THE COST OF WILDFIRES IN HEAVILY URBANIZED AREAS: MEASURING 

PROPERTY VALUE AND RECREATIONAL IMPACTS IN SOUTHERN 

CALIFORNIA 

 
By 
 

Sophia Tanner 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 

 

2018

A DISSERTATION 

Submitted to 

Michigan State University 

in partial fulfillment of the requirements 

for the degree of 

Agricultural, Food, and Resource Economics—Doctor of Philosophy 

Environmental Science and Policy—Dual Major 

 

 

 

ABSTRACT 

THE COST OF WILDFIRES IN HEAVILY URBANIZED AREAS: MEASURING 

PROPERTY VALUE AND RECREATIONAL IMPACTS IN SOUTHERN CALIFORNIA 

By 

Sophia Tanner 

Wildfire frequency and severity are increasingly important issues in the western United States, 

as fires threaten lives, properties and outdoor amenities. This dissertation seeks to measure the impact 

of wildfires in Southern California using nonmarket valuation techniques. In the first essay we employ 

the hedonic property method to estimate how wildfires affect nearby property values. Using data from 

15 years of property sales prices and 20 years of wildfire data, we find that the average impact of a 

wildfire  on  housing  sales  price  depends  on  the  market  context  and  whether  the  event  increases, 

decreases, or does not change prior risk perceptions. This suggests that public policy and availability 

of risk information can be effective tools in capitalizing wildfire risk in housing markets prior to events. 

The  second  essay  uses  evidence  from  a  choice  experiment  given  to  respondents  who  were 

intercepted at national forest sites to estimate preferences for environmental attributes of recreation 

sites. Specifically, the main attribute of interest is fire history, where fire history is given by distinct 

categories  in  relation  to  the  dominant  vegetation  at  the  site.  Using  conditional  logit,  random 

parameters logit, and latent class models, we find that tree cover, compared to shrubs or barren areas, 

and water are highly desirable attributes, while evidence of past fires decreases the value of a site. 

Forest fires that reach the crowns of trees are least desirable, while older forest fires and shrub fires 

have  less  of  a  negative  effect.  We  find  evidence  of  significant  preference  heterogeneity  over  the 

vegetation and fire attributes. 

The third essay combines revealed preference data from site intercepts and stated preference 

data from online surveys to estimate the welfare impacts of different fire scenarios at recreation sites. 

We estimate a multi-site zonal travel cost model of trips to hiking and day use sites in the Angeles 

 

National Forest. Stated preference data on reduction in trips to recreation sites under different fire 

history scenarios are used to calibrate the zonal travel cost model and estimate the welfare impacts of 

fire. The greatest estimated welfare losses are from recent fires that burn all vegetation as opposed to 

less intense fires or older fires that have had time to recover. For popular recreation sites, these losses 

from intense fires can total over $1 million in one summer. Applying this method to a large fire that 

affected many sites in our study area, we illustrate how losses decrease over time, but can continue 

well after sites are re-opened due to lasting effects on the landscape.  

 

 

 

ACKNOWLEDGEMENTS 

I would like to thank Dr. Frank Lupi for putting his name on my whiteboard, for his impeccable 

sense  of  timing,  and  for  his  brilliant  and  insightful  comments  and  commentary.  Thank  you  for 

spending the time and effort it takes to be an advisor and mentor – you are a constant source of good 

advice. Thanks also to Dr. Cloé Garnache for her support, and Dr. Joe Herriges and Dr. John Hoehn 

for the helpful suggestions and feedback. Sincere thanks also to Dr. Scott Swinton for inviting me into 

the program, for his guidance during the transition to graduate school, and for his continued support 

throughout the years. I would also like to thank Dr. Robert Myers and Ashleigh Booth for their all-

around heroism. Without you we would all be lost. 

 There are many people to whom I am grateful for assistance and support, but I would like to 

especially  acknowledge  the  people  whose  friendship  has  been  a  constant  through  difficulties  and 

celebrations. Thanks, Asa Watten, for being an incredible friend and teacher, for your generosity, and 

of course for the snacks. Thank you to Mary Doidge for your unshakably sensible perspective on life. 

It was very much necessary. Thanks to Stephen Morgan for your excellent advice and your ability to 

make all situations funny. Try to keep the chaos in check. Samantha Padilla, thank you for being always 

and aggressively on my side. Your encouragement, friendship, and willingness to advocate for me are 

incredible, and this is definitely your page. 

Finally, thank you to my brother William for taking on the role of on-call programming tutor 

and best rubber duck in exchange for gifts of food. Nothing is possible without my parents, Harold 

Tanner and Yiyun Jiang-Tanner – thank you. 

 

TABLE OF CONTENTS 

LIST OF TABLES ............................................................................................................................................ vi 

LIST OF FIGURES .......................................................................................................................................... ix 

INTRODUCTION ............................................................................................................................................ 1 
REFERENCES ................................................................................................................................... 6 

 

Burning Down the House: The Effect of Wildfires on Housing Prices .................... 8 
Introduction ............................................................................................................................. 8 
1.1 
1.2 
Literature Review .................................................................................................................. 10 
1.3  Conceptual Model ................................................................................................................. 13 
1.4  Econometric Model .............................................................................................................. 18 
Study Area and Data ............................................................................................................. 19 
1.5 
1.5.1  Study Area .......................................................................................................................... 19 
1.5.2  Housing Data .................................................................................................................... 21 
1.5.3  Wildfire and Geographic Data ........................................................................................ 25 
1.5.4  Fire Hazard Data .............................................................................................................. 27 
1.5.5  Data on Major Highways as Barriers ............................................................................. 29 
1.6  Empirical Model and Results .............................................................................................. 30 
1.6.1  Cross-Sectional Difference-in-Differences Model ...................................................... 30 
1.6.2  Repeat Sales Model ........................................................................................................... 36 
1.6.3  Effects of Fire Over Time ............................................................................................... 38 
1.6.4  Heterogeneous Effects by Fire Size ............................................................................... 42 
1.7  Discussion and Conclusions ................................................................................................ 45 
APPENDICES .................................................................................................................................. 48 
Appendix 1A. Additional Descriptive Tables .......................................................................... 49 
Appendix 1B: Robustness Checks for Essay 1 ........................................................................ 50 
Appendix 1C: Previous Robustness Checks ............................................................................. 57 
REFERENCES ................................................................................................................................. 58 

2.1 
2.2 
2.3 

  Heterogeneous Preferences Over Recreation Sites in Wildfire Prone Areas .......... 61 
Introduction ........................................................................................................................... 61 
Literature on Effects of Wildfire on Recreation Demand .............................................. 62 
Survey Data and Design ....................................................................................................... 65 
2.3.1  Study Area and Onsite Sampling .................................................................................... 65 
2.3.2  Online Survey and Choice Experiment Design ........................................................... 67 
2.4  Econometric Models ............................................................................................................ 72 
2.5  Results ..................................................................................................................................... 75 
2.5.1  Sample Characteristics ..................................................................................................... 75 
2.5.2  Conditional Logit Models ................................................................................................ 77 
2.5.3  Random Parameters Logit Model .................................................................................. 82 
2.5.4  Latent Class Models ......................................................................................................... 85 
2.6  Willingness to Drive for Attributes .................................................................................... 90 
2.7  Discussion and Conclusions ................................................................................................ 94 

 iv 

APPENDICES .................................................................................................................................. 98 
Appendix 2A: Coefficient Covariance Matrix .......................................................................... 99 
Appendix 2B: Robustness Checks for Essay 2 ..................................................................... 100 
Appendix 2C: Three and Four-Class Latent Class Models ................................................. 105 
Appendix 2D: Onsite Survey Instrument (2016) .................................................................. 109 
Appendix 2E: Online Survey Instrument (2017) .................................................................. 113 
Appendix 2F: Disposition Tables ........................................................................................... 127 
Appendix 2G: Attribute Trade-offs in WTP ......................................................................... 129 
REFERENCES .............................................................................................................................. 131 

  Estimating the Impact of Fires on Recreation in the Angeles National Forest 

Using Combined Revealed and Stated Preference Methods .................................................................. 135 
3.1 
Introduction ........................................................................................................................ 135 
3.2  Empirical Strategy .............................................................................................................. 138 
3.2.1  Zonal Data Set ............................................................................................................... 139 
3.2.2  Site Choice Model .......................................................................................................... 141 
3.2.3  Calibration to SP Data and Welfare Measures .......................................................... 143 
3.3  Data ...................................................................................................................................... 144 
3.3.1  Onsite Survey Sampling Strategy and Design ........................................................... 144 
3.3.2  Online Survey Design ................................................................................................... 146 
3.3.3  Contingent Behavior Data ........................................................................................... 149 
3.3.4  Summary Statistics ......................................................................................................... 150 
3.4  Results .................................................................................................................................. 153 
3.4.1  Site Choice Model .......................................................................................................... 153 
3.4.2  Welfare Effects of Fire ................................................................................................. 154 
3.4.3  Station Fire ...................................................................................................................... 160 
3.5  Conclusions ......................................................................................................................... 162 
APPENDICES ............................................................................................................................... 165 
Appendix 3A: Recreation sites in zonal data set and predicted trips ................................ 166 
Appendix 3B: Site Closure ....................................................................................................... 167 
Appendix 3C: Site-specific delta and welfare estimates ....................................................... 168 
REFERENCES .............................................................................................................................. 174 

 

 

 

 v 

LIST OF TABLES 

Table 1.1 Distribution of Sales Prices in the Full Sample Before and After Trimming ........................ 22 

Table 1.2 Summary Statistics on Transactions in the Full Sample and Estimation Sample ................. 24 

Table 1.3 Descriptive Statistics for Wildfires > 500 ac and within 15 km of a Property by Year ....... 26 

Table 1.4 Structural, Geographic, and Demographic Controls used in Cross-Sectional Models ........ 32 

Table 1.5 Results of Cross-Sectional DID Models; All Counties and Five Markets ............................. 35 

Table 1.6 Summary of Postfire and FHSZ Observations in the Repeat Sales Sample .......................... 37 

Table 1.7 Fixed Effects Model with Repeat Sales Only ............................................................................. 38 

Table 1.8 Effects of Fire Over Time ............................................................................................................. 40 

Table 1.9 Medium Fire Size (500-10,000 Acres) .......................................................................................... 43 

Table 1.10 Large Fires (>10,000 Acres) ........................................................................................................ 44 

Table 1.11 Correlation between Geographic Variables .............................................................................. 49 

Table 1.12 Breakdown of Sample Sizes for Moderate, High, & Very High FHSZ Properties ............ 49 

Table 1.13 Distribution of Distances (in km) to a Barrier Highway ........................................................ 49 

Table 1.14 Small Fires (10-500 Acres) ........................................................................................................... 50 

Table 1.15 Model using Transactions Five Years Before or After a Fire ................................................ 51 

Table 1.16 Effects by FHSZ Rating .............................................................................................................. 52 

Table 1.17 Barrier Highway Treatment ......................................................................................................... 53 

Table 1.18 Models with Properties up to 5 km ............................................................................................ 54 

Table 1.19 Models with Properties up to 15 km .......................................................................................... 55 

Table 1.20 Model with Postfire Interacted with 1-km Bins that Measure Distance from Fire ............ 56 

Table 2.1 Attributes and their Levels in 2016 and 2017 ............................................................................. 71 

Table 2.2 Summary Statistics for Choice Experiment Respondents ........................................................ 77 

 vi 

Table 2.3 Conditional Logit Model Parameter Estimates .......................................................................... 79 

Table 2.4 Conditional Logit Model with Interactions ................................................................................. 80 

Table 2.5 Random Parameters Logit Models with and without Correlation between Attributes ........ 84 

Table 2.6 Comparison of results for different number of latent classes .................................................. 86 

Table 2.7 Latent Class Model with Children, Income, and Hispanic ....................................................... 88 

Table 2.8 Two-Class Latent Class Model with Hispanic and Hiking ....................................................... 89 

Table 2.9 Willingness to Drive ....................................................................................................................... 93 

Table 2.10 Correlation Table for Random Parameters Logit Model 6 .................................................... 99 

Table 2.11 Conditional Logit with Travel Cost ........................................................................................ 100 

Table 2.12 Conditional Logit with Interactions using Travel Cost ........................................................ 101 

Table 2.13 Random Parameters Logit with No Correlation and Travel Cost ..................................... 103 

Table 2.14 Comparison of WTP using Models that used One-way Travel Cost ................................ 104 

Table 2.15 Three-class Latent Class Model with Hispanic, Income, and Children ............................. 105 

Table 2.16 Four-class Latent Class Model with Hispanic, Income, and Children .............................. 107 

Table 2.17 Disposition Codes for Onsite Survey (2016) ......................................................................... 127 

Table 2.18 Disposition Codes for Onsite Survey (2017) ......................................................................... 127 

Table 2.19 Disposition Codes for Online Survey (2016) ........................................................................ 128 

Table 2.20 Disposition Codes for Online Survey (2017) ........................................................................ 128 

Table 2.21 Willingness to Pay One-Way Using Average Travel Cost ................................................... 130 

Table 3.1 Contingent Behavior Scenarios for Each Vegetation Type ................................................... 148 

Table 3.2 Descriptive Statistics for Onsite Survey Respondents ........................................................... 149 

Table 3.3 Contingent Behavior Responses to Fire Scenarios ................................................................. 150 

Table 3.4 Descriptive Statistics for the Zonal Dataset ............................................................................ 152 

Table 3.5 Site Choice Model Results .......................................................................................................... 154 

 vii 

Table 3.6 Weighted Average of Delta from Contraction Map ............................................................... 155 

Table 3.7 Trip Predictions and Welfare Estimates for a Past Fire Affecting a Single Site ................. 157 

Table 3.8 Comparison of Stated Preference Data and Nested Logit Predictions ............................... 159 

Table 3.9 Sites Affected by Station Fire ..................................................................................................... 162 

Table 3.10 Recreation Sites and Predicted Trips ...................................................................................... 166 

Table 3.11 Welfare Impacts of Site Closure by Site ................................................................................. 167 

Table 3.12 Estimates of dj for All Sites and Fire Scenarios .................................................................... 168 

Table 3.13 Estimates of Per-trip Value Lost for All Sites and Fire Scenarios ..................................... 171 

 

 

 viii 

LIST OF FIGURES  

Figure 1.1 Study Area and Markets ................................................................................................................ 20 

Figure 1.2 Study Area with National Forests and Wildfires Perimeters from 1995-2015 ..................... 27 

Figure 1.3 Fire Hazard Severity Zone (FHSZ) Maps Adopted in 2008: Both SRA and LRA ............. 29 

Figure 2.1 Map of Recreation Survey Sites ................................................................................................... 67 

Figure 2.2 Illustration Depicting "Nearby" and "Farther Away" from Parking Area ............................ 68 

Figure 2.3 Choice Experiment Question Format ........................................................................................ 72 

Figure 2.4 Image of Paper Version of Survey (originally 8.5” by 11”) .................................................. 114 

Figure 3.1 Station Fire Burn Scar on Sept. 16, 2009 ................................................................................ 161 

 

 ix 

INTRODUCTION 

Throughout the western United States wildfires are increasing in size, number, and severity 

(Miller et al. 2009; Westerling et al. 2006). In a study of the past three millennia of wildfires in the 

west, Marlon and et al. (2012) conclude that historic wildfire frequency and severity are driven by large 

scale climate anomalies – anomalies of the kind we are currently creating with climate change. In 

particular, an increase in mean temperature, along with precipitation changes and earlier springs have 

lengthened  and  worsened  the  wildfire  season  in  all  western  regions  (Westerling  et  al.  2006). 

Compounding this issue, humans have contributed to large scale fire exclusion and suppression, which 

has driven a wedge between the expected number fires given climatic conditions alone and actual 

wildfire levels. This fire deficit is unsustainable, suggesting fire seasons will continue to worsen in the 

future (Marlon et al. 2012). 

Southern California is home to four national forests that provide respite and recreation for 

millions of visitors and residents in the surrounding cities: the Los Padres, Angeles, San Bernardino, 

and Cleveland National Forests. They are unique among western forests; at higher altitudes, they are 

comprised of pine and oak, but the lower altitudes are dominated by chaparral, a dense shrubland 

characteristic of the region. High-intensity chaparral fires are subject to the same forces that drive 

earlier springs, and hence longer fire seasons, but large fires closely correspond to times when the 

Santa Ana wind is blowing (Moritz et al. 2010), a legendary dry wind that rushes from high pressure 

areas above the Great Basin towards the Pacific Ocean. Because of this, perhaps wildfires have always 

been a way of life southern California; as Didion writes in 1968: “The city burning is Los Angeles’s 

deepest image of itself ... the violence and unpredictability of the Santa Ana affect the entire quality of 

life.” However, even the wind is affected by recent climate change, as Miller and Schlegel find (2006). 

Models of air pressure predict consistent shifts in Santa Ana Occurrences (SAOs) from September - 

 1 

October in the fall to November - December, suggesting an additional extension of the wildfire season 

in the opposing direction. 

Clearly these wildfires have a significant impact on the lives of the 23.8 million people living in 

southern  California  (US  Census  Bureau).  Besides  fire  making  its  way  in  to  the  local  mythos,  any 

individual  blaze  could  cause  loss  of  life,  displace  people  from  their  homes,  threaten  or  destroy 

structures, degrade air quality, close down roads and recreation sites in the national forests, and leave 

a lasting burn scar. In addition, the Forest Service is facing the rising financial cost of fire containment, 

which has started to shift resources away from non-fire related programs. For the first time, wildland 

fire management is a full 50% of its FY2017 budget ($2.45 billion out of $4.9 billion in discretionary 

funds) (“Fiscal Year 2017 Budget Overview” 2016). 

In addition to the financial cost of fire suppression and damage, there is a need to estimate the 

indirect effects of wildfires on surrounding communities. Given how wildfire prone the four southern 

California national forests are, and the densely populated areas directly adjacent to them, there may 

be significant negative effects of fire. On the other hand, southern California is unusually disposed to 

natural disasters – fires, earthquakes, flooding, and landslides coincide in the region. If wildfire risk is 

common  knowledge,  or  wildfires  are  commonplace,  we  may  see  a  more  muted  impact  of  any 

individual event.  

The objective of this dissertation is to measure the cost of wildfires to southern California in 

several different ways: first, we use the hedonic property method to estimate the impact of wildfires 

on nearby property values. The hedonic method allows us to capture impacts for those who live in 

the  direct  vicinity  of  wildfires.  However,  the  four  national  forests  of  southern  California  attract 

millions of visitors each year, many of whom travel from coastal areas or out of state. To understand 

additional effects of wildfires, the second essay uses a choice experiment to estimate impacts of fire 

on different types of national forest visitors. In the third essay, using trip data combined with stated 

 2 

preference  data,  we  take  an  alternate  approach  to  estimating  the  effect  of  wildfire  on  patterns  of 

recreation in the Angeles National Forest and welfare loss to recreationists caused by fire. We find 

evidence  that  the  effects  of  wildfires  are  heterogeneous.  They  affect  communities  and  groups  of 

people differently depending on both the physical attributes of the environment and how fire burns 

and recovers, as well as individuals’ perceived risk, knowledge of fire, and preferences. We also find 

evidence of heterogeneous impacts over time; recent wildfires cause greater welfare losses than older 

fires. However, intense forest fires can have lasting effects for many years. 

The first essay uses a 16-year multi-county housing data set that spans from the border of the 

Los Padres National Forest in the north to the Cleveland National Forest in the south to estimate the 

impact of wildfires on the value of surrounding properties. Previous studies in the area use small data 

sets,  identifying  the  impact  of  a  few  wildfires  on  the  immediate  surrounding  neighborhood.  By 

contrast, the housing data used here includes single-family residences within 30 km of a national forest 

boundary that sold between January 1, 2000 and December 31, 2015. The wildfire data set spans 21 

years, from 1995 to 2015, and includes all wildfires in the area at least 500 acres in size. Tax records 

on sales were combined with data on the location and geographic features of the property to identify 

the effect of selling after a nearby large wildfire. Using a larger dataset allows us to better estimate the 

impacts of wildfires in general, rather than focusing on immediate effects of a single event. Results 

suggest that wildfires have an ambiguous effect on housing price; we argue that this ambiguity stems 

from housing market prior expectations of wildfire risk. If a wildfire causes a large increase in risk 

perception for buyers and sellers in the market, there should be a large negative impact of fire on 

nearby properties. However, if a wildfire does not change risk perceptions overall, there should be a 

smaller or insignificant impact.  

After a major wildfire, damaged recreation sites may be closed for months or years, and many 

have  visible  wildfire  burn  scars  that  last  until  the  forest  regrows.  The  second  essay  uses  stated 

 3 

preference data from a choice experiment to explore systematic heterogeneity in visitor preferences 

over  wildfire  burned  areas.  Data  for  the  second  essay  comes  from  two  rounds  of  onsite  surveys 

administered June – August 2016 and June – August 2017 and two rounds of online survey conducted 

in the winters of 2016 and 2017 that followed up with onsite participants. Respondents made a series 

of choices between hypothetical national forest sites that differed in terms of vegetation and water 

near the site, fire history, and driving distance from home. We look for preference heterogeneity across 

respondents by comparing conditional logit, latent class, and random parameters logit models. Our 

results suggest that some environmental attributes – such as the presence of lakes or streams at a 

recreation site – are desirable and that preferences for these have little heterogeneity. Preferences for 

other attributes, including tree cover at sites and past fire history, do have heterogeneity; it may be of 

interest to forest managers that increased wildfire activity will impact some recreationists more than 

others – for some, it may be a curiosity to visit sites in fire recovery, while for others, it drives them 

towards other sites or activities. 

The third essay uses contingent behavior questions from the same online recreation survey. In 

contrast to trip choice over hypothetical sites, we instead analyze a choice about the site at which 

respondents  were  intercepted  and  interviewed.  Under  eight  different  fire  history  scenarios  which 

corresponded to the vegetation at the site they visited, respondents were asked to make a choice 

between  the  same  trip  as  before,  visiting  a  different  national  forest  site,  or  doing  something  else 

altogether.  Using  real  trip  data,  we  first  estimate  a  multi-site  zonal  repeated  logit  model  of  trip 

participation and site choices. The revealed preference model uses a full set of site-specific fixed effects 

to control for site differences.  We then use the contingent behavior data and a contraction map to 

calibrate the demand model to the stated trip visitation changes under our fire history scenarios in 

order to derive the welfare impacts of different fires. We find that recent forest fires cause larger trip 

 4 

and welfare losses than less recent forest fires or shrub fires, with forest fires decreasing welfare by 

roughly $29 per lost trip.  

 

 5 

 

 

 

 

 

 

 

 

 

 

 

 

REFERENCES 

 

 

 

 

 

 

 

 

 

 

 

 

 

 6 

REFERENCES 

Didion, J. 1968. Slouching Towards Bethlehem. Delta Book. New York: Farrar, Straus & Giroux. 

Marlon, Jennifer R., Patrick J. Bartlein, Daniel G. Gavin, Colin J. Long, R. Scott Anderson, Christy E. 
Briles, Kendrick J. Brown, et al. 2012. “Long-Term Perspective on Wildfires in the Western 
USA.” Proceedings of the National Academy of Sciences 109 (9):E535–E543. 

Miller,  J.  D.,  H.  D.  Safford,  M.  Crimmins,  and  A.  E.  Thode.  2009.  “Quantitative  Evidence  for 
Increasing  Forest  Fire  Severity  in  the  Sierra  Nevada  and  Southern  Cascade  Mountains, 
California and Nevada, USA.” Ecosystems 12 (1):16–32.  

Miller, Norman L., and Nicole J. Schlegel. 2006. “Climate Change Projected Fire Weather Sensitivity: 

California Santa Ana Wind Occurrence.” Geophysical Research Letters 33 (15).  

Moritz, Max A., Tadashi J. Moody, Meg A. Krawchuk, Mimi Hughes, and Alex Hall. 2010. “Spatial 
Variation  in  Extreme  Winds  Predicts  Large  Wildfire  Locations  in  Chaparral  Ecosystems: 
Extreme Winds And Large Wildfires.” Geophysical Research Letters 37 (4). 

US  Census  Bureau.  “American  FactFinder  -  Community  Facts.”  Accessed  October  10,  2017. 

https://factfinder.census.gov/faces/nav/jsf/pages/community_facts.xhtml. 

Westerling, A. L., H. G. Hidalgo, D. R. Cayan, and T. W. Swetnam. 2006. “Warming and Earlier 

Spring Increase Western U.S. Forest Wildfire Activity.” Science 313 (5789):940–43.  

 7 

 Burning Down the House: The Effect of Wildfires on Housing Prices 

1.1 

Introduction 

Wildfires have increased dramatically in number, size, and destructive force over the past 30 

years; especially hard hit is the American West, from forests of the Pacific Northwest through to dry 

shrub land that dominates at the U.S.-Mexico border. Two factors contribute to the increasing risk of 

wildfire. First, there are climatic or natural factors: warmer temperatures, earlier springs, insects and 

infestations affecting forests, and the associated buildup of available fuel, spark more frequent and 

intense wildfires (Westerling et al. 2006). Second, while climate change has encouraged conditions 

conducive to wildfires, development and expansion into the wildland-urban interface (WUI), land in 

transition between development and wildland, has put more people directly into their path. Syphard 

et al. (2007) find that population density and distance from WUI are important factors in determining 

fire frequency in California, suggesting human patterns of development also determine exposure to 

risk. The wildfire burned area in California may grow by as much as 74% by 2085, putting many more 

people at risk (Westerling et al. 2011). 

Wildfires have significant economic impact: federal agencies respond to tens of thousands of 

wildfires on roughly 7 million acres of land, spending a combined total of $1-2 billion each year on 

fire suppression (National Interagency Fire Center 2016). The US Forest Service expects its annual 

cost of fire suppression will reach an estimated $1.8 billion by 2025 (USDA Forest Service 2015) and 

has growing concerns that other management efforts suffer when funds are re-directed towards fire 

suppression. In addition to the direct costs of wildfire – suppression, damages, health, and loss of life 

-  people  living  near  areas  affected  by  wildfire  may  experience  indirect  costs  such  as  the  aesthetic 

disamenity of the burn scar, loss of nearby recreation opportunities, and heightened perceived risk of 

wildfires. 

 

8 

The policy background is particularly relevant for Southern California. Its native shrubland, 

chaparral, has a natural high-intensity fire regime, and so the existence of large wildfires is not a recent 

phenomenon  as  it  is  in  the  Pacific  Northwest  or  the  Rocky  Mountains.  The  largest  wildfires  in 

Southern California are driven by the Santa Ana winds, a phenomenon in which dry air from Nevada 

sweeps toward the Pacific Ocean (Moritz et al. 2010); however, dangers from these large wildfires only 

increase as the cities expand outward. In addition to this extensive experience with fire, the state passed 

a pivotal piece of legislation known as the Bates Bill in response to several severe fires affecting urban 

areas in the late 1980s and early 1990s. The Bates Bill mandates the state fire-fighting agency CAL 

FIRE develop and maintain maps of high wildfire hazard in wildland areas, where the state takes fiscal 

responsibility for fire containment costs, as well as in urban areas, where local governments have 

primary responsibility (California Govt. Code 51175-89). Homeowners are also required to disclose 

the wildfire hazard status of their property at the time of sale. These two features may mean that, 

distinct from other places, California residents may be exceptionally well informed about fire risks.  

This essay estimates the cost of wildfires to residents of southern California using a hedonic 

price approach. Our study area has several distinguishing features that make it a key place of inquiry: 

Southern California faces very high levels of development and urbanization, with suburbs of Los 

Angeles and San Diego running straight into four fire-prone national forests: the Angeles, Cleveland, 

Los  Padres,  and  San  Bernardino  National  Forests.  The  ecosystems  in  these  national  forests  are 

characterized predominantly by chaparral, a dense shrubland unique to this region with a natural high-

intensity fire regime. At higher altitudes, they are comprised of pine, oak, and other mixed forest. The 

regulatory environment also sets California apart. State law requires the disclosure of potential risks, 

including location on a wildland fire zone, to home buyers at the time of purchase. Unlike some studies 

that use small data sets and individual fires, this essay uses a large dataset with 15 years of property 

sales prices and 20 years of wildfire data to exploit extensive spatial and temporal variation to identify 

 

9 

fire effects. We employ difference-in-differences to identify the effects of proximity to a past wildfire 

and risk perceptions associated with wildfires. Using a model of subjective risk, we argue that risk 

perceptions can cause wildfires to have an ambiguous effect on welfare. The empirical results suggest 

significant heterogeneity in the impacts of wildfire, which may be explained by differences in the risk 

information communicated to buyers, as well as differences in the recovery and regrowth patterns of 

the two dominant vegetation types in Southern California. 

The  rest  of  this  essay  is  organized  as  follows:  a  brief  review  of  the  existing  literature  on 

environmental risk and property values is followed by a conceptual model, a description of the data 

and sources, the results, and a discussion.  

1.2  Literature Review 

Wildfires have become an increasingly urgent environmental and public policy issue in the past 

decade, and literature on the effects of wildfires on housing prices has developed at pace. The hedonic 

literature attempts to disentangle the aesthetic disamenity caused by a large wildfire from the effects 

of increased risk perception among potential buyers. In one of the earliest studies, Loomis (2004) 

estimates the change in property values in a town near, but not directly affected by, a major wildfire 

in Colorado. He finds that housing prices dropped 10-15% in the unburned town after the fire and 

that the effects were still present five years later. Donovan, Champ, and Butry (2007) study changes 

to housing prices after wildfire risk ratings are made publicly available. They find that both spatial lag 

and spatial error dependence are statistically and economically significant; their preferred specification 

is the joint spatial lag-spatial error model. However, evidence on the economic significance of spatial 

dependence is mixed. Mueller and Loomis (2008) using Los Angeles county data on 2,520 transactions 

find that there is little of economic significance distinguishing estimates using spatial dependence and 

those that do not. With the same dataset Mueller, Loomis, and González-Cabán (2009) estimate the 

effects of repeated wildfires in a small part of Los Angeles county. Concentrating instead on the impact 

 

10 

of successive fires that occurred within either 2 years or 4 years, the authors find a much steeper 

decrease in price after the second fire (23% as opposed to 10%).   

Like other environmental risks such as hazardous waste sites, nuclear plants, and pipelines, the 

impact of a wildfire does not have a clearly demarcated boundary – properties located within a fire 

perimeter  suffer  damage,  but  people  living  outside  the  perimeter  may  also  experience  a  loss  of 

recreational opportunities, poorer view, or greater awareness of fire risk. Researchers have approached 

the issue of the appropriate distance to use in estimating impacts of wildfires in two different ways. 

Some studies impose an artificial boundary, outside of which they assume the wildfire has no impact 

(Loomis  2004;  Mueller,  Loomis,  and  González-Cabán  2009;  Mueller  and  Loomis  2014).  Mueller, 

Loomis, and Gonzalez-Caban look at the impact of fires on properties within a 1.75-mile radius of 

one or two large wildfires in a neighborhood outside of Los Angeles. They motivate the choice of a 

distance by appealing to Superfund studies (e.g. Gayer, Hamilton, and Viscusi 2000) which consider 

impacts on property values within a very short distance of a site, usually around one mile, as well as 

conversations  with  USFS  officials  about  how  far  they  expect  an  effect.  However,  they  do  not 

empirically test their assumption that fire effects are negligible outside 1.75 miles. 

 Others estimate the impact of fires allowing for a distance decay. Evidence on the distance at 

which  wildfires  have  a  significant  impact  on  property  prices  is  mixed.  The  relevant  distance  may 

depend on the context of the study area, severity of the fire, and geographic features of the area. In a 

study on an area of northwest Montana, Stetler et al. (2010) estimated several hedonic price models 

with a suite of environmental controls, including distances to many amenities – lakes, wilderness, and 

recreation areas – canopy cover, location on wildland-urban interface, and view of the burned area. 

They estimate a hedonic price model using housing data between 1996 and 2007, and information 

from more than 200 medium to large fires over the same time period. They include a property’s 

distance  from  a  fire  and  time  since  the  nearest  fire  in  the  controls,  as  well  as  structural  and 

 

11 

environmental  characteristics  of  the  property.  The  results  suggest  importance  of  environmental 

amenities,  and  that  there  are  significant  differences  for  homes  with  a  view  of  the  burned  area  as 

opposed to without. They also find large and lasting effects of wildfires – home prices suffered at 

distances up to 10 km away from the nearest wildfire compared to homes at least 20 km from a fire. 

In addition, they do not find any significant attenuation in the effect for seven years after a wildfire, 

potentially because the time frame of covered by their data set is shorter than the long wildfire recovery 

time in the Rocky Mountain forests. 

Using data from properties in the Colorado Front Range, McCoy and Walsh (2018) utilize a 

quasi-experimental approach looking at how a wildfire affects three distinct treatment groups: houses 

in close proximity to the burn perimeter, houses with a view of the burn scar, and those located in an 

area of high latent wildfire risk. High latent risk areas are defined by geographic characteristics such 

as slope, vegetation, and housing density that make some communities more susceptible to fire than 

others. To test the sensitivity of their proximity treatment to the cutoff, they start with a treatment 

group of 1 km from a fire and increase the treatment group size in 250 m increments. In contrast to 

Stetler et al. they find no significant effect of a wildfire more than 2 km from the property. Within 2 

km of the burn perimeter, housing prices decrease by 8.7% in the first year after a fire, 7.7% the second 

year, and 6.7% the third year after a fire.  

We use a quasi-experimental approach similar to that of McCoy and Walsh to examine impacts 

of fire on nearby houses, as well as impacts of fire on areas of latent risk, but adapt the model to the 

southern  California  context.  While  other  California  studies  have  used  a  cross-sectional  hedonic 

function and smaller datasets (less than 3,000 transactions) and focus on the impacts of specific fires, 

we use a long-term data set with a large number of transactions in a region that experienced numerous 

spatially and temporally distinct fires to identify the effect of fire events on property values.  

