monetary policy.

That's why macroeconomic demand stabilisation matters. Recessions are bad, and booms may be good, but the bad and good don't cancel out. Relative to where you would be if you stabilised demand, recessions are bigger than booms.

If you add "hysteresis" to this simple story, then macroeconomic stabilisation matters even more. Because a recession has costs that persist even after the recession is over, and those long term costs of the larger recession are bigger than the long term benefits of the smaller boom.

Now maybe 2% inflation is not the right inflation rate to target. Maybe it should be 3%. But that's a separate question, about the Long Run Phillips Curve and whether it's vertical or sloped, and the point I'm making in this post about the Short Run curvature still stands. It's better to target 3% every year than to flip a coin every few years between 2% and 4%.

And maybe inflation is the wrong thing to target. Maybe it's better to target a level-path of NGDP. But again that's a separate question. Or maybe only a partly separate question. Because if supply shocks cause the Phillips Curve to shift up and down, keeping NGDP on target would stabilise unemployment better than an inflation target. And the point of this post is that you need to stabilise unemployment if you want to keep unemployment low on average over the longer term.

And maybe it's not really about Phillips Curves at all. Maybe it's about Milton Friedman's "Plucking Model": there are no booms, only recessions. (What looks like a boom is just the absence of a recession, because recessions can be big or small but booms are all the same, because big recoveries follow big recessions, and small recoveries follow small recessions, but the size of the decline doesn't match the size of the "boom" it follows). Which is like an extreme version of my curved Phillips Phillips Curve story above, where booms are smaller than recessions. And Friedman's Plucking Model always reminds me of Frances' story about her old car: most of the time it ran OK, but if something unexpected happened it was always something bad. The only good news was absence of bad news. Which is how things are with designed systems: they sometimes break down and run worse than the Toyota designer intended, but rarely "break up" and run better than the designer intended. And market economies are a bit like that, though their "designer" is the invisible hand. There can be bad monetary shocks, but the only good monetary shock is no monetary shock.

You can read this post as a critique of "running the economy hot". What do you mean by that, and how can you do it sustainably over the longer term? Or you can read it as a comment on J.W. Mason's recent good post (which I partly agree with and partly disagree with, as always). Or you can just read it on its own.

Loanable Funds Redux

Stop talking about "saving". Talk instead about "demand for assets". You will be happier, and your head will be clearer. Your students too will be happier, and their heads will be clearer.

Demand for assets is a thing; saving is a non-thing (a residual). Things are clearer than non-things. Saving is the part of your income you do not spend on consumption. OK, so what do you do with your income, if you don't spend it on consumption? You buy/accumulate assets.

Assets are things too. Like land, houses, machines, shares, bonds, IOUs, etc. And buying those assets is a thing people do. "Supplying loanable funds" sounds totally different, and much narrower, as well as confusing.

"Demand" is a familiar concept. And we are familiar with the distinctions between: demand curve (or function); quantity demanded; and quantity actually bought. There's no need for novel distinctions between ex ante/planned/desired/whatever vs ex post/actual/whatever.

Assets have prices. And if those prices are flexible, asset prices adjust so that demand equals supply. And if assets pay rents, or coupons, or dividends, or whatever you call those returns, a rise in asset prices means a drop in asset yields. You can call that drop in yields a "drop in interest rates" if you wish, but we don't normally call the rent/price ratio on houses or farmland a "rate of interest".

Talking about "demand and supply of assets", instead of "saving and investment", also clarifies the adding-up condition, so we can better understand and avoid fallacies of composition. Each individual can buy land to own more, but we can't all buy land to own more, unless the Dutch are creating more land ("investment"). So the price of land rises (and the rent/price ratio yield on land falls), until we stop all wanting to buy land. This is very standard; a downward-sloping demand curve shifts right, so it intersects a vertical supply curve at a higher price.

And of course there's a flow/stock distinction to be made when we talk about "demand for assets", just like there's a distinction between the flow of new saving and the stock of existing savings ("wealth"). The flow supply curve of new land is vertical at zero acres (unless the Dutch are doing their thing), but the stock supply curve is vertical at billions of acres.

Anyway: let's ditch that old "Loanable Funds" diagram, with "rate of interest" on the vertical axis, and "Saving" and "Investment" curves, and replace it with a new diagram, with "price of assets" on the vertical axis, and demand and supply curves for the flow of new assets. It's the same diagram. It's just that the old diagram was upside down, and had confusing misleading labels.

OK. That was the simple bit. Now for the difficult bits. Because doing it this way forces us to think about some difficult questions that we couldn't see before, because they had been swept under the rug.

1. Flow saving vs stock portfolio composition. It is standard practice (or at least common practice) for macroeconomists to separate out the Flow Consumption/Saving decision from the stock portfolio composition decision. What we are implicitly doing is taking a massively heterogeneous collection of different assets, then defining a "composite commodity" ("composite asset") that is supposed to let us treat choices about its magnitude and composition separately. Is it legitimate to do this? And if it is legitimate (if that "composite asset" exists), what does it look like? I don't know the answer to those questions. My guess is it probably isn't strictly legitimate to do this, but we can't stop ourselves from doing it anyway. And even if it were legitimate, the composite asset would probably look very different from the safe, liquid, nominal asset ("bonds"?) we have in mind when we talk about "the rate of interest".
2. Money. All assets are different, but the asset that gets used as Unit of Account and Medium of Exchange is more different than all the others. First, because Unit of Account money doesn't have a price of its own -- the price of money is just the reciprocal of the price of everything else. And (unless you believe the general price level is perfectly flexible, which I don't) that makes the price of money sticky. So even if the prices of other assets can easily adjust to equilibrate demand and supply, the price of money can't. Plus, there is only one way for an individual to accumulate more land, which is to buy more land, which means finding a willing seller, which you won't be able to do if everyone wants to buy land and the price of land is sticky. But there is a second way an individual can accumulate more Medium of Exchange money, simply by buying less of everything else, and nobody else can stop you doing that. But if everyone tries to accumulate money by buying less of everything else, we get a fall in the total volume of trade, including trade in newly-produced goods, which is what economists call "a recession". So the central bank needs to do the right thing with the money supply to prevent that happening.
3. Units. When we write down "C+S = Y = C+I" we must be measuring C, S, Y and I in the same units. And this works fine if assets and consumption goods always have the same relative price. But of course they don't (unless assets and consumption goods are perfect substitutes in supply, in which case we would just consume the existing stock of capital goods if we wanted too, and the asset supply "investment" curve would be perfectly elastic). So we can say the stock of land is fixed if we measure it in acres, but the stock of land is certainly not fixed if we measure it in units of the consumption good ("corn"). And if we think about "saving" this way, as a rising value of the stock of assets, measured in consumption goods, it is perfectly possible for everyone to save 10% of their incomes while consuming 100% of their incomes. All that's needed is for the price of land to be rising quickly enough for (realised or unrealised) capital gains on land to equal 10% of income from production of goods.

