%Paper: ewp-pe/9810006
%From: Taylorleon@aol.com
%Date: Sat, 17 Oct 1998 00:42:45 -0500
%Date (revised): Mon, 19 Oct 1998 01:24:45 -0500
%Date (revised): Tue, 20 Oct 1998 02:40:50 -0500

\documentstyle{article}
\begin{document}
\title{Do the states try to trade off environmental quality
tomorrow for jobs today?}
\author{Leon Taylor\thanks{For perspicacious comments, I thank
Noel Gaston, Jonathan B. Pritchett, Alison Rose, Robert M.
Schwab, Bruce Yandle, and participants at a conference session of
the Eastern Economic Association.  The Senate Committee on
Research at Tulane University gave financial support.}
\\ Division of Business \\ Dillard University
\\ New Orleans, La.\\ Taylorleon@aol.com}
\maketitle
%\tableofcontents
%\listoftables
\pagebreak

{\bf Do The States Try To Trade Off Environmental Quality Tomorrow 
For Jobs Today?}


\begin{abstract}

The paper models and tests the hypothesis that a self-interested
policymaker will pursue projects that create jobs now at the
environmental expense of future generations.  An optimal-control
model shows that jurisdictions are most likely to pursue such a
project when they are characterized by low income, high
unemployment, politically powerful industry, pollution-intensive
industry, poorly functioning land markets, or residents who are
near the end of their lives.  The paper tests the model with OLS
specifications of subnational expenditures per capita in the U.S.
for hazardous waste in the 1980s and for air pollution in the
1960s.  The results reject the hypothesis that jurisdictions try
to trade off future environmental quality for current
manufacturing jobs.  The results instead suggest a powerful
relationship between housing values and environmental
expenditures.   

\end{abstract}


\section{Introduction}

In 1987, a United Nations commission headed by Gro Harlem
Brundtland, prime minister of Norway, asserted that 

\begin{quote}

we borrow environmental capital from future generations with no
intention or prospect of repaying....We act as we do because we
can get away with it:  Future generations do not vote; they have
no political or financial power; they cannot challenge our
decisions (\cite{wced}, p. 8).

\end{quote}

Here are the seeds of an influential idea that I call the
``Brundtland hypothesis":  Societies overuse environmental
assets, because they do not have to fear the retaliation of
future generations. The hypothesis has become a rallying point of
those who seek ``sustainable" limits on resource use.  Yet it is
not obviously true.  Land markets might discipline polluters by
cutting property values by the present value of future pollution
damages.\footnote{Oates and Schwab discuss this argument in 
\cite{oates}.}  Through an
overlap in generations, the young might discipline the old. 
Finally, an individual might care about his progeny though not
about an entire future generation.  Recognizing that other
individuals are like him, he might contract with them to provide
a public good to the future generation in order to protect the
interests of his progeny.\footnote{ This rationale might justify
national policies to protect the interests of future generations.

Such policies would differ from the ``sustainability" paradigm
because they would not try to coerce individuals alive today to
act against their interests.}

The Brundtland hypothesis needs empirical testing.  Toward that
end, this paper will develop a model that assumes that the
Brundtland hypothesis is true.  From that model, it will develop
and test six implications.
  
The paper departs somewhat from the literature on environmental
public choice.  This literature has focused on short-lived
pollutants, which generate economic benefits and environmental
costs at the same time.\footnote{I know of no published survey of
economic papers that focuses on environmental decision-making by
self-interested public officials.  Yandle provides lively
discussion of several themes in the literature \cite{yandle1}.}   

 As a utility burns coal to generate electricity, it generates
jobs.  It also generates an eyesore, a smoke plume, which
normally dissipates quickly.  Because short-lived pollution
imposes benefits and costs at the same time, the policymaker has
some incentive to try to manage it in a way that enhances
efficiency, if spatial spillovers do not occur.
  
The paper will instead consider long-lived pollutants, which
generate benefits now and costs later.  For instance, production
of nuclear weapons during the Cold War created thousands of jobs
in rural regions, like eastern Washington.  But production also
created nuclear wastes that will remain radioactive for thousands
of years.  Did the lack of safeguards result partly from a
perceived delay in environmental costs?\footnote{ Another
example:  Lead has accumulated in soil near heavy metal smelters
and near roads in countries (particularly Mexico) that have used
lead-based gasoline \cite{allaby}.  Lead has also accumulated in
the bones and tissue of small children, largely from vehicle
exhaust and lead-based paint.  Over time, the build-up of lead
might cause mental retardation, blindness and chronic kidney
disease \cite{salvato}.  The health costs of lead occur years
after its economic benefits -- the creation of jobs for painters,
drivers and smelter workers, for instance. }      


The paper offers a stylized model of a policymaker's tradeoff
between jobs and environmental quality.  The policymaker is a
careerist whose main goal is to stay in office.\footnote{ 
Wilson's survey suggests that ideology {\sl may} influence
policymakers -- but career incentives almost certainly do
\cite{wilson}.}  She must balance the interests of two groups. 
One favors development; the other, the environment.  By
attracting industry to her jurisdiction, the policymaker creates
jobs for now, but at the expense of creating future pollution.

The model particularly concerns jurisdictions with chronic
unemployment and with many low-skill workers, since these are the
jurisdictions that compete most keenly for polluting industry. 
Because the analysis focuses on the case in which unemployment is
structural, it usually assumes that neither the wage nor
migration clears the labor market.\footnote{ The model holds
labor immobile with respect to variations in environmental
standards.  In reality, catastrophes spur migration.  But over
the time horizon $ T $ that will concern us, day-to-day decisions
about environmental standards are more likely to influence the
flow of capital than of labor.}

My aim in modeling is not to argue that myopic behavior occurs
but to create tests of whether it occurs.  Here are the
intuitions behind the main implication that I will test:  Suppose
that a pollutant would linger in the environment for 30 years. 
Suppose that residents worry about their lives, not future lives;
suppose that they do not concern themselves with any overlap in
generations.  Suppose that they expect to live only 10 more
years.  Suppose that they select, for time $ t $, the rate of
pollution emissions that is optimal for them.  Then increasing
their life expectancy by 20 more years -- say, beyond time $ T $
-- will lead them to decrease future levels of pollution
(measured, for instance, as atmospheric concentrations) by
decreasing the rate of emission at time $ t $.  For, when they
expect to live longer, then they will worry more about the
lingering effects of pollution emitted today, and they will wish
to cut emissions.  

Now suppose that residents worry as much about future lives as
about their own.  Then changing the expected length of the rest
of their own lives will not affect the pollution level allowed. 
Since they act as if generations did not overlap, they
mentally delay the start of the next generation by the addition
to their own years; in effect, over the period from $ T $ to $ T
+ 20 $, they substitute 20 years of their own lives for those of
the next generation.  Since they care no more about their own
lives than about future lives, the substitution does not
affect the way that they value emissions.

Finally, suppose that residents do concern themselves with the
overlap in generations.  Then an increase in their life
expectancy will lead them to decrease emissions at time $ t $
whether or not they value future lives as much as their own.

The paper follows this plan.  Section II develops the model and
extracts from it tests of the Brundtland hypothesis. 
Section III presents my tests on cross-sectional data in the
United States.  I cannot support the Brundtland hypothesis, but
it embodies a large idea. I also cannot support the corollary
hypothesis that jurisdictions try to trade off future
environmental quality for current jobs.  Section IV discusses the
results and suggests a new orientation for research into
environmental federalism.

Before detailing the model, I note three assumptions.  The model
concerns the decision of one jurisdiction; it holds fixed the
decisions of all others. Agents know the future consequences of
environmental decisions.  All agents die at time $ T $, succeeded
by a new generation.  These assumptions are in the spirit of the
Brundtland hypothesis, and they sharpen results.  

\section{The model}


All agents, including the policymaker, are born at time 0, when
they begin working.  They keep working until time $ T $.  They
know that they will die at $ T $, and they don't care what
happens after they die.  

Pollution creates ``blue-collar" jobs only.  Other jobs are
``white-collar."  Pollution afflicts all workers.  A policymaker
must reconcile the conflict between blue-collar jobs and
environmental quality.  He must court both groups of workers.    

Each group is homogeneous.  The subscript $ w $ denotes the
white-collar group, with $ N_w (t) $ workers at time $ t $; the
subscript $ b $ denotes the blue-collar group, with $ N_b (t) $ 
workers.  The employer pays each worker salary $ {Y^0}_i (t) $, 
$ i = b,w $.  Not all blue-collar workers have jobs.  Those 
not employed receive exogenous income, $ {Y^1}_b (t) $.

There are $ L_i (t) $ jobs in group $ i $, where 
$ L_i (t) \leq N_i (t) $ for all
$ t \in [0,T] $.  In each group, the jobs are identical.  
All white-collar workers have jobs: $ L_w (t) = N_w (t) $ 
for all $ t \in  [0,T] $.\footnote{ To permit white-collar
unemployment is to complicate the model, not enrich it.}  Each
blue-collar worker faces two states at time $ t $, employment and
unemployment.  The respective probabilities of the states are 

\begin{equation}
\frac{L_b (t) }{N_b (t) }, \; 
\frac{N_b (t) - L_b (t)}{N_b (t)}.
\end{equation}

At time $ t $, manufacturing generates a residual called
pollution, $ S(t) $.  Pollution and labor are complementary
inputs.  If the policymaker wants firms to create more 
blue-collar jobs, he must let them produce -- and pollute -- 
more.  The number of blue-collar jobs created at time 
$ t $ in his jurisdiction is given by 

\begin{equation}
\label{labor}
L_b (t) = f \left[ S(t), Y_b (t) \right], \;
0 \leq L_b(t) \leq N_b (t),
\end{equation}  and characterized by 

\begin{eqnarray}
\label{partials}
\frac{\partial f}{\partial S} & > & 0 \; S < S_0, \nonumber\\
\frac{\partial f}{\partial S} & = & 0 \; S = S_0,  \nonumber\\
\frac{\partial f}{\partial S} & < & 0 \; S > S_0, \nonumber\\
\frac{\partial^2 f}{\partial S^2} & < & 0 
\; \frac{\partial f}{\partial Y} < 0, \nonumber\\
                               &  & S_0 > 0.
\end{eqnarray}

Emissions exceeding $ S_0 $  hinder workers so much that firms
will eliminate jobs. 
     
