United States

Department 

of Agriculture

Forest Service

Pacific Southwest

Research Station

Research Paper

PSW-RP-249

Economic Value of Big Game

Habitat Production from

Natural and Prescribed Fire

Armando González-Cabán John B. Loomis Dana Griffin

Ellen Wu Daniel McCollum Jane McKeever Diane Freeman 
Pacific Southwest Research Station

Forest Service

U.S. Department of Agriculture

Abstract

González-Cabán, Armando; Loomis, John B.; Griffin, Dana; Wu, Ellen; McCollum, Daniel;

McKeever, Jane; Freeman, Diane. 2003. Economic value of big game habitat production from natural and prescribed fire. Res. Paper PSW-RP-249. Albany, CA: Pacific

Southwest Research Station, Forest Service, U.S. Department of Agriculture; 38 p.

A macro time-series model and a micro GIS model were used to estimate a production

function relating deer harvest response to prescribed fire, holding constant other environmental variables. The macro time-series model showed a marginal increase in deer

harvested of 33 for an increase of 1,100 acres of prescribed burn. The marginal deer

increase for the micro GIS model was 16. An additional 3,710 acres of prescribed burn

would produce an additional eight deer harvested regardless of the model. For an additional 3,700 acres more of prescribed burn the marginal increase in deer harvested is four

and five deer respectively for the macro time-series and micro GIS models. Using the

Travel Cost Method the change in consumer surplus or net willingness-to-pay was $257

per additional deer harvested due to the additional trips in response to increasing deer

harvest. The consumer surplus estimate using the Contingent Valuation Method was

$222. Depending on the production function model used the initial deer hunting benefit

response to a prescribed burning of 1,100 acres ranges from $3,840 to $7,920. An additional increase of 3,710 acres of prescribed burning would produce benefits of $1,920

regardless of the model used. An extra 3,700 acres more would produce only between

$960 and $1,200 depending on the model. When compared to the cost of conducting the

prescribed burning, the benefits derived from an increase in deer harvest represent no

more than 3.4 percent of the total costs of the first 1,100 acres. 

Retrieval terms: contingent valuation, deer hunting benefits, fire economics, prescribed

burning costs, travel cost method, willingness-to-pay

The Authors

Armando González-Cabán is Economist with the Pacific Southwest Research Station,

USDA Forest Service, 4955 Canyon Crest Drive, Riverside, CA 92507. John B. Loomis is

Professor at the Department of Agricultural and Resource Economics, Colorado State

University, Fort Collins, CO 80523. Dana Griffin and Ellen Wu at the time of the study

were graduate students at the Department of Agricultural and Resource Economics,

Colorado State University, Fort Collins, CO 80523. Daniel McCollum is Economist with

the Rocky Mountain Research Station, 2150 Center Avenue, Fort Collins, CO 80526. Jane

McKeever is Wildlife Biologist with the California Department of Fish and Game, Eastern

Sierra Inland Deserts Region, 330 Golden Shore, Suite 210, Long Beach, CA 90802. Diane

Freeman is Wildlife Biologist with the San Bernardino National Forest, San Jacinto

District Ranger, Idyllwild, CA 92349.

Acknowledgments

We thank Lucas Bair for research assistance regarding the cost of prescribed burning and

editorial assistance. 

Thanks also to the California Department of Fish and Game for cover photographs: deer

in the meadow (front) and the northern slope of Rouse Ridge in the San Jacinto Ranger

District prescribed burn (front and back). 

Publisher

Albany, California

Mailing address:

PO Box 245, Berkeley

CA 94701-0245

(510) 559-6300

http://www.fs.fed.us/psw

April 2003
Contents

In Brief . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Study Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Two Production Function Modeling Approaches. . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Literature Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Deer Habitat and Prescribed Burning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Geographic Information Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Multiple Regression Models for Estimating the Production Function. . . . . . . 4

Economic Evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Production Function Modeling Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Time-Series, Macro Scale Production Function . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Micro GIS Approach to Estimating the Production Function . . . . . . . . . . . . . . 7

Description of GIS-Based Micro Regression Variables . . . . . . . . . . . . . . . . . . . . 9

Estimated Production Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Macro Time-Series San Jacinto Ranger District Equations . . . . . . . . . . . . . . . . . 9

San Jacinto Ranger District Log-Log Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Summary of Micro Regressions Based on GIS Analysis . . . . . . . . . . . . . . . . . . 11

Percent of Hunting Location Area Burned, Micro Model. . . . . . . . . . . . . . . . . 11

Micro GIS-Based Equation Using Total Acres Burned . . . . . . . . . . . . . . . . . . . 11

Micro GIS-Based Equation Using OLS Log-Log Form of 

Harvest Per Acre . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Applying the Regression Production Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Applying Results of Macro Time-Series Production Function Model . . . . . . 14

Applying Results of Micro GIS Production Function Model. . . . . . . . . . . . . . 14

Valuation of Deer Hunting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Valuation Methodologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

CVM and TCM Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Data for TCM and CVM Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Survey Mailing and Response Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

USDA Forest Service Research Paper PSW-RP-249. 2003. i

Economic Value of Big Game

Habitat Production from Natural

and Prescribed Fire

Armando González-Cabán John B. Loomis Dana Griffin

Ellen Wu Daniel McCollum Jane McKeever Diane Freeman 

Pacific Southwest

Research Station

USDA Forest Service

Research Paper

PSW-RP-249

April 2003
Statistical Results of TCM and CVM Valuation Models . . . . . . . . . . . . . . . . . . . 20

Travel Cost Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Contingent Valuation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Comparing the Consumer Surplus from TCM and CVM . . . . . . . . . . . . . . . . 22

Applications of Values to Estimate Benefits of Prescribed Burning. . . . . . . . . 23

Comparison to Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Appendix I. Survey Instrument Used in the Study . . . . . . . . . . . . . . . . . . . . . . . . 29

Appendix II. San Bernardino National Forest, 

San Jacinto Ranger District . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

ii USDA Forest Service Research Paper PSW-RP-249. 2003.
In Brief 

González-Cabán, Armando; Loomis, John B.; Griffin, Dana; Wu, Ellen; McCollum, Daniel;

McKeever, Jane; Freeman, Diane. 2003. Economic value of big game habitat production from natural and prescribed fire. Res. Paper PSW-RP-249. Albany, CA: Pacific

Southwest Research Station, Forest Service, U.S. Department of Agriculture; 38 p.

Retrieval terms: contingent valuation, deer hunting benefits, fire economics, prescribed

burning costs, travel cost method, willingness-to-pay

On the San Jacinto Ranger District (SJRD) of the San Bernardino National Forest

in southern California prescribed burning is an important resource management

program. Prescribed burning is used to provide many multiple use benefits

including improved deer habitat, opportunities for dispersed recreation, and

reduced hazardous fuels in the chaparral that surround several residential communities and associated watersheds.

The main objective of this research was to quantify the economic value of the

improved deer hunting resulting from prescribed burning. Previous prescribed

firework has shown that fire positively enhances deer habitat. Enhanced deer

habitat increases deer population hence better hunting. Two approaches were

used to estimate a production function relating deer harvest response to prescribed burning, holding constant other environmental variables. We compared

a macro level, time-series model that treated the entire SJRD as one area, and a

micro geographic information system (GIS) model that disaggregated the Ranger

District into the 37 hunting locations reported by hunters. Both modeling

approaches gave somewhat mixed results in that some statistical specifications

showed no statistically significant effect of prescribed burning. However, the

better fitting (68 percent of variation explained) log-log model functional form of

the macro time-series model did show a statistically significant effect of the combined prescribed fire and wildfire acres on deer harvest over the 20 year period

of 1979-1998. 

All technical information on prescribed fire and fire effects was obtained

from USDA Forest Service personnel in the SJRD and California Department of

Fish and Game and was used in development of the hunter’s survey questionnaire used in this work. 

During the 1999 deer hunting season, a mail questionnaire was sent to a

random sample of deer hunters with licenses for deer in Zone D19, which

includes the SJRD. Of the 762 questionnaires mailed to deer hunters in

California, a total of 356 deer hunters’ responses were collected after two mailings for a response rate of approximately 47 percent. 

Two of the three micro GIS model specifications showed that the initial effect

of prescribed burning on deer harvest in the 37 hunting locations within the

SJRD was statistically significant. Lagged effects of prescribed burning were

consistently insignificant in our models, suggesting that most of the response

occurs in the year of the burn. The macro time-series model estimated a larger

response to burning of the first 1,100 acres than the micro GIS model did; but for

increases in fire of more than 1,100 acres, the two models provided nearly identical estimates. 

The net economic value of the resulting additional deer hunting benefits

was estimated by using the Travel Cost Method (TCM) and the Contingent Valuation Method (CVM). By using TCM analysis, we found the change in consumer surplus or net willingness-to-pay (WTP) is $257 per additional deer

harvested due to the additional trips the hunter took in response to increasing

deer harvest. From CVM, we found the change in consumer surplus of $222 per

additional deer harvested. The mid-point marginal consumer surplus of TCM

and CVM, therefore, is $240 per deer harvested. 

USDA Forest Service Research Paper PSW-RP-249. 2003. iii
The initial deer hunting benefit response to the current magnitude of prescribed burning of 1,100 acres ranges from $3,840 to $7,920, depending on the

model. However, the incremental gains for additional prescribed burning are

quite similar across models: the annual economic hunting benefits of increasing

prescribed burning from its current magnitude of 1,100 acres to 4,810 acres is

$1,920, regardless of the model used. Likewise, for a second increase of 3,700

acres of prescribed burning to 8,510 acres, the deer hunting benefits are calculated to be between $960 and $1,200 each year, which are fairly similar despite the

different modeling approaches. 

The costs of prescribed burning on the San Bernardino National Forest range

from $210 to $240 per acre. Using the information in this research, the full incremental costs of burning the first 1,100 acres would be $231,000, with each

additional 3,710 acres burned costing $779,100. The deer hunting benefits represent at most about 3.4 percent of the total costs of the first 1,100 acres of

prescribed burning. This finding can be used in two ways. First, the incremental

costs of including deer objectives in a prescribed burn of 1,100 acres should not

exceed $8,000, as the incremental benefits are no larger than this. Second, the

other multiple use benefits—such as watershed, recreation, and the hazard fuel

reduction benefits to adjacent communities—would need to make up the difference if the prescribed burning program is to pass a benefit-cost test. For example,

if prescribed burning 1,100 acres prevented as few as two residential structures

from burning, the prescribed burning program would likely pass a benefit-cost

test. However, such an assessment was beyond the scope of this study.

