Worthwhile Canadian Initiative

"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".

Negative Average Cost but Positive Marginal Cost of Debt-Finance

If the rate of interest on government bonds is less than the growth rate of the economy (r<g), then the average cost of bond-finance is negative. A government that has issued bonds, and issues more bonds each year to keep the debt/GDP ratio (B/Y) constant (which is sustainable), can have permanently higher spending, or permanently lower taxes, than an otherwise identical  government which has issued no bonds. Issuing bonds is a (permanent) source of government revenue. Bonds are not a "liability" in the normal sense of the word.

But it is important to distinguish between average cost and marginal cost. Unless the demand for government bonds is perfectly elastic, an increase in the debt/GDP ratio will increase the equilibrium rate of interest required for people to be willing to hold those government bonds. So the government is like a monopsonist facing an upward-sloping supply curve of finance, and the marginal cost of extra bond-finance will exceed the average cost of all bond-finance. The marginal cost of increasing the debt/GDP ratio might be positive even if the average cost is negative. It all depends on the interest-elasticity of demand for government bonds.

I will now try to do the math.

Monetary tightening can lower real interest rates

It's the investment accelerator. Monetary tightening means lower expected NGDP; real interest rates can go either way. Think of this as a teaching post, to explain the intuition. Or look at Miles Kimball's great post.

Here's a thought-experiment. Do not take this thought-experiment literally. It's just my weird way of doing the math, where I start with the answer and work back to the question it answers. Sometimes it's easier this way. Like trying to figure out the relationship between policy X and outcome Y when you know that Y/2=X but you are really bad at algebra so you can't solve for Y=2X.

Imagine that expectations are totally non-rational. Expectations are just exogenous, and do not adjust to match what is actually happening. And one day everyone wakes up expecting a permanent recession. When they went to bed they expected that output would remain at 100 forever, and nothing would ever change. Now they expect that output will be 90 forever. A permanent 10% drop in output.

But the central banker is an New Keynesian macroeconomist who years ago made a bet with his grad skool classmates that expectations are rational. He has since learned that expectations are totally non-rational and exogenous, but he doesn't want to lose his bet. So he has to figure out a way to make the world adjust to match the expectations people hold, since the expectations people hold do not adjust to match the world.

So what does the central banker need to do to the real interest rate to make those non-rational expectations of a permanent recession look like a rational expectations equilibrium? (Remember, I'm just solving for the New Keynesian equilibrium in a weird way, to make the math easier.)

The Bank of Canada's "Hot Hand" experiment and Price-level Targeting

This (pdf) might be the most important controlled experiment economists have ever run. The results of this experiment have been influential in the Bank of Canada's decision (so far) to stick with targeting inflation rather than a price-level path. And making the right decision on that question could save many billions of dollars (trillions worldwide) in reducing the risk and magnitude of recessions. I had read about the results of that experiment (by Robert Amano, Jim Engle-Warnick, and Malik Shukayev) soon after it came out, but only now decided to take a closer look.

Shocks hit the economy, and the Bank of Canada responds to those shocks to try to keep Aggregate Demand growing steadily despite those shocks. But there are lags, and the Bank of Canada does not have a crystal ball, so it will always fail. But the amount by which it fails depends on the strength of the automatic stabiliser properties of the monetary policy regime -- what the Bank of Canada targets, and what instrument it uses. And there are reasons to believe that a price-level path target would make for a stronger automatic stabiliser than an inflation target. If a shock causes aggregate demand to fall, and the Bank is (unavoidably) slow to respond, so inflation falls temporarily, a price-level path target means that people will expect temporarily higher than normal inflation thereafter, which reduces the expected real interest rate for any given nominal interest rate, which partially offsets the negative shock to aggregate demand.

The strength of automatic stabilisers will matter even more if you believe that the Zero Lower Bound on nominal interest rates may be a binding constraint on the Bank of Canada.

But it only works if people understand the difference between an inflation target and price-level path target, and expect temporarily higher inflation with a price-level path target following a negative shock. And this experiment was designed to see whether people could figure it out.

So What Happens in the Next Recession?

I’m not a macro economist by any stretch of the imagination and yet I cannot help wondering what is going to happen in terms of policy response the next time Canada goes into a downturn.  It is not a question of whether there will be another recession, only when. By policy response, I am of course wondering about the traditional tools used to affect aggregate demand such as fiscal and monetary policy.

