« On the sources of Canada's recession and recovery | Main | Blogging as crack »


Feed You can follow this conversation by subscribing to the comment feed for this post.

How does this fit in with the "value of ownership" irrationality that Dan Ariely talks about? Since people overvalue their property, is it not fair to treat the problem - from the homeowners p.o.v. - as if you are at a point on your graph just above your endowment point. And for that matter, since some of your other spending is for stuff that you own, aren't you slightly to the right also?

In other words, maybe you really don't care: not because you haven't thought through the logic but rather because you overvalue the home you own?

Thanks for another great post.

Chris: Thanks! Dunno. Interesting question, though I'm not familiar with Dan Ariely. Let me convert it into a slightly simpler question, that I think I can answer. Suppose I really get used to the house I'm living in, and I would need either a lot better house, or a lot more other stuff, to persuade me to move. Draw a regular indifference curve, then draw a dot to the south-west of the indifference curve, then rub out all of the indifference curve to the north-east of the dot. What remains of the indifference curve, plus the dot, is the new indifference curve. It would now take a much bigger price change to persuade me to move. It's rather like a moving cost (which is a similar dot to the north-east of a budget line) only it's a psychic moving cost.

Now if it's a pride of ownership per se, rather than just getting to like the place you are living in, whether you rent it or not, then it's harder. Because the indifference curve is no longer independent of the endowment point.

If I were buying I would like them cheaper, if selling, more expensive, but since I am doing neither and don't plan to for some time if ever, I really don't care. While I would prefer to have more to spend on everything, I would not care to change my allocation regardless of what happened to prices (unless I could sell before the change and repurchase after). Since my income would not allow me to take advantage of lower prices and my property would not allow me to take advantage of higher prices, that is I would not be able to devote more to housing since so much of my wealth is already in it or be willing to accept less to live in a lessor area, my indifference curve is extremely flat. Since I do pay property taxes, I have a slight preference for lower prices, but just slight.

Lord: that is totally incorrect reasoning. Absent moving costs, the only case in which you would not ever change house if house prices changed is if your indifference curve is L-shaped. Not flat. Draw the picture.

For an example of L-shaped indifference curves, put left shoes on the vertical axis, and right shoes on the horizontal. Regardless of the relative price of right and left shoes, you still only buy them in pairs.

How does the capital gain/loss on the move factor into the budget line?

Assuming spreads (between less expensive and more expensive) increase when prices go up and compress when prices go down, how is that reflected in the budget lines/indifference curves?

JKH: By "capital gain/loss on the move", do you mean "capital gain/loss relative to historic cost" (what I paid for my house when i bought it)? That doesn't affect the budget line at all. Historic cost doesn't appear anywhere. bygones are bygones. (That was what was so great about reading Steve's latest post on Interfluidity).

Spreads don't affect the indifference curve (which reflects preferences and is independent of prices, unless people have weird preferences like enjoying an expensive house just because it's expensive). When I drew my budget lines, I assumed that all house prices rose or fell in the same proportion. Suppose prices of big expensive houses fall proportionately more than smaller cheaper houses. The budget line gets steeper as before, when prices fall, but it also starts to curve, so it gets steeper still near the top.

Nick -- As usual a very thoughtful post. But I think the answer may be less counterintuitive than it first appears to be.

First, in a world with credit markets, isn't there an income effect?

With more valuable collateral, you can borrow more cheaply, allowing you to increase consumption over all time periods relative to the status quo or half-price housing scenario.

Relatedly, there is a real options/insurance argument. Suppose the price of other goods is uncertain, varying uniformly with a 10% range. That would trace out a lie of potential optima on your utility surface. We'd have to do the math to "prove" and trace the limits of the argument, but on your graph, if we fill in regular-looking and concave isoclines, we'd end up with a longer, more concave range around the low-housing-price optimum than around the high-housing-price optimum.

Suppose there is no good-collateral income effect, and the substitution effects are equivalent, so that under certainty we'd be indifferent between housing prices halving and doubling. Allowing uncertainty of the relative prices of housing and other goods drops the expected utility of the low housing price optimum more than the high housing price optimum, rendering the high housing price optimum superior.

This is a fancy way of saying that I think the naive answer to this question is correct. People with houses rationally prefer rising houses, regardless of any lack of current plans to sell. They enjoy both the capacity to borrow cheaply and greater certainty surrounding total consumption, both of which increase overall well-being.

"a bigger and better house"

Isn't that an oxymoron?

I think Steven Landsburg made this exact point in one of his books a few years back ... "The Armchair Economist," probably.

Nick, I don't think bygones are bygones in this case. Take this not totally crazy example:
- a person owns a $1 million home
- the person is 80 years old
- with no descendants
- and is planning to sell tomorrow and spend the rest of his/her life going on a continuous round the world cruise (cheaper than a nursing home)

How can a doubling of housing prices not make this person about $1 mil better off (even if we call some fraction of the cost of the cruise ship housing)?

The value of the home reflects the present discounted value of all housing services it will provide now and in the future.

But our hypothetical person is not planning to consume those services.

Just as we're born with a short position in housing, eventually home owners near the end of their lives get into a long position with respect to housing.

