[Econ 8852](
[Prof. Richard L. Sweeney](

[to print slides, append "?print-pdf" to the url]


Theory recap

Review of the first best

The short run (conditional on $J$ firms) optimality conditions:

  1. marginal benefits of consumption equal marginal costs
\[P(X) = C^j_{x_j}(x_j,e_j)\]
  1. marginal abatement costs at each firm are equal to aggregate marginal damages
\[D'(E) = -C^j_{e_j}(x_j,e_j)\]

Necessary condition, cost-effectiveness, is the primary motivation for cap and trade.

Cap and Trade

The regulator issues $L$ emission permits

If permits are auctioned at clearing price $\sigma$, firm’s maximize \(\Pi_j(x_j,e_j) = px_j - C^j(x_j,e_j) - \sigma e_j\)

Assume the market good price $p$ and emission price $\sigma$ are taken as given.*

Yields FOCs: \(\begin{eqnarray} P(X) &=& C^j_{x_j}(x_j,e_j) \\ \sigma &=& -C^j_{e_j}(x_j,e_j) \end{eqnarray}\)

Define $e_j^*$ as the optimal amount of emissions for each firm under the cap.

Comparison with an emissions standard

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].

In practice, emissions standards are typically set on an average

(rather than a firm-specific basis)

For example, if there are $J$ polluting firms, the regulator might set \(\bar e_j = \bar e = L/J \quad \forall j\)

If firms are heterogenous, then the necessary condition for cost-effectiveness will not be met.


Consider the case where this is binding for all firms.

They maximize \(\Pi(x_j,\bar e) = px - C(x,\bar e)\) With FOC: \(p= C_x(x,\bar e)\)

If firms are homogenous, ie \(C^j_e(x_j, e_j) = C_e(x_j,e_j) \; \forall j\), then the solution is again equally efficient.

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)

A more common approach is to set an emission rate standard.

For example, the regulator could pick a level of emissions per unit $\alpha$, so $e=\alpha x$.

Firms now maximize \(\Pi(x) = px - C(x,\alpha x)\) With FOC: \(p = C_x(x,\alpha x) + \alpha C_e(x,\alpha x)\)

Summary: Cap-and-trade vs uniform rate

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.


Plugging into the FOC,

\[p = C_x(x(\alpha),\bar e) + \alpha C_e(x(\alpha),\bar e)\]

Noting that $-C_e() > 0$, we can compare this the FOC from the uniform level ,

\[p -\alpha C_e(x(\alpha),\bar e) = C_x(x(\alpha),\bar e) > p = C_x(x(\bar e),\bar e)\]

From this it is clear that:

  1. $x(\alpha) > x(\bar e)$
  2. $-C_e(x(\alpha),\bar e) > -C_e(x(\bar e),\bar e)$

Also note: \(C_x(x(\alpha),\bar e) > p\)which implies that that the regulator could not have simply set $\alpha = E^*/X(\bar e)$.

How large are the cost savings from from cap-and-trade?

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.

Acid Rain Program

Title IV of the Clean Air Act Amendments of 1990

Small part of much bigger bill. Basically everything else command and control.

The Cap

Target not chosen to maximize net economic benefits


Banking and borrowing

Three compliance options

  1. Burn less coal (can just reduce output)

  2. Install a scrubber to remove sulfur from emissions

  3. 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.

Carlson et al (2000) provide and early and widely cited evaluation of the ARP

Research Questions:

  1. How much does cap-and-trade reduce costs, compared to command and control (a uniform standard)?
    • How much of heralded cost savings due to program?
  2. Are these gains realized immediately? Or does the market take time?

Empirical strategy

Main results: Cost function

Main results: Cost Effectiveness

Is this the true policy cost?

The abatement cost of going from $\hat e^x$ to $e$ is typically defined as \(\psi(x,e) = C(x,e) - C(x,\hat e^x)\) with the marginal cost of emissions reductions at a given $x$, $C_e(x,e)$.

However, in this setup, with fixed marginal revenue $p$, an increase in costs will also lead to a reduction in output.


AER, 2010


Electricity regulation

How regulation works

“Regulated” markets:

“Deregulated” markets

Dispatch curve


Why would regulation affect the cost effectiveness of compliance decisions?

Fowlie studies the NOx Budget Program

Important feature:

Different compliance options available to firms


Research Question


How do pre-existing market distortions affect performance of cap-and-trade?


  1. Has heterogeneity in electricity market regulation affected how coal plant managers chose to comply with a regional NOx emissions trading program?

  2. What were the environmental implications?

What is the empirical strategy?

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)

Program States


Merchant generation share by state (2015)


What do you think of this empirical strategy?

Says this is viable for three reasons:

  1. Restructuring entirely determined pre NBP
  2. Restructuring driven by having high electricity prices.
    • is this helpful?
  3. Plants compliance options similar across regulated and non-regulated states

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.


What does she do?

How does this compare to what Carlson et al did?

Summary stats

What econometric techniques are employed?

Assume firms face the following (latent) cost structure

\[C_{nj} = \alpha_j + \beta^v_n v_{nj} + \beta^k_n K_{nj} + \beta^{KA}K_{nj}Age_{nj} + \epsilon_{nj}\] \[V_{nj} = (V_{nj} + \tau m_{nj})Q_n\]

Goal of paper is to test if $\beta^v_n$ and $\beta^k_n$ differ for regulated and deregulated firms.

How does she do this?

Conditional Logit

Probability the $n$ unit chooses compliance option $i$:

\[P(y_n = i| X_n,\beta)=\dfrac{e^{\beta'X_{ni}}}{\sum\limits_{j=1}^{J_n} e^{\beta'X_{nj}}}\]

What are the limitations of this model?

  1. Conditional on $X$, choice probabilities are the same, and errors are assumed independent
    • Fowlie says other factors that vary unobservably across facilities might affect tastes
  2. Panel nature of the data
    • Same firm makes (presumably) correlated decisions across multiple plants/ boilers.

What were the other options here?

Random Coefficient Logit

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.

\[P(Y_m = i| X_m,\beta_m) = \prod_{t=1}^{T_m} \frac{e^{\beta_m'X_{mit}}}{\sum\limits_{j=1}^{J_{mt}}e^{\beta_m'X_{mjt}}}\]

Unconditional probabilities recovered by integrating over distribution of $\beta$

Let $b$ and $\Omega$ define the vector of coefficient means and variances.

Parameters then chosen to maximize:

\[l(b,\Omega) = \sum_{m=1}^{M} \ln \int\limits^{\infty}_{-\infty} \prod_{t=1}^{T_m}\frac{e^{\beta_m'X_{mit}}}{\sum\limits_{j=1}^{J_{mt}}e^{\beta_m'X_{mjt}}} f(\beta | b,\Omega) d \beta\]

How to actually do this

Estimated with simulated MLE

  1. guess $b$ and $\omega$

  2. for each manager take 1000 draws to calculate the integrand in $l(b,\Omega)$

  3. Search over parameters to maximize likelihood of observed choices across all managers

What identifies $b$ and $\Omega$?


Recovering manager-specific parameters

Can write likelihood of type as function of choices

(conditional on estimates)

\[h(\beta| Y_m,X_m,b,\Omega) = \frac{P(Y_m | X_m,\beta)f(\beta | b,\Omega) }{P(Y_m | X_m,b,\Omega)}\]







Required Readings

Carslon et. al. (2000) [link]
Mendelsohn and Muller (2009) [link]