A Dynamic Approach to Estimating Hedonic Prices for...

A Dynamic Approach to Estimating Hedonic Prices for Environmental Goods: An Applicationto Open Space PurchaseAuthor(s): Mary RiddelSource: Land Economics, Vol. 77, No. 4 (Nov., 2001), pp. 494-512Published by: University of Wisconsin PressStable URL: http://www.jstor.org/stable/3146936Accessed: 23/08/2010 12:25

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A Dynamic Approach to Estimating Hedonic Prices for Environmental Goods: An Application to Open Space Purchase

Mary Riddel

ABSTRACT. If housing markets exhibit slow adjustment to system shocks, then hedonic estimates of the price impact from environmental amenity trends may be time variant. This paper suggests an alternative to the cross-sectional model for estimating hedonic prices using an error correction approach that allows for endogenous environmental quality. The model is applied to data concerning an open space purchase program in Boulder, Colorado, and shows that the economic impact of an open space purchase takes several years to be fully realized. This observation ques- tions using cross-sectional, hedonic models for evaluating willingness to pay for time-trended environmental amenities. (JEL Q24, R521)

I. INTRODUCTION

Recent research has questioned the ability of cross-sectional hedonic models to deal with time-trended environmental amenities (Freeman 1993; Smith and Huang 1995). In particular, housing market inefficiencies may lead to lags in the incorporation of the amenity effects, especially when the level of the amenity is subject to a time trend (Freeman 1993; Graves et al. 1988). If the length of time until full capitalization of the amenity value is sufficiently long, then price effects estimated cross-sectionally may be a function of the time at which the effect is estimated. Thus, different values may be estimated for the environmental good at different times.

Another problem with the cross-sectional approach is that environmental quality adjustments may induce disequilibria in the housing and related markets, such as the labor market. Graves (1979) and Graves and

Linneman (1979) found support for the idea that environmental amenities, such as a relatively warm climate and low humidity, may be at least partly responsible for the influx of new residents into the western United States in the 1960s and 1970s. If the labor market is affected by environmental quality changes, then second-round housing market impacts could occur through changes in migration patterns. Unless second-round impacts are instantly incorporated into the housing market, hedonic price estimates will vary over time.

Past hedonic property models have shown evidence of this type of distortion. Correll, Lillydahl, and Singell (1978) investigated the effect of land purchase for open space on house prices in Boulder, Colorado, in three different neighborhoods with mixed results. In one neighborhood, house prices were neg- atively related to distance from open space, declining about $10 for a one-foot move away from the open space. In another neighborhood, an unexpected positive sign was estimated for the distance coefficient. In the third neighborhood the coefficient was not statistically different from zero. In another study, Lopez, Shah, and Altobello (1994) estimated the impact of parks and open space preservation on the supply of agricultural land in a cross-sectional study of the north- eastern United States. They found that the allocation of land to parks and open space did not significantly affect the supply of land to agriculture in that area.

Land Economics * November 2001 * 77 (4): 494-512 ISSN 0023-7639 ? 2001 by the Board of Regents of the University of Wisconsin System

The author is assistant professor and associate direc- tor, Department of Economics and Center for Business and Economic Research, University of Nevada, Las Ve- gas. The author would like to thank John Loomis, Har- vey Cutler, Stephen Davies, Doug Steigerwald, Keith Schwer, Paul Thistle, and an anonymous referee for their helpful comments.

77(4) Riddel: Hedonic Prices for Environmental Goods 495

The unexpected findings of Correll, Lilly- dahl, and Singell (1978) and Lopez, Shah, and Altobello (1994) could be a result of fail- ings in the model specification. Since continuous open market purchase of open space from sales tax revenues may be thought of as a time-trended amenity, cross-sectional hedonic studies could be misleading. If amenity effects are capitalized slowly into the housing price and, concurrently, extra-housing market effects impact the labor market then the measured price impacts of any given purchase will change over time.

This paper develops a model that jointly evaluates the effects of trends in environmental quality on the housing and labor markets. The model explicitly allows environmental quality to be endogenous. An error-correction approach is used to help incorporate the full impact of sustained environmental quality changes in the face of housing market in- efficiency. Applying the model to the case of an active open space purchase program in Boulder, Colorado, we find that the open space program induces disequilibrium in both the housing and labor markets. As a result, hedonic price estimates are time variant, taking approximately four years to incorporate the full impact of the open space purchase.

This research makes two important contri- butions to the regional environmental amenity research. First, the dynamic modeling approach allows us to examine the impacts on a regional housing and labor market from a change in an environmental amenity. The results show that changes in the level of a regional environmental amenity can cause upward pressure on housing prices, a decline in the real wage, and expansion in residential and commercial construction. The dynamic approach also enables us to compare the estimated implicit open space price gained from the time series method to that which would have been estimated using a hedonic cross- sectional model.

The paper is organized as follows. Section 2 details the problems encountered by the hedonic property model when estimating the price impact of a change in environmental quality. Section 3 outlines the proposed theoretical model in the context of evaluating the

effects of an open space purchase program on local housing and employment markets. Section 4 discusses estimation of the model parameters and dynamic time profiles of the effects of different disturbances. Section 5 applies the model to calculating the effects of the city of Boulder open space purchase program on housing prices and residential and commercial growth in that town. We conclude with some remarks concerning the efficacy of hedonic models when applied to environmental quality trends.

II. PERFORMANCE OF HEDONIC PROPERTY MODELS UNDER

STOCHASTIC TRENDS IN AN AMENITY

Hedonic property models have been used extensively in the non-market valuation liter- ature (Anderson and Crocker 1971; Freeman 1993; Miranowski and Hammes 1984). The standard formulation designates the ith housing price (Phi) as a function of structural (Si) and amenity characteristics of the house. Amenity benefits can arise from neighborhood (Ni) or environmental factors (ai) af- fecting the price of the house. This formulation implies a reduced-form equation for the housing price of Phi = Ph(Si, Ni, ai), with the hedonic value of the environmental amenity given by 6Phil/ai.

The hedonic property method, useful for deriving welfare measures associated with one-time environmental quality changes, may fail in analyzing the price effects of environmental quality trends.' The effects of endogeneity in environmental quality trends within the housing and related markets may be significant. Indeed, if environmental quality jointly impacts the housing and labor markets, then multi-period impacts of environmental quality changes may result, especially if housing market inefficiencies exist.

An example may be illustrative. In theory, a hedonic model could be used to evaluate the public's willingness to pay for additional

' Quality trend is defined as a sustained improve- ment or decline in environmental quality.

