# A Model of Housing Prices and Residential Investment

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1 A Model of Prices and Residential Investment Chapter 9 Appendix In this appendix, we develop a more complete model of the housing market that explains how housing prices are determined and how they interact with residential investment. We start our analysis by examining how housing prices are determined. Then, using a Tobin s q theory approach, we consider how the price of housing determines residential investment. Determination of Prices Panel (a) of Figure 9.A. shows a supply and demand analysis of the housing market, where the relative price of housing, that is, the nominal price of a house relative to the general price level, >P, is represented on the vertical axis and the stock of housing, K H, is represented on the horizontal axis. Residential housing takes time to build and wears out very slowly. As a result, we can say that in the short run, the stock of residential housing (which includes old as well as new housing) is essentially fixed. With this assumption, the supply curve of houses is vertical, that is, the stock of housing remains at K* H regardless of the relative price of houses. The demand curve for housing is downward sloping because people can afford less housing when prices are higher. In the face of higher prices, individuals may choose to live in smaller houses or live with their parents or relatives, or they might be unable to live in a house at all. As in any supply and demand analysis, the equilibrium relative price of housing occurs at the intersection of the demand and supply curves of housing. With a demand curve at D, the equilibrium is at point E, with a relative price of housing at P* H >P. More accurately, the supply curve for housing in the short run would have a slight upward slope because an increase in the relative price of housing leads to higher residential investment, which adds to the stock of housing. However, any increase in the supply of housing relative to the existing stock of housing will be very small because new housing takes time to build and will represent only a small fraction of the existing stock of housing, since houses last a long time. It is therefore reasonable to assume that the supply curve for housing is vertical.

2 chapter 9 appendix From House Prices to Residential Investment The residential investment curve in panel (b) of Figure 9A. shows the relationship between the relative price of housing and the construction of new homes, that is, the flow of residential investment. It is upward sloping: a rise in the relative price of houses leads to a higher level of new home construction. At an equilibrium relative price of P* H >P, residential investment is at I* H. To see why the curve is upward sloping, recognize that the relative price of housing is analogous to Tobin s q for the housing market. The replacement cost of a house is likely to move with the general price level P, while the price of housing is the market valuation of the house. Thus q in the housing market is P* H >P. To demonstrate the Tobin s q reasoning for residential investment, let s first suppose that the builder of a house plans to sell it. If the market valuation of the house is above its replacement cost, that is, the relative price of housing is high, then the builder profits by building it. Indeed, the higher housing prices are relative to replacement costs, the more profits builders will make from building houses, and so residential investment will be higher. uppose, on the other hand, that the relative price of a house is low, so that its market value is below its replacement cost. Then a builder will not build the house because he or she will suffer a loss by building it: the builder would have to sell the house for less than what it costs to build the house. This reasoning provides the following result: the relationship between residential investment and housing prices is positive. The reasoning behind the upward slope of the residential investment curve holds even if the house is rented out or the builder plans to live in it. If the house is rented, then the landlord (the builder) earns the rent from the renter over the life of the house, Figure 9A. Determination of Prices and Residential investment In panel (a), the demand curve for housing is downward sloping, while the supply curve is vertical at K* H. The equilibrium occurs at point E, where the supply and demand curves intersect, with a relative price of housing at P * H >P. The curve in panel (b) is upward sloping, that is, a rise in the relative price of houses leads to a higher level of new home construction. At an equilibrium relative price of P * H >P, residential investment is at I * H. P* H (a) upply and Demand for K* H E Equilibrium P* H occurs where quantity supplied = quantity demanded. D tock of, K H P* H (b) Residential Investment E I* H Equilibrium I* H is at the intersection of and P* H. Residential Investment,

3 A Model of Prices and Residential Investment 3 and so the house s market valuation is the expected discounted value of that rent over the life of the house. The higher the market valuation of the house relative to the cost of building it, the more profits the landlord makes, and so the more houses he or she will want to build. If the person building the house plans to live in it, then he or she is, in effect, earning rent on the house, called implicit rent because if that person didn t own the house, he or she would have to pay rent elsewhere. The value of the house to the homeowner is then the expected discounted value of the implicit rent he or she would otherwise pay. The higher this value is relative to the cost of building the house, the greater is the incentive for the homeowner to build the house. Changes in the Demand for What happens if the demand for housing rises, so that the demand curve shifts to the right from D to D in panel (a) of Figure 9A.? The rightward shift of the demand curve moves the equilibrium in the housing market from point to point, and the relative price of housing moves from P H>P to P H>P. Then, as we see in panel (b), the higher relative price leads to a movement from point to point on the curve, and residential investment rises from I H to I H. Neoclassical Theory and Demand. Why does the demand for housing change? The answer is provided by the neoclassical theory of investment. If the expected future marginal product of capital curve shifts up, then the desired level of capital increases. In the case of housing, the equivalent analysis is that the higher the rent (explicit or implicit) that households are willing to pay, the higher the demand for housing, and so the housing demand curve will shift to the right, as in panel (a) of Figure 9A.. The relative price of housing will then rise, and residential investment will rise as well. Households will be able Figure 9A. hift in the Demand for A rightward shift of the demand curve in panel (a) moves the equilibrium in the housing market from point to point, and the relative price of housing increases from P H>P to P H>P. Then, as we see in panel (b), the higher relative price leads to a movement from point to point on the curve, and residential investment rises from I H to I H. P H P H (a) upply and Demand for tep 3. and the relative price of housing rises. K* H tep. shifts the demand curve to the right D D tep 4. tep. An increase in the demand for housing P H P H The higher relative price of housing causes residential investment to rise. (b) Residential Investment I H I H tock of, K H Residential Investment,

