Worthwhile Canadian Initiative

Good Chart Checklist

Note: this was prepared for my ECON 3403 students, and is a list of all of the mistakes I commonly see in student charts. Please add your suggestions for things to add to this list in the comments - or steal, modify, and use for your own purposes! 

Good Chart Check List:

Is my chart self-explanatory? Does it specify

• Who: The population the chart shows (e.g. eligible voters, Facebooks users, people over the age of 12, Canadian citizens, etc)
• Where: The geographic area the chart applies to (Ottawa, Canada, G7, G20, OECD)
• When the data was collected
• The data source (e.g. Statistics Canada Table 12-345-67, World Bank). Optional: give name of survey or statistical programme data came from.

Am I using an appropriate chart type?

• Line chart to show time trends (typically 4+ observations – for just two years of data use a bar chart).
• Bar chart to compare groups of things, e.g. countries, age groups, genders, occupations, industries, provinces
• Pie charts are rarely the appropriate chart type. Use pie charts when your only concern is distribution; you only want to know how each group’s share compares to other group’s shares. If you must use a pie chart, consider using the “doughnut” option.

Are my axes clearly labelled? Is it clear

• What each axis represents Exceptions:
  • do not have to label a “year” axis, it is usually obvious that 2005, 2010, 2015, 2020 etc are years.
  • If the chart title makes it clear what the graph shows, don’t have to label the axis as well.
• What units I am using (miles, km, tonnes, millions of tonnes, Canadian dollars, 2020 (constant) dollars, nominal (not inflation adjusted) dollars, etc)

Have I put my data into perspective?

• For data showing trends over time: are dollar amounts adjusted for inflation?
• For comparisons across provinces or across countries: am I showing numbers as a percentage of the population, to adjust for population size?
• For data focussing on a particular population subgroup: have I included data for other groups to put the numbers into perspective? E.g. for a chart showing trends in 12-15 year old’s mental health, consider including mental health trends for the entire population to put the numbers into perspective. For a chart showing poverty rates for elderly, include poverty rates for the non-elderly for comparison purposes.
• For data showing trends over time: have I tried the “year 1=100” approach – i.e. divide by the year 1 value*100?

Am I being honest?

• Does my vertical (y) axis start at zero?
  • Exception: sometimes, if you’re trying to highlight trends, it’s o.k. to have a line chart that doesn’t start at zero. But be very careful! For a bar chart, the vertical (y) axis must ALWAYS start at zero!
• Am I selecting my starting year carefully to show the results I want to show? (e.g. I am I showing stock market growth starting at 2009, when the market was at very low levels, instead of at 2007?).
• Am I distorting my results using fancy graphics, especially 3-dimensional shapes?
• Are the numbers on my chart accurate?
• Have I created a combo-chart, and manipulated my axes so that my series look closely related, when they really aren’t?

Is my chart accessible?

• Can someone who is colour-blind read my chart?
  • Am I using a colour-blind friendly colour scheme, e.g. a monochromatic scheme, or a scheme designed to be colour-blind friendly?
  • Am I using dashed lines, labels, or other tools to make it easier to tell my series apart? See here for tips on how to make a graph colour-blind friendly: https://towardsdatascience.com/two-simple-steps-to-create-colorblind-friendly-data-visualizations-2ed781a167ec
• Can someone who has trouble reading small print read my chart?
  • Flip a bar chart on its side (so the bars are horizontal, not vertical). That creates room for big-enough-to-read labels!
  • Consider putting legend labels on the chart itself, rather than to the side (requires advanced Excel skills)
• Does my chart contain any unnecessary information or other clutter?
  • Avoid cluttering up a graph with too many years worth of data. Zoom in on one year and compare population groups (e.g. age, sex, industry, occupation). Alternatively, download 5+ years of data and graph a time trend (challenge: can you explain the trend?).  Statistics Canada data tables often include 3 years of data by default. However a good graph rarely includes just three years of data (exception: the years 2019, 2020, 2021).
  • Only report 2 or 3 digits worth of data – e.g. report data as 1.2 million rather than 1,234,567.
  • Cut any unnecessary lines, words or graphics
• Am I using the right words to describe wages and incomes?
  • Wage rate=$ earned per hour worked
  • Wages=total amount earned. Also known as earnings
  • Income=earnings +other sources of income.
  • For income data, try to be as precise as possible.
    • Is the data pre-tax income or after-tax? If after-tax income, does it include benefits like Canada Child Benefit?
    • Individual income or family income or household income? If family or household income, whose income is counted? (e.g. if a 25 year old is living with a parent, whose income is included in the 25 year old’s “family income”?) Check to see if the income is “census family income” or “economic family income”.

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.

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.]

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.