Nonetheless, we can conclude that incremental deer-hunting benefits from prescribed fire appear to be relatively small, compared to the cost of prescribed

burning in the SJRD.

iv USDA Forest Service Research Paper PSW-RP-249. 2003.
Introduction

Estimating the impact of fire on resources and the economic consequences of it

is very difficult. This difficulty arises because of the multiple outputs of the forest and the strong interdependence between the present output choice and the

capital stock level of natural resources (González-Cabán 1993). The problem is

further complicated because the effects of fire on the production stream of many

goods and services from the forest, particularly nonmarket outputs, is largely

unknown (SAF 1985). 

This research makes a methodological contribution to the development of

models for evaluating ecological effects of fire as well as providing results for the

San Jacinto Ranger District (SJRD) in the San Bernardino National Forest located in southern California. In her recent review of the economics of prescribed

burning, Hesseln (2000) posed the problem as “a lack of economic models to

evaluate short-and long-term ecological benefits of prescribed fire. Without

understanding the relationship between economic outcomes and ecological

effects, it will be difficult to make effective investment decisions. Research

should focus on defining a production function to identify long-term relationships between prescribed burning and ecological effects. Identifying production

functions relationships will form the basis for future cost-benefit analysis with

respect to prescribed burning ...” (Hesseln 2000, p. 331-332). To make a first

modest step in the direction suggested by Hesseln, this study estimates production relationships between prescribed burning and deer harvest by using

time-series data and geographic information system (GIS) approaches. Previous

work has shown an increase in deer population as a result of forage quality

improvement from burning their habitat (Klinger and others 1989). The models

developed were then used to predict the resulting increases in deer harvest from

prescribed burning and, subsequently, to measure the economic benefits of this

environmental improvement (increase in deer harvests) using nonmarket valuation techniques. 

The SJRD is located in southern California’s San Bernardino National Forest

between Palm Springs and Idyllwild, California. As noted by the USDA Forest

Service: “Some of the best deer hunting in Riverside County is found in this

area. It is also a very valuable watershed that includes the South Fork of the

San Jacinto River” (Gibbs and others 1995, p. 6). The SJRD is an ideal area to

demonstrate and compare different approaches to estimating a production function between prescribed burning and deer harvest, because prescribed fire has

been used for more than 20 years to stem the long-term decline in deer popula

-

tions since the 1970s (Gibbs and others 1995, Paulek 1989). Previous research on

prescribed burning shows that fire positively enhances deer habitat and populations (CDFG 1998), but the economic benefits have not been quantified. The

USDA Forest Service has a detailed database of fire history for this area predating the 1970s. The California Department of Fish and Game (CDFG) has hunter

deer-harvest records for the SJRD back to 1974. These two agencies provide the

fundamental data sets for modeling a relationship between deer harvest and

fire, whether prescribed burns or wildfires. Information from our analysis may

be relevant to policy because the SJRD plans to increase the amount of pr

e

-

scribed burning by 50 to 100 percent over the next few years (Gibbs and others

1995, Walker 2001). 

The positive effect of prescribed fire on enhancing deer habitat and populations has been shown (CDFG 1998, Klinger and others 1989), but the resulting

economic benefits of the treatments have not been quantified. We hypothesized

that prescribed burning has a systematic positive effect on deer harvest and will

use two nonmarket valuation methods to estimate the economic value of additional deer harvest. 

USDA Forest Service Research Paper PSW-RP-249. 2003.

1
Study Area

In general, southern California is characterized by a Mediterranean climate, with

hot and dry summers and cool, humid winters. There is a significant amount of

variation in temperatures and local site conditions in the SJRD. Elevation in the

SJRD ranges from 3,500 feet up to 10,800 feet. Below 5,000 feet elevation, the

dominant vegetation within the SJRD is chaparral. Annual rainfall for the chaparral biome is approximately 15 to 16 inches. Areas higher than 5,000 feet tend to

be dominated by hardwoods and conifers, such as live oak and Douglas-fir, with

annual rainfall reaching up to 30 inches. 

Within the SJRD, primarily the USDA Forest Service manages the land, with

small amounts of land administered by the Bureau of Land Management (BLM)

as well as the State of California. Mount San Jacinto State Park lies on the northeastern boundary of the SJRD and is owned by the State of California. There are

two state game refuges, one located in the Mount San Jacinto State Park and the

other in the southern portion of the Ranger District around the Santa Rosa

Mountains. Hunting is prohibited within the refuges. 

The SJRD is an area that evolved with fire as a natural environmental factor.

Declining abundance of successional vegetation communities is considered to

have the greatest long-term effects on deer populations (CDFG 1998).

Historically, fire, either prescribed or natural, has been the primary mechanism

for establishing these vegetation communities. Studies in California have noted

that after a burn, increased deer numbers can be attributed to individuals moving into the area to feed (Klinger and others 1989). These increased deer numbers

have been thought to improve reproduction due to increased forage quality and

an increase in fawn survival rates. The CDFG has noted a significant increase in

buck harvest from 1987 to 1996 in hunt locations that had large fires versus hunt

locations that did not have large fires (CDFG 1998). To improve deer habitat in

California, controlled burns have been underway in all the major parks and

forests for many years (Kie 1984). Efforts including controlled burning to remove

brush have been part of a program to create desirable deer habitat (i.e., chaparral in the open scrubland) and to mitigate the loss of deer habitat resulting from

commercial and residential development.

Two Production Function Modeling

Approaches

To test whether prescribed burning has a systematic effect on deer harvest we

used a macro or aggregate time-series approach and a micro, spatial approach.

To estimate the economic value of additional harvest resulting from prescribed

burning treatments we used two nonmarket valuation methods. By examining

prescribed burning effects on deer harvest with two different approaches—a

macro or aggregate time-series approach and a micro, spatial approach (e.g.,

GIS)—comparisons can be made between the results for consistency between

these two approaches. A macro approach would be able to test the effects of fire,

prescribed and natural, across the entire study area over a long period of time.

Although more aggregate in geographic space, data availability allows us to

cover a longer time frame, and hence test long dynamic effects. Using a micro

approach provides greater spatial detail to elements such as the influence of a

meadow or ridge, but a less temporal time frame is covered because of data limitations. Thus, each approach to estimating the production function has its

relative strengths and weaknesses. 

2 USDA Forest Service Research Paper PSW-RP-249. 2003.
Literature Review

Deer Habitat and Prescribed Burning 

There have been just a few studies indicating the positive results of fire on deer

habitat and populations. In one northern California study it was reported that

the number of deer in stands of pure chaparral that were burned by fire quadrupled during the first growing season after the burn, then gradually decreased to

pre-burn levels over the next 4 years (Klinger and others 1989). These increased

deer numbers were attributed to the movement of deer into the burned stands

where forage quality was improved and fawn survival rate was up. Using prescribed fire to benefit deer should occur during the season when the greatest

likelihood of achieving the desired plant response will occur. According to the

CDFG, dry season burns tend to result in better regeneration of shrub species

from seed than wet season burns. Fire adapted shrub species, such as chaparral,

respond best to prescribed burns during the time of year when fire occurs naturally, usually in late summer or early fall.

In arid regions such as southern California, vegetation change does not

conform to traditional patterns. Vegetation is always in a state of flux due to

harsh environmental factors and extreme events such as fire that cause a sudden shift in vegetation composition. Fire can cause the germination of seeds

that would otherwise be dormant and create changes in relative abundance of

vegetation such as chaparral. In the southern California area, there are different types of chaparral: seeding species and sprouting species. According to a

past study (Zedler and others 1983) on the impacts of fire in chaparral, fires

can produce a varying degree of results depending on the species of chaparral.

This implies that fire regimes in chaparral produce a variety of responses in

vegetation communities depending upon the type of species that exist (Zedler

and others 1983). In terms of deer harvest, this difference in chaparral vegetation may suggest that certain areas will be more productive for hunting after a

fire, depending on what type of vegetation was burned, e.g., the sprouting or

seeding species. The biotic zonation in the San Jacinto Mountains where the

SJRD is located includes coastal sage scrub up to 2,500 feet, hard (lower and

upper) chaparral from 2,500 to 5,000 feet, yellow pine forest from 5,000 to 8,000

feet, lodgepole pine forest from 8,000 to 9,500 feet, and subalpine and alpine

forest from 9,500 to 11,000 feet.

Prescribed burns have become a management tool for improving chaparral

for deer habitat. As a result, the use of prescribed fire has become a technically

viable solution for improving the carrying capacity of chaparral deer ranges such

as those in southern California. Hence, it is important to document and quantify

the magnitude of the benefits from prescribed burning compared to its costs. 

Deer hunting is considered a necessary element of deer management (Paulek

1989). Hunting is a tool to restrict deer herds to the carrying capacity of their

range. This type of herd restriction prevents “boom or bust” cycles among pop

-

ulations and helps maintain a balance of forage across a deer herd’s range. Deer

hunting also provides economic activity to local economies in California. A recent study using survey data compared the economic contribution of deer

hunting in 1997 to a previous survey in 1987 in northeastern California. The results indicated that hunters’ expenditures (not adjusted for inflation) in Lassen,

Modoc, and Plumas counties have dropped significantly, from $5.4, $4.7, and

$0.76 million, respectively, in 1987 to $0.83, $0.55, and $0.17 million, respectively, in 1997 (Loft, 1998). Nonetheless, even in 1997, deer hunters in these three

counties still accounted for an estimated $1.5 million in local expenditures. 

Geographic Information Systems A geographic information system (GIS) is a system for working with spatial

data. The Environmental Systems Research Institute (ESRI) (1995) describes GIS

USDA Forest Service Research Paper PSW-RP-249. 2003.

3
as an organized collection of computer hardware, software, geographic data,

and personnel designed to efficiently capture, store, update, manipulate, analyze, and display all forms of geographically referenced information. 

GIS can also be described by its ability to carry out spatial operations,

known as queries, through linking different data sets together. These functions

are what make a GIS a powerful tool for data analysis. Typically, a GIS links

different data sets to reveal some new or unknown relationship (Chou 1997).

For example, in the case of fires, it is possible through a GIS to discover how

many acres were burned in a particular region by examining overlaying datasets

in a spatial context. 

In order to design a digital database, some key questions must be answered:

What will be the study area or boundary? What types of data files or layers

(e.g., vegetation cover, prescribed burned areas, roads, etc.) will be needed in

order to solve the problem? What attributes are needed for each layer and how

will these attributes be stored? After these questions are answered, then spatial

data should be obtained for inputting into the database and making it usable.

The last part of building a spatial database involves specifying what necessary

attribute information will be needed by the various data layers and then adding

it on. This is usually done by relating a common item or joining the attributes

onto a particular data layer.

