The Contribution of Land and Structure to Builder Profits and House Prices1 Journal of Housing Research • Volume 7, Issue © Fannie Mae Foundation 1996. All Rights Reserved.
127 127
The Contribution of Land and Structure to Builder Profits and House Prices C. Tsuriel Somerville*
Abstract This article examines how builders’ land and structure expenditures affect house prices and builders’ profits. The new house market is treated as monopolistically competitive, where builders face downward-sloping demand curves for land and structure. The elasticity of these curves determines whether builders pass along increases in factor costs or absorb lower profits. Microdata from a major U.S. builder are used to estimate the markups associated with these elasticities. In the short run, profits are more sensitive to cost variations for land than for structure. Changes in house prices have the most significant effect on profit rates; market activity affects profit rates much less. Price changes affect profit rates through the markup on land (the structure markup is uncorrelated with price movements). These results imply that builders can readily pass short-run variations in structure costs on to consumers but cannot do the same for land costs. Keywords: builder profits; land and structure costs; house prices; builder factor expenditures
Introduction During active markets, builders and developers appear to earn profits well above those typical of more standard competitive industries. While these strongly procyclical profits can be consistent with competitive markets, they do raise the question of their relationship to the production process. Builders combine land and structure to produce housing, but the relative contribution of each of these factors to profitability and how each is affected by market conditions are unknown. This article examines the relationship between builder profitability and the variation in factor expenditures by estimating the returns to builders from structure and land and the sensitivity of these returns to real estate cycles. To do so, this research takes advantage of a unique set of microdata that contains precise measures of both the sales price and the land and structure expenditures for individual housing units built by one of the largest residential builders in the United States. These data permit a detailed examination of builder profit in the context of the microfoundations of housing supply. Though the price markup on land is smaller than expected, land is the key factor in explaining variation in builder profitability. Per-unit builder profit is more sensitive to changes in land costs than to changes in structure costs. While the profit rate elasticities for land and structure vary by market, they are almost always greater in absolute value * C. Tsuriel Somerville is an Assistant Professor in the Urban Land Economics Division of the Faculty of Commerce and Business Administration, University of British Columbia. The author is grateful to Isaac Megbolugbe, Ellen Roche, Stuart Rosenthal, and two anonymous referees for helpful comments and suggestions. The assistance of Ted Peck in obtaining these data is greatly appreciated. Finally, thanks are due to Eric Ng and Jack Yuh-ren Lin for research assistance. Any errors are the responsibility of the author alone.
128
C. Tsuriel Somerville
for land than for structure. The effect of market conditions on profit rates also works through the markup on land. Changes in house prices have a greater effect on per-unit profit rates than aggregate market activity does. And changes in house prices have a much larger effect on the contribution of land to profits than they do for structure. This work highlights the role of land and structure in housing supply but does so by examining their relationship to profits, an aspect overlooked in previous work on housing production functions. Much research has examined the relationship between land and structure in housing production. The density gradient studies by Mills (1972) and Muth (1969) reflect the substitution of structure for land in the provision of housing services as location rents rise. Considerable literature estimates the housing production function, with a particular focus on the elasticity of substitution between land and structure. Initial research on this topic was done by Muth (1971) and Smith (1976), while much of the work that has followed, reviewed by McDonald (1981), focuses on the correct specification of the production function. More recent work (e.g., Stover 1990) has extended the analysis to include more inputs in the production function. A drawback of this work discussed by Edelstein (1983) is its reliance on estimates for land and structure value. In contrast, the research presented here uses actual expenditures on land and structure. Outside of production function analysis, the use of microdata is itself rare; exceptions include Maisel’s seminal 1953 work on the housing production process, Kinzy’s 1992 estimation of implicit supply curves for housing attributes, and a study of the endogenous construction costs by Somerville (1994). Beyond the use of microdata, what distinguishes this research is the focus on builder profitability. Rather than assuming marginal cost pricing, the method used here allows for markups over input costs. Builders are assumed to face downward-sloping demand curves. Though builders are assumed to pursue the marginal pricing strategies of a local monopolist, the combination of fixed costs and entry ensures that builder operating profits are consistent with an expected zero profit equilibrium and describes a monopolistically competitive industry. Friction in entry or exit will result in additional short-run volatility in builder returns over the course of the market cycle. The degree of local monopoly power in setting prices can vary across space, time, and housing attributes. The intention is not to reject a long-run equilibrium with zero economic profit but to shed light on the cyclical relationship between land and structure inputs and builder profits. The monopolistic competition framework has the advantage of allowing for short-run operating profits without sacrificing competition. Focus on profits is desirable because they clearly motivate builder behavior, and the degree to which short-run changes in input costs reduce profits or are passed on in the form of higher prices has implications for the relationship between policy and housing affordability.
