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\begin{center}
ECONOMIC ANALYSIS GROUP

DISCUSSION PAPER


\vspace{3.8cm}


Automobile Prices, Gasoline Prices, and Consumer Demand for Fuel
Economy

\vspace{0.25cm} By \vspace{0.25cm}

Ashley Langer* and Nathan H. Miller**  \\

EAG 08-11  $\quad$ December 2008

\end{center}

\vspace{0.45cm}

\noindent EAG Discussion Papers are the primary vehicle used to
disseminate research from economists in the Economic Analysis Group
(EAG) of the Antitrust Division.  These papers are intended to
inform interested individuals and institutions of EAG's research
program and to stimulate comment and criticism on economic issues
related to antitrust policy and regulation.  The analysis and
conclusions expressed herein are solely those of the authors and do
not represent the views of the United States Department of Justice.
\vspace{0.25cm}

\noindent Information on the EAG research program and discussion
paper series may be obtained from Russell Pittman, Director of
Economic Research, Economic Analysis Group, Antitrust Division, U.S.
Department of Justice, BICN 10-000, Washington DC 20530, or by
e-mail at russell.pittman@usdoj.gov.  Comments on specific papers
may be addressed directly to the authors at the same mailing address
or at their email address.

\vspace{0.25cm}

\noindent Recent EAG Discussion Paper titles are listed at the end
of this paper.  To obtain a complete list of titles or to request
single copies of individual papers, please write to Janet Ficco at
the above mailing address or at janet.ficco@usdoj.gov.  In addition,
recent papers are now available on the Department of Justice website
at http://www.usdoj.gov/atr/public/eag/discussion\_papers.htm.
Beginning with papers issued in 1999, copies of individual papers
are also available from the Social Science Research Network at
www.ssrn.com.

\vspace{0.25cm}

\noindent\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

\noindent * \ Department of Economics, University of California,
Berkeley.  Email: alanger@econ.berkeley.edu.

\noindent **Economist, Economic Analysis Group, Antitrust Division,
U.S. Department of Justice. Email: nathan.miller@usdoj.gov.  We
thank Severin Borenstein, Joseph Farrell, Richard Gilbert, Joshua
Linn, Kenneth Train, Clifford Winston, Catherine Wolfram, and
seminar participants at the George Washington University and the
University of California, Berkeley for valuable comments. Daniel
Seigle and Berk Ustun provided research assistance. The views
expressed are not purported to reflect those of the U.S. Department
of Justice.

\newpage
\thispagestyle{empty}

\begin{abstract}            % beginning of the abstract
The relationship between gasoline prices and the demand for vehicle
fuel efficiency is important for environmental policy but poorly
understood in the academic literature. We provide empirical evidence
that automobile manufacturers price as if consumers respond to
gasoline prices. We derive a reduced-form regression equation from
theoretical micro-foundations and estimate the equation with nearly
300,000 vehicle-week-region observations over the period 2003-2006.
We find that vehicle prices generally decline in the gasoline price.
The decline is larger for inefficient vehicles, and the prices of
particularly efficient vehicles actually rise. Structural estimation
that ignores these effects underestimates consumer preferences for
fuel efficiency.
\end{abstract}              % end of the abstract


\newpage
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\section{Introduction}

The combustion of gasoline in automobiles poses some of the most
pressing policy concerns of the early twenty-first century. This
combustion produces carbon dioxide, a greenhouse gas that
contributes to global warming.  It also limits the flexibility of
foreign policy -- more than sixty percent of U.S. oil is imported,
often from politically unstable regimes.  These effects are classic
externalities. It is not clear whether, in the absence of
intervention, the market is likely to produce efficient outcomes.

One topic of particular importance for policy in this arena is the
extent to which retail gasoline prices influence the demand for
vehicle fuel efficiency.  If, for example, higher gasoline prices
induce consumers to shift toward more fuel efficient vehicles, then
1) the recent run-up in gasoline prices should partially mitigate
the policy concerns outlined above and 2) gasoline and/or carbon
taxes may be reasonably effective policy instruments. However, a
small empirical literature estimates an inelastic consumer response
to gasoline prices (e.g., Goldberg 1998; Bento et al 2005; Li,
Timmins and von Haefen 2007; Jacobsen 2008). For example, Shanjun
Li, Christopher Timmins, and Roger H. von Haefen conclude that:
\begin{quote}
[H]igher gasoline prices do not deter American's love affair with
large, relatively fuel-inefficient vehicles.  Moreover, a
politically feasible gasoline tax increase will likely not generate
significant improvements in fleet fuel economy.
\end{quote}
Interestingly, the findings of the academic literature are seemingly
contradicted by a bevy of recent articles in the popular press.
Consider Bill Vlasic's article in the \textit{New York Times} titled
``As Gas Costs Soar, Buyers Flock to Small Cars'':
\begin{quote}
Soaring gas prices have turned the steady migration by Americans to
smaller cars into a stampede.  In what industry analysts are calling
a first, about one in five vehicles sold in the United States was a
compact or subcompact car...\footnote{The article appeared on May 2,
2008.  Other recent press articles include CNN.com's May 23, 2008
article titled ``SUVs plunge toward `endangered' list,'' the
\textit{LA Times}' April 24, 2008 article titled ``Fueling debate:
Is \$4.00 gas the death of the SUV?'' and the \textit{Chicago
Tribune}'s May 12, 2008 article titled ``SUVs no longer king of the
road.''}
\end{quote}
One might be tempted to point out that four in five vehicles were
neither compact nor subcompact cars.  But suppose that the spirit of
the article is correct.  Can its perspective be reconciled with the
academic literature?

We approach the topic from a new perspective.  We ask the question:
``Do automobile manufacturers behave \textit{as if} consumers
respond to gasoline price?''  Our approach starts with the
observation that consumer choices have implications for equilibrium
automobile prices: if gasoline price shocks affect consumer choices
then one should see corresponding adjustments in automobile prices.
We derive the specific form of these adjustments from theoretical
micro foundations.  In particular, we show that a change in the
gasoline price affects an automobile's equilibrium price through two
main channels: its effect on the vehicle's fuel cost and its effect
on the fuel cost of the vehicle's competitors.\footnote{By ``fuel
cost'' we mean the fuel expense associated with driving the vehicle.
Notably, changes in the gasoline price affect the fuel costs of
automobiles differentially -- the fuel costs of inefficient
automobiles are more responsive to the gasoline prices than the fuel
costs of efficient automobiles. One can imagine that the gasoline
price may affect equilibrium automobile prices through other
channels, perhaps due to an income effect and/or changes in
production costs. Our empirical framework allows us to control
directly for these alternative channels; we find that their net
effect is small.}

To build intuition, consider the effect of an adverse gasoline price
shock on the price of an arbitrary automobile.  If consumers respond
to the vehicle's fuel cost, then the gasoline price shock should
reduce demand for the automobile. However, the gasoline price shock
also increases the fuel cost of the automobile's competitors and
should therefore increase demand through consumer substitution. The
net effect on the automobile's equilibrium price is ambiguous.
Overall, the theory suggests that the net price effect should be
negative for most automobiles, but positive for automobiles that are
sufficiently more fuel efficient then their competitors. We believe
that the framework is quite intuitive. For example, the theory
formalizes the idea that an adverse gasoline price shock should
reduce demand for fuel inefficient automobiles (e.g., the GM
Suburban) more than demand for fuel efficient automobiles (e.g., the
Ford Taurus), and that demand for highly fuel efficient automobiles
(e.g., the Toyota Prius) may actually increase.

In the empirical implementation, we test the extent to which
automobile prices respond to changes in fuel costs.  We use a
comprehensive set of manufacturer incentives to construct
region-time-specific ``manufacturer prices" for each of nearly 700
vehicles produced by GM, Ford, Chrysler, and Toyota over the period
2003-2006, and combine information on these vehicles' attributes
with data on retail gasoline prices to measure fuel costs.  We then
regress manufacturer prices on fuel costs and competitor fuel costs
and argue that manufacturers set prices as if consumers respond to
the gasoline price if the first coefficient is negative while the
second is positive.  Overall, the estimation procedure uses
information from nearly 300,000 vehicle-week-region observations; as
we discuss below, identification is feasible even in the presence of
vehicle, time, and region fixed effects.

By way of preview, the results are consistent with a strong and
statistically significant consumer response to the retail price of
gasoline. Manufacturer prices decrease in fuel costs but increase in
the fuel costs of competitors.  The median net manufacturer price
change in response to a hypothetical one dollar increase in gasoline
prices is a reduction of \$792 for cars and a reduction of \$981 for
SUVs; the median price change for trucks and vans are modest and
less statistically significant. Although the fuel cost effect almost
always dominates the competitor fuel cost effect, the manufacturer
prices of some particularly fuel efficient vehicles do increase
(e.g., the 2006 Prius or the 2006 Escape Hybrid).  The manufacturer
responses that we estimate are large in magnitude. Rough
back-of-the-envelope calculations suggest that, for most vehicles,
manufacturers substantially offset the discounted future gasoline
expenditures incurred by consumers.


The results have important policy implications.  The manufacturer
price responses that we document should dampen short-run changes in
consumer purchase behavior by subsidizing relatively fuel
inefficient vehicles when gasoline prices rise.  Structural
estimation that fails to control for these manufacturer responses
may therefore underestimate the short-run elasticity of demand with
respect to gasoline prices. Further, counter-factual policy
simulations based on such estimation are likely to understate the
effects of gasoline prices or gasoline/carbon taxes, even if the
\textit{simulations} allow for appropriate manufacturer
responses.\footnote{We formalize this argument in Appendix
\ref{app:bias}.}

Thus, the evidence presented here may help reconcile the academic
literature with the perspective of the popular press.  That is,
consumers may consider gasoline prices when choosing which
automobile to purchase but, due to the manufacturer price response,
changes in the gasoline price are not fully reflected in observed
vehicle purchases.  We speculate that a major effect of gasoline
price changes (or gasoline/carbon taxes) may occur in the long-run.
The manufacturer responses that we estimate reduce the profit
margins of fuel inefficient vehicles relative to those of fuel
efficient vehicles. It is possible, therefore, that increases in the
gasoline price (or in the gasoline/carbon tax) provide a substantial
profit incentive for manufacturers to invest in the development and
marketing of fuel efficient vehicles.

The paper proceeds as follows.  We lay out the empirical model in
Section \ref{sec:model}, including the underlying theoretical
framework and the empirical implementation. We describe the data and
regression variables in Section \ref{sec:data}.  Then, in Section
\ref{sec:res}, we present the main regression results and discuss a
number of extensions related to historical and futures gasoline
prices, pricing dynamics, selected demand and cost factors, and
manufacturer inventory levels. We conclude in Section
\ref{sec:conc}.

\section{The Empirical Model \label{sec:model}}

\subsection{Theoretical framework}

We derive our estimation equation from a model of Bertrand-Nash
competition between multi-vehicle manufacturers. Specifically, we
model manufacturers, $ \Im = 1, 2, \dots F$ that produce vehicles $j
= 1, 2, \dots J_t$ in period $t$.  Each manufacturer chooses prices
that maximize their short-run profit over all of their vehicles:
\begin{equation}
\pi_{\Im t} = \sum_{j \in \Im}{\left[ \left(p_{jt}-c_{jt}
\right)*q_{jt}-f_{jt}\right]} \label{eq:tprofs}
\end{equation}
where for each vehicle $j$ and period $t$, the terms $p_{jt}$,
$c_{jt}$, and $q_{jt}$ are the manufacturer price, the marginal
cost, and the quantity sold respectively; the term $f_{jt}$ is the
fixed cost of production.  As we detail in the empirical
implementation, we assume that marginal costs are constant in
quantity but responsive to certain exogenous cost
shifters.\footnote{We abstract from the manufacturers'
selections of vehicle attributes and fleet composition, as well as
any entry and/or exit, which we deem to be more important in
longer-run analysis.}

We pair this profit function with a consumer demand function that
depends on manufacturer prices, expected lifetime fuel costs, and
exogenous demand shifters that capture vehicle attributes and other
factors. We specify a simple linear form:
\begin{eqnarray}
q(p_{jt})=\sum_{k=1}^{J_t}\alpha_{jk}(p_{kt}+x_{kt})+ \mu_{jt},
\label{eq:tdemand}
\end{eqnarray}
where the term $\alpha_{jk}$ is a demand parameter and the terms
$x_{kt}$ and $\mu_{jt}$ capture the fuel costs and the exogenous
demand shifters, respectively.  One can conceptualize the demand
shifters as including the vehicle's fixed attributes and quality, as
well as maintenance costs and any other expenses that are unrelated
to the gasoline price. We consider the case in which demand is well
defined ($\partial q_{jt} /
\partial p_{jt} = \alpha_{jj}<0$) and vehicles are substitutes
($\partial q_{jt} / \partial p_{kt}= \alpha_{jk} \geq 0$ for $k \neq
j$).  The equilibrium manufacturer prices in each period are then
characterized by $J_t$ first-order conditions:
\begin{eqnarray}
\frac{\partial \pi_{\Im t}}{\partial p_{jt}} = \sum_k
\alpha_{jk}(p_{kt}+ x_{kt}) + \mu_{jt} + \sum_{k \in
\Im}\alpha_{kj}(p_{kt}-c_{kt}) = 0.  \label{eq:disaggFOC}
\end{eqnarray}
We solve these first-order equations for the equilibrium
manufacturer prices as a function of the exogenous
factors.\footnote{The solution technique is simple.  Turning to
vector notation, one can rearrange the first-order conditions such
that $Ap=b$, where $A$ is a $J_t \times J_t$ matrix of demand
parameters, $p$ is a $J_t \times 1$ vector of manufacturer prices,
and $b$ is a $J_t \times 1$ vector of ``solutions'' that incorporate
the fuel costs, marginal costs, and demand shifters.  Provided that
the matrix $A$ is nonsingular, Cramer's Rule applies and there
exists a unique Nash equilibrium in which the equilibrium
manufacturer prices are linear functions of all the fuel costs,
marginal costs, and demand shifters.}  The resulting manufacturer
``price rule'' is a linear function of the fuel costs, marginal
costs, and demand shifters:
\begin{multline}\label{eq:mult}
p_{jt}^* =  \phi_{jt}^1 x_{jt} +\sum_{k \notin \Im}\phi^2_{jkt} x_{kt}+ \sum_{l \in \Im,\ l \neq j}\phi^3_{jlt} x_{lt}   \\
+  \phi_{jt}^4 c_{jt} +  \phi_{jt}^5 \mu_{jt} + \sum_{k \notin \Im}
\left(\phi_{jkt}^6  c_{kt} + \phi_{jkt}^7 \mu_{kt} \right)+ \sum_{l
\in \Im,\ l \neq j}\left(\phi_{jlt}^8 c_{lt} + \phi_{jlt}^9
\mu_{lt}\right).
\end{multline}
The coefficients $\phi^1, \phi^2,\dots, \phi^9$ are nonlinear
functions of all the demand parameters.  The price rule makes it
clear that the equilibrium price of a vehicle depends on its
characteristics (i.e, its fuel cost, marginal cost, and demand
shifters), the characteristics of vehicles produced by competitors,
and the characteristics of other vehicles produced by the same
manufacturer.\footnote{We divide the terms into these three groups
because Equation \eqref{eq:disaggFOC} can be rewritten:
\begin{eqnarray*}
\alpha_{jj}(2p_{jt}+ x_{jt}-c_{jt}) + \sum_{k \notin
\Im}{\alpha_{jk}(p_{kt}+ x_{kt})} + \sum_{l \in \Im,\ l \neq j}
\left(\alpha_{jl}(p_{lt}+ x_{lt})+\alpha_{lj}(p_{lt}-c_{lt})\right)
= 0,
\end{eqnarray*}
in which each group has a distinctly different functional form.} For
the time being, we collapse the second line of the price rule into a
vehicle-time-specific constant, which we denote $\gamma_{jt}$.

