Essay！！

Cost Benefit Analysis (CBA)

Richard Martin

University of Victoria

October 2, 2019

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Review

Last couple of classes we developed a general framework to derive the socially efficient level of emissions.

We faced a trade-off between two costs to society: the damages associated with the pollution, and the cost of reducing pollution.

This marginal analysis assumes that emissions are a continuous variable: we can change emissions by small increments.

Continuity of emissions is reasonable when we are aggregating up sufficiently.

But sometimes we need to make a decision between choices that are truly discrete: this is the role of cost-benefit analysis (CBA).

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Intro to CBA

When using cost benefit analysis to guide public policy we must make use of social benefits and social opportunity cost.

This raises the issue of the boundary of our society: does the boundary of the society correspond to the boundary of the political entity making the decision?

CBA used widely in USA, not so much here.

While it seems obvious (at least to economists) that weighing the costs and benefits of all the feasible options is a sensible way to make a choice, CBA not without its critics. It has been claimed:

CBA is used for empire building in the public service. CBA is a substitute for political discourse, not a complement. CBA is a tool for the political right because costs are easier to quantify than benefits.

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Intro to CBA Steps

Steps in CBA:

1 List all the feasible mutually-exclusive options that are available.

2 Quantify the inputs and outputs associated with each choice.

3 Calculate the social opportunity cost of all inputs and the social benefit associated with each output, for each choice.

4 Choose the option with the largest net social benefit.

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Complications

Cost benefit is analysis is relatively easy for stand-alone facilities (e.g. sewage treatment), and relatively difficult for far reaching regulatory choices (e.g. carbon policy)

Complications to CBA: 1 Costs and Benefits spread out over time: need to consider that a dollar

today is worth more than a dollar tomorrow. 2 Attitudes towards risk/uncertainty. 3 Fairness: what we are doing with CBA is pie maxing. We need to

consider pie-sharing as well.

Lets do a mini experiment to illustrate Complication 1

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Complications Time

Bond auction.

I am going to auction off a $1 bond, payable by me on the last day of class. We are going to use what is known as a Japanese auction to allocate the bond. I am going to start by calling out a low bid (say zero) that everybody should be willing to pay for the bond. If you are willing to pay the amount just called out, you put up your hand, and keep it up. If more than one person has their hand up, I will call out a higher bid. The last person with their hand up wins the bond and pays the last price that I called out (the price at which the second highest bidder dropped out)

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Complications Time

$

Figure 1: Truthful bidding in Japanese Auction.

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Complications Time

In a Japanese auction you should (rationally) drop your hand when the price called out is equal to your value for the bond.1

We can use your “drop-out price” to infer your annual discount rate.

Suppose that you lower your hand when the price is $.95.

What that means is that you value $.95 today the same amount as $1 two months from now: .95 = 1

(1+r) 2 12

Presumably because you have investment opportunities that have an annual rate of return of r: You could take your $.95 and invest it for two months.

.95(1 + r) 2 12 = 1

1“truthful bidding” doesn’t max expected profits in other auctions: e.g. in first price sealed bid auctions (FPSBA) the winner pays their bid: bidding your value guarantees zero profit: you should (rationally) bid less than your value.

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Complications Time

CBA is quite sensitive to the choice of discount rate, especially over long time horizons.

No real consensus on what discount rate we should use: 1 Private discount rate (PDR): borrowing cost in private sector. 2 Social rate of time preference (SRTP): borrowing cost for government. 3 Social discount rate (SDR): either SRTP or SRTP plus social

opportunity cost (SOC).

Ideally we want our choice to be robust: it is the best choice over a wide range of discount rates... because we can’t agree on what the discount rate should be.

To complicate things further we need to be careful of the distinction between real and nominal rates.

At least here the prescription is clear: match the type of the amounts to the type of the rate: real with real and nominal with nominal.

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Complications Time

Sewage example: https: //coursespaces.uvic.ca/mod/resource/view.php?id=1141542

Spreadsheets make it quite easy to do sensitivity analysis: how sensitive is the optimal choice to:

1 The discount rate. 2 The time horizon.

Note that due to the compounding aspect of discounting the welfare of future generations is extremely under-weighted compared to our current welfare.