Model Specification The theoretical framework for this article is a variant of a hedonic model of implicit demand and offer curves. Land and structure are implicit goods in the joint product, housing. Demands for these implicit products are assumed to be separable but related, while the production technology treats them as fully independent. In this construct, capital-land substitution is a function of demand rather than technology. Housing is clearly a joint good, but separating attributes into implicit goods is an approach widely
The Contribution of Land and Structure to Builder Profits and House Prices
129
used in hedonic analysis, and it greatly simplifies the algebra that follows. The joint aspect of land and structure is retained because the implicit demand for one attribute is a function of both its own implicit price and that of the other attribute. The price-setting builder produces two implicit goods, land l and structure s, which are sold for implicit prices pl and ps. The inputs into the construction of housing are assumed to aggregate to these two attributes with unit costs cl and c s. Quantities of land and structure at location i demanded by consumers, Ds,i and Dl,i, are functions of the implicit prices of both attributes and their prices at all other locations, represented by the vector p*. Under these conditions, the builder’s profit function is Pi = (ps,i – cs)Ds,i(ps,i, pl,i, p*) + (pl,i – cl,i)D l,i(ps,i, pl,i, p*).
(1)
Taking derivatives with respect to the price of structure and land, imposing the firstorder conditions, and applying some algebra produce the following symmetric equations: 1 (p l,i – c l,i)(]D l,i /]p s,i ), p s,i – c s = – ________________ – __________________ (]D s,i/]p s,i)(1/D s,i) ]Ds,i/]ps,i (2) 1 (p s,i – c s )(]D s,i /]p l,i ). p l,i – c l,i = – ________________ – __________________ (]D l,i/]p l,i)(1/D l,i) ]Dl,i/]pl,i These equations can be manipulated into the two-product analog of the inverse elasticity rule: ps,i – cs ps,i pl,i – cl,i pl,i
=
=
( pl,i − cl,i ) Dl,i ε ls,i 1 , 1 − ε ss,i ps,i Ds,i 1
ε ll,i
(3)
( ps,i − cs ) Ds,i ε sl,i . 1 − pl,i Dl,i
The size of the markups depends on the elasticity measures εjk, the elasticity of demand for j with respect to the price of k, which are a function of the degree to which attributes at other locations are substitutes for those at a given location. If the product is sold in competitive markets, its own price elasticity is infinite, and the right-hand side of the equation collapses to zero (i.e., competitive marginal cost pricing). The cross-elasticities also affect the size of the markup and reflect the formal link between this presentation and the capital-land substitution models. Subject to the constraint that the term in brackets is positive, the markup percentage falls with the elasticity of demand, as it does in the single-product case. This framework allows for a large number of sources of variation in markups, both across and within markets over the real estate cycle. These are reflected in the model as changes in the price elasticities of demand for both land and structure with respect to their own and each other’s prices. The results of this model imply that the markup for land should exceed that for structure. Structure is the more mobile factor, so the degree of substitution across sites should be higher for it than for land. The result of this condition is a greater elasticity of demand
130
C. Tsuriel Somerville
for structure at a given site, which lowers the markup. Land is the factor to which Ricardian rents should accrue. The builder’s local monopoly is largely a result of land, so the returns to this factor should reflect the Ricardian rents. This again suggests a larger markup over the entire development and construction process for land than for structure.
