A Dynamic Model of Housing Supply

More documents

Recommendations

Info

7 shows the distribution in the marginal price of square footage across tracts. This variationacross tracts will be one of the key sources of identification of variable housing costs. The othersource of variation I use to identify variable housing costs is time-series variation in the marginalprice of square footage.Figure 7: Distribution of the Marginal Price of Square Footage in a Typical HouseFigure 8: Time Trend of the Marginal Price of Square Footage in a Typical HouseA notable feature of the pricing results is the heterogeneity in prices across both physicalspace and through time.The other key result is the decreasing importance of house size in34
determining sales price. The results strongly suggest that the value of a buildable parcel of landhas increased dramatically over the period. This can be informally seen by comparing the priceof a typical house in 1989 and 2004. The Bay Area mean price in 1989 was a little over $300,000and rose to a little over $450,000 by 2004. However, the marginal price of an additional squarefoot was almost the same in the two years – $134.50 in 1989 and $137.00 in 2004. As pricesincrease non-linearly in size, we can not formally measure the role of the typical parcel in housingprice increases. However, these results suggest that appreciation in the value of buildable parcelsis the dominant factor.6.2 Variable Cost RegressionsIn the second stage, observed square footage is regressed on a function of tract characteristics,where the functional form is dictated by the optimal value of square footage from maximizing perperiodprofits. The price components of optimal square footage are known and are constrainedto be their values as estimated in the first-stage hedonic price function. An alternative wayto look at this regression is to use the first-order condition from profit maximization where thestandard result dictates that marginal revenue should be equal to the marginal cost of adding oneadditional square foot. Given that marginal revenue is known at all points from the first-stageregression, we can identify marginal costs at points observed in the data and use the functionalform of costs to recover the variable cost function.The cost function is assumed to be linear in square footage, where the cost per square footvaries by tract, an overall Bay Area time pattern, and lot size: V C nt = exp(α 0jt + α 1 x n ) · hwhere h is square footage, x includes only lot-size, and α 0jt = α 0 + α j + α t . Recalling thatoptimal square footage is given by:h ∗ =( γ1j(n)t ρ j(n)t x γ 2j(n)tn e .5σ2 ν ) 11−γ 1j(n)texp(α 0jt + α 1 x n )and that h = h ∗ e ηh nyields the regression equationlog(h γ 1j(n)tnt) − log(h nt ) + log(γ 1j(n)t ) + log(ρ j(n)t ) + log(x γ 2j(n)tn ) + .5σν 2 = α 0jt + α 1 x n + ˜η nh35
Page 1 and 2: A Dynamic Model of Housing Supply
Page 3 and 4: period profits by choosing the opti
Page 5 and 6: future price changes and shed light
Page 7 and 8: pany, a consultant to the home buil
Page 9 and 10: Figure 1: Bay Area: Counties and Tr
Page 11 and 12: lands as well as undeveloped farms,
Page 13 and 14: Figure 3: Appreciation Rates by PUM
Page 15 and 16: 4 A Dynamic Model of Housing Constr
Page 17 and 18: expected profits are given by the v
Page 19 and 20: Housing quality is composed of thre
Page 21 and 22: 4.2.2 Optimal Discrete ChoiceThe de
Page 23 and 24: into three pieces:1. L p (θ p , x)
Page 25 and 26: y year. The results section provide
Page 27 and 28: probability of choosing to build. 4
Page 29 and 30: of ̂ε P Cnt , I can calculate ∫
Page 31 and 32: issue arises in Gowrisankaran and R
Page 33: Figure 5: Distribution of the Price
Page 37 and 38: to identifying costs is different h
Page 39 and 40: for prices and costs as well as an
Page 41 and 42: Figure 12: Geographic Distribution
Page 43 and 44: of dynamics (and in particular, the
Page 45 and 46: price cycle. The expected length of
Page 47 and 48: 8 ConclusionThe importance of the h
Page 49 and 50: DiPasquale, D., and W. C. Wheaton (
Page 51 and 52: 9 AppendixFurther Estimation Detail
Page 53: Additional ResultsTable 4: Dynamic

A Dynamic Model of Housing Supply

Create successful ePaper yourself

Delete template?

Save as template?