# RECORD 7e996f814b72e80b4de3f1e836fe30324b1e2912
# TITLE: Hedonic Valuation with Translating Amenities: Mountain Pine Beetles and Host Trees in the Colorado Front Range
# YEAR: 2014.0  VENUE: Environmental and Resource Economics  DOI: 10.1007/s10640-014-9856-y
# AUTHORS: J. Cohen; C. Blinn; K. Boyle; T. Holmes; K. Moeltner
# PAGES: 30  CANDIDATE TABLE PAGES (1-based): [17, 20, 21, 26, 27]
# ABSTRACT: 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.


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Environ Resource Econ (2016) 63:613–642
DOI 10.1007/s10640-014-9856-y
Hedonic Valuation with Translating Amenities: Mountain
Pine Beetles and Host Trees in the Colorado Front Range
Jed Cohen · Christine E. Blinn · Kevin J. Boyle ·
Thomas P. Holmes · Klaus Moeltner
Accepted: 15 December 2014 / Published online: 31 December 2014
© Springer Science+Business Media Dordrecht 2014
Abstract In hedonic valuation studies the policy-relevant environmental quality attribute of
interest is often costly to measure, especially under pronounced spatial and temporal vari-
ability. 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.
Keywords
Forest pests · Property values · Repeat-sales model · Wildland–urban interface
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.
J. Cohen · K. J. Boyle · K. Moeltner (B)
Department of Agricultural and Applied Economics, Virginia Tech, 208 Hutcheson Hall,
Blacksburg, VA 24061, USA
e-mail: moeltner@vt.edu
J. Cohen
e-mail: jedcohen@vt.edu
K. J. Boyle
e-mail: kjboyle@vt.edu
C. E. Blinn
Department of Forest Resources and Environmental Conservation, Virginia Tech, Blacksburg, USA
e-mail: cblinn@vt.edu
T. P. Holmes
USDA Forest Service, Southern Research Station, Research Triangle Park, NC, USA
e-mail: tholmes@fs.fed.us
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Mountain Pine Beetles and Host Trees in the Colorado Front Range
629
Table 6 Estimation results for
HT and fire effects
Est. estimate, (SE) standard error
*, (**), (***) significant at 10%,
(5%), (1%) level
Larimer
Boulder
Est.
(SE)
Est.
(SE)
1998 (Larimer baseline)
0.062
0.019***
−
–
1999
−0.067
0.040*
−
–
2000
−0.074
0.037**
−
–
2001
−0.024
0.044
−
–
2002 (Boulder baseline)
−0.079
0.042*
−0.127
0.029***
2003
−0.086
0.040**
0.082
0.058
2004
−0.108
0.045**
0.036
0.056
2005
−0.144
0.045***
0.015
0.057
2006
−0.133
0.048***
0.027
0.063
2007
−0.173
0.052***
0.086
0.067
2008
−0.140
0.059**
−0.011
0.075
2009
−0.213
0.063***
0.047
0.079
2010
−0.253
0.061***
0.049
0.078
2011
−0.313
0.066***
−0.006
0.086
Fire 5year, 5km
0.017
0.013
−0.042
0.011***
we only retain this single indicator in our final specification. This implies that the vector
difference wit′ −wit0 in (12) reduces to a single indicator, taking the value of −1 if a fire
occurred within 5km and 5 years preceding time t0, but not time t′, a value of 0 if such a
fire occurred preceding neither or both points in time, and a value of 1 if such an event took
place preceding time t′ only.
We estimate separate GLS models for Larimer and Boulder. Estimation results for HT
and fire effects are given in Table 6. Results for area-specific intercepts, time trends, and
age-depreciation effects are provided in Tables 12 and 13 in “Appendix 2”. These appendix
tables essentially confirm the basic sample statistics on price development discussed above:
In Larimer, prices increase vis-a-vis the baseline year of 1998 until 2005 or 2006 by up
to 30–35%, then decline for the remainder of our research period, almost back to baseline
levels for some areas. In Boulder, prices decline immediately compared to the 2002 base
year, reaching a low of 12–15% below baseline by 2011. Age-related depreciation amounts
to between 0.5 and 2% per percentage change in time elapsed between sales, i.e. t′ −t0
in our model notation, relative to time t0.16 These results are largely as expected given the
recent economic downturn and collapse of the housing market for wide parts of the western
US. While they are interesting in their own right, they serve here primarily the purpose of
providing a sound and consistent baseline against which MPB effects are to be measured.
Footnote 15 continued
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 depre-
ciation. We attribute this to the many new constructions that occurred in that area during our time span. This
can produce a large value for ai,
t′,t0, 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 δs.
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J. Cohen et al.
We thus turn our attention to the main results in Table 6, which depicts county-specific
coefficient estimates for the HT baseline effect ζ, the year-specific HT effects βt, and the
pre-sale wildfire effect ψ, as modeled in Eq. (12). As is evident from the table, in Larimer
properties within 0.1 km from host trees fetched a premium over other homes in the baseline
year of 1998. However, starting in 1999 this difference reverts and increases in magnitude
and significance up to the end of our time horizon. In other words, homes within near-
proximity of HTs sold at a progressively increasing discount compared to other residences.
By our translating commodity principle, we attribute this relative loss to MPB damage. In
stark contrast, as shown in the last three columns of Table 6, the MPB effect appears to
have been largely capitalized into home values in Boulder by the baseline year of 2002,
as indicated by the significant and negative coefficient estimate for ζ. Relative HT effects
remain insignificant for subsequent years. Fire effects, which are captured in the last row of
the table, are insignificant for Larimer, but have a significant negative effect on sales prices
in Boulder.17
4.4 Predicted Price Trajectories
There are three price trajectories of interest for our application. First, we establish the baseline
pricetrendbyestimatingtherelativedifferenceinsalespriceforanyyearcomparedtothebase
year, focusing exclusively on properties outside the 0.1 km HT perimeter. Econometrically,
this effect is given as
m1t = E
 Pit −Pi1
Pi1
|hi = 0