 

12 

1.3  Conceptual Model 

The hedonic model developed by Rosen (1974) treats houses as differentiated products, where 

price is a function of attributes including structural properties of the house, characteristics of the 

neighborhood, and environmental amenities, such as those provided by the national forests, and the 

observed market price is an equilibrium between buyers and sellers. In addition, a property’s value will 

capture the subjective perception in the market of future wildfire risk. A wildfire’s impact is at least 

two-fold: first, it will cause a change to the house’s amenities, and second, it may change the market-

wide subjective probability of risk. We argue that both these changes will have an ambiguous effect 

on the equilibrium housing price. Hansen and Naughton (2013), in a study of the impacts of natural 

disturbances to forests in Alaska, find that major disturbances such as pine beetle outbreaks and large 

wildfires  increased  assessed  property  values.  They  posit  that  for  their  study  area  the  benefits  of 

improved views after tree die-off outweigh the diminished forest amenities. The properties in our 

sample are located near a large national forest with recreation areas that wildfires diminish or destroy. 

However, a wildfire could also open up views or lead to a wildflower explosion the following spring. 

A  wildfire  also  causes  market  agents  to  update  their  subjective  probability  of  risk  but  will  not 

necessarily cause them to expect a greater probability of fire in the future. If a fire heightens buyers’ 

risk salience, we expect to find a significant decrease in property values nearby. However, in some 

areas years of fire suppression have caused an overgrowth of brush and fuel; after one fire occurs, the 

probability of a second fire decreases. In both cases the overall impact will depend on how prospective 

buyers’ priors are affected and the relative magnitude of impacts. 

More  formally,  we  lay  out  a  model  of  subjective  risk  in  the  housing  market  following  the 

example of Beron et al. (1997) who incorporate risk of earthquake damage into the hedonic price 

(1) 

function. The hedonic price function is given by Equation 1. 

!=!#$,&,'(,')('(), 

 

13 

 

 

In equation 1 Z is a set of structural, neighborhood and geographic characteristics that influence 

housing price; r is a vector of environmental and geographic characteristics of the neighborhood, 

including  elevation,  housing  density,  distance  to  the  forest,  and  forest  quality  that  are  positive 

attributes in the market, but are also related to risk of wildfire; '(is the buyer’s subjective probability 
of a fire occurring; and ') the buyer’s subjective probability of property damage, which is an increasing 
function of the probability of fire. It is important to note that after a fire occurs changes in '( could 

be due to increased risk salience – perhaps due to media attention, more accurate risk perceptions, or 

a change (either an increase or decrease) in the future risk of wildfire. For example, in the pre-fire state 

of the world, market actors could be either overestimating or underestimating objective wildfire risk 

(Beron et al. 1997). Another, perhaps unlikely, possibility is that buyers in the market are always correct 

about wildfire risk and any observed change in the marginal change in '( can be attributed to actual 
The risk term '( can be written more fully as a function of the amenity variables r and market 

changes in fire risk. 

information about wildfire risk I. 

 

'(='((&,-) 

(2) 

 

We expect that the subjective risk of fire will depend on both environmental and geographic attributes 

that are correlated with risk of wildfire as well as market information I regarding fire risk, which may 

come from local governments, the media, or other market actors. A recent wildfire is one such source 

of information that we expect to have some impact on the market price. In California another source 

of  information  comes  from  hazard  disclosure  documents  provided  to  buyers  when  a  house  is 

purchased regardless of whether a recent fire has occurred. Hazard disclosures inform buyers whether 

or not the property is located on a Fire Hazard Severity Zone (FHSZ). FHSZ status indicates that the 

 

14 

land has a high probability of experiencing a fire given its physical characteristics and historical fire 

activity. Details on construction of FHSZ are provided in the Data section. 

Since r represents characteristics positively correlated with fire risk, by construction the partial 

derivative of '( with respect to r is nonnegative. 
.'(./ ≥0 

However, we cannot sign the partial derivative with respect to I as buyers’ subjective risk perceptions 

could be either increasing or decreasing in the level of information they receive. If their priors are that 

wildfire risk is low, media coverage of wildfires in their area may increase subjective probability of fire. 

may decrease subjective probability of fire. 

If their priors are that wildfire risk is higher than it actually is, receiving more accurate risk information 

The subjective probability of damage ') is an increasing function of probability of fire and is 

(3) 

 

(4) 

 

(5) 

 

(6) 

 

 

 

 

given by the following equation, 

')=')#'((&,-), 
and its partial derivative is nonnegative.  .').'(≥0 
derivative of '( with respect to I cannot be signed. 
.').- =.').'(.'(.-><0 

 

Again,  subjective  risk  perceptions  cannot  be  signed  with  respect  to  information  since  the  partial 

In this framework, a wildfire acts as a shock to both information and forest quality. Much of 

the Southern California forests is chaparral, a dense shrubland at maturity. Though it burns with high 

intensity, it also has a quick regrowth rate: sometimes burn scars are difficult to detect one to two 

 

15 

years after a fire (Barro and Conard 1991). However, if fires occur more quickly than the natural 30 

to 150-year regime, chaparral may be replaced with non-native grasses, which are even quicker to burn 

(Barro and Conard 1991; Bell, Ditomaso, and Brooks 2009). In older forests, stand clearing fires have 

the effect of removing available fuel, making another fire less probable. Hence, the overall effect of 

fire on subjective risk is indeterminable. 

A buyer on the market maximizes expected utility across three states of the world. In the first 

state of the world, a fire is not realized, and utility depends on housing characteristics and the level of 

site attributes r. In the second, which occurs with subjective probability '( a fire occurs and may affect 
occurs with probability '), property damage is sustained, and structural characteristics Z change to 

nearby amenities denoted rf in the fire state but does not damage the property. In the third, which 

Zf. In each state, the buyer faces a budget constraint that depends on a numeraire good X and the 

price of the home P. 

Recall that equation (1) defined the hedonic price function below, where '( is a function of r. 

 

 

4=5+!(∙) 
!=!#$,&,'(,')('(), 

(7) 

(8) 

 

(9) 
 

 

Following the arguments laid out above, the effect of fire on P is now ambiguous and depends on the 

relative effects on amenities and subjective risk perceptions. The buyer’s maximization problem over 

the three states is given by 

max;,< =⟦?⟧='(∙(1−'))∙CD5,$,&EF+'(∙')∙CD5,$E,&EF	

+(1−'()∙C(5,$,&)	

 

 

subject to the budget constraint given by (7).  In the model, a buyer maximizes utility from a home 

purchase by selecting characteristics Z and site amenities r. This conceptual framework leads to four 

expectations: 

 

16 

1.  If the disamenity effects of a fire outweigh changes in risk perception, the impact of a 

recent fire will be negative.  

2.  Assuming that the nearer a property is to a wildfire perimeter, the greater the level of 

information received by that fire, we expect that the impact of a fire should be greater 

at closer distances than at farther distances. Similarly, we expect that properties selling 

more recently after a fire receive more information from the fire. 

3.  The more accurate the buyer’s information prior to purchasing a home, the less likely 

a  recent  wildfire  will  change  risk  perceptions.  We  expect  that  if  FHSZ  status  is 

conveying  accurate  information,  the  impacts  on  price  observed  at  closer  distances 

from a fire should be mitigated if a property is on FHSZ. However, if FHSZ status 

leads to a general overestimation of market risk, this may not hold.  

4.  A fire may serve as either a positive or negative information shock, so the overall 

impact of a fire on housing value will be ambiguous. 

We are able to test 2-4 by taking advantage of California’s Fire Hazard Severity Zones (FHSZ). 

Properties  sold  on  FHSZ  have  elevated  fire  hazard,  and  potential  buyers  are  made  aware  of  the 

increased risk on natural hazard disclosure forms as well as by their realtor prior to sale. Given elevated 

market  information  for  buyers  of  properties  on  FHSZ,  we  expect  that  a  recent  fire  will  have  a 

significantly smaller impact on sales price than on non-FHSZ properties. Second, we expect that larger 

or more destructive fires will serve as greater information shocks than smaller or less destructive fires. 

Finally, we expect that there may be some areas or times after which a fire when the impact on sales 

prices is ambiguous, which may depend on the market, physical characteristics of the area burned, or 

characteristics of the fire. If a large destructive fire decreases buyers’ perception of future fire risk, 

sales prices may increase after a fire. If a fire serves to increase buyers’ risk salience, prices may decrease 

after a fire.  

 

17 

1.4  Econometric Model 

The  hedonic  price  method  is  commonly  used  to  value  environmental  amenities,  from  the 

benefits of open space to air quality to risks such as nuclear waste (Anderson & West 2006; Kim, 

Phipps, & Anselin 2003; Gawande & Jenkins-Smith 2001). However, a concern in the estimation of 

hedonic price functions is that coefficients will be biased if unobserved variables that influence price 

are correlated with observed variables. To address this, we turn to a difference-in-differences (DID) 

approach commonly used in in the risk literature to identify the effects of wildfires on a group of 

treated properties (Hallstrom and Smith 2005; Gawande, Jenkins-Smith, and Yuan 2013; McCoy and 

Walsh 2018). In our case, a unique feature of using wildfires as treatments over a large area is that our 

events are scattered through time and space. As opposed to a single before and after time period for 

the study area, two properties selling in the same year far away from each other will be nearest to two 

different wildfire perimeters; one may have sold before its nearest wildfire, while the other may have 

sold after its nearest wildfire. 

To implement the DID approach, we first calculate the distance between each property and all 

wildfires within 15 km, measured as the distance from the property to the wildfire perimeter – because 

of the prevalence of wildfires in the area, many properties are within 15 km of multiple fires. We 

expect that excluding these properties from the dataset will bias estimates, so we keep them and add 

a control variable equal to the number of past fires. The past fires variable is defined by the number 

of fires 500 acres or more within 15 km prior to the transaction. The model takes this form: 

HI!JK=LM+L)JNKOPQRJK+	LSTNK!UQRVP/WJK+L)JNKSTNK(OPQR×	!UQR)JK+YZT[N\]JK 
where lnPit is the natural log of the sale price for house i selling in year t. OPQRJK is the natural log of 

+Y^\T_J+Y`\J^ZaT<bJK+YcT[`KdeJ+YKJf\gJK+hJK 

(10) 

 

 

distance from the fire perimeter. We exclude properties within the fire perimeter if they sold after the 

fire, but in order to keep properties within the perimeter that sold before a fire occurred, we transform 

 

18 

the distance variable by adding .01 (or 1 meter) before taking the natural log. Since the housing closing 

process takes 30 to 60 days, we define Postit=1 if the property is sold between 60 days and three years 

after  the  nearest  fire  occurs.1  The  coefficient  of  interest  is  bdistpost,  the  difference-in-difference 

coefficient that measures the effect of selling after a fire for houses in each treatment group. The 

model  also  controls  for  housing  characteristics  X,  geographic  characteristics  G,  neighborhood 

demographics N,  and  includes  county  fixed  effects C,  and  year  by  quarter  dummies T.  Housing 

characteristics are drawn from tax assessor data and are accurate to the most recent tax assessment. 

For  unbiasedness  in  difference-in-difference  estimates,  three  assumptions  must  be  met:  correct 

specification of the model, error terms satisfy =(hJ|5)=0, and there must be parallel trends between 

treatment and control groups.  

1.5.1  Study Area 

1.5 

Study Area and Data 

There  are  several  key  features  of  Southern  California  that  make  it  an  interesting  area  to 

investigate potential for wildfire risk. First, in many areas of the country, areas at high wildfire risk are 

remote or undeveloped. By contrast, some of the largest cities in California including Los Angeles and 

San Diego are adjacent to forested or wilderness areas with extreme wildfire risk.  In our selected study 

area  of  southern  California  in  particular,  these  high-risk  areas  also  benefit  from  amenities  from 

national  forests.  Second,  the  physical  characteristics  of  the  study  area  are  unique:  the  dominant 

vegetation in the region chaparral, which has a very different fire regime from forests in the Pacific 

Northwest or the Rocky Mountains. Finally, Californians are familiar with natural hazards and risks, 

and the housing market has many sources of fire risk information for potential home buyers. One 

major source of risk information is that the state natural hazard disclosure law requires buyers to be 

                                                

1 Models were also run defining postfire as 120 days to three years and there was little effect on results. 

 

19 

notified of homes on land that has been classified as at high wildland fire risk. These risk zones are 

defined by state and local governments; more on how they were developed in Section 1.5.4. 

The study area is geographically large and covers several of California’s biggest urban areas, 

including  Santa  Barbara,  Los  Angeles,  Anaheim,  Riverside,  and  San  Diego.  Because  we  expect 

heterogeneity between these major cities, and because it is unlikely that they share a housing market, 

in addition to running models with pooled data from all counties, where possible, we also run models 

with five smaller markets. The five markets consist of: (1) Santa Barbara and Ventura Counties; (2) 

Los Angeles County; (3) Orange County; (4) Riverside and San Bernardino Counties; and (5) San 

Diego  County.  Figure  1.1  depicts  the  entire  study  area,  county  boundaries  (labeled),  and  national 

forests (shaded). The five markets are denoted by county fill. From north to south the markets are: 

Santa Barbara & Ventura; Los Angeles; Orange County; San Bernardino & Riverside; and San Diego. 

 

Figure 1.1 Study Area and Markets 
 

 

20 

 

1.5.2  Housing Data 

We obtained property transactions data for homes sold between January 2000 and December 

2015 near the Los Padres, Angeles, San Bernardino, and Cleveland National Forests, spanning seven 

counties: Santa Barbara, Ventura, Los Angeles, San Bernardino, Riverside, Orange, and San Diego. 

The study area was defined by selecting Zip Code Tabulation Areas (ZCTA) within 30 km of the 

National Forests on the coastal side. Figure 1.2 shows the study area with the selected ZCTA as well 

as the four National Forests. Housing data was purchased from CoreLogic, a company that provides 

real estate data obtained from public records to financial and research institutions. This data includes 

transactions  data  for  residential  properties,  street  address,  a  set  of  structural  variables  including 

bedrooms, bathrooms, square footage, lot size, and features such as parking, fireplace, and pool. For 

a subset of properties, we also observe information on one prior sale. Data quality for features of the 

properties  –  e.g.  swimming  pool,  fireplace,  view  –  is  quite  low  so  models  include  only  structural 

variables such as the number of rooms and square footage. Data are limited to relevant transactions 

of owner-occupied residential single-family residences in a series of steps. To identify arms-length 

transactions as opposed to transfers between family members or built-to-order homes, we exclude 

properties built in the same year as they were sold, that sold twice in 12 months, properties transferred 

using quit claim or other unusual deeds, and those marked with a partial sale code.  

After excluding properties with missing sales data, we drop houses in the top 1% of bedrooms, 

bathrooms,  and  total  rooms,  and  the  top  1%  of  square  feet,  to  remove  extreme  values  from  the 

sample2, and remove condos and duplexes. The cleaned dataset still contains extreme values in size 

and  sales  price:  the  HPI-adjusted  sales  price  of  remaining  properties  ranges  from  $3,500  to 

$191,000,000, including some properties with a price per square foot of $1, and the minimum square 

                                                

2 Muehlenbachs Spiller and Timmins (2015) and McCoy and Walsh (2018) use similar methods to trim extreme values 

 

 

21 

footage is under 50. For all models we then further exclude properties with fewer than 500 square 

feet3, with a price per square foot of less than $404, a sales price of less than $10,000, or a sales price 

of  greater  than  $10,000,000.  After  trimming,  we  have  1,346,132  observed  transactions;  some 

properties sold twice between 2000-2015, and information from both transactions are included in the 

total observations. A comparison of sales price summary statistics before and after trimming extreme 

values  is  in  Table  1.1.  The  price  distribution  in  the  trimmed  sample  now  shows  a  more  realistic 

minimum of around $20,000 rather than $3,500, while the distribution in middle 90% of the sample 

has not changed drastically. 

 

Table 1.1 Distribution of Sales Prices in the Full Sample Before and After Trimming 

 

 

Minimum 
1st Percentile 
5th Percentile 
Median 
95th Percentile 
99th Percentile 
Maximum 

 

N 

Before Trimming 

After Trimming 

 

$ 3,496 
$ 139,598 
$ 198,511 
$ 447,159 
$ 1,069,509 
$ 1,750,977 
$ 191,000,000 

 

1,348,336 

 

$ 19,379 
$ 140,879 
$ 198,882 
$ 447,159 
$ 1,063,000 
$ 1,701,387 
$ 9,984,551 

 

1,346,132 

Table 1.1 displays summary statistics on the HPI-adjusted sales price of transactions in the full sample before and 
after trimming by four criteria: (1) properties under 500 square feet; (2) transactions with a price per square foot of 
less than $40; (3) transactions with a sales price less than $10,000; and (4) transactions with a sales price greater than 
$10,000,000. 
 

 The focus of this paper is to identify the immediate impact of a recent fire, so to minimize the 

potential for confounding influences, models are limited to transactions which occur in the three years 

                                                

3 500 square feet is the size cutoff to meet the definition of a micro-home 
4 Wolf and Klaiber (2017) remove properties with a price of less than $40/sqft 

 

22 

before or after the wildfire, and properties within 10 km of a wildfire 500 acres or more. Table 1.2 

shows summary statistics for the fully cleaned dataset and the dataset used in most of the models 

presented (transactions within three years before or after a fire, and within 10 km of a wildfire 500 

acres or more – the estimation sample). Transactions in the estimation sample have more wildfires 

prior to the sale (2.4 compared to 1.5) and are on average closer to a fire perimeter (3.5 km compared 

to  4.3  km)  than  the  full  sample.  The  structural  characteristics  of  the  properties,  including  square 

footage, price, and age, as well as year of sale, are very similar to those in the full sample of properties. 

 

 

23 

  

Variable 

 

Sales price ($) 
Price per square foot ($) 
Bedrooms 
Bathrooms 
Square feet 
Age 
Sale year 
Distance from USFS land (km) 
Distance to other open space (km) 
Number of fires prior to sale (over 
500 acres and within 15 km) 
Distance to fire perimeter (km) 
FHSZ (0/1) 
Sold after a fire (0/1) 

 

520,349 
281 
3.4 
2.4 
1,909 
36 
2007 
14.7 
0.6 
1.5 
4.3 
0.1 
0.5 

 

346,689 
145 
0.8 
0.8 
757 
23 
5 
8.2 
0.5 
1.7 
3.1 
0.3 
0.5 

 

19,379 
40 
1 
1 
500 
1 
2000 
3.0E-4 
0.0 
0 
0.0 
0 
0 

 

 

9,984,551 
8,022 
5 
5 
4,981 
214 
2015 
30.0 
6.1 
16 
15.0 
1 
1 

 

 

 
525,494 
 
284 
 
3.4 
 
2.4 
 
1,903 
 
35 
 
2006 
 
11.5 
 
0.6 
 
2.4 
 
3.5 
 
0.1 
   0.5 

 

341,233 
137 
0.8 
0.8 
750 
23 
4 
7.4 
0.5 
1.9 
2.5 
0.3 
0.5 

 

 

 

 

 

44,039 
40 
1 
1 
500 
1 
2000 
3.0E-4 
0.0 
0 
0 
0 
0 

 

 

9,637,375 
4,516 
5 
5 
4,981 
208 
2015 
30.0 
5.9 
16 
10.0 
1 
1 

 

Table 1.2 Summary Statistics on Transactions in the Full Sample and Estimation Sample 

Full sample of properties 

(N= 1,346,132) 

 

Properties in Estimation Sample 

(N= 223,323) 

Mean 

Std dev  Min 

Max 

   Mean 

Std dev  Min 

Max 

 

 

 

Table 1.2 summarizes structural and relevant geographic characteristics of properties; statistics for the full sample of properties are displayed on the left, and 
statistics for the Estimation Sample (transactions that occur in the three years before or after a wildfire) are on the right. Property characteristics, including sales 
price, size, number of rooms, and age are similar between the two samples. In addition, there is no evidence for significantly different transaction times between 
the two samples. There are some differences in terms of distance to fire perimeter and number of fires prior to sale. 

 

 

24 

1.5.3  Wildfire and Geographic Data 

Using  wildfire  perimeter  data  available  from  California’s  Fire  Resource  and  Assessment 

Program (FRAP), we select wildfires that occur between 1995-2015, and only fires at least 500 acres 

in size; earlier models suggest fires older than ten years or smaller than 500 acres have a negligible 

effect on sales. The FRAP data set obtained from the state of California includes all footprints of fires 

10 acres or greater that local agencies reported to the state. After matching each property with all fire 

perimeters within 15 km, there are 1116 individual footprints 10 acres or more – summary statistics 

for fires by year are in Table 1.3. The 25th percentile in size is 40 acres, the 50th is 131, and the 75th 

percentile in fire size is 521 acres. Thus, limiting to fire perimeters 500 acres or more allowed us to 

concentrate on a subset of significantly large fires. A total of 288 wildfires are within 15 km of a 

property in the data set and 500 acres or more. Figure 1.2 shows the selected study area and spatial 

distribution of wildfires in the greater Los Angeles area. 

Conditional on being more than 500 acres, these fires burned on average 10,900 acres and lasted 

roughly a week. Robustness checks include models with only these extra-large fires 10,000 acres or 

more. The study period spans some of California’s worst wildfire incidents, including the “California 

Fire Sieges” of 2003, in which 14 fires blazed through southern California over the course of two 

weeks, and 2007, which charred nearly one million acres between Santa Barbara and the US-Mexico 

border (Blackwell and Tuttle 2003; CAL FIRE, USFS, and OES). 

Addresses were geocoded with Texas A&M Geoservices. Fifty percent of properties matched 

with a parcel latitude and longitude, 46% matched with a street segment, and 4% were matched with 

a  zip  code  centroid.  Next,  geographic  data  for  properties  was  obtained,  including  distance  to  the 

nearest wildfire perimeter, distance to the closest National Forest boundary, and distances to other 

amenities for each individual property. Distance to primary and secondary roads was calculated using 

road data from the US Census Bureau’s TigerLine road shapefiles. Distances to city centers were 

 

25 

calculated using metropolitan boundaries from the San Diego Association of Governments and the 

city of Los Angeles – each property was matched with either Los Angeles or San Diego as the nearest 

major city – and distance to the nearest park or open space used data from the California Protected 

Area Database.  

 

Table 1.3 Descriptive Statistics for Wildfires > 500 ac and within 15 km of a Property by Year 

Year 

1995 
1996 
1997 
1998 
1999 
2000 
2001 
2002 
2003 
2004 
2005 
2006 
2007 
2008 
2009 
2010 
2011 
2012 
2013 
2014 
2015 

Number of Fires 

Smallest (Acres)  Median (Acres) 

Largest (Acres) 

23 
24 
19 
11 
16 
4 
8 
20 
21 
17 
12 
12 
27 
8 
8 
7 
5 
9 
14 
7 
5 

531 
502 
522 
580 
502 
798 
531 
555 
806 
513 
618 
500 
602 
500 
839 
522 
508 
519 
510 
959 
1,049 

1,680 
1,084 
1,326 
2,056 
3,298 
1,199 
1,599 
3,432 
8,474 
3,693 
1,630 
6,549 
3,839 
7,059 
4,824 
717 
1,027 
2,637 
2,505 
1,952 
1,462 

21,444 
19,861 
24,797 
28,136 
63,508 
11,734 
10,438 
61,691 
270,686 
16,447 
23,396 
161,816 
240,359 
30,305 
160,833 
12,582 
2,134 
11,667 
30,268 
15,186 
31,284 

Table 1.3 shows summary statistics for the sample of wildfires 500 acres or more, and within 15km of a property in 
the sample, by year. An average year had 14 wildfires, and a median fire size of around 2,000 acres. Some exceptional 
years (2003, 2007) had wildfires more than 200,000 acres. 
 

 

 

26 

 

Figure 1.2 Study Area with National Forests and Wildfires Perimeters from 1995-20155 
 
1.5.4  Fire Hazard Data 

Previous research suggests that risk of wildfire is generally not salient to potential home buyers 

except shortly after an information shock such as publicly available risk ratings, or an actual fire. A 

household survey of Colorado Springs residents found that homeowners had not been aware of fire 

risk when they purchased their homes (Champ, Donovan, and Barth 2009), and a related study on the 

impact of making available parcel-level risk ratings in the same town found that before the program 

amenities associated with risk were positively related to price, while after ratings were posted online 

the amenities were insignificant (Donovan, Champ, and Butry 2007). We therefore identify effects of 

                                                

5 Figure 1.2 shows county boundaries (labeled), USFS boundaries (labeled and denoted by a striped pattern), and fire 
perimeters in the study area. Each fire perimeter is at least 10 acres in size, within 15 km of a property in our study 
area and occurred between 1995 and 2015. Many of the fire perimeters overlap with USFS land, but several wildfires 
affect other areas.  

 

 

27 

wildfires along two main dimensions: the effect of being close to a recent fire for properties located 

on and off areas of high risk as defined by the state. 

California Department of Forestry and Fire Protection (CAL FIRE) produces statewide maps 

of areas with significant fire hazards, called Fire Hazard Severity Zones (FHSZ). Hazard zones are 

developed using information about the physical attributes of the area and fire history, including fuel 

availability, topography, typical weather, and models of ember production and movement. FHSZs do 

not  take  into  consideration  private  actions  to  reduce  fire  risk  on  a  given  property,  such  as  fuel 

reduction and defensible space. Hazard zones are divided into two main categories defined by the 

level  of  government  responsible  for  firefighting  costs:  state  responsibility  areas  (SRAs)  and  local 

responsibility areas (LRAs). For SRAs, hazard severity is rated as one of three categories: moderate, 

high, or very high. For LRAs, there is only data on areas rated “very high”. 

Maps of FHSZ have existed since the 1980s, however, early geographic records are incomplete. 

Mapping efforts were greatly expanded in the early 2000s; the current version of maps for SRA were 

proposed  in  2007  and  adopted  by  January  2008.  Current  hazard  zones  for  LRAs  were  proposed 

between 2007 and 2008 and were adopted by local jurisdictions on an individual basis afterwards6. 

Our main models define FHSZ to be a binary variable equal to one if the property is on any of the 

above zones and use the hazard zone designation that is most accurate to the sale year; properties that 

sell prior to 2008 are coded using older FHSZ maps that date back to 1985 and properties selling in 

2008 or later are coded using the more recent maps. 

FHSZ may be used in the development of building standards and defensible space requirements, 

but more importantly since 1998 California’s Civil Code has required natural hazard disclosures at the 

time of property sale, including both location on areas of wildland fire risk (any SRA rating) and 

                                                

6 The state of California advised the city of San Diego that LRA maps would be updated roughly every five years 

but as of 2018 there are no additional updates from after the 2007-2008 remapping effort 

 

28 

whether the property is in a “Very High” wildfire hazard zone (anywhere with a “very high” hazard 

rating). Location of FHSZ according to maps adopted in 2008 is shown in Figure 1.3. 

 

Figure 1.3 Fire Hazard Severity Zone (FHSZ) Maps Adopted in 2008: Both SRA and LRA7 
 
1.5.5  Data on Major Highways as Barriers 

For a robustness check presented in the appendix we use an additional treatment that uses 

highways, which often act as a physical barrier for wildfires, as an information treatment. Because it is 

rare that fires jump barriers with little fuel (e.g. a large road or river), we expect that properties in the 

interior of a highway – between a major highway and USFS land – will be more impacted by a recent 

fire than those directly on the other side. 

                                                

7 Figure 1.3 shows county boundaries (labeled), ZCTA boundaries in a light gray, and boundaries of FHSZ in the 
study area. There are two categories of FHSZ: SRA are areas where the state is responsible for fire-fighting costs, 
and LRA are areas where the local governments are responsible for fire-fighting costs. In addition, all land is either 
unclassified or classified into three hazard categories: moderate, high, or very high. 

 

 

29 

To develop a model that uses major highways as barriers we use Highway I-210 as a reference 

point for major road on Google Maps. Highway 210 runs almost parallel to the boundary of the 

Angeles National Forest from Santa Clarita to San Bernardino and is often used as a reference point 

for wildfire news. With 210 as a reference point, we select similar major roads from the TigerLine 

shapefile  in  GIS  and  individually  select  the  portions  of  road  that  run  parallel  to  all  four  forest 

boundaries. We calculate both the distance and angle to the selected roads for each property in the 

sample. Then, by selecting groups of properties based on latitude, longitude, and angle to the nearest 

of the roads, we are able to identify the properties in each county that are between the highway and 

forest (“between”) and on the other side of the highway. 

1.6.1  Cross-Sectional Difference-in-Differences Model 

1.6 

 Empirical Model and Results 

Our  empirical  approach  uses  the  hedonic  pricing  model  in  a  difference-in-differences 

framework where selling near a recent wildfire is the treatment and properties that sold prior to the 

wildfire or farther away are controls. In this specification, treatment estimates the effect of a recent 

fire but cannot separately identify amenity and risk effects. Prior studies testing the effect of wildfire 

proximity on housing prices have used a range of values from 2 km (McCoy Walsh 2018) to roughly 

3.2 km (Loomis 2004). Rather than assuming a strict distance cutoff after which proximity to a recent 

fire has no effect, we allow impacts farther away from a fire by using continuous distance as our 

treatment variable. In all models we allow for heterogeneous effects according to FHSZ classification 

by interacting an indicator variable for FHSZ with postfire and distance variables.  

The econometric specification takes the form 

 

 

 

 

30 

 

(11) 

 

!"#$%='(+'*$+%ln	(0123)$%+	'56+%#723819:$%+	';<+=>?@A 
+	'*$+%56+%[ln	(0123)×	#723]$%+'*$+%;<+=[ln(0123)×>?@A]$% 
+	'56+%;<+=[#723×>?@A]$%+'56+%;<+=*$+%[ln	(0123)×#723×>?@A]$% 
+	E<6F+GH$%+EIG6J$+EKG$I<L6MN$%+EO6FK%PQ$+E%$RGS$%+T$% 
fire perimeter, selling after a fire, and FHSZ (0/1 dummy variable). The coefficient '*$+%56+% on the 
a wildfire after the fire occurs; '56+%;<+= describes the impact of selling on FHSZ after a wildfire; and 
'56+%;<+=*$+% shows the additional impact of selling on FHSZ after a nearby wildfire. In all models we 

interaction term is the difference-in-difference coefficient which describes the effect of distance from 

The dependent variable is log of an HPI-adjusted sales price8. We control for distance from the 

control for a set of structural, geographic, and demographic characteristics; Table 1.4 is a list of all 

controls used in the cross-sectional difference-in-differences estimation.  

 

                                                

8 The dependent variable is actual sales price rather than assessed property value. 

 

31 

Table 1.4 Structural, Geographic, and Demographic Controls used in Cross-Sectional Models 

Category 

 

Structural Variables 
 
 
 
 

 

Geographic Variables 
 
 
 
 
 
 
 
 
 
 

 

Census Tract 
Characteristics 
 
 
 
  

 

 

 

Variable Name 

 

Bedrooms 
Bathrooms 
Ln(Square feet) 
Ln(Acres) 
Age 

 

Description 

 

Number of bedrooms 
Number of bathrooms 
Logged square footage 
Logged parcel acreage 
Age of the house 

 

Development density 
National forest (NF) 
Distance from NF 
Slope 
Elevation 
WUI 
Urban 
Distance to city 
Distance to open space 
Distance to highway 
Number of past fires 
Percent Bachelor's 
degree 
Median income 
Percent Hispanic 
Percent black 
Unemployment rate 

 

Indicator variables for housing development density (4 categories) 
Indicator variables for the closest national forest (4 variables) 
Logged distance from NF land in km 
Slope of property 
Elevation of property 
Indicator variable for located on Wildland-Urban Interface 
Indicator variable for located on land classified as urban 
Logged distance from the nearest major city center, either Los Angeles or San 
Diego 
Logged distance to land in the California Protected Area Database 
Logged distance to major road 
Number of fires (500 acres or more) within 15 km prior to the transaction 

 

Percent of the population 25 years and older with at least a Bachelor's degree 
Median household income 
Percent of the population that is Hispanic 
Percent of the population that is black 
Percent of the population unemployed 

 

 

32 

In the pooled model with all counties the sign of the coefficient on Ln(Distance) is positive and 

significant,  indicating  that  before  a  fire  occurs,  prices  are  higher  farther  away  from  the  area  that 

eventually buns. Given that distances from various amenities – Los Angeles or San Diego city centers, 

major highways, USFS and other wild land – are controls, we would have expected an insignificant 

sign on this variable, and its significance suggests some omitted variable correlated with fire. One 

possible explanation is that property price differentials are in part driven by insurance rates. Insurance 

companies are increasingly using sophisticated modeling techniques to estimate fire risk at a parcel 

level and may use variables beyond the controls in our model. After major fires, they update insurance 

rates not only for affected properties but also properties in other areas determined to have a high risk 

of fire. 

Closer examination of the by-county models provides evidence for a mixed impact of distance 

from fire perimeter across the sample. The positive significant coefficient on FHSZ indicates that in 

general, properties on risky areas have a premium (being on FHSZ is associated with a 7.3% higher 

sales price). In general, FHSZ areas are less developed and adjacent to areas with nice views and 

recreational opportunities and prior to a fire, the benefit from these amenities may outweigh any 

sources of risk information. The coefficient on Ln(Distance) x FHSZ describes the impact of distance 

from a fire perimeter on FHSZ before the fire happens. Similar to Ln(Distance), we expected this 

value to be insignificant. It is in the pooled county model, while in the models by market there are 

mixed impacts. 