Multiple Regression Models for Estimating the

Production Function

Estimating a production function that relates deer harvest to acres of prescribed

burning must also control for other inputs that influence the production of deer

for harvest. This includes wildfire, elevation (used as a proxy for vegetation

data that was incomplete), total precipitation, temperature, and distance to

roads. Thus, multiple regression analysis is an appropriate technique. The simplest form used in this study is ordinary least squares regression. This can be

improved upon for modeling deer harvest, especially at the micro level where

harvest in any small spatial unit is a non-integer variable, by using a count data

model. Count data models are based on probability distributions that have mass

only at non-negative integers, and it is impossible for the distribution to have a

fractional outcome or a negative outcome (Hellerstein 1992). This is certainly

the case of deer harvest, as hunters cannot harvest a fraction of a deer. The classic example of a count distribution is the Poisson process. The counts described

consist of numerical quantities, Lambda, which is the mean number of events

per unit of progression (specified as an exponential link function that ensures

nonnegativity) and is equal to the variance. As Lambda increases, the Poisson

distribution approaches the normal distribution, with a decreasing probability

mass at zero (Forsythe 1999). 

Given the stringency of the mean variance equality restriction imposed by

the Poisson distribution, a more generalized count model, such as the negative

binomial distribution, is often more consistent with the data. The negative bino

-

mial version allows the variance to move freely. Both the Poisson and the

negative binomial distributions yield the equivalent of a semi-log form where

the log of the dependent variable is regressed against the explanatory variables. 

Using ordinary least squares (OLS), it is not possible to take the log of a

zero-valued observation of the dependent variable; but if the negative binomial

count data model is used, the probability distribution allows for this—similar to

a non-linear least squares that avoids the need for transformations (Hellerstein

1992). Therefore, these features make the Poisson and negative binomial distributions useful in our micro GIS-based analysis since the variable we are trying

to explain—deer harvest in 1 of 37 sub-hunting location areas—is a non-negative

integer. The number of harvested deer recorded in specific hunting areas tends 

4 USDA Forest Service Research Paper PSW-RP-249. 2003.
to be small, such as 0, 1, and 2 or 3, rather than larger numbers like 10, 20, or 50.

Therefore, the count data is more efficient with the distribution mass at small

integers than OLS (Hellerstein 1992). 

However, when modeling the aggregate harvest for all of the SJRD, the

mean number of deer harvested is much larger and varies between 80 and 157

deer in any given year; therefore, using OLS is an acceptable approach for the

macro time-series modeling.

Economic Evaluation

Wildlife such as deer are commonly considered nonmarket goods in much of

the western United States. Although natural resources have both use and

nonuse values (e.g., existence values), the widespread distribution of deer suggests that the incremental benefits of more deer are use values. For deer, use

values are those associated with tangible uses in recreational hunting or viewing benefits. Because of difficulty in identifying deer viewers, this study focuses

on deer hunters. 

Kahn (1995) categorizes two major techniques for estimating nonmarket

goods: indirect and direct techniques. Indirect techniques (revealed preference

approaches) can be used to analyze decisions or actions in response to changes

in an environmental amenity to reveal the value of the amenity. Indirect tecniques such as hedonic pricing and travel cost models are mostly useful for

estimating the use value of nonmarket goods. Direct valuation techniques elicit values (stated preference approaches) from individuals through survey

methods, which can be used to measure both use and nonuse values. In this

study, we will apply both the Contingent Valuation Method (CVM) and the

Travel Cost Method (TCM) to estimate the use-value in deer hunting. Although

there is a substantial amount of literature comparing TCM and CVM estimates

of the value of a recreation day (Carson and others 1996), there are fewer comparisons for a change in recreation quality. 

Production Function Modeling Approaches Two primary methods for estimating a deer harvest production function were

applied in this study. Both methods were looking for a statistical relationship

between deer harvest and fire, both wildfires and prescribed fires, that occurred

in southern California’s SJRD. The distinguishing difference between the two

methods applied is the variation in spatial scale. The GIS-based approach can

be considered a micro, spatial scale examination, while the macro time- series

approach looks at the entire SJRD at a more aggregate level, using the entire

ranger district as one unit of observation in each year. This more aggregate or

macro method tests a time-series relationship between deer harvest and fire in

SJRD. The GIS-based method disaggregates fewer years of fire data and deer

harvest into a much finer level of spatial detail, breaking the SJRD into the 37

hunting locations reported by hunters (see appendix II for a general map of

SJRD).

Time-Series, Macro Scale Production Function 

The first statistical approach is based on a time-series regression model to test

for a relationship between deer harvest (the dependent variable) and prescribed

fire, controlling for other independent variables such as annual precipitation

and temperature during the hunting season (table 1). This approach used a

dataset for SJRD, provided by the CDFG and the USDA Forest Service. The fir

e

records provided data from 1975 for natural wildfire but only from 1979 for

prescribed burns within the SJRD. This ranger district represents the majority of

publicly accessible land for deer hunting in Riverside County. Deer harvest

data from 1975 were provided by CDFG. 

USDA Forest Service Research Paper PSW-RP-249. 2003.

5
A time-series model was established with this data and weather information

from the University of Nevada at Reno’s Western Climate Center database that

contains temperature and precipitation data from the SJRD dating back to 1975.

The model attempts to directly explain deer harvest within the SJRD as a function of wildfire, prescribed fire, temperatures during the October hunting

season, and total precipitation in a given year (table 1). 

The full model (equation 1) is given, and then a lagged model (equation 2)

is included that allows for harvest to be sensitive to previous years’ prescribed

fire and wildfire. In past research, the use of burned areas by deer has been

shown to increase dramatically during the subsequent years (Klinger and others 1989). Therefore, this model takes into account these subsequent years by

using lagged variables.

The SJRD time-series production function model is:

[1] SJRD deer harvest in year

t = func (RxFiret, WildFiret, TotPrecipt

,

OctTemp

t, Yeart

)

RxFire

t is the acres of prescribed fire in year t, WildFiret is the acres of wildfire in year t, TotPrecipt is the sum of precipitation for year t, OctTempt is the

temperature in October during the hunting season, and Year

t is a trend variable,

with 1975 = 1, 1976 = 2, etc.

The SJRD time-series production function lagged model is: 

[2] SJRD deer harvest in year

t = func (RxFiret-1, WildFiret-1, 

TotPrecip

t,OctTempt, Yeart

)

Using the log-log form represents the non-linear forms of equations 1 and 2.

This format allows for a non-linear relationship, and the coefficients for fire can

be interpreted as elasticities: the percent change in deer harvest with a 1 percent

change in acres burned. 

Micro GIS Approach to Estimating the Production

Function

The second statistical approach taken in this study focused on using a GIS for

integrating spatial data into an economic relationship. A similar multiple regression approach was used as in the first method, except that the study area was

divided into 37 individual hunting locations reported by hunters (see appendix I).

Thus, the primary distinction to the macro time-series model is that with the

GIS-based micro model, deer harvest was modeled for 37 smaller hunting locations instead of by using just one large hunting zone that encompassed the SJRD.

This allowed for the incorporation of other influences on deer harvest that varied spatially across individual hunting locations such as distance to roads and

elevation.

All of the spatial data for this method came either from the United States

Geological Survey (USGS) 1:100,000 digital line graphs (DLG) files or from the

USDA Forest Service Arc/Info and Arc/View files, which were provided by the

San Bernardino National Forest Supervisor’s Office. The data for all the files use

the Universal Transverse Mercator (UTM) coordinate system (Zone 11, Datum

NAD 27). The scale of the data is at 1:250,000. These spatial data files contain pr

e

-

scribed fire, wildfire, elevation, roads, and trails information. The CDFG maps

and tally sheets provided the hunting location information. The areas on the

CDFG maps were aligned with areas on USGS 7.5 minute topographical quads.

The function of the GIS portion of this project was to provide the detailed

data at a micro level, which could be used to regress the relationship between

deer harvest and prescribed fire or wildfire. Using a spatial database to identify 

6 USDA Forest Service Research Paper PSW-RP-249. 2003.
Table 1—Data for macro time-series production function model.

Acres Burned

Year SJRD-Harvest Prescribed Fire Wildfires Oct-Temp Annual

Precipitation

No. Deer °F inches

1975 105 NA1

5231 70.48 19.94

1976 145 NA 0 69.23 27.22

1977 113 NA 3948 74.32 22.63

1978 101 NA 2049 74.32 46.99

1979 148 40.00 1987 70.73 29.62

1980 139 194.10 3,7627 73.68 45.65

1981 155 291.90 1,5016 67.00 15.81

1982 157 228.00 6279 69.42 49.47

1983 143 3,119.90 7206 69.52 56.87

1984 120 971.00 13 64.42 16.96

1985 119 1,311.80 2,1128 67.29 23.58

1986 162 1,309.00 0 65.19 23.92

1987 131 181.50 1432 69.58 23.49

1988 103 1,954.00 1615 75.52 18.25

1989 128 2,009.60 2121 68.65 15.98

1990 104 423.00 119 74.19 19.12

1991 83 0.00 91 72.19 31.49

1992 117 77.70 1458 70.00 23.44

1993 93 383.00 269 69.13 43.64

1994 132 25.40 2,2416 66.68 20.84

1995 82 975.20 7116 73.84 45.09

1996 131 822.00 1,2338 68.10 28.36

1997 126 4.94 NA 69.06 24.96

1998 99 0.00 NA NA 28.47

1

NA=not available

and describe a spatial pattern and distribution between deer harvest and fires is

very useful. The focus of building a GIS was to provide data on variables to

estimate the deer production function. 

The first step was to identify the necessary layers needed to run a regression

between deer harvest and fires. A hunting layer was constructed for the regression model, which contains deer harvest by hunting locations. Then layers were

added for the independent variables, including prescribed burn, wildfire, average elevation, temperature, distance to trails, dirt roads and roads from each

hunting location, and distance to wildfires from each hunting location.

Vegetation type would have been desirable, but this information was incomplete and will not be completed for the entire area until the distant future. 

The next step in constructing a spatial model is deciding on how to determine the delineation of geographic units (Chou 1997). Decisions on size of

geographic units must balance consistent data availability as well as meaningful

units. Although a 640-acre section grid had some attractive features, deer harvest

data at that level of resolution was only available for 4 years. Further, deer herd

movement may often be larger than a 640-acre section. Therefore, we relied upon

deer harvest locations reported by hunters within the SJRD. These hunt locations

are defined by topographic features, such as streams, steep ridgelines, or sometimes features created by people, including towns or major roads. These

locations were often much larger than a single section and encompassed areas

USDA Forest Service Research Paper PSW-RP-249. 2003. 7
where deer herds and hunters might move within but not between areas. In addition, CDFG had a much longer time-series of deer harvest at the harvest location

level as compared to the section level. Because of the different size of each harvest

location, some basic assumptions had to be made when calculating distances to

roads, trails, or recently burned areas. These assumptions included finding a central point within each harvest location to serve as a point to calculate distances.

