Liquidity and the housing market Phillips Curve

I think it is a stylised fact of the housing market that, on average, houses sell quickly when house prices are rising, and sell slowly when house prices are falling. (I am talking about house prices rising or falling relative to trend). There is a negative correlation between the rate of change of house prices (relative to trend) and the length of time houses stay on the market before selling. Why should this be so?

This stylised fact is very much like a housing market Phillips Curve. When prices are rising unemployment is low (houses sell quickly). When prices are falling unemployment is high (houses sell slowly). Thinking of this stylised fact as a Phillips Curve leads immediately to the following two theories:

1. Sticky prices. You can think of this as the "New Keynesian" or Phelpsian explanation of the stylised fact. Sellers are reluctant to raise prices when demand rises and/or supply falls. And sellers are reluctant to lower prices when demand falls and/or supply rises. So actual prices lag behind equilibrium prices (the prices that would equate supply and demand). So we see excess demand for houses when equilibrium prices are rising and actual prices are rising too, but more slowly. And we see excess supply of houses when equilibrium prices are falling and actual prices are falling too, but more slowly.

2. Sticky expectations. You can think of this as the "New Classical" or Friedman/Lucas explanation of the stylised fact. Sellers have imperfect information on the current state of the housing market. They do not know the contemporaneous equilibrium price. Even if they form their expectations rationally, because they form those expectations on the basis of limited and lagged information, their expectations of the current equilibrium price will look a lot like adaptive expectations. If the full-information equilibrium price rises relative to trend, the expected equilibrium price will rise more slowly, so sellers will accept prices that are lower than they would under full information, and houses will sell more quickly. If the full-information equilibrium price falls relative to trend, the expected equilibrium price will fall more slowly, so sellers will insist on prices that are higher than they would under full information, and houses will sell more slowly. In other words, sellers face the standard Lucasian signal-processing problem. They cannot distinguish between a price for their particular house that is high/low relative to the market equilibrium price, and a price that is high/low because the market equilibrium price is high/low.

The above is what you get when a macroeconomist thinks about the housing market. Two very standard macro theories, applied to the housing market. Both those theories probably contain some truth. But I want to set them aside, and focus on trying to build a third theory, to see if I can make it fly.

3. Time-varying liquidity. (Maybe you can think of this as a New Monetarist explanation of the stylised fact??)

Houses are an illiquid asset, very much like used cars. Each house is unique in at least some way. Each potential house buyer is also unique in at least some way, and will have a different preference-ordering over particular houses than any other buyer. Matching the right houses to the right buyers is a non-trivial problem. The flow of houses, and the flow of house buyers, onto the market, is finite. Buyers face a trade-off between buying a house quickly, and waiting to buy the house that is right for them, sold at a low price by an impatient seller. Sellers face a trade-off between selling a house quickly, and waiting for the right buyer, who really likes this particular house, and who is impatient to buy quickly even at a high price. The steeper the slope of the trade-offs (in absolute value), the less liquid are houses, and the greater the incentive for sellers and buyers to wait for a better deal.

So there is a non-zero equilibrium average time-to-sell for houses that enter the market (and also an equilibrium average time-to-buy for buyers who enter the market).

Under what circumstances would the equilibrium average time-to-sell in that proto-model (OK, it's not really a formal model) be negatively correlated with the rate of change of house prices?

Sticky prices, or sticky expectations, would give us the required negative correlation. Sticky prices just mean that sellers fail to choose their optimal point on the trade-off, and just insist on a price that is too high when the equilibrium price falls and the trade-off moves against them. Sticky expectations means that sellers think the trade-off is better than it really is when the equilibrium price falls and the trade-off moves against them, so they are surprised at how long it takes their houses to sell.

But can we build a housing market Phillips Curve without either of those two assumptions?

It depends on the shock. It depends on what causes the equilibrium price to change.

Suppose it's a purely nominal shock. If the equilibrium is unique, and there are no other sources of non-neutrality elsewhere in the economy, then the standard classical doctrine of the Neutrality of Money should apply in this case as well. Both buyers' and sellers' behavioural functions should depend on real variables only, so an equi-proportionate change in all nominal variables will not change the equilibrium value of any real variable, including average time-to-sell. Nominal house prices fall, but all prices fall by the same percentage, so real house prices stay the same. The housing market Phillips Curve is vertical.