$ S(t) $ is a flow, a change in the pollution stock, $ P(t) $.  
$ S > 0 $ denotes emissions; $ S < 0 $ denotes cleanup.  
The pollution stock decays at rate $ d(t) $, 
$ 0 \leq d \leq 1 $: 

\begin{eqnarray}
\label{stock}
\frac{\partial P}{\partial t} & = & S(t) - d(t) P(t), \nonumber\\ 
                         P(0) & = & P_0 \geq 0.
\end{eqnarray}

Equating $ d $ to 1 gives the classical case of a pollutant that
dissipates immediately.  Equating $ d $ to 0 gives a pollutant
that never dissipates.  Iodine-129, a fission product of uranium 235,
almost fills that bill; its half-life stretches into millions of
years.\footnote{ See \cite{carter}.}

All residents suffer from $ P(t) $.  Blue- and white-collar
workers have utility functions $ V_i $ of the von 
Neumann-Morgenstern form, $ i = b,w $:
     
\begin{equation}
V_i (t) = \frac{L_i (t)}{N_i (t)} 
U \left[ {Y^0}_i (t), P(t) \right] + 
\frac{N_i (t) - L_i (t)}{ N_i (t)}
U \left[ {Y^1}_i (t), P(t) \right], 
\end{equation}

\begin{equation}
\frac{\partial U}{\partial Y} > 0 
\; \frac{\partial^2 U}{\partial Y^2} < 0, 
\end{equation}

\begin{equation}
\frac{\partial U}{\partial P} < 0 
\; \frac{\partial^2 U}{\partial P^2} < 0,
\end{equation}

\begin{equation}
\label{cross}
\frac{\partial^2 U}{\partial P \partial Y} < 0.
\end{equation}


Equation (\ref{cross}) reflects the observation that the rich
value environmental quality more than the poor.\footnote {See 
\cite{baumol}.}  

\subsection{The policymaker's problem}

The policymaker maximizes a weighted average of the welfare
of constituents over his career.  He might be a politician, who
considers voter welfare to win elections.  He might be a
regulator, who considers constituent welfare to win promotions. 
I assume that a committee, containing conflicting interests,
would make the same decision as a single leader who reconciles
these interests.  I posit that in a democracy with complete
information, the number of decision-makers affects the time and
resource costs of the decision; it does not affect the decision
itself.\footnote{ Here's an example.  Historically, the governor
of Minnesota has been weak.  The state has made key decisions
through small advocacy agencies run by committee.  Environmental
decisions were made by a Pollution Control Board.  Each of its
nine members represented an interest group, such as farmers,
industrialists and environmentalists \cite{haskell}.  I assume
that one can model such committee decisions as if they were made
by one person.}     

This is a dialectic model of interest groups.\footnote{ See  
\cite{becker}.}  The policymaker weights the welfare of the 
blue- and white-collar groups in terms of their political power.  
The blue-collar group weight is $ \alpha N_b $; the white-collar 
group weight is $ ( 1 - \alpha ) N_w $.  Each
group weight has two parts.  One part reflects group size -- 
$ N_b $ for the blue-collar group; $ N_w $ for the white-collar 
group.  Were all other things equal, then the larger the group, 
the greater its political influence.  

Not all other things are equal, however:  The political
influence of a group also depends upon the contribution of an
average member to its efforts.  By normalizing, I denote the
level of a member's contribution as $ \alpha $ in the blue-collar group
and as $ ( 1 - \alpha ) $ in the white-collar group.  The 
level of a member's contribution depends inversely on group size.  
In large groups, the temptation to free ride is great.\footnote{  
See \cite{olson} and \cite{stigler}.}  Adding a member to either
group will increase its political influence at a diminishing
rate.

The policymaker projects the effects of policy only for the
rest of the voter's (and policymaker's) life.\footnote{ A career
might span several terms in office. 

The supposition that the policymaker projects policy only up to
time $ T $ is part of the Brundtland hypothesis.  A skeptical reader
might ask why voters would condone such decisions.  Here are two
reasons.  The expected value of an election to a voter is small;
his incentive to think carefully about electoral issues is
meager.  Even with complete and perfect information, thinking
about the distant future is hard, because it requires one to
synthesize much information.  The voter will content himself with
analysis of the rest of his life.  

Second, some environmental costs will fall upon future
generations, which do not engage the voter's sympathy as deeply
as his own does.  Empirical evidence for this view exists. 
Cropper et al. surveyed, by telephone, several thousand
households in the United States.  They found that Program A,
undertaken 25 years from now, would have to save four times as
many lives as Program B, undertaken today, before respondents
would prefer A \cite{cropper}.}     

The discount rate of the policymaker, $ r(t) $, expresses the
immediacy with which he makes his reputation.  The policymaker's
first decisions go far toward establishing him, in the minds of
voters, as competent or not, an environmentalist or not.  I
assume that $ r > 0 $ for all $ t \in [0,T] $.  Where journalists 
are aggressive, voters' memories are likely to be long -- and 
$ r $ large.  ``Current value" is the value that a variable would take
if the policymaker made his reputation at that instant. ``Present
value" reflects the policymaker's history.

The policymaker seeks to maximize

\begin{equation}
\label{maxthis}
\int_0^T e^{-rt} 
\left[ \alpha (t) N_b (t) V_b (t) + ( 1 - \alpha (t) ) 
N_w (t) V_w (t) \right] \, dt
\end{equation}  subject to (\ref{stock}) through (\ref{cross}).  
$ P(t) $ is the state variable; $ S(t) $ is the control.  
The current-value Hamiltonian is\footnote{ I assume
that the objective functional is continuous in the control
trajectory and that the subset containing the trajectory is
compact.  Thus I rule out the possibility of an infinite jump in
pollution.  These assumptions ensure that a solution exists
\cite{intrilligator}.}

\begin{eqnarray}
\label{hamilton}
H (t) = \alpha (t) N_b (t) V_b (t) + 
( 1 - \alpha (t) ) N_w (t) V_w (t)  \nonumber\\
- m(t) \left[ S (t) - d(t) P (t) \right].
\end{eqnarray}

The first line of (\ref{hamilton}) expresses the political 
benefits to the policymaker when he allows emissions at 
time $ t $.  Emissions create blue-collar jobs and -- for 
the policymaker -- blue-collar support.  The second line 
subtracts the political cost of the
increase in the pollution stock, which is incurred over the rest
of the time horizon $ T $.  This cost is the shadow political price
paid by the policymaker for each unit of the pollution stock 
($ m $) times the change in the stock 
($ {\partial P} / {\partial t} = S(t) - d(t)P(t) $).  

The benefits are all of the moment; the costs are spread out
over time, unless the pollutant decays instantly.  In that case,
$ d(t) = 1 $ and $ P(t) = S(t) $ for all $ t  \in [0,T] $.  
The second line of (\ref{hamilton}) becomes zero.  The problem 
becomes static.  The problem is dynamic only if the pollutant 
is durable.  

\subsection{Conditions for optimality}

To maximize (\ref{hamilton}), the policymaker's choice of 
$ S(t) $ must satisfy, for every $ t \in [0,T] $,

\begin{equation}
\label{optimal}
\alpha \frac{\partial L_b}{\partial S} 
\left[ {U^0}_b - {U^1}_b \right] = m.
\end{equation}

Here, $ {U^0}_b $ is the utility of the blue-collar worker when he works;
$ {U^1}_b $ is his utility when he doesn't work.  I will suppose the
worker receives at least as much money when he works as when he
does not.  Thus $ {Y^0}_b \geq {Y^1}_b $ and 
$ {U^0}_b \geq {U^1}_b $.

From (\ref{partials}), the policymaker would gain nothing by choosing
$ S(t) > S_0 $; that choice would decrease jobs and increase
disutility from pollution.  He must choose $ S(t) $ to satisfy the
condition $ {\partial L_b} / {\partial S} \geq 0 $. 
From (\ref{optimal}), it follows that $ m(t) \geq 0 $.     

The left-hand side of (\ref{optimal}) gives the marginal benefit, to
the policymaker, of allowing emissions.  It's the net welfare
gain to blue-collar workers of the added jobs, weighted by the
political power of an average blue-collar worker.  The right-hand
side gives the marginal cost to the policymaker of adding to the
pollution stock.  

Suppose that the cost of one more unit of pollution stock
exceeds the value to the policymaker of the jobs that it
creates.  Formally, suppose that

\begin{equation}
\alpha \frac{\partial L_b}{\partial S} 
\left[{U^0}_b - {U^1}_b \right]  < m.
\end{equation}   Then he will set $ S(t) \leq 0 $, 
instigating a moratorium or a cleanup.  This will boost  
$ {\partial L_b} / {\partial S} $ until the equality in 
(\ref{optimal}) again holds.  

Optimality condition 
(\ref{optimal}) suggests several factors
that make this more likely.  First, the average environmentalist
is quite active ($ \alpha $ is small); perhaps Vermont is an
example.\footnote{ See \cite{barone}.}  Second, pollution
generates few jobs ($ {\partial L_b} / {\partial S} $ is small),
so crackdowns are cheap.  The shift of an economy from
manufacturing to informational services helps
environmentalists.  Third, the net welfare gain of blue-collar
employment to an individual is small.  That scenario is the
policymaker's dream:  Blue- and white-collar interests alike
support moratoria.  Finally, (\ref{optimal}) implies that the 
policymaker will allow higher levels of short-lived pollutants 
than of long-lived ones 
($ {\partial S(t)} / {\partial d} > 0 $, $ t  < T
$).\footnote{ The appendix derives this result.}  One cannot
dismiss the Brundtland hypothesis solely by observing that
governments control long-lived pollutants more strictly than
short-lived ones.  

The multiplier equation yields, for each $ t \in [0,T] $,

\begin{equation}
\label{multiply}
\frac{\partial m}{\partial t} = (r - d) m + 
\left[ \alpha \left( L_b 
\frac{\partial {U^0}_b }{\partial P} + 
[ N_b - L_b] 
\frac{\partial {U^1}_b}{\partial P} \right) 
+ ( 1 - \alpha) N_w 
\frac{\partial U_w}{\partial P} \right].
\end{equation}

I will show later that, under simplifying assumptions, 
$ {\partial m} / {\partial t} < 0 $ for all $ t  \in [0,T] $.  
The policymaker chooses an emissions path that reduces the 
political cost of pollution (in current value terms) over 
time.  Here is the intuition:  As the
hourglass runs out for residents, the future effects of
pollutants become increasingly irrelevant, so the marginal cost
of pollution to the policymaker falls.       