Data The data set used here contains information on more than 7,500 single-family detached units drawn from the private records of one of the largest home builders in the United States. Units are identified by metropolitan statistical area (MSA), subdivision, house type, and sales and completion dates. Additional information includes a limited set of structure characteristics and, for many of the units, the general location of the subdivision. For each unit, the data include the precise purchase price of the finished lot and the sum of all payments to subcontractors for structure services. These allow the explicit identification of actual builder gross operating profits, a value that is unavailable in the multiple listing service and Federal Housing Administration data used in most studies of metropolitan area housing supply. Mean values by MSA for these data are shown in table 1. The observations are for singlefamily detached units built and sold by the builder between 1988 and 1991 in Baltimore, Cincinnati, Columbus, Dallas, Dayton, Houston, Indianapolis, and Montgomery County, MD.1 The units range in area from 1,100 to 3,000 square feet and have three to five bedrooms. Most houses are trade-up units, though some of the less expensive models are sold to first-time buyers. All units are identified by model type, but that is not a sufficient statistic for the set of structure characteristics. A buyer may choose a set of options that adds an average of 7.4 percent to the total cost of the structure. The typical unit is fairly standard across these markets. Mean size ranges from a low of 2,051 square feet in Baltimore to a high of 2,481 square feet in Dayton, but for four of the eight markets the means are within 93 square feet of one another. The average unit in each market has close to four bedrooms and two bathrooms. Regional differences are evident in the basement and garage variables. All units in Dallas, Houston, and Indianapolis use slab foundation construction—they do not have basements—while nearly all the units in the other markets have basements. The cost and price data differ much more between markets than the mean unit characteristics do. The ratio of capital to land expenditures varies greatly across these markets, from a low of 1.437 in Baltimore to a high of 3.317 in Houston. At 42 percent of unit cost in Baltimore, land has twice the share it does in Houston. This range is primarily a function of differences in land costs. Average structure costs range from a low of $71,872 in Houston to a high of $118,019 in Montgomery County, while land costs vary from $22,405 to $78,476 for the same markets.2 Though land costs are always less than structure costs, the difference in land cost accounts for more than half the difference between prices in these markets. This article does not formally address capital-land substitution, but the 1 The firm builds throughout the Washington, DC, area, but only data from Montgomery County are included in this data set. 2 If we control for house size, the range of structure costs is smaller, $71,872 in Houston to $110,956 in Montgomery County, based on the average Houston unit of 2,185 square feet.
The Contribution of Land and Structure to Builder Profits and House Prices
131
Table 1. Mean Values by MSA Baltimore
Cincinnati
Columbus
Dallas
Unit characteristics Area (square feet) Bedrooms Baths Attached garage (%) Basement (%)
2,051 3.766 1.769 83.0 96.7
2,067 3.505 1.744 100.0 99.4
2,144 3.577 1.612 100.0 98.9
2,237 3.806 2.038 84.0 0.0
Financial data Lot cost ($) Structure cost ($) Capital-to-land ratio Price ($) Profit ($) Profit rate
68,295 94,058 1.437 193,866 31,513 1.196
30,120 79,378 2.691 125,502 16,004 1.149
27,712 72,023 2.619 115,369 15,634 1.157
29,335 73,420 2.641 114,937 12,182 1.120
1,444
570
1,006
786
Dayton
Houston
Unit characteristics Area (square feet) Bedrooms Baths Attached garage (%) Basement (%)
2,481 3.968 1.928 100.0 100.0
2,185 3.575 2.010 77.0 0.0
2,229 3.606 1.916 100.0 0.0
2,323 3.946 1.946 96.9 99.8
Financial data Lot cost ($) Structure cost ($) Capital-to-land ratio Price ($) Profit ($) Profit rate
39,468 89,336 2.315 150,137 21,333 1.167
22,405 71,872 3.317 109,081 14,804 1.158
27,985 76,031 2.728 118,334 14,318 1.139
78,476 118,019 1.530 247,031 50,536 1.249
282
2,203
862
509
No. of observations
No. of observations
Indianapolis
Montgomery Co., MD
Note: All values are in March 1994 dollars.
intercity differences in the expenditure ratio for similar units are consistent with differences in the elasticity of substitution across markets, as found by Edelstein (1983), and an elasticity that is a nonmonotonic function of the expenditure ratio, as presented by Färe and Yoon (1985). A drawback of these data is that they are from a single firm. If the behavior of this builder is idiosyncratic, the conclusions may not be generalizable to the market as a whole. For instance, unlike many builders, this firm generally does not develop raw land or hold on to developed lots for later use. Instead, the builder purchases options on developed lots, and the options are not exercised until a buyer is found.3 Much of the uncertainty in development is borne by the developer, so the returns to this uncertainty, whether from 3 Company executives note that in some active markets the company may have no choice but to purchase lots outright if it wishes to obtain land for building.
132
C. Tsuriel Somerville
market risk or risk associated with regulatory uncertainty, are already incorporated into the price the builder pays for the lots and will not be an element of the builder’s markup on structure. Though relying on a single source for the data limits the conclusions that can be drawn, the results of the analysis are not entirely idiosyncratic because many of the largest U.S. builders follow strategies similar to those followed by this builder. Despite these problems, the data represent a contribution to the literature. This data set is one of the few sources of actual cost and sales data by unit in the housing market literature. The data allow a study of builder profitability, which is not present in the existing literature. Offsetting the dangers inherent in single-source data are the wide geographic coverage and the multiple years in the data: The data reflect soft markets (Texas in 1988 and Maryland in 1991), active markets (Maryland in 1988 to 1989), and more stable conditions (the Midwest through much of the period). Given the paucity of work on housing supply in general, and work with accurate microdata in particular, there is certainly room for this research. Still, because aspects of the data are firm specific, care must be taken in generalizing the results.