496 Land Economics November 2001

public open space. However, the economic impacts of a continuous program that permanently changes the character of an area are more complex. An open space purchase program may result in fewer acres available for commercial or residential development, causing upward pressure on land prices in the area. At the same time, the program may en- courage firms to locate in the area to provide non-wage amenity benefits of open space to their employees (Blomquist, Berger, and Hoehn 1988). Though lower labor costs en- courage firms to expand, higher land costs discourage expansion. If the net affect of these forces is positive, new employment opportunities will be met to a large extent by in-migration, causing second-round impacts on the housing market through increased demand. As a result, a cross-sectional hedonic model may not be adequate to explain the housing price impacts of an open space purchase program.2

Another potential problem with hedonic models arises due to the assumption that the housing market is in equilibrium. The equilibrium assumption is problematic since the housing market has been shown repeatedly to incorporate new information with significant time lags (Case and Shiller 1989; DiPasquale and Wheaton 1994; Mankiw and Weil 1989). Studies by Case and Shiller (1989) and Meese and Wallace (1994) clearly demon- strate the existence of positive autoregressive forces in returns to housing investment. Case and Shiller document the existence of fore- castable excess returns in the Atlanta, Dallas, Chicago, and San Francisco housing markets. Meese and Wallace confirm the findings of Case and Shiller, and agree that in the short run, that inefficiencies such as information asymmetry, heterogeneous product, and high transaction costs dominate the market.

The combination of market endogeneity and housing market inefficiencies suggests that housing price impacts of trended amenities may be time variant. To formalize a time-variant index, the next section intro- duces a theoretical model that links the housing and employment markets while account- ing for joint impacts from environmental amenity acquisition.

III. A SIMPLE REGIONAL MODEL WITH ENDOGENOUS

ENVIRONMENTAL QUALITY

Because environmental amenities may affect the supply and demand for housing and labor simultaneously, each of these markets must be thoroughly specified in the model. Related markets, such as the rental market, may also be impacted by amenity changes, and are explicitly contained in the model.

The time series-based approach taken for this paper aggregates across individual environmental demands within a community. This is analogous to aggregating over individuals for market demand analysis. As such, the model presented here can be justified in the same way that we justify aggregate demand functions. We assume that each individual has the same marginal propensity to consume for any good (Phlips 1983, 99- 100). Of course, this assumption is quite strong and in reality the marginal propensity to consume almost certainly varies with different incomes. Nevertheless, the assumption is maintained and we bear in mind that, like other market demand analysis based solely on aggregate behavior, the implicit prices arising from the model include some aggre- gation error.

The Housing Market

The individual-consumer demand function for housing over time is a function of the price of housing, long-term interest rates, income, and the apartment rental rate. Rental units are thought of as a substitute for home ownership (DiPasquale and Wheaton 1994; Mankiw and Weil 1989; Poterba 1991). At the regional level, home ownership in a nearby town may be an option, so that the price level of housing in the neighboring town is also considered in the purchase deci-

2 The number of acres in the program at any point in time could be interpreted as a stochastic variable if the number of acres and the timing and location of purchase are a function of stochastic market variables. This would be the case when the program is funded by a sales tax and purchases are made through the open market.


sion. Finally, the demand function should account for the changes in environmental, neighborhood and structural characteristics of the home that may occur over time.

To obtain the market regional demand for housing, we sum over the individual demands, with two adjustments. First, when looking at the housing demand function over time, demographic shifts that lead to changes in the age distribution should be included in the model. Typically, this is done by replac- ing the number of households with the number of households that would be expected to own homes, conditioned on the age cohorts comprising the population (DiPasquale and Wheaton 1994). Second, it is convenient to evaluate demand for a typical, or "quality- adjusted" house. So, we must create a quality-adjusted price index, using hedonic or repeat-sales measures, which controls for changes in the quality and structural characteristics of the home.

We can then write a regional housing demand function as:

SDt = f(Pt, a,, hh,, rent,, mort,, ryt, pP), [1]

where SDo, is the stock of housing demanded given in units, p, is the quality-adjusted price level for homes in the region, a, is the level of amenities in the region, hh, is the number of households in the region, rent, is the average rental rate, mort, represents long-term interest rate, ry, is income and p' is the quality- adjusted price index for neighboring regions.

DiPasquale and Wheaton (1994) formu- late the following long-run equilibrium and short-run housing supply equations:

S, = v(cc,, tbillt, p,),

AS, = Ct - 8St_1

= (v(cc,, tbill, p,t) - St-1) - S,_t-, [2]

where: S, is the current stock, C, is current new construction, 8St-I equals depreciation from the previous period, v(cc,, tbill,, p,) is the equilibrium stock as a function of price, cc, is the cost of construction materials and labor, tbill, is the short-term cost of financ-

ing, and ? is the speed of adjustment to the equilibrium stock.

The Labor Market

Wage hedonic models have long recog- nized the impact that environmental amenities may play in regional wage differentials (Blomquist, Berger, and Hoehn 1988). Ac- cordingly, we may derive a market labor supply function by horizontally summing the individual supply functions:

L, = g(wage,, N,(a,)), [3]

where L, is the number of individuals in the labor force at time t, wage, represents wages at time t, and N, is the wage differential associated with the environmental amenity. An increase in the amenity shifts the labor supply curve outward, so that more labor is sup- plied at a given wage rate.

The market demand for labor at the regional level may be written as a function of wages and regional economic health, H,, so that:

L, = h(wage,, H,). [4]

Related Markets

Other markets, particularly the housing rental market, may be affected by the level of environmental amenities in a region. Allowing for endogeneity in the apartment rental rate and vacancy rates yields:

rentt = f(vact, p,, at, ryt, p)

vact = k(rent,, Pt, AS,). [5]

Rents are a function of the vacancy rate, vac,, as well as the housing price level, environmental amenities, income, and the house price in the neighboring region. People may move from one housing unit to another in response to changes in rental rates or the price of single-family homes. Alternatively, an excess or unmet supply, associated with changes in the stock of housing, may cause vacancy rates to change.


Finally, we must allow for environmental quality to be endogenous. The endogeneity could arise from a variety of sources, depending upon the nature of the environmental good. All else equal, environmental quality differentials between two regions would lead to growth concentrating in the region with the superior environmental quality. An expanding economy means more potential revenues for public programs. Therefore, if an open space purchase program is funded by a local tax, growth can lead to an increased rate of preservation. Because the open space caused the growth, the number of acres purchased is an endogenous variable.

Accordingly, we may describe the level of an environmental amenity as a function of the number of households and the level of taxes collected at time t:

a, = f(hh,, taxt). [6]

Equation set [7] defines the full set of equilibrium relationships.

