Midterm Flashcards
What is policy analysis?
Policy analysis is the application of theory and evidence to predict or evaluate the outcomes of alternative policies
- Focus of this course will be on quantitative methods for policy analysis, primarily cost-benefit analysis and related tools
- Policy analysis can use qualitative methods (e.g., interviews), but these are not covered in this course; this doesn’t mean that they aren’t valuable (there are certainly situations in which something other than CBA is the most appropriate tool), they’re simply not our focus here
What is the Informative role of policy analysis?
My questions often use the word “should”
Normative analysis, not simply positive analysis
-Does the policy make things more efficient? By how much?
-Does the policy make things more or less equitable? Who wins and loses, and by how much? How do we bring these issues together?
-“Should” is only part of the policy-making process (political feasibility, legal issues, etc.), but failing to answer the “should” question means creating policy blindly
Basic Analytical Framework
- Define the primary research question
Identify policies to be evaluated, and the measurable variables required to describe them
Specify one or more outcome variables and how they are to be measured
Note the difference between a “policy” and a “goal” - Decide who has standing
Standing: whose costs and benefits count?
E.g., should analysis of a project being considered by California government include benefits to everyone, or only benefits to California residents? - Choose a method of analysis
Cost-benefit analysis, cost-effectiveness analysis, etc.
Week 2 for CBA, weeks 5 and 7 for others - Predict the quantitative impacts of the policy
Empirical analysis guided by economic theory; may involve original empirical work or analysis of previous studies by others
Week 6 - Monetize (assign dollar values to) these impacts
Allows meaningful comparison of different impacts (common units of measurement)
Weeks 9 and 10 - Incorporate time pattern of impacts
Discount costs and benefits occurring at different points in time to make them comparable
Weeks 3 and 4 - Evaluate alternative policies using chosen criterion
E.g., compute and compare Net Present Value (NPV)
Week 2 for CBA, weeks 5 and 7 for other analyses - Address uncertainty with sensitivity analysis
Analysis often involves substantial uncertainty; how robust are the results to changes in the values used?
Weeks 11, 13
What are Challenges for effective analysis?
- Deciding whose benefits and costs count (assigning standing): What is your perspective (national, regional, etc.)?
- Selecting the portfolio of alternatives: Not just broad alternatives, but key details (when do they occur, etc.)
- Predicting quantitative impacts: The policies you analyze often haven’t occurred yet; how can you best predict what will happen?
- Valuing the impacts: What if there is no market?
- Extra complications: discounting over time, adjusting for social vs. private benefits and costs, adjusting for risk, etc.
- Performing sensitivity analysis: How many of the infinite possibilities do you present?
Different (wrong) perceptions about CBA
It’s political in nature
Promoted by Reagan, Bush, Clinton, Bush, Obama (see Cass Sunstein article, “The Stunning Triumph of Cost-Benefit Analysis”)
It ignores non-financial costs/benefits
This wouldn’t be CBA, but “revenue-expenditure analysis”
We wouldn’t need to “monetize the policy impacts” if we were only considering finances
Revenues ≠ social benefits. Expenditures ≠ social costs.
It can justify any government intervention
Only if all relevant costs and benefits are not included properly; e.g., politicians might use “constituency-support analysis”
At best, this ignores opportunity costs (“as long as somebody else pays, it’s free!”); at worst, counts them as benefits (“expenditures are good if they’re in my district!”)
Most (not all) criticisms of CBA apply to poorly done analysis, not CBA per se
Pareto Improvement
A policy creates a Pareto improvement (leads to a Pareto superior allocation) if it makes at least one person better off without making anyone worse off
Pareto Efficient
An allocation of goods is Pareto efficient if no change could make anyone better off without making someone else worse off
Another way of putting it: there are no mutually beneficial trades available (no Pareto improvements can be made)
First Fundamental Theorem of Welfare Economics
A Pareto Efficient Allocation emerges from trade if
All producers and consumers are perfect competitors (i.e., price takers, i.e., no market power), and;
A market exists for each and every commodity.
Why?
Price-taking consumers each buy a good until 𝑀𝐵=𝑃
Price-taking producers each producer a good until 𝑀𝐶=𝑃
Since consumers and producers have the same prices:
All consumers have the same marginal benefit of consumption (no efficiency gains by reallocating a given amount among consumers)
All producers have the same marginal cost of consumption (no efficiency gains by reallocating a given amount of production among producers)
Marginal benefit of consumption and marginal cost of production are equal (no efficiency gains by producing more or less of the good)
What are the Three primary justifications for public policy?
- Establishing institution framework
- Correcting market failure (the “well-functioning” caveat is not trivial)
- Promoting equity (an efficient allocation might be undesirably inequitable)
What is institutional Framework?
Government can make a major contribution to economic efficiency through its provision of an institutional infrastructure that enables the market system to function
Major example: legal system
What is Importance of institutional infrastructure?
Poor infrastructure can seriously hinder productive economic activity
A 1997 study found that average output per worker was nearly 6 times as high in countries with high-quality infrastructure as in those with low-quality infrastructure (corrupt government, weak property rights, etc.)