\subsection{Carving out hypotheses to test} 

To derive implications for testing, I will characterize the
path of $ m(t) $ in a simple environment.  

\newtheorem{axiom}{Definition}
\begin{axiom}

A {\bf simple myopic state} exists when 
          
(a)  $ \alpha, r, d, N_i, {Y^j}_b, {Y^0}_w $ and $ L_w $ 
each is constant over $ [0,T] $, where $ i \in \{ b,w \} $ and 
$ j \in \{ 0,1 \}$;

(b) the parameter $ d $ is small enough to ensure that, for
all $ t \in [0,T] $, no unit of the pollutant $ S(t) $ fully 
decays by time $ T $;

(c)  $ {Y^0}_b  > {Y^1}_b $;

(d)  $ {\partial m} / {\partial t} $ is a continuous function 
over $ [0,T] $;

(e) the policymaker chooses $ S(t), t \in [0,T] $, to
maximize (\ref{maxthis}).

\end{axiom}

The restrictions will help me obtain the following theorems,
which yield empirical tests.  Restriction (b) is strong;
Brundtland myopia might arise even if only one unit of $ S(t) $, 
for some $ t $, failed to decay by $ T $.  Control 
problems are complex, however, and their solutions 
often require parameter restrictions. Restriction (d) 
is stronger than the Maximum Principle requires
but entails little loss in economic insight for the problem 
that I have in mind.

\newtheorem{theorem}{Theorem}
\begin{theorem}

Consider any $ t \in [0,T] $. In the simple myopic
state, $ {\partial m} / {\partial t} < 0 $.

\end{theorem}

The appendix shows that $ {\partial m} / {\partial t} \neq 0 $.

\newtheorem{subthrm}{Lemma}
\begin{subthrm}

In the simple myopic state, either 
$ {\partial m} / {\partial t} < 0 $ 
for all $ t \in [0,T] $, or 
$ {\partial m} / {\partial t} > 0 $ 
for all $ t  \in [0,T] $.
               
\end{subthrm}

{\sl Proof of Lemma 1}.  To conserve notation, denote 
$ {\partial m} / {\partial t} $ as $ n $. 
By Definition 1(d), $ n $ is a continuous function, so the
Intermediate-Value Theorem applies.  Suppose $ n(0) < 0 $ 
and $ n(T) > 0 $.  Then there is a $ t \in (0,T) $ such that 
$ n(t) = 0 $.  But that contradicts Proposition 1 in the 
appendix.  A similar argument applies when $ n(0) > 0 $ and 
$ n(T) < 0 $.  It follows that $ n(0) $ and $ n(T) $ have 
the same sign.  

Consider any subset $ [t_1, t_2] $ of $ [0,T] $.  We have that 
$ n:[0,T] \rightarrow \Re^1 $ is a continuous function. 
So $ n:[t_1, t_2] \rightarrow \Re^1 $ is also a
continuous function.  From the argument in the preceding
paragraph, it follows that $ n(t_1) $ and $ n(t_2) $ 
have the same sign. 
     
{\sl Proof of Theorem 1}. Suppose that $ n > 0 $ in the neighborhood 
of $ T $.  By the transversality condition, $ m(T) = 0 $.  
So $ m( T - \epsilon ) < 0 $, where $ \epsilon $ is positive 
but arbitrarily small.  But by (\ref{optimal}), no 
$ m(t) < 0 $ in the simple myopic state.  So it is not true that 
$ n > 0 $.  Then, by Lemma 1, $ n < 0 $ in the neighborhood of 
$ T $.  By induction, $ n < 0 $ for all $ t \in [0,T] $.

\begin{theorem}

In the simple myopic state, either $ {\partial S(t)} / 
{\partial t} > 0 $ or $ S(t) > dP(t) $ for any given 
$ t \in  [0,T] $.

\end{theorem}
          
{\sl Proof}. Theorem 1 and (\ref{optimal}) together imply 
that either $ {U^0}_b - {U^1}_b $ or 
$ {\partial L_b} / {\partial S} $ diminishes over time.  
Suppose that $ {\partial L_b} / {\partial S} $ 
diminishes over time.  Then, by (\ref{partials}), 
$ S(t) $ must rise over time. 
Suppose that $ {U^0}_b - {U^1}_b $ diminishes over time.  
Then $ P(t) $ must rise over time.\footnote{ Recall that $ {Y^0}_1 $ and $
{Y^1}_b $ are fixed over time.  Also recall that $ {\partial^2 U}
/ {\partial P \partial Y} < 0 $.} So $ S(t) > dP(t) $.

Theorem 2 says either emissions or the pollution stock
increases over time. 

\begin{theorem}

Let $ \alpha > 0 $ and $ S(T) > 0 $ in the simple myopic
state. Then $ S(T) $ is the unique maximum of $ S(t), 
t \in [0,T] $.
\end{theorem}

{\sl Proof}.  I will show that $ S(T) $ is a maximum of 
$ S(t) $.  Then I will show that $ S(T) $ is the only 
maximum of $ S(t) $.

The transversality condition is $ m(T) = 0 $.  Using the
optimality condition in (\ref{optimal}), this implies 
that if $ S(T) > 0 $, then at $ T $,

\begin{equation}
\label{implies}
\alpha \left[ {U^0}_b - {U^1}_b \right] 
\frac{\partial L_b}{\partial S} = 0.
\end{equation}

This implies that

\begin{equation}
\frac{\partial L_b}{\partial S} = 0 \; or \; \alpha = 0.
\end{equation}

By (\ref{labor}) and (\ref{partials}), 
$ {\partial L_b} / {\partial S} = 0 $ at $ T $ 
implies that $ S(T) $ is a maximum of $ S(t) $.

Now I will show that $ S(T) $ is the only maximum of $ S(t) $.  
The proof proceeds by contradiction.  Suppose that $ t^*
< T $ exists such that $ S( t^* ) = S(T) $.  Then, by 
(\ref{partials}), $ {\partial L_b} / {\partial S} = 0 $ 
at $ t^* $.  From (\ref{optimal}), $ m( t^* ) = 0 $.  
From (\ref{multiply}), 
$ {\partial m} / {\partial t} < 0 $ at $ t^* $.  
Then $ t^{**} \in (t^*, T] $ exists such that 
$ m( t^{**}) < 0 $.  But if $ t^{**} = T $, the
transversality condition cannot hold.  So $ t^{**} $ 
is in $ ( t^*, T) $.  But by (\ref{optimal}), 
$ m(t) $ is not negative for any $ t \in (t^*, T) $.  
Thus $ {\partial L_b} / {\partial S} $ cannot equal 
zero for any $ t < T $. 

Theorem 3 means this:  Unless the policymaker ignores 
blue-collar workers ($ \alpha = 0 $), he will find it 
optimal, at the end of his career, to invite all 
factories that create jobs, regardless
of future environmental consequences.  The result holds even if
he cares a lot more about the environmentalists than about the
workers ($ 0 < � \ll .5 $).  Moreover, the policymaker will find it
optimal only at the end of his career to invite all factories
that create jobs. These results obtain because, at time $ T $,
selfish residents are ending their lives and have no reason to
fear pollution that outlives them.

\begin{theorem}
In the simple myopic state, $ {\partial S(t;T)} / 
{\partial T} < 0 $ at $ t = T $.
\end{theorem}          
          
{\sl Proof}.  By (\ref{partials}) and Theorem 3, $ S(T) = S_0 $.  
Push $ T $ further into the future, from $ t $ to $ t + \Delta t $.  
Now $ t $ is no longer the endpoint; so by Theorem 3,  
$ S(t) < S_0 = S( t + \Delta t) $.  More generally,

\begin{equation}
\frac{ \Delta S(T) }{ \Delta T} \equiv 
\frac{ S(t; T = t + \Delta t) - S(t; T = t)}
{ \Delta t} < 0.
\end{equation}

I will summarize the theorems.  In the simple myopic state,
the policymaker lets either emissions or the pollution stock rise
over time, because the marginal cost to him of doing so falls. 
This cost falls because a growing share of the environmental
damages shift beyond time $ T $, onto future generations.  Emissions
peak at time $ T $, when residents bear the consequences only for an
instant.  Postponing $ T $  will cause emissions at the old terminal
date to fall.

If the model holds, then time-series analysis of a long-lived 
pollutant, which controlled for the exogenous variables listed 
in Definition 1(a), would find that the level of emissions 
correlated positively with time.  Indeed, in the simple myopic 
state, a succession of generations will generate a path of 
increasing pollution much like the one predicted by the Club 
of Rome model.\footnote{ See \cite{meadows}.  The paths of the 
two models differ in one way: The Club of Rome model assumes 
that high rates of emission will eventually affect life expectancy.  
In my model, $ T $ is exogenous.}  For testing the Brundtland 
hypothesis, data is more abundant in cross-section than in time 
series.  Theorem 4 suggests a cross-section test:  At a given 
moment, jurisdictions with a long time horizon remaining will 
control long-lived emissions more strictly than jurisdictions 
with a short time horizon remaining. Section 3 discusses this
test.\footnote{ Here's a related inference that one can test: 
Suppose that older policymakers come from older populations and
that younger policymakers come from younger populations.  Then
older policymakers will support economic growth; younger
policymakers will support pollution control.}      

\subsubsection{Salvage value}

Additional tests emerge from analysis of how the policymaker
would behave if his constituents compelled him to weigh the
future consequences of his actions.  Denote the value of these
consequences as 

\begin{equation}
V[P(T)], \\ \frac{\partial V}{\partial P} < 0. 
\end{equation}

$ V $ might represent the value of land that owners would sell
at time $ T $ to a new generation; they would instantly convert 
$ V $ to consumption before dying.  

Attach the salvage value $ V $ to the original optimization
problem in (\ref{maxthis}).  Now the transversality condition 
implies that, at time $ T $,

\begin{equation}
\label{newt}
\frac{\partial L_b}{\partial S} = 
\frac{ - \frac{\partial V}{\partial P}}
{\alpha (T) [ {U^0}_b - {U^1}_b ] }.
\end{equation}


The policymaker limits industrial recruitment severely if it 
would affect future generations severely 
($ - {\partial V} / {\partial P} $ is large); 
if he cares little about blue-collar workers 
($ \alpha $ is small); 
or if employment means little to blue-collar workers 
($ {U^0}_b - {U^1}_b $ is small).  