The sheer number of terms in Equation \ref{eq:mult} makes direct
estimation infeasible.  With only $J_t$ observations per period, one
cannot hope to identify the $J_t^2$ fuel cost coefficients, let
alone the vehicle-time-specific constant.  We move toward the
empirical implementation by re-expressing the price rule in terms of
weighted averages:
\begin{eqnarray}\label{eq:reducform}
p_{jt}^* &=&  \phi_{jt}^1 x_{jt} + \phi^2_{jt} \sum_{k \notin
\Im}\omega^2_{jkt} x_{kt}+ \phi^3_{jt}\sum_{l \in \Im,\ l \neq
j}\omega^3_{jlt} x_{lt} +\gamma_{jt},
\end{eqnarray}
where the weights $\omega^2_{jkt}$ and $\omega^3_{jlt}$ both sum to
one in each period.\footnote{The weights have specific analytical
solutions given by $\omega^i_{jkt} = \phi^i_{jkt} / \phi^i_{jt}$ for
$i=2,3$, so that closer competitors receive greater weight. The
coefficients $\phi^2_{jt}$ and $\phi^3_{jt}$ are the sums of the
$\phi^2_{jkt}$ and $\phi^3_{jkt}$ coefficients, respectively.
Mathematically, $\phi^i_{jt}=\sum \phi^i_{jkt}$ for $i=2,3$.}  Thus,
the equilibrium price depends on its fuel cost, the weighted average
fuel cost of vehicles produced by competitors, and the weighted
average fuel cost of vehicles produced by the same manufacturer.
Under a mild regularity condition that we develop in Appendix
\ref{sec:app1}, the equilibrium manufacturer price of a vehicle
decreases in its fuel cost (i.e, $\phi_{jt}^1 \in [-1,0]$) and
increases in the weighted average fuel cost of vehicles produced by
competitors (i.e., $\phi_{jt}^2 \in [0,1]$). Further, the
equilibrium price of a vehicle is more responsive to changes in its
fuel cost than identical changes to the weighted average fuel cost
of its competitors (i.e., $|\phi_{jt}^1|>|\phi_{jt}^2|$).  The
relationship between the equilibrium price of a vehicle and the
weighted average fuel cost of vehicles produced by the same
manufacturer is ambiguous (i.e., $\phi_{jt}^3 \in
[-1,1]$).\footnote{As we show in Appendix \ref{sec:app1}, if demand
is symmetric (i.e., $\alpha_{jk}=\alpha_{kj} \; \forall \; j,k$),
then changes in the fuel costs of other vehicles produced by the
same manufacturer have no effect on equilibrium prices, and
$\phi_{jt}^3=0$.}

The intuition that manufacturer prices can increase or decrease in
response to adverse gasoline price shocks can now be formalized.
Assume for the moment that the gasoline price does not affect
marginal costs or the demand shifters, and therefore does not affect
the vehicle-time-specific constant (we relax this assumption
in an extension).  Denoting the gasoline price at time
$t$ as gp$_t$, the effect of the gasoline price shock on the
manufacturer price is:
\begin{equation}
\frac{\partial p_{jt}^*}{\partial \text{gp}_t} =  \phi_j^{1}
\frac{\partial x_{jt}}{\partial \text{gp}_t} + \phi_{jt}^{2} \sum_{k
\notin \Im} \omega_{jkt}^2 \frac{\partial x_{kt}}{\partial
\text{gp}_t} +\phi_{jt}^{3} \sum_{l \in \Im,\ l\neq j}
\omega_{jlt}^2 \frac{\partial x_{lt}}{\partial \text{gp}_t},
\label{eq:pder}
\end{equation}
where fuel costs increase unequivocally in the gasoline price (i.e.,
$\partial x_{jt} / \partial \text{gp}_t >0 \; \forall \; j$). The
first term captures the intuition that manufacturers partially
offset an increase in the fuel cost with a reduction in the
vehicle's price. This reduction is greater for vehicles whose fuel
costs are sensitive to the gasoline price (e.g., for
fuel-inefficient vehicles).  The second and third terms capture the
intuition that an increases in the fuel costs of other vehicles can
increase demand (e.g., through consumer substitution) and thereby
raise the equilibrium price. Although the first effect tends to
dominate, prices can increase provided that the vehicle is
sufficiently more fuel efficient than other vehicles.\footnote{The
exact condition for a price increase is:
\begin{eqnarray*}
 \frac{\partial x_{jt}}{\partial
\text{gp}_t} < - \frac{1}{\phi_{jt}^1}\left( \phi_{jt}^{2} \sum_{k
\notin \Im} \omega_{jkt}^2 \frac{\partial x_{kt}}{\partial
\text{gp}_t} + \phi_{jt}^{3} \sum_{l \in \Im, \ l\neq j}
\omega_{jlt}^2 \frac{\partial x_{lt}}{\partial \text{gp}_t}\right).
\end{eqnarray*}  We say that manufacturer prices tend to fall in the
gasoline price because $|\phi_{jt}^1| > |\phi_{jt}^2|$ and
$\phi_{jt}^3 \approx 0 $ provided that demand that is approximately
symmetric.}

\subsection{Empirical implementation}

Our starting point for estimation is the reduced-form outlined in
Equation \ref{eq:reducform}.  The empirical implementation requires
that we specify the fuel costs ($x_{jt}$), the weights
($\omega^i_{jkt}$ for $i=2,3$), and the vehicle-time-specific
constants ($\gamma_{jt}$). We discuss each in turn.

We proxy the expected lifetime fuel cost of vehicle $j$ at time $t$
as a function of the vehicle's fuel efficiency and the gasoline
price at time $t$, following Goldberg (1998), Bento et al (2005) and
Jacobsen (2007).  The specific form is:
\[ x_{jt} =\tau * \frac{\text{gp}_t}{\text{mpg}_j}, \]
where mpg$_j$ is the fuel efficiency of vehicle $j$ in
miles-per-gallon and $\tau$ is a discount factor that nests any form
of multiplicative discounting; one specific possibility is
$\tau=1/(1-\delta)$, where $\delta$ is the ``per-mile discount
rate.''\footnote{It may help intuition to note that the ratio of the
gasoline price to vehicle miles-per-gallon is simply the gasoline
expense associated with a single mile of travel.} The fuel cost
proxy is precise if consumers perceive the gasoline price to follow
a random walk because, in that case, the current gasoline price is a
sufficient statistic for expectations over future gasoline prices.
As we discuss below, we fail to reject the null hypothesis that
gasoline prices actually follow a random walk, but also provide some
evidence that consumers consider both historical gasoline prices and
futures prices when forming expectations.

To construct the weighted average variables, we assume that the
severity of competition between two vehicles decreases in the
Euclidean distance between their attributes.  To that end, we take a
set of $M$ vehicle attributes, denoted $z_{jm} ;\ m=1,\ldots,M$, and
standardize each to have a variance of one. Then, for each pair of
vehicles, we sum the squared differences between each attribute to
calculate the effective ``distance'' in attribute space.  We form
initial weights as follows:
\begin{eqnarray} \label{weights}
\omega^*_{jk}=\frac{1}{\sum_{m=1}^M{(z_{jm}-z_{km})^2}}. \nonumber
\end{eqnarray}
To form the final weights that we use in estimation, we first set
the initial weights to zero for vehicles of different types and then
normalize the weights to sum to one for each vehicle-period.  We
perform this weighting procedure separately for vehicles produced by
the same manufacturer and vehicles produced by competitors; the
result is a set of empirical weights that we denote
$\widetilde{\omega}^2_{jkt}$ and
$\widetilde{\omega}^3_{jkt}$.\footnote{Thus, the weighting scheme is
based on the inverse Euclidean distance between vehicle attributes
among vehicles of the same type.  There are four vehicle types in
the data: cars, SUVs, trucks and vans.  We use the following set of
vehicle attributes in the initial weights: manufacturer suggested
retail price (MSRP), miles-per-gallon, wheel base, horsepower,
passenger capacity, and dummies for the vehicle type and segment.
Although the initial weights are constant across time for any
vehicle pair, the final weights may vary due to changes in the set
of vehicles available on the market.  An alternative weighting
scheme based on the inverse Euclidean distance of all vehicles (not
just those of the same type) produces similar results.}  The use of
weights based on the Euclidean distance between vehicle attributes
is analogous to the instrumenting procedures of Berry, Levinsohn,
and Pakes (1995) and Train and Winston (2007).

Turning to the vehicle-time-specific constants, recall from that
Equation \eqref{eq:mult} that the constants represent the net price
effects of marginal costs and demand-shifters:
\begin{eqnarray}
\gamma_{jt}=\phi_j^4 c_{jt} +  \phi_j^5 \mu_{jt} + \sum_{k \notin
\Im} \left(\phi_{jk}^6  c_{kt} + \phi_{jk}^7 \mu_{kt}\right) +
\sum_{l \in \Im,\ l \neq j}\left(\phi_{jl}^8  c_{lt} + \phi_{jl}^9
\mu_{lt}\right)  . \nonumber
\end{eqnarray}
In the empirical implementation, we decompose this function using
vehicle fixed effects, time fixed effects, and controls for the
number of weeks that each vehicle has been on the market.  Let
$\lambda_{jt}$ denote the number of weeks that vehicle $j$ has been
on the market as of period $t$, and $\bar{\lambda}_{A,t}$ denote the
weighted average number of weeks since the vehicles in the set $A$
were first produced. The decomposition takes the form:
\begin{eqnarray}
\gamma_{jt}= \delta_t + \kappa_j + f(\lambda_{jt}) +
g(\bar{\lambda}_{k \notin \Im,t}) + h(\bar{\lambda}_{k \in \Im,\ k
\neq j,t})+\epsilon_{jt} \nonumber
\end{eqnarray}
where $\delta_t$ and $\kappa_j$ are time and vehicle fixed effects,
respectively, and functions $f$, $g$, and $h$ flexibly capture the
net price effects of learning-by doing and predictable demand
changes over the model-year.\footnote{Copeland, Dunn and Hall (2005)
document that vehicles prices fall approximately nine percent over
the course of the model-year.} In the main results, we specify the
functions $f$, $g$, and $h$ as third-order polynomials; the results
are robust to the use of higher-order or lower-order polynomials.
The error term $\epsilon_{jt}$ captures vehicle-time-specific cost
and demand shocks.

Two final adjustments produce the main regression equation that we
take to the data.  First, we incorporate regional variation in
manufacturer prices and gasoline prices and add a corresponding set
of region fixed effects.\footnote{Adding regional variation in
prices does not complicate the weight calculations because there is
no regional variation in the vehicles available to consumers.}
Second, we impose a homogeneity constraint that reduces the total
number of parameters to be estimated; the constraint eliminates
vehicle-time variation in the coefficients, so that
$\phi^i_{jt}=\phi^i \; \forall \; j,t$ (in supplementary regressions
we permit the coefficients to vary across manufacturers and vehicle
types). The regression equation is:
\begin{eqnarray}
p_{jtr} &=&  \beta^1 \frac{\text{gp}_{tr}}{\text{mpg}_j} + \beta^2 \sum_{k \notin \Im}\widetilde{\omega}^3_{jkt} \frac{\text{gp}_{tr}}{\text{mpg}_k}  + \beta^3 \sum_{l \in \Im,\ l \neq j}\widetilde{\omega}^2_{jlt} \frac{\text{gp}_{tr}}{\text{mpg}_l}  \nonumber \\
\label{est1}\rule[0mm]{0mm}{7mm} &+& f(\lambda_{jt}) +
g(\bar{\lambda}_{k \notin \Im,t}) + h(\bar{\lambda}_{k \in \Im,\ k
\neq j,t}) + \delta_t + \kappa_j + \eta_r + \epsilon_{jt},
\label{eq:reg}
\end{eqnarray}
where the fuel cost coefficients incorporate the discount factor,
i.e., $\beta^i=\tau \phi^i$ for $i=1,2,3$; for reasonable discount
factors, these coefficients should be much larger than one in
magnitude. Thus, we estimate the average response of a vehicle's
price to changes in its fuel costs, changes in the weighted average
fuel cost among vehicles produced by competitors, and changes in the
weighted average fuel cost among other vehicles produced by the same
manufacturer.