1 (1.05)100

< .01: our current welfare is considered more than 100 times

more important than the welfare of our descendants living 100 years from now.

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Complications Fairness

Not only can CBA screw over future generations, it can also screw over segments of the current populace!

Recall that CBA is a pie maxing activity: gives no consideration to how the pie is shared. If other means of redistribution are not available society might prefer an option that creates slightly less pie, but with a more equitable division of the pie. Equity or fairness can be characterized two ways:

1 Horizontal: people of same socio-economic standing treated equally. 2 Vertical: the ratio of net benefit to income is no lower in poor people

than in rich people.

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Complications Fairness

net benefit income

income

Figure 2: Proportional, progressive, regressive, and other.

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Complications Risk/uncertainty

CBA assumes that we either live in a world of certainty or we are both risk and ambiguity neutral.

Neither of these are true: thus society might prefer an option that creates slightly less (expected) pie, but with less risk/uncertainty. What is the diff between risk and uncertainty?

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Complications Risk/uncertainty

A situation is risky if we know 1 The set of potential outcomes. 2 The probabilities of each outcome. 3 The value of each outcome.

Otherwise it is uncertain.

Does a trip to Las Vegas entail risk or uncertainty... or both?

Figure 3: Stu

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Complications Risk/uncertainty

Think about the environmental problems we face (e.g. climate change)

1 We don’t know the set of potential outcomes. 2 We don’t know probabilities of each outcome. 3 We don’t know value of each outcome.

Environmental problems are not a situation of risk, they are a situation of uncertainty...

But the best we can do is model them as if they are risky rather than uncertain.

A problem with using risk and CBA to make uncertain environmental choices is that society might prefer an option that is less ambiguous than the project that looks best in terms of expected cost/benefit.

Let’s do a couple mini-experiments to investigate your risk and ambiguity preferences:

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Complications Risk/uncertainty

First mini-experiment: Japanese auction to gamble with me.

The gamble is a fair coin flip (50/50 probability heads/tails): I will pay $2 if it comes up heads, and $0 if it comes up tails. I am going to start by calling out a low bid (say zero) that everybody should be willing to pay. If you are willing to pay the amount just called out, you put up your hand, and keep it up. If more than one person has their hand up, I will call out a higher bid. The last person with their hand up wins and pays the last price that I called out (the price at which the second highest bidder dropped out) The gamble you are bidding on is risky.

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Complications Risk/uncertainty

We can compare your bid with the expected value of the gamble as a measure of risk aversion.

People can be risk loving, risk neutral, risk averse.

Your bid is what we call the certainty equivalent (CE) of the gamble.

If we compare your CE with the expected value of the gamble, it gives us a measure of your risk aversion.

What is the expected value of the gamble?

If an individual’s CE is lower than the expected value of the gamble what does that imply about their risk preferences?

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Complications Risk/uncertainty

Second mini-experiment: Japanese auction to gamble with me.

The gamble is an unfair coin flip (you do not know the probability of heads or tails): I will pay $2 if it comes up tails, and $0 if it comes up heads. I am going to start by calling out a low bid (say zero) that everybody should be willing to pay. If you are willing to pay the amount just called out, you put up your hand, and keep it up. If more than one person has their hand up, I will call out a higher bid. The last person with their hand up wins and pays the last price that I called out (the price at which the second highest bidder dropped out) The gamble you are bidding on is uncertain.

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Complications Risk/uncertainty

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Figure 4: Data from last year: Diagonal line for equal bids in both auctions: if people are ambiguity averse they should be under the diagonal line. Quite a bit of variation but the average WTP is 8% higher for risky gamble than uncertain gamble. I have trimmed the data of some bids in excess of $10 (for the risky gamble).

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Cost effectiveness

This is all rather complicated... sometimes we just give up if benefits are too difficult to quantify: we drop the benefits from CBA and just look at...

Cost effectiveness: Suppose we reach a consensus that we need to attain a given outcome but we have several options that lead to the same outcome.

In this situation we choose the option that attains the given outcome at the lowest opportunity cost to society.

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