1 An introduction to travel-cost modeling, Edward Morey, September 2010 An Introduction to the travel-cost method for estimating use damages: mining injuries in the Coeur d’Alene Basin Edward Morey: Tc-intro-coeurdalene.doc revised September 21, 20102 An introduction to travel-cost modeling, Edward Morey, September 20103 An introduction to travel-cost modeling, Edward Morey, September 20104 An introduction to travel-cost modeling, Edward Morey, September 2010 ► Objective: Estimate Damages from Injuries ► Damage: Willingness to Pay (WTP) for Uninjured State □ Damage to individual is how much he or she would pay for a world with no mining injuries in Coeur d'Alene Basin ► Travel-Cost Method Estimates Use Damages □ Use values only experienced by visiting site – If you take fewer trips to site in the injured state than you would in uninjured state, you experience use damages – In addition, you receive less benefits from trips to site in its injured state than you would in its uninjured state5 An introduction to travel-cost modeling, Edward Morey, September 2010 ► Travel-Cost Estimates Damage by Observing Behavior AND ► Inferring Value from that Behavior □ Travel-cost estimates a demand function for trips to a recreational site or sites AND □ Uses that estimated demand function to derive benefits from the site6 An introduction to travel-cost modeling, Edward Morey, September 2010 ► How Behavior Infers Value □ If trip costs $50, and one takes an additional trip, we can infer that the individual expects at least $50 worth of benefits from the trip □ If one could have taken trip to site A for $50 but instead went to site B at cost of $100, individual must value characteristics at site B at least $50 more than characteristics at site A For example I could have skied at Eldora at a cost of $50, but went instead to Vail which cost me $150, I valued, on that day, the characteristics of Vail at least $100 more than I valued the characteristics of Eldora. My behavior reveals how I value things.7 An introduction to travel-cost modeling, Edward Morey, September 2010 ► Demand Estimation and Value: Simple Example Phil’s Estimated Demand for Apples Assume for Phil: Apples = α – β (Price Apples) = 8 – 4 (Price Apples) e.g., if Price = $0.25, Apples = 7 e.g., if Price = $2.00, Apples = 0 e.g., if Price = $0.00, Apples = 8 The parameter α is how many apples Phil would consume if they were free. The parameter β is how many fewer apples Phil will consume if the price increases by $18 An introduction to travel-cost modeling, Edward Morey, September 20109 An introduction to travel-cost modeling, Edward Morey, September 2010 ► What is Phil's WTP to Have Apples Available at 25¢? □ Shaded area approximates Phil's WTP to have apples available at 25¢ □ This WTP is often called consumer's surplus10 An introduction to travel-cost modeling, Edward Morey, September 2010 ► How to Estimate Demand Curve for Apples □ Collect from number of Phils price each faced for apples, and how many eachPhil purchased □ Use this data to estimate demand curve for apples □ Choose values of α and β that best fit data □ Note: Need variation in price of apples across individuals; otherwise, cannot estimate influence of price on demand (show ex.)11 An introduction to travel-cost modeling, Edward Morey, September 2010 RECREATION ► Travel-Cost Estimates the Demand Function for Recreational Site or Sites □ Travel-cost methodology builds and estimates model to predict how many trips individual will take to each site in his choice set ► Then Uses these Estimated Demand Functions to Infer Values ► Assume Intent is to Model Recreational Fishing ► Assume Only Two Sites □ Call the two sites N (North Fork) and S (South Fork)12 An introduction to travel-cost modeling, Edward Morey, September 2010 ► Methodology is Called Travel-Cost □ Travel costs typically a major component of cost of trip □ Trip costs include transportation costs, value of the individual's time, entrance fees, equipment costs, etc. □ For a given site, trip costs vary across individuals as a function of where each lives and how each values their time □ For a given individual, trip costs vary across sites because, for one, sites are different distances from individual's residence13 An introduction to travel-cost modeling, Edward Morey, September 2010 ► Assume TripsN = αN + βN(CostN) + γN(CatchN) + βNS(CostS) + γNS(CatchS)14 An introduction to travel-cost modeling, Edward Morey, September 2010 ► And assume TripsS = αS + βS(CostS) + γS(CatchS) + βSN(CostN) + γSN(CatchN)15 An introduction to travel-cost modeling, Edward Morey, September 2010 ► Consider how demand functions shift if CatchS ↓ ► Damage Due to CatchS ↓ Approximated by Change in Areas Under the Two Curves □ WTP for trips to the South Fork are lower than would have been in absence of injury □ But, WTP for trips to the North Fork are higher than would have been in absence of injury to the South Fork □ The more easily fishing on the North Fork substitutes for fishing on the South Fork, the smaller the damages16 An introduction to travel-cost modeling, Edward Morey, September 2010 ► Need Random Sample of Users and Potential Users to Estimate Demand □ Need to know how many trips each individual took to each site during fishing season – Call these observed trip patterns Trip Data – Don't want sample to only consist of individuals who fish the injured South Fork site □ For each individual, need enough information to calculate individual's trip costs to each site – Distance to each site – Vehicle operating costs – Value of individual's time □ Use this information to calculate CostN and CostS for each individual17 An introduction to travel-cost modeling, Edward Morey, September 2010 ► Need Expected Catch Rates for Each Site, CatchS and CatchN □ Collect catch data from individuals fishing at the two sites □ Note: Need variation in expected catch rates across sites to estimate influence of expected catch on trip patterns ► Might Want to Supplement Observed Trip Data with Responses to Hypothetical Questions □ Ask individuals to choose between pairs of hypothetical sites, where the two