Suppose that an intergenerational transfer mechanism -- such
as a land market -- does not discipline Brundtland behavior. 
Then, from (\ref{implies}), the severity of the pollutant 
will not affect the jurisdiction's pollution control policy 
at time $ T $ as long as the value of $ S_0 $ itself does not 
change.  An empirical implication is that, for 
jurisdictions near the end of their time horizon, undisciplined 
Brundtland behavior implies zero correlation between the marginal 
severity of the pollutant and the level of pollution control.  
One will observe a positive correlation if Brundtland behavior 
is disciplined or absent.     

\section{Empirical tests}

\subsection{Specifying the equation to estimate}

The optimality condition (\ref{optimal}) is satisfied by a control
function of the form

\begin{equation}
\label{estimate}
S^* (t) = f \left[ {Y^0}_b, {Y^1}_b, r, d, N_b, N_w, Y_w, 
                   T, P_0; E \right], t \in [0, T].
\end{equation}

$ E $ is a vector of exogenous variables.  I seek a reduced form of
(\ref{estimate}) for estimation, using cross-state samples.

Compared to the pollution level, a more direct measure of
the intensity of a state's effort toward pollution control is its
level of expenditures on pollution control.  I will model this
variable, $ SPEND(t) $, as a decreasing monotonic transformation of
$ S^* (t) $:

\begin{equation}
\label{SPEND}
SPEND (t) = g [ d, r, N_b, N_w, Y_w, {Y^0}_b, {Y^1}_b, 
                T, P_0; E ], 
\end{equation}

\begin{equation}
sgn \left[ \frac{\partial g}{\partial x_i} \right] 
= - sgn \left[ \frac{\partial f}{\partial x_i} \right].
\end{equation}

The cross-section tests use the same pollutant for all
observations, so $ d $ becomes a constant.  One can manipulate the
first-order approximation of (\ref{SPEND}) into OLS form.  
I also express variables in per-capita terms where appropriate 
-- for instance, $ Spend = {SPEND} / {(N_b + N_w) } $.  I obtain

\begin{eqnarray}
\label{specify}
Spend =  constant + f_1 \frac{N_b}{N_b + N_w} + f_2 {Y^0}_b \nonumber\\
+ f_3 {Y^1}_b + f_4 \frac{L_b}{N_b + N_w} + f_5 r \nonumber\\
+ f_6 \frac{N_w}{N_b + N_w} + f_7 Y_w + f_8 T + f_9 P_0 
+ \sum f_i E_i + \epsilon.
\end{eqnarray}

The disturbance term captures errors due to excluding
higher-order terms or variables affecting $ Spend $ 
from (\ref{specify}).

To reduce multicollinearity, I drop 
$ { N_w }/ {( N_b + N_w )} $ as an
independent variable; and I substitute per-capita income, 
$ Y $, for $ {Y^0}_b, {Y^1}_b $ and $ Y_w $.  Lacking a 
satisfactory proxy, I omit $ r $.  Finally, for ease of 
interpretation, I substitute the blue-collar
unemployment rate, $ { N_b - L_b} )/ { N_b } $, 
for $ { L_b } / { N_b } $.  I obtain 

\begin{equation}
Spend = \bar{Spend} + g_1 \frac{ N_b }{ N_b + N_w } 
+ g_2 Y + g_3 T + g_4 P_0 + g_5 \frac{ N_b - L_b }{ N_b } 
+ \sum_6^n g_i E_{7 - i} + \epsilon.
\end{equation}

\subsection{Six hypotheses to test}

Of the model's empirical implications, I picked six for
testing  -- in part because they presented the least formidable
data problems; and in part because they illustrated most clearly
the larger hypotheses of political tradeoff and generational
selfishness.  

The first four implications come out of the optimality
condition (\ref{optimal}). Of these four, the first two arise from the
assumption that public officials make a political tradeoff
between jobs and environmental quality; the other two arise from
traditional assumptions about household demand for environmental
quality.  The fifth hypothesis comes out of Theorem 4; it arises
from the assumption that residents don't care what happens after
they die.  The sixth hypothesis comes out of the transversality
condition; it arises from the assumption that land markets can
discipline environmental decisions. 

{\sl Hypothesis 1}:  States where blue-collar interests are
politically powerful will allow higher emissions (spend less to
control emissions) than states where these interests are less
powerful.  Null hypothesis: 
$ { \partial Spend} / { \partial N_b } \geq 0 $.  
Alternative hypothesis:  
$ { \partial Spend} / { \partial N_b } < 0 $.  
Level of significance: .05.\footnote{ The choice of the level 
of significance is subjective.  Here is my criterion:  The 
alternative hypothesis must satisfy  the level of significance 
that I specify before I will recommend  that policymakers act 
upon the assumption that the hypothesis is true.  (I regard the 
condition as necessary, not sufficient, for  policy changes.)  
The alternative hypothesis need not satisfy the level of 
significance to justify more research of it.}  

{\sl Hypothesis 2}:  States where the unemployment rate in 
blue-collar industries is high will allow higher emissions 
(spend less to control emissions) than states where this 
unemployment rate is low.  Null hypothesis:  
$ {\partial Spend} / {\partial (1  - {L_b} / {N_b} ) } \geq 0 $.  
Alternative hypothesis: 
$ {\partial Spend} / {\partial (1 -  { L_b } / { N_b } ) } < 0 $.  
Level of significance: .05.

{\sl Hypothesis 3}:  States where income is low will allow higher
emissions (spend less to control emissions) than states where
income is high.  
Null hypothesis: 
$ {\partial Spend} / {\partial Y} \leq 0 $.  
Alternative hypothesis: 
$ {\partial Spend} / {\partial Y} > 0 $.  
Level of significance: .05.

{\sl Hypothesis 4}:  States that have low initial levels of
pollution will allow higher emissions (spend less to control
emissions) than states that have high initial levels of
pollution.  Null hypothesis: 
$ {\partial Spend} / {\partial P_0} \leq 0 $.  
Alternative hypothesis:  
$ {\partial Spend} / {\partial P_0} > 0 $.  
Level of significance: .05.   

{\sl Hypothesis 5}: Consider states that have a short time horizon
remaining.  They will allow a higher level of long-lived
emissions (spend less to control long-lived emissions) than
states that have a long time horizon remaining.  The time horizon
is the remaining number of years in the life of a resident.  Null
hypothesis: $ {\partial Spend} / {\partial T} \leq 0 $.  
Alternative hypothesis: 
$ {\partial Spend} / {\partial T} > 0 $.  
In both hypotheses, $ d $ satisfies $ 0 \leq d < 1 $.\footnote{ From
Theorem 4, the hypothesis is based on a difference quotient, $
{\Delta S(t;T)} / {\Delta T} $, which is negative for an
arbitrary change in $ T $.  In the cross-section sample, I will
fix $ t $ and let $ T $ vary over jurisdictions.}    

For Hypothesis 5, I set the level of significance higher
than usual, at .10, to reduce the chance of a Type II error. 
Acceptance of the null hypothesis when it is false favors me at
the expense of future generations.  To maintain my impartiality
as an observer, I should instead permit a large probability of type
I error.  Hypothesis 5 is the main test of the Brundtland
hypothesis.  

In a cross-section test of Hypothesis 5, one must somehow
control for the starting points of all jurisdictions.  Otherwise,
the relative lengths of life that remain at a given time of
observation might not correspond to the relative time horizons
that remain.  My resolution of this problem is to suppose that
all jurisdictions respond at the same time to an exogenous event
-- the 1986 passage of the Superfund Amendments and
Reauthorization Act, which called for more state involvement in
hazardous waste control.\footnote{ See \cite{epa90}.}  
By fiscal 1990, all states but Nebraska had set up cleanup programs.  
I choose fiscal 1988 as the year of observation in order to allow 
the states two years of ``planning time."  In effect, this is the 
period before time 0, in which agents solve the optimal control problem.

{\sl Hypothesis 6}:  Near terminal time $ T $, states with low
property values will allow higher emissions (spend less to
control emissions) than states with high property values.  
Null hypothesis:  $ {\partial Spend} / {\partial V} \leq 0 $.  
Alternative hypothesis: 
$ {\partial Spend} / {\partial V} > 0 $.  
Level of significance: .05.

I infer this hypothesis from (\ref{newt}), in which the level of
pollution relates negatively to the marginal severity of the
pollution for all future generations.  This marginal severity
cannot be observed directly; I assume that it would be reflected
in the property values of jurisdictions, particularly those with
residents who are close to the ends of their lives.  

Here is my strategy.  I hold constant the pollution level
$ P(T) $ and consider the family of functions $ V_i $, 
where $ i $ indexes the jurisdiction.  I assume that where 
$ V_i (T) $ is large, so is 
$ - {\partial V_i (T)} / {\partial P} $. The intuition is that 
if another unit of pollution will wreak the same physical damage 
in two jurisdictions, then the value of the damages will be greater 
in the jurisdiction where the value of property is greater.      

\subsection{Data}

\subsubsection{Endogenous variables}

The proxy for $ Spend $ is state expenditure per capita
to control hazardous waste in fiscal 1988.\footnote{ Readers 
may obtain datasets by sending me a
3.5" microfloppy and stating their preference among the formats
of major DOS or Windows spreadsheets; or readers may obtain the
datasets in ascii format from me by electronic mail.}  
Hazardous waste
seems a pollutant that might affect future generations.\footnote{
While sketchy, research on the health effects of hazardous wastes
sites indicates that most sites pose very small risks to life
\cite{dower}.  So I have not estimated simultaneous equations for
hazardous waste expenditures and for average life expectancy.}  

The state data available did not distinguish between
expenditures to control existing sites and those to control
abandoned sites.  But even expenditures to control abandoned
sites might entail, in principle, some reduction in jobs.  Most
``voluntary" cleanups and consent agreements hinge on the state's
willingness to draw down its superfund for remediation now and to
recover costs from the polluter later.\footnote{ See \cite{epa90}.}  
By spending little out of its superfund, the state signaled  
manufacturers that it would not impose high monitoring and 
enforcement costs upon them.  In addition, low spending on 
permitting slowed processing
and approval.  That could have helped polluters:  Enforcers 
preferred going into court with a violation of a permit than 
with a violation of general regulations.\footnote{  
See \cite{senate}, p. 32.}  Finally, the abandoned sites entailed 
pollutants that might have affected future generations.  
In 1991, more than half of the sites on the
National Priorities List (NPL) contained metals, solvents or
organic chemicals.\footnote{ See \cite{ceq}.}
     