Example of bad infrastructure: a 2002 World Bank study found that Russian households paid $3 billion in bribes each year, mostly to education workers and police
Context: total income another $33 billion in bribes each year
Another example: a 2006 study found that, in Guatemala, it took roughly 4 years to collect on a significant debt
…when the collector was unambiguously in the right
Correcting market failure
- Market failure: a situation in which a free market fails to achieve economic efficiency
- Four main sources of market failure
1. Market power
2. Public goods
3. Externalities
4. Asymmetric information
Define Market Power
The standard competitive model assumes small buyers and sellers that take prices as given
If producers or consumers are large, they may instead account for the effect that their behavior has on prices (they are not price-takers)
E.g., for a monopolist, MPB ≠ MSB
As a result, the market does not produce the efficient level of output (where MSC = MSB)
Public Goods
Standard model requires that goods be excludable and rival in consumption (“private goods”)
A good is rival if each unit a person consumes reduces the amount available for others
A good is excludable if people who don’t pay for it can be prevented from consuming it (without preventing everyone from consuming it)
When this is not the case, private benefits and costs are not aligned with social benefits and costs
Pure public goods (non-rival, non-excludable): underprovision of good because individuals have incentive not to pay for good (can consume without paying; “free rider problem”)
Common resources (rival, non-excludable): overconsumption because MPC < MSC
Externalities
An externality occurs when a production or consumption decision has an effect on someone who is not involved in the transaction
Whether an externality is positive or negative, the outcome produced by the free market will be inefficient (possible exception: Coase Theorem)
Negative externality
a cost is imposed on a third party
Results in overconsumption because MPC < MSC
Positive externality
a third party receives benefits
Results in underconsumption because MPB < MSB
Asymmetric information
In some situations, relevant information is only available to one side of the market
Creates two mechanisms for market failure:
Adverse selection: not all products (or customers, workers, etc.) are identical, and asymmetric information about quality causes low-quality products to drive high-quality products out of the market
Moral hazard: when protected from the consequences of their behavior as the result of a transaction (e.g., acquiring insurance), people change their behavior in a way that is detrimental to the other party (e.g., insurer
Providing Equity
Correction of market failure is justified on the basis of efficiency: there are efficiency gains produced by government intervention
The other major rationale for government activity is equity, or fairness
Important note: efficiency and equity are two separate criteria (an outcome can be efficient but not equitable, or vice versa), but improvements in one may come at the expense of the other in practice
A challenge of dealing with equity issues is that there is no single notion of what “fairness” entails (equality of opportunity, equality of outcomes, commodity egalitarianism, etc.)
Government Intervention
Direct government intervention in a market can have positive or negative effects on efficiency
In the absence of a market failure, government intervention in a market reduces efficiency
If a market is efficient (total surplus is maximized) to begin with, any movement away from the competitive equilibrium must reduce total surplus
In the presence of a market failure, government intervention can be efficiency-improving
Important note: market failure (inefficiency) does not necessarily justify government intervention, just creates a situation in which intervention could be efficiency-improving
Economics and Ethics of CBA
Conceptual economic foundations for conducting cost-benefit analysis
Review: opportunity cost and marginal analysis
Review: consumer choice problem
Economic value (individually vs. collectively)
Social welfare
Ethical issues surrounding CBA
Opportunity cost
Opportunity cost: what is given up when taking an action or making a choice
Also called the marginal cost of that action/choice
Equal to the value of the best alternative that you’ve forgone by taking that action/making that choice
Includes all relevant costs
Explicit costs: actual monetary payments
Implicit costs: non-monetary costs (e.g., value of time)
Excludes irrelevant costs
Sunk costs: paid in the past, cannot be recovered
Fixed costs: unaffected by this particular action/decision
Marginal analysis
Decision rule for rational economic behavior:
MC = MB
MC: marginal cost, MB: marginal benefit
When you see “marginal”, think “additional” or “incremental”; has to do with “a little more” of something
“Rational” means “suits the decision maker’s interest” without assuming any particular motivations (e.g. selfishness, altruism, materialism, etc.)
In words: the optimal amount of any activity is that at which its MC is equal to its MB
For yes/no decisions, an action should be taken if MB > MC (if MB = MC, indifferent between options)
Review: consumer choice problem
Fundamental problem faced by consumers: choose the bundle of goods and services that maximizes utility (well-being, satisfaction, etc.), subject to the resources available
Two basic elements: preferences and budget
Consumer achieves maximum well-being by choosing the consumption bundle that gives the highest level of utility attainable given the budget constraint they face
Economic value of policies
A key goal of of policy analysis is to determine the costs and benefits of a specific policy
Before we think about the benefits and costs across everyone in society, let’s think about a particular individual first (then later we’ll “add up” across individuals)
Economic value
What is the “value” of a policy to some individual?
A person derives utility from the consumption of goods:
U = U(X1, X2, …, XN)
Notation: subscripts are used to indicate which good we’re referring to; “Xj” is the quantity of good j (with j = 1, 2, …, N)
Recall: a “good is anything that an individual values. It need not be material and there need not be a market for it.
A policy changes the person’s consumption of the N goods by dX1, dX2, …, dXN
If the individual consumed 25 units of good 7 (X7 = 25) before the policy, and consumes 28 units after the policy, then dX7 = 3
If the individual had X2 = 15 before and has X2 = 11 after, then dX2 = -4 (dXj is negative if Xj decreases; not an absolute value)
Willingness to pay (WTP)
How much would you pay for a policy that benefits you, or pay to avoid a policy that hurts you?
Willingness to accept (WTA)
How much would you accept in lieu of a policy that benefits you, or accept as compensation for a policy that hurts you?
Willingness to pay vs. accept
These are conceptually similar, but…
Willingness to pay is constrained by current income
WTP and WTA have different reference points
In practice, which measure is appropriate is dependent on the assignment of rights
Zerbe (1998): “Whether an action that results in a positive change is felt as a loss restored or as a gain, is in large part a matter of established property rights.”
Compensating vs. equivalent variation
Two related concepts in determining economic value of policies are compensating variation (CV) & equivalent variation (EV)
Compensating variation
Compensating variation (CV) is the amount you could pay and still be as well off after the change as you were before (what you would pay to compensate for the change)
CV can be negative; this just means that you would “pay” a negative amount (i.e., receive money)
CV>0 indicates a beneficial change; CV<0 indicates harm
In the case of a beneficial policy (e.g., price decrease), CV is the amount you would be willing to give up in order to receive the benefit of the policy; i.e., “willingness to pay”
In the case of a harmful policy (e.g., price increase), (the size of) CV is the amount you would require to tolerate the cost of the policy; i.e., “willingness to accept”
Calculated by looking at original utility
In a world where the policy is implemented, how much money must you pay (or receive) in order to restore your pre-policy level of utility?
