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This Document Contains Chapters 8 to 14 Chapter 8 Exercises Predicting and Monetizing Impacts 1. Review the following CBA: David L. Weimer and Mark A. Sager, ““Early Identification and Treatment of Alzheimer’s Disease: Social and Fiscal Outcomes,” Alzheimer’s & Dementia 5(3), 2009, 215-226. Evaluate the empirical basis for prediction and monetization. 1. This CBA employs a great variety of sources to support prediction and monetization. The estimates of mean decline in the Mini-Mental State Examination (MMSE) score with and without drug treatment come from a number of studies, including several that were clinical trials with random assignment. The Lopez estimates for drug effects were from a matched-pair quasi-experimental design that followed patients over multiple years. A number of important parameters were from individual studies. For example, the risk of nursing home institutionalization as a function of MMSE scores came from a single empirical study. An interesting case is the Mittelman caregiver intervention impacts. They come from a long-term random assignment study. However, this study did not provide information on the utilization of other support services. To put plausible bounds on the likely costs associated with increased use of support services by those receiving the caregiver intervention, the authors turned to estimates from the Alzheimer’s Disease Project, which involved a randomized experiment in which the treatment group received counselling and subsidized services. 2. Imagine that a project involves putting a high-voltage power transmission line near residential property. Discuss how you might predict and monetize its impact on residents. 2. There have been a number of studies that have estimated the effects of high-voltage power lines on residential property values. For example, see Stanley W. Hamilton and Gregory M. Schwann, “Do High Voltage Lines Affect Property Values?” Land Economics 71(4), 1995, 436-444. A rough estimate from this and other studies would be that property values very close to power lines, either adjacent or within 200 meters, suffer a decline in value of between 5 and 10 percent (6.3 percent in this study for properties within 200 meters and a line-of-sight to a tower. So, an analyst could identify the value of property with this proximity to the proposed power line route and estimate the cost of the loss of amenity as this total property value multiplied by the percentage. Chapter 8 Case Study Exercises WSIPP CBA of the Nurse-Family Partnership Program 1. Imagine Washington State is considering implementing a program that pays monetary awards to families when their high school age children meet certain goals (for example, school attendance, achievement on standardized tests, receiving regular dental checkups, and receiving flu shots). WSIPP has been asked by the state legislature to assess whether the state should adopt this policy. a. Name three potential secondary impacts that WSIPP might consider in evaluating the policy. b. Indicate how WSIPP might go about making predictions of one of these impacts and then monetize them. (You need not go beyond the level of detail provided in the table to the case, but write in complete sentences.) 1.a. There are many potential secondary impacts including several found in the table to the case. For example, improved school attendance could reduce grade reputation, reduce crime, and increase high school graduation rates. Although not listed in the table, if more high school students receive flu shots, other persons may be less likely to receive the flu; and if more students receive dental checkups, future serious dental work may be less necessary. 1.b. To take just one example, WSIPP would first look at the experimental evaluations to obtain estimates of how the monetary awards affect school attendance. It would then search for studies of the relationship between improved school attendance and high school graduation rates and conduct a meta-analysis to obtain a prediction. These two estimates would be combined to determine how the monetary awards would affect high school graduation rates. Then, as the table to the case indicates, using data from the Census Bureau’s Current Population Survey, it would monetize using the discounted lifetime money earnings gain from high school graduation. Chapter 9 Exercises Discounting Future Impacts and Handling Inflation 1. A highway department is considering building a temporary bridge to cut travel time during the three years it will take to build a permanent bridge. The temporary bridge can be put up in a few weeks at a cost of $730,000. At the end of three years, it would be removed and the steel would be sold for scrap. The real net cost of this would be $81,000. Based on estimated time savings and wage rates, fuel savings, and reductions in risks of accidents, department analysts predict that the benefits in real dollars would be $275,000 during the first year, $295,000 during the second year, and $315,000 during the third year. Departmental regulations require use of a real discount rate of 4 percent. a. Calculate the present value of net benefits assuming that the benefits are realized at the end of each of the three years. b. Calculate the present value of net benefits assuming that the benefits are realized at the beginning of each of the three years. c. Calculate the present value of net benefits assuming that the benefits are realized in the middle of each of the three years. d. Calculate the present value of net benefits assuming that half of each year’s benefits are realized at the beginning of the year and the other half at the end of the year. e. Does the temporary bridge pass the net benefits test? 1. Begin by calculating the present value of the costs. This includes the construction cost of the temporary bridge, which occurs at the beginning of year 1, and the net cost of decommissioning the bridge at the end of year 3: Alternatively, average the answers to parts a and b: ($15,192 + $47,880)/2 = $31,536. 1.e. Although the NPVs vary depending on when the benefits actually arise, they are all positive, implying that the department should construct a temporary bridge, assuming that is the only alternative to the status quo. 2. A government data processing center has been plagued in recent years by complaints from employees of back pain. Consultants have estimated that upgrading office furniture at a net cost of $430,000 would reduce the incidence and severity of back injuries, allowing the center to avoid medical care that currently costs $68,000 each year. They estimate that the new furniture would also provide yearly benefits of avoided losses in work time and employee comfort worth $18,000. The furniture would have a useful life of five years, after which it would have a real scrap value equal to 10 percent of its initial net cost. The consultants made their estimates of avoided costs assuming that they would be treated as occurring at the beginning of each year. In its investment decisions, the center uses a nominal discount rate of 9 percent and an assumed general inflation rate of 3 percent. It expects the inflation rate for medical care will be either 3 percent, the same as other goods, or 6 percent. Should the center purchase the new furniture? 2. An Excel solution to this question is available to instructors on the web page using both real dollars (as below) and nominal dollars. It also contains a solution using the formula for calculating the PV of an annuity that grows at a constant rate. Assuming that medical (avoided) costs grow at the same rate as other goods (3%), the NPV = -$12,406 and buying the furniture would not be worthwhile. Assuming that medical (avoided) costs grow at 6%, the NPV = $9,813 and buying the furniture would be worthwhile. Perhaps of interest: If the consultants assumed that all of the avoided costs will occur at the end of each year instead of at the beginning of each year, the NPV would be lower. 