SDt = f(Pt, at, hh,, rent,, mort, ryt,, p)

S, = v(cc,, tbill,, pt)

L, = h(wage,, H,)

L, = g(wage,, Nt(at))

rentt = f(vac,, Pp, a,, ry, p•)

vact = k(rent,, p,, AS,)

a, = f(hh,, taxt). [7]

This may be viewed as a simple regional economic model, with environmental quality as an endogenous factor in the growth of the region. Thus, an increase in environmental quality relative to other regions will attract in-migration. This in turn leads to a larger labor pool at any wage, lowering the costs of labor relative to other regions. Firms respond by expanding the commercial base. The influx of new households also demand housing, placing upward pressure on housing prices. As prices rise and apartment vacancy rates fall, developers are signaled to provide more housing.

IV. DYNAMIC STRUCTURE AND ESTIMATION

Equation set [7] assumes rapid adjustment to system shocks for housing and employment markets. However, a large body of evidence suggests that housing markets are characterized by asymmetric information and high transaction costs, leading to slow adjustment to demographic and macroeconomic shocks (Case and Shiller 1989; DiPasquale and Wheaton 1994; Mankiw and Weil 1989; Poterba 1991). Thus we include lagged values of the endogenous and exogenous variables for a dynamic structure.

To allow for a dynamic structure, let xt be an mxl vector of m exogenous variables from the housing supply, housing demand, labor supply and labor demand. Define Yt be a nxl vector of I(1) endogenous variables.3 If we assume a linear structural form either directly or through an appropriate transfor- mation for each of the equations 1-6, then the structural form of the stochastic model is4:

Gyt + blxt + --- + bqxt-q+l

+ clyt-1 + - - - + C,yt-,p = ut. [8]

In keeping with the simultaneous modeling approach, we may write equations 1-7 in reduced form as:

Yt = -G-lblxt - -G-Ibqxt-q+i

- G-'clyt_

- -

G-cyt_p + G- u,. [9]

3 Many of the variables considered in the housing and employment markets exhibit nonstationary properties. Housing prices, the stock of housing and the level of open space are nonstationary if they are integrated ARMA processes (Granger 1981; Tsionas 1994). Em- ployment may be subject to stochastic trends introduced by correlated macroeconomic variables known to be nonstationary (Granger 1981; Johansen and Juselius 1992; Johansen and Juselius 1994).

4 We define the equations, rather than the data matrix, in this discussion. As such, ut is nxl matrix of structural error terms, G is a nxn matrix of the structural parameters, bi and ci are nxn matrices describing the system dynamics, and ?p is an nxn matrix that includes the parameters of the long-run system and the adjustment parameters. The Ki are nxn matrices that describe the short-run system dynamics.


with error correction representation:

Ay, = -G-'blxt

- - G-'bqxt-q+l

- KCIAyr-1 - - Kt+pAyt-p+l

+ A'yt-1 + et,

[10]

where Ki = •1=i+tG-1cj, G-lut = e,, A' =

,jG-'cj - I,, P is a nxh, h is the number of long-run relationships supporting the system, A is an nxh matrix of adjustment parameters, p is the lag length defining the endogenous set Yt, and q is the lag length defining the exogenous set xt.

The A matrix contains the long-run parameters. The vector A'yt-, is composed of a set of equations that describe the long-run system equilibrium in terms of the endogenous system variables. For given values of the endogenous variables, the elements of A'yt-1 describe the deviation from long-run equilibrium and are often called the disequilibrium residuals. When a disequilibrium residual is non-zero, one or more variables defining that particular equilibrium relationship is out of line with the long-run trend growth. Therefore, other system variables must adjust if the system is to return to equilibrium. For example, open space acquisition may disturb long-run equilibrium in the housing and labor markets. Equilibrium will be restored when house prices, and perhaps employment, rise.

The rate that the system returns to equilibrium may vary with the source of the dis- turbance. When the disequilibrium vector, A'yt-1, is included in the adjustment equations [10], the estimated coefficients, P, indicate how fast the market responds to disequilibrium. The G-'b; and ic terms allow the endogenous variables to adjust to changes in predetermined and exogenous influences.

The parameters of the model, P, A, Ki and S= e,e can be estimated using Johansen's

method (Johansen and Juselius 1992; Jo- hansen and Juselius 1994).5 The model, as formulated in equation set [10], also allows us to test the null hypothesis of housing market equilibrium against the alternative that disequilibrium related to environmental quality is a driving force in the housing and labor markets. This reduces to a test that the adjust-

ment parameters in any disequilibrium residual containing a non-zero coefficient for the open space variable in equation set [10] are zero. Thus, if open space significantly con- tributes to the disequilibrium residual defining the first cointegrating vector, significance of its corresponding speed of adjustment in the price, stock, or employment adjustment equations indicates that the housing market adjusts in response to open space purchase.

The advantage of the error correction approach over other models is that it allows for adjustments that are in line with respect to the long-run economic relationships. The VECM approach allows us to explicitly estimate the extent of system disequilibrium in- duced by a change in a regional amenity. At the same time, it provides a picture of the underlying equilibrium and the rate that equilibrium is restored, given the amenity change. Using impulse response functions, the VECM allows us to determine the time path of the impact from the change in amenity levels on any of the model variables.

Another advantage of the VECM is that it accounts for information included in the levels of the endogenous system variables (Hamilton 1994, 573). The cumulative impulse response function (computed using the model parameters) gives us the time path of the response of any endogenous variable to a change in any of the model variables. Spe- cifically, the cumulative impulse response from a permanent change in the amenity level at time t on endogenous variable y at

S Although several estimation techniques have been suggested for VECM's, Johansen's full system maximum likelihood estimation method has some advan- tages over other techniques. First, Johansen's technique allows for estimation of the rank of the cointegrating space which is the rank of the long run equilibrium coefficient matrix. Other techniques, such as the Engle and Granger technique or that proposed by Phillips and Hansen, take the rank of the space as given, then pro- ceed to estimate the VECM parameters (Engle and Granger 1987; Phillips and Hansen 1990). Second, the estimation method jointly estimates the short and long- run coefficients of the VECM, given the rank of the cointegrating space, leading to increased efficiency relative to models that estimate the short run parameters conditional on the long-run coefficients (Banerjee et al. 1993). Although we have chosen Johansen's method, the model presented her may be estimated using any of the above-mentioned error-correction approaches.


time t + k is simply 6E(y,+k y,)/6a,. Because it is a function of the level of the endogenous variable at time t (y), the impulse response function accounts for the current level of the endogenous variable. Thus, higher aggregate levels of open space may have more or less impact than smaller aggregates, depending on the sign of the impulse response function for that period. For instance, if the price impact from open space increases as the aggregate size of the open space grows, then the impulse response function for period t + k + j (6E(p,+k+jIyf+k)/6at+k)

will be greater than that for t + k if additional acres are purchased between t + k and t + k + j.