Estimating the initial pollutant stock, $ P_0 $, might pose a
simultaneity problem. A reasonable proxy for $ P_0 $ is the number of
hazardous waste sites in each state.  The states estimated,
however, that for every site known, three were 
suspected.\footnote{ See \cite{epa90}. }  Evidently, state 
programs with a lot of money might have uncovered more hazardous 
waste sites than state programs with less
money. To reduce simultaneity, I use the number of hazardous
waste sites in a state that are federal facilities on the 1989
National Priorities List ($ FedSites $).\footnote{ A site 
had to place on the List to qualify for Superfund cleanup.  For a site to
place, EPA had to determine that the site significantly threatened 
public health; and the U.S. Agency for Toxic Substances and
Disease Registry had to recommend site evacuation \cite{commerce}.   
State and federal agencies nominated sites for
the List.}  Since these sites were better known {\sl a priori} than
small, private sites, the number of them that were identified in a
state was less likely to vary with program expenditures.\footnote{
This variable might also capture the fiscal effects of
interjurisdictional agreements between the state and federal
agencies, such as the defense and energy departments, that
operated hazardous waste sites.}    

Representing blue-collar political power is manufacturing's
percentage of all jobs in 1989 ($ ManSh $).  Representing blue-collar
unemployment is the average unemployment rate in manufacturing
from 1986 through 1988 ($ Unem8688 $).  I focus on manufacturing,
because it generated most hazardous waste that governments
regulated.  Where unemployment in manufacturing was
high, a policymaker might have tried to conserve jobs by reducing
monitoring and enforcement at manufacturing sites that generate
hazardous waste.\footnote{ About 95 percent of the hazardous
waste generated remains on site \cite{dower}.}

Representing $ V $ is the top value of the lowest quartile of
owner-occupied houses in each state in 1990 ($ House $).  I use this
value, rather than the median value of all owner-occupied
housing, since low-income housing was the type most likely
to skirt hazardous waste sites.\footnote{  About 80 percent of
all Superfund sites were within one mile of residential areas
\cite{ceq}.}

\subsubsection{Exogenous variables}

I turn to exogenous influences.  The model assumes that all
residents are in the labor force.  To control for the number of
residents outside of the labor force and for overlap in
generations, I introduce as an independent variable the share of
the population that received Social Security benefits in 1988
($ Retired $).  I expect a positive coefficient.   

The model also assumes no federal role.  By law, federal
policy had to allow the states ``substantial" latitude in designing
programs for hazardous waste.\footnote{ See \cite{epa89}.}  
Almost all states funded and ran their own superfunds.  Even so, 
the federal government provided more than 28 percent of the 
money spent by states to control hazardous waste. I subtracted 
the estimated federal Superfund contribution from the expenditures of each
state.\footnote{ As for local programs, the state expenditures
reflect only that part of the local effort that passed through
the state budget.}  

Federal aid might also have affected state spending indirectly. 
When the state acted as the lead agency in a site response, it had 
several incentives to substitute federal dollars for its own. 
First, the state had responsibility for non-NPL sites but could 
share costs with the federal government for NPL sites. That might
have influenced the rigor with which the state inspected the site for
potential inclusion on the NPL.  

The state also paid only 10 percent of cleanup costs until 
the NPL site remedy became ``operational and functional"; then it
paid all operating and maintenance costs.\footnote{ See  
\cite{epa90}.}  The definition of ``operational and functional" 
was elastic.  If the remedy called for restoration of ground- 
or surface water, then it might legally have taken 10 years 
to become ``operational and functional."  This might have 
influenced state design of the remedy.\footnote{ A question 
for research: Did the incentive for
states to pursue permanent remedies, rather than temporary
removals, contribute to the ballooning costs of Superfund?}   

The control for these indirect effects is the federal
Superfund contribution to the state, in dollars per capita, as an
independent variable ($ FedSh $).  Given the ubiquity of the flypaper
effect, I expect a positive coefficient.

The model assumes that the jurisdiction might provide for
future generations only by improving environmental quality.  The
proxy for expenditures upon other programs with long-run benefits
is the level of state-source revenues per capita on primary and
secondary education in 1988.  I expect a negative
coefficient.\footnote{ I neither model nor empirically control
for an absolute budget constraint, because total environmental
expenditures comprise a modest share of the state budget -- 1.6
percent for the median state, Maryland, in fiscal 1988 (Brown et
al. 1990).} 

The resident's disutility from hazardous wastes depends
partly on his perception of the threat that they pose.  This, in
turn, might depend upon the spatial frequency of toxins.  My 
proxy for this frequency is the number of pounds of toxins
released to surface land in 1987, expressed per square mile of
land ($ LToxMile $).  I choose 1987 to avoid the possibility that
state spending on hazardous waste might have affected the level
of toxins.  I expect a positive coefficient.     

Waste sites often occur in out-of-the-way places.  They
might be harder to find in large rural states than in small urban
states.  The proxy for this monitoring difficulty is the number
of square miles of land per capita ($ Miles $).  I expect a positive
coefficient.

\subsection{Tests of reduced equations}

The adjusted $ R^2 $ for the
hazardous waste models is about .50 (Models 1-4 in Table 1;
\cite{aptech}). The F-tests also suggest the merit of the
linear specification.  The multicollinearity in Model 1
is significant, however.  Model 2 nearly halves the 
multicollinearity, as measured by Theil's effect, by dropping 
the $ Income $  variable.\footnote{ See \cite{theil}.}  Model 
3 reduces multicollinearity to modest amounts by dropping 
three variables from Model 2.  Inspection of these three
models suggests that multicollinearity does not affect most of
the basic results of the tests.  The $ Years $ coefficient changes
sign but the estimates are imprecise.\footnote{ Standard   
errors of coefficients are corrected for heteroskedasticity, 
using White's method.}  At any rate, in any of 
the models, the $ Years $ coefficient reflects a relatively small effect 
on hazardous waste spending, judging from the beta values.
  
Beta values also suggest that
state expenditures on hazardous waste relate most strongly to
housing values.  There are three reasons for thinking
that the relationship does not simply reflect the contribution of
the property tax to state revenues.  The variable $ House $ is the
top value of the lowest quartile of single-family homes occupied
by the owner -- a class of housing that often qualifies for
exemption from property taxation.  State governments do not rely
on the property tax as heavily as do local governments.  They
rely more on personal income taxes; but we will see that income 
has a relatively modest effect on hazardous waste spending.  
Finally, the elasticity of state
spending on hazardous waste with respect to the house value 
is not less than 1.\footnote{ The specifications treat house value as an 
independent variable.  Many studies suggest that land values 
reflect the value of such
amenities as environmental quality.  But as the modest amount of
multicollinearity in Model 3 (Table 1) suggests, a two-stage
least squares estimation is not appropriate here.}  Across the
specifications, an increase of \$10,000 in the respondent's 
estimate of the value of a low-income house is associated with 
an increase of about \$.20 per capita in
state spending on hazardous waste.  Evaluated at the means, the
point elasticity of state spending with respect to housing value
is about 1.07.  The housing market might provide a powerful
mechanism for intergenerational transfers.

The $ Income $ coefficient is positive (as expected) but 
imprecisely estimated; at any rate, its beta value suggests  
that it has only a small effect upon hazardous waste 
spending (Model 1). Perhaps affluent households support
environmental quality because they seek to protect the value of
their property, not because affluence has increased the amount 
that they would spend on environmental quality.

Hypothesis 6 particularly applies to jurisdictions near
their terminal times. Models 7 and 8 restrict the sample to
jurisdictions with the lowest values of $ Years $. The $ House $ 
coefficient is positive in both models; it reflects a 
relatively large effect on hazardous waste spending, to judge 
from beta values; and it differs from 
zero in a sense that is statistically
significant in both models at the .10 level of
significance or better.  Evaluated at the means, the point 
elasticity of state spending on hazardous waste with respect 
to housing value is 1.3 when one controls for income 
(Model 7, Table 2).

When controlling for the transfer mechanism of housing
markets, test results suggest that the Brundtland effect is
small. In most specifications that include $ Years $, states where
residents can expect to live many years spend more on cleanup
than states where residents can expect to live fewer years.  That
is what Hypothesis 5 predicts. But the effect is substantial
only in the full model of jurisdictions closest to their terminal
dates (Model 7, Table 2).  Moreover, the substitution of
educational for hazardous waste spending, in per capita terms, is
trivial (Model 4, Table 1).  An interpretation consistent with
these results is that states seek to control hazardous wastes
more to protect property values than to protect the interests of
future generations.  Of course, pursuit of the first goal might,
as a by-product, secure the second. 

Test results contradict the hypothesis that policymakers
relax their environmental demands in order to create
manufacturing jobs. The unemployment and jobs coefficients
($ Unem8688 $ and $ ManSh $) relate positively to spending in all
specifications.  In several, the t-statistics well exceed 1.    
This may partly reflects attempts by policymakers to create 
cleanup jobs to substitute for lost manufacturing jobs.

Two other interpretations are consistent with these results. 
Perhaps state policymakers make their careers by pursuing highly
visible but weak prey.  A state with a large and troubled
manufacturing sector would have high values for $ ManSh $ and
$ Unem8688 $, implying a high value for $ Spend $.  Or perhaps 
state environmental officials effectively manage a cartel of
manufacturers.  When the local manufacturing sector is large and
troubled, state officials might try to protect it from
competition by stiffening regulatory barriers to entry.          

All of the hazardous waste models suggest that an increase
in federal aid leads to a net gain in state environmental
spending (the ``flypaper effect"). Evaluated at the means, the
point elasticity of net state spending with respect to federal
Superfund aid is .19 in Model 1.  Federal aid operates with
particular power upon jurisdictions nearest their terminal dates,
however.  A dollar of Superfund aid is associated with a net
increase of \$1.11 in net state spending (Model 7, Table 2). 
Across all models, the standard estimates of the coefficients
suggest that federal aid has almost the same impact on state
environmental spending as the presence of nonworkers ($ Retired $) --
and less impact than house values ($ House $).

The results are consistent with this informal story:  In
hazardous waste policy, the states are influenced by property
owners, nonworkers and federal incentives, in that order.  The
states might also try to protect manufacturers from competition,
but the effect is small and uncertain.  The states seem more
concerned with this generation than with future ones, but land
markets and federal aid can offset the effects of present-
oriented behavior.  Indeed, the response to federal stimulus is
strongest for those states nearest their terminal dates; the
Brundtland hypothesis suggests that these are the states that
would act with the least regard for the future.