B.t.w., although I've seen this diagram many times, I still find it counter intuitive. I have some sympathy for my students' reaction towards indifference curves.

I would suggest that what you call "weird" preferences are probably actually quite normal. I expect that with housing, like any other single item, there's a limit at which consuming more fails to increase satisfaction. I expect there's also a similar limit on "all other things," but it's probably a great deal higher.

I realize that this would make modeling much more challenging, and it's nice to thing of people as straight lines, but if you want your economics model to suggest a realish world...

Steve: And I was just thinking of a new post: "Accounting conventions, the stickiest price", inspired by your two posts!

Yes, the colateral effect of house prices on borrowing rates may matter for some people, who borrow. But unless your mortgage is more than 75% of the house value, mortgage rates seem to be about flat, as far as I know. And the average person is not a net borrower, nor a net lender. I can't think that effect is very big, on average.

You lost me a bit on the options/insurance argument. I can see it working for certain utility functions, like if there's a risk the price of food might rise so much I would starve, and selling a high-priced house would let me survive, but selling a low-priced house wouldn't be enough to buy food. Not sure if it would work for general risk-averse utility functions. Maybe it would. Do you think that's what home-owners have in mind when they say they like high house prices?

asp: not at all. If bigger houses cost more, ceteris paribus, a person who has chosen the right sized house to maximise his utility would always prefer a slightly bigger one, on the margin, if it were free.

Phil: you could be right. It's very standard micro.

Frances: I don't think that's an argument for bygones. The person who owns a house and is planning to sell soon, and go on a cruise for the rest of her life, isn't really consuming at her endowment point, on average, over her remaining years. On average her consumption point has less housing than her endowment. Yes, she is net long housing.

But, (given my background) I've always taken the Barro-Ricardo-dynastic approach. The kids are gonna need housing, so the fact that my house is going to outlive me still doesn't give me a long position in housing. I'm still net short (I think, depending on....lots of things).

Neil: " I expect that with housing, like any other single item, there's a limit at which consuming more fails to increase satisfaction."

That's not weird preferences. That's just a more extreme form of the convexity (concavity, whatever) we normally assume. The indifference curves eventually go vertical (or horizontal). But the point is, unless price is zero, no person would ever consume a good to the point of satiation. He would always be on the downward-sloping part of the indifference curve.

There are at least 2 problems with using houses to illustrate this example. I would expect most peoples indifference curves to be very close to L shaped with respect to housing. the other problem is that moving costs are indeed very high. Not necessarily in laid out dollars, but the opportunity costs of the time consumed are significant.

Upon further examination, doesn't all this just come down to: If a good becomes relatively more expensive, less of it will be consumed, and if a good becomes relatively less expensive more of it will be consumed?

Nick -- I'm thinking more about home equity borrowing than about mortgages, though the collateral effect would be the same. Suppose you had a mortgage on your home and only 20% of its value in equity. Tomorrow your house value doubles. Now your home equity is 60%. Putting aside flattening of the market due to a government subsidy, you should be able to refinance your loan at a lower spread. Similarly, even if you have no mortgage at all, doubling of your home value creates opportunities for you to borrow more cash at lower rates.

Then there is the uncertainty argument. The claim is not that an expensive home increases ones security because you can outright sell it if food prices rise, but because you can reduce your housing consumption by a very small fraction in order to respond to variations in other prices. In other words, in the spirit of your diagram, I am assuming that consumption of housing (position along the Y axis) can be continuously set, that we are not restricted to zero or one unit. Under that assumption, I think it would work for pretty generally for utility functions that are concave to a similar degree in both goods. But my argument is purely graphical, for the moment.

Take the green line, and move it along the X axis by plus or minus 5%, holding the Y-intercept constant. Imagine the tangency points to the isoclines, taking cues from the one you've drawn. You get a little fingernail centered around the existing tangency point. Do the same with the red line. Housing consumption plummets quickly as red line moves inward, spikes high as the red line moves out. That's intuitive: if you can fine-tune housing consumption, you can trade only a little of it to buy more expensive goods when houses are valuable, you have to trade a lot of housing consumption when houses are cheap. Unless utility in housing consumption is very linear, uncertainty is going to favor the low variability alternative.

But is it realistic to "fine-tune" housing consumption? First, if we can't, then the original thought experiment has to be revised. You don't get to follow the substitution effect to the optimum if we take consumption to be discrete.

But it's not entirely unrealistic to fine-tune housing consumption over a medium term, since we can sell our house and buy a similar-but-smaller (or larger) house to modulate the "quantity" of housing consumed. Also, we can take borrowing against our home when other prices rise and as a partial sale, and paying down our loan as other prices fall as a means of fine-tuning housing consumption, dove-tailing with the collateral argument. It's a bit strained, because we still get to enjoy the use of the whole house even after we have sold part of it to the bank. But we do arguably get less utility in some sense from a home deeper in hock than one nearly free and clear, so it's not an entirely ridiculous parallel.

(Re your argument about inflation and accounting values, you're undisputably right. Old firms famously own real-estate at 70-year-old book values that absurdly understate their current market value. But note that is almost uniquely a real-estate phenomenon in low inflation countries, as other assets depreciate more rapidly than the rate of inflation. Accounting prices are very sticky and usually understate value, but since that is widely understood, it's not clear that the stickiness creates problems or distortions.)