The impact of the amenity on the housing price level at time t + k is 8E(p1+kly,)/ta,. Thus, the impulse response of a change in open space to housing prices may be interpreted as the implicit price, over time, of the open space purchase for a given aggregate level of open space. This is analogous to the implicit price estimated using the cross- sectional hedonic model. In cross-sectional models, the characteristics of the home are held constant, since the price level is quality adjusted. In contrast, the impulse response function controls for variables that may change over time that will affect the demand and stock of housing. At equilibrium, the cumulative impulse response function 6E(pt+klyf)/6at may be interpreted as the implicit price of the amenity at time t + k.6 When the change in amenity has been com- pletely incorporated into the house price and equilibrium has been restored, then the impulse response function will stabilize.

This leads us to the empirical test for the statistical significance of the implicit price varying over time in response to an open space purchase:

HO: 8E(pt+klyt)/6at = 8E(ply,)/6a, for all k.

versus HA: at least one of

8E(pt+kl Iy)/at 8 E(ply,)/6a,.

Intuitively, when the impulse response function stabilizes, the system has been restored to equilibrium and the impulse re-

sponse gives the implicit price of the environmental amenity at the equilibrium level.

V. A DYNAMIC MODEL FOR OPEN SPACE IN BOULDER, COLORADO

From 1950 to 1960, Boulder's population increased from 37,718 to 66,870, a 77.3% increase. As development began to encroach upon the scenic mountain backdrop, a group of concerned citizens proposed the creation of a greenbelt that would surround the city. In 1967, the group managed to have an initiative placed on the November ballot that would permanently increase the city sales tax by 4/10 of a cent to purchase and maintain the proposed greenbelt. Boulder voters passed the initiative and the Boulder City Open Space Program was born (City of Boulder Open Space Dept. 1995).

The program has seen several changes since its inception. In 1971, an amendment to the city charter was passed that allowed the city to issue bonds for open space purchase and improvements for recreation and access. The voters approved another sales tax increase in 1989 of an additional 3/10% for 15 years. The late 1980s and 1990s saw ex- tensive trail-building and recreational improvements to the land. As of 1997, the Boulder City Open Space and Real Estate Department manages approximately 25,000 acres which adjoin over 70% of the city's border.

6 Unfortunately, impulse response analysis is not without its drawbacks. In order to account for correla- tion among shocks, the shocks are orthogonalized through the Choleski decomposition of the error corre- lation matrix, fl. This orthogonalization attributes whatever common effects exist between shocks to the variable that is positioned first in the VECM system. As a result, reordering of the variables can change the impulse response functions (Hamilton 1994). This problem can be sidestepped by considering the following. We recall from equation set [10] the relationship between the estimated error under the reduced form model and the structural error is e, = G- u,. The partial differential 8yi,t+k/jei, is a function of the shocks to all the different endogenous variables. Thus, the vector

8E(yi,t+klyt)l ejt = &yi,t+k/Iujt Will isolate the shock from the jth variable.


TABLE 1 SUMMARY STATISTICS AND ADF TESTS FOR STATIONARITY: ENDOGENOUS

AND EXOGENOUS VARIABLESa'b

Variable Name Variable Mean Std. Dev. ADF Stat.

P Repeat sales housing price index for City of Boulder 42.37 18.89 -0.5751 P' Repeat sales housing price index for City of Louisville 21.32 10.81 -3.4271 ACRE Acres of open space in program (10,000 acres) 1.74 0.47 0.1331 Lc Boulder County employment (10,000 jobs) 11.48 1.65 -0.6657 RENT Average residential rent sq./ft., Boulder County ($) 0.63 0.04 -0.8574 S Housing stock, City of Boulder (10,000 units) 3.50 0.22 - 1.4660 WAGEc Real average weekly wage, Boulder County ($) 375.4 12.02 -1.9247 CCC Real average weekly wage for construction workers ($) 403.7 67.33 -1.3185 VAC Residential rental vacancy rate, Boulder County 5.56 3.37 -3.1783 TBILLd Real rate on month treasury bills 6.68 2.37 MORTd Real average interest rate on 30-year mortgages 10.73 2.64

a The 5% and 10% critical values for rejection of the null hypothesis of a unit root for the ADF test are -3.4919 and -3.1744, respectively.

b All price and wage data are inflation adjusted using the GDP deflator. c Seasonally adjusted using Census X-11 additive. d TBILL and MORT are national variables and are treated as exogenous in the model.

Data Sources

The years contained in the study were chosen to lie between two important policy initiatives. In 1980, prior to the beginning of our study, Boulder voters chose to accelerate the open space purchase program that had been in place since 1969 by creating an open space purchase fund through issuing munici- pal bonds. In 1996, after the end of our study, a ballot measure passed that constrained residential growth to 1% each year while placing caps on commercial expansion. We choose the years in between in order to control for changes in the regulatory environ- ment. Therefore, quarterly data from 1981.4 through 1995.4 are used. All of the data are seasonally adjusted using the Census X-11 procedure and inflation adjusted using the GDP deflator. Table 1 provides a list of the variables used in the model.

Not all of the variables included in the theoretical model are available over the time period of study. In particular, the number of age-adjusted households, hh,, is not available. We allow the level of employment in the County, L,, to act as a proxy for the number of households demanding housing within the city of Boulder. Using the County employment allows us to control for households that may work in Boulder but live in a neigh-

boring community. Thus, the open space impulse response functions are interpreted as the impact of open space purchase on total County employment. The employment impulse functions will remain unbiased so long as the City of Boulder's share in the County housing remains stable over the period of study.' The City of Boulder's share of housing units within the County fell from 62% in 1982 to 59% in 1995. Thus, using employment to proxy for the number of households probably induces slight but unavoidable error in the parameter estimates.

Also, city level real income and quarterly sales taxes are not available on a quarterly basis. We assume that total wages in Boulder County, WAGE,, acts as a proxy for retail spending, hence local sales tax, and real income. Including County wage data is consistent with using County employment in the equations. However, using County wage data as a proxy for sales taxes and income may be problematic if the city's proportion of retail spending or employment changed over time.

'7 Impulse response functions would be biased if the proportion of people working in Boulder and living in another county were large. This is not the case. In 1995, the residence adjustment reported by the BEA for Boul- der County was less than 1.29%, indicating that only a small percentage of the employees working in Boulder County lived elsewhere.


In fact, retail sales with the City of Boulder comprised a relatively stable proportion of total retail sales within the County over the period of study. The cities share of retail sales grew from 66% in 1985 to 68% in 1995, suggesting that the proportional relationship changed only slightly over the period investigated. The share of employment also remained reasonably stable. Thus, we expect that minimal bias will be present in the impulse response functions and wages should act as a viable proxy for sales tax and income.

