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Basic economics needed to understand climate change policy. October 16, 2007. Topics covered in this section. These notes provide basic theory that is helpful in answering two types of questions:
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Basic economics needed to understand climate change policy October 16, 2007
Topics covered in this section These notes provide basic theory that is helpful in answering two types of questions: 1. Given that we have decided to reduce emissions, what is the “best” type of policy of achieving this goal? (What should we mean by “best” -- most efficient, most politically feasible?) I emphasize taxes versus cap and trade. 2. Given estimates of the costs and the benefits associated with GHG abatement, how should we determine the optimal level of abatement – i.e. the level that “balances” costs and benefits? I emphasize uncertainty and time dimension of problem.
Begin discussing details of different policies for reducing emissions • "Best efforts approach". Encourage developed countries to undertake their best efforts to reduce emissions. This is worth doing because it is low cost, but it is not likely to lead to major reductions in emissions. • “No regrets" reforms, e.g. liberalization of energy markets, impose standards that also reduce costs. These are worth doing, their effect is questionable. (Economists' skepticism regarding $20 bill lying in the street. Discuss economic analysis of the costs of achieving California’s AB32 goals.) • Actual US energy-related publicly funded and privately funded R&D has fallen over last 10 years. Better technology will not lead to abatement unless firms have an incentive to use it, and this requires some kind of government pressure. • The two prominent mandatory (economically costly) policies are taxes and cap-and-trade.
Taxes versus “cap-and-trade” (quotas) • They have different distributional effects, depending on how tax revenues or emissions permits are distributed. • They produce the same level of output and emissions under cost certainty (and perfect competition). (Discuss analogy with tariffs and quotas, as explained in an earlier lecture.) • They produce different results under cost uncertainty. The tax enables policymaker to choose the marginal abatement cost (equal to the tax), but it leaves the amount of abatement (the amount of emissions) uncertain. The cap-and-trade has the opposite tradeoff. • For climate change, tax is likely to be more economically efficient, but may not be politically feasible.
Political and “practical” features of taxes and quotas • Political: “Taxes” is a dirty word; “revenue neutral” taxes may not be much better. Quotas are a valuable asset; quota recipients (“grandfathers”) may benefit from quota policy. The quota recipients obtain the asset, and the quota raises entrants costs – if these do not receive quota allocation. • Practical: There are costs of organizing cap and trade and also of collecting tax revenues. Both require that emissions be monitored.
Economic basis for comparing taxes and quotas • The two policies directly control different things. The quota puts a ceiling on the level of emissions. The tax puts a ceiling on the level of marginal cost of abatement. • Use (linear) random marginal abatement cost curves to illustrate point above.
Use static model to explain economic difference between taxes and quotas • This model assumes that abatement marginal costs are random. Draw example of high and low marginal abatement cost curves. Think of these as realizations of a random variable. • Explain the meaning of “expected value”. • Pick a quota and then find the tax that leads to the same expected level of emissions. • With tax the level of emissions is random; the tax determines the expected level of emissions; with (binding) quota, the level of emissions is fixed by policy.
Modeling the benefits and the damages from emissions • Emissions lead to environmental damages. Higher emissions associated with higher total and marginal damages. • Abatement is costly. A higher level of emissions means a lower level of abatement, and thus a lower level of abatement costs. The benefits of emissions = the reduction in abatement costs. Explain why benefits are likely to be concave in emissions. • I’ll explain the advantage of quotas and then explain the advantage of taxes. Determining the efficient policy requires comparing these two advantages.
Explain next slide • Next slide shows the marginal damage of emissions and the high and low marginal benefits of emissions (corresponding to high and low marginal cost of abatement). • The expected marginal benefit of emissions is the average of the low and high marginal benefit. • Under certainty (no randomness in abatement cost) objective is to maximize benefits of emissions – damages of emissions, leading to first order condition: marginal benefit = marginal damage. • With uncertain abatement cost, the objective is to maximize expected (i.e. “average”) benefits minus damages, leading to the first order condition: expected marginal benefit equal marginal damages. • Note that in absence of regulation, private industry sets marginal benefit of emissions equal to 0 (i.e. they fail to internalize the damages) leading to excessive emissions.