What about taxes?

"It's a bit strained, because we still get to enjoy the use of the whole house even after we have sold part of it to the bank."

You sold part of the equity to the bank along with a rental agreement to keep using the whole house. You do this when the "rent" is low, that happens to coincide with the price being high (tighter spread).

Those subprime mortgages with two years of low rates were really just rental agreements on the housing service plus call options on the asset.

This line of reasoning would seem to imply that, to the extent that collateral effects mean that high house prices go with low spreads for loans secured by the house (mortage or home equity loan), what you have here is an income effect.

High prices for the house go with low "rents" for the housing service and since housing is a large part of your expenditure basket the result is a powerful income effect.

The fact that it also induces a change to the household capital structure (pledging equity to the bank) is side issue, no different from a high equity price of a company meaning the company has a low cost of captial so they spend more.

How can all homeowners improve their lot by moving to a larger/better smaller/lessor house?

Something has to change about the stock of housing, but contrary to your narrative if house prices fall, you cannot trade (collectively) into a better property, that property must be constructed out of resources whose price has not changed.

Okay. That's not possible.

If house prices rise, you cannot (collectively) trade-down.

All of which should be obvious because the fairy moved a nominal variable (which causes a market-clearing problem and thus must be a transient action).

When the fairy makes something real, then we can all be better off.

Jim: "Upon further examination, doesn't all this just come down to: If a good becomes relatively more expensive, less of it will be consumed, and if a good becomes relatively less expensive more of it will be consumed?"

Yep. Demand curves slope down. And if we are showing this properly, we recognise that the goods are themselves produced by the same people, in aggregate, who consume them, so that a rise in price of a good doesn't really have an income effect, because it makes us worse off as consumers of the good and better off as producers of the good. It's the substitution effect that matters, not the income (wealth) effect.

I reckon that most people would have bought a different house if house prices had been different. So I don't agree with the L-shaped indifference curve. But I agree that moving costs are big. My guess is at least 10% of the value of the house. If you have just bought a house that is right for you, it would take a big change in prices to get you to move again. But if you were going to move anyway (job, etc.), then small price changes can have an effect on how big/good a house you buy.

Moving costs are more like a point off the normal budget lines and indifference curves.

David Friedman has "prior art" on this one: "Application: Housing Prices--A Paradox" in this micro textbook: http://www.daviddfriedman.com/Academic/Price_Theory/PThy_Chapter_3/PThy_Chapter_3.html

But, then again, the true "paradox" is that this can't happen in general equilibrium under the usual setup unless there are missing markets.

A lot depends on whether or not you live in a bubble market.

If the fairy increases prices so that price to rent ratios skyrocket, do what Dean Baker did. Sell the house and rent.

If the fairy decreases prices, you are screwed unless you own outright. If you are underwater, you quit paying housing costs altogether until evicted, then move out and rent. A free 1 year rent may recover a few thousand of your investment. Then again, the banksters often lose the papers and you might get 2 years free rent or more. Use the money you save to invest in something more profitable. Rent when you are evicted.

If prices stay the same and you own there is no reason to sell and accrue the transaction costs in this market. If you still owe, refi at the lowest rate, shortest term possible. Take an ARM and pay off the difference in the old and new mortgage principle. By the time rates go back up (at least half a decade) you can be paid off.

Steve: I'm not sure there's much difference, theoretically, between a home equity withdrawal and a mortgage. It's just that we associate the mortgage with originally buying the house, and paying it down over time as part of a savings strategy. And we associate the second with "frivolous" consumption, and taking it out as part of a dissaving strategy. But it doesn't have to be this way.

"The claim is not that an expensive home increases ones security because you can outright sell it if food prices rise, but because you can reduce your housing consumption by a very small fraction in order to respond to variations in other prices."

Yep. Agreed. I was unclear in my "sell house for food" story. I meant "downsize house for food".

"Take the green line, and move it along the X axis by plus or minus 5%, holding the Y-intercept constant."

I got that far, but then my eyes got lost in all the curves, so I switched to my verbal food example, with an extreme utility function. But I think you are right, and the point would generalise to any regular Indifference map.

Here's another verbal intuition of your result: If you are faced with uncertainty in (say) clothing prices, you would much rather clothing be a smaller percentage of your budget, and a rise in non-clothing prices, compensated by the extra income to afford those higher non-clothing prices, would make clothing prices a smaller percentage of your budget. And owning your own house, like producing your own non-clothing goods, is a way to compensate you for those higher prices.

Yep. Put like that, I'm much more confident your result is right. It's a good one.

But would your result generalise to the case where house prices are uncertain too, along with the price of other stuff? I think it would.

I think we do fine-tune housing consumption to prices over the longer term, simply because other events (jobs, family, etc.) mean we have to move anyway, so moving to a slightly better or slightly worse house isn't affected by moving costs.

You have been on a roll so far Steve, but I am going to disagree with you here:

"Also, we can take borrowing against our home when other prices rise and as a partial sale, and paying down our loan as other prices fall as a means of fine-tuning housing consumption, dove-tailing with the collateral argument. It's a bit strained, because we still get to enjoy the use of the whole house even after we have sold part of it to the bank. But we do arguably get less utility in some sense from a home deeper in hock than one nearly free and clear, so it's not an entirely ridiculous parallel."