This shows how CV depends on “rights.” It factors in utility under the status quo, effectively presuming that that’s what you’re entitled to.
Equivalent variation
Equivalent variation (EV) is the amount you must receive to make you as well off without the policy as you would be with it (the monetary equivalent of the policy)
EV can be negative; this just means that you would pay money instead of receiving money
EV>0 indicates a beneficial change; EV<0 indicates harm
In the case of a beneficial policy (e.g., price decrease), EV is the amount you would accept in place of the policy; i.e. “willingness to accept”
In the case of a harmful policy (e.g., price increase), (the size of) EV is what you would pay to avoid the policy; i.e. “willingness to pay”
Calculated by looking at new utility
In a world where the policy is not implemented, how much money must you be given (or have taken away) so that you have the same utility that you would have if the policy was implemented?
This shows how EV also depends on “rights.” It factors in utility under the new policy, effectively presuming that’s what you’re entitled to.
Producer surplus
Consumers’ welfare changes can be measured (approximately) via changes in consumer surplus
Suppliers’ welfare changes can similar be measured via changes in producer surplus
Reminder: producer surplus is the area above the competitive supply (i.e., marginal cost) curve and beneath the price suppliers are paid
Kaldor criterion
A policy should be enacted if the winners from a policy change could (in principle) fully compensate the losers and still be better off than before
Hicks criterion
A policy should be enacted if the losers could not bribe the potential winners not to enact the policy (and still be better off than if the policy had been enacted)
Kaldor-Hicks criterion
Must meet both of the criteria above
Potential Pareto rule
Potential Pareto rule
Are there side payments among individuals such that the policy, if accompanied by these side payments, would create a Pareto improvement?
Important note: there is no requirement that these side payments are actually made!
This is essentially the Kaldor-Hicks criterion; does the policy make the “social pie” bigger?
Straightforward to evaluate in practice: does the policy generate net benefits?
In order for the Kaldor-Hicks criterion to give the correct decision, what must be true about the social welfare function? (What does use of KH imply?)
Kaldor-Hicks and social welfare
In terms of social welfare function, using Kaldor-Hicks is equivalent to using weights that are all equal to 1:
𝑑𝑊=∑_𝑖▒(𝜕𝑊/(𝜕𝑈_𝑖 )∗(𝑑𝑈_𝑖)/𝑑𝑀∗∑_𝑗▒(𝑝_𝑗∗𝑑𝑋_𝑗 ) )
=∑_𝑖▒∑_𝑗▒〖𝑝_𝑗∗𝑑𝑋_𝑗 〗
This is exclusively an efficiency criterion
It asks: has the size of the “social pie” increased?
It does not care how the pie is divided (ignores equity)
Kaldor-Hicks, equity, and the real world
There are instances when Kaldor-Hicks is appropriate even if society values both equity and efficiency
Does society have a more effective alternative mechanism for attaining distributional changes?
E.g., progressive income taxes and transfers
If so, then analysis of an unrelated policy will be minimally affected by consideration of distributional issues
As we will see later in the course, it is fairly straightforward to explicitly incorporate equity into our analytical framework even though it is based on Kaldor-Hicks
The big challenge is obtaining information about how society values equity, not any methodological difficulty in incorporating this information into CBA per se
Ethical issues surrounding CBA
Kelman’s (1981) main arguments
Cost-benefit analysis is based on utilitarianism, which is not the appropriate moral standard in all cases
CBA requires the pricing of non-market goods, which distorts the true value of many important rights and duties
There may be cases in which a decision whose costs outweigh its benefits is still the correct decision
“It is not justifiable to devote major resources to the generation of data for cost-benefit calculations or to undertake efforts to ‘spread the gospel’ of cost-benefit analysis further”
Discuss!
Intertemporal resource allocation
Present consumption: 𝐶0=𝑊0 –𝑆0
Future consumption: 𝐶1=𝑆0(1+𝑟)
Solving the second equation for S0 and substituting into the first gives the multi-period budget constraint:
𝑊_0=𝐶_0+𝐶_1/(1+𝑟)
This a standard budget constraint with 𝑃0 = 1 and 𝑃1 = 1/(1+𝑟) (can look at it as 𝑊_0=〖1∗𝐶〗_0+1/(1+𝑟)∗𝐶_1)
Graphically, this is a line with a vertical (𝐶1) intercept of 𝑊0(1+𝑟), a horizontal (𝐶0) intercept of 𝑊0, and a slope of –(1+𝑟)
MRS - Marginal Rate of Substitution
An individual’s marginal rate of substitution (MRS) is the magnitude of the slope of their indifference curve
marginal rate of time preference (MRTP)
The marginal rate of time preference (MRTP) is defined as MRTP = MRS – 1 (or MRS = 1 + MRTP)
MRTP is the % increase in consumption that the individual requires in order to delay that consumption by 1 year
Time value of money
If the costs and benefits of a policy occur at different points in time, their dollar values are not directly comparable: a dollar today is not equivalent to a dollar some time in the future Why is this the case? Inflation (or deflation) Opportunity cost (could invest $1 now, earn interest) Preference for current consumption Uncertainty/risk of investment (if talking about expected dollar values, not certain dollar values)
To address this issue, all costs and benefits must be expressed in comparable units
The standard way to do this is to express all costs and benefits in terms of their present value (the amount that, if paid/received now, would be equivalent to the specified future amount)
This conversion process is called “discounting”
Discounting
An amount X available today, invested at an interest rate r, will translate into X(1+r) in one year
Future Value (FV)
This amount is referred to as the future value (FV) of the investment in one year: 𝐹𝑉=𝑋(1+𝑟)
Example: $1,000 invested today at an interest rate of 4% (or 0.04) will return $1,000 + $1,000(0.04) = $1,040 next year
Present Value (PV)
The present value (PV) of a future amount can be found by rearranging this equation
$FV received in one year is worth $PV now
𝐹𝑉=𝑃𝑉(1+𝑟)
𝑃𝑉=𝐹𝑉/(1+𝑟)
Discount Rate
In practice, the value of r may be something other than the market interest rate; r is referred to as the discount rate
Net Present Value
The present value of a project’s benefits minus the present value of its costs is called the net present value (NPV) of the project – because it is negative in this case, the city should not purchase the land ($5.25m next year is not more valuable than $5m now!)