The macroeconomic time series were obtained from Citibase. MORT is the quarterly data series for the real interest rate on primary conventional mortgages. The monthly series for the real interest rate on 3-month treasury bills, TBILL, is used to reflect short- term financing costs. The data are averaged to obtain a quarterly estimate.

Local data on open space purchases were obtained from the City of Boulder Open Space and Real Estate Department. Purchase of land for open space and purchase of development rights are included.

Wage and employment data for Boulder County were provided by the State of Colo- rado Dept. of Labor and Employment. Rental and vacancy rates for single-family homes in Boulder County were obtained from reports published by the Apartment Association of Metro Denver (AAMD). The estimates of rental and vacancy rates are calculated using survey data obtained from the quarterly housing survey performed by the AAMD. The number of building permits issued for single-family homes is used to model new construction. The data were obtained from the Current Construction Reports: Hous- ing Units Authorized by Building Per- mits (monthly, 1981-1995). Data on the stock of housing and depreciation as of 1981 were obtained from the City of Boulder Planning Department.

The repeat sales method proposed by Case and Shiller is used to estimate the housing price indices (Case and Shiller 1987). Only homes that had not been issued building or remodel permits during the period of study were used. Because the index is formed using the appreciation in sales price for individual

homes that have not undergone quality improvements, it grows in response to general price pressure in an area. As such, the index will reflect appreciation due to supply and demand changes and environmental quality improvements but not changes in the construction quality of houses in the area.

Estimation Procedures

The results of the Augmented Dickey-Ful- ler (ADF) test for the nine variables chosen to describe the regional housing and employment markets are given in Table 1 along with the exogenous macroeconomic variables. For all of the regional variables, the null hypothesis of nonstationarity cannot be rejected. This yields nine variables that potentially form long-run cointegrating relationships.

Finding the number of equilibrium relationships implied by the data is the next step in VECM estimation. To estimate the rank of the cointegrating space, Johansen's test for multi-equation cointegration was used. The results of the maximum eigenvalue test, given in Table 2, indicate a rank of three, meaning three error correction terms will be included in each reduced form adjustment equation.

Given the rank of the cointegrating space, we estimate the model parameters using Jo- hansen's full information maximum likelihood technique. Lag length for the VECM was determined using the AIC and the Schwarz criteria.

The Results

The normalized cointegrating vectors identified using the Phillip's representation are reported in Table 3. The cointegrating equations, once identified, represent the long-run structural relationships in the system. We in- terpret the first cointegrating vector as a long-run demand function for housing. When E,,,_1 is positive, then the demand for housing is not in equilibrium. The price level is too high relative to the other housing demand variables. As such, the price level will begin to fall in the next period, or, alternatively, open space must rise or the stock must fall to re-equilibrate the system. In another sce-


TABLE 2

MAXIMUM EIGENVALUE AND TRACE TEST FOR RANK OF COINTEGRATING SPACE: INCLUDED VARIABLES ARE: P, P', ACRE, Lc, RENT, S, WAGE, CC,

AND VAC

5% 1% Likelihood Critical Critical Hypothesized

Eigenvalue Ratio Value Value No. of CE(s)

0.796464 335.2708 222.21 234.41 None ** 0.739131 250.8996 182.82 196.08 At most 1 ** 0.692955 179.6815 146.76 158.49 At most 2 ** 0.511741 117.1013 114.90 124.75 At most 3 * 0.459079 79.10508 87.31 96.58 At most 4 0.375142 46.53756 62.99 70.05 At most 5 0.230722 21.61536 42.44 48.45 At most 6 0.123595 7.713281 25.32 30.45 At most 7 0.013515 0.721182 12.25 16.26 At most 8

* Denotes rejection of the hypothesis at the 5% significance level; ** denotes rejection of the hypothesis at the 1% significance level.

nario, if there is excess demand for housing in Boulder due to rising employment, we note that cointegrating equation one reveals that price may rise to re-equilibrate the system.

The second cointegrating vector defines a

long-run relationship between the price level for homes in Louisville and county employment, open space, and the stock of housing. The third vector represents the equilibrium condition that must exist to keep the employment market in Boulder in equilibrium. Ad-

TABLE 3 NORMALIZED COINTEGRATING VECTORS USING THE PHILLIP'S

REPRESENTATION (STANDARD ERRORS IN PARENTHESES, WITH t-STATISTICS BELOW)

Cointegrating Equations Elt E2t E3t

P,-1 1.000000 0.000000 0.000000

PL,_- 0.000000 1.000000 0.000000 RENT_1 0.000000 0.000000 1.000000 VAC,_I -0.499038 - 1.743584 -0.039392

(1.01139) (1.39371) (0.00726) -0.49342 -1.25104 -5.42826

L,-I -21.65946 -18.56675 -0.170460 (3.40783) (4.69602) (0.02445)

-6.35579 -3.95372 -6.97143 CC,-I -0.048644 0.076536 -0.001301

(0.06199) (0.08542) (0.00044) -0.78472 0.89598 -2.92438

WAGE,_ 0.019057 -0.037602 0.004839 (0.23112) (0.31849) (0.00166) 0.08245 -0.11806 2.91794

S,-1 192.7751 300.5871 -0.145221 (53.6319) (73.9052) (0.38481)

3.59441 4.06720 -0.37738 ACRE,_ -36.31380 -83.01811 0.249651

(19.6314) (27.0522) (0.14086) -1.84978 -3.06881 1.77239

C - 392.3316 -726.0568 0.340767

TABLE 4

MATRIX OF ADJUSTMENT PARAMETERS (DEPENDENT VARIABLES IN COLUMNS, REGRESSORS IN Rows: t-STATISTICS REPORTED

BELOW EACH COEFFICIENT)

Error Correction AP APL ARENT AVAC AL ACC AWAGE AS AACRE

Et,_I -1.358816 -0.660673 -0.002889 -0.656889 0.026034 3.400045 -0.098228 0.000433 -0.007134 -3.81646 -1.78482 -0.99284 -2.98716 2.95925 1.94093 -0.49786 0.70534 -1.53029

E2t-I 0.695078 0.245642 0.001424 0.350194 -0.020991 -2.485503 0.107633 0.000775 0.006819 2.67251 0.90844 0.66978 2.18003 -3.26631 -1.94234 0.74680 1.72605 2.00251

E3t-i -10.66229 -22.51898 -0.066620 -9.447512 1.148024 119.8646 -37.94424 -0.079250 -0.220009 -0.67366 -1.36850 -0.51506 -0.96643 2.93548 1.53923 -4.32619 -2.90148 -1.06166