It's more than strained, and for just the reason you cite.

Now this is related to what I think of as the "Garth Turner mistake". (Garth is a Canadian ex-politician who has a housing blog, is a house price bear, and who generally gives sensible advice, but gets totally wrong on this point). Garth says you should diversify your portfolio to reduce risk (so far so good), so if 100% of your equity is in your house, you should get a (say) 50% mortgage and put that money in stocks (which is wrong, because it increases risk, unless stock and house prices are inversely correlated, even if you ignore, as Garth does, the "born short" argument).

Aha! I see Adam has just picked up on the same point. So I don't need to repeat it.


I'm not referring to historical cost.

Rather the relative net wealth effects of alternative outcomes.

I'm not seeing how your budget line accommodates these differences.

How do you make rules for moving along a single budget line when the wealth effects of different outcomes that are the basis of those decisions is different?

More fundamentally, your budget line seems to conflate asset values (balance sheets) and expenses (income statements).

Greg: taxes. Like municipal taxes, that are proportional to the value of the home? My guess is that if the house price fairy doubled all house prices, all municipalities would halve mill rates, so taxes would stay the same. But maybe there's a sort of money illusion or mill rate stickiness?

Jon: yep. Presumably the fairy did this by changing everybody else's supply and or demand curves for housing (but not mine). Simplest case to analyse would be some percentage of the houses getting destroyed in an earthquake. So the average person's endowment point shifts vertically down (but I'm lucky, so mine doesn't).


I think the curves work better for, say, peanut butter. There is for most people a significant amount of non-monetary value in owning a house - independence from landlords, security against changes in power, status as a property-owner, inheritance for kids and so on. So most people only change houses for reasons only distantly related to price (family changes, commute distance...). So the indifference curve is not very curvy, and is well to the right of the black line.

There are some things where value and price are closely related (one kind of food vs another is a good example), but others where they do not - what would you say if the fairy asked the same question about your personal library, or your family photo collection?

"But notice that the budget line always swivels around my current endowment point."


Why doesn't the endowment change with the wealth effect/balance sheet effect of house prices?

Why doesn't the endowment include assets and income rather than income alone?

Agentcontinuum: well spotted! Yep, the argument is entirely too orthodox to be original. It's probably in Marshall, somewhere (though not I think in Adam Smith).

And yes, you have to think of the price change being caused by some change in everyone else's behaviour, not the person in the picture. Fairies aren't real.

jonny: notice how the fairy said she would change prices immediately? If she gave me a choice of whether I wanted her to change prices a couple of months from now that would be very different, and I would certainly take her up on the offer (even ignoring substitution effects). If she offered to halve housing prices, I would say "yes", sell my house, and buy back in after house prices fall (I would go net short housing, by owning zero, and would go net short lots of houses if I could figure out a way). And if she offered to double prices I would say "yes", and go net long houses by owning two, or lots more than two.

JKH: Let me try to give you a better answer.

The picture I drew shows me where I am today, given current house prices, given my current wealth and income, and given I am in equilibrium, with no incentive to move either up or down the housing spectrum, even if moving costs were zero.

Now, if in the past I had bought houses at low historic prices, and sold them at high historic prices, my current wealth would be bigger. And if i had done the reverse, it would be smaller. The bigger my current wealth, the further to the North-East my endowment point will be, and the budget line associated with that endowment point will be further away from the origin of the graph. But that is the only difference that historic prices make. Once I have drawn in the endowment point, they don't matter any more.

Peter T; There are many good arguments for someone with a big downpayment owning rather than renting. The ones you give, plus the whole asymmetric information/moral hazard/principal-agent problems of the landlord-tenant relationship (which are eliminated when you are your own landlord and tenant). And I have ignored them all in this picture. All that this picture can show is the "born short" argument -- it insures you against changes in the cost of housing (whether price or rent changes), by covering your inborn short position in housing.

(And the main arguments for renting are: you have a small downpayment; you think you will want to move soon).

(And if you think you can predict house prices better than the market, there is of course an additional argument for being either net short (owning zero or less) or net long housing (owning two or more)).

JKH: "Why doesn't the endowment include assets and income rather than income alone?"

It does, or should, include the income from any asset you own as part of your income. Or, if you think in stocks, rather than flows, the assets should include the present value of your labour income.

"Why doesn't the endowment change with the wealth effect/balance sheet effect of house prices?"

If your house doubles in value, that part of your endowment *measured in money* doubles too. But when we measure the value of your house, measured not in money but in terms of how much housing you can buy with it, it doesn't change, if all house prices double.

Thanks, Nick. I can probably measure my cumulative experience thinking about indifference curves in minutes. It's becoming a bit clearer now.

I find it easier to think about the diagram as including the capitalized value of future consumption. That way, it becomes a "frontier" in a portfolio mix of two assets at market values.

"But, (given my background) I've always taken the Barro-Ricardo-dynastic approach."

So the question is "Is housing net wealth?" ;-)

Frances: yes, that's precisely the question!

This is similar to portfolio rebalancing - you sell some portion of an asset when it's value becomes too high a percentage of your total portfolio.