Compound Interest Factor
(1+𝑟)𝑛 is referred to as the compound interest factor
Discounting Over Multiple Periods
An amount X available today, invested at an interest rate r, will translate into X(1+r) in one year
𝐹𝑉_1=𝑋(1+𝑟)
If this amount is then invested for another year:
𝐹𝑉_2=𝑋(1+𝑟)(1+𝑟)=𝑋(1+𝑟)^2
After being reinvested annually for n years:
𝐹𝑉_𝑛=𝑋(1+𝑟)^𝑛
Discount Factor
1/(1+𝑟)^𝑛 is called the discount factor
Net Present Value
If a project generates benefits over multiple periods, the present value of the entire stream of benefits is just the sum of the PVs of each period’s benefits:
PV(B)=𝐵_0/〖(1+𝑟)〗^0 +𝐵_1/〖(1+𝑟)〗^1 +…+𝐵_𝑛/〖(1+𝑟)〗^𝑛
NPV Assumptions
In order to use NPV to inform a decision, need to make certain assumptions:
Value(s) of discount rate(s)
Can have different rates for different periods
Capital is readily available if borrowing is required
Not generally an issue in developed countries like U.S.
Borrowing and lending have the same interest rate
Not always strictly true, but very close in U.S.
All relevant benefits and costs have been included
Transfer Payments
One caution about a common mistake when compiling your list of relevant costs and benefits to be included: watch out for irrelevant transfer payments!
A transfer payment is simply a payment from one party to another; it does not actually involve the use of resources (just moves resources from one party to another), and thus does not constitute a net cost or net benefit to society
The transfer payment represents a cost to the payer and an identically-sized benefit to the recipient; if both were included, they would cancel each other out when calculating NPV
Example: in what sense is “job creation” a benefit?
Important exception: if the two parties have different social weights, a transfer payment between them has equity implications and should thus be included
We’ll return to this issue later in the course
Single Project
Net present value as a decision rule
Using NPV as a decision rule for a single project:
If NPV > 0 (benefits exceed costs), the project increases real wealth and should be undertaken
Assumes no capital constraints (so no additional opportunity cost from an even better project that the money could have been spent on)
Using NPV to compare mutually exclusive projects:
Must identify all possible alternatives (including combinations of other alternatives, if relevant)
The project with the highest NPV increases real wealth by the largest amount, and should be undertaken
Note: If doing nothing (not undertaking any project) is an option, then no project should be chosen if all have NPV<0
If projects have different lifespans, NPVs cannot be compared directly, and must be adjusted; several methods for doing this (e.g., invest FV of the shorter project at best available rate until the end of the longer project’s lifespan)
Net present value: real or nominal?
Four Determining Factors
- benefits
- costs
- time horizon
- discount rate
We have made no mention of whether benefits and costs are expressed in real or nominal terms – it does not matter as long as you use the appropriate discount rates (real if benefits and costs are in real terms, nominal if they are in nominal terms)
Not only do real/nominal give the same conclusions about a project, they give the same NPV – in the base year (present), real and nominal are the same
The usual convention for public sector analysis is to use real values, while the private sector conventionally uses nominal values
real versus nominal values
To convert a nominal value into a real value, it must be adjusted to account for price differences between that year and the base year
Letting Pt denote the price level in year t (typically measured by the Consumer Price Index), a nominal amount (in year t dollars) can be expressed in real terms (in year 0 dollars) as follows:
〖𝑅𝑒𝑎𝑙〗_0$=〖𝑁𝑜𝑚𝑖𝑛𝑎𝑙〗_𝑡$∙𝑃_0/𝑃_𝑡
For analysis of future costs and benefits, price indexes not known yet: need to forecast future prices with estimates of future inflation (from Federal Reserve, OECD, etc.)
Discount rate vs. market interest rate
There are a number of reasons that the market interest rate may not be equal to the MRTP and to the marginal rate of return on investment
Key examples include market failures and taxes
If it is not the case that the MRTP is equal to the rate of return on investment, with both given by the market interest rate, then the appropriate social discount rate is no longer obvious
consumption rate of interest (CRI)
MTRP as social discount rate
One possibility is to use the MRTP
In the example: 8%
This is the rate at which individuals are willing to trade future consumption for current consumption
Argument for this approach:
If a project yields a return higher than the MRTP, then the increase in future consumption makes the sacrifice of current consumption worthwhile
Advocates of the MRTP approach tend to be in favor of more extensive government investment
A lower discount rate gives future benefits more weight
opportunity cost rate (OCR)
Another option would be to use the marginal return to private investment
In the example: 17%
This is also called the opportunity cost rate (OCR)
Argument for this approach:
Public investment can displace private investment by using funds that would otherwise go to private investment
If the rate of return on a project is less than the OCR, then this project is less valuable than the private investment that it displaced, and the project should not be undertaken
Whether or not the return is greater than the MRTP is irrelevant, as the alternative use of these funds is not a project with a return equal to the MRTP
Advocates of the OCR approach tend to be in favor of less government investment
A higher discount rate gives future benefits less weight
The social discount rate
Both of these approaches have some intuitive appeal; what should we actually do?