We estimate Equation \ref{eq:reg} using ordinary least squares. We
are able to identify the fuel cost coefficients in the presence of
time, vehicle, and region fixed effects precisely because changes in
the gasoline price across time and regions affects manufacturer
prices differentially across vehicles.  We argue that manufacturers
price as if consumers respond to gasoline prices if the fuel cost
coefficient is negative (i.e., $\beta^1<0$) and the competitor fuel
cost coefficient is positive (i.e., $\beta^2>0$).  The theoretical
results suggest that the fuel cost coefficient should be larger in
magnitude than the competitor fuel cost coefficient (i.e.,
$\left|\beta^1 \right| > \left| \beta^2 \right|$); more generally,
the relative magnitude of these coefficients determines the extent
to which average manufacturer prices fall in response to an adverse
gasoline shock.  We cluster the standard errors at the vehicle
level, which accounts for arbitrary correlation patterns in the
error terms.\footnote{The results are robust to the use of
brand-level or segment-level clusters.  Brands and vehicle segments
are finer gradations of the manufacturers and vehicle types,
respectively. There are 21 brands and 15 vehicle segments in the
data. Examples of brands (and their manufacturer) include Chevrolet
(GM), Dodge (Chrysler), Mercury (Ford), and Lexus (Toyota). Examples
of vehicle segments include compact cars, luxury SUVs, and large
pick-ups. The results are also robust to the use of manufacturer and
vehicle type clusters, though the small number of manufacturers and
vehicle types makes the asymptotic consistency of the standard
errors suspect.}


\section{Data Sources and Regression Variables} \label{sec:data}

\subsection{Data sources}

Our primary source of data is Autodata Solutions, a marketing
research company that maintains a comprehensive database of
manufacturer incentive programs.  We have access to the programs
offered by Toyota and the ``Big Three'' U.S. manufacturers -- GM,
Ford, and Chrysler -- over the period 2003-2006.\footnote{The German
manufacturer Daimler owned Chrysler over this period.  We exclude
Mercedes-Benz from this analysis since it is traditionally
associated with Daimler rather than Chrysler.} There are just over
190,000 cash incentive-vehicle pairs in the data.  Each lasts a
fixed period of time, and provides cash to consumers
(``consumer-cash'') or dealerships (``dealer-cash'') at the time of
purchase.\footnote{Consumer cash includes both ``Stand-Alone Retail
Cash'' and ``Bonus Cash.''}  The incentive programs may be national,
regional, or local in their geographic scope; we restrict our
attention to the national and regional programs.\footnote{We
consider an incentive to be regional if it is available across an
entire Energy Information Agency region.  We exclude incentives that
are available in only a single city or state.} Thus, we are able to
track how manufacturer incentives change over time and across
regions for each vehicle in the data.

By ``vehicle,'' we mean a particular model in a particular
model-year.  For example, the 2003 Ford Taurus is one vehicle in the
data, and  we consider it as distinct from the 2004 Ford Taurus.
Overall, there are 681 vehicles in the data -- 293 cars, 202 SUVs,
105 trucks, and 81 vans.  The data have information on the
attributes of each, including MSRP, miles-per-gallon, horsepower,
wheel base, and passenger capacity.\footnote{Attributes sometimes
differ for a given vehicle due to the existence of different option
packages, also known as ``trim.'' When more than one set of
attributes exists for a vehicle, we use the attributes corresponding
to the trim with the lowest MSRP.}  We impute the period over which
each vehicle is available to consumers as beginning with the start
date of production, as given in Ward's Automotive Yearbook, and
ending after the last incentive program for that vehicle
expires.\footnote{The start date of production is unavailable for
some vehicles.  For those cases, we set the start date at August 1
of the previous year.  For example, we set the start date of the
2006 Civic Hybrid to be August 1, 2005. We impose a maximum period
length of 24 months. In robustness checks, we used an 18 month
maximum; the different period lengths did not affect the results.}
For each vehicle, we construct observations over the relevant period
at the week-region level.

We combine the Autodata Solutions data with information from the
Energy Information Agency (EIA) on weekly retail gasoline prices in
each of five distinct geographic regions.  The EIA surveys retail
gasoline outlets every Monday for the per gallon pump price paid by
consumers (inclusive of all taxes).\footnote{The survey methodology
is detailed online at the EIA webpage.  The regions include the East
Coast, the Gulf Coast, the Midwest, the Rocky Mountains, and the
West Coast.}  In addition to the regional measures, the EIA
calculates an average national price.  Figure \ref{fig:gp1} plots
these retail gasoline prices over 2003-2006 (in real 2006 dollars).
A run-up in gasoline prices over the sample period is apparent.  For
example, the mean national gasoline price is 1.75 dollars-per-gallon
in 2003 and 2.57 dollars-per-gallon in 2006. The sharp upward spike
around September 2005 is due to Hurricane Katrina, which temporarily
eliminated more than 25 percent of US crude oil production and 10-15
percent of the US refinery capacity (EIA 2006).  Although gasoline
prices tend to move together across regions, we are able to exploit
limited geographic variation to strengthen identification.

We purge the gasoline prices of seasonality prior to their use in
the analysis. Since automobile manufacturers adjust their prices
cyclically over vehicle model-years (e.g., Copeland, Hall, and Dunn
2005), the presence of seasonality in gasoline prices is potentially
confounding.  Further, the use of time fixed effects alone may be
insufficient in dealing with seasonality because gasoline prices
affect the fuel costs of each vehicle differentially (e.g., Equation
\ref{eq:reg}).  We employ the X-12-ARIMA program, which is
state-of-the-art and commonly employed elsewhere, for example by the
Bureau of Labor Statistics to deseasonalize inputs to the consumer
price index.\footnote{We use data on gasoline prices over 1993-2008
to improve the estimation of seasonal factors, and adjust each
national and regional time-series independently.  We specify
multiplicative decomposition, which allows the effect of seasonality
to increase with the magnitude of the trend-cycle.  The results are
robust to log-additive and additive decompositions. For more details
on the X-12-ARIMA, see Makridakis, Wheelwright and Hyndman (1998)
and Miller and Williams (2004).} Figure \ref{fig:gp2} plots the
resulting deseasonalized national gasoline prices together with the
seasonal adjustments.  As shown, the program adjusts the gasoline
price downward during the summer months and upwards during the
winter months.  The magnitude of the adjustments increases with
gasoline prices.

In an extension (presented in Section \ref{sec:ext}), we explore
whether consumers consider historical and futures prices when
forming expectations about future gasoline prices. Interestingly,
statistical tests based on Dicky and Fuller (1979) fail to reject
the null that gasoline prices follow a random walk -- the
\textit{p}-statistic for the deseasonalized national time-series is
0.7035 and the \textit{p}-statistics for the deseasonalized regional
time-series are similar. These tests suggest that knowledge of the
current gasoline price is sufficient to inform predictions over
future gasoline prices.  The result is consistent with the academic
literature and statements of industry experts.  For example, Alquist
and Kilian (2008) find that the current spot price of crude oil
outperforms sophisticated forecasting models as a predictor of
future spot prices, and Peter Davies, the chief economist of British
Petroleum, has stated that ``we cannot forecast oil prices with any
degree of accuracy over any period whether short or long...''
(Davies 2007). If consumers form expectations efficiently,
therefore, one would not expect historical and/or futures prices of
gasoline to influence vehicle purchase decisions.

\subsection{Regression variables}

The two critical variables that enable regression analysis are
manufacturer price and fuel cost.  We discuss each in turn. To
start, we measure the manufacturer price of each vehicle as MSRP
minus the mean incentive available for the given week and region. We
also show results in which the variable includes only regional
incentives and only national incentives, respectively.  From an
econometric standpoint, the MSRP portion of the variable is
irrelevant for estimation because the vehicle fixed effects are
collinear (MSRP is constant for all observations on a given
vehicle).  It is the variation in manufacturer incentives across
vehicles, weeks, and regions that identifies the regression
coefficients.

At least two important caveats apply to our manufacturer price
variable. First, the variable does not capture any information about
final transaction prices, which are negotiated between the consumers
and the dealerships.  Changes in negotiating behavior could dampen
or accentuate the effect we estimate between gasoline prices and
manufacturer prices.  Second, although we observe the incentive
programs, we do not observe the actual incentives selected.  In some
circumstances, it is possible that consumers may stack multiple
incentives or choose between different incentives.  To the extent
that manufacturers are more lenient in allowing consumers to stack
incentives when gasoline prices are high, our regression estimates
are conservative relative to the true manufacturer
response.\footnote{To check the sensitivity of the results, we
construct a number of alternative variables that measure
manufacturer prices: 1) MSRP minus the maximum incentive, 2) MSRP
minus the mean consumer-cash incentive, 3) MSRP minus the mean
dealer-cash incentive, and 4) MSRP minus the mean publicly available
incentive. None of these alternative dependent variables
substantially change the results.}

We measure the fuel costs of each vehicle as the gasoline price
divided by the miles-per-gallon of the vehicle.  As discussed above,
this has the interpretation of being the gasoline expense associated
with a single mile of travel.  Since the gasoline price varies at
the week and region levels and miles-per-gallon varies at the
vehicle level, fuel costs vary at the vehicle-week-region level.  In
an extension, we construct alternative fuel costs based on 1) the
mean of the gasoline price over the previous four weeks and 2) the
price of one-month futures contract for retail gasoline.  The
futures data are derived from the New York Mercantile Exchange
(NYMEX) and are publicly available from the EIA.\footnote{We use
one-month futures contracts for reformulated regular gasoline at the
New York harbor. In order to ensure that the regression coefficients
are easily comparable, we normalize the futures price to have the
same global mean over the period as the national retail gasoline
price.} The alternative variables permit tests for whether consumers
are backward-looking and forward-looking, respectively.

Table \ref{tab:sumstat1} provides means and standard deviations for
the manufacturer price and the gasoline price variables, as well as
for five vehicle attributes used in the weighting scheme -- MSRP,
miles-per-gallon, horsepower, wheel base, and passenger capacity.
The statistics are calculated from the 299,855 vehicle-region-week
observations formed from the 681 vehicles, 208 weeks, and five
regions in the data.  As shown, the mean manufacturer price is
30.344 (in thousands).  The mean fuel cost is 0.108, so that
gasoline expenses average roughly eleven cents per mile.  The means
of MSRP, miles-per-gallon, horsepower, wheel base, and passenger
capacity are 30.782, 21.555, 224.123, 115.193, and 4.911,
respectively.

Table \ref{tab:sumstat2} shows the means of these variables,
calculated separately for each vehicle type. On average, cars are
less expensive than SUVs but more expensive than trucks and vans.
The mean manufacturer price for the four vehicle types are 30.301,
35.301, 24.482, and 24.658, respectively. Cars also require far less
gasoline expense per mile.  The mean fuel cost of 0.087 is nearly
thirty percent smaller than the means of 0.121, 0.133, and 0.120 for
SUVs, trucks, and vans, respectively.  The means of the attributes
used in the weights also differ across type, and reflect the
generalization that cars are smaller, more fuel efficient, and less
powerful than SUVs, trucks, and vans.  Of course, the vehicles also
differ along unobserved dimensions.  We use vehicle fixed effects to
control for all these differences -- observed and unobserved -- in
our regression analysis.

\section{Empirical Results \label{sec:res}}

\subsection{Main regression results}

We regress manufacturer prices on fuel costs, as specified in
Equation \ref{eq:reg}.  To start, we impose the full homogeneity
constraint that all vehicles share the same fuel cost coefficients.
The estimated coefficients are the average response of manufacturer
prices to fuel costs.  Table \ref{tab:regs1} presents the results.
In Column 1, we use the baseline manufacturer price -- MSRP minus
the mean of the regional and national incentives.  In Columns 2 and
3, we use MSRP minus the mean regional incentive and MSRP minus the
mean national incentive, respectively. Although the first column may
provide more meaningful coefficients, we believe that the second and
third columns are interesting insofar as they examine whether
manufacturers respond at the regional and national levels,
respectively.

As shown, the fuel cost coefficients of -55.40, -56.96, and -63.75
are precisely estimated and capture the intuition that manufacturers
adjust their prices to offset changes in fuel costs. The competitor
fuel cost coefficients of 50.76, 50.16, and 50.09 are also precisely
estimated and support the idea that increases in competitors' fuel
costs raise demand due to consumer substitution.  In each
regression, the magnitude of the fuel cost coefficient exceeds that
of the competitor fuel cost coefficient, which is suggestive that
the first effect dominates for most vehicles.\footnote{The fuel cost
coefficients contribute substantially to the regression fits. For
example, the $R^2$ of Column 1 is reduced from 0.5260 to 0.4133 when
the fuel cost variables are removed from the specification, so that
changes in vehicle fuel costs explain more than ten percent of the
variance in manufacturer prices.}  We make this more explicit
shortly. The same-firm fuel cost coefficients are nearly zero and
not statistically significant.\footnote{As we develop in Appendix
\ref{sec:app1}, this is consistent with demand being roughly
symmetric.} Finally, a comparison of coefficients across columns
suggests that manufacturers adjust their prices similarly at the
regional and national levels in response to changes in fuel
costs.\footnote{The results to not seem to be driven by outliers;
the coefficients are similar when we exclude the extremely fuel
efficient or fuel inefficient vehicles from the sample.}

We explore the effect of retail gasoline prices on manufacturer
prices in Figure \ref{fig:regs1}.  The gasoline price enters through
the fuel costs, average competitor fuel costs, and average same-firm
fuel costs.  We calculate the effect of a one dollar increase in the
gasoline price for each vehicle-week-region observation:
\begin{equation} \frac{\partial
p_{jrt}}{\partial\text{gp}_{rt}}=\frac{\widehat{\beta}_1}{\text{mpg}_j}+\widehat{\beta}_2
\sum_{k\neq j}
\frac{\widetilde{\omega}_{jkt}^2}{\text{mpg}_k}+\widehat{\beta}_3
\sum_{k\neq j} \frac{\widetilde{\omega}_{jkt}^2}{\text{mpg}_k}.
\label{eq:der} \nonumber
\end{equation}
We plot these derivatives (in thousands) on the vertical axis
against vehicle miles-per-gallon on the horizontal axis.  We focus
on the first dependent variable, i.e., MSRP minus the mean regional
and national incentive.\footnote{We plot each vehicle only once
because the derivatives do not vary substantially over time or
regions.  Indeed, the only variation within vehicles is due to
changes in the set of other vehicles available.} The median effect
of a one dollar increase in the gasoline price per gallon is a
reduction in the manufacturer price of \$171. The calculation varies
greatly across vehicles -- for example, the effects range from a
reduction of \$1,506 for the 2005 GM Montana SV6 to a rise of \$998
for the 2006 Toyota Prius. Although the manufacturer price drops for
83 percent of the vehicles, the price response for fuel efficient
vehicles tends to be less negative, and the prices of extremely fuel
efficient vehicles such as hybrids actually increase.  Overall, the
own fuel cost effect dominates the competitor fuel cost effect for
most vehicles; the converse is true only for vehicles that are
substantially more fuel efficient than their competitors.

We use sub-sample regressions to relax the homogeneity constraint
that all vehicles share the same fuel cost coefficients.  In
particular, we regress manufacturer prices on the fuel cost
variables for each combination of vehicle type (cars, SUVs, trucks,
and vans) and manufacturer (GM, Ford, Chrysler, and Toyota). The
sub-sample regressions may be informative, for example, if the
market for cars is more (or less) competitive than the market for
SUVs, if region- and time-specific cost and demand shocks affect
cars and SUVs differentially, or if consumers who purchase different
vehicle types are heterogeneous (for instance if they drive
different mileage or have different discount factors).\footnote{One
might additionally suspect that the response of manufacturer prices
to fuel costs changes over time. To test for such heterogeneity, we
split the observations to form one sub-sample over the period
2003-2004 and another over the period 2005-2006; the results from
each sub-sample are quite close. Similarly, we divide the sample
between the 2003-2004 model-years and the 2005-2006 model-years
without substantially changing the results. We conclude that the
effects of any time-related heterogeneity are relatively small.} For
expositional brevity we focus solely on the baseline manufacturer
price and present the results using figures. The regression
coefficients appear in Appendix Table \ref{tab:regs3}.