= E
 Pit
Pi1
|hi = 0

−1
= E

exp

ξs + αst + ψ (wit −wi1) + δsai,(t,1) + eis,(t,1)

−1
= exp

ξs + αst + ψ (wit −wi1) + δsai,(t,1) + σ 2
−1
(14)
where E is the expectation operator and the addition of 0.5 times the differenced-error
variance 2 ∗σ 2 follows from the relationship between the normal distribution of eis,(t,1)
and the log-normal distribution of exp

eis,(t,1)

(see e.g. Evans et al. 2000). This term is
negligibly small for both the Boulder and Larimer application. In implementing (14) we
follow Case et al. (2006) and set the area-specific, non-temporal component of house price
appreciation ξs to zero, as it is not related to any temporal price trajectory. We do the same
for the wildfire indicators wit −wi1 as we want our baseline price index to be untainted by
fire effects. Finally, to abstract from any specific age bracket for a given home, and given the
close-to-zero estimate of the age depreciation effect for all areas, we also exclude depreciation
effects ai,(t,1) from the computation of m1t. This leaves us with m1t = exp

αst + σ 2
−1.
Next, we compute the same year-versus-baseline effect for homes with nearby host trees,
i.e.
m2t = E
 Pit −Pi1
Pi1
|hi = 1

= E
 Pit
Pi1
|hi = 1

−1
= exp

ξs + αst + ζ + βt + ψ (wit −wi1) + δsai,(t,1) + σ 2
−1
(15)
Implementing the same adjustments as above with the addition of setting the time-invariant
host tree effect ζ to zero produces m2t = exp

