Unit 8 Economic dynamics: Financial and environmental crises
8.5 Modelling a house price bubble and collapse
Before you start
In this section and the next, we put the microeconomic supply and demand framework together with the concepts of positive feedback and tipping points to build a model of the dynamics of the housing market. If you are not familiar with supply and demand diagrams, you should first read Sections 8.2 and 8.3 of the microeconomics volume.
Positive and negative feedback processes in the housing market
If the housing market is in equilibrium, the price of housing remains at the same level from period to period—the price at which supply and demand are equal. What happens when the price is not at the equilibrium level depends on whether buyers and sellers are concerned not only about the current price, but also about future prices—that is, about how the value of their asset might change in future.
When decisions depend only on the current price
If buyers and sellers were concerned only with current prices (as in the case of food prices, because food is not an asset), we would expect a negative feedback process to restore equilibrium. The housing market equilibrium, like the equilibrium in the bread market, would be stable.
Figure 8.9 explains the dynamic process of price adjustment in this case. The left-hand panel shows the supply and demand curves for housing. The market is in equilibrium at point E, where supply and demand are equalized at price \(P^*\). We can illustrate what happens when prices are changing using the diagram on the right, with the price in period t, \(P_{t}\), on the horizontal axis and the price in the next period, \(P_{t+1}\), on the vertical axis. We have marked the point where \(P_{t}= P^*\): at this price, the market is in equilibrium so the price remains the same next period: \(P_{t+1} = P^*\). Therefore, the equilibrium corresponds to a point on the 45-degree line.
What happens if the market is not in equilibrium? Suppose the price in period t is \(P_a\), above \(P^*\). Work through Figure 8.9 to analyse what happens, and how to derive the price dynamics curve.
- price dynamics curve
- The price dynamics curve is a graph of the relationship between the price of a good in period \(t\) (on the horizontal axis) and the price in period \(t + 1\) (on the vertical axis). A point where the graph crosses the 45-degree line represents a market equilibrium: at this price demand = supply so the price stays constant from one period to the next. At other prices excess demand or excess supply leads to a change in price.
The price dynamics curve is flatter than the 45-degree line, and the intersection of the two is an equilibrium price (being on the 45-degree line means that the price will be the same in the two periods, that is, unchanging, as is required in an equilibrium). When prices are above the equilibrium level (in the left panel of the figure), the PDC (in the right panel) lies below the 45-degree line. If you start at a price below \(P^*\) and repeat the derivation you will find that (as shown in the figure) the PDC is above the 45-degree line while the price rises up to the equilibrium level.
The price dynamics curve in Figure 8.9—flatter than the 45-degree line—corresponds to the case of a stable equilibrium. If due to a shock the price moves away from its equilibrium level, a process of negative feedback along the PDC restores equilibrium in the market.
We have illustrated this process by a shock that raised the price above the equilibrium price, so the negative feedback lowered the price. But this is not why we call the feedback negative. The feedback is ‘negative’ because the actions of buyers and sellers work against (‘negate’) the initial shock. If the shock resulted in a price lower than \(P^*\), this would result in the price increasing back to the equilibrium level.
When beliefs about future prices matter
Since housing—unlike bread—is an asset, it is more realistic to assume that supply and demand for houses depends not only on the current price, but also on what people believe will happen to prices in future. Think about what might then happen if people observe that houses are selling for higher prices than usual. News spreads that the market seems to be heating up.
Depending on beliefs, equilibrium may be restored through a negative feedback process. But it is possible that a positive feedback process arises that is strong enough to result in instability—a house price bubble. Figure 8.10 illustrates these two alternative scenarios for the house price, \(P\).
The price shock leads some people to believe that future prices will be higher, so houses are becoming a more valuable asset and the demand curve for houses goes up. But if people believe that the price rise is just a blip, then as shown in the left-hand panel, the negative feedback process described above in Figure 8.10 will restore the equilibrium.
Figure 8.10 Positive and negative feedback in the housing market.
The right panel illustrates a positive feedback process. A bubble can happen if the view that prices are likely to be higher in future spreads widely. Individuals interpret a price rise to mean that other people have received news that they hadn’t heard themselves, and adjust their own expectations upwards. Or they may think there is an opportunity for speculation: to buy the house now and sell to other buyers at a higher price later. Either way, the increase in demand is large enough to put further upward pressure on prices creating a positive feedback, with further increases in demand and price.
The price dynamics curve for housing assets
We can model the two alternative scenarios as we did before, using a diagram of demand and supply and deriving the price dynamics curve. The important difference is that the demand curve depends not only on the current price, which is on the vertical axis as usual, but also on expected future prices. If the expected future price increases, demand will be higher at each level of the current price. So the demand curve will shift outwards (to the right).
- excess supply
- A situation in which the quantity of a good supplied is greater than the quantity demanded at the current price. See also: excess demand.
A price shock raises the price of houses from the equilibrium price \(P^*\) to \(P_a\). In Figure 8.9, excess supply at \(P_a\) led to a process of dynamic adjustment back to the equilibrium price. But now, some people believe that the price rise is the beginning of a period of rising prices, shifting out the demand curve.
Figure 8.11 shows what might happen next. The new demand curve is Da. In this case, the increase in demand is relatively small—perhaps because the majority of people don’t expect prices to rise further—so there is still excess supply at price \(P_a\). This means that prices will begin to fall, as before. The process of negative feedback operates similarly to the one in Figure 8.9, although with smaller price adjustments as the demand shift puts some upward pressure on prices, producing less excess supply. As prices fall and people realise that the rise in price was temporary, the demand curve will shift back to where it was before. Prices will stabilize again at \(P^*\).
Figure 8.11 The price shock is dampened: negative feedback and stable equilibrium.