APt- 0.032872 0.586764 0.002529 0.420014 -0.020071 -0.806230 0.064945 -0.000506 0.005274 0.11490 1.97269 1.08158 2.37695 -2.83920 -0.57276 0.40965 -1.02481 1.40788

APt-2 -0.065007 0.342612 0.001909 0.236328 -0.010941 -0.028885 -0.045243 0.000184 0.008010 0.19124 0.19883 0.00156 0.11812 0.00473 0.94093 0.10598 0.00033 0.00250

-0.33992 1.72317 1.22119 2.00079 -2.31531 -0.03070 -0.42692 0.55748 3.19901 APL,_t -0.201129 -0.649629 -0.002285 -0.214257 0.018545 2.194747 0.109514 0.000766 -0.004627

-0.67150 -2.08615 -0.93360 -1.15818 2.50570 1.48930 0.65980 1.48275 -1.17974 APLt-2 -0.220786 -0.170094 -0.000795 -0.155195 0.011249 0.562815 0.253001 9.32E-05 -0.002721

-1.01488 -0.75204 -0.44694 -1.15502 2.09263 0.52582 2.09864 0.24838 -0.95517

ARENT,_- -20.80399 28.39866 -0.422682 13.00015 -0.723868 -221.3573 23.07660 -0.003634 0.571080 -0.75492 0.99120 -1.87686 0.76378 - 1.06305 - 1.63258 1.51112 -0.07642 1.58274

ARENT,-2 7.839314 33.50894 -0.095420 -13.60263 0.502746 -216.2028 3.076772 0.090710 0.304308 0.25970 1.06772 -0.38680 -0.72959 0.67403 -1.45571 0.18393 1.74131 0.76994

AVAC,-I 0.010076 -0.870530 -0.000259 -0.632725 0.003863 -2.468607 -1.102004 -0.003035 -0.001032 0.01542 -1.28107 -0.04847 -1.56735 0.23920 -0.76764 -3.04256 -2.69057 -0.12058

AVACt-2 0.566146 -0.562773 -0.002257 -0.444710 0.003195 0.566509 -0.633188 -0.000452 0.002374 1.20102 -1.14832 -0.58586 -1.52745 0.27434 0.24426 -2.42398 -0.55586 0.38461

4•

bO

ALt-I 4.552065 -9.974275 -0.001641 -4.950498 0.388674 29.58235 -3.186038 0.038274 -0.096814 0.65598 -1.38252 -0.02894 -1.15505 2.26679 0.86645 -0.82853 3.19611 -1.06556

ALt-2 -4.112403 5.356947 -0.022225 -2.304432 0.394193 19.41016 8.484387 0.009385 -0.076179 -0.47006 0.58895 -0.31085 -0.42647 1.82350 0.45093 1.75004 0.62160 -0.66504

ACCt-I -0.082599 -0.052285 -0.000108 -0.033072 0.001037 -0.244381 -0.076823 -5.57E-05 -0.000660 - 1.98627 - 1.20933 -0.31792 - 1.28761 1.00891 - 1.19441 -3.33367 -0.77634 - 1.21291

ACCt-2 -0.046104 0.001213 0.000100 0.014953 0.001236 0.000770 -0.001472 -2.23E-05 -0.000399 - 1.41432 0.03579 0.37592 0.74271 1.53424 0.00480 -0.08149 -0.39681 -0.93574

AWAGE,,_ -0.125826 -0.144872 0.001010 0.329350 0.006870 -0.754107 -0.065334 -0.001064 -0.005933 -0.41877 -0.46376 0.41149 1.77472 0.92534 -0.51011 -0.39239 -2.05106 -1.50815

AWAGEt_2 0.595639 0.071298 0.000245 0.315750 -0.008676 3.634902 -0.453515 -0.000828 0.002901 1.91195 0.22013 0.09632 1.64098 -1.12711 2.37144 -2.62699 -1.53976 0.71127

AStI 40.61880 83.44735 0.343242 11.96605 -4.129826 -606.5441 -139.8617 -0.276368 1.881691 0.34378 0.67932 0.35548 0.16397 -1.41458 -1.04338 -2.13612 -1.35542 1.21635

ASt-2 63.44145 -34.88543 0.078770 -50.92022 2.163808 135.6321 -67.79479 -0.183814 0.052339 0.68157 -0.36049 0.10355 -0.88572 0.94080 0.29616 -1.31434 -1.14433 0.04295

AACRE,_ -11.13140 -10.91358 -0.063461 1.173069 -1.417665 26.69048 -1.003599 0.018576 0.238465 -0.76218 -0.71876 -0.53171 0.13005 -3.92845 0.37144 -0.12401 0.73705 1.24706

AACREt-2 1.764960 5.929671 0.022064 -10.93763 0.096793 -36.44727 5.099187 0.039555 -0.077102 0.13445 0.43448 0.20568 - 1.34903 0.29841 -0.56431 0.70098 1.74607 -0.44859

C 21.58849 21.65646 0.049653 3.499120 0.086756 -30.44408 -2.030859 0.004014 -0.023721 6.44568 6.70133 0.05268 3.98108 0.159273 1.7134 3.57187 0.01112 0.08439 3.34930 3.23167 0.94263 0.87894 0.54472 -0.95997 -0.56857 0.36086 -0.28108

MORT 0.120399 -0.896534 0.000193 0.808488 -0.037559 - 1.951075 1.891115 0.003439 0.012102 0.11608 -0.83137 0.02275 1.26200 -1.46547 -0.38231 3.29010 1.92115 0.89112

TBILL -3.636819 -1.743773 -0.008322 -1.716301 0.061997 6.868784 -2.368907 -0.004143 -0.014981 -3.00720 - 1.38688 -0.84199 -2.29775 2.07470 1.15437 -3.53478 - 1.98503 -0.94608

R2 0.735799 0.571843 0.384565 0.618404 0.720895 0.740413 0.705637 0.809137 0.471637 Adj. R2 0.526260 0.232271 -0.103539 0.315758 0.499537 0.534534 0.472177 0.657763 0.052591

A

.

ca O


ditional open space is associated with rising employment, suggesting that firms locate in the County to take advantage of the non- wage benefits from environmental quality. Another interesting feature of this equation is that additional open space is associated with falling real wages, providing additional support for the hypothesis that workers will accept a lower wage to live in a high-amenity region.

Table 4 gives the estimated parameters and their associated standard errors for the nine equations in the ECM.8 R2 values range from approximately 0.05 to 0.65, suggesting that some markets are more adequately mod- eled than others. The rent equation has virtu- ally no explanatory power, with a negative adjusted R2.9 We are particularly interested in the employment, price and investment equations. The employment equation is satisfactory with around 72% of the employment adjustments explained by the model. The investment equation also fits well with an adjusted R2 value of 0.66. The fit of the price adjustment equation is satisfactory, with 73% of the variation in price adjustments explained by the model.