Figure \ref{fig:regs3} plots the estimated effects of a one dollar
increase in the gasoline price on manufacturer prices against
vehicle miles-per-gallon, separately for each vehicle
type.\footnote{Each plot combines the results of four regressions,
one for each manufacturer.}  Converted into dollars, the median
estimated effect is a reduction in the manufacturer price of \$779,
\$981, and \$174 for cars, SUVs, and trucks, respectively, and an
increase of \$91 for vans.  Among cars and SUVs, the fuel cost
effect almost always dominates the competitor fuel cost effect: 91
percent of the cars and 95 percent of the SUVs feature negative net
effects.  Still, the estimated manufacturer price response is less
negative for more fuel efficient vehicles, so that the univariate
correlation coefficient between the price response and
miles-per-gallon is 0.6610 for cars and 0.7521 for
SUVs.\footnote{Appendix Table \ref{tab:lists} lists the largest
positive and negative price effects for both cars and SUVs.}  By
contrast, the magnitude of the estimated effects are much smaller
for trucks and vans, as is the strength of the relationship between
the effects and vehicle fuel efficiency.

In order to provide some sense of the economic magnitude of these
results, we use back-of-the-envelope calculations to (roughly)
estimate the extent to which manufacturers offset changes in
consumers' cumulative gasoline expenses.  We assume an annual
discount rate of five percent, a vehicle holding period of thirteen
years, and a utilization rate of 11,154 miles per year (the
Department of Transportation estimates an average vehicle lifespan
of thirteen years and 145,000 miles). Under these parameters, the
cumulative gasoline expense associated with a one dollar increase in
the gasoline prices ranges between \$1,972 and \$7,953 among the
sample vehicles; the expense for the median vehicle
(miles-per-gallon of 21.40) is \$5,073.  We divide the estimated
manufacturer responses, based on the regression coefficients shown
in Appendix Table \ref{tab:regs3}, by the computed cumulative
gasoline expense.  The resulting ratio is the percent of cumulative
gasoline expenses, due to a change in the retail gasoline price,
that is offset by changes in the manufacturer price.

Figure \ref{fig:poffset} plots this ``offset percentage'' against
vehicle miles-per-gallon, separately for each vehicle type.  The
median offset percentage is 18.17 and 15.27 for cars and SUVs,
respectively, but climbs as high as 52.17 for cars (the 2006 Ford
GT) and as high as 33.92 for SUVs (the 2004 GM Envoy XUV).  These
percentages fall in vehicle fuel efficiency, so that the univariate
correlation coefficients between the offset percentage and
miles-per-gallon for cars and SUVs are -0.6292 and -0.6681,
respectively. By contrast, the offset percentage is smaller for
trucks and vans. We wish to emphasize that these numbers should be
interpreted with considerable caution. Alternative assumptions
regarding the discount rate, the vehicle holding period, and the
utilization rate could push the offset percentages higher or lower.
Further, as previously discussed, the manufacturer price we use to
estimate the regressions -- MSRP minus the mean available incentive
-- could understate the manufacturer responses and the offset
percentages if some consumers stack multiple incentives.

Returning the regression results of Appendix Table \ref{tab:regs3},
in Figure \ref{fig:regs3a} we plot the estimated manufacturer price
effects against vehicle miles-per-gallon for cars, separately for
each manufacturer. The estimated effects are negative for all GM and
Ford cars, and negative for 92 percent of the Toyota cars (all but
the 2003 Echo and the four Prius vehicles). Converted into dollars,
the median estimated effect for these manufacturers is a reduction
in price of \$610, \$1180, and \$758, respectively.  By contrast,
only 38 percent of the Chrysler estimated effects are negative and
the median effect is an increase of \$107.  This difference between
Chrysler and the other manufacturers remains even for a given level
of fuel efficiency. For example, the mean effects for cars with between
25 and 35 miles-per-gallon are reductions of \$529, \$843,
and \$719, respectively, for GM, Ford and Toyota, but an increase of
\$239 for Chrysler.  One might conclude that Chrysler pursues a
different pricing strategy than GM, Ford, and Toyota.  However, an
alternative explanation is that Chrysler vehicles are simply more
fuel efficient than their competitors (e.g., Chrysler vehicles could
be closer to inefficient vehicles in attribute space). We compare
the manufacturers' pricing rules more explicitly in Section
\ref{sec:ext}.

We plot the estimated manufacturer price effects among SUVs
separately for each manufacturer in Figure \ref{fig:regs3b}. Among
the GM, Ford, and Toyota SUVs, the estimated price effects are
positive for only four vehicles: the 2006 (Ford) Mercury Mariner
Hybrid, the 2006 Ford Escape Hybrid, the 2006 Toyota Highlander
Hybrid and the 2006 Lexus RX 400 Hybrid.  The median estimated
effects for GM, Ford, and Toyota are reductions in price of \$1315,
\$663, and \$754, respectively.  The price effects are more negative
for fuel inefficient SUVs. By contrast, the estimated price effects
are positive for nearly 30 percent of the Chrysler SUVs and the
price effects are actually more negative for fuel efficient
SUVs.\footnote{The univariate correlation coefficients between the
price effects and miles-per-gallon are 0.9062, 0.8584, and 0.9447
for GM, Ford, and Toyota, respectively, and -0.1765  for Chrysler.}
The unexpected pattern among Chrysler SUVs exists because the
estimated fuel cost coefficient is positive and the competitor fuel
cost coefficient is negative (see Appendix Table \ref{tab:regs3}),
inconsistent with the profit maximizing pricing rule derived in the
theoretical framework.


\subsection{Extensions \label{sec:ext}}

\subsubsection{Lagged retail gasoline prices and gasoline futures}

The main results are based on the premise that consumers form
expectations about future retail gasoline prices based on current
retail gasoline prices.  We explore that premise here.  In
particular, we examine whether manufacturers set vehicle prices in
response to information on historical gasoline prices and gasoline
futures prices.  We construct two new sets of fuel cost variables.
The first uses the mean retail gasoline price over the previous four
weeks, and the second uses the one-month futures price for retail
gasoline. To the extent that consumers are backward-looking and
forward-looking, respectively, manufacturers should adjust vehicle
prices to these new fuel cost variables.  The units of observation
are at the vehicle-week level; we discard regional variation because
futures prices are available only at the national level.  The
results are therefore comparable to Column 3 of Table
\ref{tab:regs1}.

Table \ref{tab:fut} presents the regression results.  Columns 1 and
2 include variables based on mean lagged gasoline prices and
gasoline futures prices, respectively. The fuel cost coefficients
are -64.55 and -47.66; the competitor fuel cost coefficients are
50.01 and 63.32.  The coefficients are statistically significant and
consistent with the theoretical model.  Still, the more interesting
question is whether these variables matter after controlling for the
current price of retail gasoline. Columns 3 and 4 include variables
based on mean lagged gasoline prices and gasoline futures prices,
respectively, together with variables based on the current gasoline
price.  Each of the coefficients takes the expected sign and
statistical significance is maintained for all but two coefficients.
Finally, Column 5 includes variables based on mean lagged gasoline
prices and variables based on gasoline futures prices.  The
coefficients are precisely estimated and again take the correct
sign.

The finding that consumers may use historical gasoline prices and
gasoline futures prices to form expectations for gasoline prices is
interesting, in part because both the empirical evidence and the
conventional wisdom of industry experts suggest that gasoline prices
follow a random walk (as we outline Section \ref{sec:data}).  One
could argue that some consumers form inefficient expectations for
future gasoline prices.  Alternatively, some consumers may be
imperfectly informed about the current gasoline price; these
consumers could rationally turn to alternative sources of
information, such as historical prices and/or futures prices.  We
are skeptical that our data can untangle these informal hypotheses
and hope that future research better addresses the topic.

\subsubsection{Impulse Response Functions}

In this section, we examine manufacturer price responses for
hypothetical, ``perfectly average'' vehicles.  We define a perfectly
average vehicle as one whose miles-per-gallon, weighted-average
competitor miles-per-gallon, and weighted-average same-firm
miles-per-gallon are all at the mean (for cars the mean is 25.99;
for SUVs it is 18.80).  Hypothetical vehicles are advantageous for
comparisons of manufacturers because they strip away the vehicle
heterogeneity that may not be apparent in the main results (e.g.,
Figures \ref{fig:regs3a} and \ref{fig:regs3b}); one can essentially
compare the performance of manufacturer price rules under identical
circumstances.\footnote{For example, based on Figure
\ref{fig:regs3a} alone, it is not clear whether Chrysler employs a
fundamentally different pricing rule than GM, Ford, and Toyota, or
whether its vehicles are simply more fuel efficient than their
competitors (e.g., they could be closer to inefficient vehicles in
attribute space).}

We use impulse response functions to track the effects of a gasoline
price shock, during the week of the shock and each of the following
ten weeks.  The approach may be of additional interest to the extent
that it captures dynamics. To compute the impulse response function,
we add ten lags of each fuel cost variable to the baseline
specification, and estimate the specification separately for the
cars and SUVs of each manufacturer. We then calculate the predicted
effects of a one dollar increase in the gasoline price for the
perfectly average car and SUV (in principle, one could examine any
hypothetical vehicle).

Figure \ref{fig:lag10} shows the results.\footnote{Appendix Tables
\ref{tab:lags1} and \ref{tab:lags2} provide the regression
coefficients. The individual coefficients are difficult to interpret
due to the high degree of co-linearity among the 33 fuel cost
regressors, but the net manufacturer price effects are reasonable,
easily interpretable, and consistent with the main results.}
Starting with the cars, GM, Ford, and Toyota reduce prices by \$516,
\$495, and \$691, respectively, immediately following the gasoline
price shock, while Chrysler increases prices by \$106. The
discrepancies between the manufacturer grow steadily over the
following ten weeks; by the final week, the net price changes are
reductions of \$1,495, \$2,767, \$1,673, and \$21 for GM, Ford,
Toyota, and Chrysler, respectively.  Turning to the SUVs, GM, Ford,
and Toyota reduce their prices by \$121, \$105, and \$569,
respectively, immediately following the gasoline shock, while
Chrysler increases prices by \$63.  Again, the discrepancies between
the manufacturer grow steadily over the following weeks; by the
final week, the net price changes are reductions of \$831, \$612,
\$1,422, and \$72 for GM, Ford, Toyota, and Chrysler, respectively.
Overall, Ford reacts most aggressively relative to the other
manufacturers in adjusting its car prices;  Toyota reacts most
aggressively for SUVs. Chrysler's reactions are negligible for both
vehicle types.

Two of the results merit further discussion.  First, we find
Chrysler's price responses puzzling because the theoretical
framework indicates that demand for the perfectly average vehicle
\textit{must fall} in response to an adverse gasoline
shock.\footnote{A corollary is that the fuel cost coefficient should
be larger in magnitude than the competitor fuel cost coefficient,
i.e., $|\phi_{jt}^1|>|\phi_{jt}^2|$.  In the main regression
results, shown in Table \ref{tab:regs3}, this holds for GM, Ford,
and Toyota, but not for Chrysler.}  We are reticent to conclude that
Chrysler's pricing rule is suboptimal, however, in the absence of
more sure evidence. It is possible that Chrysler's consumers are
distinctly unresponsive to fuel costs, or that Chrysler adjusts its
prices without using incentives.\footnote{Chrysler dealerships may
adjust prices.  We note, however, that our data include cash
incentives paid to both consumers (``consumer-cash'') and
dealerships (``dealer-cash'').} Second, the result that manufacturer
prices continue to fall after the initial gasoline price shock is
consistent with the hypothesis that consumers internalize gasoline
price shocks slowly over time. The result could also be consistent
with some forms of dynamic competition or certain supply-side
frictions; we leave the exploration of these possibilities to future
research.


\subsubsection{Demand and cost factors}

In the main regressions we estimate a separate time fixed effect for
each of the 208 weeks in the data.  These fixed effects capture the
combined influence of demand and cost factors that change over time
through the sample period.  In this section, we use a second-stage
regression to decompose the fixed effects into contributions from
specific time-varying demand and cost factors.  We are particularly
interested in whether the retail gasoline price affects manufacturer
prices after having controlled for its impact on vehicle fuel costs.
Such an effect could be present if higher gasoline prices increase
manufacturer production costs or reduce consumer demand through an
income effect.\footnote{For example, Gicheva, Hastings, and
Villas-Boas (2007) identify an income effect of gasoline prices
using scanner data on grocery purchases.} One might expect these two
channels to partially offset; we can identify only the net effect.

Figure \ref{fig:timeFE2} plots the time fixed effects estimated in
Column 3 of Table \ref{tab:regs1}, together with the prime interest
rate and the unemployment rate (which may shift demand), price
indices for electricity and steel (which may shift manufacturer
costs), and the retail gasoline price (which may shift demand and
costs).  The fixed effects units are in thousands, so that a fixed
effect of 0.25 represents manufacturer prices that are \$250 on
average higher than manufacturer prices during the first week of
2003 (the base date).  The fixed effects are higher in the winter
months than in the summer months, consistent with the notion that
manufacturer prices fall as consumers anticipate the arrival of new
vehicles to the market in the summer months (e.g., Copeland, Dunn,
and Hall 2005).  The prime interest rate increases over the sample
while unemployment decreases; the means of these variables are 5.64
and 5.30, respectively.  The electricity and steel indices are
defined relative to January 1, 2003; the prices of these cost
factors increase over the sample by 10 and 61 percent, respectively.
The mean gasoline price is \$2.16 per gallon, and gasoline prices
increase over the sample.\footnote{The electricity index is publicly
available from the EIA, and the steel index is publicly available
from Producer Price Index maintained by the Bureau of Labor
Statistics.  We deseasonalize both indices using the X12-ARIMA prior
to their use in analysis.}

We regress the estimated time fixed effects on different
combinations of the demand and cost factors.\footnote{Each
regression includes week fixed effects to help control for
seasonality.  To be clear, we estimate 52 week fixed effects using
208 weekly observations; equivalent weeks in each year are
constrained to have the same fixed effect. We use the Newey and West
(1987) variance matrix to account for first-order autocorrelation.
The standard errors do not change substantially when we account for
higher-order autocorrelation. We are unable to use the more general
clustering correction because the data lack cross-sectional
variation.  Of course, the standard errors may be too small because
the dependent variable is estimated in a prior stage.}  Table
\ref{tab:regsts} presents the results. Column 1 features only the
gasoline price, Column 2 features the gasoline price and the other
demand factors, Column 3 features gasoline price and the other cost
factors, and Column 4 features all five demand and cost factors. The
coefficients are remarkably stable across specifications.  In each
column, the gasoline price coefficient is small and statistically
indistinguishable from zero; gasoline prices appear to have little
effect on manufacturer prices after controlling for vehicle fuel
costs. The remaining coefficients take the expected signs. Based on
the Column 4 regression, a one percentage point increase in prime
interest rate reduces manufacturer prices by \$164 and a one
percentage point increase in the unemployment rate reduces
manufacturer prices by \$104 (though the latter effect is not
statistically significant). Similarly, ten percent increases in the
prices of electricity and steel raise manufacturer prices by \$283
and \$55, respectively.