Anyway, that's enough for now.

Two Price-setting Monopolists Meet in the Street

Two price-setting monopolists meet in the street. One says to the other:

"I will buy 10 more of your overpriced bananas, but only if you buy 10 more of my overpriced apples in return. Deal?"

The second monopolist accepts the deal.

They meet in the street again the following day. One says to the other:

"Instead of me buying those 10 more overpriced bananas today, could I just lend you those 10 more overpriced apples, at the central bank's newly announced overpriced rate of interest, and you can repay the loan next year? Deal?"

The second monopolist refuses this second deal. So both go back to the first deal.

This is basic microeconomics. If a deal makes both parties better off, the deal happens. If a deal makes one of the parties worse off, it doesn't happen.

The first deal makes both monopolists better off (assuming the apple grower likes consuming bananas, and the banana grower likes consuming apples). Because profit-maximising monopolists set Price above Marginal Cost. So the Marginal Benefit of consuming an extra apple exceeds the Marginal Cost of producing it. And the same for bananas. The apple producer doesn't much want to buy an extra banana at the existing price, since his Marginal Benefit from consuming an extra banana equals the price he pays. But he really wants the banana producer to buy an extra apple at the existing price, since the price he gets exceeds his Marginal Cost of producing it. So he gains more from selling 10 more overpriced apples than he loses from buying 10 more overpriced bananas. Same for the banana producer. So the first deal happens. They can even get to the competitive equilibrium this way, even though both apples and bananas are overpriced, if everything is symmetric.

The second deal makes the first monopolist better off, but the second monopolist worse off. Because the central bank has set the rate of interest too high. At the old interest rate, neither wanted to borrow or lend to the other, by assumption. At the new higher rate of interest, each wants to lend to the other, but neither wants to borrow. So the second deal doesn't happen. (OK, they could do a third deal, where one agrees to borrow from the other in exchange for the other borrowing from him, but that third deal is just a wash: it's equivalent to the first deal). If the two monopolists are identical in their preferences for borrowing or lending, there will be no borrowing or lending between them, regardless of the rate of interest. The rate of interest is irrelevant; just like any price is irrelevant, for two identical individuals, who can't gain from trade anyway.

What happens when we introduce a third price-setting monopolist into the story? Now it gets more complicated. It all depends on who likes eating which fruit.

Suppose the apple producer likes eating bananas; the banana producer likes eating cherries; and the cherry producer likes eating apples. We have Wicksell's triangle, with no "double coincidence of wants". That first deal can't happen, unless all three price-setting monopolists meet in the street, at the same time and same place, and agree to a three-way deal. And that's much less likely to happen. And even if it did happen, it's harder to agree to a deal when three people must agree than when only two people must agree.

And that same Wicksellian triangle, which makes it hard for three price-setting monopolists to do the first deal, is also a very traditional economists' story for why people use a medium of exchange ("money"). Money lets them replace one three-person deal with three two-person deals. And that same story is even more compelling if we go from a 3-sided triangle to an n-sided polygon. Money lets them replace one n-person deal with n two-person deals.

And introducing money as medium of exchange into our story puts a totally new perspective on the second deal, where each price-setting monopolist wanted to lend to the other, but the deal didn't happen, because neither wanted to borrow. If you save part of your income by lending it to another person, you need that other person's consent to the deal. But if you save part of your income by simply not spending part of the money you earn, you don't need anyone else's consent. You just spend less money. Done. But if everyone spends less money, then everyone's money income falls too, so the attempts to save by accumulating money work for each but fail for all. The same amount of money just circulates more slowly. We get a recession. And if the n price-setting monopolists in my story had chequing accounts at the central bank, and used those chequing accounts to buy and sell everything else, and if the central bank set the interest rate paid on chequing account balances too high, so everyone wanted to accumulate money, we would indeed get a recession.

[You can read this as a critique, or as a reformulation/reinterpretation, of the canonical New Keynesian model, with its n identical price-setting monopolists, no Wicksellian triangles, with "money" used as unit of account but not, supposedly, as medium of exchange. The model's conclusions (monopoly power makes output too low, setting the rate of interest too high causes recessions) make no sense unless you introduce Wicksellian triangles and a medium of exchange.]

A Simple Micro/Macro Corona Tax Model

I want something you could teach to first or second year economics students. Using tools they already have in their toolkit.

MICRO

Start with a Demand and Supply model of the market for haircuts.

If we put a $1 per haircut tax on buyers of haircuts, the demand curve shifts vertically down by $1, reducing Q* and P*.

If we put a $1 per haircut tax on sellers of haircuts, the supply curve shifts vertically up by $1, reducing Q* and increasing P*.

If we put a tax on both buyers and on sellers of haircuts, both the demand and supply curves shift. We know that Q* falls. We don't know whether P* rises or falls. It depends on which tax is bigger; and it depends on whether demand or supply is more elastic.

The coronavirus is like a tax. Every haircut bought and sold comes with an extra cost to buyer and seller: the buyer risks getting sick; and the seller risks getting sick. (But the "tax revenue" isn't a gain to the government; it just gets thrown away as a net loss to everyone.)

I've drawn the above diagram with a roughly equal "Corona tax" on buyers and on sellers. Because I don't know which is bigger. But I have drawn a demand curve that is more elastic than the supply curve. Because I think that is roughly right, at least for the Short Run. And if demand is more elastic than supply, and the two taxes are the same, then P* falls.

And if the price of haircuts is sticky, and takes time to adjust to the new lower equilibrium price P*, we would see an excess supply of haircuts.

If the Corona tax is big enough, Q* may drop to zero, and the market for haircuts closes down completely.

Even if the Corona tax is not big enough to close down the market, the government might decide to close it down by law. Because the Corona tax also creates a negative externality, because if the buyer or seller gets sick, he or she might also infect other people who aren't buying or selling a haircut. So the Marginal Social Benefit of buying a haircut is less than the Private Marginal Benefit, and the Marginal Social Cost of selling a haircut is greater than the Private Marginal Cost. So the efficient quantity of haircuts Q^ might be zero, even if the market equilibrium quantity Q* is still positive.

Obviously, this will depend on the particular good. It might be efficient to ban the sale of haircuts, but allow people to buy and sell apples. Some markets close, or are closed; other markets stay open.

MACRO

That was Micro. Now lets do Macro, for those markets that do stay open, all lumped together in aggregate. So we are talking about Aggregate Demand and Aggregate Supply.

Eventually (we hope) the risks of buying and selling goods will go away, or at least get smaller. The Corona tax is a temporary tax. We can avoid the tax, by waiting to buy, or waiting to sell, until it goes away (or gets smaller). And the rate of interest is the extra price we pay for buying goods now, rather than waiting till next year; and it's the extra price we get for selling goods now, rather than waiting till next year. (Strictly, it's the real interest rate, which is the nominal interest rate adjusted for inflation.)