Rip van Winkle on Price Level vs Inflation Targets

Rip van Winkle is put in charge of a New Keynesian central bank. He sets a nominal interest rate that he believes will keep inflation at 0% and the price level constant. (It doesn't matter if I change this to rising at 2% per year.) Then he falls asleep for 70 years, and that nominal interest rate cannot be changed until he awakes. This is clearly not good, because the nominal interest rate cannot be adjusted in response to any shocks that hit the economy over the next 70 years.

But before falling asleep, he has a choice of posting one of two announcements of what he will do when he wakes up:

1 Price level target. He will do what is needed to bring the price level back to what it was when he fell asleep, and keep it there.

2 Inflation target. He will do what is needed to keep the price level constant at whatever new level it is at when he wakes up.

Which is best?

What is the worst that could happen with a price level target? Suppose the natural rate of interest rises by 1% just after he falls asleep, and stays there. If prices are perfectly flexible the equilibrium price level will double, then fall slowly at 1% per year, returning to its original level just as he wakes up. (The 1% deflation means the real interest rate is the same 1% higher as the natural rate of interest.) With sticky prices it won't rise quite as much as that, and will fall a little more slowly.

What is the worst that could happen with an inflation target, if we hit the economy with the same shock? God only knows. If prices are perfectly flexible then anything can happen. The price level doubling then falling at 1% per year is one equilibrium. The price level quadrupling then falling at the same 1% per year is another equilibrium. The price level halving then falling at 1% per year is another equilibrium. And so on. And it could switch from one equilibrium to another just on a whim. What happens depends on what people expect to happen. And there are lots of things they could rationally expect to happen. And if prices are sticky? Well, it's going to depend on the exact nature of that stickiness. As well as on what people expect to happen. I can't answer that question with any confidence at all. I don't think any macroeconomist can.

In both cases we know the inflation rate will be 0% after Rip wakes up. But with a price level target we also know what the price level will be after Rip wakes up. That helps me figure it out. That also helps the people in my story figure it out.

Now you might think that's a daft thought-experiment. Because central banks don't fall asleep for 70 years. But central banks do not and cannot respond immediately to shocks that hit the economy. They don't observe changes in the natural rate of interest (or anything else) in real time. There are always lags between something happening, the bank figuring out what has happened (is it a temporary or permanent shock?), and responding to what has happened, and the economy responding to the bank's response. Sure, it's less than 70 years. But it is exactly as if the central bank fell asleep.

Would your answer change if Rip van Winkle fell asleep for only 10 years, or 1 year, or less? Why?

Price-level targeting as an automatic stabiliser for inflation

Targeting the price level could mean lower variation of inflation than targeting inflation. The best way to target inflation might be to target the price level instead. It's one of those paradoxes of pre-commitment. A promise to do something you don't want to do can affect others' expectations, and others' actions, and help you get what you want. Price-level targeting acts like an automatic stabiliser, which works even if there's a lag between the shock and the central bank's response to that shock. If expectations of the future price level matter, lags get offset by leads. And it could be better than letting bygones be bygones, depending on the parameters.

This is supposed to be a simple "teaching" post, to try to explain a point.

Capital flows vs Kapital flows (simpler version)

Let me try to make the intuition of my previous post simpler and clearer.

Suppose a country wants to invest more, because the profitability of investment has increased. It wants to increase the stock of kapital (machines) in its factories. There are three ways it could do this:

1 Divert some of its own production away from producing consumer goods towards producing investment goods, and consume less (save more).

2 Divert some of its own production away from producing consumer goods towards producing investment goods, but keep consumption (and saving) the same by importing consumer goods.

3 Import more investment goods, keep its own production of consumer and investment goods the same, and keep consumption (and saving) the same.

A closed economy can only do 1. And this will require an increase in the rate of interest (or something) to persuade households to postpone consumption. And it will require an increase in the price of investment good relative to consumption goods, to persuade firms to switch from producing consumption to investment goods.

An open economy can also do either 2 or 3. In both 2 and 3 there will be what economists call "capital flows" (borrowing from abroad, a surplus on the capital account of the balance of payments, matching a deficit on the current account). But only 3 has what I will call "kapital flows".