Although that's a risk management concept. Any relationship there to the convexity of indifference curves?

JKH: "Although that's a risk management concept. Any relationship there to the convexity of indifference curves?"

Sort of, but I wouldn't push it too far. If you put quantity of one asset held on each axis, and assumed the two assets weren't perfectly correlated, and a risk-averse investor, the ex-ante expected utility indifference curves would look convex. And the budget line would be a straight line, given your wealth and asset prices. And you would choose a tangency point.

But changes in (say) the risk-return characteristics of assets would then cause the indifference curves to shift around. And we don't like indifference curves to shift around, if we can help it. (See Mike on Lithium...I mean...)

No, indifference curves don't shift around, the feasible set of (E(r), sigma) pairs shifts around.

And of course the tangency portfolio shifts with it.

If indifference curves weren't convex, we would nearly always choose to be at a corner solution, where we spend all our income on only one good. And we don't, so they are probably mostly convex, though there are plenty of exceptions. You *can* also be at a corner solution if they are convex (if you much prefer one good to another), but you won't always be at a corner.

"the ex-ante expected utility indifference curves would look convex ... but changes in (say) the risk-return characteristics of assets would then cause the indifference curves to shift around."

Makes sense to me.

They should be convex because as you move toward the extremes, you lose the benefit of portfolio diversification. That's a riskier portfolio, and you need compensation for it in the form of a higher value portfolio, which is off the budget line.

And changes in risk-return characteristics change that benefit and therefore change the convexity shape.

JKH: Yep. And the regular indifference curves we draw are usually convex too. It's just we don't really try to explain what causes them to be convex; we just assume that people like variety in their diets.

I think JKH's point is still valid in that the fairy's doubling of house prices today would, in the real world, raise your future income expectations. If you borrow on the now-higher collateral and raise current consumption, don't you shift the budget line outward? If you expect future income (cap gains) to rise, this does not represent a pure time-shifting of consumption, only a smoothing.

I think delving into the mechanics of the bubble in a place like CA is useful here. Roughly 15% of all purchase loans in the state in 2005 were made using Option Arm mortgages. The payment on these reflected a 1% interest rate--the rest, say 4%, was added to principal. So imagine all homeowners assumed that they could use an Option Arm to reduce their mortgage payment to the equivalent of a 1% rental yield; and further that they expected 15% p.a. house price appreciation forever. In this case, homeowners could expect to pay a very low "rent" on their home, while enjoying annual 90% capital gains (9% appreciation after 4% deferred interest, over a 10% equity position) forever.

One can quibble with the rationality of the above "logic", but it wouldn't change the fact that many, many people thought this way in California in 2005. Their choice wasn't between more housing and less "other stuff". They consumed more housing, AND they consumed more other stuff. The former is true because the rule of thumb was "lever yourself into the largest house you can, and you will enjoy the highest absolute capital gains". This is why measures of housing "velocity" went through the roof. One can imagine the impact of flat home prices on income expectations--disastrous. This is in fact what occurred during the course of 2006 in bubble states, and in early 2007 elsewhere, sparking the 2007 recession, spiking delinquencies, and eventually producing the credit crisis.

Someone asked about taxes. In Canada, no capital gains tax on principal residence - I believe there is for second/investment property.

Btw, if you watched some of the home reno/flip this house shows on HGTV (as I often did) leading up to the bust, you'd think the housing fairy was out of control. Buy a house, do some general improvements, relist for hundreds of thousands more. Something was amiss.

BTW, I wonder sometimes whether economists hold to the "debt is just redistribution" meme. If this is the case, then one person's higher current consumption is another's deferred consumption, so the net effect is zero. How realistic is this? In a period of record capital gains and record wealth inequality, isn't it reasonable to conclude that the propensity to consumer of the marginal creditor is, on the margin, much, much lower than the marginal debtor's? Combine this with higher future income expectations on the part of both, and consumption increases without the expectation that it will decline in the future.

David: I hold to the "debt is just redistribution" meme, at least as a *first-order approximation* to reality. It leaves out a lot of important stuff, which is real. But you can't start looking properly at that other stuff until you first stop thinking of debt as either negative or positive net wealth. Getting your head straight on that is the first step, not the last step.

Debtors, clearly, have *historically* had a higher *average* propensity to consume out of *past current* income than creditors. Otherwise they wouldn't be debtors and creditors (ignoring debt to finance investment, rather than consumption). Whether they now have a higher marginal propensity to consume out of future income is a different question.

David @11.53: If you as an individual expect that *future* house prices will rise, e.g. because you expect a wave of new rich immigrants to arrive on your shores, in future, you will want to go long housing, and your expected net wealth increases. Essentially that's an anticipated gain from believing you can out-guessing the market.

If everyone thinks he can outguess the market, half guessing it will go up, half guessing it will go down, the current house price stays the same, but everyone thinks they are richer.

If everyone thinks house prices will go up, because the new immigrants will arrive soon, then house prices go up today. That's just like my fairy, giving me the green budget line. And when the rich Chinese (or whoever) eventually arrive in Vancouver (or wherever), all the old Vancouverites move to point B, where they are better off.

(Barro-Ricardo bonds are net wealth when there's new immigration. An old paper by Willem Buiter got this point.)


