Hedonic Valuation with Translating Amenities: Mountain Pine Beetles and Host Trees in the Colorado Front Range

In hedonic valuation studies the policy-relevant environmental quality attribute of interest is often costly to measure, especially under pronounced spatial and temporal variability. However, in many cases this attribute affects home prices and consumer preferences solely through its impact on a readily observable, spatially delineated, and time-invariant feature of the physical landscape. We label such a feature a “translating amenity.” We show that under certain conditions changes in the marginal effect of such amenities on home values over time can be used to draw inference on the implicit price of the unobserved environmental quality of interest. We illustrate this approach in the context of a repeat-sales model and the recently intensified outbreak of the Mountain Pine Beetle in the Colorado Front Range.

1. To be clear, Phaneuf et al. (2008) specify utility as \(U=U\left( x\left( q\right) , h\left( \mathbf {a},q\right) , z, \epsilon \right) \), where \(h\left( . \right) \) is the housing function, \(\mathbf {a}\) is a vector of housing attributes, and \(\epsilon \) denotes unobserved heterogeneity. The term \(x\left( q \right) \) refers to local recreational opportunities, which are not relevant in our case. Our notation also differs in that we label the housing function as \(H\left( . \right) \), and the housing attributes as \(\mathbf {x}\). We also include preference parameters (\(\varvec{\gamma }\) and \(\varvec{\theta }\)), which are not explicitly captured in their specification. In contrast, unobserved heterogeneity does not play a major role in our context, so their error term \(\epsilon \) is absent from our model. However, both models include environmental quality \(q\) and the numeraire commodity \(z\).

2. If the relevant policy intervention directly targets trees instead of beetles, for example via the removal of diseased pines, \(\alpha \left( q \right) \) simplifies to \(\alpha \). In that case \(q\) would be the number or biomass of dead trees, and host trees at large would still be the TA.

3. This is why \(h\) is not a proxy variable in a formal econometric sense, as it can still influence home values independently of the unobserved quality variable \(q\). As discussed e.g. in Wooldridge (2012), p. 67, a genuine proxy variable must be redundant in the underlying structural relationship if the unobserved variable for which it fills in were actually included in the model. We specifically abstract from such a case by allowing trees to affect home values even in absence of MPB damage.

4. We assume for now that all other components in the price function difference out.

5. For the less common linear price function with additive attributes we have \(\frac{\partial P\left( . \right) }{\partial f\left( . \right) }=1\), and would thus obtain \(P_{t}-P_{t-1}=\left( \theta _1-\theta _2\right) \left[ \alpha \left( q_{t}\right) -\alpha \left( q_{t-1}\right) \right] h\approx \beta \left( q \right) h\). That is, the coefficient on \(h\) would directly approximate the implicit price of \(q\).

6. Naturally, the assumption of time-invariance of both characteristics and preferences is crucial for this advantage to be properly exploited. Since the time periods for our analysis are relatively short (9–12 years) we do not expect pronounced shifts in underlying preferences in our data. In addition, we control for changes in home structures by eliminating properties with documented home improvements from our sample, as discussed in the empirical section.

7. For further details and motivation for this tri-valued indicator approach see, for example, Palmquist (1982) and Case et al. (2006).

8. Conceptually, both \(\xi \) and \(\varvec{\zeta }\) can be interpreted as elements of the reduced form parameter vector \(\varvec{\delta }\) in our theoretical model [Eq. (1)].

9. In 2006, 2007, and 2012, the three worst wildfire seasons in history, wildfires consumed over 9 million acres in the US (National Interagency Fire Center 2012).