So put the real interest rate on the vertical axis, and relabel the curves "AD" and "AS".

Will the equilibrium rate of interest r* rise or fall? In other words, will the Bank of Canada need to raise or lower the rate of interest it sets to keep AD equal to AS (even though both AD and AS are lower than before). In other words, which curve shifts leftwards more, AS or AD?

That depends, on two things: it depends on whether the AD curve shifts vertically down more or less than the AS curve shifts vertically up (is the Corona tax bigger on buyers or on sellers); and it depends on which curve is more elastic (but here we are talking about intertemporal or interest-elasticity -- on how willing buyers and sellers are to postpone buying and selling until next year).

As before, I don't know whether the Corona tax is bigger on buyers or on sellers, so I've drawn it roughly equal. But I've assumed the AD curve is more interest-elastic than the AS curve, so r* falls, and the Bank of Canada needed to cut r. Because that seems plausible to me, and that is what the Bank of Canada actually did.

One big thing this model leaves out is this: buyers of goods expect to be able to buy a much wider variety of different goods (and services) in future than they can buy now. That also shifts the AD curve leftwards for the remaining goods. It's like they learn that they will be able to buy some fancy new device next year, that they can't buy now, and so want to save part of their current income because there are better things to spend their money on next year. See my previous post.

Update 1: A second big thing this model leaves out is that some sellers get hit much worse than others. Unemployed hairdressers might be borrowing constrained, and unable to buy as many apples as they want, because fully-employed apple producers aren't willing to lend to those with a bad credit risk.

[Update 2: I messed up slightly when drawing the two diagrams. If the "tax" on buyers is exactly equal to the "tax" on sellers, the point where the red S curve crosses the blue D curve should be exactly above the point where the blue S curve crosses the red D curve (same Q for both points). Which is the tax incidence irrelevance thing. Oh well.]

Relative supply shocks, Unobtainium, Walras' Law, and the Coronavirus

Here's the basic idea:

A temporary 100% output cut in 50% of the sectors (what the Coronavirus does) is very different from a 50% output cut in 100% of the sectors (what our intuitions might expect from supply shocks in aggregate macro models).

The former can easily lead to deficient demand in the unaffected sectors; the latter leads to excess demand in all sectors.

Here's the intuition:

(As they say: "Shit just got real". And one of my daft old thought-experiments just got very real.)

As you know, unobtainium is a very desirable good. Everyone wants to buy it. But nobody produces it. It doesn't exist.

You could say there's an excess demand for unobtainium, because people want to buy some of it, at any price. Maybe they want to spend half their income on unobtainium. But supply is zero. And if you do say there's an excess demand for unobtainium, and if you also believe in Walras' Law, you get into one helluva mess theoretically, because the excess demand for unobtainium must (by Walras' Law) be matched by an excess supply of other things. So even thinking about unobtainium creates a general glut -- a recession. Which is silly. Because Walras' Law is wrong. Because, as Clower said long ago, it's constrained not notional demands that matter. As I explained in my old post.

But now imagine that someone actually invents a way to produce unobtainium. They can't produce it just yet, but everyone knows they will produce it, and sell it at an affordable price, a few months from now.

What happens when they hear the news? Everybody (or everybody except borrowing-constrained Hand To Mouth agents) suddenly wants to save up to half their income, so they can spend it on unobtainium in a couple of months time. Their money will be worth more in a couple of months than it is now, because they will be able to buy unobtainium with it, and not just all the stuff they can already buy now. We get a general glut (deficient demand) now.

And that is pretty much what's happening with the Coronavirus, in the real world. Half the goods we used to buy are temporarily unobtainium. But we expect to buy them in a couple of months.

It would be very different if unobtainium were a perfect substitute for existing goods, so its invention is exactly like increasing the supply of existing goods in a couple of months. Then we would want to dissave now, like in standard aggregate macro models, because the Marginal Utility of Consumption is high when consumption is low, so we want to prepone consumption from the future to the present. But unobtainium isn't a perfect substitute for existing goods. High intertemporal substitution can beat low cross-section substitution.

(Sure, unlike in my thought-experiment, we used to be able to buy unobtainium in the past. But that's irrelevant; bygones are bygones. It's only the present and the expected future that matter.)

That's why we need temporarily looser monetary and fiscal policy. (Plus, we also need fiscal policy to redistribute between people differentially affected by the Coronavirus, but that's another story.)

Think that's (basically) right.

OK, I've oversimplified (of course). Much of the stuff that's still obtainable is the more essential stuff, like food. But not all. And, at the margin, we still face intertemporal vs cross section substitutibility.

Increased Price Flexibility is Destabilising in New Keynesian Models. (And a Price-Level Path Target is Stabilising)

Start with a very simple New Keynesian "IS" (or "Aggregate Demand") equation:

y(t) = E[y(t+1)] - a[r(t)-r*(t)]

The "real" (inflation-adjusted) interest rate r(t) is defined as the "one period" nominal interest rate, minus expected inflation for the following "one period". In order to stabilise output y(t), relative to expected future output E[y(t+1)], the central bank needs to ensure that the real interest rate r(t) always equals some "natural rate" r*(t), which varies over time as shocks hit the economy.

But the central bank can only do this if it responds to shocks instantly. And that is implausible, because it usually can't see the shocks until after they hit, and after it sees the effect of those shocks on output and inflation.

Let's assume instead that there's a "one period" lag between a shock hitting the economy and the central bank observing that shock and responding to it.

If the central banks sets a real interest rate, it's simple to see what happens when a shock hits. A 1% negative shock to r* causes an a% negative shock to y(t), which lasts for one period, after which the central banks adjusts r(t), and output can return to normal (unless another unexpected shock hits). There's a recession that lasts "one period".

But central banks in New Keynesian models set a nominal interest rate, not a real interest rate. So it's the nominal rate, not the real rate, that stays constant for "one period" after the shock hits. Which complicates things, and makes the recession worse than it would be if the central bank sets a real interest rate.

When the negative shock hits, and the economy goes into a recession, actual inflation falls, and so expected inflation will presumably fall too, so the real interest rate will rise. And that rise in the real interest rate is the exact opposite of what the doctor ordered. And the more inflation falls, and the more expected inflation falls, the more the real interest rate rises, and the bigger the recession will be, and the more inflation falls. There's a nasty positive feedback loop at work.

The best case scenario is if there's a "one period" lag before inflation responds at all. So the central bank, with the same "one period" lag, can cut the nominal rate in response to the shock, before falling inflation and expected inflation worsens the effect of the shock.

In other words, increased price flexibility is destabilising in New Keynesian models.