\subsubsection{Vehicle inventories}

We use the assumption that manufacturers have full information about
consumer demand conditions to generate a simple linear pricing rule.
It is not clear whether the assumption is appropriate. For example,
manufacturers may receive only noisy signals about demand, and
accurate information may be costly to obtain.  In such an
environment, one might expect manufacturers to set their prices
primarily based on their observed inventories; demand conditions
would affect prices only indirectly.  As a specification test, we
re-estimate the empirical model controlling for inventories.  The
main theoretical framework -- and its simple pricing rule -- should
gain credibility if the fuel cost coefficients remain important.

To implement the test, we collect data on the ``days supply'' of
inventory from Automotive News, a major trade publication.  Days
supply is the current inventory divided by sales during the previous
month (the units are easily converted from months to days).  The
measure is frequently used in industry analysis (e.g., Windecker
2003).  Intuitively, the days supply should be high when demand is
sluggish and low when demand is great.  The units of observation are
at the month-model level.  To be clear, the inventories data do not
vary across weeks within a month, and the data lump all vehicles
within a given model (e.g., the 2003 Dodge Neon and 2004 Dodge
Neon). We map the data into the main regression sample by using
cubic splines to interpolate weekly observations. We then apply the
days supply to every vehicle in the model category. The procedure
generates a regression sample of 500 vehicles and 41,822
vehicle-week observations.\footnote{We have inventory data for 500
of the 589 domestic vehicles in the data; the Toyota data are
insufficiently disaggregated to support analysis. The mean days
supply among the 41,822 vehicle-week observations is 92.18. The
25$^{th}$, 50$^{th}$, and 75$^{th}$ percentiles are 62.26, 84.63,
and 109.42, respectively.}

Table \ref{tab:inv} presents the regression results.  In Column 1,
we re-estimate the same specification as in Table \ref{tab:regs1},
Column 3 using only those observations for which we have information
on inventories.  The fuel cost and competitor fuel cost coefficients
are -69.23 and 53.16, respectively.\footnote{The fact that these
coefficients are close to those produced by the full sample provides
some comfort that the smaller inventory sample does not introduce
sample selection problems or other complexities.} We add the days
supply measure to the specification in Column 2. The fuel cost and
competitor fuel cost coefficients of -69.11 and 53.00 are virtually
unchanged.\footnote{The days supply coefficient is small and
statistically indistinguishable from zero. We are wary of
interpreting this coefficient too strongly because inventories may
be correlated with the vehicle-time specific cost and demand shocks
that compose the error term in the regression equation.}  The result
suggests that manufacturers respond to changes in demand conditions
before these changes affect inventories;  one might infer that
manufacturers are well informed about consumer preferences.  The
result also strengthens our interpretation of the main empirical
results: manufacturers intentionally set prices as if consumers
respond to gasoline prices.

\section{Conclusion}\label{sec:conc}

We provide empirical evidence that automobile manufacturers adjust
vehicle prices in response to changes in the price of retail
gasoline. In particular, we show that the vehicle prices tend to
decrease in their own fuel costs and increase in the fuel costs of
their competitors.  The net effect is such that adverse gasoline
price shocks reduce the price of most vehicles but raise the price
of particularly fuel efficient vehicles.  We argue, based on
theoretical micro foundations, that these empirical results are
consistent with the notion that automobile manufacturers set prices
as if consumers value (low) fuel costs.  In terms of policy
implications, the results suggest that gasoline and/or carbon taxes
may be effective instruments in mitigating the negative
externalities associated with gasoline combustion in automobiles.
The results do not speak, however, to the optimal magnitude of any
policy responses; we leave that important matter to future research.


\newpage
\begin{thebibliography}{99}

\singlespace

\bibitem{AlquistKilian2008}Alquist, Ron and Lutz Kilian. 2008.  What
do we learn from the price of crude oil futures?  Mimeo.

\bibitem{BentoETAL2005}Bento, Antonio, Lawrence Goulder, Emeric
Henry, Mark Jacobsen, and Roger von Haefen.  2005.  Distributional
and efficiency impacts of gasoline taxes: an econometrically based
multi-market study.  \textit{American Economic Review -- Papers and
Proceedings}, 95.

\bibitem{BerryLevinsohnPakes2004}Berry, Steve, Jim Levinsohn, and
Ariel Pakes.  2004.  Estimating differentiated product demand
systems from a combination of micro and macro data: the market for
new vehicles.  \textit{Journal of Political Economy}, 112: 68-105.

\bibitem{CopelandDunnHall2005}Copeland, Adam, Wendy Dunn, and George
Hall.  2005.  Prices, production and inventories over the automotive
model year.  NBER Working Paper 11257.

\bibitem{CorradoDunnOtoo2006}Corrado, Carol, Wendy Dunn, and Maria
Otoo.  2006.  Incentives and prices for motor vehicles: what has
been happening in recent years.  FEDS Working Paper.

\bibitem{Davies2007}Davies, Peter.  2007.  What's the value of an energy
economist?  Speech presented at the International Association of
Energy Economics, Wellington, New Zealand.

\bibitem{DickeyFuller1979}Dickey, D. A., and W. A. Fuller.  1979. Distribution
of the estimators for autoregressive time series with a unit root.
\textit{Journal of the American Statistical Association}, 74:
427–431.

\bibitem{EIA2006}Department of Energy, Energy Information Agency.
2006.  A primer on gasoline prices.

\bibitem{GichevaHastingsVillasBoas2007}Gicheva, Dora, Justine
Hastings, and Sofia Villas-Boas.  2007.  Revisiting the income
effect: gasoline prices and grocery purchases.  CUDARE Working
Paper.

\bibitem{Goldberg1998}Goldberg, Pinelopi.  1998.  The effects of the
corporate average fuel economy standards in the automobile industry.
\textit{Journal of Industrial Economics}, 46: 1-33.

\bibitem{Jacobsen2008}Jacobsen, Mark.  2008.  Evaluating U.S. fuel
economy standards in a model with producer and household
heterogeneity.  Mimeo.

\bibitem{LiTimminsvonHaefen2007}Li, Shanjun, Christopher Timmins,
and Roger H. von Haefen.  2007.  Do gasoline prices affect fleet
fuel economy?  Mimeo.


\bibitem{MakridakisWheelwrightHyndman1998}Makridakis, Spyros, Steven
C. Wheelwright, and Rob J. Hyndman.  1998.  \textit{Forecasting
Methods and Applications}.  (3$^{rd}$ ed.).  New York: Wiley.

\bibitem{MillerWilliams2004}Miller, Don M. and Dan Williams.  2004.
Damping seasonal factors: Shrinkage estimators for the X-12-ARIMA
program.  \textit{International Journal of Forecasting}, 20:
529-549.

\bibitem{NeweyWest1987}Newey, Whitney K., and Kenneth D. West. 1987.
A simple positive semi-definite, heteroskedasticity and
autocorrelation consistent covariance matrix. \textit{Econometrica},
55: 703-708.

\bibitem{Windecker2003}Windecker, Ray.  2003.  The battle of the
bulge: the intricacies and lessons of days supply.
\textit{Automotive Industries}, November.

\bibitem{WinstonTrain2007}Train, Kenneth and Cliff Winston. 2007.
Vehicle choice behavior and the declining market share of U.S.
automakers.  \textit{International Economic Review}, 48: 1469-1496.

\end{thebibliography}

\newpage
\appendix

\singlespace

\section{Elasticity Bias \label{app:bias}}

\renewcommand{\theequation}{A-\arabic{equation}}
\setcounter{equation}{0}

In our introductory remarks, we argued informally that structural
estimation can understate consumer responsiveness to fuel costs if
it fails to account for manufacturer price responses. We formalize
our argument here in the context of logit demand.  In particular, we
demonstrate that 1) estimation yields a fuel cost coefficient that
is biased downwards and 2) one can estimate the magnitude of bias
with data on gasoline and manufacturer prices.

Under a set of standard (and restrictive) assumptions, the logit
demand system generates the well-known regression equation:
\begin{equation}
   \log (s_{jt}) - \log(s_{0t}) = \psi(p_{jt}+x_{jt}) + \kappa_j +
   \nu_{jt},
   \label{eq:logit1}
\end{equation}
where $s_{jt}$ and $s_{0t}$ are the market shares of vehicle $j$ and
the outside good, respectively, $p_{jt}$ is the vehicle price,
$x_{jt}$ captures the expected lifetime fuel costs, $\kappa_{j}$ is
vehicle ``quality,'' and $\nu_{jt}$ is an error term that captures
demand shocks.

Assuming away the obvious endogeneity issues, one can use OLS with
vehicle fixed effects to obtain consistent estimates of $\psi$, the
parameter of interest. However, suppose that one observes the mean
price of each vehicle rather than the true price. The regression
equation becomes:
\begin{equation}
   \log (s_{jt}) - \log(s_{0t}) = \psi x_{jt} + \kappa_j^* +
   \nu_{jt}^*,
   \label{eq:logit2}
\end{equation}
where $\kappa_j^*=\kappa_j+\psi \overline{p}_j$ and
$\nu_{jt}^*=\nu_{jt}+\psi (p_{jt}-\overline{p}_j)$. The problem is
now apparent.  Gasoline price shocks affect not only $x_{jt}$ but
also the composite error term $\nu_{jt}^*$ through the manufacturer
response.  Since, as we document above, adverse gasoline shocks
typically induce manufacturers to lower prices, the OLS estimate of
$\psi$ is biased downwards.  Going further, the regression
coefficient has the expression:
\begin{eqnarray}
\widehat{\psi} &=& \psi + \frac{\sum (x_{jt}-\overline{x}_j)
\nu_{jt}}{\sum(x_{jt}-\overline{x}_j)^2} + \frac{\sum
(x_{jt}-\overline{x}_j)
\psi(p_{jt}-\overline{p}_j)}{\sum(x_{jt}-\overline{x}_j)^2} \nonumber\\
&\rightarrow^p& \psi \left(1+\frac{\sum (x_{jt}-\overline{x}_j)
(p_{jt}-\overline{p}_j)}{\sum(x_{jt}-\overline{x}_j)^2} \right).
\label{eq:test1}
\end{eqnarray}
Thus, it is possible to estimate the magnitude of bias simply by
regressing vehicle prices on expected lifetime fuel costs and a set
of fixed effects; one need not have market share data or any other
inputs to the structural model.

Such a procedure has its difficulties.  Perhaps the most central is
constructing an appropriate proxy for expected lifetime fuel
costs.\footnote{Of course, structural estimation also requires one
to proxy fuel costs. Goldberg (1998), Bento et al (2005) and
Jacobsen (2007) all use measures based on price-per-mile.}  We use
the discounted price-per-mile, i.e., $ x_{jt} =
(\text{gp}_t/\text{mpg}_j)/(1-\delta),  $ and impose a per-mile
discount rate of $\delta=0.999995401$; this corresponds to an annual
discount rate of 0.95, assuming 11,154 miles per year.\footnote{The
Department of Transportation estimates the average vehicle lifespan
to be thirteen years and 145,000 miles; based on these data, the
average number of miles per year is 11,154.} We measure manufacturer
prices in dollars, rather than thousands of dollars, to sidestep any
problems associated with unit conversion. We then regress
manufacturer prices on lifetime fuel costs, vehicle fixed effects,
and time fixed effects.  The resulting coefficient of -0.141
(standard error $=0.019$) corresponds to a downward bias of 14
percent.\footnote{The calculation is sensitive to the discount rate.
An annual discount rate of 0.99 produces a bias of 2.7 percent; an
annual discount rate of 0.90 produces a bias of 28.9 percent.}

Although we hope our empirical estimate of bias provides a useful
benchmark, we caution against taking the calculation too literally.
Data imperfections and/or specification errors could result in an
estimate that is too high or too low.  For example, our measure of
manufacturer prices is based on incentives offered to consumers and
does not fully capture transaction prices or even the actual
incentives selected.  Our proxy for expected lifetime fuel costs
imposes both a specific form of multiplicative discounting and an
arbitrary discount rate.  Aside from these estimation issues, the
bias formula itself is based on logit assumptions that are generally
considered too restrictive. More flexible structural models still
understate consumer responsiveness to fuel costs -- the negative
correlation between fuel costs and unobserved price responses
remains -- but the bias is nonlinear and could be substantially
larger or smaller than what we estimate here.