Determining efficient levels of taxes and quotas High marginal benefits Marginal damages $ Optimal tax Expected marginal benefits Low marginal benefits emissions Optimal quota
The advantage of quotas: quotas reduce expected damages (relative to taxes) • Next slide shows the marginal damage curve, the level of emissions under the optimal quota and the random levels of emissions under the optimal tax. • When emissions are low, damages are reduced by A (under taxes rather than quotas) . When emissions are high, damages are increased by B (under taxes rather than quotas). • Since B>A, on average damages are higher under taxes than under quotas. • Experiment by making the damage curve flatter. Notice that this causes the areas A and B to become more similar. Thus, the advantage of quotas diminishes as the slope of the marginal damage curve diminishes.
Expected damages are lower under quotas Emissions under quotas Low emissions under taxes High emissions under taxes B A
The advantage of taxes: taxes increase expected benefits (i.e., reduce expected abatement costs) relative to quotas • The next slide shows the high and low marginal benefits (corresponding to high and low marginal abatement costs). • When marginal benefits are low (so emissions are low compared to quota level) total benefits under taxes are less than total benefits under quotas by the amount C – the area under the marginal curve corresponding to difference in output under tax and quota. • When marginal benefits are high (so emissions are high) total benefits under taxes are higher than total benefits under quotas by the amount D+E. • Since D+E> C, on average benefits are higher under tax compared to quota. • Experiment by making the slope of the marginal benefit curve less steep. Notice that as you do this, the areas D+E and C become more similar. Conclude that a flatter marginal benefit curve (i.e. a flatter marginal abatement cost curve) reduces the advantage of a tax.
Expected benefits are higher under taxes (expected abatement costs are lower under taxes) High and low marginal benefits and different levels of emissions D C E
Summarize comparison • Quotas lead to lower expected damages (compared to tax). Taxes lead to lower expected abatement costs (i.e. higher benefits of emissions) compared to quotas. • The net advantage depends on which curve – marginal benefit or marginal damage – is steeper. • Flatter marginal damages favor taxes. (Steeper marginal damages favor quotas.) Flatter marginal benefits (i.e. flatter marginal abatement costs) favor quotas. (Steeper marginal benefits favor taxes.)
Another perspective • Taxes make it possible to “arbitrage emissions across states of nature”. When it is cheap to abate, we abate a lot. When it is expensive to abate, we abate less. Quotas do not permit this kind of arbitrage. • Because marginal damages increase, a unit increase in emissions creates more environmental harm than the environmental benefit due to a decrease in emissions. Therefore, on average environmental harm is higher with taxes. (Discuss Jensen’s inequality if there is time.)
Relation to global warming • Model above is “static”. It assumes that current emissions determine both abatement costs and also environmental damages. • GHGs are a “stock” pollutant. Emissions today cause a stream of future damages. We need a dynamic model to compare policies for controlling GHGs.
Complications arising from dynamics • We need to decide how to trade-off between current and future costs. • We need to know the “persistence” of the stock – how long it hangs around. • We need to decide whether future policies are set in stone today, or whether they will be adjusted in light of information that we receive in the future. (Economists and engineers call the former an “open-loop policy, and call the latter a “feedback policy”.)
Intuition from static model still useful • The chief piece of intuition from static model is that “flat” marginal damage function encourages use of tax rather than quota. • Because damages are caused by stock rather than flow of GHG, fluctuations in the flow causes only small increase in expected damages: if we chose taxes and emit a bit more this decade we can make it up by emitting a bit less the next decade. • Most models show that taxes are more efficient than quotas for controlling GHGs.