And the difference matters, because when we talk about "perfect capital mobility" in international finance/macroeconomics (and draw a horizontal BP curve in the Mundell-Fleming model and say a small open economy has the real interest rate pinned down by arbitrage at the world rate we are talking about capital flows (international borrowing and lending) and not kapital flows (importing or exporting machines).

Capital flows vs Kapital flows (very wonky)

This is only partly a response to Paul Krugman's posts. Mostly it's me trying to get my own head clear on something. This is a difficult topic, and this post is not as clear as it should be. So I don't expect many, or any, to fully understand it. I don't properly understand it myself. You have been warned.

What we call "international capital flows" (borrowing and lending across borders) aren't the same as what I shall call "international kapital flows" (flows of produced means of production -- like machines -- across borders). Yep. But they can go together, if kapital goods are tradeable goods.

But interest rates aren't the same as returns to kapital either. They are only the same in a one-good model, where the kapital good is also the consumption good.

I'm trying to bring some "kapital theory" into the picture of "international finance". And the easiest way to start out doing that is to start with a model with no kapital, only land. Land is just like kapital, except we have forgotten how to produce more. And when we do remember how to produce more land, so land becomes kapital, we get Dutch Capital Theory.

If r < g, bond-finance is like currency-finance

A world where the interest rate on government bonds is (permanently) less than the growth rate of GDP ("r<g") is a weird world. The government can run a Ponzi scheme, where it borrows (sells more bonds) to pay for the interest on the existing bonds, so the stocks of bonds grows at the rate of interest. But since r<g, the economy is growing faster than the stock of bonds, so the debt/GDP ratio is falling over time. So unlike the real Mr Ponzi's scheme, it's sustainable. The government would actually need to borrow more than is needed to pay the interest on the bonds, if it wanted to keep the debt/GDP ratio constant over time.

In a weird world, where r<g, government bonds aren't really a government "liability" in the normal sense of the word. Having a positive debt/GDP ratio, and keeping it constant over time as the economy grows, is instead a source of revenue for the government. It's like the government owning an asset, not owing a liability.

But if you think about the currency in your pocket, there's nothing weird about it at all. It's all very familiar. If r<g, financing government deficits by selling bonds is just like financing government deficits by printing currency. Because currency pays the owner 0% nominal interest (and minus 2% real interest if the central bank targets 2% inflation), which is less than the growth rate of the economy. So r<g for currency.

In our familiar world, where r<g for currency, currency isn't really a government "liability" in the normal sense of the word. Having a positive currency/GDP ratio, and keeping it constant over time as the economy grows, is instead a source of revenue for the government. It's like the government owning an asset, not owing a liability. The government-owned central bank is a profit-centre for the government. Printing currency is a profitable business. We even have a special name for those profits: "seigniorage".

Revenue from printing bonds is like revenue from printing currency, if r<g for bonds. But there's a limit to how much revenue the government can sustainably earn by doing them.

So, what *are* the differences between a Government's Budget and a Household's Budget?

You've probably seen examples. Some poor non-economist says something like: "Governments, like households, must live within their means". And economists all point their fingers and laugh and say that's a fallacy.

So, what are the differences between a government's budget and a household's budget? And do those differences matter? This is just a simple "teaching" post to give you my answers to those questions.

It's not obvious to me that there really are differences that are both qualitatively and quantitatively important.

Two Ways Central Banks can do Monetary Policy even if Bitcoin totally replaces Dollars as Medium of Exchange

Just a quickie, in response to Benjamin Vitaris' article about Warren E. Weber's Bank of Canada Working Paper (pdf) (HT Tony Yates on Twitter). [Update: and read Tony's post, on commercial banks and lender of last resort, as a complement to this post.]

Suppose that Bitcoin totally replaces the Canadian Dollar (and every other currency) as medium of exchange. When people buy things, they always pay in Bitcoin. Does this mean the Bank of Canada and other central banks are powerless?

No. There are two ways the Bank of Canada could still conduct monetary policy:

1 By varying the amount of Bitcoin reserves it holds.

Central banks cannot change the total amount of Bitcoin in existence; but they can change the total amount of Bitcoin in public hands (in circulation).