Empirical Analysis The empirical analysis consists of estimates of the markups for land and structure and their sensitivity to variations in land and structure costs. The analysis is broken into two parts. In the first set of regressions, the individual house is the unit of observation. The dependent variables—prices and profit rates—are regressed on land and structure expenditures to test the sensitivity of both prices and profits to changes in input costs. In the second group, observations are MSA averages by year, combined to constitute a panel of the eight markets in the data set. This set is used to relate average price and profit sensitivity to market conditions. Aggregating the data into a panel makes it possible to take advantage of differences in these market cycles to study how starts, prices, and changes in each affect profitability, by changing markups on land, on structure, or on both.
Price Regressions An explicit estimation of equation (3) is not possible with these data because land and structure prices are unavailable. Instead, price-to-cost ratios for both land and structure are estimated. The price-to-cost ratios (p/c) are the estimated coefficients in the regression of unit sales price (p) on land and structure expenditures (cq). For any unit of type i selling for sales price P in market j at location k, the following relationship can be defined:
p
ijk
=
ps , j cs , j
(( c
s, j
))
qs ,i +
p
l , jk
c
l , jk
(
)
c l , jk ql ,i .
(4)
These ratios are analogous to the monopolist markup in equation (3); both rise with the price of the good and fall with input costs. Regression estimates of equation (4), where the intercept is constrained to equal zero, are presented in table 2. In contrast to expectations, the markup on land is rarely
The Contribution of Land and Structure to Builder Profits and House Prices
133
Table 2. Price-to-Cost Ratio for Land and Structure (Dependent Variable Is Price) Variable Description
Baltimore
Cincinnati
Columbus
Dallas
Land expenditures
1.061*** (0.016)
0.981*** (0.043)
1.182*** (0.032)
0.921*** (0.027)
Structure expenditures
1.289*** (0.012)
1.204*** (0.016)
1.147*** (0.012)
1.196*** (0.011)
Ratio of land coefficient to structure coefficient
0.823
0.815
1.031
0.769
No. of observations R2
1,486 0.997
570 0.998
1,006 0.998
786 0.998
Variable Description
Dayton
Houston
Indianapolis
Montgomery Co., MD
Land expenditures
0.921*** (0.043)
0.952*** (0.022)
1.022*** (0.040)
1.473*** (0.059)
Structure expenditures
1.272*** (0.019)
1.221*** (0.007)
1.176*** (0.015)
1.128*** (0.031)
Ratio of land coefficient to structure coefficient
0.724
0.780
0.869
1.306
No. of observations R2
282 0.999
2,203 0.999
862 0.998
509 0.994
Note: Regression coefficients are the price-to-cost ratio or the profit rate for either land or structure. Numbers in parentheses are standard errors of coefficient estimates. All significance tests are two-tailed. *p < 0.10. **p < 0.05. ***p < 0.01.
significantly higher than that for structure (only in Montgomery County, which is probably the most heavily regulated market of the eight). In Dallas and Houston, the estimated price-to-cost ratios for land lie below unity, suggesting that builders are experiencing losses on land, a result consistent with a declining market, though the same result is also present for Cincinnati and Dayton. As expected, the markup is more volatile for land than for structure. Within markets, the estimated standard error for the land coefficient is always larger than that for structure. Across cities, the land coefficient varies from 0.921 to 1.473, while the structure coefficient has a smaller range, from 1.128 to 1.289. Both within and across markets there is more variance in the estimated markup (price-to-cost ratio) for land than for structure. The implicit markup on land does not reflect the full return on the factor. In these data, land expenditures are the cost of finished lots purchased by the builder from a developer. Since returns to land will be received by the actor who takes the risks associated with land, they should accrue to the developer. Also, though land is the likely source of any local monopoly power, it is not clear whether the builder, the developer, or the original land owner receives this return. In the data, returns that accrue to the developer and landowner are already captured in the land expenditures and cannot show up in the builder’s markup on land.
134
C. Tsuriel Somerville
Econometric problems may also explain the low markups on land. There is a problem of simultaneity bias in estimating the house price from equation (4). A Ricardian treatment of land as the inelastically supplied factor means that in equilibrium, land prices are the residual of output prices and the cost of structure. Land bids reflect expected output prices and expected costs of structure. Though land prices should be exogenous to the firm, in thin markets this condition is weakened. Correcting for simultaneity requires instruments that are correlated with land prices but not with house prices. If these instruments exist, they are certainly not available at the level of detail required for this exercise. Instead, a different set of regressions must be estimated.