To the extent that a project displaces consumption, it should be discounted at the MRTP
The project comes at the expense of current consumption, and this is the rate at which individuals are willing to trade current for future consumption
To the extent that a project displaces private investment, it should be discounted at the OCR
This is the return that would have been earned on those funds otherwise, so it is the relevant opportunity cost
The Harberger method
Social discount rate = 𝑎∗𝑂𝐶𝑅 + (1−𝑎)∗𝑀𝑅𝑇𝑃
Social discount rate obtained this way also called the WSOC (Weighted Social Opportunity Cost of capital)
𝑎 = fraction of funds displacing private investment
(1 – 𝑎) = fraction of funds displacing consumption
Conceptual motivation: if some funds should be discounted at the OCR, and some at the MRTP, then the discount rate for the project as a whole should be a weighted average of these two rates
Example:
Suppose that OCR = 17%, MRTP = 8%, and 60% of funding would come from displaced private investment
Social discount rate = (0.6)(17%) + (0.4)(8%) = 13.4%
Where do we get OCR?
This is the marginal rate of return on private investment
We might use the real (inflation-adjusted) before-tax rate of return on corporate bonds
E.g., Moody’s AAA-rated corporate bonds have typically yielded about 4.5%
Where do we get MRTP?
This is the rate at which individuals are willing to postpone current consumption for future consumption
We might use the real (inflation-adjusted) after-tax rate of return on government bonds
Generally around 1.5%
Shadow price of capital
The shadow price of capital (SPC) is the present value of the consumption that results from $1 of private investment
The SPC answers the question: how many dollars of consumption is each dollar of private investment “worth”?
Kind of like last week: even we everything is measured in $’s, not all $’s are directly comparable.
A general expression for the SPC: (no need to memorize!)
SPC= ((𝑟+𝛿)(1−𝑓))/(𝑝−𝑟𝑓+𝛿(1−𝑓))
r: net return on capital after depreciation
δ: depreciation rate
f: fraction of returns re-invested
p: marginal social rate of time preference (SRTP)
If there is no re-investment and no depreciation, this simplifies to SPC = 𝑟/𝑝 (the marginal value of displaced private investment divided by the marginal value of displaced consumption)
BGVW’s recommended baseline SPC is 1.33; ignoring re-investment and depreciation (as the Harberger method does) but otherwise using the same parameters would give SPC = 3!
Discount rate with SPC method
The SPC method converts all benefits and costs into consumption equivalents
This resolves our dilemma about which discount rate to use; since everything is now expressed in dollars of consumption, we should discount as if only consumption has been displaced (i.e., use MRTP as the discount rate)
“NPV”=∑_(𝑡=0)^𝑛▒(〖𝐵_𝑡〗^∗−〖𝐶_𝑡〗^∗)/〖(1+𝑟)〗^𝑡
Cost-effectiveness analysis
Cost-effectiveness analysis (CEA) is a common alternative to cost-benefit analysis
Similar techniques; CEA is essentially CBA without a dollar value assigned to benefits
Usually a different goal: provides information about relative efficiency of alternatives
CEA can be used when:
The goal (desired effect) is known
The budget is fixed
There are missing data or there are outcomes that we choose not to monetize
Major example: health policy
Cost-Effectiveness Ratio
𝐶𝑜𝑠𝑡/𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒𝑛𝑒𝑠𝑠
Unlike in CBA, denominator is not monetized
If we monetized the effectiveness (benefits), this would be the inverse of the Benefit-Cost Ratio (discussed when we introduced CBA)
Use of CEA requires a one-dimensional measure of effectiveness (we can sometimes get around this; more later)
E.g., lives saved, decrease in high school dropouts, tons of pollution abated
Cost-effectiveness in general
CEA was not especially helpful in either of those special cases, just reinforces what should be obvious:
Choose alternative with lowest cost if equally effective, or largest effect if equally costly
In practice, no particular reason to expect competing alternatives to have equal cost or effectiveness
Incremental Cost-Effectiveness Ratio
When considering an addition to an existing alternative (or a policy that can be implemented to various degrees), we use an Incremental Cost-Effectiveness Ratio (ICER):
𝐼𝐶𝐸𝑅=∆𝐶𝑜𝑠𝑡/∆𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒𝑛𝑒𝑠𝑠
The basic CE ratio can be thought of as a special case where the “existing alternative” is no policy (C=E=0)
Especially important to consider if diminishing returns and/or increasing costs apply
Cost-effectiveness in general
Even more generally, programs may have:
Benefits besides the effectiveness measure
Specifically, some benefits that you are willing/able to monetize
Effects that occur over time
What does the CE ratio look like then?
Denoting monetized benefits as Bt , net CE ratio is:
(∑(𝑡=0)^𝑛▒〖(𝐶_𝑡−𝐵_𝑡)/〖(1+𝑟)〗^𝑡 〗)/(∑(𝑡=0)^𝑛▒〖𝐸_𝑡/〖(1+𝑟)〗^𝑡 〗)=(𝑃𝑉(𝑁𝑒𝑡 𝑐𝑜𝑠𝑡𝑠))/(𝑃𝑉(𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒𝑛𝑒𝑠𝑠))
In other situations, we may not know the value of a key benefit
Missing data
E.g., an after-school tutoring program with unknown effect on student outcomes
Unwillingness to assign a value to an important variable
E.g., life or health status
Note: “unwillingness” is not the same as “inability.” More on valuing health later in the course.
What can the cost-effectiveness structure give us in these cases?
Is the policy a “good idea”?
Is the policy a “good idea”?
CE ratio alone can’t answer this; what additional info is needed?
CEA is a “threshold” method
It gives the minimum valuation of one unit of effectiveness required to make a policy worth enacting
E.g., if the value of an additional high school graduate is greater than $35,000, then the policy is worthwhile
Even if you’re unable or unwilling to monetize a benefit, the reality is that resources are scarce, and we need to decide among alternative uses of those resources
Should the government enact a policy that has a CE ratio of $1 per additional graduate?
How about a policy that costs $1 trillion per additional graduate?
Cost-utility analysis
What if “effectiveness” can’t be captured by a one-dimensional measure?