If they want to reduce the stock of Bitcoin in circulation, to tighten monetary policy, they simply buy Bitcoin (in exchange for government bonds, or in exchange for any asset, like their own IOU) and add it to their stock of reserves. This is just like central banks borrowing Bitcoin, and they can vary the rate of interest they offer to pay to anyone who lends them Bitcoin. This is just like central banks buying back currency in an Open Market Sale of bonds and storing it in the basement, except they are buying back Bitcoin instead of currency. This is just like central banks buying gold in exchange for bonds, which is how they could tighten monetary policy in the olden days under the Gold Standard.

And if they want to increase the stock of Bitcoin in circulation, to loosen monetary policy, they simply do this in reverse, by selling Bitcoin and reducing their stocks of Bitcoin reserves. The only difference is that central banks can always print more currency but cannot print Bitcoin, so when they run out of reserves they cannot loosen any more. Bitcoin is like gold in that regard.

(This would probably work better for a large central bank, or a lot of small central banks acting together, because a central bank of a small country might have little effect on the world stock of Bitcoin in public hands, and it might flow across borders relatively easily.)

[Update (thanks to comments by JKH and JP Koning): see David Glasner's posts on the Bank of France accumulating gold reserves and tightening world monetary policy here and here. And my old post on how the Gold Standard worked based on David's post here.]

2 By doing "Dictionary Money".

Just because Bitcoin is the medium of exchange does not mean the dollar cannot be the unit of account. Prices could be posted in dollars, even if people actually pay in Bitcoin. Like American visitors to Canada sometimes pay in US Dollars for items priced in Canadian Dollars. And every day the Bank of Canada could simply announce a new definition to say what the words "Canadian Dollar" mean in terms of Bitcoin. If it wants to tighten monetary policy it announces that "$1" means more Bitcoin than it meant yesterday. If it wants to loosen monetary policy it announces that "$1" means fewer Bitcoin than it meant yesterday. Since the Bank of Canada could stabilise the value of the Canadian Dollar in terms of real goods by doing this (or continue to target 2% inflation), it seems plausible to me that the Canadian Dollar would continue to be the unit of account (instead of the very volatile Bitcoin) even though "Canadian Dollar" is just a name for a thing that doesn't exist. The Bank of Canada does not change the number of Bitcoin in people's electronic wallets, but it does change the number of Canadian dollars those Bitcoin represent.

I have already blogged about this way of doing monetary policy. And JP Koning coined the term "Dictionary Money" and explained that it was common in the olden days.

Central Bank Communication and the Term Structure

It's a choice between being surprised by immediate small changes, and being surprised by warnings of much bigger future changes. A simple and maybe obvious point. I don't know if it's been made before; if not, it should have been.

The Bank of Canada has eight Fixed Announcements Dates per year. At each FAD it announces its target for the overnight rate of interest until the next FAD.

Suppose the Bank of Canada did it differently. At each FAD it announces the overnight rate target for the following FAD. This would give financial market participants 6.5 weeks advanced warning of any change in the overnight rate.

I think I am right in saying that financial market participants in general, and the commercial banks in particular, would prefer that second way of implementing monetary policy. I think they would say that it is a better communications strategy, with greater transparency. I think what they mean is that they don't like being surprised, and prefer to have advanced warning of any changes in the overnight rate, which is perfectly understandable.

But why stop there? Wouldn't it be better still if the Bank of Canada announced at each FAD what it would do at the FAD after the next, so everyone would get 13 weeks advanced warning of any change in the overnight rate?

But why stop there? And so on.

In the limit, when the Bank of Canada first introduced the 2% inflation target, it should have announced the whole time-path for the overnight rate target from then until eternity. Which is a contradiction, because it wouldn't be able to hit its inflation target if it couldn't ever adjust its monetary policy instrument.

It's tempting to say that it's like asking the driver of a car to give the passengers advanced warning before moving the steering wheel, which makes the driver's job of keeping the car on the road much harder. But that analogy is not quite accurate. Because the economy is like a car whose direction depends not just on the current position of the steering wheel but also on the car's expectation of the future position of the steering wheel.

In the simplest case (the pure expectations hypothesis) the current two year interest rate is equal to the (geometric) average of the current one-year interest rate and the expected one-year interest rate for next year. So by announcing changes in the interest rate one year in advance, the Bank of Canada would be able to influence all current interest rates for terms greater than one year, but not less than one year. The longer the advanced warning, the smaller the subset of the term-structure of interest rates the Bank of Canada can influence. And if Aggregate Demand depends on the whole term-structure of interest rates, from shortest to longest, the smaller the subset it can influence, the bigger the change in the overnight rate that will be needed to have the same effect on Aggregate Demand.