αst + βt + σ 2
−1.
17 Specifically, a home that experienced a recent fire within 5km between sales appreciated, on average, by
(exp(−0.042) −1) = 4.1 % less than an otherwise comparable property without a recent fire history.
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J. Cohen et al.
Table 7 MPB effects Larimer
no HT/no HT(1998)
HT/HT(1998)
Est.
(SE)
Low
Up
Est.
(SE)
Low
Up
Area 1
1999
0.072
(0.045)
−0.012
0.164
0.003
(0.036)
−0.065
0.075
2000
0.171
(0.047)
0.084
0.266***
0.087
(0.039)
0.013
0.168**
2001
0.129
(0.053)
0.031
0.237**
0.102
(0.041)
0.024
0.187**
2002
0.306
(0.059)
0.195
0.427***
0.207
(0.047)
0.119
0.303***
2003
0.313
(0.059)
0.203
0.433***
0.205
(0.047)
0.117
0.300***
2004
0.343
(0.069)
0.215
0.484***
0.205
(0.048)
0.114
0.304***
2005
0.345
(0.066)
0.221
0.480***
0.164
(0.046)
0.077
0.259***
2006
0.257
(0.067)
0.132
0.396***
0.100
(0.048)
0.009
0.198**
2007
0.234
(0.071)
0.101
0.380***
0.038
(0.050)
−0.055
0.139
2008
0.294
(0.082)
0.143
0.464***
0.125
(0.055)
0.022
0.239**
2009
0.213
(0.084)
0.060
0.389***
−0.019
(0.055)
−0.121
0.093
2010
0.281
(0.090)
0.117
0.469***
−0.005
(0.057)
−0.110
0.111
2011
0.142
(0.086)
−0.014
0.322
−0.165
(0.052)
−0.261
–0.057***
Area 4
1999
0.076
(0.039)
0.003
0.155*
0.006
(0.027)
−0.046
0.061
2000
0.195
(0.039)
0.121
0.275***
0.110
(0.028)
0.056
0.167***
2001
0.213
(0.049)
0.121
0.313***
0.184
(0.035)
0.117
0.256***
2002
0.279
(0.051)
0.184
0.382***
0.182
(0.035)
0.115
0.252***
2003
0.329
(0.048)
0.239
0.426***
0.219
(0.036)
0.150
0.293***
2004
0.368
(0.058)
0.260
0.486***
0.228
(0.038)
0.156
0.305***
2005
0.419
(0.060)
0.306
0.543***
0.229
(0.040)
0.153
0.309***
2006
0.450
(0.067)
0.325
0.590***
0.269
(0.043)
0.187
0.356***
2007
0.422
(0.074)
0.285
0.574***
0.196
(0.044)
0.112
0.286***
2008
0.335
(0.078)
0.190
0.497***
0.161
(0.048)
0.071
0.258***
2009
0.293
(0.082)
0.142
0.464***
0.045
(0.047)
−0.044
0.142
2010
0.413
(0.084)
0.258
0.588***
0.097
(0.052)
0.000
0.202*
2011
0.290
(0.082)
0.140
0.460***
−0.057
(0.045)
−0.142
0.035
HT/no HT
Est.
(SE)
Low
Up
All
1999
−0.004
(0.043)
−0.085
0.083
2000
−0.012
(0.036)
−0.080
0.062
2001
0.039
(0.043)
−0.043
0.127
2002
−0.017
(0.039)
−0.089
0.063
2003
−0.024
(0.035)
−0.091
0.048
2004
−0.045
(0.037)
−0.114
0.030
2005
−0.078
(0.034)
−0.142
−0.010**
2006
−0.069
(0.036)
−0.137
0.003*
2007
−0.105
(0.037)
−0.175
−0.030***
2008
−0.075
(0.044)
−0.158
0.017*
2009
−0.140
(0.044)
−0.221
−0.049***
2010
−0.174
(0.041)
−0.250
−0.091***
2011
−0.222
(0.043)
−0.302
−0.135***
Est. estimate, (SE) standard error; *, (**), (***) significant at 10%, (5%), (1%) level
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Mountain Pine Beetles and Host Trees in the Colorado Front Range
633
Table 8 MPB effects Boulder
Area 6
no HT/no HT(2002)
HT/HT(2002)
Est.
(SE)
Low
Up
Est.
(SE)
Low
Up
2003
−0.034
(0.036)
−0.102
0.041
0.049
(0.048)
−0.042
0.148
2004
0.013
(0.038)
−0.057
0.090
0.050
(0.045)
−0.035
0.143
2005
0.057
(0.041)
−0.020
0.141
0.073
(0.048)
−0.016
0.171
2006
0.069
(0.045)
−0.017
0.161
0.098
(0.055)
−0.005
0.212*
2007
0.038
(0.047)
−0.051
0.135
0.131
(0.060)
0.019
0.255**
2008
0.001
(0.051)
−0.094
0.105
−0.009
(0.060)
−0.119
0.115
2009
−0.039
(0.056)
−0.143
0.077
0.007
(0.060)
−0.104
0.133
2010
−0.055
(0.053)
−0.153
0.053
−0.008
(0.062)
−0.122
0.122
2011
−0.113
(0.052)