Most commonly an issue in health policy, as medical interventions may affect both life expectancy (mortality) and quality of life (morbidity)
Cost-utility analysis (CUA) can be thought of as a special case of CEA in which the “effectiveness” term is a utility index that incorporates multiple dimensions
In health policy, outcomes are often measured in terms of quality-adjusted life-years (QALYs)
What is a QALY?
Measuring a policy’s outcome in terms of years of life saved does not account for effects on quality of life, which we want to incorporate
Outcomes are converted into QALYs by multiplying years of life saved by a quality factor ranging from 0 (death) to 1 (perfect health)
E.g., 1 year in hospital = 0.16 years in perfect health, 1 year with osteoporotic fractures = 0.78 years in perfect health
So, 5 years with osteoporotic fractures = 3.9 QALYs
(5 years)*(0.78 QALYs/year) = 3.9 QALYs
Who determines quality factors?
Not everyone has the same preferences; whose do we use?
Medical experts
Patients who have experienced similar health states
General population
Other?
What are the pros and cons of each group?
How do we determine quality factors?
-Health rating method
Individuals are given a scale with death = 0 and perfect health = 1, then asked to specify the locations of intermediate health states (described in detail) on this scale
-Time trade-off method
Individuals asked to rank different combinations of length and quality of life; the tradeoffs that make individuals indifferent imply the relative quality factors
-Standard gamble
Individuals given a choice between (a) n years with a specified health state or (b) probability p of n years in perfect health and probability (1 – p) of immediate death; quality factor is the value of p that makes them indifferent
CUA in General
Same issues in CUA as in CEA (conceptually identical)
Potential issues when comparing projects of different scale
Useful for comparisons when budgets or goals are known
Is the policy a “good idea”?
Is cost per QALY < value per QALY?
Vigdor (2000) literature review puts reasonable values between $140,000 and $345,000 (tentative, with qualifiers; e.g., potential variation by age and health status)
Many medical interventions have much lower costs per QALY than this, but not always lower than alternatives
UK’s National Institute for Health and Clinical Excellence uses “threshold range” of £20,000 to £30,000 (equivalent to roughly $29,000 to $43,500 as of 2016)
NPV and policy impacts
Net Present Value can be represented by this formula:
𝑁𝑃𝑉=∑_𝑖▒〖∑_𝑗▒𝑃_𝑗 𝑑𝑋_𝑖𝑗 〗
Benefits and costs are the product of:
dX: The real impact of the policy
How much does the quantity of goods (or “bads”) change as the result of the policy?
P: The valuation (price) of the impacted goods
For each good, how much value do we place on each unit gained/lost?
This week: predicting impacts
Coming weeks: valuing impacts
Predicting policy impacts
Most policy analysis requires predicting the future
E.g., if the government implements a school voucher system, what will happen?
“Prediction is very difficult, especially about the future.” – Niels Bohr (1922 Nobel Prize winner in physics)
In order to predict the future, social scientists usually study what happened in the past
What past events can you look at?
What difficulties are there when using the past to predict the future?
What impacts should we predict?
-Primary/direct goals of policy
Changes in price and quantity of goods (bads)
Remember that “goods” defined very broadly
Who benefits and who loses from direct impacts?
-Indirect effects
Are the indirect effects good or bad? For whom?
Example: Federal minimum wage increase
Primary intended effects?
Indirect?
Unintended consequences
In addition to thinking about whether a policy will be effective at inducing the desired behavior, it is important to consider that it might cause additional unintended results
Example: Endangered Species Act of 1973 protects physical habitats of endangered species
There is often a lag between the time a species is declared to be endangered and the time that its habitats are officially established (Dubner and Levitt, 2008)
What might happen in this time?
Americans with Disabilities Act: provides protection against discrimination for disabled workers (Dubner and Levitt, 2008)
One Child Policy: China, 1978 (Ebenstein, 2010; Chen et al., 2013)
Youth bicycle helmet laws (Carpenter and Stehr, 2011)
Tax evasion and avoidance examples (Rosen and Gayer, 2013)
Three broad categories of past experiences to look to:
- Is the policy you’re evaluating an extension/replication of an existing policy?
- Is the policy you’re evaluating similar to other policies that have been implemented in other locations, with different populations, etc.?
- Can the policy be interpreted as a price change? If so, how has the relevant population reacted to price changes in the past?
Predicting impacts: single past policy
Two general concerns if using evidence from a past policy to predict the outcomes of a proposed policy
Internal validity
Can the measured difference in outcomes can be properly attributed to the policy?
External validity
Can the measured difference in outcomes be generalized to new circumstances?
Also critical to have an adequate causal theory
Explains behavior regulated by the policy and the relationship between the policy and that behavior
Guides empirical analysis (looking at the right inputs & outputs?)
Alleviates worry about “false positives”
“Inadequate causal theories lie behind many of the cases of implementation failure” – Mazmanian and Sabatier (1989)
Internal validity
Can the measured difference in outcomes be attributed to the policy?
In other words, is there a causal relationship between the policy and outcomes (not just correlation)?
Three conditions (Rosen and Gayer, 2013):
1. Policy and outcomes are correlated
2. Policy precedes outcomes
3. Other explanations for correlation must be eliminated
Counterfactual
What would have happened in the absence of the policy? (this hypothetical outcome is called the counterfactual)
Basic idea of empirical analysis:
Compare two groups that do not systematically differ except that one is subject to a “treatment” and the other is not
randomized controlled trial (RCT)
Concerns about internal validity relate to the how well the observed data reflects the scientific experimental ideal, embodied by the randomized controlled trial (RCT)
Ideal: Before and after observations for a treatment and control group; random assignment into treatment and control groups
If done successfully, then any observed differences in outcomes can be attributed to the program/treatment/policy/intervention
Dealing with Internal Validity Concerns
All empirical analysis makes some assumptions about the counterfactual
If you’re producing original research…
Be explicit (with yourself and your audience) about your assumptions
Critically assess the assumption
What seems plausible? What is concerning?