Take a simple example to illustrate my point. Suppose Aggregate Demand depends equally on the one-period interest rate and the two-period interest rate, and the two-period interest rate is the simple average of the current one-period and expected future one-period rates. And suppose the economy is hit with random shocks that are permanent (the natural rate r* is a random walk). If the Bank of Canada changes the one-period interest rate immediately it observes a 1% shock to r*, it changes the one-period rate by the same 1%, and the two-period rate changes by the same 1% (because everyone knows that shocks to r* are permanent). But if the Bank of Canada has to give one period's advanced warning, it needs to change the current two-period rate by 2% (since it cannot change the one-period rate), and it needs to announce a change of 4% in the future one-period rate (since you need to change the expected future rate by twice as much as you want to change the two-period rate). And in the following period, if there are no additional changes to r*, it announces a future cut of 3%.

It gets even hairier if changes to r* are transitory. I will leave that as an exercise for the reader.

Your call, financial market participants who don't like surprises.

[We could talk about conditional commitments, where the Bank of Canada announces in advance what it will do, conditional on future data. But that inevitably leads to the Bank of Canada committing itself to an instrument rule (like the Taylor Rule for example). Which opens up another can of worms. So I will leave that aside.]

Migration, Wages, and Corner Solutions

I'm trying to get my head straight on something. Macro farmboy lost in Urban Economics again. Read at your own risk.

If immigration always increases real wages (or well-being), do we end up in a "corner solution", where everyone bunches together in one location leaving other locations empty? If so, that's a reductio ad absurdam, because we do not observe everyone living as close together as is physically possible, like sardines in a can.

Start with the simplest model. Everyone is identical, they only care about wages, and there are no moving costs. Divide the country up into two regions (East and West), and assume an initially arbitrary distribution of the population between the two regions. Suppose that wages are higher in the West than in the East, so people move from East to West. What does the equilibrium look like?

If we assume Diminishing Returns (think of an agricultural economy where land and labour produce food, so wages are a decreasing function of the labour/land ratio) we will (usually) get an interior solution -- an equilibrium where some live in the East and some live in the West. Because East to West migration causes West wages to fall and East wages to rise, until they are equal and migration stops.

If instead we assume Increasing Returns, so wages are an increasing function of population, we get a corner solution. People migrate West, which causes West wages to rise, East Wages to fall, which increases the incentive to migrate West. The whole population moves to one of the two regions. (There is a third equilibrium where wages are exactly equal between the two regions, so nobody moves, so wages stay equal, but we only get to that equilibrium if we start there by sheer fluke, plus it's unstable, so I will ignore it.)

Now divide the country into three regions. Everyone moves to one of the three regions.

Now divide the country into four regions. Everyone moves to one of the four regions.

You can see where this is going.

Divide the country into an infinite number of regions. Everyone moves to one infinitesimally small region.

Which is not what we observe.

The exchange rate and net exports "contribution" to growth

This post is about national income accounting, and its dangers. Reading Simon Wren-Lewis' post about Brexit and real wages made me finally decide to try to get my head clear about something I've been meaning to get it clear about for some time. I think Simon might be wrong about something (I'm not sure though, and will wait for his response).

Take an extreme case, to make it simpler and clearer. The Brits produce only apples, because they can't produce anything else. But they never eat any apples; they only eat bananas. So each year they export the apples they have produced, swap them for imported bananas, and consume the bananas. Investment and government expenditure are always zero. And Brits' savings are always zero too (they swap all of their apples for bananas to be eaten immediately, and never swap any apples for IOUs).

By construction in this "model", the value of net exports is always zero. Because the value of exported apples is always equal to the value of the bananas they are swapped for.

Now suppose the price of apples (in terms of bananas) is too high, so the Brits are unable to sell all the apples they produce. The unsold apples rot on the ground, and don't get counted in GDP. The real exchange rate (the price of apples in terms of bananas) being too high causes real GDP to be too low. Then something causes the real exchange rate to fall, so the Brits are now able to sell all the apples they produce (in exchange for bananas), and so real GDP (measured in apples produced) rises to the "full employment" (of apple trees) level.

By construction, the depreciation of the real exchange rate is what caused the rise in real GDP, but net exports remain at zero and so net exports' "contribution" to GDP growth is zero.