Therefore, all distance calculations are based on averages from a central point. In

addition, regressions accounted for the size of the hunting location as one of the

explanatory variables. 

All relevant GIS data had to be exported into spreadsheet format and prepared for regression analysis. A count data model was estimated that regressed

deer harvest per hunting zone against prescribed fire and wildfire burned from

1975 to 1998. 

The models developed for the harvest areas had to account for the nonuniform

size of each hunting location. Three approaches were used. The first approach measures a percent of the area burned and includes the size of each harvest area as a

variable (equation 3). The second includes just the size and total acres of an area

burned (equation 4). The third approach transforms the dependent variable into

deer harvest per acre and uses an OLS regression (equation 5). 

The model based on percent burned, including lags, is:

[3] Deer harvest in year

t = func (AvgElev, LDirtDist, LTrailDist, 

PctRxBurn

t, PctRxBurnt-1, PctRxBurnt-2, 

PctRxBurnt-3, PctWildfir

e

t, PctWildfir

et-1, 

PctWildfiret-2, PctWildfiret-3, LHvstArea, 

OctTemp

t, Yeart

)

The model with harvest as a function of total size of fire, including lags is:

[4] Deer harvest in year

t = func (AvgElev, LtotalWildfire 

t, 

LtotalWildfiret-1, LtotalWildfir

et-2, 

LtotalWildfiret-3, LtotalRxfire

t, 

LtotalRxfiret-1, LtotalRxfiret-2, 

LtotalRxfiret-3, LDirtDist, 

LTrailDist, LHvs

tArea, OctTemp

t, 

Year

t

)

The model based on deer harvest per acre, using OLS, Log-log form is:

[5] Log deer harvest per acre in year

t = func (AvgElev, LtotalWildfiret

,

LtotalWildfiret-1, 

LtotalWildfiret-2, 

LtotalWildfiret-3, 

LtotalRxfire

t, 

LtotalRxfiret-1, 

LtotalRxfiret-2, 

LtotalRxfiret-3, 

Ldirtdistance, 

Ltraildistance, 

LHvstArea, OctTemp

t, 

Year

t

)

8 USDA Forest Service Research Paper PSW-RP-249. 2003.
Description of GIS-Based Micro Regression Variables

Elevations (AvgElev) (meters) are based on USGS digital elevation models

(DEMs) and act as a proxy for vegetation types that were not available.

However, we do not have an expected sign on elevation, but simply wish to

control for elevation differences between the 37 individual hunting areas within the SJRD. Both fire variables, wildfire (WildFire) and prescribed fire (RxBurn)

(total acres/year), are expected to have a positive sign (Kie 1984, Zedler and

others 1983). 

The distance (meters) to road (LDirtDist) and trail (LTrailDist) variables are

based on the distances from a central point in each hunting location. Two arguments can be made about the sign’s direction. One argument is based on

accessibility for hunters, in which having a close proximity to either a trail or

road would make hunting easier, more desirable, and would positively affect

deer harvest. The second argument is based on the intrusion of deer habitat by

a road or trail. This perspective would lead to a decline in deer harvest because

roads cause a break in habitat and pose a threat. Therefore, the expectation is

ambiguous.

The distance (meters) to fire variable (LDistFire) is a measure of how close

fire comes to burning into the interior of the hunting area’s vegetation. A value

of zero would indicate a fire in that year burned into the center of the hunt area.

This variable sign may be either positive or negative. 

Harvest area (LHvstArea) (acres) accounts for the size of each hunting location and is expected to have a positive sign. The rationale is that as hunting

areas become larger, then the amount of deer habitat increases, which attracts

more deer; therefore, the probability of hunter success increases. October temperature (OctTemp) (degrees Fahrenheit) and year (Year) are the other variables

used in the GIS models. October is when hunting season is open, and based on

hunters’ surveys, when temperatures are high deer tend to bed down and seek

cover. Therefore, harvest rates decline, which gives the October temperature a

negative sign. Year is a trend variable to capture any temporally varying effects

and does not carry any expected sign. 

Estimated Production Functions

Macro Time-Series San Jacinto Ranger District Equations

The basic model between deer harvest in SJRD and both prescribed fire (RxBurn)

and wildfire (WildFire) was computed (table 2). Precipitation (TotPrecip), temperature (OctTemp), and year (Year) (a trend variable) have also been included in

USDA Forest Service Research Paper PSW-RP-249. 2003. 9

Table 2—Non-lagged macro time-series ranger district linear model.

Variable Coefficient Std. error t-Statistic Probability

Constant 4,694.2070 1,535.6420 3.057 0.0092

RxBurn1 0.0010 0.0052 0.185 0.8559

Wildfire 0.0004 0.0004 0.921 0.3736

TotPrecip 0.0361 0.3648 0.099 0.9227

OctTemp -3.6472 1.4501 -2.515 0.0258

Year -2.1731 0.7754 -2.803 0.0150

R-squared 0.588 Mean dependent variable 124.895

Adjusted R-squared 0.429 S.D. dependent variable 23.758

S.E. of regression 17.947 F-statistic 2.708

Durbin-Watson statistic 1.870 Prob. (F-statistic) 0.026

1 Prescribed fire
the equation. In this linear equation there appears to be no strong statistical significance between the dependent variable and either type of fire. The coefficient

on prescribed fire is 0.0009 and has a 0.18 t-statistic, indicating this variable has

minimal effect on deer harvest and is insignificant. Wildfire is very similar to the

prescribed fire variable: the coefficient is 0.0004 and the t-statistic is 0.92, both

insignificant and insubstantial. The only significant variables are October temperature and year. 

October temperature is negative and has a significant t-statistic of 2.5. This

sign is consistent with hunter surveys indicating that when the temperature is

high, the deer harvest goes down because deer are bedded to avoid the heat.

Year has a 2.8 t-statistic and a negative coefficient of 2.17. This would indicate

that some systematic trend does exist within the data set. Possibly this variable

is capturing other influences contributing to the decline in deer population within the SJRD. Total precipitation was expected to have a strong positive effect on

vegetation growth and forage availability for deer; however, it does not show up

as being significant. The R-squared value for this model is 0.58, and adjusted Rsquared is 0.42. These values indicate some ability to explain the effects of fire on

deer harvest, as about half the variation in deer harvest is explained by “year”

and “October” temperature. At this scale and with untransformed harvest and

fire variables, there is no indication that the fire variables are related to variation

in deer harvest.

A 1-year lag-on-acres-burned model was estimated to determine if the year

after a fire allows for an increase in deer harvest. This lag is based on the expectation that new vegetation growth occurs in the year after a fire. Previous

literature found that the number of deer occupying burned stands of chaparral

quadrupled the first growing season after the burn (Klinger and others 1989).

However, a 1-year lag did not make a difference in deer harvest using this

model. The 1-year lagged value of prescribed fire (-0.0047) and wildfire (0.0003)

were both insignificant, with t-statistics of –0.70 and 0.72 respectively. October

temperature and year are almost the same as the previous model without a lag.

The R-squared values for this model were similar to the previous model, at 0.58

and 0.42. 

San Jacinto Ranger District Log-Log Model

Taking the log of the dependent variable and the log of the combined wildfire

and prescribed burn variable (LTotFire) results in a statistically significant effect.

The coefficient for total fire shows a small magnitude of 0.048, but it has a significant t-statistic of 2.3 (table 3). This appears to be in line with a previous study

where the density of deer increased after wildfire (Klinger and others 1989). The

10 USDA Forest Service Research Paper PSW-RP-249. 2003.

Table 3—Macro time-series ranger district log-log model.

Variable Coefficient Std. error t-Statistic Probability

Constant 41.8087 11.0701 3.7767 0.002

LTotFire 0.0487 0.0205 2.3719 0.033

TotPrecip -0.0001 0.0026 -0.3666 0.719

OctTemp -0.0270 0.0107 -2.5362 0.024

Year -0.0179 0.0056 -3.1993 0.006

R-squared 0.677 Mean dependent variable 4.809

Adj. R-squared 0.585 S.D. dependent variable 0.202

S.E. of regression 0.130 F-statistic 6.343

Durbin-Watson statistic 2.066 Prob. (F-statistic) 0.002
sign on this variable is positive, and the coefficient can be interpreted as elasticities by using the log-log form. Therefore, a 1 percent increase in acres burned

will lead to a 0.048 percent increase in deer harvest. The other significant variables are October temperature (OctTemp) and year (Year). Again, a negative sign

on the October coefficient relates to observations that an increase in temperature

results in a decrease in the number of deer harvested. The year variable indicates

that a systematic effect exists within the model. This model’s explanatory power

is better with an R-square value of 0.67. The Durbin-Watson statistic of 2.06 indicates that autocorrelation is not a problem. 

The same model (table 2) was also estimated with a 1-year lag. The coefficient on the log of total fire lagged 1 year was 0.01 and had a t-statistic of 0.44,

which indicates the lag is insignificant. The R-squared value did not change

from the previous model. 

Summary of Micro Regressions Based on GIS Analysis

Three regression models were estimated by using GIS-derived data (tables 4, 5, 6). Two of these regression models—count data and OLS—show prescribed

burns had a statistically significant effect on deer harvest. The count data

model based on total fires is used for calculating the marginal benefits of additional burning on deer harvest in the next section because of its superior

explanatory power. 

Percent of Hunting Location Area Burned, Micro Model

This model describes the relationship between deer harvest (dependent vari-

able) in each of the 37 hunting locations as a function of average elevation

(AvgElev), the distance to dirt roads (LDirtDist) and trails (LTrailDist), the percentage of hunting area experiencing a prescribed fire (PctRxBurn) and wildfire

(PctWildfire) in the time period considered and the size of each hunting location

(LHuntArea), the temperature in October (OctTemp) of that year, and year (Year) (table 4). The significant variables with t-statistics over 2.0 are distance to trails

and dirt roads, the size of the harvest area, and temperature in October. Wildfires

for year one—the year during which the fire occurred—have a t-statistic of 1.8,

which is considered statistically significant at the 10 percent level. However, the

coefficient on the wildfire is negative (-1.6), which would indicate that fires

decrease the probability of harvesting a deer in that year. The rest of the wildfire

and all of the prescribed fire variables for each hunting area are not considered 

significant for any of the years using this percent-burned method. According to

these fire variables across time, their insignificance demonstrates that differ

-

ences in deer harvest cannot be attributed to fire. In this model, the distance to

dirt roads, distance to the nearest trail, the size of a hunting area and the temperature statistically influence deer harvest in October. The R-squared value of 0.18

and the adjusted R-squared value of 0.17 indicate this model has relatively low

explanatory power of deer harvest (table 4).