If you’re consuming others’ research…
Identify the assumptions
Critically assess the assumptions to gauge whether you want to use the research
External validity
Can the evidence be generalized to new circumstances?
Some reasons to question external validity:
Different populations
Different socioeconomic environments
Different time periods
Different program scale
Not an exhaustive list; requires critical thinking and knowledge of the current and past programs that may go beyond that which is visible in data
Problems with obtaining experimental ideal
Often not feasible to run a random experiment; can we randomly assign treatment and control groups? Costs, ethics (though sometimes goals of being ethical and randomizing for experimental purposes align) Even with randomization, can still have threats to internal validity Selection bias (are voluntary participants different from general population?) Randomization failure (can only control for observed treatment-control differences; bias may result if unobservable characteristics not perfectly balanced) Attrition bias (participants drop out non-randomly) Hawthorne effects (people know they’re being studied, and behave differently; may respond to treatment/control status) For examples/discussion of these issues, see Krueger (1999)
Quasi-experimental methods
In practice, researchers in the social sciences often rely upon natural experiments (or quasi-experiments), which attempt to utilize the “treatment-control” framework in the absence of actual random assignment to treatment and control groups Example: Angrist and Lavy (1999), quasi-experimental variation in class size In Israel, class size capped at 40 (“Maimonides’ Rule”): if cohort has 40 students, get one class of 40; if cohort has 41, get classes of 20 and 21 Assuming no other systematic differences between cohorts of 40 vs. 41, differences in outcomes are attributable to class size
Simple treatment-control comparisons
Strict adaptation of experimental framework would entail comparing outcomes of individuals exposed to the treatment with outcomes of similar individuals not exposed to it
Example: do states with death penalty have lower crime rates?
Policy impact = T – C
Is this a good idea?
Does the control group provide a valid counterfactual?
Would their outcomes be the same the absence of the policy?
Before and after comparisons
Another possible approach would be to simply compare the outcomes of those exposed to a policy before and after the policy was implemented
Example: what were rates of smoking-related illnesses in CA before and after bans on smoking in public places?
In the “treatment-control” framework, this is essentially using the participants’ pre-treatment selves as the control group
Policy impact = Tpost – Tpre
Is this a good idea?
What counterfactual is implicitly assumed by this approach? Does that seem plausible?
In practice, it may be the best you can do (e.g., no reasonable control group); in this case, you should control for as many other relevant factors as possible, and clearly note the limitations
Difference-in-difference estimation
A better approach would use both pre- and post-treatment information on the treatment group and a control group
A common way of doing this is known as difference-in-difference estimation
This method estimates the impact of a policy by comparing the outcomes of a treatment group and a control group before and after the treatment is received
Underlying assumption: in the absence of the policy, the difference between the outcomes of the two groups would not have changed (i.e., they would have followed a common trend)
One way to start exploring whether this seems reasonable: have the outcomes for these two groups followed similar trends in the past?
The change in outcomes of the control group is viewed as the counterfactual for the change in outcomes of the treatment group
Difference-in-difference estimator:
Policy impact = (Tpost – Tpre) – (Cpost– Cpre)
T: treatment group outcome, C: control group outcome
The DD estimate is the amount by which the change for the treatment group exceeded the change for the control group
Another way of writing this equation:
Policy impact = (Tpost – Cpost) – (Tpre – Cpre)
This shows another way of thinking about the DD estimate: it’s the amount by which the difference between the treatment and control group changed
Predicting impacts: meta-analysis
In some cases, there may be many previous policies similar to the one whose effects are being predicted
If reliable evaluations have already been conducted for these policies, then their results can be used to estimate both the expected size of the new policy’s effects and the uncertainty associated with that estimate
Good examples from Washington State Institute for Public Policy: Aos et al. (2007); Drake et al. (2009); Aos and Pennucci (2013)
Key question: which existing evaluations are “reliable” and should be included in your meta-analysis?
Most straightforward approach to combining a set of estimates would be to take a simple average
However, this does not account for differences in the precision of the various estimates
E.g., if one study’s estimate is 10 with a standard error of 2, and another study’s estimate is 14 with an SE of 4, does it seem reasonable to give them equal weight (i.e., use the simple average, 12)?
Instead, common to take a weighted average, assigning a weight to each estimate that is equal to the inverse of its variance:
〖𝑊𝑒𝑖𝑔ℎ𝑡〗_𝑖=1/〖𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒〗_𝑖
Predicting impacts: price elasticities
Many policies can be thought of as price changes
Many policies explicitly change prices
Example: subsidies for hybrid and electric cars
Even if there was no previous policy that subsidized electric cars, there may be general information on how demand responds to price changes
Often true even if the policy doesn’t explicitly deal with prices
Example: school district implementing universal public preschool
Essentially a price decrease to 0; may be able to find information on how demand for preschool changes with price
The price elasticity of demand is the percentage change in quantity demanded that results from a 1% increase in price:
Ep = “%∆Q” /”%∆P”
E.g., if a good has a price elasticity of –2, a 1% increase in price will lead to a 2% decrease in quantity demanded
Therefore, if your policy is a subsidy that would decrease a good’s price by 3%, you would predict a 6% increase in quantity
Distributional considerations
Does society value redistribution?
I.e., is αi the same for all 𝑖? (Should everyone’s costs and benefits “count” equally? Does each dollar have the same value to society no matter who pays/receives it?)
Rationales for redistribution (unequal αi):
Social welfare function other than additive utilitarian
Diminishing marginal utility of income
Desire for income distribution to be more equal
“One person, one vote” principle
Price changes have bigger EV/CV effects for people with more consumption (typically higher income); can be offset by placing higher weight on the gains/losses of those with lower income
Transfer programs exist that improve equity at the cost of efficiency, implying that society does value redistribution
However, big differences in preferences across individuals/political parties
distributionally-weighted NPV
If NPV is all about efficiency, can we incorporate equity into our CBA without using a completely different method?