3. A town’s recreation department is trying to decide how to use a piece of land. One option is to put up basketball courts with an expected life of 8 years. Another is to install a swimming pool with an expected life of 24 years. The basketball courts would cost $180,000 to construct and yield net benefits of $40,000 at the end of each of the eight years. The swimming pool would cost $2.25 million to construct and yield net benefits of $170,000 at the end of each of the 24 years. Each project is assumed to have zero salvage value at the end of its life. Using a real discount rate of 5 percent, which project offers larger net benefits? 3. A spreadsheet contains some of the following calculations. As only one of these projects can be built on the site, they are mutually exclusive. The comparison is complicated because the swimming pool has an expected life three times longer than the basketball courts. Consider first the NPV of each project separately: NPV(one basketball court project) = -$180,000 + PV(.05,8,-40000) = $78,529. NPV(one swimming pool project) = -$2,250,000 + PV(.05,24,-170000) = $95,769. If we choose on the basis of this comparison, then the swimming pool has a larger present value of net benefits. However, this is not appropriate as the projects are of different lengths. There are two possible correct approaches: 1. One could choose between one swimming pool and three successive basketball court projects so that the site is used in each case for the same length of time. Thus, three successive basketball court projects offer a larger NPV than the swimming pool project. One should build the basketball pool. 2. An alternative approach for comparing these projects of different lengths is to divide each project’s NPV by its appropriate annuity factor to find its equivalent annual net benefit, an approach called "amortization." The appropriate annuity factor can be obtained by using the formula for the present value of an annuity. The 8-year annuity factor = [1-(1 + .05)-8]/(.05) = PV(.05,8,-1) = 6.4632 Annualized NB for the basketball court = $78,529/6.4632 = $12,150 The 24-year annuity factor = [1-(1 + .05)-24]/(.05) = PV(.05,24,-1) = 13.7986 Annualized NB for the swimming pool = $95,769/13.7986 = $6,940. The basketball court project offers net benefits equivalent to an annuity paying $12,150 each year over its life. The swimming pool offers net benefits equivalent to an annuity paying $6,940 each year over its life. 4. The environmental protection agency of a county would like to preserve a piece of land as a wilderness area. The current owner has offered to lease the land to the county for 20 years in return for a lump-sum payment of $1.1 million, which would be paid at the beginning of the 20-year period. The agency has estimated that the land would generate $110,000 per year in benefits to hunters, bird watchers, and hikers. Assume that the lease price represents the social opportunity cost of the land and that the appropriate real discount rate is 4 percent. a. Assuming that the yearly benefits, which are measured in real dollars, accrue at the end of each of the 20 years, calculate the net benefits of leasing the land. b. Some analysts in the agency argue that the annual real benefits are likely to grow at a rate of 2 percent per year due to increasing population and county income. Recalculate the net benefits assuming that they are correct. 4.a. A spreadsheet contains some of these calculations. The present value of the real yearly benefits is most easily calculated using the formula for the present value of an annuity presented in Appendix 6a: PV(benefits) = ($110,000)[1-(1 + .04)-20] / (.04) = PV(.04,20,-110000) = $1,494,936 4.b. In this case we use the formula for the present value of an annuity with a growth rate in benefits of 2 percent. First, calculate i0 = (.04 - .02)/(1 + .02) = .01961 PV(benefits) = PV(.01961,20, - (110000)/1.02) = [($110,000) / (1 + .02)][1-(1 + i0)-20] / i0] = $1,770,082. NPV = $1,770,045-$1,100,000 = $670,082 5. Imagine that the current owner of the land in the previous exercise was willing to sell the land for $2 million. Assuming this amount equaled the social opportunity cost of the land, calculate the net benefits if the county were to purchase the land as a permanent wildlife refuge. In making these calculations, first assume a zero annual growth rate in the $110,000 of annual real benefits; then assume that these benefits grow at a rate of 2 percent per year. 5. The benefit stream can now be viewed as a perpetuity. If the growth rate of benefits is assumed to be zero, then Thus, the land should be purchased whether the growth rate is zero or 2 percent. 6. (Instructor-provided spreadsheet recommended.) New City is considering building a recreation center. The estimated construction cost is $12 million with annual staffing and maintenance costs of $750,000 over the twenty-year life of the project. At the end of the life of the project, New City expects to be able to sell the land for $4 million, although the amount could be as low as $2 million and as high as $5 million. Analysts estimate the first year benefits (accruing at the end of the year of the first year) to be $1.2 million. They expect the annual benefit to grow in real terms due to increases in population and income. Their prediction is a growth rate of 4 percent, but it could be as low as 1 percent and as high as 6 percent. Analysts estimate the real discount rate for New City to be 6 percent, though they acknowledge that it could be a percentage point higher or lower. a. Calculate the present value of net benefits for the project using the analysts’ predictions. b. Investigate the sensitivity of the present value of net benefits to alternative predictions within the ranges given by the analysts. 6.a. The spreadsheet is setup to answer part a --- net present value is -$347,375. 6.b. Students can use the spreadsheet to answer part b by varying the assumed values for the scrap value of land ($2 million to $5 million), the growth rate of benefits (.01 to .06), and the discount rate (.05 to .07). For example, a “worst-case” analysis would yield net benefits of -$5.7 million while a “best-case” analysis would yield positive net benefits of $5.6 million. Chapter 9 Case Study Exercises A CBA of the North-East Mine Development Project 1. Would you describe this study as a Distributional CBA? 1. Yes. It considers the impacts (benefits, costs and net benefits) on different groups—different industries (sectors) and different regions (B.C. and Canada). 2. Why is there no consumer surplus included as a benefit? 2. No consumer surplus is included because the analysis is done from the perspective of Canada. The mineral is exported to, and primarily consumed by, Japanese customers. Although they would receive some surplus, this is not included because they do not have standing in an analysis that adopts a Canadian standing perspective. 3. What weaknesses do you see in this CBA? If corrected, would they increase or decrease the expected NPV? 3. The analysis should have included an estimate of the METB. If it had been included, the NPV would be lower, probably negative even for the base case. The analysis should not have used such a high real social discount rate (10%). The costs to the mining sector, the BC government and the Canadian all arise in time periods before the benefits occur. Therefore, using a lower discount rate would have increased the NPV. Chapter 10 Exercises The Social Discount Rate 1. (Instructor-provided spreadsheet recommended.) The following table gives cost and benefit estimates in real dollars for dredging a navigable channel from an inland port to the open sea.