\subsubsection{Study of early 1960s}  

Federal policy might affect state
policies in ways that the hazardous waste models do not control. 
As a check against this possibility, I studied state and local
expenditures in 1963, when the federal role in environmental
policy was minuscule.  Data are scant for the early 1960s on
hazardous waste expenditures.  I instead use state and local
expenditures on air pollution control per 1000 residents
($ AllSpend $).\footnote{ The localities spent more than twice as
much on air pollution control as the states in 1963, so I summed
state and local expenditures.}  

The variable $ Air $ controls for the initial level of
pollution.  It gives the geometric mean of the concentration of
particulates from 1957 through 1961.  $ ManSh $ proxies for blue-
collar political power.  This is the percentage of
nonagricultural jobs that were in manufacturing in 1961.  $ Unem60 $
gives the unemployment rate for the civilian labor force in
1960.\footnote{ Reliable estimates of state unemployment rates by
industrial sector for the early 1960s were not available to me.}  

$ House $ gives the median value of an owner-occupied,
single-family house in 1960.  I prefer the median to the 
lowest-quartile value since air pollution diffuses more rapidly than
does hazardous waste through its most common medium of
groundwater contamination.  
     
Despite differences in time periods, policy environments and
independent variables, the air pollution models 5 and 9 (Table 
2) conform to the pattern of the hazardous waste models.  The 
F-tests, though, suggest that the basic model might not outperform
a constant function.  In the simpler, sturdier models 6 and 10,
an increase in house values is associated with a growing increase
in pollution expenditures, given the historic level of air
pollution.
                     
\section{Conclusions and reflections}

Ehrenhalt argues that the rise of the professional
politician in the United States led to short-sighted policy;
the careerist cannot see beyond his own career \cite{ehrenhalt}.  
This paper tested a model of the argument in the environmental 
arena.  To stay in office, the politician must do the voters' 
bidding.  If voters fail to look beyond their own lives, then 
a population that expected to live only a little longer would 
spend less to control persistent pollutants than a population 
that expected to live much longer.  
     
I do not find persuasive evidence of this relationship in
studies of state expenditures on hazardous waste in the 1980s and
on air pollution in the 1960s.  Instead, I find a relationship
between housing values and public expenditures on pollution
control that is positive, statistically significant and
relatively strong.  I infer from the relationship that land
markets might be able to discipline the temptation of current
generations to shift environmental damages onto future
generations.\footnote{ To me, the empirical work suggests that
land markets might discipline intertemporal externalities,
regardless of the direction of causality between pollution
control and property values.  States with high housing values
might seek to protect valuable property by spending a lot to
control pollution; or pollution control expenditures might raise
property values by increasing the expected value of environmental
services.  In either case, the property owner has an incentive to
take into account future environmental damages.}
     
Even when controlling for housing values, I do not find
evidence that Brundtland behavior matters much. The relationship
between spending and length of remaining life is usually positive
but weak.\footnote{ An international test will also be desirable,
partly because it will introduce more variation into the Years
variable.  For the 50-state samples, the ratio of the standard
deviation to the mean is .05 for the 1980s data and .046 for the
1960s data.

In addition, my test for Brundtland myopia is indirect. 
My estimations approximate a necessary condition of Brundtland
myopia, as presented by the model.  I assume the prerequisites 
for sufficiency -- most critically, the nonconvexity of the 
relevant segment of the labor demand function, as policymakers
perceive it.}
  
A jurisdiction where the average resident can expect
to live many years spends more on pollution control than other
jurisdictions.  Brundtland behavior might occur in areas where
land markets do not work well, but its impact on state policy
seems small.

The empirical results raise questions about the
pervasiveness of an ``environmental war between the states."  The
case for national environmental standards rests partly on the
fear that the states, left to their own devices, will vie for
industry by relaxing environmental regulations.  I do not find
persuasive evidence that the states have tried systematically to
trade off environmental quality for jobs.\footnote{ Yandle 
\cite{yandle} as well as Quinn and Yandle \cite{quinn} 
find a negative and significant relationship between subnational 
expenditures on environmental regulation and the number of 
workers in polluting industries.  They view this relationship 
as evidence that jurisdictions try to trade off environmental 
quality for jobs.  I posit that if public officials sense a 
tradeoff between environmental expenditures and jobs, then 
they will be most sensitive to that tradeoff where the unemployment 
rate is high. One will observe a negative relationship between 
expenditures and the unemployment rate in pollution-intensive 
industries, ceteris paribus.}    

Perhaps the average state doesn't use environmental regulations 
to compete for jobs, because it senses that the effort would be 
futile.  Econometric studies by McConnell and Schwab as well 
as by Bartik find little evidence that subnational variations 
in environmental regulations strongly affect the locational 
decisions of firms in the United States.\footnote{ Bartik estimates 
a conditional logit model, at the state level, for new manufacturing 
plants opened by the Fortune 500 companies between 1972 and 1978.  
He infers that tightening environmental regulations is unlikely 
to have a large effect on the location decisions of the average 
industry \cite{bartik}.  McConnell and Schwab estimate a conditional 
logit model, at the county level, for firms in the motor vehicles 
industry during the 1970s.  From most results, they inferred that 
environmental regulations did not systematically affect location 
decisions. But they found some evidence that the marginal firm might avoid
cities with the highest levels of ozone \cite{mcconnell}. 

I might inject a speculative note.  Consider the industries
for which pollution control costs comprised large shares of
expenditures on new plant and equipment in 1987: electric
utilities (7.1 percent); stone, clay and glass (5.3); chemicals
(5.2) and paper (5.0) (\cite{tietenberg}, Table 20.1).  They tend
to be resource-intensive, immobile.  Questions for future
research:  Are such industries in a position to extract
environmental rents from subnational governments?  Or do they
face high relative costs because governments do the extracting?}
  
I find evidence that federal aid strongly affects state
policy on hazardous waste.  The results suggest a need to go
beyond the model of horizontal competition that shaped much of
the theory of environmental federalism and to explore a vertical
model of the federal government and the states.

Finally, I infer from the empirical results that perhaps
intragenerational equity is a more pressing issue for research
than intergenerational equity.  States with low housing values --
impoverished states -- spend less on pollution control than
wealthy states.  The apparent influence of federal aid suggests
that it might be able to redress some inequity in subnational
expenditures on pollution control.

Questions remain.  To what extent do housing values affect
environmental expenditures -- and vice versa?  Do environmental
agencies prey upon immobile manufacturers -- or do they try to
protect them?  The empirical work here suggests a ``tripod model"
of the state and federal policymakers as well as the property
owner; but in that model, who makes the decisions?  Environmental
federalism is a subfield with rich soil.

\pagebreak

\begin{table} \caption{Table 1: OLS Tests of Hazardous Waste Models}
\begin{tabular}{|l||r|r|r|r|}
\multicolumn{5}{c}{Dependent variable: Spend}\\  \hline \hline
Variable & Model 1 & Model 2 & Model 3 & Model 4\\ \hline 
Constant &   -4.546869  &   -2.590543  &   -3.211528  &   -3.194041 \\
(T-stat) &       -1.1   &   -0.83      &  -3.4        &   -3.3       \\ \hline 

House    &      2E-05   &   2.2E-05    & 1.9E-05      & 1.9E-05       \\
Beta     &       0.56   &   0.613      &   0.538      &   0.539        \\
(T-stat) &       3.48   &    5.02      &     4.4      &    4.35        \\ \hline 

Retired  &  14.525065   &  12.884735   & 16.636879    &  16.60401       \\
Beta     &      0.324   &      0.287   &     0.371    &      0.37       \\
(T-stat) &       2.36   &       2.15   &      3.25    &      3.39       \\ \hline 

FedSites &   0.073691   &   0.076723   &  0.085739    &  0.086012        \\
Beta     &      0.237   &      0.247   &     0.276    &     0.277         \\
(T-stat) &       4.38   &        4.1   &      4.36    &      3.58         \\ \hline 

Educate  &              &              &              &   -4.5E-05        \\
Beta     &              &              &              &     -0.007         \\
(T-stat) &              &              &              &      -0.03         \\ \hline 

Years    &   0.001943   &   -0.02655   &              &                    \\ 
Beta     &      0.003   &     -0.048   &              &                    \\
(T-stat) &       0.03   &      -0.46   &              &                    \\ \hline 

ManSh    &   0.025816   &   0.026142   &              &                    \\ 
Beta     &      0.151   &      0.153   &              &                    \\
(T-stat) &       1.75   &       1.75   &              &                     \\ \hline 

Unem8688 &   0.080118   &     0.06261  &              &                     \\
Beta     &      0.179   &        0.14  &              &                     \\
(T-stat) &       1.13   &           1  &              &                     \\ \hline 

Miles    &   0.002914   &    0.003145  &    0.003565  &      0.0036          \\
Beta     &      0.414   &       0.447  &       0.507  &       0.512          \\
(T-stat) &       2.73   &        3.31  &        6.86  &        2.75          \\ \hline 

LToxMile &   0.000303   &    0.000301  &    0.000233  &    0.000234          \\
Beta     &      0.152   &       0.151  &       0.117  &       0.117          \\
(T-stat) &       5.74   &         5.8  &        3.85  &        4.02          \\ \hline 

FedSh    &   0.497291   &    0.502947  &     0.46329  &    0.462217          \\
Beta     &      0.297   &       0.301  &       0.277  &       0.276          \\
(T-stat) &       4.13   &        3.95  &        3.31  &        3.19          \\ \hline 

Income   &    3.9E-05   &              &              &                       \\
Beta     &      0.101   &              &              &                        \\
(T-stat) &       0.52   &              &              &                        \\ \hline \hline 

N               &        50 &     50       &          50  &          50         \\
$ \bar{R^2} $   &     0.504 &  0.513       &        0.52  &       0.508         \\
Theil's         &    0.2513 & 0.1361       &     -0.0374  &      0.0641         \\
SEE             &     0.769 &  0.762       &       0.757  &       0.766          \\
F               &     5.977 &  6.745       &       9.841  &       8.239           \\ \hline
\end{tabular}
\end{table}