Recall hypotheses (3) the greater the buyer’s information prior to purchasing a home, the less 

likely a recent wildfire will change risk perceptions; and (4) a fire may serve as either a positive or 

negative information shock, so the overall impact of a fire on housing value will be ambiguous. The 

Postfire x FHSZ coefficient is negative and significant in the pooled county model – on average there 

is a 1.7% decrease in sales price on FHSZ after a fire. This is consistent with our hypothesis that 

 

33 

potential  buyers  and  sellers  of  properties  on  FHSZ  will  experience  either  an  increase  in  fire  risk 

salience or an increase in insurance market rates that will decrease the sales price on these zones 

compared to properties that are not rated as at greater wildfire risk. However, by looking at the models 

by market, we can see that this effect only holds for part of the sample. It may be the case that in those 

areas where we see the opposite effect, after a fire subjective risk decreases for the future. 

On average after a fire, sales price decreases as distance from the fire increases, meaning after a 

fire happens, houses are selling for higher prices near the fire perimeter. This contradicts prevailing 

results in the literature. Our study does have some significant differences from prior studies, the most 

major being that we allow for effects over a much wider distance (10 km compared to a norm of 2-5 

km or even less). Robustness checks include models that use 5 and 15 km distance cutoffs as well as 

an alternate model specification that interacts Postfire with 1-km bins from the fire perimeter (these 

results are summarized in the appendix). For models in smaller markets we are not able to detect the 

effect of distance from a recent fire on property sales prices. The Los Angeles County market model 

has an estimated parameter that is positive and significant, indicating as you get farther away from a 

recent fire, price increases. The overall effect seems to be driven mostly by Orange County. 

The coefficient on the triple interaction of Distance x Postfire x FHSZ in both the All Counties 

and Orange County models is the opposite sign than the main DID estimate Distance x Postfire. 

Considering expectation (3) above, this suggests that no matter the overall impact of a fire on risk 

expectations,  being  on  FHSZ  has  a  mitigating  impact.  In  areas  that  do  not  get  this  extra  risk 

information when houses are on the market, distance to open space or other sources of information 

are used to form priors on fire risk. However, for buyers and sellers of properties on FHSZ, each 

receive a more accurate information signal about fire risk, and so after a fire, beliefs are updated to a 

lesser amount.  

 

 

34 

Table 1.5 Results of Cross-Sectional DID Models; All Counties and Five Markets 

  
 

 

Ln(Distance) 
 
Postfire 
 
FHSZ 
 
Ln(Distance) x FHSZ 
 
Postfire x FSHZ 
 
Ln(Distance) x Postfire 
 
Ln(Distance) x Postfire x 
FHSZ 
 
Constant 
 
 
Observations 
R-squared 

 

(1) 
All Counties 

(2) 
Santa Barbara 
& Ventura 

(3) 
Los Angeles 

(4) 
Riverside & San 
Bernardino 

(5) 
Orange County  San Diego 

(6) 

 

0.013*** 
(0.000) 
0.040*** 
(0.000) 
0.073*** 
(0.000) 
-0.007 
(0.000) 
-0.017*** 
(0.000) 
-0.010*** 
(0.000) 
0.019*** 
(0.000) 
9.565*** 
(0.000) 
 
206,841 
0.830 

 

 

0.021*** 
(0.001) 
0.010 
(0.418) 
0.045* 
(0.068) 
0.029 
(0.143) 
0.055* 
(0.051) 
-0.006 
(0.436) 
-0.008 
(0.723) 
9.350*** 
(0.000) 
 
6,351 
0.793 

 

 

-0.006*** 
(0.000) 
-0.007*** 
(0.009) 
0.044*** 
(0.000) 
0.020*** 
(0.000) 
0.015* 
(0.067) 
0.014*** 
(0.000) 
-0.008 
(0.184) 
9.653*** 
(0.000) 
 
61,438 
0.777 

 

 

-0.009*** 
(0.000) 
0.030*** 
(0.000) 
0.040*** 
(0.000) 
0.023*** 
(0.000) 
-0.011 
(0.191) 
0.001 
(0.343) 
-0.001 
(0.895) 
12.075*** 
(0.000) 
 
67,791 
0.838 

 

 

0.012*** 
(0.000) 
0.066*** 
(0.000) 
0.038*** 
(0.000) 
-0.007* 
(0.092) 
-0.066*** 
(0.000) 
-0.061*** 
(0.000) 
0.043*** 
(0.000) 
9.051*** 
(0.000) 
 
31,636 
0.804 

 

 

-0.057*** 
(0.000) 
0.010*** 
(0.000) 
0.015*** 
(0.004) 
-0.006** 
(0.024) 
0.053*** 
(0.000) 
0.002 
(0.257) 
-0.032** 
(0.048) 
9.313*** 
(0.000) 
 
39,625 
0.782 

 

Table 1.5 describes the controls used in the cross-sectional DID model, including structural controls, geographic variables, and census tract characteristics. All 
logged variables have been transformed by adding one so that properties with distance=0 from open space, city center, or fire perimeter remain in the models. 

 

35 

1.6.2  Repeat Sales Model 

A concern of the cross-sectional DID approach is that there are unobservables that bias the 

treatment  effect  estimate.  We  take  advantage  of  observing  repeated  sales  from  a  subsample  of 

properties to create a two time-period panel and run property fixed effects models. The repeat sales 

to fire and price. The model takes the form: 

model should better control for time-invariant unobservables that are correlated with both distance 

!"#$%='(+	'+,-%#./01234$%+	'56-789:;$% 
+	'<$-%+,-%[ln	(A2/0)×	#./0]$%+'<$-%56-7[ln(A2/0)×89:;]$% 
+	'+,-%56-7[E./0×89:;]$%+'+,-%56-7<$-%[ln	(A2/0)×#./0×89:;]$% 
+	'FGHIJ4$%+KLH$G6M,NO$%+K%$PHQ$%+8R+S$% 
Like Equation 15, the coefficient '<$-%+,-% describes the effect of proximity to a wildfire after 
the fire; '+,-%56-7 describes the impact of selling on FHSZ after a wildfire; and '+,-%56-7<$-% shows 

 

(12) 

 

the additional impact of selling on FHSZ nearby a wildfire. The model still includes all covariates that 

change over time. FHSZ is included in the model because of the hazard zone update in 2008; each 

property’s  FHSZ  rating  corresponds  to  the  map  in  use  during  the  year  of  sale.  Census  tract 

characteristics  also  vary  over  time.  For  sales  in  2010-2015,  demographic  variables  are  from  the 

American Community Survey (ACS) 5-Year Estimates. For sales in 2009 or earlier, we use the 2009 

estimates. 

Another difference of note: in the cross-sectional DID dataset the primary unit of observation 

is the transaction. Each transaction was matched to the nearest fire; if the closest fire was more than 10 

years ago, we matched the transaction in question with the next nearest fire, expanding the dataset. 

Hence, the same house could be matched with two different relevant fires if the sales were for example 

in 2000 and then again in 2012, and standard errors were clustered at the property level to account for 

correlation in the sales. In the repeat sales models, we match each property with the nearest wildfire, 

 

36 

which could have occurred in the three years prior to the first sale, between the two sales, or in the 

three years after the second sale. 

The subset of 47,842 houses for which we observe a true repeat sale – meaning each transaction 

was arms-length, involved the whole property parcel, with reasonable sales price – is much smaller 

than the Estimation Sample. Table 1.6 shows the breakdown of the Repeat Sales Sample by Postfire 

and FHSZ.  

 

Table 1.6 Summary of Postfire and FHSZ Observations in the Repeat Sales Sample 

  
FHSZ 

 

0 
1 

 

0 

 

23,475 
1,111 

Postfire 

1 

 

21,029 
2,227 

Total 

 

44,504 
3,338 

 

 

 

Total 

24,586 

23,256 

47,842 

Table 1.6 shows the cross-tabulation of Postfire and FHSZ to illustrate that the number of treated houses decreases 
significantly in the repeat sales model compared to the cross-sectional DID model. The count includes all counties 
and only properties that were already included in the Estimation Sample. 
 

In Table 1.7 we present results from a repeat sales model on the pooled county data. The sign 

and magnitude of the coefficients of interest are fairly similar to the cross-sectional model. In the 

repeat sales model we see a price premium for selling on FHSZ before a fire (13.2%), but there is no 

significant effect of selling on FHSZ after a fire. The coefficient on the Distance x Postfire coefficient 

is insignificant. However, the coefficient of Distance x Postfire x FHSZ is negative and significant. In 

this model distance from a recent fire seems to only matter for properties on FHSZ and not for other 

properties. 

 

 

 

37 

Table 1.7 Fixed Effects Model with Repeat Sales Only 

 
 

 

Postfire 
 
FHSZ 
 
Postfire x FSHZ 
 
Ln(Distance) x Postfire 
 
Ln(Distance) x Postfire x FHSZ 
 
Constant 
 
 
Observations 
Number of Houses 
R-squared 

 

(7) 
All Counties 

 

-0.017*** 
(0.000) 
0.132*** 
(0.000) 
-0.008 
(0.389) 
-0.003 
(0.624) 
-0.017*** 
(0.000) 
0.022*** 
(0.002) 
 
47,842 
23,921 
0.449 

 

Table 1.7 shows estimates from a Fixed Effects model on the Repeat Sale Sample. Pval in parentheses, *** p<0.01, 
** p<0.05, * p<0.1. 
 
1.6.3  Effects of Fire Over Time 

So far, we have focused on the impacts of fire over space, but it may be of interest to look at 

effects over time.  Prior studies have shown evidence of a decrease in risk salience over time. In the 

wildfire literature, McCoy & Walsh (2018) estimate effects by year since a fire by interacting treatments 

with dummy variables for year. They find evidence that properties on high risk land, but which are far 

enough  away  not  to  receive  visual  disamenities  see  a  short-term  decrease  in  price,  followed  by  a 

recovery by the third year after a fire. On the other hand, they find that properties with a view of a 

burn scar see a decrease in price that remains for at least three years. We adapt their approach to look 

for evidence of diminishing effects over time and expand the original model to include interactions 

with year variables. 

 

38 

+	'56-789:;$%+T'<$-%+,-%U[ln	(A2/0)×	#./0V]$%
W
UXY

!"#$%='(T'+,-%U#./0V$%
W
UXY
+'<$-%56-7[ln(A2/0)×89:;]$%+T'+,-%U56-7[#./0V×89:;]$%
+T'+,-%U56-7<$-%[ln	(A2/0)×#./0V×89:;]$%
	
W
+	'FGHIJ4$%+KLH$G6M,NO$%+K%$PHQ$%+8R+S$%	
UXY

	

W
UXY

	

	

(13) 

	

Table 1.8 presents results from a pooled model with yearly effects as well as the five market 

models. On average we do not find any evidence that the impact of distance from a fire decreases year 

by year - the coefficient on the interaction term Distance x Postfire is significant up to three years 

after a fire. We do see a diminishing effect on FHSZ only; in the first year after a fire, there is a 2.5% 

decrease in price on FHSZ, in the second year, a 1.9% decrease, and in the third year no discernible 

decrease after a fire. An F-test for significant differences in coefficients is unable to reject the null 

hypothesis that the first and second year coefficients are equal, but the second and third year are 

significantly different from each other, as well as the first and third years. This is consistent with the 

McCoy and Walsh finding, and suggests that risk salience from a recent event is greater in the year 

after it than as time passes. However, in the sub-market models we can see that this trend is being 

driven by negative and significant estimates for Orange County, while some estimates in other counties 

are either insignificant or positive. 

 

 

39 

Table 1.8 Effects of Fire Over Time 

 
 

 

Post Year 1 
 
Post Year 2 
 
Post Year 3 
 
Ln(Distance) 
 
FHSZ 
 
Post 1 x FHSZ 
 
Post 2 x FHSZ 
 
Post 3 x FHSZ 
 
Ln(Distance) x FHSZ 
 

 

 

 

(8) 
All Counties 

(9) 
Santa Barbara & 
Ventura 

(10) 
Los Angeles 
Market 

(11) 
Riverside & San 
Bernardino 

(12) 
Orange County 

(13) 
San Diego 

 

0.018*** 
(0.000) 
0.025*** 
(0.000) 
0.040*** 
(0.000) 
-0.009*** 
(0.000) 
0.040*** 
(0.000) 
-0.022* 
(0.068) 
-0.009 
(0.461) 
0.003 
(0.811) 
0.023*** 
(0.000) 

 

 

0.061*** 
(0.000) 
0.072*** 
(0.000) 
0.073*** 
(0.000) 
0.011*** 
(0.000) 
0.037*** 
(0.000) 
-0.058*** 
(0.000) 
-0.067*** 
(0.000) 
-0.076*** 
(0.000) 
-0.006 
(0.117) 

 

 

-0.037*** 
(0.000) 
-0.046*** 
(0.000) 
-0.079*** 
(0.000) 
0.010*** 
(0.000) 
0.015*** 
(0.003) 
0.034*** 
(0.002) 
0.057*** 
(0.000) 
0.073*** 
(0.000) 
-0.006** 
(0.027) 

 

 

0.036*** 
(0.000) 
0.045*** 
(0.000) 
0.039*** 
(0.000) 
0.013*** 
(0.000) 
0.073*** 
(0.000) 
-0.025*** 
(0.000) 
-0.019*** 
(0.000) 
-0.006 
(0.262) 
-0.007*** 
(0.000) 

 

 

 

-0.002 
(0.906) 
0.031** 
(0.034) 
-0.006 
(0.669) 
0.021*** 
(0.001) 
0.043* 
(0.077) 
0.055 
(0.148) 
0.061* 
(0.070) 
0.052 
(0.148) 
0.030 
(0.129) 

 

 

-0.009** 
(0.014) 
-0.007* 
(0.053) 
-0.005 
(0.259) 
-0.006*** 
(0.000) 
0.043*** 
(0.000) 
0.009 
(0.406) 
0.015 
(0.116) 
0.024** 
(0.018) 
0.020*** 
(0.000) 

 

40 

Table 1.8 (cont’d) 

 

Ln(Distance) x Post 1 
 
Ln(Distance) x Post 2 
 
Ln(Distance) x Post 3 
 
Ln(Distance) x Post 1 x 
FHSZ 
 
Ln(Distance) x Post 2 x 
FHSZ 
 
Ln(Distance) x Post 3 x 
FHSZ 
 
Constant 
 
 
Observations 
R-squared 

 

 

-0.010*** 
(0.000) 
-0.011*** 
(0.000) 
-0.010*** 
(0.000) 
0.005 
(0.190) 
0.021*** 
(0.000) 
0.030*** 
(0.000) 
9.555*** 
(0.000) 
 
206,841 
0.830 

 

 

0.004 
(0.699) 
-0.013 
(0.267) 
-0.008 
(0.415) 
-0.012 
(0.682) 
0.005 
(0.834) 
-0.019 
(0.507) 
9.312*** 
(0.000) 
 
6,351 
0.793 

 

 

0.008*** 
(0.002) 
0.019*** 
(0.000) 
0.014*** 
(0.000) 
0.000 
(0.981) 
-0.006 
(0.381) 
-0.016** 
(0.019) 
9.656*** 
(0.000) 
 
61,438 
0.777 

 

 

0.000 
(0.828) 
0.003* 
(0.069) 
0.001 
(0.779) 
0.015 
(0.168) 
-0.020** 
(0.032) 
0.001 
(0.918) 
12.078*** 
(0.000) 
 
67,791 
0.838 

 

 

-0.059*** 
(0.000) 
-0.067*** 
(0.000) 
-0.057*** 
(0.000) 
0.033*** 
(0.000) 
0.046*** 
(0.000) 
0.048*** 
(0.000) 
9.087*** 
(0.000) 
 
31,636 
0.804 

 

 

0.005* 
(0.077) 
-0.005* 
(0.093) 
0.008*** 
(0.005) 
-0.037*** 
(0.000) 
-0.021*** 
(0.001) 
-0.035*** 
(0.000) 
9.315*** 
(0.000) 
 
39,625 
0.783 

 

Table 1.8 shows estimates from an expanded model with interactions with each year since a fire. Overall the results suggest that there is no diminishing effect of 
a fire over time in terms of how it affects distance, but there is some evidence that properties on FHSZ see an immediate decrease in sales price and recovery 
over three years. However, there is a lot of heterogeneity in the results by market. Robust pval in parentheses, *** p<0.01, ** p<0.05, * p<0.1. 

 

 

41 

1.6.4  Heterogeneous Effects by Fire Size 

Most previous literature has focused on estimating impacts of specific fire events (all papers 

prior to 2010 here). With a larger dataset and a wide range of wildfires in the study period, it is possible 

to investigate the potentially different impacts by fire size in acres, which here acts as a proxy for 

severity. A dummy variable for fires greater than 405 hectares (or 1,000 acres) in the Stetler et al. 

Montana study is negative and statistically significant, indicating that larger fires are less desirable than 

more moderately sized ones. In our study area many properties are nearby wildfires much larger than 

1,000 acres; conditional on being 500 acres or more, the average fire size in the sample is 10,000 acres. 

We run additional models splitting the data by properties closest to fires 500-10,000 acres (Medium 

Fires) and properties closest to fires 10,000 acres or more (Large Fires). These results are presented in 

Table 1.9 and Table 1.10. If fires with greater severity serve as larger information shocks, we should 

expect to see a larger impact in the Large Fire model compared to the Medium Fire model. 

In  the  Medium  Fire  model  with  all  counties  the  sign  of  the  coefficient  on  Ln(Distance)  is 

negative and significant; as a house gets farther from an (eventual) fire perimeter, sales price decreases. 

This is the opposite effect than in the model that uses fires 500 acres and above, as well as the large 

fire  model  that  includes  fire  10,000  acres  and  above.  The  coefficient  on  FHSZ  is  positive  and 

significant, as before, and suggests that there are amenities associated with being on otherwise risky 

land (2.6% in the Medium Fire model and 10.5% in the Large Fire model).  

The next two coefficients of interest have opposite signs in the two models. Postfire x FHSZ is 

positive in the Medium Fire model – after a fire, price increases by 1.9% on FHSZ – and negative in 

the Large Fire model – after a fire, price decreases by 6.1% on average.  In the Medium Fire model 

Distance x Postfire has a positive coefficient, meaning increased distance from the fire perimeter 

increases sales price while in the Large Fire model, it is negative and significant, meaning sales price 

decreases as you move farther from the perimeter. 

 

42 

Table 1.9 Medium Fire Size (500-10,000 Acres) 

 
 

 

Postfire 
 
Ln(Fire Dist) 
 
FHSZ 
 
Postfire x FSHZ 
 
Ln(Distance) x FHSZ 
 
Ln(Distance) x Postfire 
 
Ln(Distance) x Postfire x 
FHSZ 
 
Constant 
 
 
Observations 
R-squared 

 

(1) 
All Counties 

(2) 
Santa Barbara 
& Ventura 

(3) 
Los Angeles 

(4) 
Riverside & San 
Bernardino 

(5) 
Orange County  San Diego 

(6) 

 

0.012*** 
(0.000) 
-0.009*** 
(0.000) 
0.026*** 
(0.000) 
0.019*** 
(0.001) 
0.024*** 
(0.000) 
0.004* 
(0.062) 
-0.013*** 

(0.002) 
10.267*** 
(0.000) 
 
80,506 
0.858 

 

 

-0.073*** 
(0.000) 
0.035*** 
(0.000) 
0.049* 
(0.079) 
0.030 
(0.330) 
0.034 
(0.160) 
-0.023** 
(0.043) 
-0.015 

(0.578) 
10.752*** 
(0.000) 
 
3,975 
0.725 

 

 

0.014*** 
(0.010) 
-0.038*** 
(0.000) 
0.039* 
(0.057) 
0.017 
(0.452) 
0.077*** 
(0.000) 
0.020*** 
(0.000) 
-0.079*** 

(0.000) 
9.653*** 
(0.000) 
 
28,978 
0.791 

 

 

-0.012*** 
(0.000) 
-0.026*** 
(0.000) 
0.012 
(0.101) 
0.026*** 
(0.003) 
0.039*** 
(0.000) 
-0.000 
(0.931) 
-0.003 

(0.714) 
10.372*** 
(0.000) 
 
33,191 
0.830 

 

 

-0.007 
(0.535) 
-0.010*** 
(0.007) 
0.017* 
(0.055) 
0.003 
(0.803) 
0.013** 
(0.027) 
-0.008 
(0.105) 
-0.003 

(0.679) 
8.346*** 
(0.000) 
 
12,155 
0.796 

 

 

0.054*** 
(0.001) 
0.018** 
(0.018) 
0.038*** 
(0.000) 
-0.053*** 
(0.000) 
-0.022*** 
(0.004) 
-0.038*** 
(0.000) 
0.037*** 

(0.001) 
9.505*** 
(0.000) 
 
4,418 
0.840 

 

Table 1.9 shows estimates from a model with medium-sized fires (500-10,000 acres) only. Robust pval in parentheses, *** p<0.01, ** p<0.05, * p<0.1. 

 

 

 

43 

Table 1.10 Large Fires (>10,000 Acres) 

 
 

 

Postfire 
 
Ln(Fire Dist) 
 
FHSZ 
 
Postfire x FSHZ 
 
Ln(Distance) x FHSZ 
 
Ln(Distance) x Postfire 
 
Ln(Distance) x Postfire x 
FHSZ 
 
Constant 
 
 
Observations 
R-squared 

 

(1) 
All Counties 

 

0.030*** 
(0.000) 
0.017*** 
(0.000) 
0.105*** 
(0.000) 
-0.061*** 
(0.000) 
-0.011*** 
(0.000) 
-0.015*** 
(0.000) 
0.027*** 

(0.000) 
9.735*** 
(0.000) 
 
126,335 
0.815 

 

(2) 
Northern 
Market 

 

0.053*** 
(0.000) 
0.054*** 
(0.000) 
0.053** 
(0.026) 
0.059** 
(0.033) 
0.028 
(0.176) 
-0.016* 
(0.080) 
-0.002 

(0.921) 
11.616*** 
(0.000) 
 
4,969 
0.822 

 

(3) 
Los Angeles 
Market 

(4) 
Inland Empire 
Market 

(5) 
Orange County 
Market 

(6) 
San Diego 
Market 

 

-0.003 
(0.257) 
-0.008*** 
(0.000) 
0.062*** 
(0.000) 
-0.031*** 
(0.001) 
0.021*** 
(0.000) 
0.011*** 
(0.000) 
0.007 

(0.230) 
9.977*** 
(0.000) 
 
32,460 
0.790 

 

 

0.043*** 
(0.000) 
-0.009*** 
(0.000) 
0.036*** 
(0.000) 
-0.025** 
(0.013) 
0.026*** 
(0.000) 
-0.003** 
(0.039) 
-0.003 

(0.736) 
12.229*** 
(0.000) 
 
58,635 
0.838 

 

 

0.083*** 
(0.000) 
0.017*** 
(0.000) 
-0.003 
(0.891) 
-0.033 
(0.186) 
-0.026*** 
(0.000) 
-0.067*** 
(0.000) 
0.066*** 

(0.000) 
9.423*** 
(0.000) 
 
19,481 
0.824 

 

 

-0.060*** 
(0.000) 
0.003*** 
(0.009) 
-0.010 
(0.206) 
0.072*** 
(0.000) 
0.000 
(0.952) 
0.003 
(0.176) 
-0.045*** 

(0.000) 
9.273*** 
(0.000) 
 
35,207 
0.780 

 

Table 1.10 shows estimates from a model with large-sized fires (10,000 acres or more) only. Robust pval in parentheses, *** p<0.01, ** p<0.05, * p<0.1. 

 

44 

1.7  Discussion and Conclusions 

Previous hedonic literature on the impacts of wildfires finds a consistently negative effect of 

fire on nearby properties, ranging from 7-15% decrease after a fire (Loomis 2004; Stetler et al. 2010; 

McCoy and Walsh 2018). These effects are attributed to both a decrease in amenities – the presence 

of a burn scar or loss of forest recreation opportunity – and an increase in risk perception. Some argue 

that the majority of the effect is a risk salience increase rather than the impact of amenity loss (Stetler 

et al. 2010). However, the literature has tended to focus on regions with low population density and 

infrequent wildfires. Using a richer dataset and longer time frame, our analysis suggests that there is 

no reason to presuppose that all wildfire activity must result in a decrease in housing sales prices nearby 

whether due to risk salience or disamenity. Our conceptual model shows that the effect of a fire should 

depend on the way beliefs about future fire risk are updated after the fire. In contrast to floods or 

hurricanes where an event likely increases perception of future risk, a wildfire does not always indicate 

that future risk of fire will increase if available fuel was burned off. If a wildfire causes a market-wide 

increase in belief that fires will occur in the future, we expect to see a drop in nearby housing prices. 

However, in areas with fire risk priors that are very high, a wildfire may not change or even decrease 

beliefs about future risk. Prior information can come from a variety of sources including fire hazard 

severity zone (FHSZ) status (a public disclosure of risk classification unique to California) or distance 

from  some  physical  barrier  such  as  a  major  highway.  There  is  evidence  that  wildfires  provide 

information to the market: on average, over the full sample of properties, there is a large pre-fire 

premium for properties on land with high physical risk of wildfire which decreases by 2% after a fire. 

Results on the treatment effect of distance to a recent wildfire diverges from the majority of the 

hedonic literature: in most of the estimated models, properties sell for higher prices nearer the fire 

perimeter than farther away. However, this effect varies depending on the sample of properties used. 

We find heterogeneous effects of fire by geographic area – frequently, treatment effects have opposite 

 

45 

signs in Los Angeles and Orange counties – as well as according to the size of the wildfire. We find 

that for the average medium-sized fire (500 – 10,000 acres) proximity to a recent wildfire decreases 

sales price, while for the average larger ones (10,000 acres or more) proximity to a recent wildfire 

increases  sales  price.  This  is  consistent  with  the  result  from  Hansen  and  Naughton  (2013)  who 

hypothesize that larger fires in Alaska opened up views which increased property assessment values 

and that large fires reduce future risk. Finally, we find some evidence that more complete information 

prior to a wildfire has a mitigating impact on the effect, no matter the direction of the effect. The 

interaction of Distance x Postfire x FHSZ is on average in opposite direction of Distance x Postfire, 

suggesting  that  while  proximity  to  a  wildfire  changes  subjective  risk  of  future  fire,  for  properties 

located on FHSZ, subjective risk does not change as much as for properties not on FHSZ. This result 

is  consistent  with  the  hypothesis  that  FHSZ  areas  provide  information  signals  that  mitigate  how 

property markets will react to information signals from new fires. 

The results presented here suggest several directions for future research. With the frequency of 

wildfires increasing, there is a greater need for more comprehensive multi-fire studies with spatial and 

temporal variation in treatment effects. Case studies of small areas or few fires may not provide an 

accurate picture of the average treatment effect of wildfires. Further investigation into the impact that 

fire size, prevalence in the news, and proximity to urban areas have on the treatment effect will allow 

for  better  inference  about  how  future  impacts  of  wildfires  relate  to  these  other  factors  and  offer 

potential  solutions  to  better  match  actual  future  risk  with  perceptions  of  future  risk  –  e.g.  public 

information campaigns, more reliable news coverage, and other avenues of public engagement. More 

studies with larger variation in wildfire size and impacts will also provide better insight into the pattern 

of impacts across fire sizes and specifically whether the result that smaller fires reduce property prices 

while larger ones can increase them holds generally. Future research in California should also consider 

 

46 

that burns scars of large fires may reduce future fire risk but increase risk of other natural disasters 

such as flooding and mudslides.  

Second, there may be potential local policy nuances that could lead to the differing results across 

the  markets.  Fighting  wildland  fires  requires  coordination  from  state,  federal,  and  local  agencies, 

however, it is possible that wildfires indirectly increase local fire department funding. If that is the case 

and residents are aware of funding levels, this dynamic could explain an increase in sales prices after a 

wildfire.  It  is  also  possible  that  areas  newly  classified  as  having  wildland  fire  hazard  similarly  see 

changes to local funding or support for fire departments. For these reasons, future research into the 

effect that wildfires have on local or state-level mitigation strategies such as fire department funding 

or  new  fire  prevention  strategies  (e.g.,  defensible  space  requirements)  would  shed  more  light  on 

geographic differences in the effects of fire. 

Finally, an important direction for future studies is to account for not only heterogeneity in 

wildland fire characteristics but also heterogeneity in indirect preferences of market actors. In southern 

California there are large differences in wealth, demographics, and political views that might affect the 

indirect preferences across the region. Differences in income may affect the hedonic value of amenities 

and  risk,  and  future  work  in  regions  with  major  urban  areas  that  include  both  extremely  wealthy 

residents and less-affluent residents should consider whether people are sorting into many smaller 

hedonic markets.  There may also be significant differences in risk perceptions for other reasons – 

studies on the effect of flooding on housing price has found evidence of significant heterogeneity in 

risk perceptions of future flooding (Bakkensen and Barrage 2018). Future research into wildfire risk 

perceptions should account for heterogeneity in preferences by developing models of sorting behavior 

which may help explain differences in effects of fires across regions.  

 

47 

 

 

 

 

 

 

 

 

 

 

 

 

APPENDICES 

 

 

 

 

 

 

 

 

 

 

 

48 

Appendix 1A. Additional Descriptive Tables 

Table 1.11 Correlation between Geographic Variables 
 

Forest Dist  Park Dist 

Fire Dist 

 

Fire Dist 
Forest Dist 
Park Dist 
Slope 
Elevation 
FHSZ 

 

 

1 
0.4016 
0.0108 
-0.2152 
-0.3349 
-0.2078 

 

 

 
1 
-0.1248 
-0.0263 
-0.4358 
-0.0647 

 

 

 
 
1 
-0.0295 
0.2633 
0.1451 

 

Slope 

 

 
 
 
1 
0.0124 
0.2490 

 

Elev 

 

 
 
 
 
1 
0.0664 

 

FHSZ 

 

 
 
 
 
 
1 

 

 
Table 1.12 Breakdown of Sample Sizes for Moderate, High, & Very High FHSZ Properties 

  
Post 

 

0 
1 

 

 

0 

High 
1 

 

Moderate 

1 

Total 

 

 

0 

 

102,745  1,667  104,412 
99,674 
1,228  100,902 

Total 

0 

 

 

 
 
113,886  1,693  115,579 
   106,651  1,093  107,744 

 

 

 

 

 
  112,182  3,397 
   99,789 
7,955 

 

Total 

 

115,579 
107,744 

Very High 

1 

 

 

 

 

 

 

 

 

 

 

 

Total 

202,419  2,895  205,314 

   220,537  2,786  223,323 

   211,971  11,352  223,323 

 

Table 1.13 Distribution of Distances (in km) to a Barrier Highway 

  

 

All Observations  Between Barrier 

Highway and Forest 

 

2.2E-4 
0.13 
0.34 
3.33 
19.48 
29.93 
41.14 
44,461 

 

 

2.2E-4 
Minimum 
0.15 
1st Percentile 
0.47 
5th Percentile 
Median 
5.80 
95th Percentile  18.87 
99th Percentile  24.58 
41.14 
Maximum 
N 
223,323 

 

 

 

49 

 

 

 

Appendix 1B: Robustness Checks for Essay 1 

Table 1.14 Small Fires (10-500 Acres) 

 

 

Postfire 
 
Ln(Distance) 
 
FHSZ 
 
Postfire x FSHZ 
 
Ln(Distance) x 
FHSZ 
 
Ln(Distance) x 
Postfire 
 
Ln(Distance) x 
Postfire x FHSZ 
 
Constant 
 
 
Observations 
R-squared 

All 
Counties 

 

0.012*** 
(0.000) 
0.006*** 
(0.000) 
0.021*** 
(0.000) 
-0.025*** 
(0.000) 
0.036*** 
(0.000) 
0.001 
(0.482) 
-0.015*** 
(0.000) 
9.780*** 
(0.000) 
 
182,172 
0.845 

Santa 
Barbara & 
Ventura 

 

-0.017* 
(0.078) 
0.021*** 
(0.004) 
-0.004 
(0.819) 
0.024 
(0.210) 
0.012 
(0.535) 
-0.002 
(0.766) 
-0.023 
(0.258) 
10.756*** 
(0.000) 
 
9,467 
0.821 

Los 
Angeles 

 

0.015*** 
(0.000) 
0.008*** 
(0.000) 
0.067*** 
(0.000) 
-0.036*** 
(0.000) 
0.026*** 
(0.000) 
-0.011*** 
(0.000) 
0.019** 
(0.014) 
10.061*** 
(0.000) 
 
60,691 
0.822 

Riverside & 
San 
Bernardino 

 

-0.007*** 
(0.003) 
-0.025*** 
(0.000) 
-0.027*** 
(0.000) 
-0.013** 
(0.026) 
0.030*** 
(0.000) 
0.009*** 
(0.000) 
-0.005 
(0.329) 
10.204*** 
(0.000) 
 
100,286 
0.795 

Orange 
County 

 

0.010 
(0.148) 
0.001 
(0.883) 
0.043*** 
(0.000) 
-0.070*** 
(0.000) 
0.019** 
(0.042) 
-0.003 
(0.531) 
-0.000 
(0.986) 
6.049*** 
(0.000) 
 
22,877 
0.772 

San Diego 

 

0.024*** 
(0.000) 
0.013*** 
(0.000) 
-0.027*** 
(0.001) 
0.009 
(0.421) 
0.004 
(0.505) 
0.003 
(0.469) 
-0.009 
(0.235) 
9.006*** 
(0.000) 
 
15,479 
0.748 

 

 

 

 

 

 

 

Note: this table shows estimates from a model with small-sized fires (less than 500) only using the Estimation Sample 
of properties that sell within three years of a fire. Robust pval in parentheses, *** p<0.01, ** p<0.05, * p<0.1. 