Micro GIS-Based Equation Using Total Acres Burned 

The second count data model (table 5) presents a different specification by using

two separate fire variables: the log of total acres of prescribed fire in the individual hunting area during the time period, and the log of total acres of wildfire in

the individual hunting area during the time period. This equation controls for

the different size of the individual hunting areas by including a hunting area

(acres) size variable. Total acres of prescribed fire (LTotRxFires) are significant

during the year of the prescribed fire, and its significance declines over the next 

3 years. During the first year, the prescribed fire coefficient is 0.044 with a t-statistic of 2.4. Because this count data model logs the fire acreage variables, it is

equivalent to a log-log model. As such, the 0.044 is the elasticity. Total acres of

wildfire (LTotWFires) were not significant for any of the years in this equation.

USDA Forest Service Research Paper PSW-RP-249. 2003. 11
This model has more explanatory power of the effect of fire on deer harvest

than the previous model based on a percent burn of each harvest area. This total

area count data model R-squared value of 0.25 and the adjusted R-square 0.24 is

almost 40 percent greater than the percent burn count data model. 

Micro GIS-Based Equation Using OLS Log-Log Form of

Harvest Per Acre

This equation was used as an alternative method to account for the different

sizes of hunting location. Using OLS regression of deer harvest per acre as a

function of fire and the other variables provides a similar pattern of signs and

significance as the total area count data equation. In this model, a double log

form was also used, but the dependent variable acted as a control measure for

the size of each hunting location by dividing harvest in each hunting location by

the number of acres in each location. The results of this model (table 6) show that

prescribed burns (LTotRxFires) have a statistically significant effect on deer harvest in the first year with a t-statistic of 2.25. During the years after the fire,

prescribed burn areas become less significant, which corresponds to the previous

count data model. The only time wildfire has a significant impact is during the 

second year (LTotWFires(-2)) after the burn. The sign of the coefficient for wildfire in the second year is negative and less than one, which would imply a

negative effect on deer harvest in that year. Distance to dirt roads (LDirtDist) is

also significant, a t-statistic of 5.17 and a negative coefficient -0.013. This may

mean that hunting locations further away from dirt roads have a lower probability of the occurrence of hunters harvesting a deer or possibly that many hunters 

12 USDA Forest Service Research Paper PSW-RP-249. 2003.

Table 4—Count data model based on GIS with percent burned with lags.

Variable Coefficient Std. error t-Statistic Probability

Constant 2.7350 13.2598 0.2063 0.837

LAvgElev -0.1989 0.1337 -1.4872 0.137

PctRxBurn 1.6726 1.5733 1.0631 0.288

PctRxBurn (-1) 1.5721 1.5961 0.9850 0.325

PctRxBurn (-2) 2.1253 1.4669 1.4488 0.147

PctRxBurn (-3) -0.3572 1.7741 -0.2013 0.840

PctWildfire -1.6569 0.8893 -1.8631 0.063

PctWildfire (-1) -1.1365 0.8064 -1.4094 0.159

PctWildfire (-2) -0.4622 0.7290 -0.6340 0.526

PctWildfire (-3) -1.5480 0.8390 -1.8451 0.065

LDirtDistance -0.2429 0.0386 -6.2893 0.000

LTrailDistance 0.4096 0.0426 9.6125 0.000

LFireDist 0.0426 0.0467 0.9118 0.362

LHuntArea 0.9377 0.0882 10.6355 0.000

OctTemp -0.0343 0.0147 -2.3412 0.019

Year -0.0035 0.0065 -0.5416 0.588

Overdispersion parameter

Alpha:C(17) -0.1999 0.103823 -1.925655 0.054

R-squared 0.186 Mean dependent variable 1.759

Adj. R-squared 0.170 S.D. dependent variable 2.611

S.E. of regression 2.379 Avg. log likelihood -1.629

Restr. log likelihood -1922.63 LR index (Pseudo-R2) 0.300
Table 5—Count data model based on GIS using total acres burned with lags.

Variable Coefficient Std. error t-Statistic Probability

Constant 62.9643 23.1158 2.7239 0.007

LAvgElev -0.2373 0.1307 -1.8154 0.070

LTotWFires 0.0107 0.0171 0.6249 0.532

LTotWFires (-1) 0.0083 0.0170 0.4877 0.626

LTotWFires (-2) -0.0277 0.0155 -1.7903 0.073

LTotWFires (-3) -0.0247 0.0156 -1.5830 0.113

LTotRxFires 0.0441 0.0179 2.4609 0.014

LTotRxFires (-1) 0.0275 0.0270 1.0193 0.308

LTotRxFires (-2) 0.0115 0.0222 0.5169 0.605

LTotRxFires (-3) 0.0115 0.0187 0.6155 0.538

LDirtDist -0.2338 0.0377 -6.1944 0.000

LTrailDist 0.3952 0.0418 9.4633 0.000

LFireDist 0.0727 0.0474 1.5335 0.125

LHuntArea 0.9407 0.0870 10.8128 0.000

OctTemp -0.0121 0.0168 -0.7179 0.473

Year -0.0347 0.0118 -2.9535 0.003

Overdispersion parameter

Alpha:C (17) -0.281 0.1081 -2.598621 0.009

R-squared 0.257 Mean dependent variable 1.759

Adjusted R-squared 0.242 S.D. dependent variable 2.611

S.E. of regression 2.273 Avg. log likelihood -1.618

Restr. log likelihood -1920.633 LR index (Pseudo-R2) 0.305

Table 6—Least squares deer harvest per acre using GIS data model with lags.

Variable Coefficient Std. error t-Statistic Probability

Constant 1.3418 1.5883 0.8448 0.398

LAvgElev -0.0097 0.0093 -1.0461 0.296

LTotWFires 0.0012 0.0012 0.9632 0.336

LTotWFires (-1) 0.0005 0.0012 0.4293 0.668

LTotWFires (-2) -0.0022 0.0011 -2.0862 0.037

LTotWFires (-3) -0.0018 0.0011 -1.6276 0.104

LTotRxFires 0.0026 0.0012 2.2548 0.024

LTotRxFires (-1) 0.0021 0.0019 1.1349 0.257

LTotRxFires (-2) 0.0013 0.0015 0.8620 0.389

LTotRxFires (-3) 0.0012 0.0013 0.9262 0.355

LDirtDist -0.0130 0.0025 -5.1748 0.000

LTrailDist 0.0183 0.0022 8.2132 0.000

LFireDist 0.0051 0.0032 1.6072 0.108

LHuntArea -0.0087 0.0062 -1.4098 0.159

LOctTemp -0.0504 0.0860 -0.5859 0.558

Year -0.0028 0.0008 -3.4364 0.001

R-squared 0.139 Mean dependent variable -4.533

Adjusted R-squared 0.123 S.D. dependent variable 0.093

S.E. of regression 0.087 F-statistic 8.684

USDA Forest Service Research Paper PSW-RP-249. 2003. 13
do not venture very far from roads. This lower probability may be due to poaching along roads and/or to lower deer populations as a result of roads

fragmenting habitat. The positive coefficient on the distance to trails variable

(LTrailDist) implies that having a distant proximity to trails increases the probability of a deer harvest. All the other variables in this model fail to be significant

indicators of deer harvest, except for the trend variable, year. Therefore, some

unidentifiable systematic temporal change is occurring within the model.

Overall, this model has a lower level of explanatory power than the total area

micro count data model. The R-squared value by using OLS is 0.13 and the

adjusted R-squared value is 0.12 compared to twice this level of explanatory

power in the total area count data model (table 5).

Applying the Regression Production Functions 

To calculate the incremental effects of different levels of prescribed burning on

deer harvest, the acres-burned variable is increased from one level to a higher

level in the regression model. We used the double-log macro time-series model (table 2) and the micro GIS-based double-log count data models (table 5), as these

two models have the highest explanatory power. The resulting predicted change

in deer harvest will be valued in dollar terms. 

Applying Results of Macro Time-Series Production

Function Model

The double log Macro Time Series Production Function Model (table 3) is used to

estimate the change in deer harvest. This model has a high explanatory power

given that it explains almost 68 percent of the variation in deer harvest. As will

be recalled in this model, the lag effect proved insignificant. Therefore, the prescribed burning component of the total fire variable in this model is increased to

three different levels (1100, 4810, and 8510 acres, respectively) and the predicted

log of deer harvest is calculated at the mean of the other variables. The anti-log

of harvest is then calculated to provide the estimate of the deer harvest with

that level of prescribed burning (table 7). 

Applying Results of Micro GIS Production Function Model

The results of both the count data model (table 5) and the least squares model (table 6) pro

-

vide positive evidence on the desirable effects of prescribed burning programs on deer

harvest. Because the count data model has nearly double the R-squared value of the least

squares model, the economic implications from prescribed burn programs will be

evaluated by using the prescribed burn coefficients (table 5), the GIS count data

model. By using this model it is possible to calculate the additional harvest from

additional prescribed burn acres on deer harvest. In table 7, the first row forecasts

the estimated number of deer that would be harvested if only one acre of land

would burn. By using the current mean number of acres burned in each individual hunting location for the GIS micro model (table 5), 30 acres, and then

multiplying this by the total number of individual hunting locations, 37, a SJRDwide deer harvest level is calculated. The forecast feature in the statistical

software package EViews (Quantitative Micro Software 1997) does this. The

other variables are set at their mean levels. In the GIS micro model the effect of

further increasing prescribed burning is then calculated by increasing the number of acres burned in each hunting location by 100 acres and then 200 acres to

provide a wide range of prescribed burning levels in the SJRD. The first level

(1,100 acres) is about the average acres of prescribed burning over the last 20

years in the SJRD. Maintaining this level of prescribed burning does provide an

increase in deer harvest over the no burning level. However, the gain in deer

harvest increases more slowly with additional increases in burning in each hunt

area (table 7).

14 USDA Forest Service Research Paper PSW-RP-249. 2003.
Table 7—Comparison of deer harvest response to prescribed burning using the macro time- series model

and GIS micro model.

Macro time-series model GIS micro model

1 NA 83 NA 1 42 NA

1,100 1,100 116 33±3.99 2 1,100 58 16±4.45

4,810 3,710 124 8±3.99 3,710 66 8±4.45

8,510 3,700 128 4±3.99 3,700 71 5±4.45

1

Although the variable Total Acres Burned reflects the combined prescribed acres and wildfire acres,

for this simulation only, the prescribed burn acres are being changed because prescribed burned is

the management variable. 

2 Because the dependent variable is the log of deer harvested, the 95 percent confidence interval was

computed taking the antilog of the S.E. of the regression (0.13) (table 3) and multiplying it by 1.96

(antilog 0.13 = -2.04 x 1.96 = ± 3.99). 