For the employment adjustment equation, the coefficients of all three cointegrating vectors are significant; the first cointegrating vector causes employment to fall as open space is purchased. This effect is offset by the second and third cointegrating equations which impart employment increases in response to open space purchases." For the Boulder price index and new investment, the first and second cointegrating vectors are significant and operate with opposing impacts on the price index. Thus, with a mix of positive and negative effects from an increase in open space, the full impact is not immedi- ately obvious and impulse response functions are needed.

To calculate the impulse response coefficients, the order of the variables within the recursive system must be specified. The variables were ordered such that when Granger causality of A on B could be inferred with 95% confidence, variable A is placed anterior to B in the recursive set. The results of two sets of Granger causality tests on the levels of the variables are reported in Table 5. The

set of Granger causality tests imply that a possible recursive form for this set takes the sequence Acre, Vac, cc, L, P1, P, Rent, S, Wage.

Impulse Response Functions

The orthogonalized cumulative response functions of a 1,000-acre shock to the level of open space on employment, wages, the housing price level, and the stock of housing are given in Figures 1-4. The response functions are launched from the most current value of the endogenous variable: 1995.4.

The impulse response function for employment (Figure 1) clearly indicates increased employment resulting from higher levels of open space. In the first period after the open space purchase, employment falls slightly. In the following periods, however, employment begins to rise, with large gains seen the first two years after the purchase. The cumulative response function indicates that a 1,000-acre increase in open space leads to approximately 90 new jobs after two years and 100 new jobs after 6 years. These figures indicate that the employment effects of open space purchase may be significant when one considers dynamic labor and housing market effects.

As employment rises, wages fall in response to the 1,000-acre open space purchase. Figure 2 graphs the impulse response of a 1,000-acre increase in open space on real wages. Wages adjust quite quickly, with most of the adjustment made after 18

8 Because interest rates are nationally determined, we assume they are exogenous. In keeping with a small closed economy, all of the regional model variables are assumed to be endogenous.

9 The primary purpose of the model is to compute impulse response functions. As such, the individual equations are interesting, but not the focus of the investigation. Nevertheless, the fact that the rent equation fits poorly indicates that the dynamics of the rental market are not fully captured in the model. We note that the rental market is not the focus of the investigation. Thus, we decided to accept the shortcomings of the rental equation and retain it in the model in an effort to avoid bias in the impulse response functions.

" The impact of a change in an endogenous variable i on the adjustment equation j is found by multiplying the long-run parameter for i by the speed of adjustment for each vector containing j.


TABLE 5

PAIRWISE GRANGER CAUSALITY TESTS: VARIABLES IN LEVELS, LAG LENGTH = 2

Null Hypothesis Observations F-Statistic Probability

PL Does not Granger Cause P 55 1.27290 0.28893 P Does not Granger Cause PL 4.96032 0.01084 RENT Does not Granger Cause P 55 1.47508 0.23854 P Does not Granger Cause RENT 2.94172 0.06197 VAC Does not Granger Cause P 55 3.34845 0.04318 P Does not Granger Cause VAC 0.43819 0.64766 WAGE Does not Granger Cause P 55 0.22725 0.79754 P Does not Granger Cause WAGE 4.33053 0.01843 L Does not Granger Cause P 55 3.19386 0.04950 P Does not Granger Cause L 0.05962 0.94219 S Does not Granger Cause PL 55 3.52684 0.03691 PL Does not Granger Cause S 0.05016 0.95112 WAGE Does not Granger Cause PL 55 1.02686 0.36556 PL Does not Granger Cause WAGE 6.62916 0.00279 L Does not Granger Cause PL 55 2.83480 0.06820 PL Does not Granger Cause L 0.18592 0.83091 ACRE Does not Granger Cause PL 55 2.26043 0.11486 PL Does not Granger Cause ACRE 0.32856 0.72151 WAGE Does not Granger Cause RENT 55 0.04305 0.95790 RENT Does not Granger Cause WAGE 2.96961 0.06044 CC Does not Granger Cause VAC 54 3.15615 0.05137 VAC Does not Granger Cause CC 5.51909 0.00689 WAGE Does not Granger Cause S 55 2.92670 0.06281 S Does not Granger Cause WAGE 5.17569 0.00906 CC Does not Granger Cause S 54 1.08402 0.34620 S Does not Granger Cause CC 5.53607 0.00680 ACRE Does not Granger Cause S 55 0.78356 0.46231 S Does not Granger Cause ACRE 2.13094 0.12938 CC Does not Granger Cause WAGE 54 3.66297 0.03292 WAGE Does not Granger Cause CC 0.34070 0.71295 L Does not Granger Cause WAGE 55 7.05408 0.00200 WAGE Does not Granger Cause L 0.02903 0.97140 ACRE Does not Granger Cause WAGE 55 4.93650 0.01105 WAGE Does not Granger Cause ACRE 0.95960 0.38999 L Does not Granger Cause CC 54 2.12155 0.13072 CC Does not Granger Cause L 2.76829 0.07260 ACRE Does not Granger Cause CC 54 2.09223 0.13430 CC Does not Granger Cause ACRE 3.25643 0.04701 ACRE Does not Granger Cause L 55 3.57155 0.03549 L Does not Granger Cause ACRE 2.68117 0.07832

months. The observation that wages fall in response to open space purchases provides strong support for the observation that employees may be willing to accept a lower wage, ceteris paribus, to live in a high-amenity area.

Figure 3, the impulse response function for the price impact of an open space purchase over time, clearly indicates a lag between open space purchase and the time in which it is capitalized into the price. This

supports the hypothesis that hedonic estimates of the implicit price will be time-variant. We will return to this later. Meanwhile, we observe that the price level response is stagnant until the end of the first year, at which time it begins to increase steadily. Open space will lead to a wage differential as compared to similar communities without the level of amenities, other things equal, resulting in labor supply shifts. And as real wages stagnate, firms demand more labor,


change in employment 200

150 ..

100

50qr

0 1 3 5 7 9 11 13 15 17 19 21 23

-50

-100 quarter

FIGURE 1 RESPONSE OF EMPLOYMENT TO A 1,000-ACRE INCREASE IN OPEN SPACE

(DOTTED LINES DEPICT 5% CONFIDENCE INTERVAL AROUND THE ESTIMATE)

change in average wages 0.00

3 5 7 9 11 13 15 17 19 21 23

-0.05

-0.10

-0.15

-0.20

-0.25

-0.30.