Profit Rate Regressions To avoid the simultaneity problem, these regressions use the unit profit rate as the dependent variable. The problem is not entirely eliminated because land bids are a function of the desired profit rate: Bids for developed lots reflect the expected sales price of the completed unit and the desired rate of return. The advantage of per-unit profit rates is that unlike house prices they are not an additive function of land and structure. Also, the simultaneity of profit rates and land expenditures is likely to be constant within a single group, such as a subdivision. Simultaneity in group levels can be controlled with fixed effects dummies for model type and subdivision; the dummies also help separate price and quantity effects in the expenditure variables. By controlling for the average group quantity of structure or location services, the fixed effects dummy variables differentiate pure input price effects from differences in quantities of inputs across units. To help identify structure quantity, structure expenditures are split into two components: basic structure and additional options selected by the buyer. Higher builder expenditures caused by added options will principally reflect higher quantity rather than higher input costs. The first pooled profit rate regressions are presented in table 3. If added costs are simply passed on to consumers, then the elasticity coefficients should be zero. In this case an increase in costs would be matched by a similar increase in prices to keep margins constant. Dummies for fixed effects are included for MSA, subdivision, housing model type, and the intersection of model type and subdivision. When only MSA dummies are included in the model, so that there is no control on structure quantity, higher expenditures on structure inputs raise profit rates. Once model type, and thus structure quantity, are controlled for by the model type dummies, increases in structure costs either lower or have no significant effect on profit rates.4 However, greater expenditures on options always raise profit rates. This is consistent with a builder strategy of price discrimination, in which consumers reveal their preferences and type through the options they select. Higher land costs uniformly reduce profit rates. This suggests that while changes in structure costs may be passed on in the form of higher house prices, keeping profit rates constant, the builder’s incorrect expectations of land prices are not as readily offset. Though the price regressions in table 2 indicate substantial differences in the price-tocost ratio across markets, the coefficients of independent variables in table 3 are 4
Model type dummies also control for region (Maryland, Midwest, and Texas) because all model types are region specific. Some model types are also market specific.
The Contribution of Land and Structure to Builder Profits and House Prices
135
Table 3. Profit Elasticities for Land and Structure (Pooled Data with Fixed Effects Specification; Dependent Variable Is Log of Profit Rate) Fixed Effects Group
Variable Description
MSA
Subdivision
House Model
Subdivision and House Model
Ln(cost of land)
–0.044*** (0.003)
–0.141*** (0.006)
–0.044*** (0.003)
–0.144*** (0.006)
Ln(cost of structure)
0.018*** (0.035)
0.008* (0.004)
–0.111*** (0.009)
–0.0002 (0.004)
Ln(cost of options)
0.008*** (0.001)
0.006*** (0.001)
0.006*** (0.001)
0.006*** (0.001)
Constant term
0.218*** (0.012)
0.605*** (0.023)
0.773*** (0.034)
0.650*** (0.025)
No. of observations R2
7,462 0.047
7,462 0.088
7,356 0.098
7,365 0.092
Note: Regression coefficients are the price-to-cost ratio or the profit rate for either land or structure. Numbers in parentheses are standard errors of coefficient estimates. All significance tests are two-tailed. *p < 0.0. **p < 0.05. ***p < 0.01.
constrained to be equal for all markets. This constraint is relaxed in table 4. Once coefficients can vary by city, the effect of structure costs on profit rates is strengthened. A number of markets—Columbus, Dallas, Dayton, and Houston—have negative and significant structure coefficients. In these cities, higher structure costs are not fully passed on as higher prices, but instead profit rates fall. The land cost elasticity is negative and significant everywhere except for Montgomery County. In general, the profit rate regressions indicate that changes in land costs affect profit rates much more than changes in structure costs do. The results suggest strongly that while short-run variations in structure costs can be readily passed on to consumers, this is much more difficult to do with land costs. The clear variation in coefficient values for both land and structure across markets in table 4 suggests that the markups are sensitive to market conditions.