 

50 

Table 1.15 Model using Transactions Five Years Before or After a Fire 

 

All 
Counties 

 
0.030*** 
(0.000) 
0.010*** 
(0.000) 
0.075*** 
(0.000) 
-0.032*** 
(0.000) 
-0.004** 
(0.014) 
-0.012*** 
(0.000) 

 
Postfire 
 
Ln(Distance) 
 
FHSZ 
 
Postfire x 
FSHZ 
 
Ln(Distance) 
x FHSZ 
 
Ln(Distance) 
x Postfire 
 
Ln(Distance) 
x Postfire x 
FHSZ 
 
 
Constant 
 
Observations  331,796 
R-squared 

0.826 

0.022*** 

(0.000) 
9.482*** 
(0.000) 
 

Santa 
Barbara & 
Ventura 
 
0.026*** 
(0.008) 
0.008 
(0.129) 
0.044** 
(0.040) 
0.043* 
(0.070) 
0.030* 
(0.098) 
0.000 
(0.979) 

Los Angeles 

 
-0.010*** 
(0.000) 
-0.011*** 
(0.000) 
0.062*** 
(0.000) 
-0.012 
(0.102) 
0.022*** 
(0.000) 
0.019*** 
(0.000) 

Riverside & 
San 
Bernardino 
 
0.019*** 
(0.000) 
-0.008*** 
(0.000) 
0.037*** 
(0.000) 
-0.017** 
(0.028) 
0.024*** 
(0.000) 
-0.010*** 
(0.000) 

Orange 
County 

 
0.024*** 
(0.000) 
0.009*** 
(0.000) 
0.027*** 
(0.000) 
-0.053*** 
(0.000) 
-0.004 
(0.305) 
-0.044*** 
(0.000) 

San Diego 

 
-0.069*** 
(0.000) 
0.010*** 
(0.000) 
0.031*** 
(0.000) 
0.028*** 
(0.000) 
-0.002 
(0.342) 
-0.003** 
(0.024) 

-0.016 

-0.010** 

-0.001 

0.031*** 

-0.019*** 

(0.432) 
9.480*** 
(0.000) 
 
10,585 
0.787 

(0.036) 
9.616*** 
(0.000) 
 
103,661 
0.772 

(0.862) 
11.837*** 
(0.000) 
 
103,518 
0.821 

(0.000) 
8.562*** 
(0.000) 
 
54,237 
0.799 

(0.000) 
9.255*** 
(0.000) 
 
59,795 
0.776 

Note: This dataset was constructed in the same way as the Estimation Sample but includes all transactions within 
five years of a fire rather than three. Robust pval in parentheses, *** p<0.01, ** p<0.05, * p<0.1. 

 

 

 

 

 

 

51 

Table 1.16 Effects by FHSZ Rating 

 

 

Postfire 
 
Ln(Distance) 
 
Moderate 
 
High 
 
Very High 
 
Postfire x Moderate 
 
Postfire x High 
 
Postfire x Very High 
 
Ln(Distance) x Moderate 
 
Ln(Distance) x High 
 
Ln(Distance) x Very High 
 
Ln(Distance) x Postfire 
 
Ln(Distance) x Postfire x Moderate 
 
Ln(Distance) x Postfire x High 
 
Ln(Distance) x Postfire x Very High 
 
Constant 
 
 
Observations 
R-squared 

 

All Counties 

 

0.041*** 
(0.000) 
0.013*** 
(0.000) 
0.065*** 
(0.000) 
0.015** 
(0.017) 
0.088*** 
(0.000) 
-0.042*** 
(0.000) 
-0.014 
(0.133) 
-0.021*** 
(0.000) 
-0.045*** 
(0.000) 
-0.026*** 
(0.000) 
0.004* 
(0.063) 
-0.011*** 
(0.000) 
-0.013* 
(0.063) 
0.020*** 
(0.008) 
0.012*** 
(0.000) 
9.551*** 
(0.000) 
 
206,841 
0.830 

 

Robust pval in parentheses, *** p<0.01, ** p<0.05, * p<0.1. 

 

 

52 

Table 1.17 Barrier Highway Treatment 

 

 

Postfire 
 
Ln(Distance) 
 
FHSZ 
 
Between 
 
Distance to Highway 
 
Postfire x Between 
 
Ln(Distance) x Between 
 
Ln(Distance) x Between x Postfire 
 
Constant 
 
 
Observations 
R-squared 

 

No Interactions 

Interactions 

 

0.055*** 
(0.000) 
0.012*** 
(0.000) 
0.033*** 
(0.000) 
0.008*** 
(0.003) 
-4.27e-6*** 
(0.000) 
-0.030*** 
(0.000) 
 
 
 
 
9.785*** 
(0.000) 
 
75,302 
0.853 

 

 

0.056*** 
(0.000) 
0.003 
(0.151) 
0.032*** 
(0.922) 
0.00 
(0.028) 
-4.06e-6*** 
(0.000) 
-0.028*** 
(0.000) 
0.016*** 
(0.000) 
-0.011*** 
(0.000) 
9.783*** 
(0.000) 
 
74,830 
0.853 

 

Note: this table shows results from an alternate model using “Between”, meaning between a highway and the forest, 
as an indicator of risk rather than FHSZ. The positive coefficient on Distance x Between implies that price increases 
as you get farther away. Robust pval in parentheses, *** p<0.01, ** p<0.05, * p<0.1.  

 

 

53 

Table 1.18 Models with Properties up to 5 km 

 

 

Postfire 
 
Ln(Distance) 
 
FHSZ 
 
Postfire x FSHZ 
 
Ln(Distance) x 
FHSZ 
 
Ln(Distance) x 
Postfire 
 
Ln(Distance) x 
Postfire x FHSZ 
 
Constant 
 
 
Observations 
R-squared 

 

All 
Counties 

 

0.039*** 
(0.000) 
0.008*** 
(0.000) 
0.070*** 
(0.000) 
-0.017*** 
(0.000) 
0.001 
(0.487) 
-0.007*** 
(0.000) 
0.019*** 
(0.000) 
9.615*** 
(0.000) 
 
150,523 
0.843 

 

Santa 
Barbara & 
Ventura 

 

0.007 
(0.545) 
0.028*** 
(0.000) 
0.064** 
(0.012) 
0.052* 
(0.069) 
0.023 
(0.267) 
-0.020** 
(0.030) 
0.014 
(0.559) 
8.659*** 
(0.000) 
 
5,635 
0.786 

 

Los 
Angeles 

 

-0.011*** 
(0.000) 
-0.008*** 
(0.000) 
0.057*** 
(0.000) 
0.022** 
(0.010) 
0.027*** 
(0.000) 
0.010*** 
(0.000) 
0.008 
(0.175) 
9.757*** 
(0.000) 
 
42,241 
0.784 

Riverside & 
San 
Bernardino 

Orange 
County 

San Diego 

 

0.026*** 
(0.000) 
-0.007*** 
(0.000) 
0.029*** 
(0.000) 
-0.012 
(0.145) 
0.021*** 
(0.000) 
-0.007*** 
(0.000) 
0.001 
(0.850) 
11.948*** 
(0.000) 
 
54,482 
0.846 

 

0.006 
(0.267) 
0.011*** 
(0.000) 
-0.023** 
(0.013) 
-0.014 
(0.192) 
-0.011** 
(0.018) 
-0.027*** 
(0.000) 
0.012* 
(0.055) 
8.479*** 
(0.000) 
 
21,901 
0.807 

 

-0.064*** 
(0.000) 
0.010*** 
(0.000) 
0.005 
(0.341) 
0.038*** 
(0.000) 
-0.002 
(0.419) 
-0.008*** 
(0.000) 
-0.019*** 
(0.000) 
9.258*** 
(0.000) 
 
26,264 
0.788 

 

 

 

 

Note: this table shows results using a dataset constructed in the same way as the Estimation Sample but includes 
properties up to 5 km from a fire only. *** p<0.01, ** p<0.05, * p<0.1.  
 

 

 

54 

Table 1.19 Models with Properties up to 15 km 

All 
Counties 

Santa 
Barbara & 
Ventura 

Los 
Angeles 

Riverside 
& San 
Bernardino 

Orange 
County 

San Diego 

 

 

 

 

 

Postfire 
 
Ln(Distance) 
 
FHSZ 
 
Postfire x FSHZ 
 
Ln(Distance) x FHSZ 
 
Ln(Distance) x 
Postfire 
 
Ln(Distance) x 
Postfire x FHSZ 
 
Constant 
 
 
Observations 
R-squared 

 

 

0.013 
0.041*** 
(0.257) 
(0.000) 
0.023*** 
0.014*** 
(0.000) 
(0.000) 
0.045* 
0.070*** 
(0.000) 
(0.066) 
-0.015***  0.056** 
(0.000) 
(0.047) 
-0.008***  0.025 
(0.207) 
(0.000) 
-0.012*** 
-0.007 
(0.303) 
(0.000) 
0.021*** 
-0.006 
(0.790) 
(0.000) 
9.423*** 
9.654*** 
(0.000) 
(0.000) 
 
 
6,729 
221,870 
0.823 
0.793 

 

-0.005* 
(0.058) 
-0.004*** 
(0.001) 
0.038*** 
(0.000) 
0.014* 
(0.085) 
0.020*** 
(0.000) 
0.011*** 
(0.000) 
-0.004 
(0.524) 
9.906*** 
(0.000) 
 
66,878 
0.778 

-0.057*** 
(0.000) 
0.010*** 
(0.000) 
0.013*** 
(0.008) 

0.030*** 
(0.000) 
-0.009*** 
(0.000) 
0.040*** 
(0.000) 
-0.011 
(0.196) 
0.023*** 
(0.000) 
0.001 
(0.318) 
-0.001 
(0.891) 
12.088***  8.991*** 
(0.000) 
 
67,898 
0.838 

0.092*** 
(0.000) 
0.016*** 
(0.000) 
0.046*** 
(0.000) 
-0.082***  0.053*** 
(0.000) 
(0.000) 
-0.006** 
-0.014*** 
(0.000) 
(0.020) 
-0.074***  0.001 
(0.440) 
(0.000) 
0.059*** 
-0.031*** 
(0.000) 
(0.000) 
9.344*** 
(0.000) 
 
40,439 
0.785 

(0.000) 
 
39,926 
0.816 

 

 

 

 

 

 

 

Note: this table shows results using a dataset constructed in the same way as the Estimation Sample but includes 
properties up to 15 km from a fire. *** p<0.01, ** p<0.05, * p<0.1.  

  

 

 

55 

Table 1.20 Model with Postfire Interacted with 1-km Bins that Measure Distance from Fire 

 

 

All Counties  P-value 

 

-0.037*** 
-0.108*** 
-0.092*** 
-0.090*** 
-0.091*** 
-0.102*** 
-0.104*** 
-0.073*** 
-0.042*** 
-0.025*** 
-0.024*** 
-0.024*** 
-0.012** 
-0.021*** 
-0.027*** 
-0.021*** 
-0.017*** 
-0.004 
-0.016*** 
0.070*** 
0.002 
-0.015*** 
0.000 

Postfire 
0-1 km 
1-2 km 
2-3 km 
3-4 km 
4-5 km 
5-6 km 
6-7 km 
7-8 km 
8-9 km 
Postfire x 0-1 km 
Postfire x 1-2 km 
Postfire x 2-3 km 
Postfire x 3-4 km4 
Postfire x 4-5 km 
Postfire x 5-6 km 
Postfire x 6-7 km 
Postfire x 7-8 km 
Postfire x 8-9 km 
FHSZ 
Ln(Distance) x FHSZ 
Post x FHSZ 
Ln(Distance) x Post 
Ln(Distance) x Post x FHSZ  0.011*** 
9.691*** 
Constant 
 
 
206,841 
Observations 
R-squared 
0.830 

 

 

 

(0.000) 
(0.000) 
(0.000) 
(0.000) 
(0.000) 
(0.000) 
(0.000) 
(0.000) 
(0.000) 
(0.000) 
(0.002) 
(0.000) 
(0.037) 
(0.000) 
(0.000) 
(0.000) 
(0.001) 
(0.487) 
(0.008) 
(0.000) 
(0.342) 
(0.000) 
(0.926) 
(0.000) 
(0.000) 
 
 
 

 

Note: this table presents estimation results from a model where distance from a fire is measured in 1-km bins. We 
use all counties and include both FHSZ and non-FHSZ properties. *** p<0.01, ** p<0.05, * p<0.1.  

 

 

56 

Appendix 1C: Previous Robustness Checks 

Robustness Check 

Note 

Exclude years affected by the housing crisis 
(2007-2009) 

Exclude properties that experience multiple fires 
in the past five years 

This was tested in a previous iteration with 
data on transactions within five years of the 
nearest fire and results were not significantly 
different 

This was tested in a previous iteration with 
data on transactions within five years of the 
nearest fire and results were not significantly 
different 

 

 

 

 

57 

 

 

 

 

 

 

 

 

 

 

 

 

REFERENCES 

 

 

 

 

 

 

 

 

 

 

 

 

 

58 

REFERENCES 

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Dynamics: Going Under Water?”. Cambridge, MA: National Bureau of Economic Research.  

Barro,  Susan  C.,  and  Susan  G.  Conard.  1991.  “Fire  Effects  on  California  Chaparral  Systems:  An 

Overview.” Environment International 17 (2–3): 135–149. 

Bell, Carl E., Joseph M. Ditomaso, and Matthew L. Brooks. 2009. “Invasive Plants and Wildfires in 

Southern California.” University of California ANR Catalog 8397 (August). 

Beron, Kurt J., James C. Murdoch, Mark A. Thayer, and Wim P. M. Vijverberg. 1997. “An Analysis 
of the Housing Market before and after the 1989 Loma Prieta Earthquake.” Land Economics 73 
(1): 101. 

Blackwell,  Jack  A.,  and  Andrea  Tuttle.  2003.  “California  Fire  Siege  2003:  The  Story.”  California 
Service. 

Department  of  Forestry 
http://www.fire.ca.gov/downloads/2003FireStoryInternet.pdf. 

and  Fire  Protection 

and  USDA  Forest 

Brown, Ryan NK, Randall S. Rosenberger, Jeffrey D. Kline, Troy E. Hall, and Mark D. Needham. 
2008. “Visitor Preferences for Managing Wilderness Recreation after Wildfire.” Journal of Forestry 
106 (1): 9–16. 

Brennan,  Deborah  Sullivan.  2013.  “Forests  Healing  Slowly  from  Cedar  Fire.”  San  Diego  Tribune, 

October 27, 2013. 

CAL FIRE, USFS, and OES. “California Fire Siege 2007: An Overview.” 

Champ, Patricia Ann, Geoffrey H. Donovan, and Christopher M. Barth. 2009. “Homebuyers and 

Wildfire Risk: A Colorado Springs Case Study.” Society & Natural Resources 23 (1): 58–70.  

Donovan, Geoffrey H., Patricia A. Champ, and David T. Butry. 2007. “Wildfire Risk and Housing 

Prices: A Case Study from Colorado Springs.” Land Economics 83 (2): 217–233. 

Gawande, Kishore, Hank Jenkins-Smith, and May Yuan. 2013. “The Long-Run Impact of Nuclear 
Waste  Shipments  on  the  Property  Market:  Evidence  from  a  Quasi-Experiment.”  Journal  of 
Environmental Economics and Management 65 (1): 56–73.  

Hallstrom,  Daniel  G.,  and  V.  Kerry  Smith.  2005.  “Market  Responses  to  Hurricanes.”  Journal  of 

Environmental Economics and Management 50 (3): 541–61.  

Hansen, Winslow D., and Helen T. Naughton. 2013. “The Effects of a Spruce Bark Beetle Outbreak 
and Wildfires on Property Values in the Wildland–Urban Interface of South-Central Alaska, 
USA.” Ecological Economics 96 (December): 141–54.  

McCoy, Shawn J., and Randall P. Walsh. 2018. “Wildfire Risk, Salience & Housing Demand.” Journal 

of Environmental Economics and Management, August.  

 

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Muehlenbachs,  Lucija,  Elisheba  Spiller,  and  Christopher  Timmins.  2015.  “The  Housing  Market 

Impacts of Shale Gas Development.” The American Economic Review 105 (12): 3633–3659. 

Westerling, A. L., H. G. Hidalgo, D. R. Cayan, and T. W. Swetnam. 2006. “Warming and Earlier 

Spring Increase Western U.S. Forest Wildfire Activity.” Science 313 (5789): 940–43.  

Westerling, A. L., B. P. Bryant, H. K. Preisler, T. P. Holmes, H. G. Hidalgo, T. Das, and S. R. Shrestha. 
2011. “Climate Change and Growth Scenarios for California Wildfire.” Climatic Change 109 (S1): 
445–63.  

Wolf, David, and H. Allen Klaiber. 2017. “Bloom and Bust: Toxic Algae’s Impact on Nearby Property 

Values.” Ecological Economics 135 (May): 209–21.  

 

 

60 

 Heterogeneous Preferences Over Recreation Sites in Wildfire Prone Areas 

2.1 

Introduction 

Residents and visitors to southern California benefit from ecosystem services provided by four 

major National Forests that surround the Los Angeles Basin – Angeles, Cleveland, Los Padres, and 

San Bernardino National Forests. These forests cover the San Gabriel, San Emigdio, San Jacinto, and 

San Bernardino mountains, that shield the cities from the Mojave Desert. Areas adjacent to national 

forests are pleasant to live in, offering views and solace from the busier urban area. In addition, there 

are many recreation opportunities – trails, picnic areas, fishing, visitor centers, and other attractions 

located in the national forests. This essay examines visitor preferences for the environmental attributes 

of national forest sites, including vegetation, water, and wildfire history. 

Preferences regarding wildfire history are especially relevant for this area, as these forests are 

frequently affected by fire. The four national forests are largely covered by chaparral, a vegetation 

characterized by dense, dry shrubs and grasses, found primarily in southern California and northern 

Mexico, though oak and pine dominate in higher elevations. Chaparral in southern California burns 

every  30  years  or  more  in  high-intensity  stand-replacing  fires  that  play  an  important  part  in 

regeneration (Moritz et al. 2014; Rundel 2018). However, this unique environment is home to millions 

of people in the Los Angeles and San Diego metro areas, whose presence changes the natural fire 

regime. Humans not only suppress or contain natural wildfires, potentially leaving dry fuel to spark 

another, but also cause as many as 84% of all wildfires through negligence or intentional actions (Balch 

et al. 2017). Smaller, less severe forest wildfires may shut down a road for a few days; larger fires can 

cause  mass  devastation.  In  2002,  the  Curve  Fire  destroyed  20,000  acres  of  forest,  and  affected 

campsites were closed for nearly a decade afterward. The 2009 Station Fire burned for over a month 

along the entire Angeles Crest Highway, a major road that cuts from one side of the Angeles National 

 

61 

Forest to the other. Charred trees left in its wake are still visible today in many campgrounds, trails, 

and picnic areas along the highway.  

We use evidence from choice experiments to explore how the visible effects of past wildfires 

might affect recreation decisions by visitors to National Forests, and, given the diverse user groups in 

Southern  California,  we  also  test  for  systematic  differences  in  preferences  for  recreation  sites  in 

wildfire prone areas. The simplest way to estimate preference heterogeneity with discrete choice data 

is to interact demographic variables with choice attributes in a conditional logit model. However, the 

conditional logit model has fairly rigid assumptions about choice behavior, specifically it suffers from 

independence  of  irrelevant  alternatives  (IIA).  In  addition  to  conditional  logit  models,  we  turn  to 

random  parameters  logit  and  latent  class  logit  models  to  relax  the  IIA  assumption  and  explore 

heterogeneity.  

2.2  Literature on Effects of Wildfire on Recreation Demand 

The  earliest  studies  to  consider  the  impact  of  wildfire  on  recreation  tend  to  use  direct 

approaches such as contingent valuation. Vaux, Gardner, and Mills (1984) use contingent valuation to 

estimate willingness to pay for entry to recreation sites recovering from wildfires of varying intensity 

with a group of 69 university students in California. They find that less intense fires have beneficial 

effects, whereas more severe fires decrease willingness to pay for recreation. This result suggests that 

there may be some groups of visitors who prefer sites affected by moderate fires – these visitors could 

be interested in the new growth that occurs after a fire or may be attracted by clearer hiking paths. 

Most of the wildfire valuation literature of the past two decades uses revealed preferences methods to 

estimate recreational welfare impacts of fire and suggests the effects vary significantly over time and 

across recreational groups. 

There is evidence of time-varying impacts of wildfire – in some cases, there are per-trip welfare 

benefits  directly  after  a  fire,  which  then  decline  quickly  before  recovering.  Englin,  Loomis,  and 

 

62 

González-Cabán (2001) estimate an initial sharply positive trip response lasting two years after fires in 

the western US (forests in Colorado, Wyoming, and Idaho), followed by a decline in visitation before 

a final slow recovery in trip numbers. Hilger and Englin (2009) as well as Englin, Holmes, and Lutz 

(2008) affirm this result – a short term increase in trips – using hiking trip data from the Cascade 

Mountains in Washington. However, Boxall and Englin (2008) present conflicting evidence. Using 

pooled RP-SP models, they incorporate correlation between the respondents’ series of choices by 

using dummy variables for lagged choices. In models allowing for state dependence they observe initial 

decreases in visitation, while those without state dependence mimic the short-term increase pattern 

found in other papers.  

Potential  differences  across  user  groups  creates  another  potential  source  of  heterogeneity. 

Loomis, González-Cabán, and Englin (2001) use a count data travel cost model and find that fires do 

not  affect  recreational  values  equally  across  hikers  and  mountain  bikers  in  Colorado.  Trips  by 

mountain bikers are adversely affected by a crown fire in terms of both quantity of trips and the value 

of each trip, while for hikers the number of trips remains steady after a crown fire and per-trip welfare 

increases. Hesseln et al. (2003) use a Poisson count model and combined RP-SP data and find that 

while  demand  by  mountain  bikers  is  nearly  nonexistent  after  a  wildfire,  fire  is  associated  with  a 

decrease in the number of hiking trips but also an increase in per trip net benefits. 

Forest  recreation  studies  have  focused  primarily  on  preference  heterogeneity  across 

management  attributes.  Applying  this  framework  to  wilderness  and  forest  areas,  Boxall  and 

Adamowicz  (2002)  develop  a  latent  class  model  to  explore  preferences  for  wilderness  parks  in 

Manitoba, allowing underlying motivations for wilderness trips as well as sociodemographic factors to 

predict preferences. Their results support significant heterogeneity over preferences for site attributes 

among the park visitors including management attributes. A study of forest users in Great Britain 

found  significant  heterogeneity  both  between  and  within  user  groups  (Christie  et  al.  2007).  More 

 

63 

specialized user groups within each recreation category (mountain bikers are more specialized than 

general bikers) had greater willingness to pay for facilities than general forest users. Nordén et al. 

(2017) also analyze preferences for forest landscapes and facilities across stakeholder groups using 

random parameters models and latent class models, finding significant differences in their preferences 

over forest management practices.  

Comparing separate models for classes of people is informative when there are distinct groups 

of recreational users but ignores other potential sources of heterogeneity and is not ideal in a setting 

where people could participate in many activities on a single trip. At day-use sites in the Angeles 

National Forest, most visitors are hiking, but a large portion of them also participate in other activities 

such  as  relaxing,  picnicking,  or  swimming.  An  alternate  way  of  modeling  heterogeneity  across 

individuals is to use a choice experiment to examine the trade-offs between attributes. In this essay 

we employ a RUM modeling framework that has been frequently used to examine preferences for 

water quality and beach attributes (Beharry-Borg and Scarpa 2010; Kosenius 2010; Schaafsma et al. 

2014; Peng and Oleson 2017). Given the evidence of heterogeneous preferences over site attributes 

in the recreation literature (Beharry-Borg and Scarpa 2010; Kosenius 2010; Scarpa and Thiene 2005; 

Zhang and Sohngen 2018) and in forest management (Christie et al. 2007; Nordén et al 2017; Japelj 

et al. 2016), our discrete choice experiment examines the role of individual preferences over wildfire-

burned areas in forest sites. 

This  essay  has  three  main  contributions:  first,  efforts  to  value  the  effects  of  wildfire  on 

recreation have concentrated on forest areas. Chaparral has a significantly different wildfire regime 

and recovery pattern than conifer or hardwood forests, distinguished by intense crown fires which 

burn everything, but recover quickly. Hence, a fire’s impacts on recreation in a chaparral dominated 

area could look significantly different than in a forested area. Second, the majority of wildfire studies 

occur in sparsely populated areas, whereas our data comes from one of the largest metropolitan areas 

 

64 

in  the  world.  Third,  there  is  little  information  about  systematic  heterogeneity  within  recreationist 

categories with respect to preference over past wildfires. 

2.3.1  Study Area and Onsite Sampling 

2.3 

Survey Data and Design 

The Angeles National Forest spans 700,000 acres of open space only an hour’s drive from 

downtown Los Angeles and receives more than 3 million visits per year (US Forest Service 2001). In 

addition to visitor’s centers and developed recreation areas, it contains all or part of five different 

designated wilderness areas and manages most of the recently established San Gabriel Mountains 

National Monument. Data for this study comes from two onsite intercept surveys with follow-up 

surveys  conducted  in  the  Angeles  National  Forest  during  consecutive  summers.  The  first  onsite 

intercept  survey  was  conducted  June  17  –  August  14,  2016  with  a  follow-up  survey  conducted 

November 2016 – February 2017. The second onsite intercept survey conducted June 16 – August 

20, 2017 with a follow-up survey conducted December 2017 – February 2018. 

For the two intercept surveys we used a random sampling plan which stratified sites according 

to the day of the week and expected use level. Work shifts were drawn throughout the week where 

Friday afternoons and weekends had a higher probability of sampling compared to weekday mornings 

and afternoons, and for each shift two sites were drawn for sampling. Site visitation data from the 

USFS National Visitor Use Monitoring survey (NVUM) was used to classify sites as high or low use 

according to number of visits they generally receive on a weekend. Sites classified as high use were 

over-sampled compared to low-use sites. In 2016 the Angeles National Forest was also being sampled 

by NVUM, so the sites in our sample were also grouped into three geographic clusters. On any given 

day, sampling was only conducted in the geographic clusters without active NVUM enumerators. In 

summer 2017 we sampled at the same set of 39 sites as in 2016, using a similar stratified sampling 

strategy.  

 

65 

National forest visitors were intercepted as they exited the recreation site. At low-traffic sites, 

or where the parking lot was easily monitored, enumerators intercepted people as they approached 

their vehicle for a short questionnaire, while at high-traffic trailheads where that was not possible, 

visitors were intercepted as they existed the trailhead for their vehicles. To ensure a random selection 

of  people,  for  each  vehicle  or  group  of  visitors  the  person  with  the  most  recent  birthday  was 

interviewed. For each shift we recorded all exiting vehicle or foot traffic. 

Onsite  participants  answered  a  short  questionnaire  that  asked  respondents  for  information 

about their current trip: the length of the visit, what activities they participated in, the number of 

people in the vehicle, and some information about who they were – gender, age, and racial identity. 

In addition, all onsite survey respondents were asked to provide an email or mailing address for the 

online survey. Of 2260 completed onsite surveys in 2016, 1755 (77.7%) provided contact information 

– 1685 email addresses and 70 mailing addresses. In 2017, 1726 individuals completed an onsite survey, 

with 1245 (72.1%) providing either an email or mailing address. 

 

 

66 

 

Figure 2.1 Map of Recreation Survey Sites 
 
2.3.2  Online Survey and Choice Experiment Design 

The survey was designed in three stages. Forty-nine in-person semi-structured interviews were 

conducted at recreation sites in July 2015, some of which test our intercept instrument and some of 

which probed people on their recreation habits and what they might do if a fire occurred nearby. 

Choice experiment questions were further tested in-person using paper survey instruments followed 

by cognitive interviews with 15-20 people at several sites in the Angeles National Forest (ANF) in 

May 2016. In October and November of 2016, the instrument was tested online in a webinar setting 

 

67 

in a series of four individual cognitive interviews with people who had been intercepted at a site in the 

ANF previously and provided an email address. The four major sections of the survey are as follows: 

 Section  1  primes  respondents  on  the  attributes  they  faced  choices  over  in  the  choice 

experiment.  Attributes  and  levels  are  in  Table  2.1.  Respondents  were  also  asked  to  think  about 

attributes located “nearby” and “farther away” from the parking area: nearby is within a 5-minute walk 

from the parking area, and farther away is between 5 and 60 minutes away from the parking area. 

Figure 2.2 was used to illustrate the nearby and farther away areas. This allows us to capture differences 

in  preferences  for  attributes  by  distance  for  people  who  may  engage  in  different  activities,  e.g. 

picnicking vs. hiking. Section 2 consists of information designed to introduce the choice attributes 

including vegetation types and fire effects followed by the stated preference questions. Section 3 asks 

about respondents’ habits regarding national forest visits as well as how they receive information about 

fires and site closures, and additional demographic information was collected in Section 4. 

 

Figure 2.2 Illustration Depicting "Nearby" and "Farther Away" from Parking Area 

 

 

 

68 

Respondents  from  the  onsite  survey  ranged  from  people  living  in  nearby  communities  to 

international  visitors.  To  ensure  that  they  saw  realistic  choices  in  the  online  survey,  the  choice 

experiment section was tailored to respondents according to the distance between their home zip code 

and a mid-point in the Angeles National Forest. The survey attribute levels and combinations were 

altered between 2016 and 2017 to allow for a greater spread in the distance variable and to increase 

the D-efficiency of the design. All other attribute levels and elements of the survey were the same. 

In 2016 (Round 1) respondents were categorized into four origin distance zones, (1) less than 

60 miles, (2) 60-150 miles, (3) 150-300 miles, and (4) over 300 miles. Respondents in zones 1, 2, and 

3 saw different distances from home in their options, tailored to their distance from ANF. Those in 

bin 4, living more than 300 miles away from the Angeles National Forest, received a version of the 

survey without choice experiment questions.  

Three choice sets were shown to each respondent, and the overall design was grouped into 12 

blocks of 3 questions each. In each of three scenarios they faced, respondents were asked to choose 

between two unlabeled National Forest sites to visit. These sites varied according to a) vegetation 

nearby and farther away from the parking area, b) presence of lakes or streams nearby and farther 

away from the parking area, c) fire history farther away,9 and d) driving distance from home. Choice 

experiment attributes and levels are in Table 2.1, and an example of a question format is found in 

Figure 2.3. As shown in Table 2.1, driving distance from home is equal to baseline miles (ranging from 

0 to 60) plus 20 if the respondent was in zone 1, plus 60 if in zone 2, and plus 120 if in zone 3. 

The relevant choice experiment elements that vary by survey version are: choice set block and 

distance bin. There are 36 combinations of block and bin. In 2016, each survey version was also 

                                                

9 The survey stated that the sites we were asking about “are safe” and “have no history of fire near the parking 

area.” This was done to alleviate safety concerns that arose during pre-testing.  

 

69 

available in Spanish. Respondents in 2017 (Round 2) were also categorized into four distance zones, 

(1) less than 50 miles, (2) 50-100 miles, (3) 100-300 miles, and (4) over 300 miles. Again, those in the 

first three zones see site choices with different distances, while those in zone 4, living more than 300 

miles away from the Angeles National Forest, received a version of the survey without the choice 

experiment.  In 2017 the Spanish version of the questions were not offered because only 14 people 

opted to complete the 2016 survey in Spanish. As shown in Table 2.1, for 2017 the baseline miles used 

for the driving distance attribute was given a greater spread, ranging from 0 to 100, plus 10 if the 

respondent was in zone 1, plus 50 if in zone 2, and plus 100 if in zone 3. Round 2 choice sets were 

grouped into 14 blocks of three questions each, resulting in 42 survey versions for the combinations 

of choice set blocks and distance zones. 

In both 2016 and 2017, NGene software (ChoiceMetrics 2014) was used to develop the attribute 

combinations using a design to minimize D-error subject to constraints on the feasible combinations 

of attributes.  The feasibility constraints ensured the types of fire were consistent with the types of 

vegetation.    For  example,  since  shrubs  recover  quickly  and  effects  of  a  fire  that  burned  some 

vegetation would be hard to see, we ruled out an “old” fire if the vegetation was shrubs. Likewise, the 

fire type could not be a recent shrub fire if the vegetation near and far was trees. 

 

 

70 

Table 2.1 Attributes and their Levels in 2016 and 2017 

Attributes 

 

Plants 
 
 
 

 

Lakes or streams 
 
 
 
Fire history farther away (over a 5-minute 
walk) 
 
 
 
 
One-way driving distance from home  
(miles) 2016 survey 
 
 
One-way driving distance from home  
(miles) 2017 survey 
 
 

 

 

 

Levels 

 

Trees nearby, trees farther away 
Trees nearby, shrubs farther away 
Shrubs nearby, trees farther away 
Shrubs nearby, shrubs farther away 

 

 

Some nearby, some farther away 
Some nearby, none farther away 
None nearby, some farther away 
None nearby, none farther away 
Old forest fire that burned all plants (some new 
grass and plants) 
Recent forest fire that burned some plants  
Recent forest fire that burned all plants 
Recent shrub fire (some new grass and plants) 
None visible 

 

Zone 1: 20,   30,   40,   60 ,  80 
Zone 2: 60,   70,   80 ,  100, 120 
Zone 3: 120, 130, 140, 160, 180 

 

Zone 1: 10,   30,   50,   80,   110       
Zone 2: 50,   70,   90,   120, 160 
Zone 3: 100, 120, 140, 170,  200  

 

 

Table 2.1 displays choice experiment attributes and levels for 2016 and 2017. The only difference between the two 
rounds of the survey were in the driving distance levels.  