Df56: AH! My eyes! As they say on the car forums: lose the CapsLock key buddy; It's shouting!

The question of whether people are saving too little is a separate question.


A slight digression, but on a topic I think you like:

“But you can't start looking properly at that other stuff until you first stop thinking of debt as either negative or positive net wealth.”

I know this has been a theme of yours going back for some time.

In a straightforward sense, this is true, since debt held as an asset is also debt issued as a liability. In aggregate, the two cancel.

In another sense, it requires qualification.

Suppose a real economy consists of real assets R held by corporations (forget real assets such as house held by households).

Suppose corporations have financed R by issuing debt D and equity E, and that all such financial claims are held directly by households.

Suppose there are no other real or financial assets in the economy (including no banks).

Then the net worth of the economy is equal to the net worth of households.


R = D + E = net worth

First, note that your theme applies to both debt and equity claims, since both cancel themselves out respectively as financial assets and liabilities, such that R = net worth.

I think it’s important that while you have focused on debt in this way, you should be applying the same reasoning to all financial claims, debt and equity.

Second, your theme requires further qualification.

There is a difference between saying that the net worth added by D and E is zero, and saying that net worth is equivalent to D + E. Both are true. The first doesn’t negate the second.

Now, suppose I add a financial institution to the economy. This institution holds D + E as assets while issuing claims itself of D2 + E2.

Then R = D + E = D2 + E2 = net worth.

As per your theme, the net worth added by D, E, D2, and E2 is zero.

But net worth is still equivalent to D + E, as well as D2 + E2.

But net worth is not equivalent to D + E + D2 + E2.

Bottom line: notwithstanding your theme of zero net contribution, a subset of aggregate debt and equity can still correspond to net worth.

One must be carefully to identify that subset accurately, because the rest of it cancels out in a way that is somewhat different than the more basic meaning that you infer in your theme.

This distinction is why I think some economists (e.g. Steve Keen) have exaggerated the trend in debt/GDP ratios – because for example there is double counting in the case of mortgage debt that has been securitized by MBS or CDO securities. There has been “horizontal duplication” of debt in the more recent history of these ratios. That exaggerates the trend at some level of meaningfulness.

Cool paradox! And new to me, though judging by the comments I am practically the only person on the planet who can say that.

Naturally, I agree with all the exogenous "escape clauses" that have been raised here to refute the paradox: can't be supported in general equilibrium, doesn't account for income effects, neglects considerable transaction costs, etc. One could go on in this vein.

But this is not like many economic paradoxes, such as the St. Petersburg, in which one has to introduce the exogenous point that nobody will really bet infinite (or all available) wealth on order to reach a paradox in the first place. Here the paradox is endogenous: no matter what the current relative house price, there always exist both higher and lower prices that one would prefer, with no obvious discontinuity in the preference function. It seems there ought to be a narrow, technical refutation. But I have to admit, I can't spot it.

Mine is very L shaped. I tend to view housing as a life purchase, so the initial cost of purchase is important and the final price of selling is important, but what happens in between as unimportant. Collateral is just debt requiring offsetting income. While a lower rate is a benefit, any rate is a cost. While doubling or halving would present a convenience or inconvenience during a move in between, and a large one if one moves between expensive and inexpensive areas, I would probably not move again unless I won a lottery. Doubling or halving instantly is unimportant, only that at the end it is worth more. It is easier to believe it will be worth more if it doubled than halved, and halving says bad things about the economy, but if it ended up at the same place, I would not mind. I did consider selling at the peak and renting, but calculated at least a 30% decline to break even; as it was it ended up a 40% decline but that isn't much difference for the inconvenience and uncertainty. Naturally I am probably more exception than rule and it probably wouldn't be as L shaped at other periods of my life. Double it if it will stay doubled or increase more, leave it unchanged if it will not, halve it only if it will double again in the future.


I agree with your "Vancouver" logic, but I'm not sure it reflects the reality of expectations at the time of the bubble.

Of course the essence of a bubble is the expectation that one will always find a buyer to pay more for the asset, whether now or ten years from now. You might respond that prices will rise immediately to reflect that, and then stop rising, and that everyone would recognize what just occurred. However, this misses the fact that bubbles start out with 50% optimists and 50% pessimists. It is the migration of pessimists to the optimistic camp that creates the bubble. When there are 100% optimists, the bubble pops -- the immigrants, you see, never show up. At that point, faced with the fact that income "smoothing" was actually time-shifting, the former optimists have to consume less of both sets of goods. Again, you might respond that as the optimists de-levered, they would pay back debt and raise the consumption of creditors--so zero net effect on consumption. I'm not sure this is correct. It may be the case that creditors continue to try to defer consumption and just buy less-risky assets with the proceeds of debt repayment, driving their price up. Isn't this the essence of the AD drop/Treasury bubble we are experiencing now?

JKH: What you say seems correct to me, subject to the careful qualifications you make. If all real investment is financed by debt and equity, and if debt and equity finance finances only real investment, and if we exclude (or carefully account for) all cases where individuals and firms both borrow and lend (act as financial intermediaries), Then total debt+equity equals wealth (but if we added in real assets as well we would be double-counting, of course).