Dredging and Savings to Value of Pleasure
Year Patrol Costs ($) Shippers ($) Boating ($)
0 2,548,000 0 0
1 60,000 400,000 60,000
2 60,000 440,000 175,000
3 70,000 440,000 175,000
4 70,000 440,000 175,000
5 80,000 440,000 175,000
6 80,000 440,000 175,000
7 90,000 440,000 175,000
The channel would be navigable for seven years, after which silting would render it un-navigable. Local economists estimate that 75 percent of the savings to shippers would be directly invested by the firms, or their shareholders, and the remaining 25 percent would be used by shareholders for consumption. They also determine that all government expenditures come at the expense of private investment. The marginal social rate of time preference is assumed to be 3.5 percent, the marginal rate of return on private investment is assumed to be 6.8 percent, and the shadow price of capital is assumed to be 2.2. Assuming that the costs and benefits accrue at the end of the year they straddle and using the market-based interest rate approach, calculate the present value of net benefits of the project using each of the following methods: a. Discount at the rates suggested by the U.S. Office of Management and Budget. b. Discount using the shadow price of capital method. c. Discount using the shadow price of capital method. However, now assume that the social marginal rate of time preference is 2.0 percent, rather than 3.5 percent. d. Discount using the shadow price of capital method. However, now assume that the shadow price of capital is given by equation (10.9). Again assume that the social marginal rate of time preference is 3.5 percent. e. Discount using the shadow price of capital method. However, now assume that only 50 percent of the saving to shippers would be directly invested by the firms or their shareholders, rather than 75 percent. Again assume that the social marginal rate of time preference is 3.5 percent and that the shadow price of capital is 2.2. The spreadsheet as provided is set up to answer immediately parts a and b. 1.a. The OMB suggests discounting at 3% and 7%, yielding NPVs of $682,891 and $236,135, respectively. Thus the project would pass the net benefits test set by the OMB. 1.b. Using the shadow price of capital method one obtains an NPV = -$579,188. Thus, using the SPC method, the project would not pass the net benefits test. The spreadsheet can provide the answers to the remaining parts by varying the parameters. 1.c. Using a lower discount rate (2%) raises the NPV based on the SPC method to -$281,410, but it is still negative. 1.d. Using a lower shadow price of capital (1.943) also raises the NPV based on the SPC method, but it is still negative. 1.e. Assuming that a lower percentage of the savings to shippers (50% instead of 75%) would be directly invested lowers the NPV to -$1,374,713. 2. An analyst for a municipal public housing agency explained the choice of a discount rate as follows: “Our agency funds its capital investments through nationally issued bonds. The effective interest rate that we pay on the bonds is the cost that the agency faces in shifting revenue from the future to the present. It is, therefore, the appropriate discount rate for the agency to use in evaluating alternative investments.” Comment on the appropriateness of this discount rate. 2. The use of the effective rate of interest on the agency's bonds is appropriate as the agency's discount rate from the perspective of a purely financial analysis. Such an analysis may be administratively relevant for public agencies that are required to be self-financing. However, from the social (national) perspective, using the effective borrowing rate facing the agency as the discount rate is not appropriate. What matters is changes in consumption. If we restrict standing to residents of the municipality, then there are two possibilities. On the one hand, one can argue that the borrowing rate in the national market may be the appropriate "social" discount rate, because it indicates what the municipality --"society" under the restricted standing-- must pay to trade future for current revenue. On the other hand, projects that the municipality funds through bonds typically result in a flow of benefits to its citizens that are realized at different points in time than the flow of tax expenditures that the citizens must make to repay the loan. Thus, projects that are funded by bonds affect the net consumption flows of the municipality's citizens over time. Hence, the rate of time preference of the citizens of the municipality may be the appropriate discount rate, because it represents their trade-off between consumption that occurs in different time periods. As suggested in the chapter, because of taxes, the rate of time preference is probably substantially less than the rate the agency must pay to borrow on the national market. 3. Assume the following: Society faces a marginal excess tax burden of raising public revenue denoted METB; the shadow price of capital equals θ; public borrowing displaces private investment dollar for dollar; and public revenues raised through taxes displace consumption (but not investment). Consider a public project involving a large initial capital expenditure, C, followed by a stream of benefits that are entirely consumed, B. a. Discuss how you would apply the shadow price of capital method to the project if it is financed fully out of current taxes. b. Discuss how you would apply the shadow price of capital method to the project if it is financed fully by public borrowing, which is later repaid by taxes. 3.a. If the project is financed fully by current taxes, then the first step is to multiply the capital expenditure by one plus the marginal excess burden -- (1 + METB)(C) -- to account for the deadweight loss resulting from the additional taxes. Second, find the fraction of the investment coming at the expense of investment, (1 + METB)(C)(s), and the fraction coming from consumption, (1 + METB)(C)(1-s). Third, calculate an adjusted investment cost by applying the shadow price of capital to forgone investment: (Pc)(1 + METB)(C)(s) + (1 + METB)(C)(1-s) Fourth, discount the stream of consumption benefits, B, at the social marginal rate of time preference. 3.b. If the project is financed fully by borrowing that displaces private investment, then the initial capital cost must be multiplied by the shadow price of capital: (Pc)(C). The fact that the borrowing will be repaid by taxes must also be taken into account. Each repayment of the loan must be multiplied by (METB) to take account of the social losses associated with raising the revenue to repay the loan. (The payment itself need not be taken into account because it represents a transfer from taxpayers to creditors.) If we assume that the fraction of these social losses representing forgone investment is s, then a cost equal to the following would be recorded for each dollar of repayment: (METB)(1-s) + (METB)(s)(Pc) To obtain an adjusted stream of net benefits, the expression appearing above should be multiplied by the dollars of taxes used for repayment purposes each year and then subtracted from the dollars of consumption benefits generated by the project during the year. Finally, this adjusted stream of net benefits should be discounted at the social marginal rate of time preferences. 4. Assume a project will result in benefits of $1.2 trillion in 500 years by avoiding an environmental disaster that otherwise would occur at that time. a. Compute the present value of these benefits using a time-constant discount rate of 3.5. b. Compute the present value of these benefits using the time-declining discount rate schedule suggested in this chapter. A spreadsheet contains the calculations for both parts. 4.a. NPV = $1,200,000,000,000 x e-(0.035 x 500) = $30,132 (using continuous compounding). 4.b. The resultant NPV is given by: NPV = ($1,200,000,000,000) x (e-(0.035 x 50)) x (e-(0.025 x 50)) x (e-(0.015 x 100)) x (e-(0.005 x 100)) x (e-(0.00 x 200)) = $8,085,536,399. Chapter 11 Exercises Dealing with Uncertainty: Expected Values, Sensitivity Analysis, and the Value of Information 1. The initial cost of constructing a permanent dam (i.e., a dam that is expected to last forever) is $830 million. The annual net benefits will depend on the amount of rainfall: $36 million in a “dry” year, $58 million in a “wet” year, and $104 million in a “flood” year. Meteorological records indicate that over the last 100 years there have been 86 “dry” years, 12 “wet” years, and 2 “flood” years. Assume the annual benefits, measured in real dollars, begin to accrue at the end of the first year. Using the meteorological records as a basis for prediction, what are the net benefits of the dam if the real discount rate is 5 percent? 1. Spreadsheet provided that contains these calculations. The first step is to calculate the expected value of the annual net benefits: (.86)($36 million) + (.12)($58 million) + (.02)($104 million) = $40 million The second step is to find the present value of the stream of annual net benefits. As the dam is assumed to be permanent, the formula for the present value of a perpetuity can be used: PV = ($40 million)/(.05) = $800 million. The final step is to subtract the cost of construction from the present value of the annual benefit stream to obtain the overall present value of expected net benefits (PVENB): E(NB) = $800 million - $825 million = -$30 million. Thus, the dam does not pass the net benefits test. 2. Use several alternative discount rate values to investigate the sensitivity of the present value of net benefits of the dam in exercise (1) to the assumed value of the real discount rate. 2. Using a spreadsheet, we obtained the following values of the present value of expected net benefits for different real discount rates:
SDR (%) E(NB) ($millions)
0.01 3,170.0
0.02 1,170.0
0.03 503.3
0.04 170.0
0.05 -30.0
0.06 -163.3
0.07 -258.6
0.08 -330.0
The "breakeven" value of the discount rate, dBE, can be found by solving for the rate at which the present value of the stream of expected annual net benefits just equals the cost of construction: Thus, the discount rate would have to be no larger than 4.7% for the present value of expected net benefits for the dam to be positive. 3. The prevalence of a disease among a certain population is 0.40. That is, there is a 40 percent chance that a person randomly selected from the population will have the disease. An imperfect test that costs $250 is available to help identify those who have the disease before actual symptoms appear. Those who have the disease have a 90 percent chance of a positive test result; those who do not have the disease have a 5 percent chance of a positive test. Treatment of the disease before the appearance of symptoms costs $2,000 and inflicts additional costs of $200 on those who do not actually have the disease. Treatment of the disease after symptoms have appeared costs $10,000. The government is considering the following possible strategies with respect to the disease: S1. Do not test and do not treat early. S2. Do not test and treat early. S3. Test and treat early if positive and do not treat early if negative. Find the treatment/testing strategy that has the lowest expected costs for a member of the population. In doing this exercise, the following notation may be helpful: Let D indicate presence of the disease, ND absence of the disease, T a positive test result, and NT a negative test result. Thus, we have the following information: 3. First notice that the strategies being considered by the government are not exhaustive. For example, one could test and then treat no matter what the result. Obviously, with costly testing this strategy would be dominated by S2. Similarly, testing and then not treating no matter what the result would be dominated by S1. All the logical possibilities could be discovered by displaying a decision tree with chance and decision nodes. In this problem, only S1, S2, and S3 need to be considered. Now, calculate the expected cost of each strategy: As the expected cost of strategy S2 is less than the expected cost of strategy S1, early treatment should be given in the absence of testing. Thus, the best testing strategy, S3, must have expected costs less than $2,120 to be chosen over not testing. As S3 has a lower expected cost than either S1 or S2, it is the optimal strategy. 4. In exercise (3) the optimal strategy involved testing. Does testing remain optimal if the prevalence of the disease in the population is only .05? Does your answer suggest any general principle? 4. Using the same procedures as in exercise 3: E(cost of S1) = $500 E(cost of S2) = $2190 E(cost of S3) = $530 If the prevalence of the disease in the relevant population is only .05, the optimal strategy is S1, which is simply to treat the disease after symptoms appear. The general point is that the optimal testing strategy depends on the prevalence of the disease. Thus, if the probability of having the disease is low in the general population, tests may not be cost-effective for the general population. However, they may be cost-effective for subsets of the population sharing specific risk factors that give them a higher probability of having the disease. 5. (Use of a instructor-provided spreadsheet recommended for parts a through e, and necessary for part f) A town with a population of 164,250 persons who live in 39,050 households is considering introducing a recycling program that would require residents to separate paper from their household waste so that it can be sold rather than buried in a landfill like the rest of the town’s waste. Two major benefits are anticipated: revenue from the sale of waste paper and avoided tipping fees (the fee that the town pays the owners of landfills to bury its waste). Aside from the capital costs of specialized collection equipment, household containers, and a sorting facility, the program would involve higher collection costs, inconvenience costs for households, and disposal costs for paper that is collected but not sold. The planning period for the project has been set at eight years, the expected life of the specialized equipment. The following information has been collected by the town’s sanitation department: Waste Quantities: Residents currently generate 3.6 pounds of waste per person per day. Over the last 20 years, the daily per capita amount has grown by about 0.02 pounds per year. Small or no increases in the last few years, however, raise the possibility that levels realized in the future will fall short of the trend. Capital Costs: The program would require an initial capital investment of $1,688,000. Based on current resale values, the scrap value of the capital at the end of eight years is expected to be 20 percent of its initial cost. Annual Costs: The department estimates that the separate collection of paper will add an average of $6/ton to the cost of collecting household waste. Each ton of paper collected and not sold would cost $4 to return to the landfill. Savings and Revenues: Under a long-term contract, tipping fees are currently $45 per ton with annual increases equal to the rate of inflation. The current local market price for recycled paper is $22/ton but has fluctuated in recent years between a low of $12 per ton and a high of $32 per ton. Paper Recovery: The fraction of household waste made up of paper has remained fairly steady in recent years at 32 percent. Based on the experience of similar programs in other towns, it is estimated that between 60 and 80 percent of paper included in the program will be separated from other waste and 80 percent of the paper that is separated will be suitable for sale, with the remaining 20 percent of the collected paper returned to the waste stream for landfilling. Household Separation Costs: The sanitation department recognized the possibility that the necessity of separating paper from the waste stream and storing it might impose costs on households. An average of 10 minutes per week per household of additional disposal time would probably be needed. A recent survey by the local newspaper, however, found that 80 percent of respondents considered the inconvenience of the program negligible. Therefore, the department decided to assume that household separation costs would be zero. Discount Rate: The sanitation department has been instructed by the budget office to discount at the town’s real borrowing rate of 6 percent. It has also been instructed to assume that annual net benefits accrue at the end of each of the eight years of the program. a. Calculate an estimate of the present value of net benefits for the program. b. How large would annual household separation costs have to be per household to make the present value of net benefits fall to zero? c. Assuming that household separation costs are zero, conduct a worst-case analysis with respect to the growth in the quantity of waste, the price of scrap paper, and the percentage of paper diverted from the waste stream. d. Under the worst-case assumptions of part (c), how large would the average yearly household separation costs have to be to make the present value of net benefits fall to zero? e. Investigate the sensitivity of the present value of net benefits to the price of scrap paper. f. Implement a Monte Carlo analysis of the present value of net benefits of the program. 