10. A full-fledged damage analysis via satellite imagery and visual damage coding by a remote sensing expert for all included properties in our data would have been infeasible given resource constraints and our relatively large sample size. In addition, high-quality satellite images covering our entire research area are only available for a select few years of our research period, which would hamper a seamless analysis of the MPB damage trajectory over time. The ADS, in turn, uses fly-overs and hand-drawn polygons to identify infested areas. Each polygon, in turn, receives an estimate for the total number of infested trees within its boundary. Price et al. (2010) use these polygons for their study of MPB damage and property values in neighboring Grant County to compute the expected number of diseased trees within different perimeters of each residence. Using a cross-sectional regression model with spatial lags they estimate the marginal implicit price per tree for each perimeter. They also report that the accuracy of this polygon-based damage information ranges between 61 and 79 %, based on a 2005 FS assessment. However, MPB damage was more confined and localized in the mid-90s to mid-2010s (the time span of their analysis), generally allowing for tighter, stand-specific polygons. This accuracy has suffered in recent years, as polygons had to be drawn at ever larger scales to keep pace with the dramatic acceleration and expansion of the infestation. For our time frame, which reaches to 2011, a polygon-based estimation approach did not produce reliable results. Too many homes are included within the same large-scale polygon, and thus receive identical damage metrics in the last four to five years of our research period. In addition, a comparison with satellite images for sub-areas and years for which they are available revealed a high degree of imprecision between polygon boundaries and actual damage. The results of the polygon-based version of our model are available upon request.

11. A comparison of the repeat-sales sample with the general sample (including single-transaction residences) based on basic home features did not reveal any systematic differences between the two groups. We thus conclude that repeat-sales properties do not constitute a systematically different segment of the housing market.

12. Specifically, we used release 2 of the ESRI StreetMap Premium/NAVTEQ USA software package to geo-code each property. A majority of geocodes provided by this package (greater than 88 % for both counties) are based on exact property centroids, as opposed to uniformly assigned street segments.

13. Specifically, our GIS layer includes the following groups of pine species: White/Red/Jack, Lodgepole, Longleaf/Slash, Loblolly/Shortleaf, Pinyon/Juniper, Ponderosa, and Western White. Of these, the relevant species for Colorado are Lodgepole, Ponderosa, and Limber (a member of the Western White group). All of them are equally susceptible to an MPB attack (personal communication with Dr. Barbara Bentz, research entomologist at the US Forest Service. Logan, Utah). Since our host tree indicator \(h_i\) is also indiscriminant over these species, the accuracy rating for correctly identifying any host tree community likely exceeds that for specific pine types.

14. We matched home sales with fire damage based on the assumption that the fire season begins on May 1 of each year. Thus, a home that sold before May in a given calendar year is paired with fire events for the preceding calendar year for the 1-year binary indicator. The remaining indicators for temporally further removed fire occurrences are adjusted in analogous fashion.

15. The diminished effect of fires within 1 km from a home compared to the 5 km buffer is likely related to the small sample size (less then 1 % of observations) for this distance category. The absence of a stronger effect may also be linked to burn visibility. Stetler et al. (2010) find that fires at any distance from a residence (even 0–5 km) have limited effect on sales prices if the burned area is not visible for a given property. In our case, it is possible that nearby burns are less visible than burns in the 1–5 km range, depending on the morphology of the local landscape. In addition, home owners may perceive a lower future fire risk to their property if close-by fuel has been consumed by a recent fire, which could counter-act the direct amenity effect of nearby burns. This risk-reducing effect may be absent or even reversed for burns in the 1–5 km range. Third, there may be a counter-balancing positive amenity effect related to better views that open up in the short run for close-to-home burns (see Hansen and Naughton 2013). Similarly, the insignificant effect of burns within 5 km, but closer in time (within 1 or 3 years of sale) are likely due to small sample size (less than 0.5 % of observations).

16. Area 5 (southern Fort Collins, Loveland) produces a counterintuitive positive effect for age-related depreciation. We attribute this to the many new constructions that occurred in that area during our time span. This can produce a large value for \({a_i,}_{\left( t^{\prime },t^0\right) }\), even for pairs of sales that are closely positioned in time, with little to no age-related depreciation. A large enough share of such properties in the data can then produce a positive estimate for the depreciation coefficient \(\delta _s\).