OK. So what, if anything, can the central bank do about this problem? It can try to improve its crystal ball so it learns about the shocks more quickly, and can better distinguish permanent from temporary shocks, and demand shocks from supply shocks. But unless it finds a perfect crystal ball, some lag between shock and central bank response is inevitable.

It can target the price level (or price level path) rather than target inflation. It can make an advance commitment that if there is a recession, and if inflation falls, it will eventually (when it does respond) bring the price level back up to where it would have been without that recession. It will "repair" its past "mistakes". Which means that expected inflation, between now and "one period" ahead, won't change at all. Which eliminates that nasty positive feedback loop between lower inflation and higher real interest rates that would worsen the effect of the negative shock.

In other words, a price-level path target, relative to an inflation target, acts like an automatic stabiliser in New Keynesian models.

It's more complicated than this, of course. Because I have over-simplified the model by assuming that the central bank has a lag of "one period", and that the only real interest rate that matters is that same "one period" real interest rate.

But you get the gist.

Boiling Frogs - Slow Recoveries are Deep Recoveries, with Flatter Phillips Curves

Andy Harless' tweet (about the US economy) got me thinking.

"There’s a frog-boiling aspect to this economy. The consistent lack of *rapid* improvement throughout the recovery is enabling us to reach levels of employment that might not otherwise have been attainable."

It reminds me of my old post "Short Run 'Speed Limits' on recovery".  The basic idea is simple: actual inflation (relative to expected inflation) might depend not just on the level of employment (relative to some unknown level of "full employment"), but also on the speed at which employment increases.

I've added an epicycle to the Phillips Curve that I think makes it fit the facts better. But I added that epicycle 10 years before the facts that Andy's tweet asks us to explain. And it's based on an idea that make sense, and goes back further still:

It's difficult and costly to increase employment quickly, and easier and cheaper to increase employment more slowly, even for the same cumulative increase in employment. So if demand for output suddenly increases by (say) 10%, individual firms will raise prices and wages relative to the prices and wages they expect at other firms, or raise them more than they would otherwise have done if demand for output had slowly increased by that same 10%. Even with no underlying trend growth in productivity. Even with the same average level of demand for output.

The search/matching approach to understanding the labour market gives us one reason to think that it's more difficult and costly to increase employment quickly rather than slowly. Workers and jobs are heterogeneous. It's a bit like the marriage market. Getting the right match is important, and difficult and costly. And getting the right match between workers and jobs is even more difficult if you have to find a match quickly.

If demand for your output increases, and it's too difficult and costly to increase employment to increase your output to meet that increased demand, you increase price instead. The more quickly demand increases, the more likely you are to increase price rather than increase employment.

Thinking about "discouraged workers" adds something important to this story.

An individual firm can increase employment by attracting workers away from other firms, by increasing its wage compared to other firms' wages. But that doesn't increase aggregate employment; it doesn't work if all firms try to do the same thing. The only thing that happens in aggregate is that wages rise; and so prices rise too. The only way we can get an increase in total employment from increased demand for output is if unemployment falls, or if discouraged workers (who had given up looking for work, or who didn't even start looking, because they thought they wouldn't find a job) are encouraged to enter or re-enter the labour force.

It seems plausible to me that the quickest way for an individual firm to increase employment and output is to raise wages to attract workers who are currently employed at other firms. There's a lot of them, you know where to find them, and you know they can do the job and hit the ground running. Increasing employment by hiring the unemployed will be slower. There's fewer of them, and finding the ones who can do the job will take time, and they may need on-the-job-training to get them up to speed. And increasing employment by hiring discouraged workers will be even slower. Discouraged workers are like unemployed workers, except they are harder to find than unemployed workers, because the unemployed workers are trying to find you.

What this suggests to me is that a quickly-increasing demand for output, following a recession, will result in more inflation than slowly-increasing demand for output, even if you compare those two paths at the point where they cross and have the same demand for output. And a slow recovery in demand will pull more discouraged workers into the labour force, resulting in a bigger labour force and higher total employment, before the central bank needs to stop demand increasing to prevent inflation rising above target.

Hilbert's Hotel and the National Debt when r < g

Hilbert's Hotel has infinitely many rooms. Even if every room is full, you can still make room for one more guest in room 1, by moving the guest currently in room 1 to room 2, moving the guest currently in room 2 to room 3, and so on forever.

When the rate of interest r is less than the growth rate of GDP g ("r < g"), the national debt in an infinitely-lived economy is a bit like Hilbert's Hotel. The government prints some bonds, which it gives (as a freebie) to generation 1 (this is like giving generation 1 a deficit-financed transfer payment, or tax cut). When they get old, generation 1 sells those bonds to the young in generation 2, in exchange for apples. So generation 1 eats more apples when old, and generation 2 eats fewer apples when young. When they get old, generation 2 sells those bonds to the young in generation 3. So generation 2 eats more apples when old, which more than compensates them for eating fewer apples when young (if it didn't more than compensate them, they wouldn't have been willing to buy the bonds at the prevailing market rate of interest). And so on forever.

If r < g, the government never needs to raise taxes to service the debt. It can just rollover the debt + interest, so the debt grows at rate r, while the economy grows at rate g, and if r < g the debt/GDP ratio is falling over time, so this is sustainable. Generation 1 is much better off (it gets free apples), and all subsequent generations are at least a little bit better off (they have a way of saving for their retirement that wasn't available before, and they chose it). A national debt makes all generations better off. There is no burden on any future generation.

But it won't work if the economy has a finite life; just like Hilbert's Hotel won't work if it has a finite number of rooms. The last generation is stuck with bonds it can't sell, and no compensation for consuming fewer apples when old young. So they wouldn't buy the bonds, and the whole thing unravels backwards. Unless the government raises taxes to retire the debt before the economy ends, but then those taxes would make the generations that pay them worse off.

Can we safely assume that the Canadian economy is infinitely-lived? No. But how much does this matter, if the Canadian economy will likely last for a very long time?

One way to tackle this question, and the one I'm going to use here (though there may be other better ways), is to start out with a finite-horizon economy, that survives for H periods, then ask what happens as H approaches infinity. Does the burden of the debt on the final generation approach zero as H approaches infinity? If so, this is not a problem we should worry about much.

I'm going to look at two examples. Both those examples will assume r=0 (to keep it simple for me, but not totally unrealistic at the moment, if we interpret r as the real (inflation-adjusted) interest rate, and g as the real growth rate).

In my first example, population is assumed constant, and all the GDP growth is coming from productivity growth, so GDP per capita grows at rate g. In this case I think the burden of the debt on future generations can be ignored. Even though the debt stays constant over time measured in apples (since r=0), future generations get richer and richer, so if we assume diminishing Marginal Utility of consumption, the burden of the debt on the final generation, measured in disutility, gets smaller and smaller, presumably approaching zero, as the horizon H approaches infinity. (Strictly, I need more than diminishing MU for this result; MU must approach zero in the limit as consumption approaches infinity, but I'm OK with that.) So Hilbert's Hotel still works in the limit (it's like the rooms get bigger and bigger as the numbers go up, so it's no big deal to squeeze two guests into the last room).