5.a. A spreadsheet can be used to do the following calculations: The present value of the capital costs and their scrap value equal: Turning to the amount of waste generated in the first year, the total tonnage is W0 = (3.6 lbs/p/d)(164,250 persons)(365 days)/(2000) = 107,912 tons. Total waste tonnages for successive years are obtained by adding the amount of increase WA = (.02 lbs/p/y)(164,000 persons)(365 days)/(2000) = 600 tons to the previous year's tonnage. The total waste in year i is thus Wi = W0 + (WA)(i). The total weight of paper diverted from the waste stream in each year is DPi = (.32)(.7)(Wi), where the .32 is the fraction of waste that is paper and .7 is the fraction of paper waste that is separated. With a tipping fee of $45/ton, a paper price of $22/ton, an additional $6/ton in collection costs, and a $4/ton cost of returning paper to the landfill, the net benefits in terms of year i operating costs are: Bi = ($45 + $22)(DPi)(.8)-($4)(DPi)(.2)-($6)(Wi). Thus, the "best" estimate of the present value of net benefits (PVNB) for the program is: 5.b. The expression for Bi would include an additional term if we allow for non-zero household separation costs. The term would be (HSC)(39,050), where HSC is annual household separation costs per household and 39,050 is the number of households. If the calculations are done using a spread sheet, then we can simply guess at values for HSC until we find the value that causes PVNB to fall to zero. Through such trial and error, we find that if annual household separation costs are $10.31 per household, then PVNB equals zero. Which is a more reasonable assumption, HSC = 0 or HSC = $10.31? An average household will spend about 10 minutes per week or 8.7 hours per year on separation. If we assume that the local wage rate is $12/hour, people value their leisure time at 40 percent of the wage rate, and only 20 percent of households view waste separation as a loss of leisure (a possible interpretation of the newspaper survey!), then we have a very rough estimate of HSC = ($12)(8.7)(.4)(.2) = $8.35. Thus, this reasonable upper bound would not change the sign of PVNB. Indeed, people may actually have a positive "non use" value (see Chapter 13) for recycling, which would more than offset the household separation costs. 5.c. As reasonable "worse case" we assume that WA equals zero, the price of paper is $12/ton, and only 60 percent of paper is diverted from the waste stream. The result is a PVNB = $267,000, which is still positive, but much smaller than the estimate obtained with the original assumptions. 5.d. With the above assumptions, we discover through trial and error that PVNB = $0 when HSC = $1.23. 5.e. Setting all the parameters the values used in part (a), we find the following relationship between PVNB and the price of paper: Such calculations are trivial once the formulas are set up on a spreadsheet. 5.f. The first step in doing a Monte Carlo analysis is to identify the parameters that one wants to treat as random variables. These parameters would include the annual increase in total waste, the price of waste paper, and the percentage of paper diverted from the waste stream (the diversion rate). Other parameters could also be treated as random variables, but it is best to focus on those parameters that are least certain. The second step is to define the random variables in terms of the random number generator available in the spreadsheet. For example, if the spreadsheet generates a uniform random variable, R, over the range zero to one, then we could obtain a random diversion rate distributed uniformly over the range .6 to .8 by the formula (.6) + (.2)(R). The third step is to replicate the basic formulas needed to calculate PVNB from the parameter values. This can usually be most easily done by arranging the parameters, fixed and random, and formulas in a single column. The fixed parameters and the formulas can then be copied a number of times, usually between 10 and 100, depending on capabilities of the computer software and hardware. To avoid replicating the same draws, the random parameters must then be entered in column by column. The result is a number estimates of PVNB that are based on independent draws of the random parameters. Finally, replicate the third step until a sufficiently large number of PVNB values have been calculated so that the shape of the distribution of PVNB becomes clear. For only three random parameters, several hundred draws of PVNB may be sufficient, though most spreadsheets easily facilitate a thousand or more draws. The provided spreadsheet implements these steps. For each Monte Carlo experiment, students must construct their own histograms. 6. Imagine that the net present value of a hydroelectric plant with a life of 70 years is $25.73 million and that the net present value of a thermal electric plant with a life of 35 years is $18.77 million. Rolling the thermal plant over twice to match the life of the hydroelectric plant thus has a net present value of ($18.77 million) + ($18.77 million)/(1 + 0.05)35 = $22.17 million. Now assume that at the end of the first 35 years, there will be an improved second 35-year plant. Specifically, there is a 25 percent chance that an advanced solar or nuclear alternative will be available that will increase the net benefits by a factor of three; a 60 percent chance that a major improvement in thermal technology will increase net benefits by 50 percent; and a 15 percent chance that more modest improvements in thermal technology will increase net benefits by 10 percent. a. Should the hydroelectric or thermal plant be built today? b. What is the quasi-option value of the thermal plant? 6.a. The present value of the hydro plant remains $25.73 million. The expected present value of two successive 35-year thermal plants is: PV(2 35-year plants) = ($18.77 million) + {[(.25)(3) + (.6)(1.5) + (.15)(1.1)]($18.77 million)}/(1 + .05)35 = $24.95 million Thus, even taking account of the possible improvements in technology, the 35-year thermal plant has a lower expected present value of net benefits than the 70-year hydro plant. 6.b. The quasi-option value of the 35-year plant is the difference between the present value of net benefits when the decision problem is correctly specified and the present value of net benefits assuming a simple roll-over of the project for the second 35 years: Quasi-option value = $24.95 million - $22.17 million = $2.77 million In this problem, the quasi-option value is not sufficiently large to change the decision from building the hydro plant to building the thermal plant. Of course, to get the quasi-option value, we must first correctly specify the decision problem. If we can do so, then there is no need to worry about quasi-option value. Chapter 11 Case Study Exercises Using Monte Carlo Simulation: Assessing the Net Benefits of Early Detection of Alzheimer’s Disease 1. What information would be needed to estimate the net benefits of a state-wide Alzheimer's disease screening program for 65 year olds? One would want to know the distribution of the MMSE for 65-year old men and women in the early stage of AD in the state. One could then multiple these numbers by the gender-specific MMSE estimates from the model and sum to get an estimate of the net benefits from universal screening of 65 year olds. However, as screening would almost certainly not be universal in practice, some assumptions would have to be made about the probabilities that these groups would actually be screened. As the distribution of AD among 65-year olds would be very uncertain, and almost certainly based on national rather than state-specific data, more reliable estimates could be made of the net benefits of screening at an older age, though actually screening at an older age would potentially be less beneficial. 2. Imagine that you wanted to use a life-course model similar to the Alzheimer's disease model to estimate the net benefits of helping someone quit smoking. What would be the most important similarities and differences? Important similarities: 1. Most of the benefits of smoking cessation would occur in the future, perhaps decades in the future for young quitters. 2. The primary benefits would be avoided costs. Rather than avoided nursing home and community care, the benefits would be avoided medical costs from reductions in the risks of diseases like lung cancer, stroke, and heart disease. 3. Just as the AD model takes account of mortality from other sources, important because of the advance aged of the patients, the smoking cessation model would have to take account of mortality from other sources, especially because the risks of the relevant diseases start relatively low for young smokers and grow with age. Important differences: 1. Unlike AD, which has a progression that currently cannot be reversed, smoking cessation can be. Indeed, many smokers have to quite multiple times before they are able to quit "permanently." Therefore, the model would have to include probabilities of relapse following an initially successful quit. 2. For modeling purposes, the MMSE provides a reasonable index of AD severity so that the modeling is path independent––institutionalization and mortality risks depend only on current characteristics of the patient. However, the risks to smokers depend on their prior smoking history. Therefore, a practical index of past smoking would be needed and related to disease risks. Further, to capture changes in risk, the index would have to be updated to take account of additional smoking during relapses. Chapter 12 Exercises Risk, Option Price, and Option Value 1. A large rural county is considering establishing a medical transport unit that would use helicopters to fly emergency medical cases to hospitals. Analysts have attempted to estimate the benefits from establishing the unit in two ways. First, they surveyed a random sample of residents to find out how much they would be willing to pay each year for the unit. Based on responses from the sample, the analysts estimated a total willingness to pay of $8.5 million per year. Second, the analysts estimated the dollar value of the improvements in health outcomes and avoided medical costs of users of the unit to be $6.2 million per year. Taking the analysts’ estimates at face value, specify the following: a. The aggregate of individuals’ annual option prices for the unit. b. The annual total expected gain in social surplus from use of the unit. c. The annual aggregate option value for the unit. 1.a. If we take the survey results at face value, then it would be reasonable to interpret the $8.5 million annual willingness to pay as the aggregate annual option price. If the costs of the unit were certain, then this would be the appropriate benefit measure. As discussed in Chapter 13, however, there are many reasons why we might be sceptical of the accuracy of such a willingness-to-pay estimate. 1.b. The analysts' estimate of the annual dollar value of improved outcomes and avoided costs, $6.2 million, can be interpreted as the annual gain in expected social surplus. If this estimate is based on a large number of users, then it is likely to be close the annual gain in social surplus actually realized. It would thus be a reasonable lower bound for the annual benefits of the unit. 1.c. The aggregate annual option value would be the difference between the aggregate annual option price and the annual expected gain in social surplus: $8.5 million - $6.2 million = $2.3 million. This large option value for a program that uses helicopters to fly emergency medical cases to hospitals might be expected because the program functions similarly to insurance by helping to reduce the magnitude of unlikely but severe losses. 2. Imagine that we want to value a cultural festival from the point of view of a risk-averse person. The person’s utility is given by U(I) where $I is her income. She has a 50 percent chance of being able to get vacation time to attend the festival. If she gets the vacation time, then she would be willing to pay up to $S to attend the festival. If she does not get the vacation time, then she is unwilling to pay anything for the festival. a. What is her expected surplus from the cultural festival? b. Write an expression for her expected utility if the festival does not take place. c. Write an expression incorporating her option price, OP, for the festival if the festival takes place. (To do this, equate her expected utility if the festival takes place to her expected utility if the festival does not take place. Also, assume that if the festival does take place, then she makes a payment of OP whether or not she is able to attend the festival.) d. Manipulate the expression for option price to show that the option price must be smaller than her expected surplus. (In doing this, begin by substituting 0.5S - e for OP in the equation derived in part c. Also keep in mind that since the person is risk-averse, her marginal utility declines with income.) e. Does this exercise suggest any generalizations about the benefits of recreational programs when individuals are uncertain as to whether or not they will be able to participate in them? 2.a. Expected surplus: E(S) = (.5)(S) + (.5)(0) = .5S 2.b. Expected utility without the program: E(U0) = (.5)U(I) + (.5)U(I) = U(I) 2.c. Expression for option price, OP: (.5)U(I + S-OP) + (.5)U(I-OP) = EU0 where the first term on the left-hand side of the equation is the probability of attending times the utility of attending, taking account of the certain payment; and the second term is the probability of not attending times the utility obtained if not attending, taking account of the certain payment. The right-hand side of the equation is the expected utility if there is no festival. 2.d. Rewriting: 2U(I) = U(I + S - OP) + U(I - OP) Substituting .5S - e for OP into the right-hand side of the equation gives: 2U(I) = U(I + S-.5S + e) + U(I-.5S + e) U(I) = [U(I + .5S + e) + U(I-.5S + e)]/2 Because the marginal utility of persons who are risk averse must decline with income, it is apparent that the above equation could not hold for e = 0. The gain from increasing income by .5S would be smaller than the loss from decreasing income by .5S. The equation can hold only when e is positive. Thus, option price must be smaller than the expected surplus. The option value, OP-ES = -e, which, because e is positive, is negative. 2.e. Programs, like recreational improvements, that can be interpreted as additions to, rather than replacements of, income generally have negative option values. 3. (Spreadsheet required.) Imagine that a rancher would have an income of $80,000 if his county remains free from a cattle parasite but only $50,000 if the county is exposed to the parasite. Further imagine that a county program to limit the impact of exposure to the parasite would reduce his income to $76,000 if the county remains free of the parasite but increase it to $70,000 if the county is exposed to the parasite. Assume that there is a 60 percent chance of exposure to the parasite and that the rancher’s utility is the natural logarithm of his income. What is the rancher’s option price for the county program? (Set up an appropriate equation and solve through iterative guessing.) 3. By trial and error, the option is found to be $7,245. Chapter 13 Exercises Existence Value 1. Imagine a wilderness area of 200 square miles in the Rocky Mountains. How would you expect each of the following factors to affect people’s total willingness to pay for its preservation? a. The size of the total wilderness area still remaining in the Rocky Mountains. b. The presence of rare species in this particular area. c. The level of national wealth. 1.a. Other things equal, we would expect people to place a higher value on preserving this particular area, the smaller the total stock of Rocky Mountain wilderness remaining. The reason is that we generally expect declining marginal utility as more of any good is "consumed," whether through use or non use. 1.b. Other things equal, the "rarer" the wilderness area is in terms of either its physical characteristics or the species that make it their habitat, the higher people's willingness to pay to preserve it. One way to view rareness is in terms of the stock of comparable areas. People are likely to have the largest willingness to pay for areas that are unique in some significant way, because, if it is really unique, the area constitutes the total remaining stock. 1.c. Other things equal, the wealthier people are the more they are willing to pay for all normal goods, including those that offer non-use value. This may be one reason why environmental movements appear stronger in more developed countries. 2. An analyst wishing to estimate the benefits of preserving a wetland has combined information obtained from two methods. First, she surveyed those who visited the wetland - fishers, duck hunters, and bird watchers - to determine their willingness to pay for these uses. Second, she surveyed a sample of residents throughout the state about their willingness to pay to preserve the wetland. This second survey focused exclusively on non-use values of the wetland. She then added her estimate of use benefits to her estimate of non-use benefits to get an estimate of the total economic value of preservation of the wetland. Is this a reasonable approach? (Note: In responding to this question assume that there was virtually no overlap in the persons contacted in the two surveys.) 2. There is a danger that summing the estimates will result in an overestimate of total willingness to pay. The reason is that some of the respondents from the state-wide survey may also be users and potential users. These respondents would probably give a smaller willingness to pay for non-use if they were first asked to give their willingness to pay for use. It would be conceptually correct simply to ask respondents in the state-wide survey their willingness-to-pay amounts for use and non-use together. This approach is problematic, however, if only a small fraction of state residents are users -- the sample may provide too few users to make reliable estimates of use values. On the other hand, estimating non-use values based only on the responses of users would not be a good alternative because the users probably differ in important ways from the general population -- users are probably more familiar with the wetland and they also probably live closer. Chapter 14 Exercises Valuing Impacts from Observed Behavior: Experiments and Quasi Experiments 1. Using the scheme shown in Table 14.1, diagram the evaluation design used in each of the following demonstration programs. a. To evaluate a government training program that provides low-income, low-skilled, disadvantaged persons job-specific training, members of the target population are randomly assigned to either a treatment group that is eligible to receive services under the program or to a comparison group that is not. Data are collected on the earnings, welfare receipts, and so forth of both groups during the training period and for two years thereafter. b. To evaluate a government training program that provides low-income, low-skilled, disadvantaged persons job-specific training, members of the target population who live in the counties in the eastern half of a large industrial state are assigned to a treatment group that is eligible to receive services under the program, while members of the target population who live in the counties in the western half of the state are assigned to a comparison group that is not. Information is collected on the earnings, welfare receipts, and so forth of both groups for one year prior to the beginning of training, during the training period, and for two years thereafter. c. To evaluate a government training program that provides low-income, low-skilled, disadvantaged persons job-specific training, information is collected on the earnings, welfare receipts, and so forth of those persons who receive training. This information is collected for the year prior to the beginning of training, during the training period, and for two years thereafter. 