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17. Specifically, a home that experienced a recent fire within 5 km between sales appreciated, on average, by \(\left( exp(-0.042)-1 \right) = 4.1\,\%\) less than an otherwise comparable property without a recent fire history.

18. Estimates from such “erroneously pooled” models are available upon request.

19. As is the case with most hedonic studies, our model cannot distinguish between actually experienced and expected MPB effects on home prices. Our estimated price trajectories and loss estimates include both components. However, since our time series of home sales starts well before the explosive expansion of the MPB, we are confident that our estimates captures the full MPB effect, that is actual plus expected.

20. The full set of results for Spokane are available upon request.

21. This rate is composed of a county-wide conversion factor of 0.0796 that translates assessed market value into “tax-assessed value”(Larimer County Treasurer 2013a) We found the assessed market value to be generally very close to observed sales prices for homes sold in 2011 in our data. Thus, implicitly departing from our predicted sales prices for 2011 before assessing these tax rates appears justified. A district-specific “mill levy” is then applied to this taxable amount. In 2011, mill levies for Estes Park varied between 7 and 8 % for most tax districts (Larimer County Assessor 2013b). We use a mill levy of 7.5 % for our calculations.

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Authors and Affiliations

1. Department of Agricultural and Applied Economics, Virginia Tech, 208 Hutcheson Hall, Blacksburg, VA, 24061, USA

   Jed Cohen, Kevin J. Boyle & Klaus Moeltner

2. Department of Forest Resources and Environmental Conservation, Virginia Tech, Blacksburg, USA

   Christine E. Blinn

3. USDA Forest Service, Southern Research Station, Research Triangle Park, NC, USA

   Thomas P. Holmes

Corresponding author

Correspondence to Klaus Moeltner.

We thank seminar participants at the 2013 Meetings of the W3133 Western Regional Science Project (Coeur d’ Alene, ID, Feb. 27–March 2), and the US Airforce Academy, Colorado Springs (March 15, 2013), for insightful and stimulating comments. Funding provided by the Southern Research Station, USDA Forest Service, is gratefully acknowledged.

Appendix 1

See Tables 10, 11, 12, 13 and 14.

Appendix 2: Details for Loss Predictions

In step one we seek the counterfactual price of a home near host trees in absence of any MPB effects, for each year of our series. From Eq. (16) we have

For a given home in the HT zone with observed price \(P_{it}\) we then obtain

Next, we compute the pure price differential between the final time period \(T\) and year \(t\) in absence of any MPB disturbance. Following the derivation in (14) we obtain

Ignoring the time-invariant spatial index, as well as fire and depreciation effects leaves \(\kappa _{s,t,T} =exp\left( \alpha _{sT} - \alpha _{st} + \sigma ^2\right) - 1\). The counterfactual price of affected home \(i\) in absence of any MPB impacts and projected to the final year \(T\) can then be computed as

We implement these predictive steps via simulation along the lines proposed by Krinsky and Robb (1986) as follows: We take 100,000 draws of each contributing coefficient in the last line of (22) from their respective finite sample distribution, taking account of all involved covariances. For each draw we then compute \(\rho _{s,t,T}\) as given in the last line of (22) and capture the mean, 2.5th, and 97.5th percentile of the resulting empirical distribution. We repeat this procedure for every \(t \ne T\). We then multiply observed price \(P_{it}\) by the appropriate year-specific mean conversion factor [term \(\rho _{s,t,T}\) in the last line of (22)] as well as by the confidence bounds for all HT homes in our data. This produces an estimate and confidence bounds for the predicted “MPB purged” sales price \(\tilde{P}_{iT}\) in 2011.

In a final step, we then apply the point estimate of MPB loss in 2011 (see Tables 7, 8) to each predicted mean price, the lower bound of the MPB loss estimate to each upper bound for predicted price, and the upper bound of MPB loss estimate to each lower bound for predicted price to derive a point estimate and confidence bounds for predicted MPB losses, in 2011 dollars, for each property.

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