1. Anticipation, Incentives, and the Housing Cycle
by Casey B. Mulligan 1

2. Model Characteristics
National
(current and future migration will add to some region’s prices and construction, subtract from others)
Quantitative
Structures are not the only housing input
Structures supplied more slowly than other inputs
General Equilibrium
link housing with non-housing consumption and non-residential capital.
Constant budget share for housing
Financial issues put in one corner
Rational Expectations
Continuous time
Welfare Theorem: calculate an efficient (or near efficient) allocation, then the prices that support it
 housing dynamics isomorphic to corporate q-theory, with more detail provided about the MPK function 3

3. Housing Services are Provided with Structures and Other Inputs
s(t) = date t housing services
h(t) = net stock of housing structures
x(t) = non-structures inputs
r(t) = housing service rental rate
px(t) = non-structures input price
(t) = operating surplus going to structure’s owners 4

4. Tastes and Technology ,(t) = preference parameters
w(t) = exogenous labor income
k(t) = non-residential capital, with net marg. product A
c(t) = non-housing consumption
B(t) = MRT between x and c
I(t) = housing investment (depreciates at )
h(t)Sf(I(t)/h(t)) = installation costs
Homogeneous hf  perfectly elastic LR supply
Convex f  imperfectly elastic SR supply
S is an exogenous supply shifter
where does this appear in the national accounts? 5

5. Installation Costs per Unit Stock
The Figure displays the amount of consumption foregone as a function of the amount of gross investment
Need delta version

6. Marginal Installation Costs
The Figure displays the amount of consumption foregone at the margin as a function of the amount of gross investment

7. Is Housing Wealth Really Wealth? The Intertemporal Production Set
Shows how the housing sector is connected to the non-housing sector
housing demand does not affect this set, just the choice of allocation from it
 more housing demand decreases c
housing supply technology does affect the set
 more productive x (i.e., lower B) expands it
 investment supply shift (i.e., lower S) expands it
possible sources of housing wealth reductions
destruction of housing capital: an adverse wealth effect
less productive intermediates: an adverse wealth effect
change in housing service demand: no wealth effect
subsidy to housing: no wealth effect
investment supply shift: a favorable wealth effect 8

9. Co-state Variable Defined
(t) = intermediates’ subsidy rate (used later)
integral is present value of operating surplus
market interpretation: purchase price of one unit of housing structure 10

10. Equilibrium Interpretation
owner of structure has a leveraged claim on housing output
r(t) = housing service rental rate
px(t) = non-structures input price
pI(t) = price a new house 11

11. Complements and Incidence: Theory
An outward shift in the supply of one complementary input (x) raises the demand for the other (h)
Price of the h input rises according to the elasticity of that input’s supply
if the h input is perfectly elastically supplied, the x supply shift raises the quantity of h, but not its price
if the h input is in fixed supply
the x supply shift raises the price of h, but not its quantity
the price of h also depends on expected future supply conditions for x
Natural leverage: A shift in the demand for the joint output has a greater-than-proportionate effect on the rental rates of the less elastically supplied inputs 12

12. Complements and Incidence: Housing Application
x is clothing, toys, furniture, real estate services, banking services, property management
h is housing, which is inelastically supplied in the short run, elastically supplied in the long run (q theory)
Intermediates supply shift  Housing prices and construction should increase in the short run, and the housing stock increase in proportion with x in the long run
Natural leverage: Housing service demand shift  structures’ operating surplus increases more than proportionally 13

13. Allocations Described by 2-D Dynamical System
 is the investment supply function
boundary conditions are given h(0) and transversality condition
system is stationary when parameters are constant over time
saddle path stable 14

14. Fig 9. Phase Diagram for the Stationary System
The Figure shows the stationary system’s steady state, dynamics, and stable manifold.

15. Approximations: Linear, and Fixed Supply
linear approximation for small parameter changes
linear approximation for large technology changes
Fixed supply is the limit of highly convex installation costs: S/   16

16. Derived Demand Shift Shift in the derived demand for houses
 the immediate increment to the housing stock that would make the housing price be S
with finite adjustment costs, the demand shift is just the gap ln(hss/h(0))
not necessarily the same as housing service demand shift
The derived demand curve is the stable manifold: values for housing prices that are consistent with various housing supplies, given tastes and technology
Any assumed parameter vector implies
a value for the demand shift: a prediction for the long run housing stock
an amount of price elevation q(0)/S
Can infer the demand shift from any observed price elevation
depends somewhat on whether tastes or technology are changing (tastes have more leverage on prices)
depends on adjustment costs 17