2. Consider a government training program that provides low-skilled men job-specific training. To evaluate this program, members of the target population were randomly assigned to either a treatment group that was eligible to receive services under the program or to a comparison group that was not. Using this evaluation design, the following information was obtained: • Members of the treatment group were found to remain in the program an average of one year, during which time they received no earnings, but were paid a tax-free stipend of $4,000 by the program to help them cover their living expenses. During the program year, the average annual earnings of members of the control group were $10,000, on which they paid taxes of $1,000. During the program year, the welfare and unemployment compensation benefits received by the two groups were virtually identical. • Program operating costs (not counting the stipend) and the cost of services provided by the program were $3,000 per trainee. • During the two years after leaving the program, the average annual earnings of members of the treatment group were $20,000, on which they paid taxes of $2,000. During the same period, the average annual earnings of members of the control group were $15,000, on which they paid taxes of $1,500. • During the two years after leaving the program, the average annual welfare payments and unemployment compensation benefits received by members of the treatment group were $250. During the same period, the average annual welfare payments and unemployment compensation benefits received by members of the control group were $1,250. a. Using a 5 percent discount rate, a zero decay rate, and a five-year time horizon, compute the present value of the net gain (or loss) from the program from the trainee, nonparticipant, and social perspectives. In doing this, ignore program impacts on leisure and assume that all benefits and costs accrue at the end of the year in which they occur. b. Once again ignoring program impacts on leisure, re-compute the present value of the net gain (or loss) from the program from the trainee, nonparticipant, and social perspectives, assuming that at the end of the two-year follow-up period program impacts on earnings and transfer payments begin to decay at the rate of 20 percent each year. 2.a. Trainee perspective: Since members of the control group received $9,000 in after tax earnings during the program year, on average, it is reasonable to presume that this was the amount of earnings forgone by an average trainee while undergoing training. However, this cost to trainees was partially offset by the $4,000 stipend they received. Thus, trainees incurred a net cost of $5,000 during the program year. During each of the next two years, trainees received after tax earnings of $18,000, while members of the control group received after tax earnings of only $13,500. Thus, the program's impact on the after-tax earnings of trainees during each of the two post-training follow-up years was $4,500. However, during each of these years, members of the control group received $1,000 more in transfer benefits than members of the treatment group. Hence, the program's net impact on the average income of trainees was $3,500 during each of the two follow-up years. Using this information, the present value of the net benefits received by the trainees (PVNBT) can be computed for the five-year time horizon as follows: PVNBT = -$5,000/(1 + .05) + $3,500/(1 + .05)2 + $3,500/(1 + .05)3 + $3,500/(1 + .05)4 + $3,500/(1 + .05)5 = $7,058 Non-Participant Perspective: During the program year, non-participant taxpayers incurred program operating and service costs of $3,000 and stipend costs of $4,000. Moreover, since members of the control group paid an average of $1,000 in taxes during the program year, while trainees paid no taxes, we can infer that $1,000 in tax payments were forgone by non-participants. Thus, during the program year, non-participants incurred total costs of $8,000 ($3,000 + $4,000 + $1,000) for a typical trainee. During each of the two post-training follow-up years, however, trainees paid $500 more in taxes, on average, than members of the control group and received $1,000 less in transfer benefits. Hence, non-participants received net benefits totaling $1,500 during each of the two follow-up years. Using this information, the present value of the net benefits received by non-participants (PVNBNP) can be computed for the five-year time horizon as follows: PVNBNP = -$8,000/(1 + .05) + $1,500/(1 + .05)2 + $1,500/(1 + .05)3 + $1,500/(1 + .05)4 + $1,500/(1 + .05)5 = -$2,552 Social Perspective: During the program year, the per trainee cost of the program to society was $13,000, the sum of the resources used to operate the program and provide services to those participating in it ($3,000) and the gross earnings that were forgone as a result of trainees participating in the program ($10,000). Note that the stipend received by the trainees was a transfer from taxpayers to trainees and, hence, is not counted as a cost to society. The per trainee benefits received by society during each of the two post-training follow-up years were $5,000, the program's impact on the average gross earnings of the trainees. Notice that the program's impact on transfer benefits is treated as a transfer from trainees to taxpayers, rather than as a benefit or cost to society. The present value of the net benefits received by society (PVNBS) can be computed for the five-year time horizon as follows: PVNBS = -$13,000/(1 + .05) + $5,000/(1 + .05)2 + $5,000/(1 + .05)3 + $5,000/(1 + .05)4 + $5,000/(1 + .05)5 = $4,506 Alternatively, PVNBS can be computed by simply summing PVNBT and PVNBNP -- that is, $7,058 + (-$2,552) = $4,506. 2.b. Because benefits and costs are directly observed during the program year and during the two post-training follow-up years, it is only necessary to take account in the decay of the program's impact on earnings and transfer benefits during the last two years of the five-year time horizon. Since the decay rate is assumed to be 20 percent, but the decay process is assumed not to begin until year 4, the undiscounted benefits received by the trainees in year 4 equal $3,500/(1 + .2) = $2,917 and the undiscounted benefits received by the trainees in year 5 equal $2,917/(1 + .2) = $2,431. Similarly, the undiscounted benefits from the non-participant perspective for years 4 and 5 equal $1,500/(1 + .2) = $1,250 and $1,250/(1 + .2) = $1,042, respectively. And the undiscounted benefits from the social perspective for years 4 and 5 equal $5,000/(1 + .2) = $4,167 and $4,167/(1 + .2) = $3,473, respectively. After making these calculations, the formulas used in 2.a. are altered as follows: PVNBT = -$5,000/(1 + .05) + $3,500/(1 + .05)2 + $3,500/(1 + .05)3 + $2,917/(1 + .05)4 + $2,431/(1 + .05)5 = $5,740 PVNBNP = -$8,000/(1 + .05) + $1,500/(1 + .05)2 + $1,500/(1 + .05)3 + $1,250/(1 + .05)4 + $1,042/(1 + .05)5 = -$3,118 PVNBS = -$13,000/(1 + .05) + $5,000/(1 + .05)2 + $5,000/(1 + .05) + $4,167/(1 + .05)4 + $3,473/(1 + .05)5 = $2,622 As can be seen, the estimated present values of net benefits are not very sensitive to assuming that benefits decay over time, even though a rather large decay rate is used. The major reason for this is the very short time horizon used in the analysis; benefits were allowed to decay for only two years. 