Hybrid policies • The chief (economic) disadvantage of the quota is that it could lead to very high marginal abatement costs. • A particular hybrid policy uses a quota with a price ceiling. If the price of a quota license reaches a ceiling, the govt provides more licenses (increases the quota) to keep the price from exceeding the ceiling. • Taxes and quotas are each just a “special case” of the this hybrid policy. The hybrid policy can be adjusted so that it has some of the advantages and disadvantages of both the tax and quota. Since the hybrid policy is more flexible than either the tax or quota, it is at least potentially more efficient. It is also (slightly) more complicated – a disadvantage for any policy.
Determining optimal level of abatement • Discussion above examined optimal choice of policy – the means by which we achieve a particular objective. • Now I want to consider how we determine the optimal level of abatement. This requires “balancing” costs and benefits for groups that differ by geographic location, income, time during which they alive, and many other considerations
The basic point • Costs of reducing emissions, and the costs of climate change, occur to people in different locations and at different points in time. • Abatement costs are likely to fall on people in the near term, in richer countries (since they are the ones – presumably – doing the abating). • Costs of climate change are likely to fall most heavily on poorer people, in the (possibly distant) future – since climate change will occur in the future and will disproportionately affect the South. • A cost-benefit analysis of abatement effort requires that we make these costs comparable.
Comparing costs over different income groups • “Decreasing marginal utility of income” says that an extra dollar is worth less to a rich person than to a poor person. Compare the magnitudes “a” and “b”. utility b a income
Weighting costs for different income groups • Suppose that one dollar is worth 50% more to a poor person than to a rich person. • Suppose that a “project” (e.g. reducing CO2 concentration) costs the rich 1 unit of income (e.g. $100 billion). • By how much (x) does the project have to increase poor income by (e.g. by avoiding costs that they incur from climate change) for the project to increase welfare? • Answer: x(1.5)>1, i.e. x>.66 • I multiplied x (the savings to the poor) by 1.5 because (by assumption) one unit of income for rich is worth 1.5 units of income to poor.
Discussion of example • This example says that the project increases aggregate utility if it saves the poor at least .66 units of income – even though it costs the rich 1.0 unit of income. • I used the “price” 1.5 to convert units of “income to poor” into “income to rich”. • (We use prices all the time to make the values of different goods – apples and oranges – commensurable.) • Practical significance: In the Stern report, weighting the income of the poor more heavily leads to an increase from 15% to 20% of the estimate of value of annual reduction in gross world product, due to concentration of 550 ppm of GHG.
Effects of giving higher weight to income of poor • Since climate change is more likely to harm the poor than the rich, increasing the weight given to the poor (in the cost benefit analysis) increases the estimated cost of climate change. • This weighting scheme leads to an increase in the recommended level of abatement (and the costs of abatement) that society should be willing to incur.
Arguments for and against this kind of weighting • Pro: It reflects a reasonable ethical judgment. • Con: (i) The weights are very subjective. You can get “any kind of answer” by choice of weights. This subjective element reduces the value of the exercise. • Con: (ii) Climate change policy is an inefficient means of transferring income. We have more efficient methods of transferring income.
Elaborate on efficiency argument • Suppose (using my example above) that the project costs the rich 1 unit of income and increases the income of the poor by 0.8 units. This project increases world welfare, because 1.5(0.8)>1. • However, both the rich and the poor would be better off if the rich simply gave the poor 0.9 units of income, rather than undertaking the project. • The same logic holds whenever the project increases income of poor by less than 1 unit of income. • Thus, the test for efficiency of the project is not related to the weight we give to the income of the poor.
More on the efficiency argument • The basic point of the argument against using different weights on income of rich and poor is that doing so encourages viewing climate change policy as a means of redressing income inequality. • Climate change policy should be “targeted” to the problem of climate change, not to the problem of unfair income distribution. Climate change policy would be a very “leaky bucket” if it were used to transfer income. • The objection to efficiency argument is that it is a theoretical test: it asks whether it would be possible for the winners to compensate the losers. It does not ask whether the winners actually compensate the losers.