\pagebreak

\begin{tabular}{|l|rrrr|l|rr|}                
\multicolumn{8}{c}{Table 2: OLS Tests of Air and Land Pollution Models} \\
\multicolumn{5}{c}{Air pollution model} &
\multicolumn{3}{c}{Hazardous waste model} \\
\multicolumn{5}{c}{Dependent variable: AllSpend} &                                           
\multicolumn{3}{c}{Dependent variable: Spend} \\  \hline \hline 
Variable  &  Model 5  & Model 6 &  Model 9  &  Model 10  & Variable  &   Model 7 &   Model 8 \\ \hline \hline 
Constant  &   -82.552653  &    -23.757873 &     -317.918665  &   -23.097002  &   Constant  &      -16.697856 &     -7.038734 \\
(T-stat)  &      -0.67  &         -1.96 &            -0.6  &        -1.41  &   (T-stat)  &           -1.49 &         -1.34 \\ \hline 
Unem60    &   5.281138  &               &        9.211232  &               &   Unem8688  &        0.095637 &      0.084273  \\
Beta      &      0.206  &               &           0.234  &               &   Beta      &           0.196 &          0.16  \\
(T-stat)  &       2.18  &               &            1.72  &               &   (T-stat)  &            0.82 &          1.26  \\ \hline 
Income    &    0.001906  &               &                  &               &   Income    &          -2E-05 &                 \\        
Beta      &      0.021  &               &                  &               &   Beta      &          -0.063 &                  \\          
(T-stat)  &     0.17  &               &                  &               &   (T-stat)  &           -0.13 &                  \\ \hline      
ManSh     &   0.228386  &               &        0.021046  &               &    ManSh    &        0.007906 &       0.011333   \\
Beta      &      0.065  &               &           0.004  &               &    Beta     &           0.045 &          0.061   \\
(T-stat)  &      0.69  &               &            0.04  &               &   (T-stat)  &            0.31 &           0.85   \\ \hline 
Air       &   0.054385  &      0.09118  &        0.060558  &      0.05088  &   LToxMile  &        0.000466 &       0.000322   \\
Beta      &      0.048  &         0.08  &           0.044  &        0.037  &   Beta      &           0.292 &          0.166    \\
(T-stat)  &       0.86  &         1.18  &             0.6  &          0.4  &   (T-stat)  &            2.49 &           2.22    \\ \hline 
House     &    0.00669  &               &        0.007547  &               &    House    &         2.4E-05 &         2.4E-05     \\
Beta      &      0.469  &               &           0.447  &               &    Beta     &           0.716 &           0.694    \\
(T-stat)  &       3.12  &               &            1.57  &               &   (T-stat)  &            1.86 &            4.59     \\ \hline 
Retire63  &   253.810967  &               &      207.316749  &               &   Retired   &       15.720635 &       14.955388      \\
Beta      &        0.123  &               &           0.072  &               &   Beta      &           0.277 &            0.25       \\
(T-stat)  &         1.23  &               &            0.63  &               &   (T-stat)  &             2.2 &            2.46       \\ \hline 
Years     &    -1.058683  &               &        4.391178  &               &    Years    &        0.337408 &        0.084188        \\
Beta      &       -0.052  &               &           0.095  &               &    Beta     &           0.273 &           0.094         \\
(T-stat)  &        -0.45  &               &            0.39  &               &   (T-stat)  &            1.41 &            0.75         \\ \hline 
HouseSq   &               &      0.000231 &                  &      0.000289 &             &                 &                         \\
Beta      &               &         0.414 &                  &         0.392 &             &                 &                         \\
(T-stat)  &               &          2.37 &                  &          1.57 &             &                 &                         \\ \hline 
	  &              &               &                  &               &  FedSites   &        0.156094 &         0.055087         \\
	  &               &               &                  &               &  Beta       &           0.241 &            0.206         \\
	  &               &               &                  &               &  (T-stat)   &             1.4 &             2.33         \\ \hline 
	  &                 &               &                  &               &  Miles      &       -0.007666 &        -0.004582         \\
	  &                  &               &                  &               &  Beta       &          -0.142 &           -0.151         \\
	  &                  &               &                  &               &  (T-stat)   &           -1.97 &            -1.53         \\ \hline 
	  &                  &               &                  &               &   FedSh     &        1.108719 &         0.673934          \\
	  &                  &               &                  &               &   Beta      &           0.333 &            0.454          \\
	  &                  &               &                  &               &   (T-stat)  &            7.22 &             5.75          \\  \hline \hline 
N             &              50  &           50  &             37   &          33   &    N        &              25 &               40          \\
$ \bar{R^2} $ &           0.098  &        0.139  &          0.066   &       0.103   & $ \bar{R^2} $  &           0.559 &            0.631          \\
Theil's       &          0.1045  &       -0.003  &         0.0059    &     0.0057   &  Theil's    &          0.4953 &           0.3139           \\
SEE           &          37.221  &       36.352  &         42.653    &     43.976   &  SEE        &           0.694 &            0.633           \\
F             &           1.758  &        4.968  &          1.422    &      2.831   &  F          &           4.046 &            8.419           \\ \hline
\end{tabular}

\pagebreak

\begin{tabular}{|l|l|l|l|} 
\multicolumn{4}{c}{Table 3: Test Results for Full Samples} \\ \hline
No. & Description of hypothesis &  80s Test Results & 60s Test Results \\  \hline \hline
1   & Manufacturing power cuts  &  Wrong sign;      & Wrong sign;    \\
    & state pollution spending  &   T $ \approx $ 1.75        &   T = 0.69      \\ \hline
2   & (Manufacturing)           &  Wrong sign;      &  Wrong sign;    \\
    & unemployment decreases    &   T $ \approx $ 1.06        &   T $ \approx  $ 2.18     \\
    & state pollution spending  &                   &                 \\ \hline
3   & High income increases     &  Right sign;      &  Right sign;    \\
    & state pollution spending  &   T $ \approx $ 0.52        &  T = 0.17       \\ \hline
4   & High pollution level      &  Right sign;      &  Right sign;    \\
    & increases state pollution &   T $ \approx $ 4.1         &   T = 1         \\ 
    & spending                  &                   &                 \\ \hline
5   & Long time horizon         &  Mixed signs;     &  Wrong sign;    \\
    & increases state pollution &  T $ \approx $ -.43         &  T $ \approx $ -.45       \\
    & spending                  &                   &                  \\ \hline
6   & Well-functioning land     &  Right sign;      & Right sign;     \\
    & market increases state    &  T $ \approx $ 4.31         & T $ \approx $ 3.12         \\
    & pollution spending        &                   &                  \\ \hline
\end{tabular}

\pagebreak

\begin{tabular}{lrrl}                                              
\multicolumn{4}{c}{Table 4: Descriptive Statistics} \\
\multicolumn{4}{c}{\bf Variables in hazardous waste study} \\ 
Variable &  Mean   &  Std Dev &   Description  \\ \hline
Educate  &  360.56  &   162.19 &   State spending on pri/sec education per capita \\
FedSh    &  0.4248  &   0.6525 &   Federal Superfund aid to state; dollars per capita  \\
FedSites &  2.3     &   3.5182 &   Number of federal facilities on NPL                 \\
House    &  57850   &   30901  &   Lowest-quartile value of occupied, one-family homes  \\
Income   &  15542   &   2802   &   Personal income per capita                            \\
LToxMile &  249.42  &   546.4  &   Pounds per sq mile of toxic chemical releases to land  \\
ManSh    &  16.99   &   6.3865 &   Percent of nonfarm employees in manufacturing          \\
Miles    &  50.1105 &  155.217 &   Square miles of land per capita                        \\
Retired  &  0.1541  &  0.0243  &   Percent of residents receiving Social Security benefits  \\
Spend    &  1.0841  &  1.0921  &   State spending on hazardous waste per capita           \\
Unem8688 &  6.502   &    2.44  &   Manufacturing unemployment rate, 3-yr average          \\
Years    &  39.136  &   1.957  &   Years left in average resident's lifetime            \\ 
\multicolumn{4}{c}{\bf Variables in air pollution study} \\ 
Variable &  Mean    &    Std Dev &  Description   \\ \hline
Air      &  104.14  &  34.48   &  Micrograms of particulates per cubic meter of air       \\
AllSpend &  16.1216 &  39.1851 &  State, local spending on air pollution/1000 residents    \\
House    &  11142   &  2727    &  Median value of owner-occupied, one-family homes         \\
HouseSq  &  131540  &  70255   &  Square of House variable (\$1,000s)                       \\
Income   &  2082    & 430      &  Personal income per capita                               \\
ManSh    &  26.14   &  11.15   &  Percent of nonfarm employees in manufacturing            \\
Retire63 &  0.0977  &  0.019   &  Percent of residents receiving Social Security benefits  \\
Unem60   &  5.23    &  1.53    &  Percent of civilian labor force unemployed               \\
Years    &  41.445  &  1.917   &  Years left in average resident's lifetime                \\
\end{tabular}          

\pagebreak

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\pagebreak

\section{Appendix A: Derivations}

\subsection{ Derivations for Theorem 1}

\newtheorem{prop}{Proposition}
\begin{prop}

In the simple myopic state, $ {\partial m} / {\partial t} \neq 0
$ for any interval $ [t^*, t^* + \epsilon ] \in [0,T] $, $
\epsilon  > 0 $.

\end{prop}

{\sl Proof}.  Suppose that $ {\partial m} / {\partial t} = 0 $
over the interval $ [t^*, t^* + \epsilon] $.  Then, in the simple
myopic state, the multiplier equation (\ref{multiply}) yields

\begin{equation}
\label{A1}
m(t) = - \frac{\alpha \left( L_b 
\frac{\partial {U^0}_b}{\partial P} 
+ \left( N_b - L_b \right) 
\frac{\partial {U^1}_b}{\partial P} \right) 
+ ( 1 - \alpha ) N_w 
\frac{\partial U_w}{\partial P}}
{ r - d },
\end{equation} for any $ t  \in [t^*, t^* + \epsilon] $.  

The right-hand side of (\ref{A1}) gives the current value of the
marginal disutility of the pollutant stock over the interval $
[t, \infty ) $, with political weights.  The left-hand side of
(\ref{A1}) gives the marginal cost to the policymaker of the
pollutant stock at time $ t $.  By construction of the problem,
however, the policymaker cares only about the effects of the
stock up to time $ T $.  So the right-hand side of (\ref{A1})
overstates the actual value of $ m(t) $ in the model.  It follows
that $ {\partial m} / {\partial t} $ is nonconstant over any
interval $ [t^*,t^* + \epsilon] \in [0,T] $.

\subsection{Deriving comparative statics for empirical
tests}

Hypotheses 1-4 apply the implicit function theorem to 
(\ref{optimal}).  