The results suggest there is a substantial gain in deer harvest with the first

1,100 acres burned (table 7), especially as calculated from the macro time-series

model. However, a very similar diminishing marginal effect is evident from

both the macro time-series production function regression and the micro GIS

production function regression after burning more than 1,100 acres. In other

words, regardless of the spatial level of detail adopted, burning an additional

3,710 acres is expected to result in about eight more harvested deer in the SJRD. 

To determine the economic efficiency of additional prescribed burning, it is

necessary to compare the benefits of additional prescribed burning in the form

of the economic value of deer harvest against the costs. 

Valuation of Deer Hunting

In the SJRD the deer hunting regulation allows for a 1-month hunting season

and a one-deer bag limit. According to CDFG, deer hunting is considered one of

the major outdoor recreation activities in SJRD every year. Deer hunting has

offered opportunities for recreational enjoyment as well as produced economic

benefits to the town of Idyllwild, California. Previous research on deer hunting

in California showed that increased success rates and opportunities to harvest a trophy deer (Creel and Loomis 1992) increase the economic value of

deer hunting. 

Linking hunter trips and success to economic values will result in a bioeconomic relationship that ties fire management decisions to economics. Thus,

we estimated the economic value of the additional deer harvest resulting from

the prescribed burning program in the SJRD. By using both the travel cost

method (TCM) and the contingent valuation method (CVM) we can compare

the estimates of the change in consumer surplus for harvesting another deer in

the SJRD. This economic information will be useful to future policy decisions

regarding funding and implementation of a prescribed burning program. 

Valuation Methodologies

Contingent Valuation Method

CVM uses simulated (hypothetical) markets to quantify monetary values similar to actual markets (Loomis and Walsh 1997). The method uses survey

questions to elicit people’s net economic value or consumer surplus for an

USDA Forest Service Research Paper PSW-RP-249. 2003. 15

Total acres1

burned

Additional 

acres burned

No. deer 

harvested

Marginal 

increase in

deer harvested

Prescribed

acres

burned

No. deer

harvested

Marginal

increase in

deer harvested
improvement in environmental or site quality by asking what additional amount

they would pay for a specified improvement. Thus, the method aims at eliciting

people’s willingness-to-pay (WTP) in dollar amounts. In our application, CVM

presents hunters with a hypothetical market in which they can pay higher trip

costs to receive an increase in deer harvest opportunities. For simplicity in survey design and administration, an open-ended WTP question was asked. In

addition, the accumulated evidence to date is that the open-ended formats tend

to produce conservative WTP estimates relative to dichotomous choice (Schulze

and others 1996). Although open-ended questions are more difficult to answer

than dichotomous-choice questions, hunters who have completed the deer-hunting season at this area are quite familiar with the goods (deer) they are asked to

value. Therefore, we felt this simplification was acceptable. The basic improvement being valued is the deer hunter’s consumer surplus per trip for a

guaranteed deer harvest during the season, which is the difference between people’s maximum WTP per trip with guaranteed deer harvest (i.e., 100 percent

chance of harvesting a deer) and people’s current maximum WTP per deer hunting trip (i.e., deer hunting demand with around 9 percent deer harvest success

rate). 

The CVM model is specified as (equation 6): 

[6] MWTPDeer = MaxWTPKill – MaxWTPCur

In which MWTPDeer is the change in hunter’s WTP for increasing deer harvest rate, MaxWTPKill is the maximum WTP per trip with certainty of deer

harvest, and MaxWTPCur is the current maximum WTP per trip.

Travel Cost Method

The TCM has been a primary indirect approach for valuing environmental

resources associated with recreation activity over the last several decades.

Clawson (1959) was the first to empirically estimate benefits using a travel-cost

framework. The basic concept of TCM is that travel cost (i.e., transportation

cost, travel time) to the site is used as the proxy for the price of access to the site.

When recreationists are surveyed and asked questions about the number of trips

they take and their travel cost to the site, enough information can be generated

to estimate a demand curve. From the demand curve, net WTP or consumer

surplus can be calculated. The explanatory variables that are often included in

travel cost demand curves include age, income, family size, educational level,

and other socioeconomic variables (Kahn 1995). Since we are interested in the

benefits of improvements at just one site with no changes at other sites, a single 

site TCM demand model will suffice for empirical analyses, and more complex

multi-site models such as hedonic TCM (Hybrid hedonic travel cost method

developed by Brown and Mendelsohn 1984) or multinomial logit models

(Sometimes called Random Utility Models [RUMs]) are more costly and complex

than warranted. 

Definitions of TCM Price Variable

Besides variable travel cost or its proxy, travel distance, many articles discuss the

inclusion of a travel time variable in the demand function. Knetsch (1963) was

the first to point out the opportunity cost of time is part of travel costs as well.

Cesario (1976) suggested one-fourth the wage rate as an appropriate estimate of

the opportunity cost of time based on commuting studies. For individuals with

fixed workweeks, recreation takes place on weekends or during pre-designated

annual vacation and cannot be traded for leisure at the margin. In such cases,

Bockstael and others (1987), Shaw (1992), and Shaw and Feather (1999) suggest

the opportunity cost of time no longer need be related to the wage rate. These

16 USDA Forest Service Research Paper PSW-RP-249. 2003.
studies suggest that both the travel cost and travel time be included as separate

variables, along with their respective constraints—income and total time available for recreation. 

This study chooses its variables according to the consumer demand theory

and past literature (table 8). For instance, private hunting land serves as a substitute (or complement) for public hunting land in SJRD. Hunters were not asked

the distance to substitute sites nor to identify if there was a substitute site for the

SJRD deer hunting. Because there are two other deer hunting areas in southern

California that could be substitutes, our TCM estimates of consumer surplus

may overstate hunter’s net WTP for the SJRD by a slight amount. Hunters who

hunt on opening day, belong to hunting organizations, hunted in previous seasons, and had a successful deer harvest may take potentially more hunting trips

because such hunters have higher preferences, experience, or skill in deer hunting recreation. Because a majority of hunters in our dataset work a fixed

workweek, we assume the deer hunters maximize utility level subject to their

income and time constraints (Shaw 1992). In other words, time is a constraint

like income for time intensive activities like hunting. Total time budget is constructed for the TCM model according to the demographic time information. 

For example, for a person who took a paid vacation to hunt, his/her total

time budget (days) is obtained by 8 weekend days during the month of the hunting season plus the number of weeks of paid vacation of the individual

multiplied by 5 days per week, for up to a maximum total of 30 days, which is

the length of the hunting season. For a person who took unpaid vacation time or

reduced work hours to hunt, his/her total time budget is 16 days. For those

who work their usual amount and hunt when they can, their total time budget

is 8 days, the number of weekend days during the October hunting season.

Furthermore, for those unemployed and retirees, their total time budget is 31

days. In this study, the total time budget ranges from 8 to 31 days, since the

deer-hunting season in SJRD lasted for 1 month only.

Table 8—Variables included in Regression Models and their Definitions.

Variable Definition

Dependent: 

NUMTRIPS Number of primary purpose of deer hunting trips taken to 

the SJRD during 1999 deer hunting season.

Independent: 

Age Hunter’s age

DeerKill Did you harvest a deer in this area during this hunting season?

1= YES, 0 = NO

HuntOpen Did you hunt on opening day of the D-19 season?

1= YES, 0 = NO

HuntOrg Are you a member of a Sportsman’s organization?

1= YES, 0 = NO

PrevSeas Have you hunted in this area in a previous season? 

1= YES, 0 = NO

PrivLand Did you hunt on private land? 

1= YES, 0 = NO

RTravMiles Round-trip travel miles from home to the hunt location

PcInc Hunter income

ToTimeBud Total time budget. 

TravTime Number of hours one-way travel time

USDA Forest Service Research Paper PSW-RP-249. 2003. 17
Count Data Nature of TCM Dependent Variable

The non-negative integer characteristic in every observation for the dependent

variable (i.e., NUMTRIPS) is the so-called “count data.” Given the count data

form of the dependent variable, a preferred estimation model should be able to

control for integer nature of the dependent variable (Creel and Loomis 1990). In

this study, the negative binomial count model was used to estimate the demand

function. The negative binomial is the more generalized form of the Poisson distribution, which allows the mean of trips to be different from its variance. The

negative binomial and Poisson count data models are equivalent to a semi-log of

the dependent variable functional form.

The count data TCM model is specified in equation 7:

[7] NUMTRIPS = EXP (C(1) + C(2) x Age + C(3) x DeerKill + C(4) x

HuntOpen + C(5) x HuntOrg + C(6) x PrevSeas +

C(7) x PrivLand - C(8) x RTravMiles + C(9) x 

PcInc + C(10) x ToTimeBud - C(11) x TravTime)

In equation 7, we expected the coefficient for DeerKill [C(3)] to have a positive sign, since hunters would likely take more hunting trips if the hunting

quality had been good. Also, if hunters hunted on the opening day [C(4)], private

land [C(7)], and/or previous seasons [C(6)] and belong to hunting organizations

[C(5)], then we expected a positive effect on the number of trips the hunter took,

as these variables indicated a strong preference for the deer hunting activity. For

those hunters with a higher income level [C(9)] and/or higher total time budget [C(10)], we expected more hunting trips as well, as a result of less binding

income and time constraints. However, round-trip travel distance [C(8)] and

travel time [C(11)] are expected to have negative effects on the number of hunting trips because increases of these two variables increase hunter’s expense.

Calculation of Consumer Surplus in TCM 

The consumer surplus from deer hunting is computed from the demand curve as

the difference between people’s WTP (e.g., the entire area under the demand

curve) and what they actually pay (e.g., their travel costs). Because the count

data model is equivalent to a semi-log functional form, consumer surplus from

a trip is calculated as the reciprocal of the coefficient on round-trip travel miles

times the average cost per mile, expressed in RTravMiles x $0.30/mile (see equation 9) (Sorg and others 1985). 

CVM and TCM Comparisons

Literatures in CVM and TCM comparisons have usually just compared the average

consumer surplus for existing conditions. For example, Carson and others (1996)

found in their study that on average, CVM-derived values were usually smaller

than revealed preference estimates like TCM. To test the consistency between two

nonmarket good valuation methods, we compared the CVM and TCM in this

study for the improvement in deer hunting quality due to the prescribed burning

program. A Tobit model was used for the analysis of open-ended WTP responses

from CVM because our open-ended dependent variable only has a single bound at

0. The Tobit model uses the open-ended WTP response as the dependent variable

in CVM (i.e., people’s current WTP), and the independent variables similar to

TCM. The same variables are used because both methods are trying to explain

consumer surplus. For TCM, this is done via the demand curve. Meanwhile, for

CVM, it may be thought of as the inverse demand function.