4 4 chapter 9 appendix to pay higher rent if their expected future income is higher, or if an increase in the number of households that will want housing bids up rent. The analysis in Figure 9A. therefore produces the following result: higher expected income or increases in household formation lead to higher demand for housing, an increase in relative housing prices, and higher residential investment. The user cost concept in the neoclassical theory of investment also applies in the housing market and provides another source of shifts in the demand curve for housing. uppose the real interest rate on mortgage loans declines. Then the cost of financing a house purchase declines and the user cost of housing falls, so people will be able to buy a new or a bigger house. The analysis in panel (a) of Figure 9A. then shows that the demand curve will shift to the right, yielding the following result: a decline in real mortgage rates leads to a higher demand for housing, a higher relative price of housing, and an increase in residential investment. As we saw with the neoclassical theory, another component of user cost is the expected rate of change in the real price of the capital asset. In the context of housing, this term is the expected rate of change in real housing prices, and it can be a very important source of changes in housing demand. If households expect housing prices to appreciate, then the user cost declines, causing the demand for housing to increase and shifting the demand curve to the right, as in panel (a) of Figure 9A.. The relative price of housing will then rise, and residential investment will increase. aid another way, if housing is expected to be a good investment, demand for housing will increase and the demand curve will shift to the right. We thus have the following result: a higher expected real appreciation of house prices leads to a higher demand for housing, a higher relative price of housing, and an increase in residential investment. demand can also be affected by financing constraints. If mortgage lenders loosen lending standards and so make loans more readily available to households, then financing constraints become less binding and households that otherwise would have been unable to purchase houses will now be able to. As we have seen previously, the increased demand for housing will shift the demand curve to the right, as we see in panel (a) of Figure 9A., causing the relative price of housing to rise, which, as shown in panel (b), will lead to higher residential investment. We then get the following result: looser financing constraints lead to a higher demand for housing, a higher relative price of housing, and an increase in residential investment. Using similar reasoning, tighter financing constraints lead to a lower demand for housing, a lower relative price of housing, and a decrease in residential investment. ummary: Residential Investment In summary, residential housing prices and investment are driven by the following determinants: expected future income, the rate of household formation, real mortgage rates, expected appreciation of housing prices, and financing constraints. We summarize the impact of each determinant on housing prices and residential investment in ummary Table 9A..

5 A Model of Prices and Residential Investment 5 Table 9A. Determinants of Residential Investment Change in Change in Prices Determinant Determinant and Residential Investment Expected future income, Y e c c P H P H D D K H I H I H Household formation c c P H P H D D K H I H I H Real mortgage rates c T P H P H D D K H I H I H Note: Only the effects of increases in the determinants are shown. The effects of decreases in the determinants on investment would be the opposite of those indicated in the third and last columns.

6 6 chapter 9 appendix Table 9A. Determinants of Residential Investment (Continued ) Determinant Expected real appreciation of housing prices Change in Determinant c Change in Prices and Residential Investment c P H P H D D K H I H I H Financing constraints c T P H P H D D K H I H I H Application Boom and Bust in the Market, From 00 to 006, U.. housing construction was on a tear, with housing starts (the number of new houses put into construction) rising from around.5 million in 00 to a peak of over million in 006, among the highest numbers of housing starts recorded in U.. history (see Figure 9A.3). Then, residential investment collapsed, with housing starts falling to around 500,000 in 009. What caused this boom and bust in residential investment? Our theory of the housing market suggests that we should first examine housing prices. Notice in Figure 9A.3 that housing prices inflated like a bubble and then burst: relative