 

 

71 

 

Figure 2.3 Choice Experiment Question Format 

 
For the online survey, 1755 people total were contacted by email or by mail in Round 1, which 

ran  November  2016  to  January  2017:  of  those,  1685  were  email  addresses,  and  70  were  mailing 

addresses. In Round 2, running from November 2017 to February 2018, 1244 individuals, 1220 by 

email and 24 by mail. Overall 1054 (35%) responded to both rounds of the survey, 662 (38%) in 

Round 1 and 392 (32%) in Round 2; 607 of whom saw the choice experiment.  

2.4  Econometric Models 

The standard framework for analyzing choice experiment data is based on random utility theory 

(McFadden  1973).  We  assume  that  the  utility  for  an  individual  facing  a  choice  is  made  of  a 

 

72 

deterministic component and a random component. The utility function for individual i with option j 

!"#=%&"#+ e"# 

 

Where the observable component %&"# depends on preference parameters % and a vector of 
attributes &"#, and e"# is the random or unobservable component. Therefore, the probability that we 
available choice set C:  ((*)=((%&"#+ e"#>%&"-+ e"-)	∀012 

observe individual i select site j is the probability that the utility from site j was the greatest in the 

(2) 

(1) 

 

 

 

When the random error follows a type I extreme value distribution, the probability of observing choice 

is:  

j is: 

 

((*)= 345(%&)
∑ 345(%&-)
-

Estimating  this  model  with  a  common  parameter  vector %  for  the  population  leads  to  the 

(3) 

 

 

conditional logit model. However, given results from prior studies showing that groups of visitors 

have differing responses to fire damage, we expect to find evidence of preference heterogeneity, and 

turn  to  more  flexible  forms.  Three  ways  of  modeling  heterogeneity  in  preferences  are  explored: 

introducing demographic interaction terms with the preference parameters within conditional logit; 

random parameters logit models, which assume a continuous distribution of preference parameters 

%" throughout the population; and latent class models, also called finite mixing models, which assume 

there are discrete groups of preference parameters within the population. 

The probability of observing choice j in a random parameters set-up is:  

((*)= 3457%"&#8
∑ 345(%"&-)
-

 

 

 

73 

(4) 

 

Here, the %" is distributed across the population. The difference in estimation between the random 
%9 while random parameters logit estimates a mean and standard deviation for %9" where i = 1, …, I. 

parameters logit and conditional logit is that the conditional logit model estimates a population average 

Although these models allow for preference heterogeneity, they do not lend themselves to explaining 

the types of people with different preferences (Boxall & Adamowicz 2002).  To address this, we also 

consider latent class models, which assume that preferences systematically vary across classes that, to 

the researcher, are unobservable. The probability that an individual belongs to a certain class depends 

on  demographics  and  other  respondent  characteristics  such  as  attitudes  towards  the  good  being 

evaluated. The choice probability is then defined as the joint probability of observing a choice and the 

probability of belonging to a class. Suppose individual i belongs to class s in the set of classes S. Then 

the probability of observing choice j is dependent on class membership: 

((site *|class :)= 3457%;&#8
∑ 345(%;&-)
-

 

(5) 

 

 

 

Within class s, the choice probability typically follows a conditional logit. Following Swait (1994) 

and Boxall and Adamowicz (2002), we assume there is an unobservable class-membership function, 

<";∗=>;?"+@"; 

where sociodemographic characteristics predict class membership, 

where <";∗   is  the  class  membership  latent  variable  for  individual  i  in  class  s, ?"  are  demographic 
characteristics, >;  are  parameters  to  be  estimated,  and @";  is  a  random  error  term.  Assuming  the 

(6) 

 

random error follows a type-I extreme value distribution and is independent across individuals and 

classes, the probability of class membership is 

((:)= 345(>;?")
∑345(>;?")
;

 

(7) 

 

 

 

74 

Since the choice experiment asked respondents to make tradeoffs between site attributes and 

distance, marginal rates of substitution estimates are presented as willingness to drive and estimated 

as the negative of the ratio between the driving distance parameter, %A, and the site attribute parameter, 
%-. For the conditional logit where the average coefficient is estimated, the willingness to drive for 

attribute k estimate is: 

 

BCD"=−%-%A 

(8) 

 

2.5  Results 

Results use data collected from the onsite surveys conducted in 2016 and 2017 and the online 

surveys conducted winter 2016-2017 and winter 2017-2018. This section describes the demographics 

of the choice experiment respondents used in the analyses, and results from conditional logit, random 

parameters logit, and latent class models. 

2.5.1  Sample Characteristics  

Summary statistics for respondents who received a choice experiment are in Table 2.2 below. 

Respondents were around forty years old on average. One third of respondents were female, and two-

thirds male. They tended to be well off, with more than half of respondents having annual household 

incomes of $75,000 or more. The largest minority group to respond were Hispanics or Latinos (24% 

in Round 1 and 30% in Round 2) followed by Asians (16%). Most respondents cited their main activity 

as hiking or walking – roughly 75% – while another 8-9% were picnicking or relaxing. Many of them 

are regular forest visitors: 23% visited 11-25 times in the past two years, and 33% visited more than 

25 times in the past two years. 

The respondents were asked to rate how important certain site attributes are to their site choice 

prior to completing the choice experiment. Results from these attitudinal questions show that most 

 

75 

people agreed that the presence of water and plant type at recreation sites affects their decision to 

visit. However, they were split on whether the presence of burned vegetation affects their decision; 

32% strongly disagreed or somewhat disagreed, 34% were neutral, and the last 34% somewhat agreed 

or strongly agreed—evidence of substantial heterogeneity. A majority were neutral or not concerned 

about safety or air quality at sites with visible fire damage. The majority also did not have experience 

with wildfires affecting their planned forest visits; 58% had never cancelled a forest visit because of 

an ongoing wildfire. In the extended models we explore whether experience with fire significantly 

affects preferences for fire history attributes. 

 

 

 

76 

Table 2.2 Summary Statistics for Choice Experiment Respondents 

 
 

 

Demographics 
 
 
 
 
 
 
 
 
Experience with 
site closure 

 

 
Variable 

 

Age 
Has children 
College degree 
Employed full time 
Gender 
Hispanic 
Asian 
White 
Income ($1000s) 

 

Experience 

Mean 

 

41 
0.30 
0.67 
0.63 
0.67 
0.27 
0.16 
0.57 
101 

 

0.83 

 

Likert (1/5) 

 

 

 
 
 
Main activity 
 

 

 

 

2.9 

2.7 

Air quality affects decision-
making 
Presence of burned plants 
affects decision-making 
Vegetation type affects 
decision-making 
Safety concerns affect 
2.4 
decision-making 
Water affects decision-making  3.6 
Wildfires are natural 
4.3 

3.2 

 

Hiking 
Relaxing / Picnicking 

 

0.72 
0.08 

Choice Experiment Sample 

Std dev  Min 

Max 

 

15 
0.46 
0.47 
0.48 
0.47 
0.45 
0.37 
0.49 
67.5 

 

0.38 

 

1.3 

1.1 

1.1 

1.3 
1.1 
1.0 

 

0.45 
0.27 

 

18 
0 
0 
0 
0 
0 
0 
0 
12.5 

 

0 

 

1 

1 

1 

1 
1 
1 

 

0 
0 

 

87 
1 
1 
1 
1 
1 
1 
1 
250 

 

1 

 

5 

5 

5 

5 
5 
5 

 

1 
1 

Table 2.2 describes the sample of respondents used in the choice experiment analysis. Annual household income is 
converted to a continuous measure using midpoints of the following categories: Less than $25,000; $25,000-49,999; 
$50,000-74,999;  $75,000-99,999;  $100,000-149,999;  $150,000-199,999;  Over  $200,000  (coded  as  $250,000). 
Experience means they indicated that they had altered or cancelled a trip due to concerns about site closure or health, 
or that they experienced actual site closure due to fire.  
 
2.5.2  Conditional Logit Models 

Table 2.3 shows the results of the conditional logit model. The conditional logit model correctly 

predicts the preferred alternative about 70% of the time using the option with the largest probability 

as the prediction criteria. The conditional logit coefficients for all the site attributes have the expected 

 

77 

sign, with trees being preferred vegetation over shrubs, water is a positive attribute, and fire damage a 

negative  attribute  in  general.  The  omitted  vegetation  attribute  level  is  “shrubs  nearby  and  shrubs 

farther away” – the results clearly show a strong preference for tree cover, especially locations with 

trees both nearby and farther away. Similarly, compared to sites with no water nearby, sites with lakes 

or streams were preferred, with the largest coefficient on the attribute for water both nearby and 

farther away. The fire history attributes are more mixed. Though all the coefficients are negative and 

significant at the 10% level, there is less strong evidence for the parameters on types of fires where 

some vegetation may be recovering (old forest fires and recent shrub fires). There is much stronger 

evidence that recent forest fires are undesirable. 

Three  additional  models  introduce  heterogeneity  in  the  conditional  logit  by  interacting 

individual  characteristics  with  site  attributes.  Conditional  logit  models  with  interaction  terms  are 

presented in Table 2.4. Model 2 includes the interaction of income10 with distance; Model 3 interacts 

all fire attributes with a dummy variable for experience with fire; and Model 4 interacts all fire attributes 

with a dummy variable for Hispanic. Estimates indicate neither income nor experience with decision-

making over fire-affected sites contributes to heterogeneity. Although the interaction was insignificant, 

the model fit criteria AIC and BIC as well as the log likelihood suggest that Model 2 which included 

an interaction between driving distance and income is a better fit for the data than the conditional 

logit with no interactions. However, there is evidence that on average Hispanic respondents have a 

lower preference for sites where water is only available farther away, and that they have a higher 

preference for trees nearby. In net, recent shrub fires at recreation sites do not matter as much to 

Hispanic respondents; a linear test of the hypothesis that the sum of the coefficients on recent shrub 

fire and the interaction are equal to zero is insignificant. Forest managers in Southern California are 

                                                

10 In the interaction term, income was re-scaled to $100,000s 

 

78 

interested  in  expanding  outdoor  access  to  underserved  minority  populations.  Our  results  suggest 

minority populations could recreate in a significantly different way than other forest users.  

 

Table 2.3 Conditional Logit Model Parameter Estimates 

Attribute 

Level 

 

 

Shrubs near, trees far 
 
Trees near, shrubs far 
 
Trees near, trees far 
 
None near, some far 
 
Some near, none far 
 
Some near, some far 
 

Vegetation 
 
 
 
 
 
Water 
 
 
 
 
 
Fire History (farther away)  Old forest fire that burned all plants 
 
 
 
 
 
 
 
Driving Distance (one-way)  Distance 
 
 
Observations 
AIC 
BIC 
Log Likelihood 

 
Recent forest fire that burned all plants 
 
Recent forest fire that burned some plants 
 
Recent shrub fire 
 

 
 
 
 
 
 

 

 
 

 

 

P-values in parentheses: *** p<0.01, ** p<0.05, * p<0.1 

 

79 

Model 1 

 

0.670*** 
(0.000) 
0.646*** 
(0.000) 
1.149*** 
(0.000) 
1.032*** 
(0.000) 
1.014*** 
(0.000) 
1.405*** 
(0.000) 
-0.194* 
(0.057) 
-1.054*** 
(0.000) 
-0.341*** 
(0.001) 
-0.178* 
(0.055) 
-0.014*** 
(0.000) 
 
4,968 
3069.75 
3141.37 
-1523.88 

 

Table 2.4 Conditional Logit Model with Interactions 

Attribute 

 

Vegetation 
 
 
 
 
 
Water 
 
 
 
 
 
Fire History (farther 
away) 
 
 
 
 
 
 
 
Driving distance 
(one-way) 
 
Income x Distance 
 
Experience x Fire 
 
 
 
 
 
 
 

 

 

Level 

 

Model 2  Model 3  Model 4 

 

0.726*** 
Shrubs near, trees far 
(0.000) 
 
0.682*** 
Trees near, shrubs far 
(0.000) 
 
1.209*** 
Trees near, trees far 
(0.000) 
 
1.048*** 
None near, some far 
(0.000) 
 
1.046*** 
Some near, none far 
(0.000) 
 
1.510*** 
Some near, some far 
 
(0.000) 
Old forest fire that burned all plants  -0.173 
(0.120) 
 
Recent forest fire that burned all 
-1.104*** 
plants 
(0.000) 
 
Recent forest fire that burned some 
-0.344*** 
plants 
(0.002) 
 
-0.167* 
Recent shrub fire 
 
(0.095) 
-0.013*** 
Distance 
(0.000) 
 
Income by distance 
-0.003 
(0.176) 
 
 
Old forest fire that burned all plants 
 
 
Recent forest fire that burned all 
 
plants 
 
 
Recent forest fire that burned some 
 
plants 
 
 
Recent shrub fire 
 
 
 

 

0.672*** 
(0.000) 
0.653*** 
(0.000) 
1.152*** 
(0.000) 
1.035*** 
(0.000) 
1.021*** 
(0.000) 
1.414*** 
(0.000) 
-0.091 
(0.650) 
-0.848*** 
(0.000) 
-0.283 
(0.146) 
-0.393* 
(0.064) 
-0.015*** 
(0.000) 
 
 
-0.132 
(0.540) 
-0.256 
(0.240) 
-0.078 
(0.707) 
0.263 
(0.248) 

 

0.612*** 
(0.000) 
0.555*** 
(0.000) 
1.089*** 
(0.000) 
1.126*** 
(0.000) 
1.025*** 
(0.000) 
1.437*** 
(0.000) 
-0.112 
(0.346) 
-1.146*** 
(0.000) 
-0.367*** 
(0.002) 
-0.281*** 
(0.009) 
-0.015*** 
(0.000) 
 
 
 
 
 
 
 
 
 
 

 

 

 

 

80 

Table 2.4 (cont’d) 

Attribute 

Level 

Model 2  Model 3  Model 4 

 

 

Shrubs near, trees far 
 
Trees near, shrubs far 
 
Trees near, trees far 
 
None near, some far 
 
Some near, none far 
 
Some near, some far 
 
Old forest fire that burned all plants 
 
Recent forest fire that burned all 
plants 
 
Recent forest fire that burned some 
plants 
 
Recent shrub fire 
 

Hispanic x Veg 
 
 
 
 
 
Hispanic x Water 
 
 
 
 
 
Hispanic x Fire 
 
 
 
 
 
 
 
Hispanic x Distance  Distance 
 
 
Observations 
AIC 
BIC 
Log Likelihood 

 
 
 
 
 
 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
4,290 
2623.00 
2699.36 
-1299.50 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
4,968 
3073.86 
3171.52 
-1521.93 

 

0.262 
(0.383) 
0.412* 
(0.087) 
0.259 
(0.427) 
-0.398** 
(0.041) 
0.097 
(0.671) 
-0.033 
(0.892) 
-0.313 
(0.182) 
0.325 
(0.214) 
0.161 
(0.538) 
0.393* 
(0.070) 
0.001 
(0.802) 
 
4,938 
3044.89 
3187.99 
-1500.44 

 

 

 

 

 

Table 2.4 shows parameter estimates from conditional logit models with interactions. Model 2 includes an interaction 
between distance and income; Model 3 includes interactions between dummy variables for experience with fire-affected 
sites and fire attributes; and Model 4 includes interactions of all attributes with an indicator variable for whether the 
respondent is Hispanic. where site choice is determined by the attributes of the sites. Standard errors are clustered at the 
individual level. P-values in parentheses: *** p<0.01, ** p<0.05, * p<0.1 
 

 

 

 

81 

2.5.3  Random Parameters Logit Model 

The random parameters logit model allows for taste heterogeneity by assuming a continuous 

distribution of parameters across the population. In the specification used, vegetation, water, and fire 

attributes are assumed to have a normal distribution. Use of a normal distribution allows for the fact 

that any attribute could be positive or negative to different people. We expect that for the vegetation 

and water attributes, there may be some people who care more strongly about tree cover or bodies of 

water  nearby  and  others  who  care  more  strongly  about  having  those  attributes  farther  away.  In 

addition, in pre-testing, some respondents indicated an interest in recreation sites with visible fire 

effects, suggesting there could be heterogeneity in preferences for sites with fire history. 

Model  5  assumes  that  all  site  attributes  (vegetation,  water,  and  fire  history)  are  randomly 

distributed in the population and independent from each other, while preferences for driving distance 

are fixed. Table 2.5 reports coefficients and standard errors for the random parameters. Because we 

observe repeated choices by individuals, the model was estimated as a panel. In Model 6, we assume 

preferences for water are also fixed in the population but allow preferences for vegetation and fire 

history to be randomly distributed and correlated with each other. Table 2.5 also reports coefficient 

estimates for the correlated model, and the covariance matrix between correlated random attributes is 

found in the appendix. Although a joint significance test of the off-diagonal elements is significant at 

the  1%  level,  only  two  attributes  have  significant  covariance  variation  between  their  preference 

distributions at the 10% level. Preferences for trees nearby and trees farther away are significantly 

positively correlated with preferences for trees nearby and shrubs farther away. Preferences for recent 

shrub fire and recent forest fire that burned some plants are also significantly positively correlated 

with each other – these two fires are likely both thought of as less severe than a forest fire that burns 

all plants, but because they are recent, still have some significant impact on the landscape. Overall the 

random parameters logit models suggest that not only are preferences over fire history heterogeneous, 

 

82 

but the standard deviations are large compared to the coefficient, which indicates that there are visitors 

for whom signs of a previous fire are a positive attribute. 

 

 

83 

Table 2.5 Random Parameters Logit Models with and without Correlation between Attributes 

 
Attribute 

 

Vegetation 
 
 
 
 
 
Water 
 
 
 
 
 
Fire History 
(farther away) 
 
 
 
 
 
 
 
Driving 
Distance (one-
way) 
 
 
Observations 
AIC 
BIC 
Log Likelihood 
Correlation 

 

 
Level 

 

Shrubs near, trees far 
 
Trees near, shrubs far 
 
Trees near, trees far 
 
None near, some far 
 
Some near, none far 
 
Some near, some far 
 
Old forest fire that 
burned all plants 
 
Recent forest fire that 
burned all plants 
 
Recent forest fire that 
burned some plants 
 
Recent shrub fire 
 

Distance 

 
 
 
 
 
 
 

 

Model 5 

Std. Dev. 

Coef. 

Model 6 

Std. Dev. 

Coef. 

 

0.879*** 
(0.000) 
0.891*** 
(0. 000) 
1.559*** 
(0. 000) 
1.425*** 
(0. 000) 
1.396*** 
(0. 000) 
1.959*** 
(0. 000) 
-0.248* 
(0. 074) 
-1.432*** 
(0. 000) 
-0.465*** 
(0. 000) 
-0.280** 
(0. 033) 

-0.020*** 

(0.000) 
 
4,968 
3060.11 
3196.83 
-1509.05 
No 

 

 

0.378 
(0.362) 
1.047*** 
(0.290) 
0.865*** 
(0.227) 
-0.213 
(0.365) 
0.397 
(0.365) 
0.541 
(0.381) 
0.825*** 
(0.277) 
-1.044*** 
(0.303) 
1.013*** 
(0.331) 
0.863** 
(0.370) 

 

 
 
 

 

 

 
 
 

 

1.020*** 
(0.000) 
1.018*** 
(0.000) 
1.816*** 
(0.000) 
1.609*** 
(0.000) 
1.603*** 
(0.737) 
2.219*** 
(0.000) 
-0.321** 
(0.034) 
-1.702*** 
(0.000) 
-0.617*** 
(0.001) 
-0.289* 
(0.073) 

-0.022*** 

(0.010) 
 
4,968 
3073.86 
3327.78 
-1497.93 
Yes 

 

 

0.267 
(0.483) 
1.527*** 
(0.000) 
1.324*** 
(0.000) 
 
 
 
 
 
 
0.574* 
(0.050) 
1.581*** 
(0.000) 
1.592*** 
(0.000) 
1.494*** 
(0.000) 

 

 
 
 
 
 
 
 

 

Note: Model 5 allows vegetation, water, and fire history parameters to be randomly distributed in the population. Model 
6 only allows vegetation and fire history to be randomly distributed, and also allows the random parameters to be correlated 
with  each  other.  Coefficient  and  p-values  are  shown  here,  and  variance-covariance  matrix  estimates  for  the  random 
parameters shown in the appendix. *** p<0.01, ** p<0.05, * p<0.1 

 

 

 

84 

2.5.4  Latent Class Models 

If preferences are not continuously distributed across individuals but characterized by discrete 

classes of people with similar average preferences within classes, latent class models may be a better 

fit. An advantage of latent class models is that they allow class membership to be determined by 

demographic variables, which can help with understanding drivers of preferences among forest users. 

The specification in Model 7 allows children (binary), income (continuous), and Hispanic (binary) to 

determine  class  membership.  The  log-likelihood  of  the  children,  income,  and  Hispanic  model 

improved significantly compared to a model with no demographics. However, models with more 

demographic variables such as gender and age performed poorly (singular variance matrix) or offered 

little improvement to the selected model. All latent class models are estimated using the expectation 

maximization algorithm (Pacifico and Yoo 2013). 

When estimating latent class models, it is also necessary to determine the number of classes 

estimated. Because likelihood ratio tests are not possible with non-nested models, information criteria 

such as the AIC, CAIC, and BIC are frequently used in model selection (Dimitropoulos et al. 2016; 

Kermagoret et al. 2016; Von Haefen and Domanski 2018). Simulation studies have found that more 

parsimonious criteria such as CAIC, BIC, and bootstrapped LR test outperform AIC in selecting the 

true model (Tein et al. 2013). Using both the CAIC and BIC as model selection criteria, we prefer 

two-class models after testing the performance of 2, 3, 4, and 5-class models. Both information criteria 

also suggest an improvement over the conditional logit model. Table 2.6 shows a comparison of results 

for different numbers of classes in the latent class model. 

 

 

 

 

85 

Table 2.6 Comparison of results for different number of latent classes 

Number of classes 

Log-likelihood (LL)  Number of parameters 

CAIC 

 

2 
3 
4 
5 
6 
7 

 

 

 

-1250.385 
-1237.862 
-1208.098 
-1189.758 
-1179.217 
-1174.698 

 

 

26 
41 
56 
71 
86 
101 

 

 

2697.576 
2786.073 
2840.087 
2916.948 
3009.409 
3113.913 

 

BIC 

 

2671.576 
2745.073 
2784.087 
2845.948 
2923.409 
3012.913 

 

Table 2.7 shows results from the 2-class latent class model that uses children, income, and 

Hispanic in the class membership equations. The prior probabilities of class membership predict that 

90% of respondents are in Class 1, while 10% of respondents are in Class 2. Parameter estimates for 

respondents in Class 1 are similar to those in the conditional logit and random parameters models 

with positive preferences for trees and water and recreation sites, and negative preferences for recent 

forest fires. The two fire attributes significant at the 10% level are a recent forest fire that burned some 

plants  and  a  recent  forest  fire  that  burned  all  plants.  The  coefficients  on  the  socio-demographic 

variables are standardized to zero in a reference class (Class 2), indicating that those with a higher 

annual household income are less likely to be in Class 1 compared to Class 2, and those with children 

are more likely to be in Class 1 than Class 2. 

In the second class of respondents they also have a significant, negative probability of choosing 

a recreation site with a recent forest fire that burned all plants. However, of all the environmental 

attributes, vegetation, water, and past fires, that was the only significant attribute level. In both Class 

1 and Class 2 the driving distance attribute is negative and significant. Those without children and 

with a higher annual household income are more likely to be in Class 2 than in Class 1, where the only 

characteristics influencing decisions are distance and a severe recent fire. This subset of visitors might 

be driving the large amounts of heterogeneity seen in the RPL results. 

 

86 

Two groups of people are likely to be of interest to forest managers in the national forests 

around  southern  California:  the  Angeles  National  Forest  is  one  of  the  most  important  outdoor 

recreation areas for the city of Los Angeles, whose population is half Hispanic. However, minorities 

are traditionally underrepresented among outdoor recreation visitors (Flores et al. 2018). In keeping 

with other literature which examines heterogeneity by activity group, we also include a dummy variable 

for hiking equal to one if the visitor cited hiking as their main activity. The two-class latent class model 

with Hispanic and Hiker determining class membership is reported in Table 2.8. The model results 

show  that  Hispanic  respondents  are  significantly  more  likely  to  be  in  Class  2  than  Class  1.  The 

preferences in Class 2 are fairly consistent with results from Model 4 (conditional logit with Hispanic 

interacted with site attributes). In general, individuals in Class 2 are less sensitive to driving distance 

than those in Class 1, although it is still negative and significant. They have stronger preferences for 

trees as opposed to shrubs, and for water at the site. Compared to people in Class 1, for whom all 

recent fires have negative and significant coefficients, people in Class 2 are less sensitive to fire. The 

only fire type with a significant coefficient is for a recent forest fire that burned all plants farther away 

from the parking area. Note however, in models (not shown) where the income and children variables 

are also included, the Hispanic and hiker variables become insignificant at predicting class membership 

and class attribute preferences are similar to model 7. 

 

87 

Table 2.7 Latent Class Model with Children, Income, and Hispanic 

  
  

  
  

Model 7 

Class 2 

Class 1 

 

 

 
Shrubs near, trees far 
 
Trees near, shrubs far 
 
Trees near, trees far 
 
None near, some far 
 
Some near, none far 
 
Some near, some far 
 

Driving Distance (one-way)  Distance 
 
Vegetation 
 
 
 
 
 
Water 
 
 
 
 
 
Fire History (farther away)  Old fire that burned all plants 
 
 
 
 
 
 
 
Class Membership 
 
 
 
 
 
 
  
 
Membership Share 
Observations 
CAIC 
BIC 
Log Likelihood 

 
Recent fire that burned all plants 
 
Recent fire that burned some plants 
 
Recent shrub fire 
 
Has children under 18 
 
Income 
 
Hispanic 
 
Constant  
  
 
 
2,115 
2697.58 
2671.58 
-1250.38 

 

-0.015*** 
(0.000) 
1.491*** 
(0.001) 
1.408*** 
(0.004) 
2.336*** 
(0.000) 
1.946*** 
(0.000) 
2.322*** 
(0.002) 
2.812*** 
(0.000) 
-0.298 
(0.216) 
-1.117*** 
(0.000) 
-0.587* 
(0.071) 
-0.156 
(0.569) 
0.738** 
(0.020) 
-0.005** 
(0.049) 
0.154 
(0.651) 
0.589 
(0.552) 
 
0.90 
 
 
 
  

 

-0.023*** 
(0.010) 
0.109 
(0.827) 
-0.091 
(0.824) 
0.098 
(0.892) 
0.272 
(0.607) 
-0.093 
(0.874) 
0.465 
(0.439) 
-0.086 
(0.750) 
-1.488*** 
(0.000) 
-0.443 
(0.214) 
-0.458* 
(0.095) 
 
 
 
 
 
 
 
 
 
0.10 
 
 
 
  

 

 

 

 

 

88 

Table 2.8 Two-Class Latent Class Model with Hispanic and Hiking 

  
  

  
  

 

 

Driving Distance (one-way)  Distance 
 
Vegetation 
 
 
 
 
 
Water 
 
 
 
 
 
Fire History (farther away) 
 
 
 
 
 
 
 
Class Membership 
 
 
 
 
  
 
Membership share 
Observations 
AIC 
BIC 
Log Likelihood 

 
Shrubs near, trees far 
 
Trees near, shrubs far 
 
Trees near, trees far 
 
None near, some far 
 
Some near, none far 
 
Some near, some far 
 
Old fire that burned all plants 
 
Recent fire that burned all 
plants 
 
Recent fire that burned some 
plants 
 
Recent shrub fire 
 
Hispanic 
 
Hiker 
 
Constant  
  
 
 
2,086 
2515.69 
2656.76 
-1212.80 

 

 

 

89 

Class 1 

 

-0.019*** 
(0.000) 
0.322 
(0.138) 
0.196 
(0.400) 
0.591* 
(0.086) 
0.763*** 
(0.002) 
0.465 
(0.133) 
0.910*** 
(0.001) 
-0.053 
(0.789) 
-1.222*** 

(0.000) 
-0.329* 

(0.078) 
-0.381** 
(0.022) 
-0.712** 
(0.034) 
0.145 
(0.608) 
2.090*** 
(0.000) 
 
0.92 
 
 
 
  

 

Model 8 

Class 2 

 

-0.010* 
(0.061) 
2.031 
(0.194) 
2.086 
(0.130) 
3.102* 
(0.091) 
2.112*** 
(0.004) 
3.188* 
(0.072) 
3.450** 
(0.045) 
-0.687 
(0.108) 
-1.062** 

(0.012) 
-0.612 

(0.344) 
0.011 
(0.982) 
 
 
 
 
 
 
 
0.08 
 
 
 
  

 

2.6  Willingness to Drive for Attributes 

In choice experiments, a common way to compare the strength of preferences across models 

to express them in terms of people’s willingness to trade off one attribute to obtain another. In this 

section, the estimated preference parameters are used to compute the additional distance an individual 

would  drive  one  way  for  a  change  in  a  site  attribute,  the  willingness  to  drive  (WTD)11.    For  the 

conditional  logit  and  random  parameters  models  we  estimated  average  willingness  to  drive  for  a 

change in attributes, and this was computed using the full sample. Model 1 is conditional logit with 

no interactions, Model 2 is conditional logit with distance x income, Model 3 is conditional logit with 

experience x fire history, and Model 4 is conditional logit with Hispanic x all attribute interactions. 

Models 5 and 6 are random parameters logit with and without correlation, respectively. Model 7 is the 

two-class latent class model with children, annual household income, and Hispanic determining class 

membership and Model 8 is a two-class latent class model with Hispanic and hiking determining class 

membership. 

In all the models presented, willingness to drive for vegetation and water attributes is positive, 

while  willingness  to  drive  for  fire  attributes  is  negative.  Comparing  the  Model  7  estimates  for 

vegetation and water for latent classes 1 and 2, we see that the WTD are much larger in magnitude for 

Class 1 respondents than Class 2 respondents or in the conditional logit or random parameters models. 

For Class 1, WTD for all the plant and water levels are significant at the 5% level. The only WTD 

estimate for fire that is significant at the 5% level is a recent fire that burned all plants farther away. 

For Class 2, only WTD for recent fire that burned all plants farther away is significant. Model 8 

                                                

11 In Appendix G, this willingness to drive (WTD) is also converted to a monetary measure using travel costs to 

estimate the willingness to pay (WTP) for an attribute change (see Table 2.21). 

 

90 

similarly identifies one latent class with extremely high WTD and one with WTD that are smaller in 

magnitude but none of the WTD in Class 2 are significant at the 5% level. 

From the conditional and random parameters logit WTD results in Table 2.9 we see that on 

average respondents will drive about 45 miles more to visit a site with trees either nearby or farther 

away compared to sites with shrubs nearby and shrubs farther away. Sites with tree cover both nearby 

and farther away from the parking lot are valued even more, with average willingness to drive being 

at least 70 miles one-way. Sites with a water feature – in the Angeles National Forest these tend to be 

sites with rivers or streams, but sometimes lakes – are highly valued, with average willingness to drive 

ranging between around 70 miles for sites with water at a distance from the parking area, to around 

100 for sites with water nearby and farther away. These results are consistent with observed recreation 

patterns, as those sites with streams and large shaded picnic areas were among the most heavily visited 

in our sample. 

As expected, sites with fire history are less desirable than those with no visible effects of past 

fires, but there is a wide variation in WTD estimates between four categories of fire history. If a site 

has been affected by an older forest fire that is in recovery on average respondents would drive 12 

fewer miles one-way to visit that site. However, if a site was affected by a recent forest fire that burned 

all vegetation, they would drive on average 79 fewer miles for that site. Recent forest fires that only 

affected some plants (like shallow ground fires as opposed to crown fires) and older shrub fires that 

are in recovery lie in between those two extremes. 

Estimates of WTD for attributes across the four specifications of the conditional logit model 

and the two random parameters logit models are very similar. WTD to sites with mixed tree and shrub 

vegetation  is  roughly  45  miles  one-way  in  Model  1,  which  estimated  average  preferences  in  the 

population. Both the random parameters logit models also show that visitors would be willing to drive 

about 45 more miles to those sites compared to sites with only shrubs. Similarly, WTD for trees nearby 

 

91 

and farther away, water attributes, and fire history attributes are  nearly the same for three  of  the 

conditional logit model specifications and the two random parameters logit models. Model 2, in which 

income was interacted with the distance attribute, consistently estimates greater WTD for trees and 

water, and less WTD for sites with fire history. The first latent class where children, income, and 

Hispanic  determined  class  membership,  the  model  identifies  a  group  of  respondents  whose 

preferences are very strong and would be willing to drive 100 or more miles for sites with desirable 

attributes, and a second group with little WTD for any of the attributes presented. Although not 

shown in the table, the weighted average WTD for attributes for Model 7 is much higher than the 

conditional logit estimate. Model 8 identifies a group of people less with similar preferences to the 

average estimated by the conditional logit and a second group with no significant WTD for attributes. 