−0.211
−0.005**
−0.119
(0.061)
−0.231
0.010*
HT/no HT
Est.
(SE)
Low
Up
2003
−0.044
(0.060)
−0.154
0.081
2004
−0.087
(0.051)
−0.182
0.019
2005
−0.106
(0.047)
−0.194
–0.009**
2006
−0.095
(0.051)
−0.189
0.010
2007
−0.040
(0.054)
−0.140
0.071
2008
−0.128
(0.055)
−0.230
−0.015**
2009
−0.077
(0.060)
−0.187
0.048
2010
−0.075
(0.058)
−0.181
0.045
2011
−0.125
(0.059)
−0.234
−0.001**
Est. estimate, (SE) standard error
*, (**), (***) significant at 10%, (5%), (1%) level
over time. By 2011, MPB-induced losses took substantial proportions. We will translate these
percentage differentials into dollar losses per home and for the region as a whole below.19
4.5 Robustness Check: Spokane
To guard against the possibility that our estimated trend of increasing relative losses for
HT homes simply reflects changing preferences of home buyers over the years, we repeat
our analysis for a “control area” with similar population size and abundant host trees, but
no documented MPB damage. Specifically, we estimate our model in (12) for the city of
Spokane, Washington. Assuming home owner’s preferences with respect to “trees” and
woody surroundings in Spokane are at least somewhat similar to those for our Front Range
communities, price trends in Spokane for no-HT homes and HT homes should move in
equal or at least parallel fashion in absence of increasing “tree aversion.” In other words, a
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.
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634
J. Cohen et al.
homogeneous price trajectory for no-HT and HT properties in Spokane would rule out a
general and widespread shift in preference away from trees and towards open land in the
mountainous west. This, in turn, would lend additional credibility to our interpretation of
no-HT/HT price differentials in Colorado as attributable to MPB damage.
The Spokane data comprises 23,841 observations for 18,428 homes with repeat sales
between 1997 and 2011. We estimate the Spokane RSM using the exact same variables as for
our main analysis. We allow for separate price trends for three different markets, but continue
to specify a common annual series of HT effects. Estimation results for the latter are given
in Appendix Table 14.20 As is evident from the table, starting with the base year of 1997, HT
effects are—at worst—close to zero and insignificant. In fact, homes with nearby host trees
actually fetch a highly significant price premium of 2–3% for several years in our series.
Clearly, there is no indication of a price discount for HT homes, let alone one that is
progressively increasing over time. The Spokane counter-study thus provides strong support
for our interpretation of value losses in the Colorado Front Range as MPB-induced.
4.6 Loss Predictions and Policy Implications
To translate the percentage losses discussed above into 2011 currency for HT homes in areas
one, four, and six, we proceed in three conceptual steps. First, we compute the year-specific
counterfactual price that each home would have received in absence of MPB damage, using
˜Pit =
Pit
1 + m3t
,
(17)
where Pit is the observed price, and m3t is defined in (16). Second, we translate this “HT
purged” value into the price the same home would have sold for in the final year T (2011 in
our case) via
ˆPi,T = ˜Pit