18 USDA Forest Service Research Paper PSW-RP-249. 2003.
The CVM Tobit model is equation 8: 

[8] MaxWTPCur = C(1) + C(2) x Age + C(3) x DeerKill + 

C(4) x HuntOpen + C(5) x HuntOrg + 

C(6) x PrevSeas + C(7) x PrivLand - 

C(8) x RTravMiles + C(9) x PcInc + 

C(10) x ToTimeBud - C(11) x TravTime

For the same reasons as in the TCM equation, we expected round-trip

travel miles and travel time to hold negative signs in equation 8. 

Data for TCM and CVM Models

For cost effectiveness in data collection, a mail questionnaire was used. There

were six sections along with one demographic section. The first section gave a

brief introduction of the questionnaire and then asked about the number of

hunting trips taken this season to the SJRD and prior hunting experiences in

the SJRD. The second section gathered information on the land ownership of the

area hunted, weapon type used, and information on deer harvest characteristics

if the hunter had been successful. The third section asked about the hunter’s

involvement in opening day of the hunting season. Section four inquired about

the travel distance and travel time to the hunting area. The fifth section asked

questions about the hunter’s expenses as well as the hunter’s WTP higher trip

costs for the hunting experience on the most recent trip. Specifically, hunters

were asked an open-ended question pertaining to the maximum increase in deer

hunting expenses before they would not have taken this trip. Also, the CVM

analysis was used to measure hunter increases in WTP associated with increasing deer harvest success, including a 100 percent chance of harvesting a deer

during the season. Our WTP estimate from CVM is compensating variation,

rather than consumer surplus, but the two measures are nearly identical in most

applications since the income effect is quite small for deer hunting. The sixth section asked about the characteristics of the hunter’s preferred hunting area. The

final section of the survey detailed demographic information such as age,

income, family size, educational level, and other socioeconomic variables from

the respondents. 

Survey Mailing and Response Rate

During the 1999 deer hunting season, a mail questionnaire (appendix I) was sent

to a random sample of deer hunters with licenses for deer in Zone D19, which

includes the SJRD. Of 762 questionnaires mailed to deer hunters in California

during the 1999 hunting season, 7 were undeliverable. A total of 356 deer

hunters’ responses were collected after two mailings. Response rate is, therefore, approximately 47 percent. Among these respondents, 69 did not hunt deer

in the San Bernardino National Forest, SJRD. 

Descriptive Statistics

More than 72 percent of respondents did hunt on opening day. The average deer

hunter is around 43 years old, with a mean income slightly more than $33,000

dollars (table 9). 

USDA Forest Service Research Paper PSW-RP-249. 2003. 19
The distribution of dependent variable observations reflects how many

hunting trips the hunter took during the 1999 deer-hunting season: 

Number of trips Number of deer hunters

NA 58

0 2

1-5 207

6-10 53

11-15 13

16-20 10

21-30 6

31-40 0

41-50 1

Above 50 1

Total 351

The majority of deer hunters took at least one hunting trip during the season. Two hunters indicate they did not take any hunting trip in the 1999

deer-hunting season. Fifty-eight hunters did not answer this question because

they did not hunt within the SJRD. In addition more than 70 hunters took more

than 6 hunting trips in the 1999 deer-hunting season. One reasonable explanation for this is that those deer hunters live close by the SJRD. 

Statistical Results of TCM and CVM Valuation

Models

Travel Cost Method

A negative binomial count data model was used to estimate the statistical relationship between number of trips and all the independent variables (table 10).

There is a negative effect of travel miles (RTravMiles), travel time (TravTime),

and income (PcInc): increase in travel distance and time results in a decrease in

the number of trips the hunter will take. The negative coefficient explains the

20 USDA Forest Service Research Paper PSW-RP-249. 2003.

Table 9—Statistical information of TCM variables.

Variable1 Mean Median Maximum Minimum Std. Deviation

NUMTRIPS 5.56 4.0 62.0 1.0 6.26

Age 43.0 42.0 80.0 13.0 13.40

PctDeerKill 9.7 0.0 NA NA 0.29

HuntOpen (Pct) 72.3 NA NA NA 0.45

HuntOrg (Pct) 35.0 NA NA NA 0.48

PrevSeas (Pct) 81.3 NA NA NA 0.39

PrivLand (Pct) 15.0 NA NA NA 0.36

RTravMiles 103.80 80.0 800.0 0.5 95.11

PcInc $33,148.00 $32,500.00 $100,000.00 $833.00 $18,287.00

ToTimeBudget 19.78 23.0 31.0 0.0 10.27

TravTime 1.43 1.2 9.0 0.10 0.98

1 See table 8 for definition of variables
disutility effect caused by travel time and travel cost increases. Income, in this

study, is insignificant. Also, regression results of this study indicate whether a

hunter successfully harvested a deer during the hunting season (i.e., DeerKill),

whether the individual hunted on opening day (i.e., HuntOpen), whether the

hunter hunted in this area in a previous season (i.e., PrevSeas), and whether total

time budget (i.e., ToTimeBud) had significant effects on the number of hunting

trips hunters took. Indeed, hunters who hunted the opening day hunted in this

area last year, harvested a deer, had a larger time budget, and took more hunting

trips. Consistent with economic theory, hunters with longer round-trip travel

miles (RTravMiles) and travel time (TravTime) tended to take fewer hunting trips. 

The consumer surplus is calculated by using Sorg and others’ (1985)

method (equation 9) in which the $0.30 is the 30 cents per mile sample average cost per mile. 

[9] Consumer Surplus = 1/β (i.e. coefficient of distance) x $0.30/mile 

(i.e. cost per mile) = 1/0.002230 x $0.30 

= 448.43 x $0.30 = $134.53/trip

Finally, the 90 percent confidence interval (table 10) is obtained by equation 10:

[10] 90 percent confidence interval on Consumer Surplus per Trip 

= 1/(βDIST ± 1.64 x 0.000895) x $0.30/mile 

= $81.13 - $393.59 per trip

Estimating the Benefits of Harvesting an Additional Deer

The average number of trips per hunter is 5.56 trips, and 1 out of 10 deer hunters

successfully harvests a deer. Therefore, average consumer surplus per deer harvested is 10 x 5.56 x 134.53 = $7,480 per deer harvested. To calculate the

incremental or marginal value of an additional deer suitable to compare to marginal costs, we can use the TCM demand equation to predict the extra number of 

trips deer hunters would take if they knew they would harvest a deer that season. This essentially shifts the demand curve out by the amount of the coefficient

USDA Forest Service Research Paper PSW-RP-249. 2003. 21

Table 10—Estimated negative binomial count data TCM demand equation.

Variable1 Coefficient Std. Error Z-Stats Probability

Constant 1.325 0.216 6.123 0.00

Age 0.001 0.004 0.369 0.71

DeerKill 0.367 0.155 2.370 0.02

HuntOpen 0.524 0.115 4.564 0.00

HuntOrg 0.068 0.106 0.639 0.52

PrevSeas 0.285 0.135 2.122 0.03

PrivLand 0.038 0.132 0.289 0.77

RTravMiles -0.002 0.0009 -2.490 0.01

PcInc -1.00E-06 2.78E-06 -0.360 0.72

ToTimeBud 0.010 0.005 2.099 0.04

TravTime -0.289 0.087 -3.334 0.00

R2 = 0.21, Adjusted R2 = 0.17

Consumer surplus = $134.53/trip 

90 Pct confidence interval: $81.13 - 393.60

Marginal consumer surplus per deer harvested = $257.17/deer 

90 Pct confidence interval: $155 - $752
22 USDA Forest Service Research Paper PSW-RP-249. 2003.

on deer harvest. The equation predicts that each hunter would take 1.9116 more

trips each season if hunters knew they would harvest a deer. Therefore, the marginal value of another deer harvested (i.e., marginal consumer surplus) is equal

to $134.53 x 1.9116 = $257.17 per deer harvested. Finally, the 90 percent confidence interval (CI) in table 10 for an additional deer harvested is obtained by

applying the 90 percent CI on the value per trip times the additional number of

trips taken by the hunter:

[11] 90 percent confidence interval of the value of harvesting an 

additional deer = 1.9116 x $81.13 - 1.9116 x 393.59 = $155 - $752

per deer harvested. 

Contingent Valuation Method

In the survey, people were asked their maximum WTP for their most recent trip

under current conditions, and their maximum WTP per trip for a 100 percent

guaranteed chance to harvest a deer over the season. The consumer surplus and

people’s maximum WTP per trip were computed (table 11). The CVM estimate of

consumer surplus under current low success rate (9 percent) conditions was

$17.59 per trip, while with 100 percent chance of harvesting a deer over the season the consumer surplus estimate rose to $116.19 per trip. The per trip figure

requires multiplying by the change in number of trips over the season to allow

comparison with TCM, since TCM indicates a change of 1.9116 trips when deer

harvest is certain over the season. In CVM, therefore, consumer surplus is equal

to MaxWTPKill (at the mean) multiplied by 1.9116 trips, or $222/deer. 

Table 11—CVM results (dollars per trip). 1

MaxWTPKill MaxWTPCur MWTPDeer

Mean 116.19 17.59 98.60

Median 50.00 0.00 50.00

Maximum 2300.00 500.00 2300.00

Minimum 0.00 0.00 0.00

Std. dev. 200.24 58.68 191.99

Marginal consumer surplus per deer harvested = $222/deer, 

90 Pct confidence interval: $178 - $265

1 See table 8 for definition of variables

The 90 percent Confidence Interval (C.I.) on seasonal consumer surplus for

harvesting an additional deer is: 

[12] 90 pct C.I. = DTrips x Mean ± (t-value@90Pct) x ((St. Dev.) /√n)

= 1.9116 x [$116.19 ± 1.64 x (200.2411/√210)]

= $178 - $265 per deer harvested, 

in which D is the change in number of trips when deer harvest 

is certain.

Comparing the Consumer Surplus from TCM and CVM

The marginal consumer surplus of harvesting an additional deer estimated by

TCM is $257 (table 10), and the marginal consumer surplus estimated by CVM is

$222 a deer (table 11). Comparing the 90 percent confidence intervals, TCM has a

range from $154 to $752, and CVM ranges from $178 to $265 per deer harvested.
Table 12—CVM inverse demand curve.