 

92 

Table 2.9 Willingness to Drive 

 
Model 
 

Vegetation 
Shrubs near, trees far 
Trees near, shrubs far 
Trees near, trees far 

Water 
None near, some far 
Some near, none far 
Some near, some far 

Fire History (farther away) 
Old fire that burned all plants 
Recent fire that burned all plants 
Recent fire that burned some plants 
Recent shrub fire 

 

Conditional Logit 

 

 

 

(1) 
 

46 
45 
79 

71 
70 
97 

-13 
-73 
-24 
-12 

 

 

 

 

(2) 
 

45 
43 
76 

66 
65 
94 

-11 
-69 
-21 
-10 

 

 

 

 

(3) 
 

46 
45 
79 

71 
70 
97 

-14 
-72 
-24 
-13 

 

 

 

 

(4) 
 

46 
45 
78 

70 
71 
97 

-13 
-72 
-22 
-12 

 

 
 

 
 
 
 

 
 
 
 

 
 
 
 
 

 

 Random 
Parameters 
(6) 
(5) 
 
 

 
 
  Class 1  Class 2 

(7) 

Latent Class 

(8) 

 
  Class 1  Class 2 

 

 

 

44 
44 
77 

71 
69 
97 

-12 
-71 
-23 
-14 

 

 

 

 

46 
46 
82 

73 
73 
101 

-15 
-77 
-28 
-13 

 

 
 
 
 

 
 
 
 

 
 
 
 
 

 

 

 

 

103 
97 
161 

134 
160 
194 

-21 
-77 
-41 
-11 

 

 

 

 

5 
-4 
4 

12 
-4 
20 

-4 
-64 
-19 
-20 

 

 
 
 
 

 
 
 
 

 
 
 
 
 

 

 

 

 

17 
10 
31 

40 
24 
47 

-3 
-63 
-17 
-20 

 

 

 

 

204 
210 
312 

212 
320 
347 

-69 
-107 
-62 
1 

 

Note: All values rounded to the nearest mile and bold cells indicate values significantly different than zero at the 5% level. Models 2, 3, and 
4 use Krinsky and Robb (1986) 95% confidence intervals using the mean of the demographic variable. Confidence intervals for the other 
models were computed using the delta method. 

 

 

93 

2.7  Discussion and Conclusions 

In  this  study,  we  use  results  from  a  choice  experiment  survey  to  model  forest  visitors’ 

preferences for environmental attributes of national forest recreation sites and estimate willingness to 

pay for sites with different vegetation, water, and fire histories. The fire attributes span forest and 

chaparral vegetation types, include different burn intensities, and capture temporal effects of fire via 

old versus recent fires. We introduce and test for evidence of preference heterogeneity by employing 

conditional logit models with interactions, random parameters logit models, and latent class models. 

The dominant vegetation type in much of southern California is chaparral, which is a shrubland. 

Many recreation sites in the southern portions of the Angeles National Forest and nearby forests 

mostly have chaparral nearby, with the exception of large picnic sites along rivers, where there is 

usually tree cover by the water. At higher altitudes, and also at greater driving distance from any 

respondents living in Los Angeles or its immediate suburbs, the Angeles National Forest is dominated 

by pine and conifer forests. Sites with some tree cover are favored by respondents, with sites with 

trees both near the parking lot as well as farther away being the most preferred. This indicates a 

preference for sites with long, shaded hiking trails as opposed to those that are more exposed. 

Some of the busiest recreation sites in the national forest are those with streams or lakes. Many 

sites along a stream are popular picnic sites in addition to having hiking trails, as opposed to other 

sites without water near the parking lot, which may have long hiking trails, but are not picnic sites. It 

makes sense then, that across the board, sites with water nearby, farther away, or both, are highly 

preferred to sites that have no river, stream, or lake within hiking distance.12  

                                                

12 Our sampling design favored sites with many visitors. Future extensions of this work will incorporate sampling 

weights to better address potential differences in user groups at high and low use sites. 

 

94 

The study area is frequently affected by severe wildfires that sometimes close recreation sites 

and when sites re-open they can be left with visible burn scars that vary depending on the vegetation 

type and fire severity. We find evidence, as expected, that sites with visible effects from wildfires are 

less desirable than those with no visible effects of wildfires, but that as time and recovery increase, the 

effect is mitigated. Previous recreation literature has found that trips increase after a recent wildfire 

for a short time – however, we find that in the case of severe wildfires in California that burn all the 

vegetation, recent wildfires are larger dis-amenities than older forest fires or shrub fires. Recent forest 

fires that burned some plants, recent shrub fires, and old forest fires that are still visible also cause 

welfare losses, but less so than severe, recent forest fires. 

These basic results are consistent across the three classes of models we use. As expected, the 

average  preferences  across  models  are  roughly  similar  to  the  basic  conditional  logit,  which  only 

measure  average  preferences.  While  the  other  models  reveal  some  heterogeneity,  each  model 

incorporates  preference  heterogeneity  differently.  In  the  conditional  logit  model,  we  interacted 

variables that may influence preferences with the site attributes which allows for a clear interpretation 

of  how  preferences  vary  with  demographics.  The  interacted  models  suggest  that  experience  with 

changing trips due to site closures or fire conditions do not contribute to preference heterogeneity, 

however, we do find evidence that different groups of people may have heterogeneous preferences 

across site attributes. Model 4 shows that Hispanic forest visitors are more likely than others to visit 

sites with trees nearby and shrubs far away, and less likely to visit sites with no water nearby but some 

far away. This is consistent with previous literature that shows that minority groups use public forest 

areas differently than other groups.  In our random parameters model estimation, we find significant 

standard deviations for the vegetation and fire history attributes, suggesting that there is considerable 

heterogeneity in preferences for these characteristics. However, the standard deviation estimates for 

 

95 

water are insignificant suggesting that the presence of lakes, rivers, or streams at a site is uniformly 

desirable. 

Latent class models can be useful for identifying classes of people who have distinct preferences. 

To explore heterogeneity, we examined latent class models and found that fewer classes were preferred 

to more classes across a range of specifications. We present results from two latent class models. In 

the first model respondents with children under 18 are more likely to belong to a class of people for 

whom many of the site attributes – tree cover, the presence of water, and fire history – are significant 

drivers of their choices over recreation sites. Those with a higher annual income are less likely to be 

in that class and more likely to be in a class of respondents who are only sensitive to distance and 

recent fires. The second latent class model predicts that Hispanic forest visitors are more likely to 

belong to a class who have strong preferences for water at the site, and for trees both nearby and 

farther away, but are less sensitive to the fire history attributes. 

The results identify two sources of heterogeneity in preferences for the vegetation, water, and 

fire history attributes of recreation sites that may be of interest to forest managers. The construction 

of the attribute levels allows us to draw some conclusions about how the welfare effects of forest fires 

change over time. We find significant evidence for differences in effects of fire over time. Sites that 

have been affected by wildfires are less preferred to sites with no visible fire history, but unlike some 

previous recreation literature, we find that recent wildfires cause greater welfare loss than older forest 

fires  and  that  visible  damage  can  have  a  significant  effect  on  site  choices.  Second,  we  identify 

heterogeneity across groups of people. The urban national forests in our study area are an important 

recreational opportunity for the diverse residents of Los Angeles and Southern California. One of the 

most important demographic trends in this area is a large and growing Hispanic population, who, 

compared to other demographic groups, are under-represented among forest visitors. Managers have 

an interest in understanding how recreation preferences differ across user groups. Past literature has 

 

96 

looked at preferences for levels of development and amenities and diversity in the types of activities 

that  visitors  engage  in  (Chavez  et  al.  2008).  We  find  that  there  are  also  significant  differences  in 

preferences  over  environmental  attributes  of  recreation  sites  that  could  provide  insight  into  how 

management activities can differentially affect people. Improvements in water quality and protection 

of forest quality nearby parking or picnic areas appear more beneficial to some visitors such as those 

who  are  Hispanic,  have  young  children,  and  those  with  lower  household  income,  while  trail 

maintenance  and  fire  recovery  in  forested  areas  appear  more  valuable  to  visitors  who  are  non-

Hispanic, have higher household income, and do not have children. 

 

 

 

97 

 

 

 

 

 

 

 

 

 

 

 

 

APPENDICES 

 

 

 

 

 

 

 

 

 

 

 

98 

Appendix 2A: Coefficient Covariance Matrix 

Table 2.10 Correlation Table for Random Parameters Logit Model 6 

  

Shrubs 
near, trees 
far 
Trees near, 
shrubs far 
Trees near, 
trees far 
Old fire, all 
plants 
Recent fire, 
all plants 
Recent fire, 
some 
plants 
Recent 
shrub fire 

Shrubs 
near, trees 
far 

Trees 
near, 
shrubs far 

Trees 
near, 
trees far 

Old fire, 
all 
plants 

Recent 
fire, all 
plants 

Recent fire, 
some 
plants 

Recent 
shrub 
fire 

0.072 

 

-0.243 

2.330** 

 

 

-0.142 

0.999* 

1.752** 

 

 

 

-0.079 

0.365 

0.641 

0.330 

 

 

 

 

0.267 

0.5 

0.413 

-0.087 

2.499** 

 

 

 

 

 

0.146 

-0.368 

-0.454 

-0.545 

0.723 

2.535** 

 

 

 

 

 

 

0.043 

0.379 

0.180 

-0.146 

0.755 

1.097* 

2.233** 

 

99 

 

 

Appendix 2B: Robustness Checks for Essay 2 

Table 2.11 Conditional Logit with Travel Cost 

 

 

Shrubs near, trees far 
 
Trees near, shrubs far 
 
Trees near, trees far 
 
None near, some far 
 
Some near, none far 
 
Some near, some far 
 
Old forest fire that burned all plants 
 
Recent forest fire that burned all plants 
 
Recent forest fire that burned some plants 
 
Recent shrub fire 
 
Travel cost (one-way) 
 
 
Observations 
AIC 
BIC 
Log Likelihood 

Conditional 
Logit 

 

0.731*** 
(0.000) 
0.682*** 
(0.000) 
1.216*** 
(0.000) 
1.049*** 
(0.000) 
1.049*** 
(0.000) 
1.517*** 
(0.000) 
-0.181 
(0.104) 
-1.108*** 
(0.000) 
-0.349*** 
(0.002) 
-0.169* 
(0.089) 
-0.069*** 
(0.000) 
 
4,290 
2621.64 
2691.64 
-1299.82 

 

 

Robust pval in parentheses, *** p<0.01, ** p<0.05, * p<0.1 

 

100 

Table 2.12 Conditional Logit with Interactions using Travel Cost 

 

 

Travel cost (one way) 
 
Shrubs near, trees far 
 
Trees near, shrubs far 
 
Trees near, trees far 
 
None near, some far 
 
Some near, none far 
 
Some near, some far 
 
Old forest fire that burned all plants 
 
Recent forest fire that burned all plants 
 
Recent forest fire that burned some plants 
 
Recent shrub fire 
 
Hispanic x Shrubs near, trees far 
 
Hispanic x Trees near, shrubs far 
 
Hispanic x Trees near, trees far 
 
Hispanic x No water near, some far 
 
Hispanic x Some water near, none far 
 
Hispanic x Some water near, some far 
 
 

 

 

 

101 

Experience x 
Fire 

Hispanic x 
Attributes 

 

-0.069*** 
(0.000) 
0.728*** 
(0.000) 
0.688*** 
(0.000) 
1.216*** 
(0.000) 
1.054*** 
(0.000) 
1.055*** 
(0.000) 
1.528*** 
(0.000) 
-0.147 
(0.467) 
-0.879*** 
(0.000) 
-0.379* 
(0.075) 
-0.342 
(0.135) 
 
 
 
 
 
 
 
 
 
 
 
 

 

 

-0.069*** 
(0.000) 
0.683*** 
(0.000) 
0.599*** 
(0.000) 
1.155*** 
(0.000) 
1.155*** 
(0.000) 
1.052*** 
(0.000) 
1.554*** 
(0.000) 
-0.093 
(0.472) 
-1.190*** 
(0.000) 
-0.365*** 
(0.004) 
-0.222* 
(0.055) 
0.184 
(0.557) 
0.347 
(0.143) 
0.208 
(0.512) 
-0.467** 
(0.022) 
0.101 
(0.641) 
-0.089 
(0.686) 

 

 

 
 
 
 
 
 
 
 
-0.042 
(0.850) 
-0.280 
(0.240) 
0.037 
(0.871) 
0.211 
(0.389) 
 
4,290 
2626.68 
2722.14 
-1298.34 

 

 

-0.323 
(0.173) 
0.337 
(0.222) 
0.155 
(0.586) 
0.175 
(0.446) 
 
 
 
 
 
 
 
 
 
4,260 
2599.94 
2733.43 
-1278.97 

 

Table 2.12 (cont’d) 

 

Hispanic x Old fire, all 
 
Hispanic x Recent fire, all 
 
Hispanic x Recent fire, some 
 
Hispanic x Recent fire, shrub 
 
Experience x Old fire, all 
 
Experience x Recent fire, all 
 
Experience x Recent fire, some 
 
Experience x Recent fire, shrub 
 
 
Observations 
AIC 
BIC 
Log Likelihood 

 

 

102 

Table 2.13 Random Parameters Logit with No Correlation and Travel Cost 

 

 

Travel cost (one-way) 
 
Shrubs near, trees far 
 
Trees near, shrubs far 
 
Trees near, trees far 
 
None near, some far 
 
Some near, none far 
 
Some near, some far 
 
Old forest fire that burned all plants 
 
Recent forest fire that burned all plants 
 
Recent forest fire that burned some plants 
 
Recent shrub fire 
 
 
Observations 
AIC 
BIC 
Log Likelihood 

 

 

Coef. 

 

-0.102*** 
(0.000) 
1.036*** 
(0.000) 
1.020*** 
(0.000) 
1.798*** 
(0.000) 
1.509*** 
(0.000) 
1.480*** 
(0.000) 
2.240*** 
(0.000) 
-0.268* 
(0.087) 
-1.613*** 
(0.000) 
-0.488*** 
(0.005) 
-0.293* 
(0.061) 
 
4,290 
2613.95 
2747.59 
-1285.97 

 

Std. Dev. 

 

 
 
0.199 
(0.709) 
1.210*** 
(0.000) 
1.020*** 
(0.000) 
-0.587** 
(0.046) 
0.681** 
(0.037) 
-0.776** 
(0.021) 
0.474 
(0.309) 
-0.991*** 
(0.003) 
1.304*** 
(0.001) 
1.045** 
(0.010) 
 
 
 
 
 

 

 

103 

Table 2.14 Comparison of WTP using Models that used One-way Travel Cost 

  

  

 

Shrubs near, trees far 
Trees near, shrubs far 
Trees near, trees far 
None near, some far 
Some near, none far 
Some near, some far 
Old fire that burned all plants 
Recent fire that burned all plants 
Recent fire that burned some plants 
Recent shrub fire 

 

 

  

  

 

Vegetation 
 
 
Water 
 
 
Fire History (farther 
away) 
 
 
  

 

 

 

Conditional Logit 

 

Random 
Parameters 

No 
Interactions 

Exp x Fire 

Hisp x 
Attributes 

  No Corr 

 

 

  $ 10 
  $ 10 
  $ 18 
  $ 15 
  $ 14 
  $ 22 
 
-$ 3 
 
-$ 16 
 
-$ 5 
 
-$ 3 

 

 

 

$ 11 
$ 10 
$ 18 
$ 15 
$ 15 
$ 22 
-$ 3 
-$ 16 
-$ 5 
-$ 3 

 

 

$ 11 
$ 10 
$ 17 
$ 15 
$ 16 
$ 22 
-$ 2 
-$ 16 
-$ 5 
-$ 3 

 

 

$ 11 
$ 10 
$ 18 
$ 15 
$ 15 
$ 22 
-$ 3 
-$ 16 
-$ 5 
-$ 2 

 

104 

Table 2.15 Three-class Latent Class Model with Hispanic, Income, and Children 

Appendix 2C: Three and Four-Class Latent Class Models 

  

  

Class 1 

Class 2 

Class 3 

Driving Distance (one-way) 
 
Vegetation 
 
 
 
 
 
Water 
 
 
 
 
 
Fire History (farther away) 
 
 
 
 
 
 
 

 

 

 

Distance 
 
Shrubs near, trees far 
 
Trees near, shrubs far 
 
Trees near, trees far 
 
None near, some far 
 
Some near, none far 
 
Some near, some far 
 
Old fire that burned all plants 
 
Recent fire that burned all plants 
 
Recent fire that burned some plants 
 
Recent shrub fire 
 

105 

-0.016*** 
(0.003) 
1.371*** 
(0.257) 
1.271*** 
(0.218) 
2.117*** 
(0.286) 
1.396*** 
(0.166) 
1.755*** 
(0.210) 
2.228*** 
(0.224) 
-0.152 
(0.201) 
-1.184*** 
(0.194) 
-0.631*** 
(0.205) 
-0.003 
(0.183) 

0.017 
(0.015) 
-2.587* 
(1.338) 
-1.381 
(1.083) 
-3.344** 
(1.550) 
0.980 
(0.876) 
-0.230 
(0.723) 
0.023 
(1.040) 
-0.515 
(0.687) 
-2.086** 
(1.015) 
0.530 
(0.699) 
-3.099*** 
(1.193) 

-0.262*** 
(0.025) 
2.043** 
(0.889) 
1.575** 
(0.788) 
4.996*** 
(0.991) 
3.664*** 
(0.571) 
3.670*** 
(0.524) 
6.129 
NA 
-2.347*** 
(0.660) 
-3.718 
NA 
-1.115* 
(0.644) 
-2.075** 
(0.810) 

Table 2.15 (cont’d) 
Class Membership 
 
 
 
 
 
 
  
 
Observations 
CAIC 
BIC 
Log Likelihood 

 

 

Has children under 18 
 
Income 
 
Hispanic 
 
Constant  
  
 
2,115 
2786.46 
2745.46 
-1238.06 

 

1.214** 
(0.500) 
-0.006** 
(0.003) 
-0.194 
(0.478) 
1.806*** 
(0.469) 
 
 
 
 
  

0.451 
(0.752) 
-1.38E-4 
(0.004) 
-1.088 
(1.022) 
-0.226 
(0.842) 
 
 
 
 
  

 
 
 
 
 
 
 
 
 
 
 
 
  

106 

Table 2.16 Four-class Latent Class Model with Hispanic, Income, and Children 

  

 

Driving Distance (one-way) 
 
Vegetation 
 
 
 
 
 
Water 
 
 
 
 
 
Fire History (farther away) 
 
 
 
 
 
 
 

 

 

 

  

 

Distance 
 
Shrubs near, trees far 
 
Trees near, shrubs far 
 
Trees near, trees far 
 
None near, some far 
 
Some near, none far 
 
Some near, some far 
 
Old fire that burned all plants 
 
Recent fire that burned all plants 
 
Recent fire that burned some plants 
 
Recent shrub fire 
 

 

 

107 

Class 1 

Class 2 

Class 3 

Class 4 

 

 

 

 

-0.016*** 
(0.004) 
0.163 
(0.616) 
1.258*** 
(0.318) 
1.166*** 
(0.294) 
1.522*** 
(0.402) 
1.844*** 
(0.457) 
2.450*** 
(0.636) 
0.0468 
(0.283) 
-0.375 
(0.491) 
-0.0920 
(0.276) 
-0.412 
(0.258) 

-1.302*** 
(0.0296) 
170.6*** 
(1.753) 
29.35 
NA 
235.4*** 
(1.095) 
153.3 
NA 
40.50*** 
(1.564) 
117.3*** 
(1.434) 
-62.68*** 
(2.904) 
-156.7*** 
(1.387) 
-77.56*** 
(1.318) 
52.17*** 
(1.053) 

0.005 
(0.016) 
3.403*** 
(1.011) 
-0.626 
(0.858) 
0.599 
(1.291) 
-0.0547 
(0.886) 
0.690 
(1.087) 
-0.506 
(1.361) 
-2.747* 
(1.587) 
-5.858** 
(2.738) 
-1.797* 
(0.991) 
-0.444 
NA 

-0.531*** 
(0.045) 
6.927*** 
(1.301) 
4.634*** 
(1.006) 
13.33*** 
(1.570) 
4.750*** 
(1.122) 
6.380*** 
(1.188) 
11.50*** 
(2.070) 
-4.622*** 
(1.293) 
-10.38*** 
(1.382) 
-3.187** 
(1.534) 
-3.006*** 
(0.951) 

 

 

 

 

Table 2.16 (cont’d) 

 

Class Membership 
 
 
 
 
 
 
  
Observations 
CAIC 
BIC 
Log Likelihood 

 

 

 

Has children under 18 
 
Income 
 
Hispanic 
 
Constant  
  
2,115 
2840.09 
2784.09 
1208.10 

 

 

0.925 
(0.769) 
-0.005 
(0.003) 
0.456 
(0.637) 
1.577*** 
 
 
 
 
 

 

 

0.759 
(1.022) 
-0.021* 
(0.011) 
-0.579 
(0.782) 
1.854** 
 
 
 
 
  

 

 

0.394 
(0.693) 
-0.004 
(0.004) 
0.091 
(0.790) 
0.452 
 
 
 
 
  

 

 

 
 
 
 
 
 
 
 
 
 
 
  

 

 

108 

 

 

	

	

	

	

	

Appendix 2D: Onsite Survey Instrument (2016)  

	

Interviewer:	_________________		Site:		__________________	

⃞  Yes 
⃞  No à Thank you for your time. (END INTERVIEW) 

(Or	say	“	I	am	hoping	to	speak	with	the	person	in	your	group	who	had	the	most	recent	
birthday”	and	then	prompt	with	the	question	if	needed.)	

	
#	_______		
	Hi,	I	work	with	Michigan	State	University	and	I’m	conducting	interviews	for	the	Forest	Service	
for	a	research	study	that	will	help	them	serve	visitors.	Your	participation	is	voluntary	and	all	
information	is	confidential.	This	survey	should	take	5	minutes.		
	1.	Would	you	be	willing	to	take	a	few	minutes	to	participate	in	this	interview?	
	2.	I	need	to	select	just	one	of	you	to	complete	this	interview.	Which	of	you	had	the	most	recent	
birthday	and	is	18	years	of	age	or	older?	
	3.	What	is	your	home	ZIP	code?	_____________	
If	visitor	is	from	another	country,	zip	code	=	00000	à	proceed	to	Q3a,	otherwise	skip	to	Q4	
If	don’t	know	/	refuse	to	answer,	zip	code	=	99999	
	
3a.		If	visitor	is	from	another	country,	select:		
	4.	What	is	the	primary	purpose	of	your	visit	to	(site	name)?	
	5.	When	do	you	plan	to	leave	(site	name)	for	the	last	time	on	this	visit?	
	6.	When	did	you	first	arrive	at	(site	name)	for	this	visit?		Date	and	time:		____________________	

à end interview 
⃞  Working or commuting to work    
⃞  Only stopping to use the bathroom   
à end interview 
⃞  Only passing through, going somewhere else    à end interview 
⃞  Some other reason    
à end interview 
⃞  Recreation  à  proceed to Q5; if any other reason, end interview 

⃞  Not leaving this site today 
⃞  Don’t know 
⃞  Leaving now 
⃞  Leaving later today à     Time:  _____________ 

⃞  Canada 
⃞  Mexico 
⃞  South & Central America 
⃞  Asia 
⃞  Europe 
⃞  Other   ______________ 

 

 

 
 

 

 

 

109 

 

⃞  Yes  
⃞  No 

 

Section 2: National Forest Visit  

7.	On	this	visit	to	this	NF,	did	you	go	or	do	you	plan	to	go	to	any	areas	for	recreation	other	
than	this	one?	
	
	8.	In	which	of	the	following	activities	have	you	participated	or	will	you	participate	during	this	
NF	visit?	

Questions	8-11	ask	the	visitor	about	the	activities	they	participated	in	during	their	national	forest	visit.		
Since	the	activity	choice	list	is	very	long,	hand	them	the	activity	flash	card	then	ask:	

⃞  Hiking or walking 
⃞  Bicycling, including mountain bikes 
⃞  Driving for pleasure on roads (paved, gravel, or dirt) 
⃞  Relaxing, hanging out, escaping heat 
⃞  Viewing/photographing wildlife or scenery 
⃞  Picnicking and family day gatherings   
⃞  Camping  
⃞  Fishing 
⃞  Canoeing or boating without a motor  
⃞  Boating with a motor  
⃞  OTHER (write in activity)_________________________ 

		9.	Which	one	of	those	is	your	primary	activity	for	this	recreation	visit	on	this	NF?				

⃞  Hiking or walking 
⃞  Bicycling, including mountain bikes 
⃞  Driving for pleasure on roads (paved, gravel, or dirt) 
⃞  Relaxing, hanging out, escaping heat 
⃞  Viewing/photographing wildlife or scenery 
⃞  Picnicking and family day gatherings   
⃞  Camping  
⃞  Fishing 
⃞  Canoeing or boating without a motor  
⃞  Boating with a motor  
⃞  OTHER (write in activity)_________________________ 

	
	10.	In	which	of	the	following	activities	have	you	participated	or	will	you	participate	at	this	
site?	

If	Q7=No,		skip	to	Q12.			

⃞  Hiking or walking 
⃞  Bicycling, including mountain bikes 
⃞  Driving for pleasure on roads (paved, gravel, or dirt) 

110 

 
 

 

 

 

⃞  Fishing 
⃞  Canoeing or boating without a motor  
⃞  Boating with a motor  
⃞  OTHER (write in activity)_________________________ 

		11.	Which	one	of	those	is	your	primary	activity	for	this	recreation	visit	at	this	site?					

⃞  Hiking or walking 
⃞  Bicycling, including mountain bikes 
⃞  Driving for pleasure on roads (paved, gravel, or dirt) 
⃞  Relaxing, hanging out, escaping heat 
⃞  Viewing/photographing wildlife or scenery 
⃞  Picnicking and family day gatherings   
⃞  Camping  
⃞  Fishing 
⃞  Canoeing or boating without a motor  
⃞  Boating with a motor  
⃞  OTHER (write in activity)_________________________ 

 
Section 3: Demographics 
The	next	questions	provide	statistics	about	the	basic	demographics	of	forest	visitors.		This	
allows	the	forest	managers	to	better	understand	who	their	clientele	are.			

	12.	Including	this	visit,	about	how	many	times	have	you	come	to	this	NF	for	recreation	in	
the	past	12	months?				__________	
	
	13.	How	many	people,	including	you,	traveled	here	in	the	same	vehicle	as	you?			_______	
	14.	How	many	of	those	people	are	less	than	18	years	old?			__________	
	15.	What	is	your	age?				___________	
	16.	Record:		
	17.	Are	you	Hispanic	or	Latino?	
	18.	With	which	racial	group(s)	do	you	most	closely	identify?	

⃞  Male 
⃞  Female  

⃞  Yes 
⃞  No 
⃞  Refused 

⃞  American Indian / Alaska Native 

 

 

111 

 
Section 4: Contact Info 

it	written	correctly.	

⃞  Native Hawaiian or other Pacific Islander 
⃞  White 
⃞  Refused 

	
Do	you	have	an	e-mail	address	where	we	can	send	you	a	short	follow-up	survey?	The	invitation	
would	come	in	a	couple	weeks	from	Michigan	State	University.		It	is	strictly	confidential	and	your	
e-mail	would	never	be	used	in	any	other	way.	Read	their	email	back	to	them	to	make	sure	you	have	
	Email:	______________________________________________________________________	
		
(Thank	you.	We	will	send	you	a	link	to	the	follow-up	survey	in	August.)	
	
Would	you	be	wiling	to	share	your	mailing	address	instead?	
	Full	name:	___________________________________________________________________________________	
Address	Line	1:	_____________________________________________________________________________	
Address	Line	2:	_____________________________________________________________________________	
City,	State,	Zip	Code:	________________________________________________________________________	
		
			Date:	__________________________________________	
Interview	end	time:	__________________________	
	

	
If	the	respondent	was	unwilling	to	share	their	email	address,	ask	for	a	mailing	address:	

Thank	you	for	your	time!	

 

 

 
 

 

 

 

112 

 

 

Appendix 2E: Online Survey Instrument (2017) 

The following pages show images of a paper version of the survey that was mailed in 2017 (Figures 

2.4a - 2.4m). The survey was originally 8.5 by 11 inches but is downscaled here to fit the pages. 

 

 

 

113 

 

 

Figure 2.4 Image of Paper Version of Survey (originally 8.5” by 11”) 

 

 

 

114 

 

 

Figure 2.4 (cont’d) 

 

 

115 

 

 

 

Figure 2.4 (cont’d) 

 

 

116 

 

 

 

Figure 2.4 (cont’d) 

 

 

117 

 

 

 

Figure 2.4 (cont’d) 

 

 

118 

 

 

 

Figure 2.4 (cont’d) 

 

 

119 

 

 

 

Figure 2.4 (cont’d)  

 

 

120 

 

 

 

Figure 2.4 (cont’d) 

 

 

121 

 

 

 

Figure 2.4 (cont’d) 

 

 

122 

 

 

 

Figure 2.4 (cont’d) 

 

 

123 

 

 

 

Figure 2.4 (cont’d) 

 

 

124 

 

 

 

Figure 2.4 (cont’d) 

 

 

125 

 

 

Figure 2.4 (cont’d) 

 

 

126 

 

 

Appendix 2F: Disposition Tables 

Table 2.17 Disposition Codes for Onsite Survey (2016) 

Disposition 

Description 

 

0 
1 
2 
3 
4 
5 
6 

 

  

 

 

Declined to participate 
Not recreating 
Incomplete survey 
No contact information 
Contact information 
Less than 18 years old 
Not contacted (duplicate email or no zip code) 

 

Total 

Table 2.18 Disposition Codes for Onsite Survey (2017) 

Disposition 

Description 

 

0 
1 
2 
3 
4 
6 

 

  

 

 

 

Declined to participate 
Not recreating 
Incomplete survey 
No contact information 
Contact information 
Not contacted (duplicate email or no zip code) 

 

Total 

 

127 

Freq. 

 

1,300 
60 
9 
505 
1,755 
16 
6 

 

3,651 

Freq. 

 

1,404 
49 
4 
481 
1,245 
4 

 

3,187 

Percent 

 

35.61 
1.64 
0.25 
13.83 
48.07 
0.44 
0.16 

 

100.00 

Percent 

 

44.05 
1.54 
0.13 
15.09 
39.06 
0.13 

 

100.00 

 

Table 2.19 Disposition Codes for Online Survey (2016) 

Disposition 

Description 

 

 

0 
1 
2 
3 
4 
5 
6 

 

  

 

 

Did not respond 
Did not continue past the consent page 
Incomplete survey 
Complete survey 
Incorrect contact information 
Refusal 
Did not record ID number 

 

Total 

Table 2.20 Disposition Codes for Online Survey (2017) 

Disposition 

Description 

 

0 
1 
2 
3 
4 
5 

 

  

 

 

Did not respond 
Did not continue past the consent page 
Incomplete survey 
Complete survey 
Incorrect contact information 
Refusal 

 

Total 

128 

Freq. 

 

904 
38 
110 
552 
135 
16 
4 

 

1,759 

Freq. 

 

683 
26 
69 
323 
130 
10 

 

1,241 

Percent 

 

51.39 
2.16 
6.25 
31.38 
7.67 
0.91 
0.23 

 

100.00 

Percent 

 

55.04 
2.10 
5.56 
26.03 
10.48 
0.81 

 

100.00 

 

 

Appendix 2G: Attribute Trade-offs in WTP 

In addition to expressing the attribute trade-offs in willingness to drive (WTD), as in the main 

text, the WTD can be converted into willingness to pay units using travel costs per mile. We estimate 

average travel cost per mile using the following formula: 

!"#$%&'()*=,-)*#.'%∗(,"-$-.1	'()*)+*"#$%&	*-5%∗6789::;9<	=:>?@A
BCCC

D            (9) 

 

 

Driving  costs  are  calculated  using  the  2016  and  2017  AAA  Your  Driving  Cost  handbook; 

driving costs are equal to the cost of fuel, tires, and oil plus marginal depreciation costs for a medium 

sized sedan that drives 15,000 miles per year. For travel time, we assume that individuals drive 45 miles 

per hour on average, and annual income is self-reported in the survey. Using this formula, our travel 

cost estimate is $.236 per mile in 2017 CPI-adjusted dollars.  

Translating the willingness-to-drive to a dollar value,13 the average willingness to pay for shrubs 

nearby and trees farther away or for trees nearby and shrubs farther away across all models is about 

$10 one way. The average across all models of willingness to pay for trees nearby and farther away is 

about $20, and for water nearby and farther away is $25. The average willingness to pay for a recent 

fire that burned all plants is -$17 one way or $34 round-trip, while for other fires, the willingness to 

pay is about -$10 per round trip. Willingness to pay values are found in Table 2.21. 

 

 

                                                

13 The conditional logit and random parameter logits presented in this essay were also run using travel cost instead 
of distance, and the resulting WTP values are nearly the same as when willingness to drive is converted to WTP using 
average travel cost. 