1 + κs,t,T

,
(18)
where κs,t,T = exp

αs,T −αst + σ 2
−1, and the α-terms are the area and year-specific
generic price effects as given in (12). For Boulder, where estimated wildfire effects are
significant, we also control for forest fires that may have occurred (or subsided) between any
year t and 2011 by adding (or subtracting) the wildfire coefficient ψ in the exponent of κs,t,T .
These first two steps yield the predicted sales price in 2011 for all HT-homes in our sample,
purged of any MPB-induced value losses. In step three, we then simply apply the MPB-
induced percentage losses for 2011, as reported in Tables 7 and 8, i.e. −22.2% for Larimer
and −12.5% for Boulder. We implement these three steps for every HT property in our repeat-
sales data, as well as for all remaining single-sale homes located in the HT zone that are not
included in our principal analysis. Importantly, throughout all three steps we carry forward
the standard errors for all coefficients involved to generate accurate uncertainty bounds for
our final predictions. The details for these derivations are given in “Appendix 2”.
Predicted losses per home and aggregate losses for various sub-sets of our data are given
in Table 9. The first row of the table shows the number of properties that are located within
0.1 km from host trees for each county and the entire region. Within each county, the first
column refers to all such homes, including single-sale properties. The second column refers
to all HT homes that were actually included in our RSM (i.e. those with multiple sales during
our research period). On a per-home basis, MPB induced losses amount to $70,000 for the
broader sample in Larimer, and $61,000 for Boulder. However, while the lower confidence
bound for Larimer is still a sizable $41,000, the lower bound for Boulder is near-zero.
20 The full set of results for Spokane are available upon request.
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638
J. Cohen et al.
Table 11 Price statistics by area,
Boulder (2011 dollars, units of
000s)
SD standard deviation; min (max)
minimum (maximum)
Year
Area 6
Area 7
Mean
SD
Min
Max
Mean
SD
Min
Max
2003
862
420
489
1,464
438
189
193
1,061
2004
621
241
274
1,284
415
259
119
2,797
2005
622
264
216
1,419
416
237
126
3,278
2006
730
361
224
2,019
404
232
106
2,296
2007
750
493
162
3,051
384
238
82
3,078
2008
764
354
146
2,007
356
208
73
2,293
2009
616
302
144
1,524
348
200
82
3,045
2010
591
273
157
1,329
364
219
69
2,189
2011
627
436
108
2,500
370
231
75
2,600
Table 12 Additional estimation results, Larimer
Est.
(SE)
Est.
(SE)
Est.
(SE)
Area 1
Area 2
Area 3
Intercept
−0.088
(0.025)***
−0.041
(0.005)***
−0.008
(0.003) ***
1999
0.070
(0.042)*
0.065
(0.013)***
0.047
(0.005)***
2000
0.158
(0.040)***
0.128
(0.013)***
0.113
(0.005)***
2001
0.122
(0.047)***
0.193
(0.012)***
0.180
(0.005)***
2002
0.267
(0.045)***
0.236
(0.012)***
0.213
(0.005)***
2003
0.273
(0.045)***
0.255
(0.013)***
0.213
(0.005)***
2004
0.295
(0.051)***
0.248
(0.013)***
0.217
(0.005)***
2005
0.296
(0.049)***
0.253
(0.013)***
0.212
(0.005)***
2006
0.229
(0.054)***
0.237
(0.014)***
0.198
(0.006)***
2007
0.210
(0.057)***
0.166
(0.014)***
0.156
(0.006)***
2008
0.258
(0.063)***
0.124
(0.016)***
0.089
(0.007)***
2009
0.193
(0.069)***
0.115
(0.016)***
0.103
(0.007)***
2010
0.248
(0.070)***
0.116
(0.017)***
0.093
(0.007)***
2011
0.133
(0.075)*
0.073
(0.018)***
0.077
(0.008)***
Age depr.
0.000
(0.007)
−0.023
(0.001)***
−0.005
(0.001)***
Area 4
Area 5
Intercept
−0.072
(0.024)***
0.008
(0.004)***
1999
0.073
(0.036)**
0.058
(0.007)***
2000
0.179
(0.033)***
0.120
(0.007)***
2001
0.193
(0.040)***
0.178
(0.008)***
2002
0.246
(0.039)***
0.207
(0.008)***
2003
0.285
(0.036)***
0.196
(0.008)***
2004
0.313
(0.042)***
0.192
(0.008)***
2005
0.350
(0.042)***
0.173
(0.008)***
2006
0.372
(0.047)***
0.151
(0.009)***
2007
0.352
(0.052)***
0.079
(0.010)***
2008
0.289
(0.059)***
−0.013
(0.011)
2009
0.257
(0.063)***
−0.009
(0.011)
2010
0.345
(0.059)***
−0.025
(0.011)**
2011
0.254
(0.063)***
−0.062
(0.012)***
Age depr.
−0.005
(0.005)
0.003
(0.001)***
Est. estimate, (SE) standard error, Age. depr age-related depreciation
*, (**), (***) significant at 10%, (5%), (1%) level
123