But notice how your (very careful) conclusion leads to considering debt+equity as *positive* wealth. The normal meme is "shit! look at all that debt! we are really poor!". It's treated as *negative* wealth.

The "horizontal duplication" seems important to me. It seems to be pro-cyclical. That leads people to falsely conclude "It's all a mirage! We just thought we were rich, because we had all borrowed so much to buy stuff with!"

But trying to clear up this conceptual mess, as you are doing, is a Herculean task. Key TooMuchFed in 3,2,1.. ;-)

Phil: "It seems there ought to be a narrow, technical refutation. But I have to admit, I can't spot it."

Well, it's because the fairy only comes to me, and she must be messing with everyone else's demand or supply curves to get the change in house prices, but she doesn't mess with mine. It's an individual, not a general equilibrium experiment.

To convert it into a GE experiment, you could think of immigration as the exogenous factor that changes prices, and the preferences drawn in my diagram are those of the native born. The fairy could then either suddenly bring in a wave of immigrants, raising prices, or suddenly deport previous immigrants, lowering prices. Either way, the native born would gain on the housing market. (I think I've got that right).


I'm not sure I understand your example. Since all corporations are owned by households then we can say that debt instruments cancel out, the households that own the corporation that issues debt are the ultimate borrowers and the households that buy the bonds the lenders. Lenders have a positive D associated with them, borrowers get negative number -D so the net value of debt in the economy is zero.

How does equity cancel? Holders of equity have a positive value of E, which households have a negative value of E?

David: we need to be careful in defining "optimist" and "pessimist". It's expectations about future prices, but compared to what? If it's compared to current prices, then we always have 50% optimists and 50% pessimists at equilibrium (otherwise prices would be higher). If it's compared to some fundamental value, then you are right. A bubble has 100% optimists. (I'm speaking loosely, of course.)

Adam: if you think of equity as shares, and shares as just debt with slightly funny state-contingent dividends, then the parallel is clearer. Shares are a liability of the corporation that issues them to borrow money.

Phil: here's a better though-experiment: the fairy either builds lots of new houses (with her magic wand) and sells them in the market, lowering prices. Or else buys lots of houses with other stuff she created with her magic wand, and destroys them, raising prices.

Nick, shares may be viewed as a liability of the corporation but the corporation is owned by households.

Debt cancels out becuase you can "look through" the corporate structure and say that there are households who have borrowed D (owners of the issuing corporation) and other households who have lent D.

You can view equity as a type of debt that the corporation owes to the households that own the corporation, so the owners of the companies are long an amount E of equity claims. But which *housholds* are short E?

JKH is most definitely wrong when he says that "your theme applies to both debt and equity claims, since both cancel themselves out respectively as financial assets and liabilities".

Debt is zero net supply, equity is in positive net supply. In the example D = 0 and E = R, after netting out.

Dammit! The fairy in that second thought experiment is just like that free trade example. We can load corn onto ships, sail it out to see and by magic it gets converted into cars on the return journey. Or vice versa. And we always gain, either way, unless the Japanese have exactly the same relative price of corn and cars as us.

Adam: we are agreed that (given JKH's assumptions) Net wealth = R = D+E.

Now if someone says that wealth = R+D+E. Or Wealth = R-D+E, or Wealth =R-D-E, in other words, if someone insists that R and D and E all belong in the formula, we reply "No, R belongs, as an asset of the corporation, *or* of the household that owns the corporation, but not both, but net D is zero, and net E is zero, because they are both assets of the household an liabilities of the corporartion

We agree that R = D + E.

I claim that also R = E. Do you agree?

Adam P,

Households have net worth (right hand side of the balance sheet), but do not issue equity claims against it.

Households may hold equity claims (left hand side of the household balance sheet), which are effectively liabilities of corporations.

Equity claims net to zero, like debt claims.

There's no difference in the zero netting characteristics of financial assets in general - debt, equity, pension liabilities, etc.

On the other hand household net worth, which is not represented by equity claims, does not net to zero.

"David Friedman has "prior art" on this one: "Application: Housing Prices--A Paradox" in this micro textbook: http://www.daviddfriedman.com/Academic/Price_Theory/PThy_Chapter_3/PThy_Chapter_3.html"

I might be the first one to have published the argument, but I didn't invent it. It was put to me as a puzzle at a party at UCLA about thirty years ago by one of my colleagues there.

David Friedman

David: (Wow, and David Friedman actually reads my stuff! Though someone must have tipped him off.)

I thought it was a really great example of applied basic micro for your textbook. You gave a really clean presentation (but you missed out on the fairy!). It shows how much mileage you can get out of really basic micro.

Now, I vaguely remember Milton Friedman saying something relevant to this, as well. On what you hold constant when you draw a Marshallian demand curve, and about income effects of price changes not being really there. Something like that. Do you, or does anyone else, remember the article I have in mind?


Take the situation just as you've just described and to simplify aggregate the household sector into one big household.

Now assume the coporation issues new debt D1 to finance a new investment that makes real asset worth R1. Now, now worth must be R + R1. Where does the increase show up?

Well, befoe R1 has appeared the household debt holdings have increased from D to D+D1, but household net worth is still R. E has fallen by an amount D1.