 

129 

 

Table 2.21 Willingness to Pay One-Way Using Average Travel Cost 

 
Model 
 

Vegetation 
Shrubs near, trees far 
Trees near, shrubs far 
Trees near, trees far 

Water 
None near, some far 
Some near, none far 
Some near, some far 

Fire History (farther 
away) 
Old fire that burned all 
plants 
Recent fire that burned 
all plants 
Recent fire that burned 
some plants 
Recent shrub fire 

 

Conditional Logit 

(1) 

 

(2) 

 

(3) 

 

(4) 

 

 
$ 11 
$ 11 
$ 19 

 
$ 17 
$ 17 
$ 23 

 
-$ 3 

 
$ 11 
$ 10 
$ 18 

 
$ 16 
$ 15 
$ 22 

 
-$ 3 

 
$ 11 
$ 11 
$ 19 

 
$ 17 
$ 17 
$ 23 

 
-$ 3 

 
$ 11 
$ 10 
$ 18 

 
$ 17 
$ 17 
$ 23 

 
-$ 3 

-$ 17 

-$ 16 

-$ 17 

-$ 17 

-$ 6 
-$ 3 

 

-$ 5 
-$ 2 

 

-$ 6 
-$ 3 

 

-$ 5 
-$ 3 

 

 

 
  $ 10 
  $ 10 
  $ 18 

 

 
  $ 17 
  $ 16 
  $ 23 

 
-$ 3 

 
 

 

 
 

 

 
$ 11 
$ 11 
$ 19 

 
$ 17 
$ 17 
$ 24 

 
-$ 4 

 

 
  $ 24 
  $ 23 
  $ 38 

 

 
  $ 32 
  $ 38 
  $ 46 

 
 

 

 
 

 

 
-$ 5 

-$ 18 

-$ 10 
-$ 3 

 

 
$ 1 
-$ 1 
$ 1 

 
$ 3 
-$ 1 
$ 5 

 
-$ 1 

-$ 15 

-$ 4 
-$ 5 

 

-$ 17 

-$ 18 

-$ 5 
-$ 3 

 

-$ 7 
-$ 3 

 

 

 
 
 

Random 
Parameters 
(5) 
(6) 

 

 

Latent Class 

 
 
  Class 1  Class 2 

(7) 

(8) 

 
  Class 1  Class 2 

 
 
 
 

 
 
 
 

 
 

 

 
 

 

 
$ 4 
$ 2 
$ 7 

 
$ 9 
$ 6 
$ 11 

 
-$ 1 

-$ 15 

-$ 4 
-$ 5 

 

 
$ 48 
$ 50 
$ 74 

 
$ 50 
$ 75 
$ 82 

 
-$ 16 

-$ 25 

-$ 15 
$0.25 

 

Note: Values in bold indicate the WTP is significant at the 5% level using the delta method 

 

 

130 

 

 

 

 

 

 

 

 

 

 

 

 

 

REFERENCES 

 

131 

 

 

 

 

 

 

 

 

 

 

 

 

 

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134 

 

 Estimating the Impact of Fires on Recreation in the Angeles National Forest 

Using Combined Revealed and Stated Preference Methods 

3.1 

Introduction 

A multitude of factors including fire suppression and exclusion, drought, warming temperatures, 

and increased human activity have made wildfire season in the Western United States more intense 

and severe than ever in recent years. California, as the most populous state and home to many unique 

national parks and forests, is especially vulnerable to the financial, health, and recreational impacts of 

these  wildfires.  The  2017  fire  season  was  particularly  destructive.  In  December  2017  southern 

California  experienced  an  outbreak  of  ten  separate  wildfires  in  and  around  the  Los  Angeles 

metropolitan area, many starting in one of the four national forests that surround the area. These 

national forests are an important outdoor recreation opportunity for a population of millions of people 

in Los Angeles, San Diego, and surrounding cities. A review of 49 studies estimated that access to 

recreational sites in the Pacific western states has an average estimated value of $35 per trip in 2018 

dollars (Loomis 2005). Road closures, site closures, and lasting site damage due to wildfires every 

season impact patterns of recreation in these high-use national forests. With wildfire intensity and 

severity expected to increase throughout the west, there is a need to understand how wildfire activity 

affects forest recreation in southern California. This essay examines the impacts of fire activity in 

national forests by using revealed and stated preference data on site choice in one of the most heavily-

used national forests in the country. 

The study area focuses on the Angeles National Forest. This forest is the largest area of open 

space  in  Angeles  County  and  an  important  source  of  outdoor  recreation  for  the  dense  urban 

population of Los Angeles and its suburbs, receiving over 3 million visits annually from local trips as 

well as nationwide and international visitors (Garnache et al. 2018). Vegetation in the forest is primarily 

chaparral,  with  mixed  conifer  and  hardwood  forests  at  higher  altitudes.  Both  these  predominant 

 

135 

 

species are prone to fire; the forests experience both mild surface fires and intense crown fires, while 

chaparral primarily experiences intense, stand-burning fires but recovers more quickly. Sites in the 

Angeles National Forest span a wide variety of activities from hiking to fishing, picnicking, historical 

sites, and camping. Variation in land cover, site attributes, and burn and recovery patterns, make this 

a unique area to study the effects of visible fire damage to forest visitors. 

There  is  a  growing  literature  on  the  effects  of  wildfire  on  outdoor  recreation.  An  early 

contingent valuation study by Vaux, Gardner, and Mills (1984) gave university students at UC Davis 

a series of photographs to elicit preferences over fire damage. The photographic series they used 

showed typical forest vegetation before and after fire in a series of western conifer forest including 

Southern  California.  The  respondents  were  asked  which  series  they  preferred  given  that  both 

represented typical recreation areas nearby. They found that in general intense fires are detrimental, 

while more moderate fires may increase welfare. 

Instead of asking people how they react to fire, some studies use revealed preference data and 

recreation  demand  models.  Englin  et  al.  (1996)  use  data  from  canoe  registrations  in  Manitoba  to 

estimate the impacts of fire damage along popular canoe routes in a state park ten years after a series 

of large fires, finding a per-trip welfare loss of $15 per lost trip in 1993, ten years after the fires. 

Baerenklau et al. (2010) use a combination of geographic data and zonal travel cost models to map 

recreational value in the San Bernardino National Forest, which is adjacent to Angeles National Forest 

on the eastern side. They find that on average the value of a lost trip to a trailhead in the San Jacinto 

Wilderness  is  $19,  but  that  recreational  value  is  highly  spatially  concentrated  in  higher  elevations, 

suggesting that a major wildfire – such as the 2006 Esperanza Fire which affected the forest – would 

have varying costs across landscapes. 

Much of the literature into the cost of fires on recreational sites combines revealed preference 

(RP) and stated preference methods (SP) (Hesseln et al. 2003; Hesseln, Loomis, and González-Cabán 

 

136 

 

2004; Boxall and Englin 2008; Hilger and Englin 2009; Rausch, Boxall, and Verbyla 2010; Duffield et 

al. 2013). Revealed preference data can be used jointly with stated preference data from contingent 

valuation (e.g. Loomis 1997), discrete choice experiments (e.g. Christie, Hanley, and Hynes 2007), or 

contingent  behavior  methods  (e.g.  Englin  and  Cameron  1996)  to  draw  on  the  strengths  of  both 

approaches. A consistent finding of this literature is that forest fires decrease recreational value, but 

that there is heterogeneity across groups of recreationists and types of fires. Englin, Loomis, and 

González-Cabán in a pair of papers (Loomis, González-Cabán, and Englin 2001; Englin, Loomis, and 

Gonzalez-Caban 2001), and work by Hesseln et al. (2003; 2004) pool data on actual trips per season 

with  people’s  intended  trips  following  a  fire.  They  each  find  different  effects  depending  on  the 

intensity of the fire and the time since it occurred. Englin, Loomis, and González-Cabán (2001) find 

evidence of an “s-shaped” path of damages, suggesting that as an area recovers from a fire there may 

be  some  benefits  as  well  as  costs  to  recreationists.  Similarly,  Boxall  and  Englin  (2008)  find  both 

positive and negative parameters on burn variables depending on the time since fire. This suggests 

that as a forest recovers, there may be some benefits to a recent fire – perhaps some people are 

interested in the regrowth or prefer a less obstructed view of other scenery. The non-linear recovery 

pattern of damages lasts for several decades (Englin, McDonald, and Moeltner 2006; Boxall and Englin 

2008). Most of these studies take place in mountainous forested regions – the Rocky Mountains and 

western Canada and none of these studies take place in chaparral. 

Contingent behavior in the recreation literature has mostly been used to estimate hypothetical 

trips per year or season following a change. We take an alternate approach similar to that used by 

Adamowicz, Louviere, and Williams (1994), Boxall et al. (2003), and most-closely related to Parsons 

and Stefanova (2011) in which the respondents’ task is to decide whether an observed trip would have 

changed given various fire scenarios. This way, discrete decisions over scenarios are easily comparable 

 

137 

 

to discrete site choice decisions in the RP data. In addition, the approach helps to ground respondents 

in a real decision for which we have trip data.  

Given that wildfires are expected to become more frequent, there is a greater need to understand 

the effects of site closures and the continuing welfare effects of wildfire burn scars on the landscape. 

In this study we use visitation data to estimate a multi-site zonal travel cost model of demand for trips 

to  sites  in  the  Angeles  National  Forest.  Contingent  behavior  responses  are  embedded  within  the 

demand system and the implied fire preference parameters are estimated using contraction maps, 

allowing us to value both site closures and the impacts of fire history on sites after they reopen. Results 

contribute to forest management when facing increasing threats of site closures by providing insight 

into potential impacts during and after closures in a popular urban national forest. Of the fire scenarios 

presented, recent forest fires are the costliest, causing estimated welfare losses of up to $2.2 million 

per summer season for one affected site. The remainder of this essay is organized as follows: Section 

3.2 describes empirical strategy used to estimate the effects of fire. Section 3.3 describes the sampling 

strategy  for  the  onsite  survey  and  the  data,  and  Section  3.4  presents  model  results  and  welfare 

estimates. Section 3.5 concludes. 

3.2  Empirical Strategy 

This essay combines data on revealed site choice with information on stated choices under 

several  wildfire  scenarios.  First,  we  collected  onsite  visitation  data  at  day  use  sites  in  the  Angeles 

National Forest. Random sampling of recreation sites was stratified by expected use level (high or 

low), weekend or weekday, and morning or afternoon. We followed up with an online survey to collect 

contingent behavior data. The empirical strategy exploits both the onsite and contingent behavior data 

to estimate welfare effects of fires. Using respondents’ observed site choice, we employ a multi-site 

zonal  travel  cost  model  following  the  approach  developed  by  von  Haefen  et  al.  (2015)  for  the 

Deepwater Horizon oil spill. The zonal model uses on-site sampling and intercept probabilities to 

 

138 

 

estimate rates of visitation from each origin zip code, allowing us to estimate a multi-site recreation 

demand system with a full set of alternative specific constants (ASCs). This model provides estimates 

of visitation to each site under unchanged conditions which are then calibrated via contraction maps 

to estimates of the percentage of visitors who would have still visited the site at which they were 

intercepted under alternate fire history scenarios. 

3.2.1  Zonal Data Set 

Onsite trip data for this essay was collected June – August 2016 in the Angeles National Forest. 

Visitors were intercepted at hiking and picnicking sites; our random sampling strategy stratified sites 

according to the number of visits they generally receive over the weekend, and sampling times were 

stratified according to time of the day and day of the week (morning or afternoon, and weekend or 

weekday). Interviewers intercepted visitors as they exited the main hiking trail at the site or approached 

their vehicles to exit and kept a count of the number of exiting vehicles in each work shift. Sampling 

weights were constructed using the intercept probabilities which take into account the count of visitors 

to each sampled site as well as the probability of sampling that site. Using the trip intercept data and 

sampling weights, we estimate visitation to each site from each origin zip code. The zip code-level 

visitation is then used to estimate a multi-site zonal travel cost model that included non-participation 

using a method developed for the Deepwater Horizon oil spill (von Haefen et al. 2018)14 and recently 

implemented to estimate the impact of the Thomas fire in California (Garnache and Lupi 2018). The 

model is specified as a repeated random utility model (RRUM; Morey et al. 1993) using the zonal data 

and treating each origin as if it is composed of a representative agent from that zone. This section 

                                                

14 von Haefen et al. (2018) show a multi-site zonal model that included non-participation that was estimated using 
site intercept data yielded welfare measures that are strikingly similar to those of a multi-site model with non-participation 
that was estimated from a large general population sample of individuals (English et al. 2018). 

 

139 

 

describes the creation of the zonal data set, and a later section lays out the RRUM theory, choice 

probabilities and welfare measures. 

To create the zonal dataset, estimated trips are needed for each origin zone and destination 

sites.  Let j = 0, …, J be the set of sites in our dataset; j=0 corresponds to the outside option, or no-

trip option in a RRUM.  After removing sites for which we have no intercept data, e.g. no observations 

of individuals’ origin zones, the total number of sites in the choice set is J=31, and the total number 

of alternatives, including no-trip, is J+1=32. For each origin zip code i we identify the one or more 

sites visited by individuals from that zip code. Let Tij be the estimated total number of trips from zip 

code i to site j, derived from the survey sampling probabilities, where Ni is the set of intercepted 

individuals who live in zip code i, and !"# is the probability that individual n was intercepted at site j, 

which is derived from the sampling design. Trips from each origin to each site are estimated by  

 

We can also define Ti, the total number of trips from zip code i across all sites by summing Tij 

The total number of trips from all zip codes to a site j, Tj, is given by the sum of Tij over the I origin 

										.≠0 

$%#=' 1!"#
)*
"+,
1
$%='$%#
#+,
										.≠0 
$#='$%#
2
%+,

 

140 

over the J sites in the choice set: 

 

zip codes in the dataset. 

 

 

(1) 

 

(2) 

 

(3) 

 

For each zip code the Tij will serve as the weights in our estimation of the zonal RRUM. Following 

 

von Haefen et al (2018), we use the zip code population to construct the number of times in each 

where A is a scaling factor that allows the total choice occasions in zip code i to be greater than the 

 

origin that j=0 is chosen:  

$%3=4∗676%−$% 
population 676%.  A is defined as follows: 
<1.1∗ $%676%> 
4=max%
choice occasions for each origin zip code, ?@%, which equals 4∗676%. 

 

(4) 

 

(5) 

 

The aggregated zonal dataset contains trips for each origin-destination pair and the total number of 

3.2.2  Site Choice Model 

Site choice is modeled using the RP data following random utility maximization (RUM) theory. 

We have a sample of individuals from i zip codes, each with a set of J potential sites to visit; in our 

data j = 0, 1, …, 31, where j=0 is the no-trip option. In our zonal model assume an individual from 

site j≠0 has an observed component and a random error term. 

zip code i makes a choice of site j from a set of sites J. The utility for a person from zip code i at some 

B%#=C%#+E%#=FGHIJKL7MF%#NOPQRSTUVWO+X#+E%#										.≠0  
alternative specific constant X# that captures utility from attributes of site j that do not vary across 

The deterministic portion of utility depends on the travel cost from zip code i to site j and an 

(6) 

 

 

individuals.15  The utility for a person from zip code i from the no-trip option (j = 0) depends on the 

demographic characteristics of the zip code. 

 

                                                

15 Each of the J sites has a fixed effect, X#, commonly referred to as alternative specific constants (ASCs). Since 

random utility models are only defined up to utility differences, we can only identify ASCs for J of the J+1 alternatives. 

 

141 

B%3=C%3+E%3=YJZ		[\L7YJ%]%"UV^S+YJZ	H_J%]Q`S 
          +6LF	L7KKJ_J%]UVTTS`S+6LF	ℎ[M6H\[L%]b%WcQ"%U+E%3 

 

 

(7) 
 

 

The individual chooses site j only if the utility of site j is greater than all other sites in the choice 

 

 

 

expressed 

probabilities of site j≠0 take the nested-logit form and are equal to 

set,  including  the  no-trip  option.  The  probability  of  observing  that  individual  i  goes  to  site  j  is 

that  the  respondent  takes  a  trip  is  taken.  Assuming  the  error  term  has  a  GEV  distribution,  the 

d%#=d%	OP%cd%#|OP%c										.≠0  
where d%	OP%c is the probability of taking a trip, and d%#|OP%c is the conditional probability of site j given 
f∑
Jh6i,jC%kl
mj
d%,OP%c=
1k+,
Jh6(C%3)+f∑
Jh6i,jC%kl
mj 
1k+,
d%#|OP%c= Jh6i,jC%#l
∑
Jh6i,jC%kl
1k+,
where p is the nesting parameter, which captures the correlation between alternatives in the nest with 
qq='r$%3s%3K\(d%3)+'$%#s%#K\id%#l
2
%+,

recreation sites. Then the weighted log-likelihood function is 

1
#+,

(10) 

(11) 

t

 

(8) 

(9) 

 

 

 

 

 

 

where yij=1 if an individual from zip code i visits site j, and 0 otherwise, and Tij is the number of choice 

The number of predicted trips to site j is equal to the sum over zip codes of the number of 

occasions for which a person from zip code i visits site j. 

choice occasions in zip code i, $%, times the probability d%# given by the formula: 
$G[6M#='$%d%#
2
%+,

 

(12) 

 

 

 

142 

 

Our welfare predictions rely on calibration of the RRUM site choice model to the contingent 

estimate of value per lost trip, we divide the total welfare loss by the change in predicted trips with 

ÖjÜ−K\yJh6(C%3)+x' Jh6z{*|jÑ

ÖjÜÖ

 

analysis. For each fire type, the average welfare loss for a fire s at site j is given by the log-sum equation: 

behavior data. For each site j under some fire history scenario s we add by adding an additional term 

u#W to the estimated ASC. Then for each fire type we take the weighted average u̅W to use in welfare 
C#W='$%,wxK\yJh6(C%3)+x' Jh6z{*|}2~[ÄÅÅÅÇ]
Ñ
j
k
%
In  this  equation á#[u̅W]=<u̅W	[à	M[FJ=.
0	[à	M[FJ≠.   is  an  indicator  function;  if  site=j  we  add  the  weighted 
average u̅W to the utility for site j and $% is the number of choice occasions in zip code i. To get an 
åjÜ−K\zJh6(C%3)+f∑ Jh6i{*|jl
CâWä=∑$%,wxK\yJh6(C%3)+ã∑ Jh6z{*|}2~[ÄÅÅÅÇ]
Ñ
mjÑÖ
−∑ $[d[.M
∑ $[d[.
%
j
á[=1
á[=1
To estimate the value of site closures, we add term u#3 to the relevant estimated ASCs, which is a 
by Equation (15) where á#[u.0]=çu.0	[à	M[FJ	.	∈?
Cê='$%,wëK\íJh6(C%3)+ë' Jh6í{*|}2~ãÄ~ìå
î
j
%

0	[à	M[FJ	.∉?  and C is the set of closed sites. 
ïjî−K\yJh6(C%3)+x' Jh6z{*|jÑ
ÖjÜï
k

constant that drives predicted trips to closed sites to zero. Total welfare loss from site closure is given 

and without fire.  

k

k

(13) 

 

 

k

k

 

 

 

(14) 

 

(15) 

 

3.2.3  Calibration to SP Data and Welfare Measures 

 

The two-level nested logit model is estimated using the zonal dataset created from onsite trip 

data.  While it can be used to estimate the effect of fire-induced site closures, we would like to estimate 

the welfare impacts of wildfire histories on recreation sites after they reopen following fires. To do 

this, we use the data on respondents’ changes to site choice from the contingent behavior questions 

in the online survey. This approach of calibrating the model to outside data on site visitation has been 

 

143 

 

employed  by  English  et  al.  (2018).  In  our  case  we  choose  adjustments  to  site  alternative-specific 

constants such that the estimated pattern of demand matches the changes to visitation from the survey 

contingent behavior questions. For each fire scenario s in the dataset we have a percentage reduction 

site j so that 

in trips to some affected site j, or target trips to site j. We adjust the alternative specific constants to 

X#W=X#+u#W,											.≠0 
$G[6M#W=ñ$G[6M#,										.≠0 

These u#W solve the problems that equates predicted trips under fire and no fire conditions: 
Here, ñ is the proportion of respondents who chose “I would go to the same site” when presented 
fire scenario we solve for some u#W  using a contraction mapping (Berry et al, 1995; Murdock 2006). 
guesses values of uâWó so that $Gò6MâWô  and $G[6M#W are arbitrarily close. It is given by the equation 

with scenario s found in Table 3.4 (noting that not all fires occur at each site; a site in an area with 

The contraction mapping algorithm is specified in terms of predicted trips to site j and iteratively 

predominantly trees cannot have a shrub fire nearby). For each site in the choice set and each relevant 

Wô=uâ,kWó+lni$Gò6Mâlô −lnfàiú,uâ,kWólm 
uâ,k},

 

 

 

(16) 

(17) 

 

 

(18) 

 

where k indexes iterations. For each iteration, the guess is updated by adding the difference in logs 

between estimated trips to site j and target trips to site j.  

3.3  Data  
3.3.1  Onsite Survey Sampling Strategy and Design 

This chapter uses data from a two-stage survey. The first stage was conducted in-person during 

the  summer  of  2016,  with  a  follow-up  online  survey  in  the  winter.  The  onsite  recreation  survey 

conducted June 17 – August 14, 2016 intercepted visitors at a total of forty trailheads and day use sites 

 

144 

 

in the Angeles National Forest. During the summer, eight enumerators were assigned to six-hour 

shifts that occurred either in the morning (8 AM – 2 PM) or in the afternoon (2 PM – 8 PM). For 

each week of the survey, five “weekday” slots were drawn from nine potential weekday shifts; all five 

possible “weekend” – weekends included Friday afternoons – shifts were drawn on each week for 

which all workers were available. On each assigned shift, two sites were selected. Each shift followed 

a clustered sampling strategy in which sites were separated by location into one of three clusters; first, 

a cluster was drawn, and then two sites within that cluster. Within each cluster, sites were stratified by 

the number of visits they generally receive on a weekend – high or low use.  

At low-traffic sites, or where the parking lot was easily monitored, enumerators intercepted 

people as they approached their vehicle to leave, while one person per shift was recorded exiting 

vehicle traffic. At some heavily used trailheads, enumerators intercepted people as they returned from 

a hike, as one person recorded the number of individuals exiting the trail. Visitation counts based on 

vehicles were converted to people using the data from the intercepts on the number of people per 

vehicle. With these exit counts and the total number of interviews at a site during a given shift, we 

estimate the probability that an individual was interviewed conditional on being at that recreation site 

on that day. The sampling weights for the site strata were used to calculate the probability that a site 

was drawn in any particular work shift. Finally, we estimated the probability that interviews were 

conducted during a work shift given the time of day and day of the week. These three were combined 

to form an intercept probability equal to the probability of intercepting an individual at a given site 

during a given shift.  

 

145 

 

The onsite survey received a response rate of 62%. This percentage includes only complete 

responses  by  people  who  were  recreating  at  the  national  forest  site.16  Respondents  provided 

information about their trip, main activity in the forest, demographic information, and were asked to 

provide an email or mailing address for a follow-up online survey.17 Of 2266 complete in-person 

interviews, 1755 (77.7%) respondents provided either an email address (1685) or mailing address (70) 

for the web survey.  
3.3.2  Online Survey Design 

In the online follow-up survey, respondents are first primed on major attributes of interest – 

vegetation, the presence of water at the site, and fire history. Vegetation and water were chosen as 

they  are  likely  to  be  some  of  the  most  salient  environmental  attributes  for  visitors:  the  Angeles 

National  Forest  has  diverse  vegetation  but  can  be  broadly  classified  into  forest  or  chaparral,  and 

recreation  sites  with  a  stream  or  lake  attract  different  visitors  and  different  activities  than  those 

without. Respondents are also asked to think about attributes “nearby” and “farther away” from the 

parking area because pretesting suggested that some people differentiated between whether a fire had 

been off in the distance or was visible in the area around the parking lot and picnic areas, which tend 

to be right by the parking lots.18 Thus, nearby was defined as the area within a 5-minute walk from the 

parking area, and farther away was defined as the area beyond a 5-minute walk. Next, respondents 

were introduced to the vegetation types and to fire impacts for chaparral and forests prior to receiving 

two to six contingent behavior questions depending on the vegetation type at the site they visited. We 

                                                

16 Disposition codes for the onsite and online surveys are provided in the Appendix 2F of Essay 2. 

17 See the appendix for replicas of the paper versions of on-site and online survey instruments. 

18 Survey development included 49 in-person interviews conducted at Angeles National Forest (ANF) recreation 
sites in July 2015, with some testing our site intercept instrument and some probing what people would do in response to 
fires. Paper questionnaires were tested in 15 in-person interviews at ANF in May 2016. In Fall 2016, the online instrument 
was tested in a webinar setting in four individual cognitive interviews with people previously intercepted at ANF. 

 

146 

 

also collected information on respondents’ national forest visits, attitudes towards sites with visible 

fire history, and how they receive information about national forest site closures and fire conditions. 

Contingent behavior questions were tailored to the type of site at which the respondent was 

intercepted. There were three possible sets of questions corresponding to vegetation at their site: 1) 

trees nearby and trees farther away, tree/tree; 2) trees nearby and shrubs farther away, tree/shrub; 3) 

shrubs nearby and shrubs farther away, shrub/shrub. The number of contingent behavior scenarios 

depends on the site type because not all types of fire are feasible at every vegetation combination. 

Forest fires can be broadly categorized as either high-intensity crown fires, which burn all plants 

to the crown of the trees, or surface fires which burn the grasses and scorch tree trunks, but do not 

reach to the tops of trees. High-intensity forest fires leave large areas of burned vegetation visible from 

long distances that may take years to recover. Low-intensity surface fires are more difficult to see from 

a distance, however, close up they leave lasting marks at recreation sites. Chaparral fires tend to burn 

with high intensity, and also recover more quickly than trees; sometimes, after a year it is difficult to 

see where chaparral burned. Therefore, for the contingent behavior scenarios we assume that past 

fires that burned in areas of mostly trees could have burned some plants or all plants and could have 

been recent or old fires. Both types of fires (tree or shrub) could have been near the parking lot or farther 

away. However, we assume old forest fires that burned only some plants are not visible farther away 

and were not included. Fires that burn in areas of mostly shrubs we assume can only burn all plants, 

and could only be recent, as fires more than a couple years old are not visible. Therefore, respondents 

with an intercept site that was tree/tree saw contingent behavior questions with six possible past fire 

combinations, respondents to tree/shrub sites saw four scenarios, and respondents to shrub/shrub 

sites saw two contingent behavior scenarios. 

Contingent behavior scenarios correspond with the predominant vegetation at sites at which 

respondents were intercepted: see Table 3.1 for a list of the three site vegetation categories and their 

 

147 

 

fire history scenarios. Sites were categorized according to their vegetation nearby (within a 5-minute 

walk  of  the  parking  area)  and  farther  away  (more  than  5-minutes  but  less  than  an  hour’s  hike). 

Vegetation  types  were  defined  according  to  what  visitors  would  see  and  how  sites  are  used.  For 

example, nearby was “mostly trees” if there was some shade present, for example a group of trees 

near a picnic table, and “mostly shrubs” otherwise. Sites were “mostly trees” farther away if the major 

trail from the parking lot followed a shaded path, and “mostly shrubs” if the path was exposed. We 

used a combination of visual evidence from visiting each site, aerial images from Google Earth, and 

information about major hikes in the area to determine vegetation type. 

 
Table 3.1 Contingent Behavior Scenarios for Each Vegetation Type 

Vegetation type 

Contingent Behavior Scenarios 

 

 

Old fire that burned all plants farther away 
Old fire that burned all plants nearby 
Recent fire that burned all plants farther away 
Recent fire that burned all plants nearby 
Recent fire that burned some plants farther away 
Recent fire that burned some plants nearby 

Trees near, trees far 
 
 
 
 
 
Trees near, shrubs far  Old fire that burned all plants nearby 
 
 
 
Shrubs near, shrubs far  Recent shrub fire farther away 
  

Recent fire that burned all plants nearby 
Recent shrub fire farther away 
Recent fire that burned some plants nearby 

Recent shrub fire nearby 

 

 

 

 

 

 

 

The online survey ran from November 2016 to January 2017. Email addresses were contacted 

a total of 8 times and mailing addresses 6 times. Overall 662 out of 1755 people contacted (38%) 

responded to the survey. The majority (576) were at sites where there were trees both nearby and 

farther away and saw six contingent behavior scenarios. Descriptive statistics for the full dataset of 

 

148 

onsite survey respondents are in Table 3.2; we have information on education and income for online 

 

survey respondents only. 

 

Table 3.2 Descriptive Statistics for Onsite Survey Respondents 

Variable 

 

Mean 

 

37 
Age (years) 
0.63 
Male (0/1) 
0.39 
Hispanic (0/1) 
0.54 
White (0/1) 
0.67 
College degree (0/1) 
101.23 
Income ($1000) 
One-way distance to site visited (miles)  47.12 
0.71 
Hiker 
 

 

 

Min 

 

18 
0 
0 
0 
0 
12.50 
1.30 
0.00 

 

Max 

 

87 
1 
1 
1 
1 
250.00 
558.80 
1.00 

 

 N  

 

3,124  
3,141  
3,130  
2,907  
774  
716  
3,150  
3,150  

 

3.3.3  Contingent Behavior Data 

We derive welfare estimates of the eight different fire scenarios presented in the contingent 

behavior section of the online survey. For each fire scenario, we have an estimate of the percent of 

trips to a site that would switch to either another site or no trip. Table 3.3 shows responses from the 

online survey data: the worst fire scenario, which causes the most switching, is a recent fire that burned 

all plants farther away from the parking lot. Fifty-eight percent of respondents would continue to go 

to the same site, while 36% would go to a different site, and 6% would do something else. Roughly 

10-15% of trips are altered in scenarios with fires that burn only some plants, or an old fire near the 

parking area. 

 

 

149 

Table 3.3 Contingent Behavior Responses to Fire Scenarios 

 

Fire Scenario 

 

Old all, far 

Old all near 

Recent all far 

Recent all near 

Recent far shrub 

Recent near shrub 

Recent some far 

Recent some near 

 

Do Something 
Else 

Go to Another 
Site 

Go to the Same 
Site 

Vegetation 
Types 

 

2.92% 

1.89% 

6.42% 

4.38% 

2.23% 

3.86% 

0.80% 

1.86% 

 

12.69% 

7.35% 

35.90% 

30.89% 

12.26% 

4.41% 

12.81% 

10.62% 

 

84.39% 

90.76% 

57.69% 

64.74% 

85.51% 

91.73% 

86.39% 

87.52% 

 

Tree/tree 

Tree/tree 
Tree/shrub 
Tree/tree 

Tree/tree 
Tree/shrub 
Tree/shrub 
Shrub/shrub 
Shrub/shrub 

Tree/tree 
Tree/shrub 
Tree/tree 

3.3.4  Summary Statistics 

Summary statistics for the zonal dataset and the individual data prior to aggregation are found 

in Table 3.4. The zonal dataset was created with data from onsite interviews conducted in 2016. In 

2016 intercepted individuals were on average 38 years old. Sixty-four percent were men, and 68% 

college educated. Household income was relatively high, $103,000 annually, and the majority (58%) 

of respondents were white, and the largest minority was people of Hispanic or Latino origin (36%). 

Our dataset consists of 2,045 individuals from 467 origin zip codes.19 The average value of Tij, or the 

number of trips from zip code i to site j, is 593, while the average number trips from any given zip 

code 1,568. The number of trips to a site j ranges from 146 to 320,044 with an average of 23,617, and 

the total number of trips to any site is 732,127.  

                                                

19 For the current version of this chapter we limit the data to individuals from zip codes in California only and 

individuals for which we had previously estimated distances and travel costs from PC Miler 

 

150 

 

The travel cost from zip code to site latitude and longitude is calculated: 

$GHIJKL7MF%#=Z[MFH\LJ∗($.23	6JG	Y[KJ)+FGHIJK	F[YJ∗13yH\\†HK	[\L7YJ
2000

 

Ü 

(6) 

 

Where distance is round-trip distance and travel time is round-trip travel time in hours calculated by PC 

Miler. The cost of driving per mile is calculated using the 2016 AAA Your Driving Costs report and 

includes both operating costs and the marginal cost of depreciation using values for a medium-sized 

sedan driving 15,000 miles per year20. The opportunity cost of time is the one-third median household 

income of the zip code divided by 200021, or roughly one-third the hourly wage.  

                                                

20  Operating  costs  (fuel,  tires,  and  oil)  are  $.1753  per  mile,  and  the  average  marginal  depreciation  per  mile  is 

(290+225)/10,000 = $.0515 per mile, for a total per mile driving cost of $.2268 

21 Assumes a 40-hour work week, and 50 weeks worked per year 

 

151 

 

Table 3.4 Descriptive Statistics for the Zonal Dataset 

 

 

Variable 

 

Individual-Level Demographics  Age (years) 
 
Male (0/1) 
 
Hispanic (0/1) 
 
White (0/1) 
 
College degree (0/1) 
 
Income ($1000) 

 

Aggregating Variables 
 
 

 

Trips from zip code i to site j (Tij) 
Trips from zip code i (Ti) 
Trips to site j (Tj) 

 

 

Zip Code-Level Demographics  Median household income ($) 
 
 
 
 
 

College degree (%) 
Median age (years) 
Hispanic (%) 
White (%) 
Unemployment rate (%) 

Mean 

 

38 
0.64 
0.36 
0.58 
0.68 
103.10 

 

593 
1,568 
23,617 

 

Min 

 

18 
0 
0 
0 
0 
12.50 

 

29 
45 
146 

 

Max 

 

84 
1 
1 
1 
1 
250.00 

 

12,024 
13,008 
320,044 

 

N 

 

2,032 
2,045 
2,038 
1,881 
500 
463 

 

1,234 
467 
31 

 

67,732.70  12,370.00  195,051.00  1,699 
1,701 
20.11 
1,701 
37 
59.76 
1,701 
1,701 
59.27 
8.51 
1,701 

2.21 
21 
2.10 
11.85 
0.00 

47.57 
66 
98.34 
96.88 
26.20 

 

Trip Statistics 
 
 
 

 

Round-trip distance to any site (miles) 
Round-trip travel cost to any site ($) 
Round-trip distance to site visited (miles) 
Round-trip travel cost to site visited ($) 

 

 

 

147.14 
68.54 
116.75 
55.66 

 

 

2.00 
1.17 
2.60 
1.76 

 

 

1,199.00 
578.08 
1,117.60 
574.49 

 

52,731 
52,669 
1,234 
1,233 

 

 

Table 3.4 includes descriptive statistics for the zonal data set. The section on individual-level demographics are descriptive statistics for the individuals whose weights 
were then aggregated at the zip code level. Aggregating variables including Tij, Ti, and Tj are used to develop the zip code level data set and weights used for estimation. 
Zip code-level demographics are taken from the US Census Bureau 2016 American Community Survey 5-year estimates. Trip statistics are summary statistics for distance 
and travel cost between zip codes and sites. 