OK, suppose it's a real shock. There are two things that could cause the real price of houses to fall: a fall in demand; and a rise in supply. The big difference is that a fall in demand will cause a decrease in equilibrium quantity traded, and a rise in supply will cause an increase in equilibrium quantity traded.

Other things equal, thick markets are more liquid than thin markets. For example, if you double the number of buyers and sellers entering the market every period, holding the variances constant, sellers find a suitable buyer twice as quickly for a given price, and buyers find a suitable house twice as quickly for a given price and quality. The trade-off curves facing buyers and sellers become flatter, and both sides will choose to buy and sell more quickly (though generally not twice as quickly). The thicker the market, other things equal, the shorter the average equilibrium time-to-sell.

Suppose all fluctuations in (real) house prices were caused by fluctuations in (real) demand (the supply curve never shifts). An increase in demand will cause house prices to rise, and will also make the market thicker and more liquid and so reduce the equilibrium average time-to-sell. A decrease in demand will cause house prices to fall, and will also make the market thinner and so increase the equilibrium average time-to-sell. Yep, that generates a housing market Phillips Curve, even without sticky prices or sticky expectations.

But suppose instead that all fluctuations in (real) house prices were caused by fluctuations in (real) supply (the demand curve never shifts). Supply increases would cause falling prices, but thicker and more liquid markets, and shorter equilibrium average time-to-sell. The predicted housing market Phillips Curve would slope the wrong way, contradicting the stylised fact.

Is it reasonable to assume that most fluctuations in house prices are caused by fluctuations in demand, rather than by fluctuations in supply? Because if it is reasonable to assume this, you can generate a housing market Phillips Curve without resorting to sticky prices or sticky expectations. Otherwise, you can't (or, at least, I can't).

Comments

[Nick Rowe]

By the way, the above also serves as an example to illustrate how economists work, and how they relate theory to facts.

I start with a very loose impressionistic "stylised fact". I list a couple of theories that could maybe explain that fact, then sketch a new theory that might also work. But I note that whether this theory would work depends on another fact, which may or may not be true.

If I were a really good, hard-working, competent economist, doing this properly, I would also: get the data and plot a scattergram just to check how much of a "fact" my stylised fact really is; do a thorough literature survey to see if any other economist has ever said anything vaguely similar or relevant; crank out a mathematical formal version of my proto model, so I could check rigourously that my conclusions follow from my assumptions, and specify those assumptions more precisely; spend time trying to derive more implications from my model, especially testable implications, and especially testable implications that might distinguish my model from alternatives; collect the data and run some regressions to test those implications.

But I'm not. And this is just a blog post anyway.

[Andrew F]

Now you're providing your own snark, Nick.

[Mike Moffatt]

He's cutting out the middle man and passing the savings along to you.

[Nick Rowe]

This comment is from Ian Lee (again, he had trouble posting. Sometimes TypePad won't let me post comments either. I have to log out, then log back in again):

Nick,

While I very much appreciate your always logical analyses on the issues you have selected, nonetheless there is a ``war going on òut there`` that is burning with a white heat.

I refer to Krugman (and his wingmen Rob Parenteau at Levy Institute, Prof Mitchell at U Newcastle, Australia and Scott Fullwiler at wallstreetpit.com) who (i.e. Krugman) attacked Ken Rogoff for his research on the negative impact of high levels of government debt on economic growth. And when Krugman is not criticizing Rogoff, he is going after Niall Ferguson for noting that throughout western history, countries with high levels of government debt do not always end in a happy place (I recall that some British kings lost their head, so to speak, over the issue).

And referring to the earlier discussion that tangentially dealt with scholarly economists versus business economists, contra Krugman, Bill Gross and El-Erian at PIMCO and David Rosenberg at Gluskin Sheff are deeply concerned over the high and escalating levels of sovereign debt.

Perhaps the academic economists have insights above and beyond the business economists or it is, perhaps, conceivable that the latter group, working with or employed by the bond vigilantes (that Krugman claims are imaginery - but why then did the EU provide a $ 1 Trillion bailout if the banks were still willing to lend to Greece?), know something that the rest of us do not know.