\section{Analytical solutions to the theoretical model \label{sec:app1}}

\renewcommand{\theequation}{B1-\arabic{equation}}
\setcounter{equation}{0}

\subsection{Three single-vehicle manufacturers}

We derive analytical solutions to the theoretical model for the
specific case of three single-product manufacturers that compete in
prices.  The profit equation specified in Equation \ref{eq:tprofs}
takes the form:
\begin{equation}
\pi_{j} = ( p_{j}-c_j ) * q_j(\widetilde{p}_{\cdot}) - f_{j},
\end{equation}
where $p_j$ is the price of vehicle $j$, the scalar $c_j$ captures
the marginal cost of production, the quantity demanded $q_j$ is a
function of the ``full'' vehicle price, inclusive of fuel costs, and
$f_j$ is a fixed cost.  We specify the linear demand system:
\begin{equation}
q_j = \alpha_{jj} (p_j+x_j) + \sum_{k \neq j} \alpha_{jk} (p_k+x_k)+
\mu_j
\end{equation}
in which the scalar $x_j$ is the fuel cost of vehicle $j$, and the
scalar $\mu_j$ is an exogenous demand shifter. We are concerned with
the case in which demand is well-defined (so that $\alpha_{jj}<0 \;
\forall j$) and vehicles are substitutes (so that $\alpha_{jk}>0 \;
\forall j \neq k$). The first-order condition for the equilibrium
price of vehicle $j$ can be expressed as follows:
\begin{equation}
p^*_j = \frac{1}{2} \left(c_j - \frac{1}{\alpha_{jj}} \mu_j \right)
- \frac{1}{2}x_j - \frac{1}{2} \sum_{k \neq j}
\frac{\alpha_{jk}}{\alpha_{jj}} (p_k+x_k)
\end{equation}
We solve the system of equations for the equilibrium vehicle prices
as functions of the non-price variables.  The equilibrium price for
vehicle 1 has the expression:
\begin{eqnarray}
p_1^* &*& \left[ 1
-\frac{1}{4}\frac{\alpha_{23}}{\alpha_{22}}\frac{\alpha_{32}}{\alpha_{33}}
-\frac{1}{4}\frac{\alpha_{12}}{\alpha_{11}}\frac{\alpha_{21}}{\alpha_{22}}
-\frac{1}{4}\frac{\alpha_{13}}{\alpha_{11}}\frac{\alpha_{31}}{\alpha_{33}}
+\frac{1}{8}\frac{\alpha_{12}}{\alpha_{11}}\frac{\alpha_{23}}{\alpha_{22}}\frac{\alpha_{31}}{\alpha_{33}}
+\frac{1}{8}\frac{\alpha_{13}}{\alpha_{11}}\frac{\alpha_{32}}{\alpha_{33}}\frac{\alpha_{21}}{\alpha_{22}}
\right]  \nonumber \\
\nonumber \\
&=&- \frac{1}{2} \left[ 1
-\frac{1}{4}\frac{\alpha_{23}}{\alpha_{22}}\frac{\alpha_{32}}{\alpha_{33}}
-\frac{1}{2}\frac{\alpha_{12}}{\alpha_{11}}\frac{\alpha_{21}}{\alpha_{22}}
-\frac{1}{2}\frac{\alpha_{13}}{\alpha_{11}}\frac{\alpha_{31}}{\alpha_{33}}
+\frac{1}{4}\frac{\alpha_{12}}{\alpha_{11}}\frac{\alpha_{23}}{\alpha_{22}}\frac{\alpha_{31}}{\alpha_{33}}
+\frac{1}{4}\frac{\alpha_{13}}{\alpha_{11}}\frac{\alpha_{32}}{\alpha_{33}}\frac{\alpha_{21}}{\alpha_{22}}
\right] * x_1  \nonumber \\
\nonumber \\
&&- \frac{1}{4} \left[ \frac{\alpha_{12}}{\alpha_{11}}
-\frac{1}{2}\frac{\alpha_{13}}{\alpha_{11}}\frac{\alpha_{32}}{\alpha_{33}}
\right] * x_2 - \frac{1}{4} \left[ \frac{\alpha_{13}}{\alpha_{11}}
-\frac{1}{2}\frac{\alpha_{12}}{\alpha_{11}}\frac{\alpha_{23}}{\alpha_{22}}
\right] * x_3  \\
\nonumber \\
&&+ \frac{1}{2} \left[ 1
-\frac{1}{4}\frac{\alpha_{23}}{\alpha_{22}}\frac{\alpha_{32}}{\alpha_{33}}
\right] * \left(c_1 - \frac{1}{\alpha_{11}} \mu_1 \right) \nonumber \\
\nonumber \\
&&- \left[ \frac{1}{4} \frac{\alpha_{12}}{\alpha_{11}}
-\frac{1}{8}\frac{\alpha_{13}}{\alpha_{11}}\frac{\alpha_{32}}{\alpha_{33}}
\right] * \left(c_2 - \frac{1}{\alpha_{22}} \mu_2 \right) - \left[
\frac{1}{4} \frac{\alpha_{13}}{\alpha_{11}}
-\frac{1}{8}\frac{\alpha_{12}}{\alpha_{11}}\frac{\alpha_{23}}{\alpha_{22}}
\right] * \left(c_3 - \frac{1}{\alpha_{33}} \mu_3 \right) \nonumber
\end{eqnarray}
The equilibrium prices for vehicles 2 and 3 are analogous.  One can
combine the two competitor fuel cost terms into a single term that
captures the influence of the weighted average competitor fuel cost.
This single term has the expression:
\begin{eqnarray}
- \frac{1}{4}\left[
\frac{\alpha_{12}}{\alpha_{11}}+\frac{\alpha_{13}}{\alpha_{11}}-\frac{1}{2}\frac{\alpha_{12}}{\alpha_{11}}\frac{\alpha_{23}}{\alpha_{22}}
-\frac{1}{2}\frac{\alpha_{13}}{\alpha_{11}}\frac{\alpha_{32}}{\alpha_{33}}
\right] * \left(\omega_{12}x_2 + \omega_{13}x_3 \right),
\end{eqnarray}
where the weights $w_{12}$ and $w_{13}$ sum to one.  The weights are
functions of the demand parameters:
\begin{eqnarray}
\omega_{12} &=&
\frac{\frac{\alpha_{12}}{\alpha_{11}}-\frac{1}{2}\frac{\alpha_{13}}{\alpha_{11}}\frac{\alpha_{32}}{\alpha_{33}}}
{\frac{\alpha_{12}}{\alpha_{11}}+\frac{\alpha_{13}}{\alpha_{11}}-\frac{1}{2}\frac{\alpha_{12}}{\alpha_{11}}\frac{\alpha_{23}}{\alpha_{22}}
-\frac{1}{2}\frac{\alpha_{13}}{\alpha_{11}}\frac{\alpha_{32}}{\alpha_{33}}} \nonumber \\
\\
\omega_{13} &=&
\frac{\frac{\alpha_{13}}{\alpha_{11}}-\frac{1}{2}\frac{\alpha_{12}}{\alpha_{11}}\frac{\alpha_{23}}{\alpha_{22}}}
{\frac{\alpha_{12}}{\alpha_{11}}+\frac{\alpha_{13}}{\alpha_{11}}-\frac{1}{2}\frac{\alpha_{12}}{\alpha_{11}}\frac{\alpha_{23}}{\alpha_{22}}
-\frac{1}{2}\frac{\alpha_{13}}{\alpha_{11}}\frac{\alpha_{32}}{\alpha_{33}}}.
\nonumber
\end{eqnarray}
A single regularity condition generates the following results
regarding the relationship between equilibrium prices and fuel
costs:
\begin{eqnarray*}
\text{Result A1-1:} && \frac{\partial p^*_1}{\partial x_1} \in
[-1,0] \; \text{and} \; \frac{\partial p^*_1}{\partial
(\omega_{12}x_2 +
\omega_{13}x_3)} \in [0,1]    \\
\\
\text{Result A1-2:} && \left|\frac{\partial p^*_1}{\partial
x_1}\right|>\left|\frac{\partial p^*_1}{\partial (\omega_{12}x_2 +
\omega_{13}x_3)}\right|
\end{eqnarray*}
Thus, in any empirical implementation, one should expect that the
regression coefficient on fuel costs should be negative, that the
coefficient on the weighted average competitor fuel costs should be
positive, and that the first coefficient should be larger in
magnitude than the second.  If one proxies cumulative fuel costs
using a measure of current fuel costs -- for example, the ``price
per-mile'' variable that we employ -- then the coefficients may be
much larger than one in magnitude. The same regularity condition
generates the following results regarding the weights:
\begin{eqnarray*}
\text{Result A1-3:} && \omega_{12} \in (0,1) \; \text{and} \; \omega_{13} \in (0,1)\\
\\
\text{Result A1-4:} && \frac{\partial \omega_{12}}{\partial
\alpha_{12}}>0 \; \text{and} \; \frac{\partial \omega_{13}}{\partial
\alpha_{13}}>0
\end{eqnarray*}
Since the parameters $\alpha_{12}$ and $\alpha_{13}$ govern the
severity of competition between vehicles, it is appropriate to
weight ``closer'' competitors more heavily when constructing the
empirical proxies for the weights.  The regularity condition that
generates these results is:
\begin{eqnarray}
1>&-&\frac{1}{2}\frac{\alpha_{12}}{\alpha_{11}}-\frac{1}{2}\frac{\alpha_{13}}{\alpha_{11}} + \frac{1}{2}\frac{\alpha_{12}}{\alpha_{11}}\frac{\alpha_{21}}{\alpha_{22}}+\frac{1}{2}\frac{\alpha_{13}}{\alpha_{11}}\frac{\alpha_{31}}{\alpha_{33}}+\frac{1}{4}\frac{\alpha_{23}}{\alpha_{22}}\frac{\alpha_{32}}{\alpha_{33}} \nonumber \\
\\
  &+&\frac{1}{4}\frac{\alpha_{12}}{\alpha_{11}}\frac{\alpha_{23}}{\alpha_{22}}+\frac{1}{4}\frac{\alpha_{13}}{\alpha_{11}}\frac{\alpha_{32}}{\alpha_{33}}
  -\frac{1}{4}\frac{\alpha_{12}}{\alpha_{11}}\frac{\alpha_{23}}{\alpha_{22}}\frac{\alpha_{31}}{\alpha_{33}}-\frac{1}{4}\frac{\alpha_{13}}{\alpha_{11}}\frac{\alpha_{32}}{\alpha_{33}}\frac{\alpha_{21}}{\alpha_{22}}.
  \nonumber \label{eq:regular}
\end{eqnarray}
The condition holds provided that the own-price parameters are
sufficiently large relatively to the cross-price parameters. For
intuition, it may be useful to note that each right-hand-side term
enters as a positive because the own-price parameters are negative
and the cross-price parameters are positive. Although these results
extend naturally to cases with $J>3$ manufacturers, the algebraic
burden associated with obtaining analytical solutions increases
exponentially with $J$.

\subsection{One manufacturer with three vehicles}

\renewcommand{\theequation}{B2-\arabic{equation}}
\setcounter{equation}{0}

We derive analytical solutions to the theoretical model for the
specific case of a single manufacturer that produces three distinct
products.  The first-order conditions for profit maximization are
identical to those presented in Section \ref{sec:model}, i.e.,
\begin{eqnarray}
\frac{\partial \pi_{\Im t}}{\partial p_{jt}} = \sum_k
\alpha_{jk}(p_{kt}+ x_{kt}) + \mu_{jt} +
\sum_{k}\alpha_{kj}(p_{kt}-c_{kt}) = 0.
\end{eqnarray}
We solve the system of equations for the equilibrium vehicle prices
as functions of the non-price variables. The equilibrium price for
vehicle 1 has the expression:
\begin{eqnarray}
p_1^* &*& \left[ 1
-\frac{1}{4}\frac{(\alpha_{23}+\alpha_{32})^2}{\alpha_{22}\alpha_{33}}
-\frac{1}{4}\frac{(\alpha_{12}+\alpha_{21})^2}{\alpha_{11}\alpha_{22}}
-\frac{1}{4}\frac{(\alpha_{13}+\alpha_{31})^2}{\alpha_{11}\alpha_{33}}
+\frac{1}{4}\frac{\alpha_{12}+\alpha_{21}}{\alpha_{11}}\frac{\alpha_{23}+\alpha_{32}}{\alpha_{22}}\frac{\alpha_{13}+\alpha_{31}}{\alpha_{33}}
\right] \nonumber \\
\nonumber \\
&=&- \frac{1}{2} \left[ 1
-\frac{1}{4}\frac{(\alpha_{23}+\alpha_{32})^2}{\alpha_{22}\alpha_{33}}
-\frac{1}{2}\frac{\alpha_{12}+\alpha_{21}}{\alpha_{11}}\frac{\alpha_{21}}{\alpha_{22}}
-\frac{1}{2}\frac{\alpha_{13}+\alpha_{31}}{\alpha_{11}}\frac{\alpha_{31}}{\alpha_{33}} \right. \nonumber \\
\nonumber \\
&& \qquad  \qquad \left.
+\frac{1}{4}\frac{\alpha_{12}+\alpha_{21}}{\alpha_{11}}\frac{\alpha_{23}+\alpha_{32}}{\alpha_{22}}\frac{\alpha_{31}}{\alpha_{33}}
+\frac{1}{4}\frac{\alpha_{13}+\alpha_{31}}{\alpha_{11}}\frac{\alpha_{23}+\alpha_{32}}{\alpha_{33}}\frac{\alpha_{21}}{\alpha_{22}}
\right]
 * x_1  \nonumber \\
\nonumber \\
&&- \frac{1}{2} \left[ \frac{\alpha_{12}}{\alpha_{11}} -
\frac{1}{2}\frac{\alpha_{12}+\alpha_{21}}{\alpha_{11}}
-\frac{1}{2}\frac{\alpha_{13}+\alpha_{31}}{\alpha_{11}}\frac{\alpha_{32}}{\alpha_{33}}
+\frac{1}{4}\frac{\alpha_{13}+\alpha_{31}}{\alpha_{11}}\frac{\alpha_{32}+\alpha_{23}}{\alpha_{33}}
\right. \nonumber \\
\\
&& \qquad \qquad \left.
+\frac{1}{4}\frac{\alpha_{12}+\alpha_{21}}{\alpha_{11}}\frac{\alpha_{23}+\alpha_{32}}{\alpha_{22}}\frac{\alpha_{32}}{\alpha_{33}}
-\frac{1}{4}\frac{\alpha_{23}+\alpha_{32}}{\alpha_{22}}\frac{\alpha_{23}+\alpha_{32}}{\alpha_{33}}\frac{\alpha_{12}}{\alpha_{11}}
\right] * x_2 \nonumber \\
\nonumber \\
&&- \frac{1}{2} \left[ \frac{\alpha_{13}}{\alpha_{11}} -
\frac{1}{2}\frac{\alpha_{13}+\alpha_{31}}{\alpha_{11}}
-\frac{1}{2}\frac{\alpha_{12}+\alpha_{21}}{\alpha_{11}}\frac{\alpha_{23}}{\alpha_{22}}
+\frac{1}{4}\frac{\alpha_{12}+\alpha_{21}}{\alpha_{11}}\frac{\alpha_{23}+\alpha_{32}}{\alpha_{22}}
\right.\nonumber \\
\nonumber \\
&& \qquad \qquad \left.
+\frac{1}{4}\frac{\alpha_{13}+\alpha_{31}}{\alpha_{11}}\frac{\alpha_{23}+\alpha_{32}}{\alpha_{33}}\frac{\alpha_{23}}{\alpha_{22}}
-\frac{1}{4}\frac{\alpha_{23}+\alpha_{32}}{\alpha_{33}}\frac{\alpha_{23}+\alpha_{32}}{\alpha_{22}}\frac{\alpha_{13}}{\alpha_{11}}
\right] * x_3 \nonumber \\
\nonumber \\
&&+f(c_1,c_2,c_3,\mu_1,\mu_2,\mu_3) \nonumber, \label{eq:appbsol}
\end{eqnarray}
where, for brevity, we focus on the fuel cost terms.  Again, one can
combine the fuel cost terms of vehicles 2 and 3 into a single term
that captures the weighted average influence of these vehicles. A
single regularity condition, slightly stronger than that presented
in Equation \ref{eq:regular}, generates the following results:
\begin{eqnarray*}
\text{Result A2-1:} && \frac{\partial p^*_1}{\partial x_1} \in
[-1,0]
\; \text{;} \; \frac{\partial p^*_1}{\partial x_2} \in [-1,1] \; \text{and} \; \frac{\partial p^*_1}{\partial x_3} \in [-1,1]    \\
\\
\text{Result A2-2:} && \left|\frac{\partial p^*_1}{\partial
x_1}\right| \lessgtr \left|\frac{\partial p^*_1}{\partial
x_2}\right| \lessgtr \left|\frac{\partial p^*_1}{\partial
x_3}\right|
\end{eqnarray*}
Thus, the manufacturer partially offsets changes in fuel costs of a
specific vehicle with changes in price of that vehicle.  Changes in
the fuel costs of \textit{other} vehicles produced by the same
manufacturer, however, have ambiguous implications for the vehicle
price.  Interestingly, in the specific case of symmetric demand
(i.e., $\alpha_{jk}=\alpha_{kj} \; \forall \; j,k$), changes in the
fuel costs of other vehicles produced by the same manufacturer have
no effect on the equilibrium price.  The regularity condition that
generates these results is:
\begin{eqnarray}
1&>&\frac{1}{4}\frac{(\alpha_{12}+\alpha_{21})^2}{\alpha_{11}\alpha_{22}}+\frac{1}{4}\frac{(\alpha_{13}+\alpha_{31})^2}{\alpha_{11}\alpha_{33}} + \frac{1}{4}\frac{(\alpha_{23}-\alpha_{32})^2}{\alpha_{22}\alpha_{33}} \nonumber \\
\nonumber \\
  &+&\frac{1}{2}\frac{\alpha_{12}+\alpha_{21}}{\alpha_{11}}\frac{\alpha_{21}}{\alpha_{22}}+\frac{1}{2}\frac{\alpha_{13}+\alpha_{31}}{\alpha_{11}}\frac{\alpha_{31}}{\alpha_{33}}\\
\nonumber\\
  &-&\frac{1}{4}\frac{\alpha_{12}+\alpha_{21}}{\alpha_{11}}\frac{\alpha_{23}+\alpha_{32}}{\alpha_{22}}\frac{\alpha_{31}}{\alpha_{33}}-\frac{1}{4}\frac{\alpha_{13}+\alpha_{31}}{\alpha_{11}}\frac{\alpha_{23}+\alpha_{32}}{\alpha_{33}}\frac{\alpha_{21}}{\alpha_{22}}
  \nonumber \label{eq:regular}
\end{eqnarray}
The condition holds provided that the own-price parameters are
sufficiently large relatively to the cross-price parameters. Again,
the intuition underlying these results extends naturally to cases
with $J>3$ vehicles.