Yes! Instead of the basic version of NPV that we have been using, we use distributionally-weighted NPV
Before we compare our costs and benefits, we weight them according to the relative values that society assigns to changes in the well-being of those paying/receiving them
For example, if benefits to one person are considered to be twice as valuable as benefits to another person, we could incorporate this into our analysis by doubling the value of the benefits received by first person (e.g., if they gain $100, we treat this as equivalent to a gain of $200 for the other person)
Internal weights
Internal weighting is a threshold technique analogous to the internal rate of return (IRR)
Remember that IRR answers the question: what is the discount rate that makes the policy just break even?
I.e., at what threshold does the policy switch from + to – NPV?
If the true discount rate is greater, then the policy has negative NPV; if the true discount rate is lower, then the policy has positive NPV
Internal weights answer the question: what is the weighting scheme that makes the policy just break even from a social welfare perspective?
Only meaningful in cases where there’s a trade-off between efficiency and equity
The internal weight for a disadvantaged group (relative to an advantaged group) is calculated as the size of the effect on the advantaged group divided by the size of the effect on the disadvantaged group
Suppose that a policy generates benefits of $5 million for a disadvantaged group (e.g., poor), and costs of $7 million for an advantaged group (e.g., rich)
The unweighted social NPV is:
$5 million – $7 million = –$2 million
What is the internal weight on the disadvantaged group?
internal weight=|𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑛 𝑎𝑑𝑣𝑎𝑛𝑡𝑎𝑔𝑒𝑑|/|𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑛 𝑑𝑖𝑠𝑎𝑑𝑣𝑎𝑛𝑡𝑎𝑔𝑒𝑑| =($7 𝑚𝑖𝑙𝑙𝑖𝑜𝑛)/($5 𝑚𝑖𝑙𝑙𝑖𝑜𝑛)=1.4
Internal weights in general
Is the policy a “good idea”?
Just like the internal rate of return (IRR) in CBA, internal weights do not provide a direct answer to this question
However, internal weights (and even the intermediate step of providing a simple breakdown of costs and benefits for different groups) provide decision-makers with valuable information
Internal weights explicitly demonstrate the trade-off between efficiency and equity
If the “true” distributional weights are determined to be higher or lower than the internal weights, then this indicates whether or not the policy is worth enacting
What are the right weights?
No consensus on what the social weights should be
“Opportunity cost” argument provides an upper bound
If a program increases equality but reduces efficiency, it should be rejected if an alternative transfer program could be used with lower loss in efficiency
If a program decreases equality but increases efficiency, it should be accepted if an alternative transfer program could compensate the losers without a net reduction in efficiency
Note similarity to Kaldor-Hicks
How much do transfers cost per dollar provided to beneficiaries?
Gramlich (1990): $1.50-$2.00
A policy that results in a Pareto superior outcome will necessarily satisfy the Kaldor-Hicks
Criterion; however, it may not increase social welfare.
False. A Pareto superior outcome leaves at least one person better off, and no one worse off.
Therefore, the first statement regarding the Kaldor-Hicks Criterion is in fact true. Since Kaldor-
Hicks places equal weight on all individuals, then those individuals who are better off increase
the equally-weighted social welfare function. However, the second statement regarding social
welfare is false. So long as no individual has a negative weight in the social welfare function (a
negative weight implies that that person’s well-being negatively affects social welfare), then
even an unequally-weighted social welfare function must increase if some individuals are better
off and no one is worse off.
When determining changes in social welfare, changes in individual utility are less important
than the social weight placed on each person’s changes in utility.
False. The equation for measuring changes in social welfare is
𝑑𝑊 = Σ
𝜕𝑊
𝜕𝑈𝑖
𝑁
𝑖=1
⋅ 𝑑𝑈𝑖
which shows that both the social weight (
𝜕𝑊
𝜕𝑈𝑖
) and the change in individual utility (𝑑𝑈𝑖) are
equally important. For instance, if person A has double the social welfare weight of person B
but half the change in utility, then person A and person B will each change social welfare by the
same amount.
Explain the difference between equivalent variation and compensating variation. How are
they measured?
Compensating variation measures the amount of income an individual must be compensated (positive or negative) to be as well off after an intervention as he or she was before the intervention. Equivalent variation on the other hand measures the amount of income an individual must be given/have taken away to be as well off as he or she would have been had an intervention taken place. They differ to the extent that compensating variation assumes that individuals are entitled to the initial utility (i.e. utility under the status quo) while equivalent variation assumes that individuals are entitled to the post-intervention utility. Both compensating and equivalent variation are measured as the area under the Hicksian
(compensated) demand curve, but note that compensating variation uses the Hicksian curve that corresponds to initial utility while equivalent variation uses the Hicksian curve that corresponds to post-intervention utility.
4) When can we use consumer surplus as an approximation of compensating or equivalent variation?
Change in CS falls somewhere between CV and EV and is a good approximation of CV and EV when those two are close together. CV and EV are close together when a policy has relatively small effects, if it affects goods with small income elasticities, or if it affects goods that represent relatively small shares of income.
1) Discounting future benefits and costs is only necessary when one expects a positive rate of inflation in the future
False. Discounting of future benefits and costs is required regardless of inflation. For instance, discounting is required even when inflation is zero. Discounting accounts for the opportunity
cost of cash flows in the future relative to today, as well as intertemporal preferences for consumption sooner rather than later. In contrast, netting out of inflation accounts for changes in the purchasing power of a dollar due to price changes – even after accounting for that, the issues related to opportunity cost and intertemporal preference remain.
2) Time-declining discount rates are used because future generations are more important than current generations
False. Standard discounting, with constant discount rates, leads the benefits and costs to future generations to be almost entirely ignored even if those benefits and costs are very, very large. Furthermore, it is harder to imagine that current generations can compensate (or be compensated by) future generations. In a sense then, standard discounting seems to place too little importance on future generations, and time-declining discount rates rectify that issue.