In my second example, per capita GDP is assumed constant, so all the GDP growth is coming from population growth. In this case I think the burden of the debt on the final generation cannot be ignored. Even though the per capita burden (whether measured in apples or disutility) shrinks as the population grows, we are multiplying that per capita burden by a growing population, so the total burden on the final generation does not approach zero as the horizon H approaches infinity.

Based on these two examples, my guess is that we should replace the "r < g" condition with an "r < per capita g" condition, if we are looking for the condition under which we can talk about sustainable debt-finance and reasonably ignore any burden on future generations. (We've also gotta be careful to distinguish between the average burden of the existing debt vs the marginal burden of extra debt, since extra debt could be a Bad Thing even if the existing level of debt is a Good Thing, though that is a topic for another post.)

[I thank someone who's name I have forgotten, but I think it was a commenter on an old post, for suggesting the relevance of Hilbert's Hotel, which I only DuckDuckGo'd last night. And I thank Ivan Werning and Foggy Anabasis for their replies on my initial Twitter musings on this topic. All without implication of course.

And yes, I am out of my math depth (or beyond my limits) on this question.

And though it sounds utterly arcane, it does seem to be policy-relevant, given current low interest rates.

And BTW, please leave a space either side of < and > in comments, because Typepad sometimes goes html nuts if you don't.]

On not "running out of ammo": Monetary Policy as Farmland Price Policy

Imagine a central bank that pegs the price of farmland. It announces it will buy or sell unlimited amounts of farmland for $10,000 per hectare. So "one dollar" doesn't mean some number of ounces of gold; it means "one square meter of farmland".

So the central bank owns farmland, which it rents out to farmers at market rents. It uses those rents to pay for paper and ink and economists' salaries, and gives the rest to the government which owns the central bank.

Or it could have a crawling peg, so the price of farmland always appreciates at 2% per year (or whatever).

That central bank policy would influence interest rates. Because if land is expected to yield a (say) 1% rental return, plus 2% appreciation, land will yield a total nominal return of 3%. And lenders will compare the interest rates they earn by lending money to the 3% they could expect to earn by buying land instead. By setting a crawling peg that crawls at 3% instead of 2%, the nominal rate of return on land would rise from 3% to 4% (if the rental return stays the same), and nominal interest rates would rise too. But the central bank would not set any market rate of interest.

Or it could have an adjustable crawling peg. If CPI inflation were too low, and the bank wanted it higher, it could raise land price inflation. If CPI inflation were too high, and the bank wanted it lower, it could reduce land price inflation. Just like Irving Fisher's Compensated Dollar Plan, only with farmland replacing gold.

Could this central bank ever "run out of ammo", and find itself unable to create inflation? Is there any parallel to the alleged Zero Lower Bound constraint for central banks that set a rate of interest?

No.

Yes, the central bank could run out of farmland to buy. If everyone prefers owning currency to owning any farmland. But in that case the central bank can simply announce a new crawling peg that crawls faster than the old one, so farmland appreciates more quickly, so people will be more willing to own land instead of currency.

Plus it could reduce the risk of that happening, for a given crawling peg for farmland, by buying other assets too, so there's more currency in public hands for any given amount of farmland in public hands. But in the last resort, when it runs out of any suitable assets to buy, it could simply make the crawling peg crawl faster.

Loosening monetary policy, by making the crawling peg crawl faster, causes higher nominal rates of return on owning land, and so higher nominal interest rates. Nominal interest rates that are too low mean monetary policy that is too tight.

Central banks (unless they run out of paper and ink) simply cannot "run out of ammo" to create inflation. The idea that they can "run out of ammo" is a fallacy that comes from the Neo-Wicksellian heresy of thinking of monetary policy as interest rate policy.

We don't need no stinking fiscal policy to create inflation.

Yes of course farmland is heterogeneous, so implementing this particular policy has some practical difficulties. So what; it's a thought-experiment, just to show how monetary policy works. Use an index of farmland prices, or crawling peg the stock market total return index instead. Monetary policy is not interest rate policy.

Conflict of interest declaration: I own some farmland.

Update: heading off canoeing tomorrow. May be slow responding to comments.

Alpha Beta and the Libra Twist

Suppose I promise to be in the same place as you; but you make no promise to be in the same place as me. Then I am Beta follower and you are Alpha leader; because you go where you want to go and I must go to the same place to keep my promise.

We get the same Alpha-Beta relationship with asymmetrical fixed exchange rates. If the US Fed decided (for some unknown reason) to peg the exchange rate of the US dollar to the Canadian dollar, but the Bank of Canada makes no such promise the other way, then the US Fed becomes the Beta follower and the Bank of Canada becomes the Alpha leader. US monetary policy is now decided in Ottawa.

It's the same Alpha-Beta relationship between central bank and commercial banks. The Bank of Montreal pegs the exchange rate of the BMO dollar to the Bank of Canada dollar; but not vice versa. So the Bank of Montreal is Beta follower to the Bank of Canada's Alpha leader. The Bank of Canada decides Canadian monetary policy, not the Bank of Montreal.

Now let's add the Libra twist to this simple story.

Suppose I promise to be at a point midway between you and Alice; but you and Alice make no promises about where you will be relative to me. I am Beta follower. But Alpha leadership is now shared 50-50 between you and Alice.

If I understand it correctly (I quite possibly don't) Facebook's new Libra currency is supposed to be pegged to a basket of international currencies. Libra is then a Beta follower, just like a normal commercial bank. But unlike a normal commercial bank, which follows only one Alpha leader central bank, Libra will be following a basket of several central banks. So Alpha leadership is now shared (in proportion to those basket weights) between those central banks.

Which is an interesting twist.

My guess is that Libra will not take off into wide usage (JP Koning's good post explains why). But suppose it does take off, and replaces the money created by normal commercial banks which follow only one central bank each. What happens if the US Fed wants to loosen world monetary policy and the ECB wants to tighten? It's like you and Alice both running off in opposite directions, each trying to run faster than the other, to get me to follow in your direction rather than her direction and vice versa.

Update: it's like Libra creates the incentive for a Tug-of-War between the Fed and the ECB, with Libra tied to the middle of the rope. Except that it's not a rope but a very elastic rubber band.

This doesn't look like a stable equilibrium to me.

Accounting Identities and the Implicit Theory of Inertia

Animals can be divided into Carnivores and Non-Carnivores: A = C + NC. Therefore, if we add some wolves to an island of sheep, the number of animals on that island will increase.