\newpage

\begin{figure}[h]
        \centering
                \includegraphics[height=3in]{gasprice1.eps}
        \caption{The weekly retail price of gasoline by region over
        2003-2006, in real 2006 dollars.}
        \label{fig:gp1}
\end{figure}

%The figure plots gasoline prices over 2003-2008, nationally and by
%region.  Prices increase from around $1.50 per gallon to over $2.50
%per gallon.  There is substantial season variation so that prices
%are higher in the summer.  Prices are somewhat lower in the Gulf
%Coast and higher in the West.  Estimation will exploit the variation
%across time and regions.

\begin{figure}[h]
        \centering
                \includegraphics[height=3in]{gasprice2.eps}
        \caption{Seasonally adjusted retail gasoline prices at the
        national level over 1993-2008, in real 2006 dollars.
        Seasonal adjustments are calculated with the X-12-ARIMA program.}
        \label{fig:gp2}
\end{figure}

%The figure plots national gasoline prices over 1993-2008, after the
%seasonal variation has been removed via the way of the X-12-ARIMA.
%Prices increase from $1.50 to over $3.00.


\begin{figure}[h]
        \centering
                \includegraphics[height=3in]{econsig1.eps}
        \caption{The estimated effects of a one dollar increase in
        the retail gasoline price on the manufacturer price, based
        on the regression results in Column 1 of Table \ref{tab:regs1}.
        Each point represents the price effect for a single vehicle.
        See text for details.}
        \label{fig:regs1}
\end{figure}

%The figure is a scatterplot that plots the estimated effects of a one
%dollar increase in the gasoline price on manufacturer prices (the
%vertical axis) against vehicle miles-per-gallon (the horizontal
%axis).  Most the effects are negative and the median effect is
%negative \$171.  The effects are more negative for fuel inefficient
%vehicles.  See text for details.


\begin{figure}[h]
        \centering
                \includegraphics[height=3in]{econsig3.eps}
        \caption{The estimated effects of a one dollar increase in
        the retail gasoline price on the manufacturer price, based
        on the regression results of Appendix Table \ref{tab:regs3}.
        Each point represents the price effect for a single vehicle.
        See text for details.}
        \label{fig:regs3}
\end{figure}

%The figure is a scatterplot that plots the estimated effects of a one
%dollar increase in the gasoline price on manufacturer prices (the
%vertical axis) against vehicle miles-per-gallon (the horizontal
%axis), separately for each vehicle type.  For cars and SUVs, most the effects
%are negative and the effects are more negative for fuel inefficient
%vehicles.  There is little relationship between fuel efficiency and the
%effects for trucks and vans.  See text for details.

\begin{figure}[h]
        \centering
                \includegraphics[height=3in]{poffset.eps}
        \caption{The percentages of consumer cumulative gasoline
        expenses, due to changes in the retail gasoline price, that
        are offset by changes in the manufacturer price.  Each
        point represents the percentage for a single vehicle.
        Based on back-of-the-envelope calculations and the
        regression results of Appendix Table \ref{tab:regs3}.}
        \label{fig:poffset}
\end{figure}

%The figure is a scatterplot that plots the ``offset percentage,'' as
%defined in the text, against vehicle miles-per-gallon, separately
%for each vehicle type.  For cars and SUVs, the offset percentages
%are generally positive, and more positive for fuel inefficient
%vehicles.  For trucks and SUVs, there is little relationship between
%the offset percentage and miles-per-gallon.  See text for details.

\begin{figure}[h]
        \centering
                \includegraphics[height=3in]{econsig3a.eps}
        \caption{The estimated effects of a one dollar increase in
        the retail gasoline price on the manufacturer price, based
        on the regression results of Appendix Table \ref{tab:regs3}.
        Each point represents the price effect for a single vehicle.
        See text for details.}
        \label{fig:regs3a}
\end{figure}

%The figure is a scatterplot that plots the estimated effects of a one
%dollar increase in the gasoline price on manufacturer prices (the
%vertical axis) against vehicle miles-per-gallon (the horizontal
%axis) for cars, separately for each manufacturer.  Most the effects
%are negative and the effects are more negative for fuel inefficient
%vehicles.  The Chrysler effects are more likely to be positive.  See
%text for details.

\begin{figure}[h]
        \centering
                \includegraphics[height=3in]{econsig3b.eps}
        \caption{The estimated effects of a one dollar increase in
        the retail gasoline price on the manufacturer price, based
        on the regression results of Appendix Table \ref{tab:regs3}.
        Each point represents the price effect for a single vehicle.
        See text for details.}
        \label{fig:regs3b}
\end{figure}

%The figure is a scatterplot that plots the estimated effects of a one
%dollar increase in the gasoline price on manufacturer prices (the
%vertical axis) against vehicle miles-per-gallon (the horizontal
%axis) for SUVs, separately for each manufacturer.  Most the effects
%are negative.  For GM, Ford, and Toyota, the effects are more negative
%for fuel inefficient vehicles; for Chrysler they are less negative.
%See text for details.

\begin{figure}[h]
        \centering
                \includegraphics[height=3in]{timeFE-2.eps}
        \caption{Time-series plots of time fixed effects together
        with selected demand and cost factors. There are 208 weekly
        values over 2003-2008.  The time fixed effects are estimated
        in the regression presented in Table
        \ref{tab:regs1}, Column 3.}
        \label{fig:timeFE2}
\end{figure}

%The figure plots the time fixed effects estimated in
%Column 3 of Table \ref{tab:regs1}, together with the prime interest
%rate and the unemployment rate (which may shift demand), price
%indices for electricity and steel (which may shift manufacturer
%costs), and the retail gasoline price (which may shift demand and
%costs).  The fixed effects units are in thousands, so that a fixed
%effect of 0.25 represents manufacturer prices that are \$250 on
%average higher than manufacturer prices during the first week of
%2003 (the base date).  The fixed effects are higher in the winter
%months than in the summer months, consistent with the notion that
%manufacturer prices fall as consumers anticipate the arrival of new
%vehicles to the market in the summer months (e.g., Copeland, Dunn,
%and Hall 2005).  The prime interest rate increases over the sample
%while unemployment decreases; the means of these variables are 5.64
%and 5.30, respectively.  The electricity and steel indices are
%defined relative to January 1, 2003; the prices of these cost
%factors increase over the sample by 10 and 61 percent, respectively.
%The mean gasoline price is \$2.16 per gallon, and gasoline prices
%increase over the sample.

\begin{figure}[h]
        \centering
                \includegraphics[height=3in]{lag10.eps}
        \caption{The estimated effects of a one dollar increase in the
        retail gasoline price for a hypothetical, ``perfectly average''
        vehicle, in the ten weeks following a gasoline price shock.
        A perfectly average vehicle is one whose miles-per-gallon,
        weighted-average competitor miles-per-gallon, and weighted-average
        same-firm miles-per-gallon are all at the mean (for cars the
        mean is 25.99; for SUVs it is 18.80).  The impulse response
        function is calculated based on the regression coefficients
        shown in Appendix Tables \ref{tab:lags1} and
        \ref{tab:lags2}.}
        \label{fig:lag10}
\end{figure}

%The figure  shows the results of the impulse response function.
%Starting with the cars, GM, Ford, and Toyota reduce prices by \$516,
%\$495, and \$691, respectively, immediately following the gasoline
%price shock, while Chrysler increases prices by \$106. The
%discrepancies between the manufacturer grow steadily over the
%following ten weeks; by the final week, the net price changes are
%reductions of \$1,495, \$2,767, \$1,673, and \$21 for GM, Ford,
%Toyota, and Chrysler, respectively.  Turning to the SUVs, GM, Ford,
%and Toyota reduce their prices by \$121, \$105, and \$569,
%respectively, immediately following the gasoline shock, while
%Chrysler increases prices by \$63.  Again, the discrepancies between
%the manufacturer grow steadily over the following weeks; by the
%final week, the net price changes are reductions of \$831, \$612,
%\$1,422, and \$72 for GM, Ford, Toyota, and Chrysler, respectively.
%Overall, Ford reacts most aggressively relative to the other
%manufacturers in adjusting its car prices;  Toyota reacts most
%aggressively for SUVs. Chrysler's reactions are negligible for both
%vehicle types.

\renewcommand{\thetable}{\arabic{table}}
\setcounter{equation}{1}

\begin{table}[h]
\begin{center}
\caption{Summary Statistics}
\begin{tabular}[h]{l c c c c  }
    \hline \hline

\rule[0mm]{0mm}{5.5mm}Variables  & Definition      & Mean  & St. Dev.        \\
      \hline

\rule[0mm]{0mm}{5mm}Manufacturer price   & $\text{MSRP}_j - \overline{\text{INC}}_{jrt}$    & 30.344  & 16.262    \\
\rule[0mm]{0mm}{5mm}Fuel cost            & gp$_{rt} /$mpg$_j$                               & 0.108   & 0.034     \\
\rule[0mm]{0mm}{5mm}MSRP                 & MSRP$_{j}$                                       & 30.782  & 16.299     \\
\rule[0mm]{0mm}{5mm}Miles-per-gallon     & mpg$_{j}$                                        & 21.555  & 5.964     \\
\rule[0mm]{0mm}{5mm}Horsepower           &                                                  & 224.123 & 71.451    \\
\rule[0mm]{0mm}{5mm}Wheel base           &                                                  & 115.193 & 12.168    \\
\rule[0mm]{0mm}{5mm}Passenger capacity   &                                                  & 4.911   & 1.633     \\

    \hline
\multicolumn{5}{p{4.1in}}{\footnotesize{\rule[0mm]{0mm}{0mm}Means
and standard deviations based on 299,855 vehicle-region-week
observations over the period 2003-2006.  The manufacturer price is
defined as MSRP minus the mean regional and national incentives (in
thousands). The fuel cost is the gasoline price divided by
miles-per-gallon, and captures the gasoline expense per mile.  The
manufacturer price, the fuel cost, and MSRP (in thousands) are in
real 2006 dollars; wheel base is measured in inches.}}
\label{tab:sumstat1}
\end{tabular}
\end{center}
\end{table}


\begin{table}
\begin{center}
\caption{Means by Vehicle Type}
\begin{tabular}[h]{l c c c c  }
    \hline \hline

\rule[0mm]{0mm}{5.5mm}Variables         & Cars   & SUVs  & Trucks  &  Vans   \\
      \hline