Variable1 Coefficient Std. Error Z-Stats Probability

Constant -143.8908 66.9346 -2.1497 0.032

Age -0.0958 1.0850 -0.0883 0.930

DeerKill 123.0983 42.4801 2.8978 0.004

HuntOpen 15.4554 32.3074 0.4784 0.632

HuntOrg 34.3721 29.8438 1.1517 0.249

PrevSeas -44.9252 35.8284 -1.2539 0.210

Privland -19.1205 39.4412 -0.4848 0.628

RTravMiles 0.3784 0.2262 1.6727 0.094

PcInc 0.0004 0.0008 0.5516 0.581

ToTimeBud 0.7401 1.4302 0.5175 0.605

TravTime -27.7475 24.8721 -1.1156 0.265

Marginal value per deer harvest = 1.9116 trips x 123.0983 = $235/deer

1 See table 8 for definition of variables

To estimate the CVM inverse demand curve, 246 observations were used

after 103 observations were dropped due to one or more missing variables. The

results (table 12) show consistency between the CVM inverse demand function

and the TCM demand function for most independent variables except whether

the hunter had hunted in this area in a previous season (i.e., PrevSeas), whether

the hunter had hunted on private land (i.e., Privland), and round-trip travel miles

from home to the hunt location (i.e., RTravMiles). Specifically, the remaining

seven variables were either the same sign or insignificant in both TCM and

CVM. The comparison results indicate that the variable “whether the hunter

successfully harvested a deer” (i.e., DeerKill) plays a vital role in influencing

people’s current WTP (i.e., MaxWTPCur) for deer hunting in the SJRD—similar

to the TCM demand function. The coefficient on whether the hunter harvested a

deer (i.e., DeerKill) (table 12) offers a second CVM way to calculate the marginal value per deer harvest per hunter. By multiplying $123/deer/trip with 1.911

trips, marginal value per deer harvest is $235/deer. This value is still consistent

with previous TCM and CVM analysis in tables 10 and 11.

Applications of Values to Estimate Benefits of

Prescribed Burning

Both CVM and TCM were used to evaluate the change in deer hunting benefits

due to an increase in deer harvest resulting from additional prescribed burning.

In the TCM analysis, we found the change in consumer surplus is $257 with

additional trips the hunter took in response to increasing deer harvest. From

CVM, we found the change in consumer surplus is slightly less than the TCM

result: $222 per deer harvested. The mid-point marginal consumer surplus of

TCM and CVM, therefore, is $239.5 per deer harvested, or $240 with rounding.

The annual deer hunting benefit of additional acres of prescribed burning

was computed (table 13). While the initial deer hunting benefit response to prescribed burning of 1,100 acres ranges from $3,840 to $7,920 depending on the

model, the incremental gain for more than the current acreage of prescribed

burning is quite similar across models. In other words, the annual economic

hunting benefit of increasing prescribed burning from its current level of 1,100

acres to 4,810 acres is $1,920, regardless of the model used. Likewise for an addiUSDA Forest Service Research Paper PSW-RP-249. 2003. 23
tional 3,700 acres of prescribed burning, to 8,510 acres, the deer hunting benefit

is between $960 and $1,200 each year, which is fairly similar despite the different modeling approaches. 

Table 13 Annual deer hunting benefits from increased prescribed burning: macro time-series model and GIS

micro model results.

Macro time-series model GIS micro model

NA NA NA NA NA NA

1,100 33 $7,920 1,100 16 $3,840

3,710 8 $1,920 3,710 8 $1,920

3,700 4 $960 3,700 5 $1,200

Comparison to Costs

The costs of prescribed burning on the San Bernardino National Forest range

from $210 to $240 per acre (Walker 2001). This is a much lower total cost per acre

than reported by González-Cabán and McKetta (1986) but substantially higher

than the direct costs per acre for southwestern National Forests reported in

Wood (1988). Nonetheless, if we use the $210 per acre figure, the full incremental costs of burning the first 1,100 acres would be $231,000, with each

additional 3,710 acres burned costing $779,100. The deer hunting benefits represent, at most, about 3.4 percent of the total costs of the first 1,100 acres of

prescribed burning. 

This finding can be used in two ways. First, the incremental costs of including deer objectives in the prescribed burn should not exceed $8,000, as the

incremental benefits are no larger than this. Second, the other multiple use benefits such as watershed and recreation as well as hazardous fuel reduction

benefits to adjacent communities would need to make up the difference if the

prescribed burning program is to pass a benefit-cost test. If prescribed burning

of 1,100 acres prevented as few as two residential structures from burning, the

prescribed burn program would likely pass a benefit-cost test. Such an assessment is beyond the scope of this study, however. Many of these multiple use

benefits from a prescribed fire are received for at least 5 years and as many as 10-

12 years (Gibbs and others 1995). Thus, a simple annualization of the costs

brings the 1,100-acre figure down to $23,100. Deer hunting benefits would cover

between 16 and 34 percent of the annual costs of the first 1,100 acres. However,

deer hunting benefits would only be minimal (less than 1 percent) compared to

further increases in prescribed burning. 

Conclusion

This study evaluated the response of deer harvest and deer hunting benefits to

prescribed burning in the SJRD of California. To estimate hunters’ benefits or

WTP for harvesting an additional deer, the individual observation TCM and

open-ended CVM were used. The mean WTP to harvest another deer is about

$257 for TCM and $222 for CVM. One reason for such consistency may be due to

the respondents’ hunting in the SJRD in previous years. About 80 percent of the

deer hunters in SJRD hunted there in the previous season. Also, the changes in

trips for the increase in harvest estimated from TCM were used to scale up both 

TCM and CVM per trip benefits to get a seasonal change. Because TCM contains

no hypothetical bias and the TCM result is consistent with the CVM estimate, it

may be that the hypothetical bias in this study was minimal for CVM. 

24 USDA Forest Service Research Paper PSW-RP-249. 2003.

Additional

acres

burned

Marginal 

increase in

deer harvest

Annual increase

in deer hunting

benefits

Additional

prescribed

acres burned

Marginal

increase in

deer harvest

Annual increase

in deer hunting

benefits
With regard to the response of deer harvest to prescribed fire and wildfire,

we compared a macro level, time-series model that treated the entire SJRD as one

area and a micro GIS model that disaggregated the SJRD into the 37 hunting

locations reported by hunters. Both models gave somewhat mixed results in that

some statistical specifications showed no statistically significant effect of prescribed burning and/or a negative effect of lagged wildfire. However, the better

fitting (68 percent of variation explained) log-log model functional form of the

macro time-series model did show a statistically significant effect of the combined prescribed fire and wildfire acres on deer harvest over the 20-year period

of 1979-1998. Two of the three micro GIS model specifications indicate that the

initial effect of prescribed burning had a statistically significant effect on deer

harvest in the 37 hunting locations within the SJRD. Lagged effects of prescribed

burning were consistently insignificant in our models, suggesting that most of

the benefits occur in the year of the burn. The macro time-series model estimated a larger response to burning of the first 1,100 acres than the micro GIS model

did, but for increases in fire beyond 1,100 acres, the two models provided nearly identical estimates. 

Combining the average of the TCM and CVM estimated economic benefits

with the deer harvest response to fire yields annual economic benefits ranging

from $3,840 to $7,920 for the first 1,100 acres burned. For 3,710 additional acres

burned, the gain is $1,920 annually, while for an additional 3,700 acres the

increase ranges from $960 to $1,200 per year. 

The costs of prescribed burning on the San Bernardino National Forest range

from $210 to $240 per acre. Thus, the costs to burn an additional 1,100 acres are

$231,000, which is an order of magnitude larger than the deer hunting benefits

gained. Specifically, the deer hunting benefits of the first 1,100 acres represent

about 3.4 percent of the total costs. Thus, the other multiple use benefits of pre-

scribed burning, such as providing opportunities for dispersed recreation,

protecting watershed, and reducing hazardous fuel in surrounding communi-

ties, would have to cover the rest. Investigating the extent of these benefits

would be a logical next step in evaluating the economic efficiency of prescribed

burning in the SJRD. 

Although fire management practices have been identified as having wide-

spread impacts on deer habitats, many other factors that affect deer habitat exist.

These other factors include livestock grazing, timber harvesting, urban develop-

ment, diseases, and habitat loss along with annual weather patterns (CDFG

1998). This study attempted to take into account as many factors as possible.

However, the amount of data and time available for modeling were a constraint. 

The macro time-series model demonstrated positive and significant effects

from total fire when both wildfire and prescribed fire variables were combined.

This appears to be in line with a previous study where the density of deer

increased the growing season after the burn (Klinger and others 1989). A study

of prescribed burning in northern California found prescribed burning to only

have modest effects of increasing deer habitat use and mentioned that any

increases in use are difficult to quantify (Kie 1984).

Some future improvements in our modeling effort that may better isolate the

effects of prescribed burning on deer habitat include controlling for the severity of wildfire because different fire severities will have different effects on

vegetation and soils (Ryan and others 1983). Furthermore, including a vegetation

and soils layer in the GIS model, rather than using elevation as a proxy, could

improve the predictive ability of the GIS-based model as well. 

Subject to these caveats, this paper has demonstrated two approaches to

estimate a production function relating prescribed burning to effects on deer

harvest. We found positive and significant effects on deer harvest for two of the

three GIS models and the positive impact of fire using a macro time-series

model. The USDA Forest Service and CDFG can make use of these approaches

for future cost benefit analysis of prescribed burning. 

USDA Forest Service Research Paper PSW-RP-249. 2003. 25
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USDA Forest Service Research Paper PSW-RP-249. 2003. 27
28 USDA Forest Service Research Paper PSW-RP-249. 2003.
USDA Forest Service Research Paper PSW-RP-249. 2003. 29

Appendix 1. Survey instrument used in the study
30 USDA Forest Service Research Paper PSW-RP-249. 2003.
USDA Forest Service Research Paper PSW-RP-249. 2003. 31
32 USDA Forest Service Research Paper PSW-RP-249. 2003.
USDA Forest Service Research Paper PSW-RP-249. 2003. 33
34 USDA Forest Service Research Paper PSW-RP-249. 2003.
USDA Forest Service Research Paper PSW-RP-249. 2003. 35

USDA Forest Service Research Paper PSW-RP-249. 2003. 37

Appendix 2. San Bernardino National Forest
38 USDA Forest Service Research Paper PSW-RP-249. 2003.
The Forest Service, U.S. Department of Agriculture, is responsible for Federal leadership

in forestry. It carries out this role through four main activities:

• Protection and management of resources on 191 million acres of National Forest

System lands;

• Cooperation with State and local governments, forest industries, and private landowners to help protect and manage non-Federal forest and associated range and

watershed lands;

• Participation with other agencies in human resource and community assistance 

programs to improve living conditions in rural areas; and

• Research on all aspects of forestry, rangeland management, and forest resources 

utilization.

The Pacific Southwest Research Station

• Represents the research branch of the Forest Service in California, Hawaii, American

Samoa, and the western Pacific.

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Economic Value of Big Game HabitatProduction from Natural and Prescribed Fire