{\sl Hypothesis 1}: Comparative statics yield

\begin{equation}
\label{hypo1}
\frac{\partial S}{\partial N_b} = 
\frac{ \frac{\partial m}{\partial N_b} - 
\frac{\partial \alpha}{\partial N_b} 
\frac{\partial L_b}{\partial S} 
\left[ {U^0}_b - {U^1}_b \right] }
{\alpha 
\frac{\partial^2 L_b}{\partial S^2} 
\left[ {U^0}_b - {U^1}_b \right] 
- \frac{\partial m}{\partial S} }.
\end{equation}

In interpreting (\ref{hypo1}), recall that the co-state variable 
$ m $ can be expressed as a function of parameters when 
evaluated at the solution to the Hamiltonian.

The denominator is negative.  In the numerator, 
$ {\partial m} / {\partial N_b} $ is
negative:  As the blue-collar group grows, the 
marginal cost to the policymaker of permitting the 
pollutant stock to increase will decrease, given that 
the flow is not so large as to cut the productivity  
of workers and to trigger layoffs ( $ S < S_0 $ ).  
But the rest of the numerator is positive.  
So, signing $ {\partial S} / {\partial N_b} $ requires 
more assumptions.  The numerator is negative -- and 
$ {\partial S} / {\partial N_b} $ is positive -- if and
only if

\begin{equation}
\label{A3}
\frac{\partial m}{\partial N_b} < 
\frac{\partial \alpha}{\partial N_b} 
\frac{\partial L_b}{\partial S}
\left[ {U^0}_b - {U^1}_b \right].
\end{equation}

In (\ref{A3}), the right-hand side represents the decrease 
in the political value (to blue-collar workers) of increasing 
the blue-collar group.  Adding another member to the blue-collar 
group induces some free-riding by the average member of the 
group ($ {\partial \alpha} / {\partial N_b} $). 
This free-riding reduces blue-collar political power.  It becomes
easier for the policymaker to tighten pollution controls,
eliminating blue-collar jobs.  The resulting loss in blue-collar
welfare is the decrease in individual welfare due to losing a job
($ {U^0}_b - {U^1}_b $) times the number of jobs lost 
($ {\partial L_b} / {\partial S} $).  

In sum, $ {\partial S} / {\partial N_b} $ is positive if the 
free-riding incurred by adding a member to the blue-collar 
group is not too great.
     
Using (\ref{SPEND}) yields $ {\partial Spend} / 
{\partial N_b} < 0 $.

{\sl Hypothesis 2}:  Comparative statics yield

\begin{equation}
\label{hypo2}
\frac{\partial S}{\partial (\frac{L_b}{N_b}) } = 
\frac{ \frac{\partial m}{\partial (\frac{L_b}{N_b})}}
{\alpha 
\frac{\partial^2 L_b}{\partial S^2} 
\left[ {U^0}_b - {U^1}_b \right] 
- \frac{\partial m}{\partial S}} 
< 0.
\end{equation}

So

\begin{equation}
\frac{\partial S}{\partial \left( 1 - \frac{L_b}{N_b} \right)} 
> 0.
\end{equation}

Using (\ref{SPEND}) yields

\begin{equation}
\frac{\partial Spend}{\partial \left( 1 - \frac{L_b}{N_b} \right)} 
< 0.
\end{equation}

{\sl Hypothesis 3}: Comparative statics yield

\begin{equation}
\label{A7}
\frac{\partial S}{\partial Y_b} = 
\frac{ \frac{\partial m}{\partial Y_b} - 
\alpha \frac{\partial L_b}{\partial S} 
\left( \frac{\partial {U^0}_b}{\partial Y_b} -  
\frac{\partial {U^1}_b}{\partial Y_b} \right)}
{ \alpha \frac{\partial^2 L_b}{\partial S^2} 
\left( {U^0}_b - {U^1}_b \right) 
- \frac{\partial m}{\partial S} } 
< 0.
\end{equation}

and

\begin{equation}
\label{A8}
\frac{\partial S}{\partial Y_w} = 
\frac{ \frac{\partial m}{\partial Y_w} }
{\alpha \frac{\partial^2 L_b}{\partial S^2} 
\left( {U^0}_b - {U^1}_b \right) 
- \frac{\partial m}{\partial S} } 
< 0.
\end{equation}

Let $ Y $ be a linear combination of $ Y_b $  and $ Y_w $.  
Then, from (\ref{A7}) and (\ref{A8}), 
$ {\partial S} / {\partial Y} < 0 $.  
Use (\ref{SPEND}) to obtain 
$ {\partial Spend} / {\partial Y} > 0 $.

{\sl Hypothesis 4}:  Comparative statics yield

\begin{equation}
\frac{\partial S}{\partial P_0} = 
\frac{ \frac{\partial m}{\partial P_0} - 
\alpha \frac{\partial L_b}{\partial S} 
\left( \frac{\partial {U^0}_b}{\partial P} - 
\frac{\partial {U^1}_b}{\partial P} \right) 
\frac{\partial P}{\partial P_0} }
{\alpha \frac{\partial^2 L_b}{\partial S^2} 
\left( {U^0}_b - {U^1}_b \right) 
- \frac{\partial m}{\partial S} } 
< 0.
\end{equation}

Use (\ref{SPEND}) to obtain $ {\partial Spend} / {\partial P_0} > 0 $.

\subsection{Effect of pollutant decay rate on emissions}

Applying the implicit function theorem to (\ref{optimal}) 
yields

\begin{equation}
\frac{\partial S}{\partial d} = 
\frac{ \frac{\partial m}{\partial d} }
{ \alpha \frac{\partial^2 L_b}{\partial S^2} 
\left( {U^0}_b - {U^1}_b \right) 
- \frac{\partial m}{\partial S}} 
> 0.
\end{equation}

\pagebreak

\section{Appendix B:  Notes on the data}

\subsection{Hazardous waste study}

$ Educate $:  State-source revenues per capita for primary and
secondary education for state fiscal year 1988.  Includes direct
state aid as well as state contributions on behalf of local
school systems.  State-source revenues originate from state
governments; they do not include federal aid.  
Source: \cite{commerce-ed}, Table 9, page 13. 

$ FedSh $: Federal grants to state and local governments from
the Hazardous Substance Response Trust Fund (Superfund) for
federal fiscal year 1988.  Expressed in terms of dollars per
capita.  Source: \cite{commerce-cen}, Table 2, page 7.

$ FedSites $: Federal-facility sites of uncontrolled hazardous
waste on the National Priorities List, 1989.  Includes final and
proposed sites for the Superfund program.  Source:  
\cite{commerce}, Items 624 and 626, page 240.

$ House $: Upper limit of the lowest quartile of current values
of owner-occupied, one-family homes in 1990.  Owners estimated
the values.  The tracts are smaller than 10 acres, and they
contain no business.  Source: \cite{statab}, Table 1228, 
page 718.

$ Income $:  Personal income per capita in 1988, expressed in
current dollars.  Source: \cite{commerce}, Item 807, page 251.

$ LToxMile $:  Pounds per square mile of toxic chemical releases
to the land in 1987.  Includes toxins released to landfills,
ponds and pits; toxins released for land treatment or application
as well as for farming; and toxic leaks or spills. Includes on-
site releases and off-site transfers generated in the specific
state.  Roughly 40 percent of transferred wastes are disposed out
of state. Discharges were reported by manufacturing facilities
using or releasing at least 50,000 pounds of 322 chemicals,
including 123 carcinogens. I exclude chemicals that EPA delisted
by 1991, since typically their toxicity would have been in
question years before their delisting.  
Source: \cite{toxic}, Table E-1, page E-3.

$ ManSh $: Percent of all nonfarm employees that was in
manufacturing in 1989.  Source: \cite{statab}, Table 668.

$ Miles $:  Square miles of land per capita in 1980 in the
state.  Source: \cite{commerce}, Item 590, page 238.

$ Retired $:  Percentage of the state population that received
Social Security benefits on Dec. 31, 1988.  Includes dependents
of retired and disabled workers as well as other types of
beneficiaries.  Retired workers alone account for 62 percent of
the recipients.  Source: \cite{commerce}, Item 441, page 229.

$ Spend $: State expenditures on hazardous waste per capita in
state fiscal year 1988, which ended on June 30, 1988 for most
states. Includes funds used to develop and maintain a
comprehensive hazardous waste management program.  This can
include remediation of Superfund sites and of leaking storage
tanks that are underground.  From gross state expenditures, 
I subtracted federal Superfund aid (see the entry for $ FedSh $).
Source: \cite{brown}, pp. 84-93.

$ Unem8688 $:  The simple average of the annual unemployment
rate in manufacturing from 1986 through 1988.  Source: 
\cite{bls}, Table 16.

This source provides no estimate for the 1988 unemployment
rate in Alaska.  I've estimated this rate with a linear
interpolation of 1989 and 1987 data.

$ Years $:  Years left in average lifetime.  Average lifetime in
years, 1979-1981, taken from \cite{commerce}, Item 178,
page 213.  Mean age for 1989 calculated from \cite{statab}, 
Table 28.

\subsection{Air pollution study}

$ Air $:  The geometric mean of the number of micrograms of
suspended particulate matter per cubic meter of air for each
state from 1957 through 1961.  I use the geometric -- not
arithmetic -- mean because particulates follow a log-normal
distribution in concentration.  Source: \cite{air},  
Table 22, pp. 16-21.

$ AllSpend $: State, city and county expenditures on air
pollution in 1963 per 1000 residents.  Source: \cite{oldair}.   

$ House $:  Median value of owner-occupied, single-family house
in 1960.  Source: \cite{city}, Table 1, Item 61, page 5.  

$ Income $:  State personal income per capita in 1960.  Excludes
wages and salaries received by federal military and civilian
employees temporarily stationed abroad. Source: \cite{statab}, 
1962, Table 431, page 319.  

$ ManSh $: Percentage of nonagricultural jobs that were in
manufacturing in 1961.  Source: \cite{statab}, 1961,
Table 281, page 212.

$ Unem60 $:  Percent of civilian labor force unemployed 
in 1960.  Source: \cite{city}, Item 35, page 4.

$ Years $:  Number of years left in mean life in 1960s. 
Estimates of average lifetimes by state are from 
\cite{life}, page 8-6.  I computed the mean age of the 
population by state in 1960 from \cite{statab}, 1962, 
Table 19, page 27.  To obtain $ Years $, I subtracted 
the mean age from the estimated average lifetime.

\end{document}

 