It's easy to see why that argument might not be right. Wolves kill sheep. But if you didn't know that fact about wolves and sheep, the argument looks very appealing. But the equation A = C + NC tells us absolutely nothing about the world; it's an accounting identity that is true by definition. The only thing it tells you is how I have chosen to divide up the world into parts. And I can choose an infinite number of different ways to divide the world up into parts.

Here are two more examples:

1. Y = C + I + G + X - M. Therefore an increase in Government spending will increase GDP.

2. Y = C + S + T. Therefore an increase in Taxes will increase GDP.

My guess is that you are much more uncomfortable with the second of those two examples than the first. You have probably seen the first argument before, but have probably not seen the second. But they are both equally correct accounting identities and are both equally rubbish arguments.

How can a purely arbitrary choice of which accounting identity I write down make any difference at all to how we think about the world?

I call it "The Implicit Theory of Inertia": We assume a thing will keep on doing the same as it would otherwise have done, unless you give me a good reason why it wouldn't. The onus is on you to explain why more wolves would mean fewer sheep, and unless you give me a good reason I will assume that the number of sheep stays the same (or keeps growing or declining at the same rate) regardless of the number of wolves. You need the force of a good argument to overcome the assumed inertia of things. So by choosing one accounting identity over another, I am dividing the world up into one set of things rather than another, and then exploiting your Implicit Theory of Inertia to rig the argument in my favour.

Sadly, we don't just fool other people when we write down accounting identities to divide the world up one way rather than another. We fool ourselves too.

Theorising starts when we write down the variables.

Fiat Bling

I visited a country where people wore paper money as jewelry. Richer people wore larger denomination notes, to signal how wealthy they were, and poorer people wore smaller denomination notes. Only the very poorest wore none at all.

Then I learned the paper money wasn't used as money. They only produced one homogeneous good called "corn", so didn't need a medium of exchange. What I thought was money was in fact bling.

Bling was issued by the central bank. It wasn't bling unless it had the authorised signature of the central bank's governor, and wearing forged bling was severely punished by ridicule. The governor's signature was performative; the Governor said "Fiat bling", and there was bling.

Commercial banks also issued bling. But commercial bank bling was convertible on demand, at par, into central bank bling. And commercial banks need sufficient assets (central bank bling, corn, promises to pay future corn or bling) to give people confidence that convertibility could be maintained.

Different banks issued bling in different colours. And different people preferred different colours, with some preferring a mix of colours. So the varieties of bling were substitutes, but imperfect substitutes.

It is easy to understand that commercial bank bling would be valuable, given commercial banks' promise to maintain convertibility at par into central bank bling. But what made central bank bling valuable? In the olden days central bank bling had been redeemable for gold, but fashions had changed, so paper bling had replaced gold bling (it was more comfortable), and gold convertibility had been suspended, temporarily at first, and then permanently.

What made fiat bling valuable was simply demand and supply. The demand for bling (Md = P.L(Y,r), where Md is the stock of bling demanded, P the price of corn in terms of bling, Y the level of corn income, and r the nominal interest rate on loans of bling, and thus the opportunity cost of wearing bling), together with a central bank that limited the supply of bling, created an equilibrium with a positive stock of bling (M > 0) with a positive value (P < infinity). Some academic theorists worried about a possible second equilibrium, in which a self-fulfilling belief that fiat bling was worthless would cause people to stop wanting to wear worthless bling; but normal people's customary belief that fiat bling was valuable prevented that happening. Plus they knew the central bank had enough assets to buy back all the bling if it really needed to.)

There are many ways the central bank could limit the supply of bling. Simply fixing Ms (or the growth rate of Ms) would be one way. But the central bank in this country instead chose to control the rate of interest r at which it would lend bling. If the price of corn in terms of bling was rising too quickly, the central bank would raise r to discourage borrowing of bling; and if the price of corn in terms of bling was rising too slowly the central bank would cut r to encourage borrowing of bling. So the stock of bling in public hands was determined by the stock of bling demanded at the rate of interest set by the central bank.

A shortage or surplus of bling might affect people's ability to signal their wealth. But central bank policy didn't affect the rest of the economy. Self-sufficient people kept on consuming the corn they produced regardless of anything the central bank did, lending or borrowing corn between themselves depending on who had a relatively better or worse harvest. The only thing that caused aggregate production to fall was bad weather across the whole country.

Robinson Crusoe and the Carbon Tax Rebate

Suppose I impose a carbon tax on Robinson Crusoe. But I give him a rebate exactly equal to the tax he pays. That tax plus rebate will have no effect on Robinson Crusoe's behaviour. He knows that if he cuts carbon by 1kg, and pays $1 less tax, his rebate also falls by $1, so his net tax (= tax minus rebate) stays the same. He has no incentive to cut carbon.

Now imagine an archipelago of 100 identical islands, each with one identical Robinson Crusoe clone. And suppose I impose the same tax per kg on each of them, but give each one a rebate equal to 1% of the total tax I collect from all.

You might think the result would be exactly the same. But it's now very different.

Each of the clones knows that if he were to cut carbon by 1kg, and pay $1 less tax, while the 99 other clones kept doing the same thing, his rebate would fall by only $0.01, so his net tax falls by $0.99. Which gives him an incentive to cut carbon.

In the new equilibrium (we call it a "Nash Equilibrium") they all cut carbon by the same amount, and so each gets a rebate equal to the tax he pays. But each knows that if he alone were to move away from that equilibrium, by increasing carbon, his net tax would increase by $0.99 per 1kg of extra carbon. Which is sufficient incentive not to move away from that equilibrium. Which is what makes it an equilibrium.

It's like a competition, where each entrant has to put the same $10 into a pot for prize money, and the total pot is divided between them in proportion to how quickly they each run. That creates an incentive for each to try to run faster relative to all the other competitors. Only if they all collude, and collectively agree to walk the race slowly, and none cheats on the agreement, would the incentive fail. Except the carbon tax works in reverse, because they pay money into the pot in proportion to how much carbon they create, and share the pot equally. So they compete to create less carbon.

What is true for each of the parts is not necessarily true for the whole, and vice versa, even if each part is identical to the others. What is individually rational is not necessarily collectively rational, and vice versa, even if each individual is identical to the others. Prisoner's Dilemma is one example that illustrates this point. My carbon tax example is another.

This post is not really about the carbon tax. I know nothing useful about the carbon tax, except for this one point. It's about teaching economics. The point I am making above is true and important, but it is not obvious. Teaching is hard.

Maybe what non-economists don't get is not income effects vs substitution effects; it's the Fallacy of Composition and the difference between individual rationality and collective rationality. Free riders, collective choice problems, and all that. (If there were no difference we wouldn't need a carbon tax anyway.) And the best way to explain the difference is in a representative agent model, because the difference is at its starkest and clearest in a symmetric equilibrium.

[Update: I changed the title from "Robinson Crusoe and the Carbon Tax". Because it dawned on me that it's about the rebate, not the tax.]