-0.35 quarter

FIGURE 2 RESPONSE OF AVERAGE WAGE TO A 1,000-ACRE INCREASE IN OPEN SPACE



change in housing price level 0.50

0.20

0.10

1 3; 5 7 9 11 13 15 17 19 21 23 -0.10-

-0.20 quarter

FIGURE 3 RESPONSE OF HOUSING PRICE TO A 1,000-ACRE INCREASE IN OPEN SPACE


moving along their demand curve for labor. Consequently, in an open economy, some of the new employment opportunities will be filled by in-migration, meaning more households demanding houses in the region. Therefore, the price level will rise as demand shifts out.

Examination of Figure 4, the impulse response function for the housing stock, shows housing stocks rising in response to the 1,000-acre open space purchase for the first 12 quarters. This may be due to the desire of developers to build homes near open space to capture spatial price appreciation from open space proximity. After 6 years, a 1,000-acre increase in open space will translate into approximately 10 new residential units.

We measure the impact of the program on housing prices and employment over the range of the data employed, namely 1981 through 1995. According to the model, the 15,000 acres of open space purchased between 1981 and 1995 caused prices to rise by 3.75%. For the median-priced home of $270,000 this means a payment of $10,125. The model results indicate that slightly more than 1,650 jobs were created in Boulder County in response to the program, through

either direct employment by the Open Space Department or due to firm location and expansion from the program. That represents around 3.3% of the 50,000 jobs created during that time.

Examination of the impulse response functions resulting from open space changes reveals an important consequence of the program. Nonstationarity in the system variables requires all shocks to the system to have permanent effects. Hence, the observed impulse response functions, unlike those derived from stationary systems, will not necessarily go to zero. Thus, each open space acquisition moves the housing and labor markets to a new equilibrium. In the impulse response functions in Figures 1-4, the new equilibrium is attained when the impulse response functions stabilize. After five years (the time it takes to reach the new equilibrium) the leg- acy of a 1,000-acre increase in open space is a higher housing price level, a slightly higher stock of housing, and more employment. In the case of the housing market, supply and demand have shifted to a higher price with a slightly larger stock of housing. With respect to the labor market, employment increases and real wages fall.


change in housing stock 16

14 . .. ..... .

12 ... .

10

8

1 3 5 7 9 11 13 15 17 19 21 23 quarter

FIGURE 4 RESPONSE OF STOCK TO A 1,000-ACRE INCREASE IN OPEN SPACE


Though an explicit goal of the program was to limit residential growth, this did not happen. The program may be purchasing acres that do not have attached development plans. Alternatively, open space may make development of neighboring lands more at- tractive. In the short run, open space may ac- tually increase residential growth, as we observe on a modest scale in the case of Boulder. In the long run, however, we would expect the open space program to limit residential growth as developers compete for fewer and fewer acres. The data indicate that this point had not been reached in Boulder during the period of study.

Another unintended impact of the program is the expansionary effect observed on commercial growth. Considering the information concerning open space and employment contained in Figure 1, we see that open space is correlated with a larger workforce within the county. This is consistent with the hypothesis of firms locating or expanding in the area in order to provide non-wage benefits in an attempt to attract workers.

The evidence supports the conclusion that though the open space program may restrict commercial growth in the city of Boulder, it

attracts firms to locate in the county, thereby expanding the commercial base. This effect has been seen in the expansion of communities surrounding Boulder. In order to house individuals working in these new positions, Louisville, a community near Boulder, has seen rapid expansion in the last two decades. The number of residential units has increased four-fold during that time.

VI. POLICY IMPLICATIONS AND LIMITATIONS OF THE

HEDONIC MODEL

Hedonic models are limited to capturing price changes that have been capitalized into the value of the land by the time the hedonic study is performed. The results concerning the effects of open space purchase on prices and commercial and residential growth may be contrasted with those that could be obtained if a hedonic approach were used. The cumulative response functions indicate significant changes in employment, price and housing stock resulting from changes in the level of open space. If a hedonic approach were used to calculate the effects of an open space increase of 1,000 acres on prices two


years after the purchase it would estimate prices rising by 0.17% as a result of the purchase. If, however, the study waited another four years, a 0.25% increase in the price level would be recorded for the same 1,000 acres of open space.

Thus, in the face of endogenous stochastic growth in the level of open space, hedonic estimates will be a function of the time period in which the study is made. Failure to take account of systemic market changes may be one possible explanation for the mixed findings of Correll, Lillydahl, and Singell (1978) concerning the price effects of open space purchase in Boulder. Price effects may not have had time to fully realize their impact on the system resulting in inconclu- sive results concerning open space impacts.

A similar story may be told for the effects of open space purchase on residential and commercial growth. Cross-sectional models used by Lopez, Shah, and Altobello (1994) and Greenwood and Hunt (1989) should be used with caution. To make inference about long-run variables such as the stock of housing, one must use long-run covariates to account for the true underlying relationships.

The finding of slow market adjustment leads to time-variant implicit prices for some environmental goods exposes a weakness in hedonic property modeling. While random disturbances in implicit prices will not intro- duce bias in estimates of willingness to pay, a trend in the observed implicit price may lead to biased estimates of environmental values (Freeman 1993). If households are not consuming their utility maximizing bundle of housing services, then willingness to pay for environmental amenities may not coincide with the observed implicit price. One must wait until market equilibrium returns before hedonic prices are valid estimates of willingness to pay.

VII. CONCLUSION

The VECM approach to estimating the impacts of changing environmental quality gives needed insight into the dynamic effects of environmental programs on local housing and labor markets. The work presented here shows that an active open space purchase

program was responsible for higher house prices, a modest amount of commercial and residential expansion, and a drop in the average wage.

One important outcome of the Boulder open space purchase program has been leap- frog development of areas outside the greenbelt. Many critics of the program maintain that development was not thwarted, but rather re-located. Our results support this conclusion. In fact, commercial and residential expansion occurred because of the program. However, the positive implicit price of open space clearly expresses the value of the program to residents, even though growth management goals were not realized.

The VECM model of the Boulder open space program also underscores the limitations of applying cross-sectional methods such as the hedonic property method when environmental quality trends are the focus of the investigation. Significant lags in incorporation of resource value combined with the potential endogeneity of the environmental good provision may lead to erroneous inference regarding the market effects of a trending non-market good.

Many environmental goods exhibit pro- gressive upward and downward trends. It may be insightful to re-estimate the regional economic effects of goods such as air quality and water quality given the evidence in favor of slow market adjustment reported in this paper. Similar conclusions concerning these goods may offer further support for the hypothesis that trending environmental quality should be estimated in a time series frame- work (when possible) to capture the full economic effects.

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