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1. Calculation of Non-Financial Recreation Value
2. Shortcomings with Methodology
We calculate the non-financial recreation value of the Buffalo National River (BNR) by a method known as the "Travel Cost Method" (TCM). The "non-financial recreation value" is the additional value that visitors receive, above that which they explicitly pay for (i.e., this recreation value is free value to visitors, above any financial value paid to concessionaires). We estimate their additional valuation as the travel costs that they incur to get to the BNR. The theoretical basis of TCM is that the distance that visitors travel, and the costs incurred in traveling, represent a "willingness to pay," and hence can be used to construct a "demand function" for the BNR can be assigned. The method requires counting the number of visitors by points of origin, multiplying that number by the estimate their travel costs from that origin. The BNR's recreation value estimated from this technique is $37.6 million per year.
1. Determination of Visitor Origins
To estimate the travel costs incurred by recreation visitors to
the BNR, we first determined how many visitors come from different
regions. We reviewed a sample of invoices from three different
concessionaires, over a period of two years, to determine origin
points of visitors. We chose the five most common states of origin,
and assigned visitors from other states to a general category
of "Others." The percent of the total for each state
is shown in Table
F-1. We counted both the number of visitors, to determine origin
proportions, and the number of vehicles they used, to determine
their travel costs later. The number of visitors per vehicle was
fairly constant across states, so we use the average (2.63 visitors
per vehicle) for all origins.
Visitor Origins Table F-1
Arkansas Missouri Louisiana Texas Oklahoma Others Total
No. of 416 109 87 72 44 239 967
Visitors
Percent of 43.0% 11.3% 9.0% 7.4% 4.6% 24.7%
Total
No. of Cars 157 40 32 29 16 93 367
Percent of 42.8% 10.9% 8.7% 7.9% 4.4% 25.3%
Total
Visitors per 2.6 2.7 2.7 2.5 2.8 2.6 2.63
Car
2. Determination of Visitation Rate
We further broke down Arkansas into four regions, by counting up the home addresses of Arkansas visitors from concessionaire invoices. Texas and Louisiana have major cities at large distances from the BNR, so we broke down those two states into two parts: "within 350 miles" and "beyond 350 miles" from the BNR (a complete discussion of the distance selection appears in Appendix H). We calculated the populations in the two parts by adding up the city populations in each region; 33% of Texas' population was within 350 miles, and 56% of Louisiana's population was within 350 miles. The populations of those two states which are beyond 350 miles are counted as "the rest of the USA." The populations of Oklahoma and Missouri are all counted as within 350 miles, since all of their major cities fall within that distance. We hence have nine regions: four within Arkansas, the four most commonly visiting states, and the rest of the USA (foreign visitors count as "the rest of the USA" also).
We then determined a "visitation rate" for each region. To calculate the total number of visitors from each region, we multiplied the percent of total visitors (from row 2 of Table F-1) by the total number of visitors to the BNR. The total number of visitors comes from the National Park Service's "Monthly Use Reports," as detailed in Appendix C. We used an average of 1992 and 1993 visitation, a total of 1.1 million visitors per year. The populations of each of those regions, divided by the number of visitors from those regions, provides the "visitation rate," shown in Table F-2, which is the basis of the TCM calculations below. The visitation rate indicates what percentage of people from each region visit the BNR each year (over 100% means, on average, each person in the region visits more than once per year).
Visitation rates Table F-2
Percent Population Average No. of Visitation
Origin of Total within 350 mi. Visitors 92-93 Rate
Local AR 8.5% 86,991 92,920 107%
Fayetteville 10.6% 113,409 115,044 101%
Little Rock 9.7% 505,600 106,194 21%
Rest of AR 14.2% 1,693,000 154,866 9.1%
Missouri 11.3% 5,193,000 119,496 2.3%
Texas 7.4% 5,897,104 86,635 1.5%
Oklahoma 4.6% 3,212,000 47,799 1.5%
Louisiana 9.0% 2,405,007 95,597 4.0%
Rest of USA 24.7% 222,335,000 277,829 0.12%
3. Determination of Travel Costs
We estimated the average distance traveled by measuring the distance (on a map) from the largest city in each region to the nearest point of the BNR. Those distances are shown in Table F-3, column 1. The distance for the "Rest of USA" region is necessarily arbitrary; we used 500 miles as the distance traveled by a typical visitor who came from outside of the other eight regions. This region is important because it accounts for 25% of all BNR visitors. The distances will be used again in section 7.4 to predict visitation.
We broke down the costs of traveling to the BNR into two components: the cost of operating a vehicle, and the cost of the time spent traveling. The cost of operating a vehicle for one visitor's trip to the BNR is the cost per mile, times the number of miles, divided by the number of people per vehicle. We use a vehicle operation cost of 15.8¢ per mile, based on the US Department of Transportation's estimate of variable cost per mile of travel, inflated to 1993 dollars. That rate, multiplied by the miles in column 1, divided by the number of people per vehicle (2.63) from Table F-1, times two for a round-trip, yields the "Two-way Car Cost."