 

152 

 

3.4  Results 

3.4.1  Site Choice Model 

Estimated  parameters  for  the  site  choice  model  are  presented  in  Table  3.5.  The  travel  cost 

parameter is negative and significant, indicating that sites with a higher travel cost are less likely to be 

chosen. A full set of J ASCs were estimated, with the no-trip ASC !"=0; for brevity the coefficients 

are omitted from Table 3.5. The nesting parameter t is between 0 and 1, and significantly different 

from 1. It is a measure of the correlation between the sites in the Trip nest, and implies that the nested 

logit model, which allows for correlation within alternatives in a nest, is a better fit for our data than 

the conditional logit model. The participation level parameters, which are interacted with the J=0 no 

trip  alternative,  show  that  origins  with  higher  median  household  income,  age,  education  and 

percentage non-Hispanics have higher participation levels (are less likely to choose the not rip option). 

The standard errors and confidence interval in Table 3.5 were estimated by constructing bootstrapped 

samples of the individual-level trip data22.  

The site choice model allows us to estimate the welfare effects of site closures. Major wildfires 

often cause recreation sites to close either while the fire is suppressed or in the case of areas that 

sustain major infrastructure damage, sites sometimes remain closed for months or years. We find that 

the average per-trip welfare loss from the closure of a day-use site range from $24 to $29 per trip. The 

closure of high-use sites for an entire season results in welfare loss up to $9 million (a table describing 

welfare loss from site closure can be found in the appendix).  

 

                                                

22 The dataset of individuals was expanded so that the person’s frequency in the data was proportional to their 
resampling probability. Replicate datasets were then drawn for each site so that the number of trips in each site remained 
the same. 

 

153 

Table 3.5 Site Choice Model Results 

Level 

Variable 

 

Trip 

 

Travel cost 

  Nesting parameter 

 

 

No trip  Median household income 

  Median age 
  Pct college graduate 
  Pct Hispanic 
Log likelihood 
N 

 

 

 

 
  

 

 

Coef. 

 

 

 

 

1.82E-04 
0.005 

-0.017*** 
0.419*** 
-1.96e-06***  1.15E-07 
3.62E-04 
-0.057*** 
0.025 
-1.591*** 
0.011 
0.866*** 

Std. Err.  95% Confidence Interval 

 

-0.018 
0.410 

 

-2.16E-06 
-0.057 
-1.640 
0.843 

 

-0.017 
0.427 

 

-1.74E-06 
-0.056 
-1.551 
0.889 

 

-5910159.1 
4.797e+09 

 

 

 
 

 

 

 
 

 

 

 
 

 

Note: For brevity the site-specific constants (the ASCs) are not presented here. 
 
3.4.2  Welfare Effects of Fire 

In this section we present results from the contraction map and estimate the welfare impacts of 

our eight fire scenarios, which are specific to the type of vegetation found at the recreation site. The 

eight scenarios are: 

1.  Old forest fire that burned all plants farther away 

2.  Old forest fire that burned all plants nearby 

3.  Recent forest fire that burned all plants farther away 

4.  Recent forest fire that burned all plants nearby 

5.  Recent shrub fire farther away 

6.  Recent shrub fire nearby 

7.  Recent forest fire that burned some plants farther away 

8.  Recent forest fire that burned some plants nearby 

For each site j and fire scenario s we estimate a set of parameters %&' that equate the expected 
trips to site j with predicted trips using the site choice model. Table 3.6 shows the average %̅' and the 

 

154 

95% confidence intervals for %̅' computed using the bootstrapped datasets, weighted by predicted 
under the given scenario. The parameters %̅' are used as inputs into the welfare estimation24. 

trips to sites.23 In Table 3.6 σ is the proportion of people who would choose to go to the same site 

 

 

Table 3.6 Weighted Average of Delta from Contraction Map 

%̅' 

Confidence Interval	
(%̅') 

, 

Vegetation types 

Fire Scenario 

 

Old all far 
Old all near 
Recent all far 
Recent all near 

Recent far shrub 
Recent near shrub 
Recent some far 
Recent some near 

 

 

-0.0873 
-0.0490 
-0.2747 
-0.2144 

-0.0682 
-0.0377 
-0.0754 
-0.0672 

 

 

(-0.0888, -0.0858) 
(-0.0499, -0.0482) 
(-0.2795, -0.2698) 
(-0.2182, -0.2105) 

(-0.0696, -0.6685) 
(-0.0385, -0.3694) 
(-0.0767, -0.0741) 
(-0.0684, -0.0660) 

 

 

 

84.39%  Tree/tree 
90.76%  Tree/tree 
Tree/shrub 
57.69%  Tree/tree 
64.74%  Tree/tree 
Tree/shrub 
85.51%  Tree/shrub 
Shrub/shrub 
91.73%  Shrub/shrub 
86.39%  Tree/tree 
Tree/shrub 
87.52%  Tree/tree 

 

 

 

the change in predicted trips to site j under the change, and the value per lost trip -.'/. Naturally when 

For each fire s we calculate the total welfare loss for one summer season25 with the fire at site j, 

we compare across the sites, sites with larger numbers of trips experience larger losses, making it 

sensible to report the value per lost trip. Table 3.7 shows weighted average value per lost trip for each 

scenario – welfare losses range from $24.94 per lost trip to $29.52 per lost trip. Results are as expected, 

with  forest  fires  mattering  more  than  shrub  fires,  and  fires  farther  away  from  the  parking  area 

                                                

24 The site-specific estimates %&' are presented in the appendix 

23 The bootstrapping for these calculations has not yet accounted for the underlying variation in each σ. 

25 Welfare estimates correspond to the sampling period for the intercept survey, early June to mid-August 

 

155 

 

mattering more than fires nearby the parking area. Given that a large majority of respondents were 

hikers – roughly 70% of intercepts – it is reasonable to expect that fire conditions at some distance 

from the parking area will have a greater welfare impact than conditions nearby, where the average 

respondent spends less time. However, the overall difference in the estimates per lost trip between 

nearby and farther away is small in magnitude (around $1 per lost trip). The large differences in value 

lost are between shrub fires and forest fires; per-lost-trip from shrub fires either nearby or farther 

away is around $25, while for forest fires it is $29 per lost trip. This is potentially because shrubs or 

chaparral grow back relatively quickly after a fire, and because visitation is lower at these sites. Our 

presented scenarios were on a time scale at which there would be significant regrowth in chaparral 

areas; we only ask respondents to consider shrub fires 1-3 years old, whereas chaparral areas generally 

see significant regrowth within one year. 

 

156 

 

Table 3.7 Trip Predictions and Welfare Estimates for a Past Fire Affecting a Single Site 

Fire Scenario 

Welfare loss 

 

Old all far 
Old all near 
Recent all far 
Recent all near 
Recent far shrub 
Recent near shrub 
Recent some far 
Recent some near 

 

 

 $       951,186  
 $       488,600  
 $    2,535,967  
 $    1,843,208  
 $       175,601 
 $       103,572  
 $       830,337  
 $       658,974  

 

Confidence Interval 
(Welfare loss) 

Δ Trips to site j  Confidence Interval 

(Δ Trips) 

Value per lost trip 

 

($ 914,513,     $ 982,420) 
($ 469,699,     $ 504,619) 
($ 2,437,628,  $ 2,618,989) 
($ 1,771,761,  $ 1,903,490) 
($ 168,783,     $ 181,304) 
($ 99,554,       $ 106,940) 
($ 798,341,     $ 857,609) 
($ 633,464,     $ 680,573) 

 

 

30,263  
15,589  
83,196  
60,436  
6,990  
4,139  
26,361  
21,093  

 

 

(29,072,    31,240) 
(14,973,    16,094) 
(79,932,    85,878) 
(58,056,    62,387) 
(6,717,      7,215) 
(3,978,      4,273) 
(25,323,    27,212) 
(20,260,    21,775) 

 

 

 $ 29.47  
 $ 28.94  
 $ 28.73  
 $ 28.32  
 $ 24.94  
 $ 24.99  
 $ 29.52  
 $ 28.86  

 

Note: Welfare loss, change in trips, and value per lost trip are a weighted average across sites for the summer season. 95% confidence intervals 
were computed using the bootstrapped datasets. 

 

157 

 

For each recreation site in the choice set, the contraction mapping used to estimate welfare 

losses calibrates that site’s ASC until the new predicted trips to the site are equal to the predicted trips 

under some fire scenario according to responses from the survey data. However, for each fire scenario 

we also have a contingent behavior estimate of the percentage of respondents who would have stayed 

at home rather than take a trip to another site in the forest. The contraction mapping results do not 

take into account the percentage of people who stated they would go to another site in the forest or 

stay at home. Rather, the pattern of substitution away from the site in question is determined by the 

estimated  parameters  from  the  zonal  travel  cost  model.  Table  3.8  compares  how  the  estimated 

distribution of diverted trips from site j after a fire using our calibrated ASCs differs from respondents’ 

stated  behavior  in  the  contingent  behavior  data.  Overall,  we  find  that  our  model  predictions  for 

continuing to go to the same site are very close. However, the estimated nested logit model structure 

is less likely to predict that people will choose the no-trip option than our survey respondents stated 

preferences. For each of the fire scenarios, with the exception of recent forest fires that burned all 

plants, roughly 2% of respondents would choose the no-trip option. For recent forest fires that burned 

all plants, that number is closer to 8% who would choose to do something else rather than recreate in 

the forest. The model predicts well below 1% choosing to do something else for all possible scenarios, 

and nearly all diverted trips going to other recreation sites in the forest. 

 

158 

Table 3.8 Comparison of Stated Preference Data and Nested Logit Predictions 

 

Survey Responses 

Model Predictions Using !̅# 

 

Fire Scenario 

 

Old all far 
Old all near 
Recent all far 
Recent all near 
Recent far shrub 
Recent near shrub 
Recent some, far 
Recent some near 

 

Do something 

else 

Go to another 

site 

Go to the same 

site 

Do something 

else 

Go to another 

site 

Go to the same 

site 

 

2.92% 
1.89% 
6.42% 
4.38% 
2.23% 
3.86% 
0.80% 
1.86% 

 

12.69% 
7.35% 
35.90% 
30.89% 
12.26% 
4.41% 
12.81% 
10.62% 

 

84.39% 
90.76% 
57.69% 
64.74% 
85.51% 
91.73% 
86.39% 
87.52% 

 

0.0111% 
0.0057% 
0.0295% 
0.0215% 
0.0020% 
0.0012% 
0.0097% 
0.0077% 

 

15.77% 
9.36% 
42.45% 
35.46% 
14.49% 
8.27% 
13.76% 
12.63% 

 

84.22% 
90.63% 
57.52% 
64.52% 
85.51% 
91.73% 
86.23% 
87.36% 

 

 

 

 

 

 

Note: Model predictions are averaged across the results for each of the 31 sites. 

 

159 

3.4.3  Station Fire 

 

To illustrate the temporal effect of wildfires in the Angeles National Forest we estimate the 

welfare effects of three different fire scenarios, using a group of sites affected by the Station Fire 

(2009) as an example.26 The Station Fire is one of the largest wildfires in Angeles County – it burned 

for nearly two months (August- October 2009) and affected 160,577 acres, mostly in the southwestern 

portion of the Angeles National Forest. Figure 3.1 shows the extent of the burn scar as captured by 

the MODIS satellite in September 2009 (NASA 2009). In addition to causing fire damage at recreation 

sites, over 40 miles of the Angeles Crest Highway, which runs through the forest and provides access 

to campgrounds, trailheads, and visitors’ centers in the forest, remained closed after the fire due to 

continued risk from debris and mudslides until June 2011 (Pasadena Star-News 2011). In addition to 

site  closures  within  the  fire  perimeter,  the  Angeles  Crest  Highway  closure  prevented  visits  to 

unaffected sites north of the fire perimeter for the better part of two years. Twelve of the sampled 

sites from the intercept survey are located within the burn scar, ten of them along the Angeles Crest 

Highway. An additional five sites are accessible only by the highway but were not in the fire perimeter. 

Even after the opening of sites, our model results suggest there will be impacts if effects of fire are 

visible at sites. Lasting damage from the Station Fire was still visible at many of the affected forested 

sites during our site visits in 2016, seven years after the fire. To illustrate the dynamic effect of the 

Station Fire we model three scenarios, each lasting one season: (1) a highway closure that prevents 

access to all sites on the Angeles Crest Highway; (2) a recent fire that burned all vegetation (both 

forests and shrubs) far from the parking area within the Station Fire burn scar; and (3) an old fire that 

                                                

26 The purpose here is to apply the model to this scenario to illustrate how the model addresses the immediate, 
mid, and longer-term effects of a large fire on recreation sites. This is not meant to be an exact recreational damage 
assessment of the station fire. 

 

160 

 

burned all vegetation far from the parking area within the Station Fire burn scar (at a time when far 

shrub fires would no longer be noticeable).  

 

 

Figure 3.1 Station Fire Burn Scar on Sept. 16, 2009 

 

The sites used in the analysis with their predicted trips under the status quo are shown in Table 

3.9. They are predominantly sites that provide access to major trails located in forested areas although 

four sites are located in less shaded shrubland. In the road closure scenario all sites on the Angeles 

Crest Highway are inaccessible and receive no trips. We estimate that, in the first scenario, the fire and 

highway closure would have caused $2.8 million in forest recreation-related welfare losses. The second 

scenario is a recent fire that burned all vegetation (trees or shrubs) far from the parking area. We find 

that in the year after re-opening, when fire effects would be clearly visible at recreation sites, the Station 

Fire would have caused 22,196 diverted trips to the affected sites, resulting in a total welfare loss of 

 

161 

 

about $563,000. Later, as vegetation began to recover in our third scenario, fire damage would still 

affect roughly 6,870 trips to the forest and cause welfare losses of about $171,000.  

 

Table 3.9 Sites Affected by Station Fire 

Site 

 

Burn perimeter  Angeles Crest Hwy  Predicted 

summer trips 

 

Yes 
Buckhorn Picnic Area 
Yes 
Charlton Flat Picnic Area 
Yes 
Chilao Visitor Center 
Yes 
Devil's Canyon Trailhead 
Josephine/Colby Road Trailhead  Yes 
Yes 
Mt. Wilson Observatory 
Red Box Picnic Area 
Yes 
Yes 
Hidden Springs Picnic Area 
Yes 
Stonyvale Picnic Area 
Wildwood Picnic Area 
Yes 
No 
Islip Saddle Trailhead 
No 
Eagle Roost Picnic Area 
Grassy Hollow Visitor Center 
No 
No 
Inspiration Point 
Vincent Gap 
No 

 

 

 

 

Yes 
Yes 
Yes 
Yes 
Yes 
Yes 
Yes 
No 
No 
No 
Yes 
Yes 
Yes 
Yes 
Yes 

 

 

850 
3,686 
1,112 
202 
678 
5,212 
11,299 
357 
3,969 
19,675 
5,841 
631 
12,609 
8,432 
763 

 

3.5  Conclusions 

The  Angeles  National  Forest  is  one  of  the  most  important  areas  of  outdoor  recreation  for 

people in Los Angeles County as well as visitors from farther away. In recent years the forest has 

frequently experienced wildfires in the forest boundary, often causing road closures and site closures, 

sometimes causing lasting damage. In 2016 the Sand Fire consumed a large section of the forest near 

Santa Clarita, causing site closures that are still in place two years later. Even when recreation sites 

reopen, popular hikes and picnic sites may have visible fire damage. 

 

162 

 

This essay uses combined revealed preference and stated preference data to estimate the welfare 

impacts of fire at recreation sites in the forest. In particular, we use stated response data for several 

types  of  fires  that  could  previously  have  occurred  at  the  site  they  were  intercepted  at,  for  which 

respondents stated whether they would go to the same site, go to some other national forest site, or 

choose to do something else. A multi-site zonal recreation demand model was estimated with the 

intercept revealed preference data, and it was calibrated to the contingent behavior results in order to 

estimate the demand and welfare impacts of fires after sites reopen. 

From our nested logit zonal model specification, we find that there is significant correlation 

between site alternatives. Individuals from zip codes that are on average wealthier and more educated 

are more likely to take trips to the Angeles National Forest; individuals in areas that are less wealthy 

or have a higher share of Hispanics are less likely to recreate in the forest. Our multi-site zonal model 

is  specified  using  alternative-specific  constants;  we  use  contraction  maps  to  calibrate  these  site 

constants to estimate the change in site characteristics that results in the same number of reduced trips 

as in the contingent behavior data. We find welfare loss of forest fires of roughly $29 per lost trip. 

When considering the average effect of a past fire on a single site, a recent forest fire that burned all 

plants farther away has the greatest total welfare loss, $2.5 million, followed by a recent forest fire that 

burned all plants nearby, at $1.8 million. This suggests that increasing fire activity in the national forest 

as  well  as  other  wilderness  areas  in  California  not  only  have  immediate  economic  impacts  from 

potential destruction of property and loss of life, but that indirect welfare losses to recreation continue 

for years afterwards. 

The largest wildfires in the forest do not affect one site at a time. Usually several in the same 

area are impacted, and in some cases, such as the Station Fire in 2009, over ten major day use, hiking, 

and camping areas experience fire damage. For large wildfires that impact multiple sites, our single site 

welfare estimates are an understatement of the actual impact. To demonstrate how large fires such as 

 

163 

 

the Station Fire can have a lasting impact over time, we model the welfare effects of a fire and road 

closure that affected many major hiking and picnic sites both within and outside of the Station Fire 

burn perimeter. We also illustrate how major wildfires have lasting impacts over time by modeling 

recent and older fires that burn all plants farther away from the parking area on hiking trails. The 

model predicts that in the summer after the fire when sites were inaccessible, the Station fire caused 

welfare losses of over $2 million. After re-opening but while significant damage was still visible, it 

caused over 20,000 altered trips to the forest, and years later even as the forest began to recover and 

shrubs had recovered, the impacted sites still see 5,000 fewer visits per year.  

Finally, the substitution pattern in our calibrated zonal model predicts many fewer no-trips than 

suggested by our stated preference data. In the contingent behavior data, 1-6% of trips to sites are 

diverted to the stay-home option under our fire scenarios. In our calibrated demand model we predict 

0.002% of those trips become stay-home when there is a shrub fire. Under the worst-case scenario, a 

recent forest fire that burned all plants farther away, we predict 0.0295% of the trips become stay-

home  option.  Future  extensions  to  this  work  should  consider  the  stated  preference  substitution 

between other sites and no-trip in order to more accurately predict the pattern of stated responses to 

fire. 

 

 

 

164 

 

 

 

 

 

 

 

 

 

 

 

 

 

APPENDICES 

 

 

 

 

 

 

 

 

 

 

 

165 

 

Appendix 3A: Recreation sites in zonal data set and predicted trips 

Table 3.10 Recreation Sites and Predicted Trips 

Vegetation 

Predicted summer trips 

 

Site 

 

East Fork Trailhead 
shrub/shrub 
Elizabeth Lake Canyon Road 
shrub/shrub 
Josephine/Colby Road Trailhead  shrub/shrub 
Upper Bear Creek Trailhead 
shrub/shrub 

 

Barrett Stoddard Road 
Bear Divide Vista Picnic Area 
Elizabeth Lake Picnic Area 
Frenchman’s Flat 
Hidden Springs Picnic Area 
Stonyvale Picnic Area 
West Fork  
Wildwood Picnic Area 

 

Buckhorn Picnic Area 
Chantry Flat Picnic Area 
Charlton Flat Picnic Area 
Chilao Visitor Center 
Devil's Canyon Trailhead 
Eagle Roost Picnic Area 
Grassy Hollow Visitor Center 
Icehouse Canyon Trailhead 
Inspiration Point  
Islip Saddle Trailhead 
Jackson Lake Picnic Area 
Mt. Wilson Observatory 
Red Box Picnic Area Area 
San Antonio Falls Trailhead 
Switzer Picnic Area 
Three Points Trailhead 
Vincent Gap 
Vista Picnic Area 
Windy Gap Trail 

 

 

 

tree/shrub 
tree/shrub 
tree/shrub 
tree/shrub 
tree/shrub 
tree/shrub 
tree/shrub 
tree/shrub 

 

tree/tree 
tree/tree 
tree/tree 
tree/tree 
tree/tree 
tree/tree 
tree/tree 
tree/tree 
tree/tree 
tree/tree 
tree/tree 
tree/tree 
tree/tree 
tree/tree 
tree/tree 
tree/tree 
tree/tree 
tree/tree 
tree/tree 

 

166 

 

 

 

51,904 
1,040 
678 
168 

 

1,517 
4,781 
1,353 
3,652 
357 
3,969 
66,450 
19,675 

 

850 
318,695 
3,686 
1,112 
202 
631 
12,609 
85,395 
8,432 
5,841 
4,911 
5212 
11299 
94524 
20887 
762 
763 
537 
149 

 

 

Appendix 3B: Site Closure 

Table 3.11 Welfare Impacts of Site Closure by Site 

Site 

 

Islip Saddle Trailhead 
Elizabeth Lake Canyon Road 
Barrett Stoddard Road 
Bear Divide Vista Picnic Area 
Buckhorn Picnic Area 
Chantry Flat Picnic Area 
Charlton Flat Picnic Area 
Chilao Visitor Center 
Devil's Canyon Trailhead 
Eagle Roost Picnic Area 
East Fork Trailhead 
Elizabeth Lake Picnic Area 
Frenchman’s Flat 
Grassy Hollow Visitor Center 
Hidden Springs Picnic Area 
Icehouse Canyon Trailhead 
Inspiration Point Area 
Jackson Lake Picnic Area 
Josephine/Colby Road Trailhead 
Mt. Wilson Observatory 
Vincent Gap 
Red Box Picnic Area 
San Antonio Falls Trailhead 
Stonyvale Picnic Area 
Switzer Picnic Area 
Three Points Trailhead 
Upper Bear Creek Trailhead 
Vista Picnic Area 
West Fork 
Wildwood Picnic Area 
Windy Gap Trail 

 

Welfare loss from site closure 
for summer season 

 

 $ 140,378  
 $ 24,927  
 $ 36,346  
 $ 114,848  
 $ 20,357  
 $ 9,112,321  
 $ 88,427  
 $ 26,631  
 $ 4,827  
 $ 15,114  
 $ 1,272,097  
 $ 32,473  
 $ 87,896  
 $ 304,189  
 $ 8,548  
 $ 2,158,100  
 $ 202,918  
 $ 117,950  
 $ 16,236  
 $ 125,086  
 $ 18,288  
 $ 272,061  
 $ 2,397,999  
 $ 95,216  
 $ 505,392  
 $ 18,245  
 $ 4,014  
 $ 12,854  
 $ 1,639,062  
 $ 475,993  
 $ 3,574  

 

 

 

167 

 

Appendix 3C: Site-specific delta and welfare estimates 

Table 3.12 Estimates of dj for All Sites and Fire Scenarios 

Site 

Vegetation 

Old, all, 

far 

Old, all, 

near 

Recent, all, 

far 

Recent, all, 

near 

Recent, 
far, shrub 

Recent, 
near, 
shrub 

Recent, 
some, far 

Recent, 

some, near 

 

 

shrub/shrub 

shrub/shrub 

shrub/shrub 

East Fork 
Trailhead 
Elizabeth Lake 
Canyon Road 
Josephine/ 
Colby Road 
Upper Bear 
Creek Trailhead  shrub/shrub 
Barrett 
tree/shrub 
Stoddard Road 
Bear Divide 
Vista Picnic 
Area 
Elizabeth Lake 
Picnic 
Frenchman’s 
Flat 
Hidden Springs 
Picnic 
Stonyvale 
Picnic 
West Fork 
Wildwood 
Picnic Area 

tree/shrub 
tree/shrub 
tree/shrub 

tree/shrub 

tree/shrub 

tree/shrub 

tree/shrub 

 

 

 

 

 

 

 

 

 

 

-0.0684 

-0.0378 

-0.0657 

-0.0362 

-0.0656 

-0.0362 

-0.0655 

-0.0361 

-0.1822 

-0.0656 

-0.1830 

-0.0659 

-0.1826 

-0.0658 

-0.1835 

-0.0661 

-0.1821 

-0.0655 

-0.1826 
-0.1909 
-0.1850 

-0.0658 
-0.0692 
-0.0668 

 

 

 

 

 

 

 

 
 
 

 

 

 

 

 

 

 

 

 

 

 

 
 
 

 

 

 

 

 

 

-0.0559 

-0.0561 

-0.0560 

-0.0563 

-0.0558 

-0.0560 
-0.0589 
-0.0569 

 

 

 

 

 

 

 

 

 

 

 

 
 
 

 

 

 

 

 

 

-0.0406 

-0.0408 

-0.0407 

-0.0410 

-0.0406 

-0.0407 
-0.0429 
-0.0414 

 

 

 

 

 

 

 

 

 

 

 

 
 
 

 

168 

Table 3.12 (cont’d) 

 

 

Buckhorn 
Picnic 
Chantry Flat 
Picnic Area 
Charlton Flat 
Picnic Area 
Chilao Visitor 
Center 
Devil's Canyon 
Trailhead 
Eagle Roost 
Picnic 
Grassy Hollow 
Visitor Center 
Icehouse 
Canyon 
Trailhead 
Inspiration 
Point 
Islip Saddle 
Trail Head 
Jackson Lake 
Picnic 
Mt. Wilson 
Observatory 
Vincent Gap 
Red Box Picnic 
Area 
San Antonio 
Falls Trailhead 

 

 

 

 

 

 

 

 

 

 

 

tree/tree 

tree/tree 

tree/tree 

tree/tree 

tree/tree 

tree/tree 

tree/tree 

-0.0711 

-0.0406 

-0.2304 

-0.1821 

-0.0961 

-0.0554 

-0.2987 

-0.2390 

-0.0713 

-0.0407 

-0.2309 

-0.1825 

-0.0711 

-0.0406 

-0.2304 

-0.1822 

-0.0711 

-0.0406 

-0.2303 

-0.1820 

-0.0711 

-0.0406 

-0.2304 

-0.1821 

-0.0720 

-0.0412 

-0.2329 

-0.1842 

tree/tree 

-0.0781 

-0.0447 

-0.2496 

-0.1981 

tree/tree 

tree/tree 

tree/tree 

tree/tree 
tree/tree 
tree/tree 

tree/tree 

-0.0717 

-0.0410 

-0.2320 

-0.1835 

-0.0715 

-0.0409 

-0.2315 

-0.1831 

-0.0714 

-0.0408 

-0.2313 

-0.1829 

-0.0713 
-0.0711 
-0.0718 

-0.0408 
-0.0406 
-0.0410 

-0.2311 
-0.2304 
-0.2322 

-0.1827 
-0.1821 
-0.1836 

-0.0786 

-0.0451 

-0.2511 

-0.1993 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 
 

 

 

169 

 

 

 

 

 

 

 

 

 

 

 

 
 
 

 

 

-0.0613 

-0.0558 

-0.0831 

-0.0758 

-0.0614 

-0.0560 

-0.0613 

-0.0559 

-0.0613 

-0.0558 

-0.0613 

-0.0558 

-0.0621 

-0.0566 

-0.0674 

-0.0614 

-0.0618 

-0.0563 

-0.0616 

-0.0562 

-0.0616 

-0.0561 

-0.0615 
-0.0613 
-0.0619 

-0.0560 
-0.0558 
-0.0564 

-0.0679 

-0.0619 

 

 

Table 3.12 (cont’d)  

 

 

Switzer Picnic 
Area 
Three Points 
Trailhead 
Vista Picnic 
Area 
Windy Gap 
Trail 

 

 

 

 

 

 

 

 

 

tree/tree 

-0.0724 

-0.0414 

-0.2340 

-0.1851 

tree/tree 

-0.0711 

-0.0406 

-0.2304 

-0.1821 

tree/tree 

-0.0711 

-0.0406 

-0.2304 

-0.1821 

tree/tree 

-0.0711 

-0.0406 

-0.2303 

-0.1820 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

  

 

 

 

-0.0624 

-0.0569 

-0.0613 

-0.0558 

-0.0613 

-0.0558 

-0.0612 

-0.0558 

 

 

 

170 

 

Table 3.13 Estimates of Per-trip Value Lost for All Sites and Fire Scenarios 

Site 

Vegetation 

Old, all, 

far 

Old, all, 

near 

Recent, all, 

far 

Recent, all, 

near 

Recent, 
far, shrub 

Recent, 
near, 
shrub 

Recent, 
some, far 

Recent, 

some, near 

 

 

 

 

 

 

 

 

 

 

 
 
 

 

 

shrub/shrub 

shrub/shrub 

shrub/shrub 

shrub/shrub 

tree/shrub 

tree/shrub 

tree/shrub 

tree/shrub 

tree/shrub 

tree/shrub 
tree/shrub 
tree/shrub 

 

 

East Fork 
Trailhead 
Elizabeth Lake 
Canyon Road 
Josephine/Col
by Road 
Trailhead 
Upper Bear 
Creek 
Trailhead 
Barrett 
Stoddard Road 
Bear Divide 
Vista Picnic 
Area 
Elizabeth Lake 
Picnic Area 
Frenchman’s 
Flat 
Hidden Springs 
Picnic Area 
Stonyvale 
Picnic Area 
West Fork 
Wildwood 
Picnic Area 

 

 

 

 

 

 

 

$ 23.98 

$ 24.09 

$ 24.04 

$ 24.17 

$ 23.95 

$ 24.03 
$ 25.31 
$ 24.41 

 

 

 

 

 

 

 

 

 

 

 

 
 
 

 

171 

 

 

 

 

 

 

 

$ 24.99 

$ 25.03 

$ 24.00 

$ 24.00 

$ 23.96 

$ 23.96 

$ 23.95 

$ 23.95 

$ 23.97 

$ 23.98 

$ 24.07 

$ 24.09 

$ 24.02 

$ 24.04 

$ 24.14 

$ 24.17 

$ 23.95 

$ 23.95 

$ 24.02 
$ 25.11 
$ 24.34 

$ 24.03 
$ 25.29 
$ 24.40 

 

 

 

 

 

 

 

 
 
 

 

 

 

 

 

 

 

 

 

 

 

 
 
 

 

 

 

 

 

 

$ 23.98 

$ 24.09 

$ 24.04 

$ 24.17 

$ 23.95 

$ 24.03 
$ 25.29 
$ 24.40 

 

Table 3.13 (cont’d) 

 

 

Buckhorn 
Picnic Area 
Chantry Flat 
Picnic Area 
Charlton Flat 
Picnic Area 
Chilao Visitor 
Center 
Devil's Canyon 
Trailhead 
Eagle Roost 
Picnic Area 
Grassy Hollow 
Visitor Center 
Icehouse 
Canyon 
Trailhead 
Inspiration 
Point  
Islip Saddle 
Trailhead 
Jackson Lake 
Picnic Area 
Mt. Wilson 
Observatory  
Vincent Gap 
Red Box Picnic 
Area 
San Antonio 
Falls Trailhead 

 

 

 

 

 

 

 

 

tree/tree 

tree/tree 

tree/tree 

tree/tree 

tree/tree 

tree/tree 

tree/tree 

$ 23.96 

$ 23.96 

$ 23.96 

$ 23.96 

$ 32.48 

$ 32.75 

$ 31.36 

$ 31.69 

$ 24.02 

$ 24.03 

$ 24.01 

$ 24.01 

$ 23.97 

$ 23.97 

$ 23.97 

$ 23.97 

$ 23.95 

$ 23.95 

$ 23.95 

$ 23.95 

$ 23.96 

$ 23.96 

$ 23.96 

$ 23.96 

$ 24.27 

$ 24.28 

$ 24.22 

$ 24.23 

tree/tree 

$ 26.31 

$ 26.39 

$ 25.97 

$ 26.06 

tree/tree 

tree/tree 

tree/tree 

tree/tree 
tree/tree 
tree/tree 

tree/tree 

$ 24.16 

$ 24.17 

$ 24.13 

$ 24.14 

$ 24.10 

$ 24.11 

$ 24.08 

$ 24.08 

$ 24.08 

$ 24.08 

$ 24.06 

$ 24.06 

$ 24.05 
$ 23.97 
$ 24.19 

$ 24.05 
$ 23.97 
$ 24.20 

$ 24.03 
$ 23.96 
$ 24.15 

$ 24.03 
$ 23.96 
$ 24.16 

$ 26.49 

$ 26.58 

$ 26.12 

$ 26.23 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 
 

 

 

172 

 

 

 

 

 

 

 

 

 

 

 

 

 
 
 

 

 

 

 

$ 23.96 

$ 23.96 

$ 32.56 

$ 32.62 

$ 24.03 

$ 24.03 

$ 23.97 

$ 23.97 

$ 23.95 

$ 23.95 

$ 23.96 

$ 23.96 

$ 24.27 

$ 24.28 

$ 26.33 

$ 26.35 

$ 24.16 

$ 24.17 

$ 24.10 

$ 24.10 

$ 24.08 

$ 24.08 

$ 24.05 
$ 23.97 
$ 24.19 

$ 24.05 
$ 23.97 
$ 24.19 

$ 26.52 

$ 26.54 

 

 

 

Table 3.13 (cont’d) 

 

Switzer Picnic 
Area 
Three Points 
Trailhead 
Vista Picnic 
Area 
Windy Gap 
Trail 

 

 

 

 

 

 

 

tree/tree 

tree/tree 

tree/tree 

tree/tree 

$ 24.40 

$ 24.42 

$ 24.33 

$ 24.35 

$ 23.96 

$ 23.96 

$ 23.96 

$ 23.96 

$ 23.96 

$ 23.96 

$ 23.96 

$ 23.96 

$ 23.95 

$ 23.95 

$ 23.95 

$ 23.95 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

$ 24.41 

$ 24.41 

$ 23.96 

$ 23.96 

$ 23.96 

$ 23.96 

$ 23.95 

$ 23.95 

 

 

 

173 

 

 

 

 

 

 

 

 

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174 

 

 

 

 

 

 

 

 

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177