Your analysis concerning this debate and the related ``financial balances`` reinterpretation of macro concerning S-I and its relationship to the current account, would be most appreciated.

I mention the latter, as the Levy Institute folks are using the `financial balances` theory to support what is essentially Canadian equalization grants whereby the surplus EU north recycles funds to structurally imbalanced EU south on the basis that:

``the domestic private sector and the government sector cannot both deleverage at the same time unless a trade surplus can be achieved and sustained. Yet the whole world cannot run a trade surplus``

The Levy proposal is contra the radical restructuring currently being attempted by Greece or Simon Johnson`s proposal that Greece default on its debt and leave the Euro for the Drachma and then depreciate the new Drachma to get back to `balance``.

These various arguments revolve around understandings concerning appropriate levels of sovereign debt and whether additional stimulus should be injected in the US economy and the EU economies.

I hope that you and your colleagues weigh in on this issue.

Ian

Ian Lee, Ph.D
Sprott School of Business
Carleton University
Ottawa, Canada

http://sprott.carleton.ca/faculty_and_research/ilee.html

[Nick Rowe]

Ian: I've been following this debate, sort of. My only real observation is the following:

There are two sort of countries: "printers" (who can print their own currency and borrow in that currency); and "non-printers" (who can't). Canada, US, UK, etc., are printers. Greece, Spain, Ireland, etc., are non-printers. At the moment, some (many) of the non-printers have to watch the "bond-vigilantes". The printers don't. (I think there are good theoretical reasons for this.)

At some time in the future, it may be that the printers too have to worry about the bond vigilantes. I actually welcome this. I worry more that this won't happen. Because when it happens, it will be a sign that investors are beginning to flee away from money and financial assets, and will flee into real assets. That means the excess supply of real goods is ending. And it means that governments will be able to cut deficits without fear of worsening the recession.

But I worry a bit that governments may not be able to change direction quickly enough when it happens.

[Too Much Fed]

"Houses are an illiquid asset, very much like used cars."

I think greenspan made something similar to this mistake too.

[Too Much Fed]

I don't really see anything about the medium of exchange, specifically currency denominated debt.

I don't see anything about financial asset speculators and interest rates and whether someone is investing for a return or actually to live in the home.

If interest rates are between 2% and 5% and housing prices are expected to rise 6% to 12%, will financial asset speculators start trying to make capital gains?

I believe a look at the "budgets" of the financial asset speculators and the people who actually live in the home is warranted along with wage income expectations.

[Too Much Fed]

"This stylised fact is very much like a housing market Phillips Curve. When prices are rising unemployment is low (houses sell quickly). When prices are falling unemployment is high (houses sell slowly)."

Budget (balance sheet) effects?

Have you read CalculatedRisk's post(s) about housing usually leading the recovery in the USA? I would say due to lower interest rates.

[Too Much Fed]

"That means the excess supply of real goods is ending."

That sounds like you think this is a problem. Just enough excess supply of real goods should be aimed for and wonderful.

[Too Much Fed]

The way Bill Mitchell explains sectoral balances:

trade deficit = gov't deficit plus private sector deficit

What happens if the private sector smartens up and refuses to go into currency denominated debt and then elects people who refuse to go into gov't currency denominated debt?

I also believe this is why housing in Canada and Australia did not follow the USA (probably Spain followed the USA version). I don't have the numbers but I'm guessing Canada and Australia had smaller trade deficits (specifically with china).

[Too Much Fed]

About Ian Lee's post, I believe the similarities and differences between private currency denominated debt and gov't currency denominated debt should be discussed.

Here is one thing that I think is correct. When cities, states, and private entities borrow in currency, they have to repay both interest and principal so the loan is paid off at the end of the term so there is no rollover risk. I don't believe that is true for gov't currency denominated debt. Why is that?

[Too Much Fed]

A little off-topic.

Here is a real world example of why when discussing apples, I wanted to break it down into workers/consumers and corporations.

http://www.washingtonpost.com/wp-dyn/content/article/2010/08/20/AR2010082005165_3.html

If that link does not work, you can get it from here.

http://www.calculatedriskblog.com/2010/08/ceo-no-need-to-invest-right-now.html

[Nick Rowe]

Too Much Fed: "I don't really see anything about the medium of exchange, specifically currency denominated debt.

