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.
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).