After R1 has been built new worth has increased to R+R1, the increase is entirely reflected in the value of E.

This was true from the first issuance of any claim, in this economy net debt D = 0 and equity E = R.

Adam P.,

Original example:

R = D + E = household net worth, where households hold all D and E

The capital structure of firms is D + E

D and E are both financial claims

They both represent a claim on corporate cash flow

They are just ranked by priority of claim on cash flow

Both net to zero when considered as claims issued and claims held

Nick’s theme applies to all financial claims, not just debt

JKH: "Nick’s theme applies to all financial claims, not just debt"

Yep. With the exception of financial claims like money, only if they are issued by some monopoly issuer. But let's not go there now.

Adam P.,

Again, household net worth is not a financial claim, and specifically it is not an equity financial claim.

If corporate assets increase by R1, and corporate liabilities by D1, and household assets by D1, then household net worth increases by R1 = D1.

Gross debt claims have increased by D1 and net debt claims by zero.

Gross equity claims have increased by zero, and net equity claims by zero.

Household net worth has increased by R1 = D1.


"But let's not go there now"


Also venturing perilously close to MMT "vertical" and "horizontal" distinctions - another stinky variation on the reasonably straight forward generality of the subject.

So let's really not go there now.

Nick, JKH,

Imagine a world with no uncertainty and no assets. R = 0, the consumption good just appears but everyone's endowment is know with certainty (to all agents) for all eternity. This implies that their is no default but there may be debt issuance for the purposes of consumption smoothing.

Their is also equity issuance although in this setup equity is indistinguishable from debt.

We have R = 0, D = 0 and E = 0 (all net numbers).

Now magically (the one unexpected thing, ever) a productive asset appears that has value of R.

Nobody's debt is worth more than it was before, we still have D = 0.

The asset was given to a household who had, in the past issued equity. That equity is now worth R more than before to the holders.

Why? Well, when the equity was issued to raise an amount, say E0, it did not *obligate* the issuing household to pay anything back. However, it did entitle the equity holders to *all* of the consumption good that the issuing household has over an above it's endowment. Of course, before the asset appeared this was just equal to E0 so the equity was indistinguishable form debt.

Now that the asset has appeared and produces extra consumption the household that owns the asset has an amount of consumption greater than its endowment but *all* of the excess is owned by the equity holders. This is not true of that household's debt holders (its creditors).

Thus, once the asset has appeared the value of equity to it's holders is now E0 + R. The issuing household didn't pay for the asset though, in terms of the consumption good the equity issuing household still suffers -E0 less consumption going forward. The issuing household doesn't lose any of its endowment.

To make this all consistent with JKH's example rename the equity issuing household as a corporation.

The point is that when the asset of value R appeared the value of equity in the economy went up by R, the value of debt didn't change. R = E and D = 0.

The reason is that equity isn't just a claim junior to debt, equity is a claim to *all* the excess over what is owed to debt holders.

Adam P.,

“The asset was given to a household who had, in the past issued equity. That equity is now worth R more than before to the holders.”

Once again, households do not “issue” equity claims.

“To make this all consistent with JKH's example rename the equity issuing household as a corporation. The point is that when the asset of value R appeared the value of equity in the economy went up by R, the value of debt didn't change. R = E and D = 0.”

The institutional difference between households and non-households is critical to understanding the financial claims netting process. This difference doesn’t permit the assumption of mere “renaming” with any logical coherence.

Starting with your “renamed” entity, the household can’t realize that value without having a financial claim on it. The default claim is an equity claim. It doesn’t matter that the example includes no debt. In fact, it just reinforces the point that there is no difference between the notions of netting debt claims and equity claims.

By review:

I tend to distinguish between equity claims (issued by non-households) and household net worth (no claims issued).

Non-household equity claims and household net worth can also be grouped as equity more broadly.

I usually refer to household net worth as household equity in this sense.

This is partly definitional, but largely conceptual in that households do not issue equity claims on the household balance sheet.

You can think of household equity as residual equity in the economy, since all equity nets to zero before it hits the household balance sheet. The chain of equity in the economy stops at the household in that sense.

The net of all equity in the economy is household net worth or equity (apart from net foreign claims).

JKH, believe me I understand what you're saying.

You're basically saying that when you net out, the corporate sector nets to zero because corporate balance sheets have assets of total value R and liabilities of total value D + E.

Household balance sheets have asset side of D + E and no liability side. It follows that D + E = R.

"You can think of household equity as residual equity in the economy, since all equity nets to zero before it hits the household balance sheet. The chain of equity in the economy stops at the household in that sense."

Yes, nothing I've said disagrees with that.

Your just making a semantic argument, fine. Everything you said in this last comment makes sense.

But you can't have D = 0 and E = 0 but D + E > 0.

Adam P.,

That's not what I'm saying at all, except for what you quoted.

But I'll have to leave this for now, because of time - sorry.

Maybe Nick can add.


If one sells shares in a company which projects gains from a yet-to-be-discovered gold deposit, or sales on the internet which have yet to materialise, or anything similar, surely one has created a debt. But it seems to me to be stretching the definition to claim there is an "asset" to balance the debt - unless you count hope as an asset.

The comments to this entry are closed.

Search this site

  • Google

Blog powered by Typepad