Applied Economics

Cost-Benefit Analysis (440.632, Spring 2025)

Assignment 2: Travel cost to artificial reefs

This assignment is worth 70 points and is due by 11:59 pm on April 6, 2025.

You may discuss the assignment and how to solve it with your classmates, but you must do your own work. Ultimately, it is an individual assignment. All calculations and written narratives should be your own.

On May 17, 2006, the ex-USS Oriskany, an Essex Class aircraft carrier, was deliberately sunk off the coast of Pensacola, Florida, to become “the world’s largest artificial reef.” It was hoped that the new artificial   reef would provide many of the same ecosystem services supplied by a natural reef, including increased  fish and sea-life habitat, improved fish stocks and angling quality, and new recreational diving opportunities. If successful in providing these services, the Oriskany will also relieve some of the use pressure on the area’s other reefs. Since its sinking, thousands of divers have visited the site.

A spreadsheet entitled “Oriskany survey data.xls” has been posted on the class site containing two tabs. The first tab is a data dictionary, and the second tab is a subsample of the data from a web-based survey of individuals known to have dived to the Oriskany in the years just after its sinking.

A printed copy of the actual survey has been posted in a file entitled “Oriskany survey.pdf.” The survey asked respondents to report their:

(i)   The actual number of dive trips to the Oriskany taken during the 2006 dive season,

(ii)  their expected number of trips in 2007, assuming 2006 conditions, and

(iii)  their expected number of trips in 2007, assuming a second diveable warship is sunk in the vicinity of the Oriskany.

For the last question, respondents were told that there was the possibility of creating a “multiple-ship reefing area” by sinking a Spruance class destroyer in the permit area with the Oriskany. This would create the option to dive the Oriskany on the first dive and then travel to the new destroyer and dive it before returning to port.

1.    (20 points) Collect and clean the data necessary to estimate the non-market value of recreational

diving to the Oriskany artificial reef. (This can be done in Excel or your econometrics package.)

a)    (2 points) The data has been given to you in its raw form, including non-usable observations and errors. Clean the data for use in your statistical package.

i)     Load the data into Stata (or Excel) and remove all observations for which the party took no day trips in 2006.

ii)    Report the number of observations remaining after eliminating the data in part 1.a.i.

b)    Calculate the total travel cost for each respondent. Measure the travel cost as the sum of the travel expenses and the opportunity cost of time in 2023 dollars.

i)     (2 points) The Department of Transportation’s Bureau of Transportation Statistics estimates the average cost per mile of owning and operating a vehicle. The latest data is for 2023.

Search the internet for the “Average Cost of Owning and Operating an Automobile Bureau of Transportation Statistics.” Report the 2023 value for the average total cost per mile to operate and maintain a new vehicle, assuming the owner drives it 15,000 miles per year.

ii)    (2 points) Estimate the travel expense to the Oriskany site as the round trip distance in miles times the average cost of operating the vehicle per mile (which you just reported in part 1.b.i.), divided by the size of the traveling party. Note that the time reported in the survey is only for a one-way trip. Report the mean value of this travel expense.

iii)   (2 points) The income reported in the survey data reflects earnings in 2006. Update the income to what income would be in 2023 in real terms (that is without inflation) using a real earnings index for wage and salary workers. This can be found in the Federal Reserve Bank of St. Louis FRED database at https://fred.stlouisfed.org/. Search for “median weekly real earnings” and choose the series for “Employed full time: Median usual weekly real earnings: Wage and salary workers: 16 years and over.” Make sure that you use the “1982-84 CPI Adjusted Dollars, Quarterly, Seasonally Adjusted” series. Click the “Edit Graph” button on the right-hand side, above the graph and to the right, and modify the frequency to be annual data. You can download this data using the ”Download” button. Use this data to create a “wage deflator index” to update the 2006 income reported in the survey to 2023 real dollars. This is done by dividing the real wage in 2006 by the real wage in 2023 and multiplying it times the income in 2006. Report the real wage form 2006 and 2023, the wage deflator index you created, the mean value for the income reported in the survey, and your estimate of income in 2023 dollars.

iv)   (2 points) For each observation, estimate the opportunity cost of time for travel to the Oriskany site as the round trip travel time in hours times 50% of the average wage per hour. The per-hour wage can be estimated by taking the annual income (in 2023 dollars) and dividing it by 2,080 working hours per year. Again, note that the time reported in the survey is only the time for a one-way trip. Report the mean of this opportunity cost of time in 2023 dollars.

v)    (2 points) Measure the travel cost (in 2023 dollars) to the Oriskany as the sum of the travel expenses and the opportunity cost of time. Report the average travel cost for the sample here.