I don't see anything about financial asset speculators and interest rates and whether someone is investing for a return or actually to live in the home."

I don't see anything in this post about badgers, either.

[Frances Woolley]

"I think it is a stylised fact of the housing market that, on average, houses sell quickly when house prices are rising, and sell slowly when house prices are falling. (I am talking about house prices rising or falling relative to trend). There is a negative correlation between the rate of change of house prices (relative to trend) and the length of time houses stay on the market before selling. Why should this be so?"

Loss aversion.

[Nick Rowe]

Frances: Thanks!

Yep, I would classify "loss aversion" under the sticky price theory. It's one explanation of why prices are sticky. There has to be something to it, but it has a couple of problems: it only explains why prices are sticky downwards, not upwards (though maybe they are more sticky down than up); and if people insist on too high a price, even if they do eventually get the price they previously paid for the house, and don't lose money on the sale, they still face losses through having to wait too long to get a seller. And, by definition, if they wait longer than the Umax time, those losses must be bigger than if they had rationally chosen an asking price. (Maybe they delay moving to a better job, or have to rent an apartment, or keep on paying the mortgage on an empty house, or whatever.)

[Frances Woolley]

I think they are more sticky downwards. And I think people do view losing $50,000 on a house differently from sacrificing $50,000 by not looking for a better job in another city.

This doesn't mean your theory is wrong, it just means that commenting on your blog is more interesting than refereeing a paper for the 4th time.

[JP Koning]

"An increase in demand will cause house prices to rise, and will also make the market thicker and more liquid..."

Hi Nick. Question about the above. Is this because an increase in demand brings more buyers into the market, and more buyers means a thicker market?

As you point out, there are many theories to go about explaining a stylized fact. Here's (yet) another way to explain why the increasing rate of housing prices seems to be correlated with their increasing liquidity. Markets are in equilibrium, then something causes a thicker and more liquid housing market than before. The liquidity-premium of a typical house rises as a result. Since this saleability/liquidity is a valuable feature of a house there will be an increase in demand for houses. Prices rise.

[Nick Rowe]

JP: Yes, but an increase in demand causes an increase in the equilibrium quantity of both buyers *and* sellers. At the front of my mind, when I wrote that, was the standard intro economics supply and demand diagram. If the demand curve fluctuates, while the supply curve stays fixed, we see a positive correlation between P and Q. But if the supply curve fluctuates, while the demand curve stays fixed, we see a negative correlation between P and Q.

I like your 4th theory. It makes logical sense. But the something that causes markets to become thicker, and houses more liquid, would have to be a fairly permanent thing, if it were to have much impact on house prices.

Here's a fifth theory. It's a self-fulfilling version of your 4th theory. Tinkerbell says that houses are more liquid. People believe Tinkerbell. People who would not previously have bought a house, because they knew they would have to sell again in 5 years when they have to move province, now decide to buy a house. So the housing market becomes thicker, as more mobile people buy and sell houses, so Tinkerbell's prophecy is self-fulfilling. (And house prices rise too, as in your 4th theory, because liquid assets are more valuable). Then 20 years later Tinkerbell has a pessimistic spell, and says houses are less liquid.

[JP Koning]

Ok, I see where you're coming from. As an aside, seems to me the stylized fact you are trying to explain applies not only to housing markets but most asset markets. In the stock market, for instance, it's seems to be a rule that higher prices correlate with higher volume/lower bid ask spreads.

[Nick Rowe]

JP: Good point. There's a Phillips Curve for all assets, maybe?

I have just found it a lot easier to think about assets like houses and used cars. The illiquidity is just so much more transparent.

[Sriram]

Loss Aversion... and the flipside? Exuberance maybe? (ie. rising prices results in more speculation, which would beget quicker turnovers).

I'd expect that since a lot of sellers would also simultaneously be buyers (ie. selling house A in order to buy house B) this would affect their willingness to delay acting in a falling market (he's reluctant to sell past the peak, while also scared of buying something that's currently declining in value).

In a rising market, the current (sell) house is rising in price making the owner feeling wealthier and more apt to spend on a new home. But the pool of new homes is also rising in price, so he's further motivated to buy more quickly to lock in at a lower acquisition cost.