Interest Rates and Money Growth; Two Types of Central Bank

I want to imagine two different types of central bank. The first type of central bank cuts nominal interest rates to increase money growth. The second type of central bank raises nominal interest rates to increase money growth. In both cases the increase in money growth causes Aggregate Demand to start growing, and eventually causes the inflation rate to rise. But the initial change in interest rates is the opposite in the two cases.

Here is a simple example of the first type of central bank. It issues currency which pays the holder 0% nominal interest. It sets a rate of interest at which it will freely lend that currency to all (safe) borrowers. If it wants to increase money growth, it cuts that rate of interest, so people borrow more currency from the central bank.

Here is a simple example of the second type of central bank. It issues demand deposits (chequing accounts) which pay a rate of interest set by the central bank. The stock of money in those chequing accounts grows at that rate of interest, so if it wants to increase money growth it raises that rate of interest.

Eventually, of course, the first type of central bank will need to raise nominal interest rates, above where they were initially, to match the higher inflation rate, to restore real interest rates to where they were initially, to prevent money growth and inflation spiralling ever-upwards. (The second type of central bank doesn't need to worry abut that.) So they end up in the same place eventually. But the way they get there is very different.

I think that most macroeconomists have something like my simple example of the first type of central bank at the back of their minds. I am unsure what Neo-Fisherians have at the back of their minds, but if it were something like my simple example of the second type of central bank, that would make sense of what they say.

Simple New Keynesian models assume the central bank sets a rate of interest, but are silent on money growth. Or, if they do add a money demand equation, this extra equation has no effect on the rest of the model. Which means that New Keynesian models are ambiguous between an orthodox and Neo-Fisherian interpretation.

Real world central banks are more complicated than either of my two simple examples, but contain elements of both.

The lesson I want you to draw from this post is that thinking of central banks setting a rate of interest and that rate of interest affecting desired investment and desired saving is a very inadequate way of thinking about monetary policy. A better way to think about monetary policy is to think of central banks setting a rate of interest in order to influence money growth. The exact mechanism by which central banks use an administered interest rate to influence money growth can vary, and even the direction of that effect can vary too. The rate of interest set by the central bank matters because, and only because: it affects money growth; it may affect the spread between the interest rate paid on money (if any) and the interest rate (or yield) of other assets, because the velocity of circulation of money will be a positive function of that spread. MV=PT.

Inflation and the Debt/GDP ratio

I'm trying to write a simple explainer. The best way to understand how inflation affects the debt/GDP ratio is to start out with a scenario where it doesn't. Then look at ways in which the real world is not like that scenario.

Here's the "No Effect" scenario: The Bank of Canada suddenly decides to raise the inflation target by one percentage point (1ppt). Like from 2% to 3% (which is a 50% increase, which is why I'm being picky and saying 1 ppt instead).

Assume that inflation immediately increases by 1ppt, but real GDP (RGDP) growth is not affected, so nominal GDP (NGDP) growth immediately increases by 1ppt.

Assume that expected inflation also immediately rises by 1ppt, and that nominal interest rates also immediately rise by 1ppt (because borrowers and lenders only care about real interest rates, which are unaffected in this scenario).

Assume that the nominal interest paid on all government bonds also immediately rises by 1ppt (because those bonds have a very very short term to maturity, so all get immediately rolled over at the new higher nominal interest rate).

Assume that nominal government spending and tax revenues also immediately grow 1ppt faster (so real government spending and taxes are unaffected).

In this scenario, the nominal debt grows 1ppt faster, but NGDP grows 1ppt faster too, so the nominal debt/NGDP ratio is unaffected by the higher inflation rate. Everything just scales up ("inflates") in the same proportion. But nothing "real" (inflation-adjusted) changes.

To see why, note that the "primary" deficit (the deficit ignoring interest on the national debt) stays the same as a ratio of NGDP. But the "full" deficit (including interest on the national debt) increases by the 1ppt increase in nominal interest times the national debt. So the debt is growing 1ppt faster than before. Just like NGDP is growing 1ppt faster than before. So the ratio of the two is unaffected by inflation.

The main reason that scenario is wrong is because things don't all change immediately. There are lags. And all those lags tend to work the same way: they make the debt/GDP ratio tend to fall initially when the Bank of Canada decides to increase the inflation target.

1. The first important lag is due to the fact that government bonds do not all have a very very short maturity. Take the extreme opposite case: suppose all bonds are perpetuities, that never mature, but pay a fixed coupon every year forever. In this case the interest on the previously-existing debt is unchanged by higher inflation. So higher inflation causes the debt/GDP ratio to start falling over time. In the simple case where the government keeps the budget balanced, so issues no new debt, 1ppt higher inflation alone will cause the debt/GDP ratio to fall by 1% (not 1ppt) every year, so it halves in 70 years (because it causes NGDP to double while debt stays the same). And a 2ppt inflation increases alone will halve the debt/GDP ratio in 35 years, etc.

The real world has a mixture of government bonds, of varying maturities, so it's somewhere between my original scenario and the extreme opposite case. (And some bonds are indexed to inflation, so the interest rate rises immediatly with inflation.)

2. The second important lag is that nominal interest rates may not immediately rise when the Bank of Canada decides to target higher inflation. They may even fall initially. This is especially likely if the Bank of Canada keeps its decision secret. An essential part of modern inflation targeting is that the Bank of Canada clearly announces its commitment to keeping inflation at the 2% target, and it's hard to imagine the Bank of Canada raising its target in secret. But before the 1990s central banks did not have explicit inflation targets. And actual inflation depends on expected inflation, as well as on what central banks do. So a central bank could cut nominal interest rates, and inflation would eventually rise, and expected inflation would eventually rise too, when people saw that higher actual inflation, and eventually learned it wasn't just a temporary blip but was likely to continue, because it had continued.

So if the Bank of Canada secretly reneged on its commitment to target 2% inflation, and lowered nominal interest rates, it might take decades before people fully understood what had happened, and the Bank of Canada needed to raise nominal interest rates, 1ppt higher than they were initially, to bring real interest rates back to where they were initially, to prevent inflation spiralling even higher. And in the meantime the debt/GDP ratio would be falling, due to nominal interest rates being lower than the 1ppt increase in my original scenario.

[But notice something interesting about the interaction between my 1st and 2nd lags: the second lag (lower nominal interest rates) only matters when the bonds are rolled over and refinanced at the new interest rate. So in the extreme case where all bonds are perpetuities, the second lag wouldn't matter for existing debt.]

There may be other effects. Like if the tax and benefit system is not fully indexed to inflation. Or if a secret decision to target higher inflation causes temporarily higher real GDP. But I think I will stop there.