Builder Per-Unit Profits and Market Conditions: MSA Aggregate Regressions This section examines the link between housing market conditions and builder profitability in an attempt to explain differences across markets found in table 4. The analysis has two parts. In the first, profit rates are regressed directly on measures of market activity. These regressions indicate that the unit profit rate is more sensitive to changes in house prices than to changes in the level of aggregate new construction. In the second stage, estimated land and structure coefficients from profit rate regressions are regressed on market conditions to determine the mechanism by which market activity affects profits. The results indicate that the contribution of land to average profit rates is notably more elastic than the similar measure for structure. Using MSA aggregates, the data are formed into a panel of eight markets by four years. The small size of the panel precludes the use of fixed effects because of the need to
136
C. Tsuriel Somerville
Table 4. Profit Elasticities for Land and Structure by MSA (within Estimator, by Subdivision and Model Type; Dependent Variable Is Log of Profit Rate) Variable Description
Baltimore
Cincinnati
Columbus
Dallas
Ln(cost of land)
–0.304*** (0.019)
–0.166*** (0.021)
–0.163*** (0.016)
–0.209*** (0.010)
Ln(cost of structure)
0.028*** (0.007)
0.011 (0.016)
–0.075*** (0.011)
–0.070*** (0.014)
Ln(cost of options)
0.010*** (0.001)
0.011*** (0.003)
0.006*** (0.002)
0.008*** (0.001)
Constant term
1.299*** (0.084)
0.636*** (0.086)
0.987*** (0.066)
1.107*** (0.069)
No. of observations R2
1,432 0.182
535 0.130
Montgomery Co., MD
Dayton
Ln(cost of land)
–0.198*** (0.022)
–0.036*** (0.010)
–0.102*** (0.019)
–0.036 (0.045)
Ln(cost of structure)
–0.054** (0.021)
–0.051*** (0.010)
0.037*** (0.011)
0.034** (0.017)
Ln(cost of options)
0.009*** (0.003)
0.004*** (0.001)
0.001 (0.002)
0.008*** (0.003)
Constant term
1.094*** (0.109)
0.473*** (0.047)
0.307*** (0.069)
0.201 (0.198)
269 0.290
2,112 0.030
Indianapolis
720 0.412
Variable Description
No. of observations R2
Houston
958 0.167
832 0.042
498 0.020
Note: Regression coefficients are the price-to-cost ratio or the profit rate for either land or structure. Numbers in parentheses are standard errors of coefficient estimates. All significance tests are two-tailed. *p < 0.10. **p < 0.05. ***p < 0.01.
conserve degrees of freedom. Instead, a random effects model is used to analyze these data. The random effects model breaks the error term into two components, v, which is constant within a group, such as an MSA, and g, which varies. Formally, a regression of profit rates Π on market conditions X for MSA i and year t is expressed as
(
)
(
)
ln( ⌸it ) =  ln( Xit ) + i + ␥ it , ~ 0, 2 , ␥ ~ 0, ␥2 .
(5)
The random effects approach has certain advantages over fixed effects in this application. With an efficient internal allocation of a firm’s resources, the expected value of the error term is zero. However, there is no reason for the variance of these returns to be constant across groups, and the random effects specification allows the volatility of the unexplained component of the profit rate to differ across markets. Builder profit rates are treated as a function of market conditions. Profit rates are expected to vary with the number of permits, the National Association of Realtors (NAR)
The Contribution of Land and Structure to Builder Profits and House Prices
137
Table 5. Profit Elasticities: Effects of Market Conditions (Random Effects, with Error Group by MSA; Dependent Variable Is Log of Profit Rate) Variable Description
(1)
(2)
(3)
Ln(total permits)
0.008 (0.014)
0.022* (0.012)
0.022* (0.012)
Ln(permits(t)/permits(t – 1))
–0.025 (0.046)
–0.038 (0.037)
Ln(NAR median price)
0.050 (0.043)
Ln(NAR median price(t)/ NAR median price(t – 1))
0.280** (0.120)
0.236** (0.116)
0.218* (0.114)
Hausman test probability No. of observations R2
0.00 32 0.524
0.00 32 0.398
0.03 32 0.329
(4)
–0.036 (0.039)
0.268** (0.118) 0.11 32 0.353
Note: Regression coefficients are the price-to-cost ratio or the profit rate for either land or structure. Numbers in parentheses are standard errors of coefficient estimates. All significance tests are two-tailed. *p < 0.10. **p < 0.05. ***p < 0.01.