===== PAGE 27 (score 44, numeric-paren 28, table-words 4, var-words 1) =====

Mountain Pine Beetles and Host Trees in the Colorado Front Range
639
Table 13 Additional estimation
results, Boulder
Est. estimate, (SE) standard error,
Age. depr age-related
depreciation
*, (**), (***) significant at 10%,
(5%), (1%) level
Area 6
Area 7
Est.
(SE)
Est.
(SE)
Intercept
0.046
(0.026)*
−0.017
(0.005)***
2003
−0.034
(0.038)
−0.028
(0.007)***
2004
0.013
(0.037)
−0.020
(0.007)***
2005
0.056
(0.039)
−0.002
(0.007)
2006
0.067
(0.042)
−0.011
(0.008)
2007
0.037
(0.046)
−0.056
(0.009)***
2008
0.001
(0.051)
−0.111
(0.010)***
2009
−0.039
(0.058)
−0.105
(0.010)***
2010
−0.057
(0.056)
−0.116
(0.011)***
2011
−0.120
(0.059)**
−0.146
(0.012)***
Age depr.
−0.004
(0.005)
−0.005
(0.001)***
Table 14 Estimation results for
HT effects, Spokane
Est. estimate, (SE) standard error
*, (**), (***) significant at 10%,
(5%), (1%) level
Est.
(SE)
Baseline
−0.001
0.003
1998
−0.008
0.009
1999
0.005
0.009
2000
0.015
0.009*
2001
0.013
0.009
2002
0.019
0.009**
2003
0.019
0.009**
2004
0.028
0.009***
2005
0.035
0.009***
2006
0.031
0.010***
2007
0.015
0.011
2008
0.019
0.012
2009
0.007
0.012
2010
−0.004
0.013
2011
0.015
0.014
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
E
 Pit|hi = 1
Pit|hi = 0

= 1 + m3t = exp (ζ + βt)
(19)
For a given home in the HT zone with observed price Pit we then obtain
˜Pit = E [Pit|hi = 0] =
Pit
1 + m3t
=
Pit
exp (ζ + βt)
(20)
123


===== PAGE 28 (score 6, numeric-paren 0, table-words 0, var-words 6) =====

640
J. Cohen et al.
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
κs,t,T = E
 PiT −Pit
Pit
|hi = 0

= E
 PiT
Pit
|hi = 0

−1
= E

exp

ξs + αsT −αst + ψ (FiT −Fit) + δsai,(T,t) + eis,(T,t)

−1
= exp

ξs + αsT −αst + ψ (FiT −Fit) + δsai,(T,t) + σ 2
−1
(21)
Ignoring the time-invariant spatial index, as well as fire and depreciation effects leaves
κs,t,T = exp

αsT −αst + σ 2
−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
˜PiT = ˜Pit

1 + κs,t,T

= Pit
1 + κs,t,T
1 + m3t
= Pitexp

αsT −αst −ζ −βt + σ 2
= Pitρs,t,T
(22)
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 ρs,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 ̸= T . We then multiply observed price Pit by the appropriate
year-specific mean conversion factor [term ρs,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 ˜PiT 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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