But there's one historical question that's stuck in my mind and that I don't have the answer for. How much of the history of the debt/GDP ratio, from the end of WW2 until when things had mostly settled down to the 2% inflation target (say 2000?) is a story of the rise and then fall of the inflation rate? Not all of it, obviously, because other things happened too. But my guess is that an important part of it is. We didn't just grow our way as (in part) inflate our way out of a high debt/GDP ratio, and then it went into reverse as inflation came back down again. It's as if the government has a valuable reputation for keeping inflation low, and it can spend that reputation bringing the debt/GDP ratio down, and then suffers the costs of re-investing in that reputation if it wants to bring inflation down again. But lots of other important things mattered too, and history is the net effect of all those things. (And my thought-experiment above, where the Bank of Canada secretly raises its inflation target, is hard to imagine happening today, but much more applicable to the time before explicit inflation targets.) But I don't know what the post WW2 counterfactual would have looked like.

"Are we at full employment yet?"

I vaguely remember having seen this movie before, the earlier British version. And it's a frustrating movie to watch, because nobody knows where full employment is, except maybe when we've driven past it and can see it in the rear-view mirror. And the question itself always gets confused between asking where full employment ought to be, according to someone's map of an ideal world, and where it actually is, given the world as it is, and what can be achieved with aggregate demand policy alone.

If deviations of inflation from target responded instantly and consistently to deviations of employment from full employment, we wouldn't need to ask the question. Just keep inflation on target, and employment will look after itself. And if you think that "full employment" thus defined isn't ideal enough for your world, then OK, tell us what microeconomic (non aggregate demand) policies you would like to use to try to improve things.

But deviations of inflation from target don't respond instantly and consistently to deviations of employment from full employment. Inflation is a lagged and noisy signal. And inflation targeting itself, it seems to me, has made inflation an even more lagged signal, with an even lower signal/noise ratio. Divine coincidence doesn't work very well, and basing your policy on it seems to make it work even less well. So we still ask "Are we at full employment yet?" in order to try to keep inflation on target.

The main cost of overshooting full employment is not the inflation that results from doing so. The main cost is the cost of the extra unemployment when you bring inflation back down again. I've seen that movie before, in the 1980's, and I don't want to see it again.

Set aside the other benefits of switching from an inflation target to an NGDP level path target. If switching targets meant we wouldn't need to ask "Are we at full employment yet?" in order to figure out whether monetary policy is too tight or too loose, that would be a major advantage. Because it's a question we can't answer until it's too late. Instead we would simply hope that we are not at full employment yet: we would hope that target NGDP growth would in future be composed more of real GDP growth and less of inflation. And we would be forced to concentrate instead on microeconomic policies that might improve that composition.

Are Open Market Operations wrong-signed when nominal rates are negative? (No)

I'm going to start out with a silly unrealistic thought-experiment. Then I'm going to say why I think my silly unrealistic thought-experiment might matter.

A central bank issue two types of money: $1 notes; and $100 notes. The two types of money are not perfect substitutes: the $1 notes are convenient for small purchases; the $100 notes are convenient for large purchases. The central bank is willing to exchange $1 notes for $100 notes at a fixed exchange rate of 100 to 1. There are no other denominations, no other banks, and no other forms of money.

The $1 notes and $100 notes pay the bearer a nominal rate of interest that is chosen daily by the central bank. Those two rates of interest can be the same or different, and can be positive or negative.

1. Suppose the central bank sets the same rate of interest on both notes. What happens if the central bank cuts that rate of interest, holding the total $ value of the stock of notes constant? That's an easy question to answer. The opportunity cost of holding money increases, so the demand for money falls, the Velocity of circulation increases so MV rises, so Aggregate Demand increases. It's an "expansionary" monetary policy. It doesn't matter whether the interest rate is positive or negative.
2. Suppose the central bank always sets the rate of interest on $1 notes at 0%. What happens if the central bank cuts the rate of interest on $100 notes, holding the total $ value of the stock of notes constant? That's a slightly harder question to answer, but I think the answer is qualitatively the same as in the previous question above. It's still an expansionary policy, because the opportunity cost of holding money has increased, on average, so the demand for money has decreased, though it's less expansionary than the first policy. But the answer is complicated by the fact that some $100 notes will be exchanged for $1 notes, so the composition of the money supply changes, even though the total stays constant.
3. Suppose the central bank wants to change the composition of the money supply, so there are more $1 notes and fewer $100 notes in public hands, holding the total $ value of the stock of notes constant. And it adjusts the rate of interest on $100 notes, holding constant the rate of interest on $1 notes, to hit that new target for the composition of the money supply? The answer to question 3 is the same as the answer to question 2 above. It's the same question, except the exogenous and endogenous variables have been swapped in the central bank's targeting perspective. If the central bank buys $100 notes and sells $1 notes, and adjusts the rate of interest on $100 notes so the exchange rate stays at 100 to 1, it's an expansionary policy, even though the total money stock stays the same. Because the rate of interest on $100 notes will fall.

The above thought-experiment was a metaphor. The "$1 notes" in my thought-experiment stand for all central bank money (currency and reserves). The "$100 notes" in my thought-experiment stand for Treasury bills. My policy experiment 3 above stands for an Open Market Operation where the central bank buys Treasury bills.

And if my thought-experiment metaphor is correct, Open Market Operations still have the "right" sign, even if nominal interest rates on Tbills are negative, and even if Tbills are used as money, and even if those negative nominal interest rates on Tbills indicate that Tbills are more liquid (more money-like) than the money (currency and reserves) issued by the central bank.

Which might matter again soon, if pessimistic forecasts turn out to be right.

[Liquidity Preference is a bad theory of "the" rate of interest, but a good theory of interest rate differentials (people prefer more liquid to less liquid assets, other things equal). Silvio Gesell was right about interest on money being what matters for Aggregate Demand.]

Explaining S=I: Inventories vs Adding up Individuals

It's easy to teach students the arithmetic showing that actual saving must equal actual investment (S=I). But many students (quite rightly) want more than the arithmetic. Because S=I is not intuitive, and good students want to understand the intuition. I think that most profs will try to explain the intuition by talking about inventories of unsold goods. But I think it would be better to explain the intuition behind S=I by talking about the difference between individual saving and aggregate saving; some types of individual saving don't add up to aggregate saving.

A student's email is what prompted me to write this post. He's read three textbooks on the subject, and has read my old post, and understands the arithmetic, but still doesn't understand the intuition. Here's one of his questions: "Or, suppose I buy a used car. Is it saving? How will in this example saving be equal to investment?". Here's how I would answer his question: "Yes, your buying a used car is saving, because you spent part of your income on something that is not a newly-produced consumption good. Which is how we define "saving" in National Income Accounting. But someone else must have sold you that same used car, so if you were saving (buying an asset), that someone else was dissaving (selling an asset). It is impossible for everyone to save by buying used cars."

Keynesian Beauty Contest SRAS shocks

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

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

 

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

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

But the SRAS and LRAS curves may also shift.

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

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

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

Here is a story of SRAS shocks: