Welcome to Cost Benefit Analysis

Foundations of CBALecture 2: April 2, 2015 (RHP)Foundation 1: The Policy What policy(s) will you consider? To what will you compare the policy? What is the status quo? Is it an option? -> if yes, include the SQ! What are the relevant options? Define the policy change sufficiently narrowly to allow analysis When will the policy change occur? Over what time period are you interested in resulting costs and benefits?-> CBA can be conducted ex ante, ex post, or in media res; best practices vary between the three timing optionsFoundation 2: The UniverseGenerally, give everyone in society standing their costs and benefits will be included in the analysis. Define society geographically:

Global everyoneNational everyone in a countryRegionally everyone in a state, metro area, county, city, etc.Institutional everyone affiliated with an organizationFoundation 3: Estimate Costs & BenefitsFor each person / group with standing, determine:CostsCalculate as opportunity costs (value of the inputs if put to the next best use)Market prices ok if markets are perfectly competitive

BenefitsHow should we monetize benefits? -> What would someone be willing to pay to ensure a policy change occurred?Under most circumstances, changes in consumer surplus can appropriately be used as reasonable approximations of societys willingness to pay for policy changes (Boardman p. 51)-> BUT consumer surplus is not willingness to pay! (more on this later)

Foundation 4: Choose Policy(s)BUT this is too simple! 5Micro Review: CBAWhy CBA? -> Applied systematically, choosing policies based on CBA should result in increased economic efficiency policies are selected based on net social benefits

Review: Pareto efficiency & welfare theorems Kaldor-Hicks & net benefits criterion Distributional considerationsHow should we make social decisions?Government policy is inherently a social question: we choose a single policy, which individuals will value according to individual preferences.

How do we translate individual preferences into policy?Unanimous voting if everyone in society prefers one policy, then so should societyVoting majority rule (ignores intensity of preferences)Social welfare functions measure individual utility functions, combine with a social welfare function to maximize welfareKaldor-Hicks efficiency choose Pareto improvements (implement transfers)Compensation principle choose potential Pareto improvements (most CBA)Arrows Impossibility Theorem: No reasonable mechanism exists for translating individual ordinal rankings into a sensible social rankingTANGENT!

Unanimous voting is true but unhelpful and prefernces status quoVoting ignores intensity of preferencesSocial choice impractical we cant measure those things and still requires selecting a particular social welfare function

Kaldor-Hicks solves the problem by using cardinal rankings! BUT at the cost of quasilinear utility assumption. Explicitly separates the efficiency question from the equity question.7Review: Welfare EconomicsPareto Efficiency - resources are Pareto efficiently allocated if there are no other ways to reallocate resources to make any person better of without making anyone worse off than before

Pareto Improving - an allocation is Pareto improving if it makes any person better off while making no one worse offFirst Welfare TheoremWhen markets are in equilibrium under perfect competition, the resulting resource allocation is Pareto efficient.

Alternately, at competitive equilibrium, total surplus (PS+CS) is maximized

Failure of First Welfare TheoremWhen are the assumptions of the theorem violated? Imperfect competition Public goods Externalities Incomplete markets Information failures

-> Government may be able to improve efficiencySimple Model: Edgeworth BoxSuppose a 2-person (Bart & Lisa), 2-good endowment economy Trade allowed at mutually-agreed upon prices Consume good 1 / good 2 bundles after tradeSimple Model: Edgeworth BoxAny point on the contract curve is Paretoefficient even ones where eitherparty gets nothing! (Pareto-frontier infigure 2.1 of text)

Suppose point E is the endowment-> Any point on the contract curve between X & Y is Pareto improving

Reality Check: Edgeworth BoxSuppose you are unable to reachCE due to some market failure.

Should we adopt a policy thatmoves us to W?-> Pareto-efficient-> NOT Pareto-improving (Bart is worse off)-> potentially Pareto-improving IFF Lisa compensates Bart

Kaldor-Hicks criterionA policy should be undertaken of if the winners can IN PRINCIPLE compensate the losers -> CBA decides in favor of any policy that is POTENTIALLY PARETO IMPROVING

Put differently: If Net Benefits > 0, it should be possible to construct transfers that would be Pareto-improving.

THUS, CBA recommends adopting policies that are potentially rather than actually Pareto-improving NOTE: Economists arent blind to the distributional problems of this approach. More on this later.Possible Decision RulesNet Benefits Rule: Net Benefits > 0

Benefit/Cost Ratio Rule: Benefit-Cost Ratio > 1

Internal Rate of Return Rule:IRR > Social Discount RateTo pre-sage the NB rule is best! (BCR is occasionally helpful)15Example: Mutually Exclusive ProjectsYou can build one dam on a river should it be big or small (or not built)?

You can build one overflow reservoir for storm water should it be expanded to a large one from the current small one?

You can choose one of two curricula for early reading instruction in Head Start programs in Chicago.

Maximize Net BenefitsBCR can be misleading!16Example: Mutually Exclusive PoliciesSuppose you could choose policies that resulted in Q=20,Q=30, or Q=50.

Using the BCR, you getit WRONG!

Calculation of BCR: Benefits are area under the SMB curve, Costs are area under SMC curveSo, at Q=50, Benefits = 50*50 + (50)(50)=3750 & Costs= (50)(50)=1250 -> BCR=3At Q=20, Benefits= 80*20+1/2 (20)(20) = 1800 & Costs=1/2 (20)(20)=200 -> BCR=90017What if Projects Arent Mutually Exclusive?Adopt all projects with positive net benefits!Reality Check: Resource ConstraintsIn practice, options are often constrained by financial considerations.-> For mutually exclusive projects, choose project with highest NB within the constraint-> For other projects, start with the project with the highest BCR, and keep adopting additional projects until all money is spent.

The goal is always to maximize net benefits, within constraints!

Example: Which project(s) should you adopt if:Mutually Exclusive?M.E. with $400 budget cap?Not M.E., no resource limits?Not M.E. with $400 cap?ProjectBenefitsCostsNet BenefitsBCRA$150$100$501.50B$150$200-$500.75C$400$300$1001.33D$90$100-$100.90E$650$500$1501.30Example: Which project(s) should you adopt if:Mutually Exclusive? EM.E. with $400 budget cap? CNot M.E., no resource limits? A, C, ENot M.E. with $400 cap? ???ProjectBenefitsCostsNet BenefitsBCRA$150$100$501.50B$150$200-$500.75C$400$300$1001.33D$90$100-$100.90E$650$500$1501.30Notice BCR & NB rules are interchangeable under not ME, no resource constraints!21What about scale?In the previous example, it depends whether projects can be divided / partially implemented and still achieve the same (scaled) NB-> Sometimes OK, sometimes not

If project E is divisible (you can adopt part but not all of it), do 4/5th of the project, since it has the highest BCR. If not.

What about scale?In the previous example, it depends whether projects can be divided / partially implemented and still achieve the same (scaled) NB-> Sometimes OK, sometimes not

If projects can be EXPANDED (scaled up) and still achieve the same BCR (scaled NB), then we might want to pick the single project with the largest BCR and expand it, spending up to the resource constraint. From the example, do project A repeatedly.

Note: the assumption that the BCR doesnt change with scale is nontrival!Reality Check: Resource ConstraintsIn practice, options are often constrained by financial considerations.-> For mutually exclusive projects, choose project with highest NB within the constraint-> If projects can be scaled up, pick the highest BCR and expand; If projects are divisible, do a fraction of the last best project-> For other projects, start with the project with the highest BCR, and keep adopting additional projects until all money is spent.The goal is always to maximize net benefits, within constraints!

Example: Ranked by NB: E,C,A -> Do 4/5th of project E. NB = $120Ranked by BCR: A,C,E -> Do A, C. NB = $150BCR rule seems attractive. ProjectBenefitsCostsNet BenefitsBCRA$150$100$501.50B$150$200-$500.75C$400$300$1001.33D$90$100-$100.90E$650$500$1501.30Not mutually exclusive, $400 resource constraint, projects divisible but not scaleable up.BCR: Issues of ReliabilityWhile BCR is sometimes helpful, it can be unreliable depending on how we think about costs and benefits:

Suppose project A is a criminal justice policy expanding the use of jury trials, with the following on the benefits side:$500 gain for defendants from speedy trials$350 loss for jurors in time and wages

Should the $350 be a NEGATIVE BENEFIT or a COST?$150 in benefitsBCR: Issues of ReliabilityNB rule is unaffected -> NB = $120 BCR: C, 20% of E -> NB = $130

ProjectBenefitsCostsNet BenefitsBCRA (old)$150$100$501.50A (new)$500$450$501.11B$150$200-$500.75C$400$300$1001.33D$90$100-$100.90E$650$500$1501.3027BCR: Issues Note the BCR rule still did better in terms of maximizing total net benefits, but issues of negative benefits or positive costs should be examined closely before applying the rule Unlike the case of a firm costs = $ out, benefits = $ in CBA often deals with flows between members of society with standing, making it hard to categorize things clearly as costs or benefits BCR can be complicated by the inherent lumpiness of projects and policies, where questions of scaleability (up or down) constrain choices

Internal Rate of ReturnExample: Using IRRSuppose the social discount rate is 10%.

The IRR rule suggests we should do this project.YearProject A0-1000147524753475IRR20%Example: Using IRRSuppose the social discount rate is 10%Projects are mutually exclusive. YearProject AProject B0-1000-500147525624752563475256IRR20%25%Example: Using IRRIRR gets it WRONG! NPV(A) > NPV(B)It preferences the smaller project with less initial outlayYearProject AProject BDiscountPV (A)PV (B)0-1000-5001-1000-50014752560.9091431.82232.7324752560.8264392.56211.5734752560.7513356.87192.34IRR20%25%NPV$181.25136.63Possible Decision RulesNet Benefits Rule: Net Benefits > 0

Benefit/Cost Ratio Rule: Benefit-Cost Ratio > 1

Internal Rate of Return Rule:IRR > Social Discount Rate33CBA Decision RulesNet Benefits Rule: Net Benefits > 0CBA prefers the Kaldor-Hicks rule, maximizing net benefits

Rules based on BCR or IRR can be misleading.Do not use if projects are mutually exclusiveBCR may be helpful, but use with caution when projects are lumpy or if the categorization of items as costs vs. benefits is somewhat arbitrary34Distributional ConcernsCBA recommends adopting policies that are potentially rather than actually Pareto-improvingImbedded assumptions in CBADistributional IssuesIf a policy results in transfers between groups (where some win and others lose), the CBA should often include an analysis of the distributional impacts of the policy.

E.g. Consider impacts on low vs. high income groups. Why? Diminishing marginal utility of money Increased equality may improve social welfare Democratic values (one person, one vote -> each individuals preferences should have equal weight)

Altruism, existence value of equality, etc.Distributional WeightsTo integrate distributional considerations into a CBA, you can use distributional weights simple numerical multipliers to adjust the relative value of the costs and benefits for separate groups.

ProjectNB Group 1NB Group 2Aggregate NBI105060II203050Weight11ProjectNB Group 1NB Group 2Aggregate NBI3(10)=305080II3(20)=603090Weight31Distributional WeightsWhen policies may have substantially different impacts on various groups, particularly when one group is relatively disadvantaged, it may be utility-improving to adopt policies that fail the NB rule or to rank policies using distributional weights.Which policies?-> efficient but unfair/inequitable-> inefficient but fair / equitable-> calculate the total NPV and the NPV for relevant subgroup consider subgroups separately & consider weighting if efficiency and equity move in opposite directions

Distributional WeightsWhen policies may have substantially different impacts on various groups, particularly when one group is relatively disadvantaged, it may be utility-improving to adopt policies that fail the NB rule or to rank policies using distributional weights.What weights should you use?-> good question, no easy answer-> always display both weighted and unweighted values-> compute internal weights (break-even weights) how big would the weights need to be to change the policy recommendation?Example: MDRC Welfare-to-Work The WV CWEP program is efficient but unfair Would need to weight participants 8.74 times as heavily as nonparticipants to reach break-even NPV.

Distributional ConcernsIn practice, CBAs should:Identify to whom the various costs and benefits of the policy accrueThis includes transfers which are neutral with regards to the calculation of net benefits but create winners and losersFor policies where distribution is a significant consideration, include both unweighted and weighted calculations, and calculate break-even weights to illustrate the relative weighting which would change the policy recommendation