c)    (5 points) Calculate the travel cost to the alternative site, Key Largo, FL, the USS Spiegel Grove location, using the same assumptions you used in part 1.b. Again, note that time and distance to Key West are one way. Report the mean values (in 2023 dollars) for the travel expense, opportunity cost of time, and total travel cost to Key West here.

d)   After calculating the travel cost, create a new variable: household income (in 2023 dollars) divided by 10,000. You don’t need to report anything about this variable, but it will make reading the coefficients easier in your regressions.

e)    (3 points) Create a table containing the summary statistics for all your data, including the original data from the survey. Include the number of observations, the mean, the minimum, and the maximum. You can do this in Excel or Stata. Report that table of summary satistics here.

2. (25 points) Estimate the non-market value of recreational diving on the Oriskany in 2006

A survey of actual divers is equivalent to an on-site sample, so you need to correct for the fact that all respondents will have taken one or more trips. In other words, you have no observations for which the individual reported zero trips. (It is true that you deleted some observations where the response was zero for day trips, but those were divers who took multi-day trips, which we are excluding.) The easiest way to correct for this is to use a “zero-truncated” Poisson model. This is done using the “tpoisson” command in Stata (or the “ztp” command for older versions of Stata.) (For other statistical packages, you will have to find the correct command.

For example, in Limdep, you would add the “Truncation $” option to the Poisson command.

If you are using SAS or other statistical models, the zero-truncation model may not be available. In that case, just use the standard Poisson model, but please explain in your answer sheet that you are not using a zero-truncated Poisson model.)

a)    Run a zero-truncated Poisson model for the number of day trips taken in 2006. Use the following independent variables:

i)    The travel cost (in 2023 dollars) to the Oriskany.

ii)   The age of the respondent.

iii)  The household annual income (in 2023 dollars) (the one created in part 1.d.).

iv)  The number of years diving.

v)   A dummy variable indicating a technical diver.

vi)  The travel cost (in 2023 dollars) to the alternative site in Key West.

vii) A constant term (which should happen automatically in most statistical packages).

b)   (5 points) Report the results of your Poisson model. Make sure to include the number of observations used in the regression.

c)     (10 points) Write a paragraph on your results, commenting on the sign, significance, and how one should interpret the all of coefficients.

d)   (2 points) Estimate the per-person-per-trip value for divers in 2006. The formula for this can be found in the lecture on Single Site Travel Cost Models.

e)    (4 points) Estimate the aggregate consumer surplus value for the Oriskany in 2006. Don’t worry about on-site vs. off-site corrections; this was addressed using the zero-truncated Poisson model. This formula is on the same slide as the one you used for part 2.d.

f)    (4 points) Estimate the present discounted value in perpetuity to the divers in this survey for this artificial reef. Assume a discount rate of 3%. Write a sentence or two commenting on what this value implicitly assumes about future changes in using this resource.

3. (15 points) Estimate the expected non-market value of recreational diving if a sunken destroyer was available as a second artificial reef for diving nearby

a)    (2 points) Beginning with all observations in the data posted on the class site, remove the observations that report zero expected trips if a sunken destroyer was available for diving nearby. (In other words, start over with the original data set. Then remove the observations with zero expected trips for the sunken destroyer. You can include the observations of those who had zero trips to the Oriskany in 2006.) Report the number of observations that are now in this sample.

b)   (2 points) Calculate the total number of expected trips in 2007 for this new sample and report that number here.

c)    (3 points) Run a zero-truncated Poisson model for the expected number of trips with this second artificial reef. Use the same independent variables as you did for the 2006 analysis. (If you reload the original data, you will have to recalculate the travel cost to the Oriskany and the Key West site again.) Report the results of that regression here.

d)   (3 points) Estimate and report the expected per-person-per-trip value, the aggregate consumer surplus, and the present discounted value in perpetuity for this site, assuming the addition of a  second reef.

e)    (5 points) Write a paragraph commenting on the change in economic value associated with adding this second reef compared to your results for the expected economic value in 2006 that you reported in part 2. Does the change make sense to you? How would you interpret the change in the per-person-per-trip value, the aggregate consumer surplus, and the present discounted value in perpetuity?

4) (10 points) Write a one-page summary of the results of your analysis for this policy? How would

you explain this type of analysis to a decision-maker who is familiar with economics but is not an economist? What are the estimated benefits of recreational diving on the Oriskany in 2006 and the estimated benefits in 2007 with a second reef? How did you use this information to predict the estimated benefits of sinking a second destroyer? Are there any uncertainties in this analysis? Is there any reason why the valued changed or monetized benefits that you estimated might be under- or over-stated?