We estimated the number of hours required to travel to the BNR, by analyzing the road conditions from each region's largest city to the BNR; our estimate is in column 3. We use an "opportunity cost of leisure time" as one-third of the per capita income for each region. The "Two-way Time Cost" is that per capita hourly income, divided by three for leisure time, times the number of hours spent traveling, times two for a round trip.
The "Total Travel Cost" is the sum of the two components of expenses. We then calculated a weighted average for all travel to the BNR, for later use in our demand curve (section 7.6). The weighted average is the average cost per mile (the total travel cost divided by the number of miles), weighted by the number of visitors from each region (from Table F-2 column 3). We estimate the average cost of travel to the BNR as 22.5¢ per visitor per mile.
Travel Costs Table F-3
Miles Per Capita Hours Two-way Two-way Total
Origin to BNR Income to BNR Car Cost Time Cost Travel
Cost
Local AR 40 $10,753 1 $4.78 $3.45 $8.23
Fayetteville 50 $12,756 1.5 $5.98 $6.13 $12.11
Little Rock 96 $15,776 2.5 $11.48 $12.64 $24.12
Rest of AR 150 $12,271 3 $17.94 $11.80 $29.74
Missouri 252 $18,189 4 $30.15 $23.32 $53.47
Texas 348 $18,731 7.5 $41.63 $45.03 $86.66
Oklahoma 222 $17,220 4.5 $26.56 $24.84 $51.39
Louisiana 300 $15,672 7 $35.89 $35.16 $71.05
Rest of USA 500 $16,184 10 $59.81 $51.87 $111.68
4. Calculation of Predicted Visitation
We next came derived an equation to predict visitation rates based on distance, so that we can add distances formulaically to make postulated fees for a demand curve. To make this equation, we fit a regression "best line" to the visitation rate (Table F-2 col. 4 as the dependent variable) and the distance data (Table F-3 col.1 as the independent variable). We used a standard statistical method for TCM, ordinary least squares regression, which gave us this equation:
log(Visitation Rate) = 4.7066 - 0.01376 x Distance "t-statistics": (6.64) (-8.31) R2 = 90.8%
Those numbers demonstrate that there is a very strong correlation between distance and visitation rate (in statistical jargon, well over the 99% confidence level), and distance accounts for 91% of the reason that visitors come to the BNR. We used a "log relationship" because we want to estimate the effect of a one-unit change in distance on the rate (in percentage) of visitation. We considered "left out variable" bias, but for our purposes, this equation is adequate, especially considering the strong confidence levels.
We then used our econometric equation to predict total visitation at the actual distances of each region. Table F-4 compares the predicted rate of visitation from our equation (column 1) with the actual visitation rates (column 2, copied from Table F-2). Our predictions are low for the regions closest to the BNR, but roughly accurate for most regions (Oklahomans, evidently, visit far less than their close distance would imply). We multiply the predicted visitation by the population of the region, to get the predicted number of visitors (column 3), which can be compared to the actual number of visitors (column 4, copied from Table F-2). Our prediction for total visitation is a little high overall, 1.2 million predicted versus 1.1 million actual visitors.
Predicted Visitation Table F-4 Predicted Actual Predicted Actual Origin Visitation Visitation No. of No. of Rate Rate Visitors Visitors Local AR 63.8% 106.8% 55,525 92,920 Fayetteville 55.6% 101.4% 63,082 115,044 Little Rock 29.5% 21.0% 149,339 106,194 Rest of AR 14.0% 9.1% 237,861 154,866 Missouri 3.5% 2.3% 179,285 119,496 Texas 0.9% 1.5% 54,335 86,635 Oklahoma 5.2% 1.5% 167,563 47,799 Louisiana 1.8% 4.0% 42,894 95,597 Rest of USA 0.11% 0.12% 252,995 277,829 Total 1,202,879 1,096,380
5. Calculation of Postulated Visitation
Next, we add distance to the actual distance that visitors from each region travel, and calculate the number of visitors who would still visit at the further distance, based on our formula from section 4. Adding distance to the mileage is directly translatable into adding a fee to the cost of visiting the BNR -- for example, adding 10 miles is the same as adding an entry fee of $4.50 (10 miles, round trip, times 22.5¢ per mile from section 3). Our formula yields a predicted visitation rate (column 2 in Table F-5) for each region at the new distance (column 1), which we multiply by the region's population to get a predicted number of visitors (column 3). The sum of the number of visitors represents a demand at that price -- for example, 1,048,000 visitors would still come if there were a $4.50 entry fee. Repeating the process at higher mileages comes up with other points on the demand curve -- for example, at a postulated distance of 100 miles shown in columns 4 through 6 of Table F-5, 304,000 people would visit with an entry fee of $45.00. We repeated for distances up to 200 miles, resulting in the demand curve shown below.