17. Reasons for Optimism Mortgage Technology Real estate technology
application screening
“Recent years have seen great improvements in data, especially the introduction of credit scores, which gave lenders new powers to forecast mortgage defaults and to adjust interest rates offered to prospective borrowers. In 1990, credit scores were rare; by 1996, they were standard.” (Hall and Woodward)
: Loan origination costs fall by a factor of four relative to loan amount (Himmelberg et al)
home equity loans: Facilitating improvements
Real estate technology
Virtual Web Office sites proposed to do the work of a realtor at a fraction of the cost
Prospect of reducing vacancy rates
Property management
Familiar IT paradox: real productivity gains lag technology adoption 18

18. Fig 7. Possible Paths for Tastes and Technologies
(2002 ?) T
(2006)

19. Dynamics Before and After 2006

20. Bailouts as Distorted Probabilities
At time T a subsidy will be paid to residential property owners of an asset
The subsidy is zero if prices jump up at time T. Let qH(T) be the price in that contingency, and  the probability.
The subsidy is L per unit of housing if prices jump down at time T, where L is the size of the price jump, and qL(T) is the ultimate price.
The price immediately before time T, q(T), must satisfy the Euler equation: 21

21. Bailouts as Distorted Probabilities
Asset market behaves as if there were no bailout, but were excessively optimistic about the state H
The bailout would not matter if states L and H had the same fundamentals  fundamentals interact w bailout
Hereafter, ignore  but interpret  as a distorted probability 22

22. Inelastic Supply Boom
after time T: replace expectations with realizations and replace T with t
progress anticipation: prices jump up and then appreciate, peaking at time T
e.g., cut B in half  peak price up 32%
raise  by 10%  peak price up 20%+
high and rising prices are efficient
high ratio of price to GOS indicates that prices are elevated due to anticipation 23

23. Inelastic Supply Bust
size of the price bust depends on the range of outcomes and the probability of the high outcome
bust prices do not fall below pre-boom prices (not true with elastic supply) 24

24. 25

25. Derived Demand Shift with Fixed Supply
With fixed supply and demand, the operating surplus from owning a house is constant over time and the price of a house is the present value of that surplus
(assume that the housing price was S prior to knowledge of the parameter shift. The operating surplus includes the ongoing maintenance/depreciation cost of S of existing housing)
The demand shift implied by the observation that q(t) > S can be calculated by inferring the housing stock that would make the equilibrium price S: 26

26. Fixed supply case is exact solution. Elastic Supply is linear approx.27

27. Fig 8. Possible Housing Stock Paths
The Figure shows three housing stock time paths corresponding to three alternative assumptions about the costs of investment.
h(t)
no adjustment costs
finite adjustment costs
infinite adjustment costs
h(0)
t = time T 28

28. Fig 11a. Phase Diagram for Anticipated Changes: One State
The Figure shows the system’s dynamics and stable manifold. The dynamics shown by the red arrows correspond to the “old” taste and technology parameters. When the new parameters are first anticipated at date 0, price jumps up. The economy then follows the red path, reaching the end exactly at time T when the new parameters take effect. The new stable manifold (shown as a black path) describes dynamics thereafter. 29

29. Fig 11b. Phase Diagram for Anticipated Changes: Two States
The Figure shows the system’s dynamics and stable manifold. The dynamics shown by the red arrows correspond to the “old” taste and technology parameters. When the new parameters are first anticipated at date 0, price jumps up. The economy then follows the red path, reaching the end exactly at time T when the new parameters take effect. The new stable manifolds (shown as black paths, one for each possible realization of the parameters) describes dynamics thereafter. 30

30. Fig 12a. Time Path for Housing Prices: Small Supply Response31

31. Fig 12b. Time Path for Housing Prices: Large Supply Response32

32. nobubble.xls 33

33. 34

35. Calibrating Installation Cost Convexity
Quadratic installation cost function implies a linear investment supply curve, with steady state elasticity of:
Empirical literature has estimated the supply elasticity from previous housing cycles. E.g., Topel and Rosen’s median elasticity is With 2.5%/year depreciation, this implies a investment supply slope of S/(1) = 25.4 years.
Half-life of the system
 absent new information, it would have taken decades for boom prices to get close to the steady state 37

36. 38

37. Needs to be deflated better

38. Fig 11b. Phase Diagram for Anticipated Changes: Two States
The Figure shows the system’s dynamics and stable manifold. The dynamics shown by the red arrows correspond to the “old” taste and technology parameters. When the new parameters are first anticipated at date 0, price jumps up. The economy then follows the red path, reaching the end exactly at time T when the new parameters take effect. The new stable manifolds (shown as black paths, one for each possible realization of the parameters) describes dynamics thereafter. 41