The short run (conditional on $J$ firms) optimality conditions:
Necessary condition, cost-effectiveness, is the primary motivation for cap and trade.
The regulator issues $L$ emission permits
If permits are auctioned at clearing price $\sigma$, firm's maximize
Assume the market good price $p$ and emission price $\sigma$ are taken as given.*
Yields FOCs:
Define $e_j^*$ as the optimal amount of emissions for each firm under the cap.
In the simplest case, instead of issuing permits, the regulator fixes the total amount of emissions at each firm, $e_j \le \bar e_j$.
If the regulator simply sets $\bar e_j = e_j^*$ then this policy is equivalent to the cap from an efficiency perspective.
[Note that the regulator loses revenue $\sigma L$ compared to the auctioned permits case].
(rather than a firm-specific basis)
For example, if there are $J$ polluting firms, the regulator might set
If firms are heterogenous, then the necessary condition for cost-effectiveness will not be met.
[Notes:]
Consider the case where this is binding for all firms.
They maximize
If firms are homogenous, ie
If firms are heterogenous, then the necessary condition for cost-effectiveness will not be met.
A more obvious problem is that if firms are very different (for example different sizes)
For example, the regulator could pick a level of emissions per unit $\alpha$, so $e=\alpha x$.
Firms now maximize
Can show that a uniform emission standard achieves its E at greater output levels and higher cost than a uniform standard (or a cap)
Intuition: Under a emission rate standard, the firm can "comply" by increasing output.
[Notes:]
Plugging into the FOC,
Noting that $-C_e() > 0$, we can compare this the FOC from the uniform level ,
From this it is clear that:
Also note:
Clearly depends on the shape and distribution in abatement cost functions over the relevant range.
In practice will also depend on
C&T has been implemented in US leaded gasoline, SO2, and numerous CO2 policies world wide.
For a recent review of major programs to date, see Stavins and Schmalensee (REEP 2019).
For a list of global C&T policies in place, see World Bank 2018.
Small part of much bigger bill. Basically everything else command and control.
The Cap
Target not chosen to maximize net economic benefits
Allocation
Banking and borrowing
Burn less coal (can just reduce output)
Install a scrubber to remove sulfur from emissions
Fuel switch to a lower sulfur coal.
Ex ante, people were afraid of 1 and thought 2 was the most important strategy. Ex post it was primarily 3.
Research Questions:
How much does cap-and-trade reduce costs, compared to command and control (a uniform standard)?
Are these gains realized immediately? Or does the market take time?
Estimate cost of producing electricity as a function of output, input, capital and coal type
Hold cost function as fixed and calculate costs of meeting same quantity under alternative policies:
The abatement cost of going from $\hat e^x$ to $e$ is typically defined as
However, in this setup, with fixed marginal revenue $p$, an increase in costs will also lead to a reduction in output.
In SO2 program, costs did not appear minimized.
One possible explanation is other factors / constraints which also distort behavior in this sector.
Fowlie (2009) looks at one particularly obvious and important one: electricity regulation.
Historically electric power was entirely vertically integrated, and believed to be a natural monopoly.
Cost overruns/ poor investments in 70's and 80's lead people to reconsider this
Realization that while distribution was a natural monopoly (probably...), electric power generation need not be
For a recent review of experience with deregulation, see Borenstein and Bushnell (2015)
Fowlie says by 2001, 19 states had deregulated.
"Regulated" markets:
"Deregulated" markets
Regulation tied to capital (Averch and Johnson 1962)
General lack of price incentives (Fabrizio, Rose and Wolfram AER)
Political incentives (Cicala 2015)
NOx is a precursor for tropospheric ozone (O3)
19 eastern states covered
Important feature:
Broad:
How do pre-existing market distortions affect performance of cap-and-trade?
Specific:
Has heterogeneity in electricity market regulation affected how coal plant managers chose to comply with a regional NOx emissions trading program?
What were the environmental implications?
Says "ideally coal generators would be randomly assigned to different regulatory regimes"
Instead relies on interstate variation in electricity market regulation (all covered under the same CAT program)
Says this is viable for three reasons:
Still, at the end of the day, comparison is between northern states with high prices (deregulated) and southern states with low prices (regulated). Up to author to convince us that's still informative.
702 generating units
doesn't observe: variable or fixed costs, or beliefs about resulting emissions from different choices
What does she do?
How does this compare to what Carlson et al did?
Show that regulated firms made different decisions
Then shows that compliance options and costs across the two look basically the same
What are the main estimating equations?
Why not OLS here?
capital costs $K_{nj}$
variable costs $v_{nj}$ a function of permit price and (fixed?) output
How does she do this?
Probability the $n$ unit chooses compliance option $i$:
What are the limitations of this model?
Conditional on $X$, choice probabilities are the same, and errors are assumed independent
Panel nature of the data
What were the other options here?
Assume tastes for capital ($\beta^v$) and capital ($\beta^K$) are distributed bivariate normal, and estimate the mean and variance of that distribution.
Draws from this distribution are assumed constant within manager $m$ across $T_m$ units.
Let $b$ and $\Omega$ define the vector of coefficient means and variances.
Parameters then chosen to maximize:
Estimated with simulated MLE
guess $b$ and $\omega$
for each manager take 1000 draws to calculate the integrand in $l(b,\Omega)$
Search over parameters to maximize likelihood of observed choices across all managers
in estimation, likelihood of each manager's choices based on 1000 draws from same distribution.
Fowlie then attempts to recover where in that distribution each manager's draw was given observed choices
Trick is to apply Bayes Rule
(conditional on estimates)
first term you get from CL formula for a given $\beta$
second term ($f$) recovered already during estimation
denominator can be obtained from simulation