median price, and changes in these measures.5 As shown in table 5, profit rates are most sensitive to price changes. The number of permits issued in the market is also correlated with an increase in the per-unit profit, though the elasticity is not significantly different from zero. The Hausman tests in table 5 indicate that for some of the regressions, the random effects error terms may be correlated with the right-hand-side covariates, leading to biased coefficient estimates. As an alternative to the random effects model, the same question was examined by using regional fixed effects in a generalized least squares (GLS) regression (table 6).6 The relationship between permits and the profit rate is not robust across specifications; in table 6 the number of permits is uncorrelated with unit profit rate. In contrast, the effect of changes in house prices is consistent across the two specifications. The effect of housing market conditions on the relative contributions of structure and land to profitability is tested by a two-stage method. In the first stage, regressions similar to those in table 4 are estimated by year for each MSA. The structure and land coefficients generated in these regressions are the dependent variables in the second stage, which analyzes how the relative contribution of land and structure expenditures to profits is affected by housing market conditions. These second-stage regressions are presented in table 7 using a GLS specification similar to that used in table 6. The regressions in table 7 are in pairs, where the same regression specification is tested once with the structure coefficient as the dependent variable and once with the land coefficient as the dependent variable. 5 Prices are measured using NAR medians. Though these medians are not quality controlled, the difference between changes in NAR medians and in quality-controlled prices is small (DiPasquale and Somerville 1995). The advantage of using the NAR numbers is that unlike the Freddie Mac–Fannie Mae indices, they allow both prices and price changes to be included in the regressions. 6 The weight matrix for these regressions is diagonal, with the elements of the diagonal being the number of units started in market i in year t, which is identical to a breakdown by year of the number of observations in table 1.
138
C. Tsuriel Somerville
Table 6. Profit Elasticities: Effects of Market Conditions (GLS with Regional Dummies; Dependent Variable Is Log of Profit Rate) Variable Description
(1)
(2)
Ln(total permits)
0.010 (0.018)
0.008 (0.013)
Ln(permits(t)/ permits(t – 1))
–0.008 (0.048)
Ln(NAR median price)
–0.011 (0.048)
Ln(NAR median price(t)/ NAR median price(t – 1))
0.233* (0.123)
0.233** (0.107)
0.247** (0.116)
Midwest
–0.039** (0.017)
–0.038** (0.015)
–0.044*** (0.011)
Texas
–0.039* (0.022)
–0.037*** (0.011)
–0.036** (0.016)
No. of observations R2
32 0.494
(3)
–0.006 (0.042)
32 0.530
32 0.525
Note: Regression coefficients are the price-to-cost ratio or the profit rate for either land or structure. Numbers in parentheses are standard errors of coefficient estimates. All significance tests are two-tailed. *p < 0.10. **p < 0.05. ***p < 0.01.
Land and structure sum to house value, so increases in the contribution of one factor tend to be associated with decreases in the other. This problem is particularly pronounced in the annual regressions, since the time path of the land coefficient is usually the inverse of the path of the structure coefficient. To help control for this condition, the second-stage regressions shown in table 7 include market-specific trend variables if such measures are statistically significant. This approach is somewhat successful, since the estimates for land are not the inverse of those for structure. The effect of house price changes on builder profit rates is captured entirely by changes in the markup on land. The house price change measure is significant only when the land expenditure coefficient from the profit rate regressions is the dependent variable. The coefficient of the log of house price growth is at least six times as large when the land coefficient is the dependent variable as it is when the structure coefficient is the dependent variable. The coefficients on permits are inconclusive, though growth in permits tends to increase the contribution of structure to per-unit profit rates and decrease that of land.7 Combining the results shown in tables 5 and 6 with those in table 7, it is evident that changes in profit rates are primarily a result of increases in house prices, which operate through their effect on the markup on land.
7 Random
effects regressions gave results similar to those for the GLS regressions for changes in house prices. However, unlike the results in tables 5, 6, and 7, the coefficient on changes in permits was also significant, though its sign was positive for structure and negative for land.
–0.0004*** (0.0001) 0.0031 (0.0028)
Trend for Houston
Constant term 32 0.741
0.0056** (0.0060)
–0.0012** (0.0005)
32 0.649
–0.0018*** (0.0002)
–0.0004*** (0.0001)
–0.0004** (0.0002)
–0.0005*** (0.0001)
–0.0004*** (0.0001)
0.0007*** (0.0001)
0.0003 (0.0026)
Profit Rate on Structure
(2)
32 0.738
–0.0011** (0.0005)
–0.0009** (0.0003)
–0.0014*** (0.0003)
–0.0004* (0.0002)
–0.0012*** (0.0003)
–0.0005** (0.0002)
0.0101* (0.0052)
Profit Rate on Land
32 0.683
0.0024 (0.0026)
–0.0004*** (0.0001)
–0.0006*** (0.0002)
–0.0004*** (0.0001)
–0.0005*** (0.0001)
0.0007*** (0.0001)
–0.0005 (0.0003)
Profit Rate on Structure
(3)
32 0.700
0.0012 (0.0061)
–0.0010* (0.0005)
–0.0016*** (0.0003)
–0.0005* (0.0002)
–0.0012*** (0.0003)
–0.0005** (0.0002)
–0.0003 (0.0007)
Profit Rate on Land
Note: Dependent variables are the estimated coefficients from annual regressions of prices on land and structure expenditures, as in table 2. Numbers in parentheses are standard errors of coefficient estimates. All significance tests are two-tailed. *p < 0.10. **p < 0.05. ***p < 0.01.