3. Perhaps the most careful effort to measure the effects of compensatory preschool education was the Perry Preschool Project begun in Ypsilanti, Michigan in 1962. Children, mostly three years old, were randomly assigned to treatment (58 children) and control (65 children) groups between 1962 and 1965. Children in the treatment group received two academic years of schooling before they entered the regular school system at about age five, while children in the control group did not. The project collected information on the children through age 19, an exceptionally long follow-up period. Using information generated by the study, analysts estimated that two years of preschool generated social net benefits (1988 dollars) of $13,124 at a discount rate of 5 percent. [For a more complete account, see W. Steven Barnett, “Benefits of Compensatory Preschool Education,” Journal of Human Resources 27(2), 1992, 279-312.] a. Before seeing results from the project, what would be your main methodological concern about such a long follow-up period? What data would you look at to see if the problem exists? b. Benefit categories beyond the age of 19 included crime reduction, earnings increase, and reductions in welfare receipts. If you were designing the study, what data would you collect to help measure these benefits? 3.a. In a study with such a long follow-up period, one might be concerned about the possibility of "attrition," the loss of members of the treatment and control groups, if for no other reason than the difficulty of keeping track of people. If the attrition was greater in one group than the other, then one might be especially concerned about there being some unmeasured difference between the groups. Even if the attrition was roughly equal between the groups, one might be concerned that samples sizes would fall to such low levels that statistical tests would not be able to detect real differences between the treatment and control groups. To see if attrition is a problem, one would look at the number of members of each group remaining at the end of the follow-up period. (Amazingly, the Perry Project did not lose any subjects from the treatment group and only two from the control group.) 3.b. Income, crime, and welfare data could be measured as the difference in the averages for the treatment and control group. Estimates of crime could be either self-reported or collected from police records. The former raises the issue of the truthfulness of responses on a sensitive topic, while the latter raises confidentiality issues and the likelihood of missing offenses for which there was no arrest (In the Perry Project, the data from the two sources were consistent.) A shadow price for crime is also needed to convert the difference in offenses to a dollar value. Chapter 17 provides values that can be used for this purpose. Estimates of earnings can be based on self-reporting. Interestingly, most of the benefits in the Perry Project were due to increases in hours worked, rather than from higher wages. Estimates of impacts on welfare could be measured either using self-reported amounts or welfare department records. (In the Perry Project, self-reports were used because the welfare department would not provide data.) It is important to note that not all of the welfare savings to taxpayers are a benefit – most of the reduction is a cost to participants in reduced benefits and, hence, is best viewed as a transfer. 4. Five years ago a community college district established programs in ten new vocational fields. The district now wants to phase out those programs that are not performing successfully and retain those programs that are performing successfully. To determine which programs to drop and which to retain, the district decides to perform CBAs. a. What perspective or perspectives should be used in the studies? Are there any issues concerning standing? b. Using a stylized cost-benefit framework table, list the major benefits and costs that are relevant to the district’s decision and indicate how each affects different pertinent groups, as well as society as a whole. Try to make your list as comprehensive and complete as possible, while avoiding double counting. c. What sort of evaluation design should the district use in conducting its CBAs? What are the advantages and disadvantages of this design? Is it practical? d. Returning to the list of benefits and costs that you developed in 4.b., indicate which of the benefits and costs on your list can be quantified in monetary terms. How would you treat those benefits and costs that cannot be monetized? e. What sort of data would be required to measure those benefits and costs that can be monetized? How might the required data be obtained? 4.a. Possible perspectives of interest are those of the students and taxpayers and, of course, society as a whole. One possible issue concerning standing is whether former students who now reside outside the community college district should be given standing in the CBAs. In addition, since the district may receive financial support from the state or federal government, one can also ask whether taxpayers who reside outside the district should receive standing. 4.b. A number of alternative cost-benefit frameworks could be developed. Therefore, the framework that appears below should be considered as only suggestive. STYLIZED COST-BENEFIT FRAMEWORK FOR A VOCATIONAL TRAINING PROGRAM
SOCIAL STUDENTS TAXPAYERS
Benefits After tax earnings Fringe benefits Tax payments Psychic benefits + + + + + + 0 + 0 0 + 0
Costs Tuition and fees School support from gifts and taxes Foregone after tax earnings Foregone fringe benefits Foregone net taxes Psychic costs Foregone transfer payments - - - - - - 0 - 0 - - 0 - - 0 - 0 0 - 0 +
4.c. An experimental design probably would not be feasible. Students could not be prevented from selecting the vocational program that they desire. Consequently, a nonexperimental design would have to be used. The major problem with this would be finding an appropriate control group. Probably the best available control group would be high school graduates who did not go on to either two year or four year colleges. However, these persons may differ from the community college students in terms of such characteristics as ability, motivation, and drive. 4.d. Obtaining data on earnings would probably require that both current and previous graduates of each program, as well as members of the control group, be contacted and interviewed, an expensive undertaking. Information about tuition, fees, gifts, and school tax support could probably be obtained from school administrative records. This part of the study would probably be relatively easy. 4.e. Psychic benefits and costs probably cannot be monetized. It may also be difficult to obtain good interview data on fringe benefits. Therefore, qualitative CBAs might be considered. Chapter 14 Case Study Exercises Findings from CBAs of Welfare-to-Work Programs 1. If you were running a state welfare agency and had to choose one of the programs listed in the table, which table’s columns would you particularly focus upon? Why? 1. Most economists would probably focus on column H, the net social gain or loss, because that column provides the best measure of the overall efficiency of the programs listed in the table. However, as a person responsible for operating a state welfare agency, you might want to focus instead on column D, the net present value from the nonparticipant perspective, because it provides the best estimate of the costs and benefits that accrued to the states operating the programs. Note however that part of the tax and transfer amounts listed in column F, which are included in computing column D, accrue to the Federal government and another part accrue to other agencies within the state. The costs that most directly affect the budget of the welfare agency, operating costs, appear in column G. 2. If you were running a state welfare agency and had to choose one of the programs listed in the table, what information would you like in addition to that provided in the table? 2. Chapter 14 discusses potential benefits and costs that are not incorporated into most CBAs of E&T programs including those listed in the table (e.g., effects on crime, health, and intangible benefits received by nonparticipants). You may want to learn something about how these possible benefits and costs differ among the listed programs. You may also want to know how the target populations of the listed programs and the local economic environmental differ from the welfare population and environment in your own state. You probably would also like to learn more about the services provided by the programs and how easy or difficult they are to implement. Finally, and rather subtlety, the control groups in some of the listed programs may have received services similar to those received by the treatment groups while controls in other programs may not have been receiving many services at all. Everything else the same, the latter programs will have larger costs and benefits than the former. Therefore, it would be useful to learn about the circumstances facing the control populations used in evaluating the listed programs. Much of the above can be learned by reading the evaluation reports for the listed programs. Solution Manual for Cost-Benefit Analysis: Concepts and Practice Anthony E. Boardman, David H. Greenberg, Aidan R. Vining, David L. Weimer 9781108415996,9781108401296