Postulated Visitation Table F-5 Distance Predicted Predicted Distance Predicted Predicted Origin + 10 Visitation Visitors + 100 Visitation Visitors mi. mi. Local AR 50 55.6% 48,387 140 16.1% 14,025 Fayetteville 60 48.5% 54,972 150 14.0% 15,934 Little Rock 106 25.7% 130,141 196 7.5% 37,721 Rest of AR 160 12.2% 207,283 250 3.5% 60,081 Missouri 262 3.0% 156,237 352 0.9% 45,285 Texas 358 0.8% 47,350 448 0.2% 13,724 Oklahoma 232 4.5% 146,022 322 1.3% 42,324 Louisiana 310 1.6% 37,380 400 0.5% 10,835 Rest of USA 510 0.10% 220,472 600 0.03% 63,903 Total 1,048,245 303,831
See Figure F-5: Demand Curve for Recreational Use of the BNR
6. Total Value of Non-Financial Recreational Demand
The demand curve represented graphically in Figure F-5 is shown numerically in Table F-6. At an added mileage of zero miles, the added cost is $0, and the predicted number of visitors is the total predicted from our formula, in Table F-4. At an added mileage above 200 miles (the equivalent of an entry fee of $90), the demand drops off to zero. Since the actual "entry fee" to the BNR is zero, all of the willingness to pay a fee is a "consumer surplus," since visitors get the benefits of visiting while paying less than they are willing. The entire area under the demand curve, therefore, represents the recreational benefit of the BNR.
To calculate the area, we add up the area of columns on the curve, one for each mileage. (the area under the curve between 10 miles and 20 miles is: a rectangle of height $4.51, by width 1,048,000 minus 913,000; plus a triangle of the same width, by height $9.01 minus $4.51). The area of each column is shown in Table F-6 column 4. Its sum is the area under the entire demand curve, which represents the entire consumer surplus of the recreational value of the BNR. Thus, the non-financial recreational value of the BNR is $37.6 million per year.
TCM-Based Demand Curve Table F-6
Added Predicted Added Cost Approx. Cost
Mileage No. of Visitors (22.5¢ per (area under
mile) curve)
0 1,202,879 $0.00 $348,480
10 1,048,245 $4.51 $911,046
20 913,490 $9.01 $1,323,214
30 796,059 $13.52 $1,614,355
40 693,723 $18.03 $1,808,776
50 604,543 $22.54 $10,165,203
100 303,831 $45.07 $8,514,716
150 152,700 $67.61 $5,991,059
200 76,744 $90.14 $6,917,958
Total $37,594,807
Technical Notes
Our methodology follows the recommendations of US Water Resource Council, an agency of the federal Department of Interior. Our raw data (for determining the proportions of visitors from each region, for estimating distances and times for each region, and our spreadsheet work to calculate the tables here) are available for inspection but are not included in this report.
Shortcomings with Our Methodology
1) Concessionaires' customers may not be representative of BNR origins. We may have a "selection bias" in our method of choosing particular concessionaires as the source of visitor origins (in Table F-1), since one concessionaire's customers are not a random sample of actual visitors. For example, BOC (one of our concessionaires) advertises in Missouri and hence BOC's customers are more likely to be from Missouri than are BNR visitors in general. We address this bias by using data from multiple concessionaires. More generally, people who use concessionaires may not be representative of BNR visitors as a whole. In particular, the closer visitors lives to the BNR, the more likely is it that they will bring their own equipment, and hence not appear on concessionaire ledgers. We do not address this problem, and it is a potential source of overestimate, since perhaps the actual visitor origin ratios should be at lesser distances.
2) Our total travel cost per mile is based on average estimates. Because our regions of origins are fairly large, we had to estimate the typical time and distance traveled by a person coming to the BNR from that region (in Table F-3). We did this by measuring distances on a map, and by estimating the time by observing the type of highways which connect each region to the BNR. Our accuracy is hence limited by our ability to properly estimate travel time and distance, which is probably accurate only to the nearest 1/2 hour and the nearest 20 miles. We addressed this problem by intentionally estimating low on travel time, so that the resulting travel cost is conservative.
3) The "predicted visitation" formula doesn't account for local preferences. We assume there are some "left out variables" in our formula which determines visitation rate based only on distance from the BNR. We assume that more Arkansans, and more Ozark residents especially, visit the BNR than do residents from other states, just because the Buffalo River is in their "home" (as reflected in the under-prediction of local visitation in Table F-4). We also do not account for the nearness of other similar amenities (e.g., whether there are other rivers nearer to a point of origin), which may the reason for the low representation of Tennessee, for instance. We do not address this problem because it would make our TCM "non-standard." We have no guess as to whether this biases our estimate up or down.