Two examples of costs and benefits of climate change policy • Number in ( ) shows weighted benefits as in example above, where income of poor is weighted 50% higher than that of rich. • If we use equal weights for the rich and the poor benefits, neither of these projects should be undertaken. Neither of these projects passes the efficiency test. • If we weight the poor benefits by 1.5 of rich benefits (as in my example), the first but not the second project should be undertaken.
Comparing costs and benefits over time • Discussion above considered whether costs and benefits for different income groups should be weighted equally. • Now I want to consider how to “add up” costs and benefits that occur at different points in time. • In order to do this, we use a discount factor.
The need for discount rates • We can’t add apples and oranges. We need to convert them to a common unit (e.g. pieces of fruit) in order to add them. Ten dollars today and ten dollars a year from now are both in units of dollars, so it might seem that it makes sense to add them up. • However, a dollar today is generally not the same as a dollar a year from now. There is an opportunity cost of delaying receipt of the dollar. Therefore, to add up dollars in different periods, we need to convert them to common units. • Discount rates (or discount factors) are used to make this conversion. We use the discount factor to convert a “future dollar” into units of “today’s dollar”. This conversion is called “the present value” of the future dollar.
Discount rates and discount factors • If I face an annual interest rate of 5%, I am indifferent between $0.9524 today and $1 in one year: investing $0.9524 for one year gives me (1.05)0.9524=1. • If I face an annual interest rate of r%, I am indifferent between 1/(1.0+.0r) today and $1 in one year. • (Converting from percentages to numbers: The numerical value of a discount rate of 5% is .05, so the numerical value of a discount rate of r% is .0r.) • 1+.0r = the number of dollars I need to receive one year from now in order to be willing to give up one dollar today. • 1/(1+.0r) is the one year discount factor corresponding to a one year interest rate (also called the “discount rate”) of r%. • The discount factor is the “price” today of one dollar in one year. • A larger discount rate translates to a smaller discount factor.
The “tyranny” of compound discounting • The “price” today of one dollar n years from now is 1/(1+.0r)**n. (This is 1/(1+.0r)) raised to the n.) • This is the amount that I would be willing to pay today (e.g. in order to reduce GHG emissions) to avoid having to pay $1 (e.g., resulting from climate change) n years from now. • Table shows amount we would pay today to avoid $100 in damages at different future times. • With a non-negligible discount rate, we would not spend much to avoid damages in the distant future
The social discount rate • The social discount rate is used to compare costs and benefits at different points in time for a public project (such as climate change policy). • It is analogous to the private discount rate (or interest rate), except that it reflects society’s preferences and opportunity costs, rather than the individual’s. • If the annual social discount rate is r, the discount factor for n years in the future (the “price” today of one dollar of income n years in the future) is 1/(1+.0r)**n. (“**” means “raised to the n”).
The components of the social discount rate • The social discount rate equals: (pure rate of time preference) + (elasticity of marginal utility times growth rate of income). • Pure rate of time preference reflects society’s preference to consume earlier rather than later. A larger value means that we are more impatient, i.e. that we place less weight on the utility of future generations. A larger value means that the current generation is more selfish. Thus, low values of the pure rate of time preference are often defended on ethical grounds. • Elasticity reflects our willingness to have different income levels in different periods. A larger value means we care less about income equality over different periods in time (i.e. we care less about “smoothing” income over time). • If income is growing, we are less willing to transfer income to the future. • Larger social discount rate means that we put less weight on future.