The price dynamics curve is similar to the previous one. We have drawn a steeper curve, representing smaller price adjustments, but it is still flatter than the 45-degree line. The housing market equilibrium is stable.
Positive feedback and amplification of a house price shock
But if many people believe that the initial price rise signals further increases, the shift in the demand may be bigger, in turn causing further price rises. Figure 8.12 models this case of runaway price increases. (To show prices above \(P_a\), we have used a different scale on the vertical axis.)
- excess demand
- A situation in which the quantity of a good demanded is greater than the quantity supplied at the current price. See also: excess supply.
When the price \(P_a\) is observed, the demand curve shifts to Da. There is now excess demand for houses. So the price begins to rise above \(P_a\), reaching \(P_b\) in the next period. This is the first point marked above \(P^*\) on the PDC in the right-hand panel. The rise to \(P_b\) reinforces beliefs that prices are rising and the demand curve shifts again to Db. Again there is excess demand, leading to more price rises and demand shifts.
Figure 8.12 The price shock is amplified: positive feedback and instability.
In Figure 8.12, price rises lead to further price rises—a process of positive feedback—magnifying the initial price shock rather than working against it and taking us further and further from equilibrium. Likewise, a decrease in price below \(P^*\) would set in motion a set of positive feedbacks magnifying the initial price fall setting off a process of runaway falling prices (as Exercise 8.2 will discuss). Both of these cases correspond to a PDC that passes through \(P^*\) and is steeper than the 45-degree line. The equilibrium at E is unstable.
Figure 8.12 describes the beginning of a bubble of runaway increases in house prices. In this scenario the positive feedback process will continue until something happens to change the expectation of continuously rising prices.
For a mathematical model of a bubble as shown in Figure 8.12, read this mathematical supplement.
Exercise 8.2 Modelling a bust in the housing market
Construct a diagram similar to Figure 8.12 and provide a step-by-step explanation of how a housing market bust can occur. As the starting point, assume a negative shock: a fall in price resulting from causes external to the model.
The dynamics of house prices: Boom-bust cycles
Figure 8.13 summarizes the price dynamics curves for stable and unstable equilibria. In an unstable equilibrium, the PDC is steeper than the 45-degree line; in a stable equilibrium, it is flatter than the 45-degree line.
Figure 8.13 Unstable and stable equilibria in the housing market.
So far, we have drawn PDCs as straight lines for convenience, but there is no reason why they should not be curves (as we named them). And if so, they may cross the 45-degree line more than once, representing a situation in which there is more than one equilibrium in the housing market with different levels of prices that are unchanging from year to year.
Figure 8.3
We can use PDCs to model what we observe, with periods of stability around more than one equilibrium house price, and other unstable periods of boom and bust. It appears that both stable and unstable equilibria coexist. In Figure 8.14, we model the housing market like the ‘hill’ in Section 8.2, with two stable equilibria, and an unstable equilibrium—the tipping point at the top of the hill—between them. This gives us an S-shaped PDC, as shown in Figure 8.14.
There is a stable equilibrium with a low price at point C. Here, the PDC is flatter than the 45-degree line, so the equilibrium is stable. A small price shock would result in dynamic adjustment with negative feedback working against the shock and moving the price along the curve back to point C. Point D is stable for the same reason.
Point T is also an equilibrium, but it is an unstable tipping point. This means that a small price shock would set off positive feedbacks leading either to prices falling towards C (if the shock was a fall in price), which is a stable equilibrium at a low price, or rising towards D (if the shock was a rise in price), which is a stable equilibrium at a high price.
Unlike the poverty trap, in this case—the housing market—we do not have a ‘good’ and a ‘bad’ equilibrium. Whether high or low house prices are preferable depends on whether you are owning a house and would like to sell, or without a house and would like to buy. The problem in the housing market is that prices can change dramatically—boom or bust—imposing substantial uncertainty on all households.
To understand why the equilibrium at T is unstable, at T the PDC is steeper than the 45-degree line, whose slope is equal to 1. This means that along the 45-degree line, a change in the price in time t is associated with the same magnitude of price change in period \(t + 1 (\Delta P_\text{t} = \Delta P{_\text{t+1}})\). If the PDC has a slope greater than 1, this means that a change in the price in period t is associated with a price change in period t + 1 that is greater than the change in period t. In other words, the reaction to a price shock at point T (either up or down) does not dampen but instead magnifies the shock. An important insight from Figure 8.13, is that we would expect to observe the economy much more frequently close to a stable than an unstable equilibrium.
Follow the steps through Figure 8.14 to understand how, starting from the low-price equilibrium at C, a housing boom could occur.
Similarly, a large fall in the price of housing can produce a collapse from the high-price equilibrium to the low-price equilibrium.
Exercise 8.3 Differences between equilibrium and stability
Explain in your own words, giving examples, the difference between the terms ‘equilibrium’ and ‘stability’.
Question 8.4 Choose the correct answer(s)
Read the following statements and choose the correct option(s).
- Positive feedback processes reinforce the initial shock (movement away from equilibrium), so if the initial shock causes prices to fall, then positive feedback processes will cause the price to continue to fall.
- If the economy is at a stable equilibrium, any small movement away from this equilibrium will eventually result in prices returning to the same equilibrium, so the economy will remain at this equilibrium unless there is a large shock. However, if the economy is at an unstable equilibrium, any small movement away from this equilibrium will result in the economy moving further and further away, so it is more difficult to sustain an unstable equilibrium.
- The low-price equilibrium is stable because any small movement away from this equilibrium will eventually result in prices returning to the same equilibrium. The stability of the equilibrium is unrelated to whether or not it still exists when the price dynamics curve shifts.
- The opposite is true: a housing price boom occurs because people treat current changes in price as information telling them that prices will continue to rise.