32 0.678
–0.0006*** (0.0002)
Trend for Dayton
No. of observations R2
–0.0004** (0.0001)
Trend for Dallas –0.0012*** (0.0003)
–0.0005** (0.0002)
–0.0005*** (0.0001)
–0.0005** (0.0002)
Trend for Columbus
0.0006*** (0.0001)
Trend
0.0121** (0.0055)
–0.0007 (0.0007)
Profit Rate on Land
–0.0013*** (0.0003)
0.0020 (0.0027)
NAR median price(t)/ NAR median price(t – 1)
(1)
Trend for Cincinnati
–0.0005* (0.0003)
Total permits
Variable Description
Profit Rate on Structure
Dependent Variable
Table 7. Effects of Market Conditions on Land and Structure Profit Rate Coefficients (GLS Regression)
The Contribution of Land and Structure to Builder Profits and House Prices 139
140
C. Tsuriel Somerville
Conclusion This article uses microdata on builder costs, house prices, and profits to study the effect of land and structure costs on house prices and builder profitability. The modeling framework used here departs from the conventional perfect-competition model by allowing the builder, who produces a joint product, to face downward-sloping implicit demand curves for land and structure. A goal of this work is to study the contribution of each factor to per-unit profits. The detailed breakdown of the contributions of land and structure to profits indicates that the variation in per-unit builder profit is most sensitive to land costs. This suggests that unexpected variations in structure costs either are small or can be passed on directly to consumers in the form of higher prices. In contrast, higher land costs directly reduce profit rates. When the analysis is extended to the relationship between housing market conditions and profitability, the results are as expected: Only changes in house prices affect the per-unit profit rate. The level of and growth in new construction (permits) appear to have little effect on per-unit returns, though aggregate profits will rise with increases in output. Changes in house prices affect profit rates through land. The contribution of structure to per-unit profits is not correlated with movements in house prices, while that of land is. Overall, these findings are not necessarily surprising, but they have important implications: Structure costs matter because unexpected variation in structure costs is much more readily passed on to consumers than is the case for land costs. In contrast, builder behavior would be expected to be much more sensitive to land costs because it more directly affects the builder’s bottom line.
References DiPasquale, Denise, and C. Tsuriel Somerville. 1995. Do House Prices Based on Transacting Units Represent the Entire Stock? Evidence from the American Housing Survey. Journal of Housing Economics 4:195–229. Edelstein, Robert H. 1983. The Production Function for Housing and Its Implications for Future Urban Development. In North American Housing Markets into the Twenty-First Century, ed. George W. Gau and Michael A. Goldberg, 93–125. Cambridge, MA: Ballinger. Färe, Rolf, and Bong Joon Yoon. 1985. On Capital-Land Substitution in Urban Housing Production. Journal of Urban Economics 17(1):119–24. Kinzy, Scott A. 1992. An Analysis of the Supply of Housing Characteristics by Builders within the Rosen Framework. Journal of Urban Economics 32(1):1–16. Maisel, Sherman J. 1953. Housebuilding in Transition. Berkeley, CA: University of California Press. McDonald, John F. 1981. Capital-Land Substitution in Urban Housing: A Survey of Empirical Estimates. Journal of Urban Economics 9(2):190–211. Mills, Edwin S. 1972. Studies in the Structure of the Urban Economy. Baltimore: Johns Hopkins University Press. Muth, Richard. 1969. Cities and Housing: The Spatial Pattern of Urban Residential Land Use. Chicago: University of Chicago Press.
The Contribution of Land and Structure to Builder Profits and House Prices
141
Muth, Richard. 1971. The Derived Demand for Urban Residential Land. Urban Studies 8(2): 243–54. Smith, Barton A. 1976. The Supply of Urban Housing. Quarterly Journal of Economics 90(3): 389–405. Somerville, C. Tsuriel. 1994. Analyzing Construction Costs: Behavior and Sub-Contractor Reputation in Homebuilding. Working Paper 94-ULE-010. University of British Columbia, Canadian Real Estate Research Bureau. Stover, Mark Edward. 1990. Specification Error in the Estimation of the Elasticity of Substitution between Capital and Land in Residential Construction. Annals of Regional Science 24(2):125–32.
142
C. Tsuriel Somerville