Should the pure rate of time preference be constant? • A pure rate of time preference of 5% means that society would be willing to give up $1.65 in ten years in order to avoid having to pay $1 today. • How much would we be willing to take away from the generation living 210 years from now, in order to give $1 to the generation living 200 years from now? • We can distinguish between individuals consuming now and ten years from now, so we might have a preference for one group rather than the other – leading to a positive pure rate of time preference for the near term. • We can’t (?) distinguish between generations living in the distant future, so why should we have a positive pure rate of time governing consumption in the distant future? • This argument suggests that the pure rate of time preference should be a decreasing function of “time in the future”, possibly approaching 0.
Effects of a declining pure rate of time preference • It makes us put more weight on the future. • A declining pure rate of time preference also means that the optimal program is (typically) “time inconsistent”. • One form of time inconsistency is the desire to procrastinate. We want to put off costs (or something unpleasant) until “the future”. But when the “the future” arrives, it has become “the present” – so we still want to put off costs. • “Time inconsistent” programs are not “plausible”. It is technically harder to obtain “time consistent” programs. We need to solve a game amongst a succession of agents.
The economic value of reducing risks • Risky events are those that might occur in the future. Since we incur costs today to reduce these risks, we need to compare the discounted expected future benefits to the current costs. • We can measure the risk of an event (e.g. an abrupt increase in sea level) using a “hazard rate”, which I call h. The hazard rate is the probability that the event occurs over a given unit of time (e.g. one year) given that it has not yet occurred. • With typical social discount rates (e.g. 3-5%) we would not be willing to pay much to reduce the risk of a low probability event.
The reason we would not spend much to reduce these risks • Low probability events are those with low hazard rates (h). • These events are not likely to occur until the distant future. • With non-negligible discounting, we don’t care about the distant future. • (But the distant future lasts a long time.)
Example to show magnitudes • Suppose that an “event” (which occurs at a random time) reduces flow of utility by 1 util (e.g. 1 util = $100 billion per year). • Let h = constant hazard rate of this event. • Suppose that we can eliminate the risk (set h=0) by sacrificing the flow x. • What is the maximum amount that we would be willing to give up in order to eliminate the risk?
Solid line: graph of utility flow if “the event” occurs at (random) time T. Dashed line: graph of utility flow when risk is eliminated income U+1 U+1-x U 0 time T
How much would we spend to eliminate risk? • The expected present discounted value (PDV) of the risky flow is 1/(r+h). • The PDV of the safe flow is (1-x)/r. • The largest x we would accept in order to eliminate the risk is x*= h/(h+r) • If r=0.05 and there is a 5% risk of occurrence per century, x*=.01 (WTP is 1% of value at risk.)
Point of this example • This example shows that if we have a constant and non-negligible pure rate of time preference, and if the hazard rate is low, we should not spend much to eliminate the risk. • The model leading to this conclusion is “coherent” (logically correct), but it is based on the assumption that the pure rate of time preference remains much greater than 0. • Models that assume that pure rate of time preference remains much larger than hazard rate have a “built in” conclusion that it is not worth spending much to reduce the risk. • The conclusions of these models are based on an implicit ethical judgment, not just on “science”.
A different view • If the pure rate of time preference declines (as I argued above that it “should”), a cost benefit analysis implies that society should be willing to spend much more in order to reduce the risk of low probability catastrophic events. (See the paper “Discounting” in the box of lecture notes.)
A different perspective on low probability events • Most models of climate change assume that utility is concave in consumption (i.e., decreasing marginal utility of consumption). Climate change makes consumption riskier. • Most of these models use numerical methods to calculate the value of reducing risk. • These numerical models typically “truncate” the distribution: if the probability of the even is below some threshold, the model sets the probability equal to 0.
The effect of “truncating the distribution” • The expected cost of the event equals the probability of the event times the cost given that the event occurs. Even if the probability is extremely small, the expected cost can be very large. • When utility is concave in consumption, the loss of an additional unit of consumption (starting from a low level of consumption), can lead to a large loss in utility. • Ignoring very low probability events can therefore substantially reduce the expected utility costs of climate change, thereby leading to an underestimate of the amount that society should be willing to spend to abate GHGs.