7 A Model of Prices and Residential Investment 7 Figure 9A.3 Real-time data Prices and Residential Investment, From 00 to 006, the number of housing starts rose from around.5 million to a peak of over million, while from 006 to 009, the number fell to around 500,000 and remained at about that level for several years afterward. prices showed similar rises and falls, rising by over 70% from 00 to 006, then falling by over 5% by 009. Prices (index), 000Q=00 (right axis) tarts (millions) (left axis) starts prices Year ource: Prices, Case-hiller U.. National Composite House Price Index, available from: tarts, New Privately Units tarted, at housing prices boomed from 00 to 006 by over 70%, but then collapsed, falling by over 5% by 009, marking the greatest swing in home prices in the U.. post World War II period. Our Tobin s q theory of residential investment indicates that this housing price boom and bust should result in a similar boom and bust in residential investment. That trend is exactly what we see in Figure 9A.3, in which housing prices and housing starts move closely together, with the upward and downward swings of both series coinciding. The relationship between residential investment and housing prices begs a deeper question: what caused such large swings in housing prices? Our theory of the housing market again suggests several contributing forces that increased the demand for housing, shifted the demand curve to the right, and increased housing prices, as is shown in panel (a) of Figure 9A.4. The first force was the decline in real mortgage rates, which lowered the user cost of capital and thereby increased the demand for housing. ome economists attribute the fall in real mortgage rates to loose monetary policy, which kept real interest rates below zero from 00 to 005. Others attribute the decline in real mortgage rates to the large flows of capital from countries like China into the United tates. No matter the source, declining real mortgage rates lowered the cost of financing a housing purchase and decreased the user cost of housing. The result was increased demand for housing, a rightward shift of the housing demand curve from D to D, and a rise in housing prices, as depicted in panel (a) of Figure 9A.4. A second and very important force was the irrational exuberance displayed by households that believed housing prices would keep on climbing at a rapid rate. Households ee the Policy and Practice case in Chapter 5 that discusses the role of monetary policy in the housing boom.

8 8 chapter 9 appendix Figure 9A.4 Boom From 00 to 006, the decline in mortgage rates, households beliefs that housing prices would keep climbing at a rapid pace, and the relaxation of credit standards fueled the demand for housing. The demand curve shifted to the right and housing prices increased, as shown in panel (a). Then, as shown in panel (b), the rise in housing prices led to a boom in residential investment. P H P H (a) upply and Demand for tep 3. and raising the relative price of housing K* H tep. shifting the demand curve to the right P H P H D D tep. Low mortgage tep 4. which rates, relaxation of led to higher credit standards, and residential high expected future investment. price increased the demand for housing (b) Residential Investment I H I H tock of, K H Residential Investment, expected large appreciation of housing prices, which lowered the user cost of housing and stimulated demand. The result is depicted in panel (a) of Figure 9A.4: the demand for housing increased, the demand curve shifted to the right from D to D, the relative price of houses rose, and residential investment boomed. A third important force in creating the housing boom was the relaxation of lending standards, as described in Chapter 5. o-called subprime borrowers, borrowers who were not especially good credit risks, now found that they had easier access to credit. This relaxation of lending standards increased the demand for housing, shifted the demand curve to the right from D to D, raised housing prices, and increased residential investment, as indicated in Figure 9A.4. The bust in housing prices occurred when the second and third forces turned in the opposite direction. At some point, households recognized that the boom in asset prices could not go on forever. Once they came to this realization, expected appreciation of housing prices ended, thereby raising the user cost of housing and causing demand to fall. The bubble burst and housing prices began to decline. Even worse, when housing prices began to decline, sentiment changed so drastically that the public began to expect declines in housing prices, lowering housing demand even further. With the bursting of the housing bubble and the onset of the financial crisis in 007 (discussed in Chapter 5), financial frictions rose sharply, and so mortgage lenders began to tighten credit standards appreciably. Increased financing constraints made it harder to finance homes with mortgages, and demand for housing fell. The combination of the end of expected appreciation of housing prices and the tightening of financing constraints cut the demand for housing and shifted the demand curve to the left, as shown in panel (a) of Figure 9A.5. The result was a decline in housing prices and a collapse of residential investment, as demonstrated in panel (b) of Figure 9A.5. As we saw in Chapter 5, the housing price collapse resulted in the most serious financial crisis since the Great Depression, leading to a sharp contraction in economic activity.

9 A Model of Prices and Residential Investment 9 Figure 9A.5 Bust tarting in 006, expected declines in housing prices and tightening of credit standards led to a drop in the demand for housing and a leftward shift of the demand curve, as shown in panel (a). The result was a decline in housing prices and a collapse of residential investment, as demonstrated in panel (b). P H P H (a) upply and Demand for tep 3. and lowering the relative price of housing K* H tep. shifting the demand curve to the left P H P H D D tep. Expected tep 4. which declines in prices and led to lower tightening credit residential standards decreased investment. the demand for housing (b) Residential Investment I H I H tock of, K H Residential Investment,

10 0 chapter 9 appendix ummary. Residential housing prices and investment are positively related to expected future income, the rate of household formation, and the expected appreciation of housing prices. Residential housing prices and investment are negatively related to real mortgage rates and financing constraints. Review Questions and Problems. How is residential investment related to housing prices?. What forces cause the demand for housing to increase, and how do each of these determinants affect housing prices and residential investment? 3. By 0, in the aftermath of the global financial crisis, mortgage rates in the United tates had fallen to historically low levels. Yet both housing prices and housing starts remained very depressed. How can financing constraints and expected real appreciation of housing prices explain this situation? 4. What would happen to housing prices and residential investment if, as part of an effort to balance the federal budget, Congress rescinded tax deductibility of mortgage interest payments?

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