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Cost-Benefit Analysis (440.632, Summer 2022)
Assignment #2
This assignment is worth 55 points and is due by 11:59 pm on Sunday, August 14, 2022.
You may discuss the assignment and how it can be solved 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.
In 1996, a survey was mailed to 2,500 randomly selected Maine residents soliciting their preferences for
timber-harvesting practices. Respondents were given an information booklet regarding current forest
practices and the possible changes to these practices. This information booklet has been posted on the
class site (maine_forest_management_info.pdf). Respondents were then given a survey, asked to
consider seven timber harvesting attributes described in the information booklet, and asked to choose
among four possible forest management plans. The survey has also been posted on the class site
(maine_forest_management_survey.pdf).
Within the survey, a scenario described a proposal for the State of Maine to purchase 23,000 acres of
forest land. The forest practices described represent those that could be used to manage this parcel.
Respondents were then presented with four management plans, each of which included a randomly
assigned set of forest management attributes. Each of the four forest management plans also included a
one-time increase in state income taxes to pay for the purchase of land and associated management.
The survey was identical for all respondents except for the conjoint questions.
Choose one – Some respondents were asked to circle the letter of the one management plan out of four
that they would choose. The management plan chosen was coded as “1” in the results and all other
plans were coded as “0.”
Rating – Some respondents were asked, “How would you rate the desirability of each of the proposed
forest management plan for this piece of forest land?” Respondents were then given a rating scale that
ranged from 0 (very undesirable) to 6 (very desirable) for each plan. Each plan was coded with the rating
provided by the respondent. Plans that were not rated or for which there were data problems were
coded with a “9” or a “7”.
Ranking – Some respondents were asked, “How would you rank the desirability to you of each of the
proposed forest management plans for this piece of forest land, with one (1) being the most desirable
and being least desirable?” (Note, this is the version of the survey posted on the class site. We don’t
have an example of the other versions.) Each plan was coded with the rank given by the respondent,
with ties being given the same number for the lowest (most preferable) rank. Plans that were not
ranked or for which there were data problems were coded with a “9”.
The data from this survey (preference_methods_data.xls) can be found on the class assignment site.
Using the rating data, you will calculate the implied compensating variation (i.e., the willingness to pay).
Assignment #2
Cost Benefit Analysis, Summer 2022
1
1. (5 points) Data summary
a. Obtain the survey data, “preference_methods_data.xls,” from the class site. Load the data
from the “Survey Data” tab into Stata or the econometric package you are using.
b. (5 points) Report the summary statistics (number of observations, mean, standard
deviation, minimum, and maximum) for all variables. (In Stata, use the summarize
command)
2. (40 points) Estimate the willingness to pay for moving from current harvest practices to more benign
harvest practices using the “ratings” data.
a. (3 points) Look at the “Data Description” tab in the survey data spreadsheet and determine
how missing and bad data were coded. Remove all observations in your dataset in which the
RATE variable is coded as missing or bad data. Also, remove any observations where the
RATE variable is missing (that is, remove the observations where the RATE variable is not
coded as missing or bad, it just doesn’t exist.). After removing this missing or bad data,
summarize your data and report the summary statistics here.
b. (5 points) Run an ordered probit analysis (In Stata, use the oprobit command) on the ratings
data. Use RATE as the independent variable and the forest management practices (ROADS,
DEAD10, DEAD5, LIVE153, LIVE459, HOPEN125, HOPEN35, H2OZONE, PERH80, PERH50,
REMSLASH, DSTSLASH) and the tax variable, TAX, as your dependent variables. Report the
results of that ordered probit analysis here.
c. (5 points) The ordered probit model estimates the relationships between an ordinal
dependent variable and a set of independent variables, where larger values of the
dependent variable correspond to “higher” outcomes. The official description can be found
here: https://www.stata.com/manuals/roprobit.pdf.
Very briefly, in an ordered probit model, the dependent variable is a “z score,”
estimated as a linear function of the independent variables, X. That is, z = βX, where β are
the estimated parameters. A z-score is a measure of how far a data point is from the mean,
controlling for the standard deviation of the data. An alternative way of saying this is that it
is a measure of how many standard deviations below or
above the mean the data point is. Because the deviation
from the mean is normalized by the standard deviation,
the z-score can be evaluated on a normal distribution
curve, with a mean of zero and a standard deviation of
one.
Because the dependent variable is a set of ordinal
categories, the ordered probit model also estimates a
set of cut points between each category. This is
illustrated in the figure from the right (taken from the
following site https://data.princeton.edu/wws509/notes/c6s5). In simple terms, the ordinal
categories, 1…5 in this figure, are projected onto a normal distribution and the cut points
are the lines dividing the categories. A brief article explaining cut points can be found here
http://www.stata.com/support/faqs/statistics/cut-points/, and a more detailed explanation
Assignment #2
Cost Benefit Analysis, Summer 2022
2
can be found in the “Methods and formulas” section of the ordered logit description:
https://www.stata.com/manuals/rologit.pdf#rologitMethodsandformulas.
Mathematically, the probability of observing category i corresponds to the probability
that the estimated linear function, or the “z score,” is within the range of the cut points. In
our case, with 7 rating categories from 0 to 6, the probability of observing each category is
as follows:
Pr(choice = 0) = Φ(z ≤ cut1)
= Φ(β0 + β1*roads + β2*dead5 + … ≤ cut1)
= Φ(cut1 – z)
Pr(choice = 1) = Φ(cut1 < z ≤ cut 2) = Φ(cut 1 < β0 + β1*roads + β2*dead5 + … ≤ cut2) = Φ(z - cut2) – Φ(z - cut1) … Pr(choice = 6) = φ(cut6 < z) = Φ(cut 6 < β0 + β1*roads + β2*dead5 + …) = 1 – Φ(z - cut6) Φ(z) is the standard normal cumulative distribution function. For your data, report the probability of each rating assuming the dependent variables are all set at their means. (In Stata, this is done using the “margins, atmeans” command. If you do not have access to Stata, please let us know and we will provide a way to do this in a spreadsheet like Excel). Provide a brief commentary of these results. If all the dependent variables were set to their mean values, which rating category would most like to have been chosen by the respondent? Which category is second most likely? Does anything surprise you about these results or do they make sense to you? d. (5 points) The coefficients from your ordered probit will shift the probability density function to the right or left. A positive coefficient moves the density function to the right, increasing the probability of choosing the highest category and decreasing the probability of selecting the lowest category. But the impact on the probability of choosing a middle category is ambiguous as the normal distribution curve shifts to the right. This makes it hard to interpret the coefficients in an ordered probit model. To keep things simple, we will work with the highest rating category (rate=6), where the impact is unambiguous. The positive coefficient increases the probability of choosing category 6 and a negative coefficient decreases the probability. However, we need to use another command to get these marginal effects. Find the marginal effect of each dependent variable on choosing the highest rating (rate=6) using the Stat command margins, dydx(*) predict(outcome(6)) atmeans Report your results here. (Let us know if you don’t have Stata and we will find a solution). Comment on the sign and significance of the marginal effects of these variables on choosing the highest rating (rate=6). How do you interpret the coefficient for each variable? Does the sign of the coefficient make sense? Is the coefficient significant? Assignment #2 Cost Benefit Analysis, Summer 2022 3 e. Find the “Current and Benign Practice” tab in the survey data spreadsheet. This gives the setting (0 or 1) for the dummy variable for all of the dependent variables except the tax rate. Familiarize yourself with this tab. f. (5 points) Use the ordered probit model results to estimate the probability of choosing each rating assuming that all variables are set according to the current harvest practices. This is done using the Stata command margins, at(roads=0 dead5=0 … tax=0) where all of the variables are set equal to a zero or one as identified by “current harvesting practices” on the “Current and Benign Practice” tab. Report the probabilities of choosing each rating. g. (5 points) Use the ordered probit model results to calculate the probability of choosing each rating assuming that all the variables are set according to the more benign harvest practices and report those probabilities. This is done using a similar Stata command as you used in part 2.f, but all the variables are set according to the current harvest practices. Use a tax rate of zero for this part. Report the probabilities of choosing each rating for the more benign practices. h. (5 points) Using the same values for the more benign harvest practices as you used in part 2.g., increase the value for the TAX variable (remember it is not a dummy variable) until the probability of choosing each rating is the same value you obtained for the current harvest practices in part 2.f. This tax rate is the amount of taxes a consumer would be willing to pay to obtain the more benign harvest practices and be just as well off as he or she would be with current practices. Report that tax value. Note: • This will require some guessing on your part. Just keep changing the “tax=” value in your margins command until you zero in on the value. • For a number of technical reasons, you can’t get all of the probabilities for each rating exactly the same as in part 2.f. To make things easy, choose the tax rate that makes the probability of choosing the highest rating (rate=6) as close as possible. i. (7 points) Comment on this willingness to pay value. Does this seem like a reasonable value? Why do you think this? 3. (10 points) Provide a one or two paragraph commentary on your analysis. How would you explain your results to a decision-maker who may be less familiar with economic concepts and terms? What problem were you analyzing? What did you do for your analysis? What were your results? Is there anything you could do to improve this analysis if you could collect additional data? Are there any non-economic factors that should be considered in choosing harvest practices? The is no correct answer for this part. You will be graded on how you analyze this as an economist. Assignment #2 Cost Benefit Analysis, Summer 2022 4 Variable ID RATE RANK CHOICE ROADS DEAD10 DEAD5 LIVE153 LIVE459 HOPEN35 HOPEN125 H2OZONE PERH80 PERH50 REMSLASH DSTSLASH TAX Description Respondent ID Rating (0-6) for forest management practice. Missing or bad data coded as 9 or 7. Ranking (1-4) for forest management practice. Missing or bad data coded as 9. Choice one option. 1=choice, 0 = Otherwise. 1= One road every mile 1= Leave one dead or dying tree about every 66 feet (ten trees per acre) 1= Leave one dead or dying tree about every 93 feet (five trees per acre) 1= One tree 6-inches thick about every 17 feet (153 trees per acre) 1= One tree 6-inchesthick about every 5 feet (459 trees per acre) 1= Maximum size of harvest openings 5–35 acres 1= Maximum size of harvest openings 36–125 acres 1= Size of watershed protection zones at least a 500-foot zone 1= 80% of land availbe for for timber harvesting and 20% as a natural area 1= 50% of land availbe for for timber harvesting and 50% as a natural area 1= Remove all bark, branches, and stumps after harvesting 1 = Distribute bark, branches, and stumps along skid trails after harvesting Dollar value of a one time increase in state income tax to pay for the land and program. ID RATE 3 3 3 3 5 5 5 5 6 6 6 6 12 12 12 12 14 14 14 14 15 15 15 15 16 16 16 16 20 20 20 20 23 23 23 23 26 26 26 26 27 27 27 27 29 29 29 29 30 30 30 RANK CHOICE ROADS 2 1 4 3 1 1 5 5 5 0 4 1 6 2 2 2 9 9 9 9 0 0 1 0 2 0 4 6 1 2 4 3 5 6 3 2 4 1 6 1 4 4 2 1 0 0 0 1 0 0 1 DEAD10 0 1 1 1 1 1 0 1 1 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 1 1 DEAD5 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 LIVE153 0 0 1 1 0 0 0 1 0 0 1 1 1 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 LIVE459 1 0 1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 30 31 31 31 31 34 34 34 34 39 39 39 39 44 44 44 44 46 46 46 46 51 51 51 51 53 53 53 53 61 61 61 61 65 65 65 65 67 67 67 67 71 71 71 71 72 72 72 72 75 75 75 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 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0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 160 10 140 1 80 200 200 180 140 160 140 40 200 40 60 140 20 1 1600 60 1600 400 400 80 20 20 100 60 60 60 160 1 1 10 10 60 20 10 200 80 140 120 140 800 1600 60 40 100 400 20 400 120 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 1 140 160 1600 200 10 120 40 40 10 100 10 80 120 180 10 1600 800 1600 10 160 200 800 60 1 800 120 40 200 Forest Management Practice Levelsof harvesting practicesbelieved to be in most common usage are denoted in bold Road density Dead and dying trees left standing in harvest openings Live trees left standing in harvest openings Maximum size of harvest openings Percentage of land available for timber harvesting Size of watershed protection zones Slash disposal (bark, branches, and stumps left after harvesting) Levels or Options mon usage are denoted in bold One road every mile One road every half mile Remove all Leave one dead or dying tree about every 93 feet (Five trees per acre) Leave one dead or dying tree about every 66 feet (ten trees per acre) No trees greater than 6 inches left standing One tree 6-inches thick about every 17 feet (153 trees per acre) One tree 6-inchesthick about every 5 feet (459 trees per acre) Less than 5 acres 5–35 acres 36–125 acres 80% for timber harvesting and 20% as a natural area 50% for timber harvesting and 50% as a natural area 20% for timber harvesting and 80% as a natural area At least a 500-foot zone At least a 250-foot zone Leave where it falls on the ground Distribute along skid trails Remove all Variable ROADS DEAD5 DEAD10 LIVE153 LIVE459 HOPEN35 HOPEN125 H20ZONE500 PERH50 PERH80 REMSLASH DSTSLASH TAX Current Harvesting Practice 0 = 1/2 mile 0 = none 0 = none 1 = 153/acre 0 = otherwise 1 = 5–35acres 0 = otherwise 0 = 250 feet 0 = otherwise 1 = 80% 1 = remove 0 = otherwise 0 = current More Benign Harvesting Practices 1 = 1 mile 1 = 5/acre 0 = otherwise 0 = otherwise 1 = 459/acre 1 = 5–35 acres 0 = otherwise 0 = 250 feet 1 = 50% 0 = otherwise 0 = otherwise 1 = distribute Purchase answer to see full attachment

  
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