Project Link update

It's past time for my annual update for Project Link, my attempt to piece together the fragments of Statistics Canada's published data into coherent time series.

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.

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.]

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.

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:

Micro Profs teaching Intro Macro

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

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

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

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

This is what I think is going on:

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

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

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

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

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

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

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

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

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

Suppose we introduced Short Run Macro like this:

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

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

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

Project Link update

I've just updated Project Link, my attempt to piece together the bits and pieces of published Statistics Canada data into a coherent history of the post-war Canadian economy. (The introductory post is here, and a post on the first update is here.)

Here are the main elements:

1. Incorporating Statistics Canada's long-awaited publication of its expenditure accounts from 1961-1980. As you may recall, when they revised the GDP numbers back in 2012, the new series started in 1981 instead of 1961. (This is what I had in mind when I fumed that "Statistics Canada must be the statistical only agency where the average length of its time series gets shorter from one year to the next.")
2. Pushing back the starting date for the LFS and SEPH employment numbers to 1946, along with unemployment rates and average weekly wages. The CPI and CPI inflation have also been pushed pack to 1946.
3. Including the income measures of the economic accounts : GNI (what we used to call GNP), NNI and disposable income. I've also gone out on a limb and tried to construct measures of Gross Domestic Income consistent with StatsCan's methodology, and that's covered in a separate post.

More details below the fold.

Gross Domestic Income in Canada, 1947-2018

The latest update of Project Link includes estimates for national accounts income measures: Gross National Income (formerly known as Gross National Product), Net National Income, compensation of employees, and disposable income, all going back to 1947Q1.

I've also added Gross Domestic Income. GDI is a fairly recent arrival in the national accounts, and it takes into account the income effects of changes in the terms of trade. Looking at GDI has been particularly useful in understanding the Canadian economy over the past fifteen years, since it picked up the incomes gains and losses incurred as the prices of Canadian resource exports rose and fell. Since GDP measures activity - and not necessarily the income it generates, GDP was not as useful as it usually is. (See my beer and pizza explainer.)

The Tale of the Two Cobblers (collusive price cuts)

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

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

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

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

Is this (one reason) why firms exist?

Math appendix:

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

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

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

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

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

"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.

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.)

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.

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.

The Devil You Know vs The Market For Lemons

I told my friend Mike I was thinking of trading my car in for one that used less gas. Nowadays I would talk about the Market for Lemons as a reason against doing what I was thinking of doing. But in 1974 I didn't know about Akerlof's famous paper, and neither did Mike, who was majoring in music. "Better to stick with the devil you know" he said.

"The Devil you know" and "the Market for Lemons" are similar: both use asymmetric information (the seller knows more about the car than the prospective buyer) to explain a low volume of trade. But they are not the same. A thought-experiment can explain the difference.

Suppose the government made a surprise announcement: everybody who owns a used car must sell it next week to the highest bidder. If you still want a car you must sell yours and buy someone else's.

Making sales compulsory solves the Market for Lemons problem. The sample of cars offered for sale represents the whole population of cars; those who know their own car is a cream puff can't hold it back from the market. If the Market for Lemons was the only problem in the used car market, then the compulsory universal sale would improve efficiency in the allocation of cars. People who found themselves needing to drive more miles could sell their gas guzzlers to the people who found themselves driving fewer miles.

But universal compulsory sales of cars does not solve the Devil You Know problem.

First there's simple risk aversion. Suppose everyone knows that half the cars need a $1,000 repair and the other half don't, but only the seller knows if his own car needs that repair. Sellers of lemons have a 50% chance of winning $1,000, which is worth less than a certain $500 if they are risk-averse. Sellers of cream puffs know they have a 50% chance of losing $1,000, which is worth more than a certain $500 loss if they are risk-averse. (Remember that everyone buys a car for the same price they sell their car, so price is a wash, if this is the only difference.) The value of the expected gains to the expected gainers are worth less than the value of the expected losses to the expected losers.

Second, even if everyone is risk-neutral, there's the problem of not knowing what particular repairs are needed. If your car needs to have the brake pads replaced soon, it's better to know that fact before they wear down too much and you need to replace the rotors too (or worse). And if your car won't start on a cold morning, or overheats on hot days, it's better to know that fact in advance, so you can plan accordingly.

[And if the government's surprise announcement is not a surprise, but is announced well in advance, there's an additional problem. Nobody will change the oil if they know they are going to sell the car anyway. But that's the standard Moral Hazard problem, which is distinct from the Devil You Know problem.]

I wonder which problem matters more, in the used car market. Or in finance?

I started to think about the Devil You Know when thinking about the choice of textbook for Intro Economics. You never really know the flaws in a textbook until you have taught from it. Changing textbooks is always risky; and the flaws catch the teacher unprepared. Most of our switches have gone OK, but one didn't.