\rule[0mm]{0mm}{5mm}Manufacturer price   & 30.301 & 35.782 & 24.482 & 24.658  \\
\rule[0mm]{0mm}{5mm}Fuel cost            & 0.087  & 0.121  & 0.133  & 0.120  \\
\rule[0mm]{0mm}{5mm}MSRP                 & 30.835  & 36.124  & 24.881  & 25.048  \\
\rule[0mm]{0mm}{5mm}Miles-per-gallon     & 25.991 & 18.803 & 17.121 & 18.815  \\
\rule[0mm]{0mm}{5mm}Horsepower           & 209.947  & 241.858  & 254.383  & 191.152  \\
\rule[0mm]{0mm}{5mm}Wheel base           & 107.723  & 114.880  & 129.527  & 123.196  \\
\rule[0mm]{0mm}{5mm}Passenger capacity   & 4.799  & 5.849  & 3.763  & 4.451  \\
\\
\# of observations  & 125,660 & 90,270 & 46,615 & 37,310  \\
    \hline
\multicolumn{5}{p{4.1in}}{\footnotesize{\rule[0mm]{0mm}{0mm}Means
based on vehicle-region-week observations over the period 2003-2006.
The manufacturer price is defined as MSRP minus the mean regional
and national incentives (in thousands).  The fuel cost is the
gasoline price divided by miles-per-gallon, and captures the
gasoline expense per mile. The manufacturer price, the fuel cost,
and MSRP (in thousands) are in real 2006 dollars; wheel base is
measured in inches.  }} \label{tab:sumstat2}
\end{tabular}
\end{center}
\end{table}

\begin{table}
\begin{center}
\caption{Manufacturer Prices and Fuel Costs}
\begin{tabular}[h]{l c c c }
    \hline \hline
\rule[0mm]{0mm}{5mm}                     & \multicolumn{3}{c}{Incentive level:} \\
                                         & Regional+ & Regional & National     \\
                                         & National  & Only     & Only         \\
Variables                                & (1)       & (2)      & (3)          \\
      \hline
\rule[0mm]{0mm}{5mm}Fuel cost            & -55.40*** & -56.96*** & -63.75*** \\
                                         & (7.73)    & (7.86)    & (8.77)    \\

\rule[0mm]{0mm}{7mm}Average competitor   & 50.76***  & 50.16***  & 50.09***  \\
                    $\;$ fuel cost       & (7.15)    & (7.39)    & (8.12)    \\

\rule[0mm]{0mm}{7mm}Average same-firm    & 1.15      & 2.62      & 1.31      \\
                    $\;$ fuel cost       & (2.29)    & (1.78)    & (2.30)    \\
\\
\rule[0mm]{0mm}{4.5mm}$R^2$              & 0.5260    & 0.6763    & 0.5289    \\
\rule[0mm]{0mm}{4.5mm}\# of observations & 299,855   & 299,855   & 59,971    \\
\rule[0mm]{0mm}{4.5mm}\# of vehicles     & 681       & 681       & 681       \\
    \hline
\multicolumn{4}{p{4.0in}}{\footnotesize{\rule[0mm]{0mm}{0mm}Results
from OLS regressions.  The dependent variable is the manufacturer
price, i.e., MSRP minus the mean regional and/or national incentives
(in thousands). The units of observation in Columns 1 and 2 are at
the vehicle-week-region level. The units of observation in Column 3
are at the vehicle-week level. All regressions include vehicle and
time fixed effects, and Columns 1 and 2 include region fixed
effects.  The regressions also include third-order polynomials in
the vehicle age (i.e., weeks since the date of initial production),
the average age of vehicles produced by different manufacturers, and
the average age of other vehicles produced by the same manufacturer.
Standard errors are clustered at the vehicle level and shown in
parenthesis. Statistical significance at the 10\%, 5\%, and 1\%
levels is denoted by *, **, and ***, respectively.}}
\label{tab:regs1}
\end{tabular}
\end{center}
\end{table}




\begin{table}
\begin{center}
\caption{Gasoline Price Lags and Futures Prices}
\begin{tabular}[h]{l l c c c c c }
    \hline \hline
\rule[0mm]{0mm}{5.5mm}Variables          & Metric        & (1)       & (2)       & (3)        & (4)      & (5)  \\
      \hline
\rule[0mm]{0mm}{5mm}Fuel cost            & Lagged        & -64.55*** &           & -36.51*** &          & -30.08*** \\
                                         & Retail        & (8.77)    &           &  (10.65)  &          & (8.42)    \\

\rule[0mm]{0mm}{7mm}Average competitor   & Lagged        & 50.01***  &           &  23.19**  &          & 30.24***  \\
                    $\;$ fuel cost       & Retail        & (8.16)    &           &   (10.09) &          & (9.93)    \\

\rule[0mm]{0mm}{7mm}Fuel cost            & Futures       &           & -47.66*** &           & -35.52** & -31.69*** \\
                                         &               &           &  (7.11)   &           & (16.42)  & (9.39)    \\

\rule[0mm]{0mm}{7mm}Average competitor   & Futures       &           &  63.32*** &           & 19.87    & 27.73**   \\
                    $\;$ fuel cost  &               &           &   (10.44) &           & (24.95)  & (13.21)   \\

\rule[0mm]{0mm}{7mm}Fuel cost            & Retail        &           &           & -29.70*** & -22.58   &           \\
                                         &               &           &           &  (10.83)  & (16.46)  &           \\

\rule[0mm]{0mm}{7mm}Average competitor   & Retail        &           &           &  27.70*** & 33.38*   &           \\
                    $\;$ fuel cost       &               &           &           &  (8.14)   & (18.87)  &           \\

\\
\rule[0mm]{0mm}{4.5mm}$R^2$              &               & 0.5291    & 0.5286    & 0.5295    & 0.5295   & 0.5305    \\
    \hline
\multicolumn{7}{p{6.2in}}{\footnotesize{\rule[0mm]{0mm}{0mm}Results
from OLS regressions.  The dependent variable is the manufacturer
price, i.e., MSRP minus the mean national incentive (in thousands).
The sample includes 59,971 observations on 681 vehicles at the
vehicle-week level.  Fuel cost variables labeled ``lagged retail''
are constructed using the mean retail gasoline price over the
previous four weeks.  Fuel cost variables labeled ``futures'' are
constructed using the one-month futures price of retail gasoline.
Fuel cost variables labeled ``retail'' are constructed using the
current retail gasoline price.  All regressions include the
appropriate average same-firm fuel cost variable(s).  The
regressions also include vehicle and time fixed effects, as well as
third-order polynomials in the vehicle age (i.e., weeks since the
date of initial production), the average age of vehicles produced by
different manufacturers, and the average age of other vehicles
produced by the same manufacturer. Standard errors are clustered at
the vehicle level and shown in parenthesis. Statistical significance
at the 10\%, 5\%, and 1\% levels is denoted by *, **, and ***,
respectively.}} \label{tab:fut}
\end{tabular}
\end{center}
\end{table}

\begin{table}
\begin{center}
\caption{Demand and Cost Factors}
\begin{tabular}[h]{l c c c c }
    \hline \hline

\rule[0mm]{0mm}{5mm}Variables            & (1)       & (2)       & (3)       & (4)       \\
      \hline
\rule[0mm]{0mm}{5mm}Gasoline Price       & -0.015    & 0.011     & -0.102   & -0.096    \\
                                         & (0.036)   & (0.059)   & (0.088)  & (0.067)   \\

\rule[0mm]{0mm}{7mm}Interest Rate        &           & -0.128*** &          & -0.164*** \\
                                         &           & (0.027)   &          & (0.034)   \\

\rule[0mm]{0mm}{7mm}Unemployment Rate    &           & -0.315*** &          & -0.104    \\
                                         &           & (0.073)   &          &  (0.091)  \\

\rule[0mm]{0mm}{7mm}Electricity Price Index &        &           & 0.950*   & 2.832***  \\
                                         &           &           & (0.540)  & (0.726)   \\

\rule[0mm]{0mm}{7mm}Steel Price Index    &           &           & 0.405*** & 0.549***  \\
                                         &           &           & (0.113)  & (0.152)   \\

\\
\rule[0mm]{0mm}{4.5mm}$R^2$              & 0.5160    & 0.6117    & 0.5829   & 0.6454    \\
    \hline
\multicolumn{5}{p{4.6in}}{\footnotesize{\rule[0mm]{0mm}{0mm}Results
from OLS regressions.  The data include 208 weekly observations over
the period 2003-2006.  The dependent variable is the time fixed
effect estimated in Column 3 of Table \ref{tab:regs1}.  The
regressions also include 52 week fixed effects; equivalent weeks in
each year are constrained to have the same fixed effect.  Standard
errors are robust to the presence of heteroskedasticity and
first-order autocorrelation.  Statistical significance at the 10\%,
5\%, and 1\% levels is denoted by *, **, and ***, respectively.}}
\label{tab:regsts}
\end{tabular}
\end{center}
\end{table}


\begin{table}
\begin{center}
\caption{Manufacturer Prices, Fuel Costs, and Inventories}
\begin{tabular}[h]{l c c c }
    \hline \hline

\rule[0mm]{0mm}{5mm}Variables            &$\qquad$& (1)       & (2)          \\
      \hline
\rule[0mm]{0mm}{5mm}Fuel cost            && -69.23*** & -69.11*** \\
                                         && (11.57)   & (11.54)   \\

\rule[0mm]{0mm}{7mm}Average competitor   && 53.16***  & 53.00***  \\
                    $\;$ fuel cost       && (9.79)    & (9.76)    \\

\rule[0mm]{0mm}{7mm}Average same-firm    && 1.95     & 1.94      \\
                    $\;$ fuel cost       && (3.36)   & (3.36)    \\

\rule[0mm]{0mm}{7mm}Vehicle inventory    &&           & 0.0001     \\
                                         &&           & (0.0001)   \\
\\
\rule[0mm]{0mm}{4.5mm}$R^2$              && 0.6202    & 0.6203    \\
    \hline
\multicolumn{4}{p{3.6in}}{\footnotesize{\rule[0mm]{0mm}{0mm}Results
from OLS regressions.  The dependent variable is the manufacturer
price, i.e., MSRP minus the mean national incentive (in thousands).
The sample includes 41,822 observations on 500 vehicles over the
period 2003-2006, at the vehicle-week level. The regressions include
vehicle and time fixed effects, as well as third-order polynomials
in the vehicle age (i.e., weeks since the date of initial
production), the average age of vehicles produced by different
manufacturers, and the average age of other vehicles produced by the
same manufacturer. Standard errors are clustered at the vehicle
level and shown in parenthesis. Statistical significance at the
10\%, 5\%, and 1\% levels is denoted by *, **, and ***,
respectively.}} \label{tab:inv}
\end{tabular}
\end{center}
\end{table}

\renewcommand{\thetable}{A-\arabic{table}}
\setcounter{table}{0}

\begin{landscape}
\begin{table}
\begin{center}
\caption{Manufacturer Prices by Vehicle Type and Manufacturer}
\begin{tabular}[h]{l c c c c c c c c c }
    \hline \hline
\rule[0mm]{0mm}{4.5mm}Vehicle Type:          & \multicolumn{4}{c}{Cars} & $\;$ &   \multicolumn{4}{c}{SUVs}   \\
\rule[0mm]{0mm}{3.5mm}Manufacturer:      & GM        & Ford      & Chrysler  & Toyota    && GM        & Ford      & Chrysler  & Toyota   \\
      \hline
\rule[0mm]{0mm}{5mm}Fuel cost            &-97.52***  &-146.80**  &-152.09*** & -77.13*** && -75.98*** & -72.10*** & 45.87*    & -62.11***  \\
                                         & (17.85)   & (71.68)   & (30.81)   & (21.55)   && (23.26)   & (23.50)   & (24.92)   & (17.82)   \\

\rule[0mm]{0mm}{7mm}Average competitor   & 85.78***  & 80.61     & 159.99*** & 46.38***  && 64.08***  &  66.75*** & -29.56    & 44.25***  \\
                    $\;$ fuel cost       & (18.25)   & (57.25)   & (41.91)   & (18.52)   && (21.67)   & (23.79)   & (19.01)   & (16.41)   \\

\rule[0mm]{0mm}{7mm}Average same-firm    & -6.47     & 41.10     & -2.56     &  6.12     && 8.19      & -1.51     & -17.88*   & 1.73      \\
                    $\;$ fuel cost       & (8.79)    & (29.64)   & (11.33)   & (4.48)    && (9.02)    & (6.28)    & (10.42)   & (4.27)    \\

\rule[0mm]{0mm}{7mm}$R^2$              & 0.6173    & 0.5254    & 0.5294    & 0.7282    && 0.7861    & 0.6758    & 0.7126    & 0.8352    \\
\rule[0mm]{0mm}{4.5mm}\# of vehicles     & 101       &   92      & 34        & 66        && 94        &   50      & 24        & 34        \\

    \hline
\rule[0mm]{0mm}{4.5mm}Vehicle Type:          & \multicolumn{4}{c}{Trucks} & $\;$ &   \multicolumn{4}{c}{Vans}   \\
\rule[0mm]{0mm}{3.5mm}Manufacturer:      & GM        & Ford      & Chrysler  & Toyota    && GM        & Ford      & Chrysler  & Toyota   \\
      \hline
\rule[0mm]{0mm}{5mm}Fuel cost            &-43.10***  &-61.49***  & 26.07     & 2.70      && 2.26      & 4.02      & 8.60      & 30.47     \\
                                         & (5.46)    & (17.91)   & (20.50)   & (15.35)   && (1.75)    & (6.93)    & (8.61)    & (14.26)   \\

\rule[0mm]{0mm}{7mm}Average competitor   & 37.77***  & 57.54***  & -30.63    & -0.68     && -1.12     &  -1.51    & -4.40     & -28.52*   \\
                    $\;$ fuel cost       & (5.74)    & (17.39)   & (19.31)   & (14.07)   && (3.51)    & (7.48)    & (10.78)   & (11.91)   \\

\rule[0mm]{0mm}{7mm}Average same-firm    & 2.70*     & 5.13      & -1.69     &  -0.36    && 0.88      & -0.39     & -15.33*** & -5.33     \\
                    $\;$ fuel cost       & (1.44)    & (3.49)    & (2.27)    & (1.18)    && (2.28)    & (1.50)    & (4.84)    & (3.65)    \\

\rule[0mm]{0mm}{7mm}$R^2$                & 0.8946    & 0.7959    & 0.8248    & 0.5659    && 0.9051    & 0.8610    & 0.7074    & 0.8769    \\
\rule[0mm]{0mm}{4.5mm}\# of vehicles     & 59        &   22      & 16        & 8         && 30        &   19      & 28        & 4         \\

    \hline
\multicolumn{10}{p{8.3in}}{\footnotesize{\rule[0mm]{0mm}{0mm}Results
from OLS regressions.  The dependent variable is the manufacturer
price, i.e., MSRP minus the mean regional and national incentives
(in thousands). The units of observation are at the
vehicle-week-region level. All regressions include vehicle, time,
and region fixed effects, as well as third-order polynomials in the
vehicle age (i.e., weeks since the date of initial production), the
average age of vehicles produced by different manufacturers, and the
average age of other vehicles produced by the same manufacturer.
Standard errors are clustered at the vehicle level and shown in
parenthesis. Statistical significance at the 10\%, 5\%, and 1\%
levels is denoted by *, **, and ***, respectively.}}
\label{tab:regs3}
\end{tabular}
\end{center}
\end{table}
\end{landscape}

\begin{landscape}
\begin{table}
\begin{center}
\caption{Fuel Efficient and Inefficient Vehicles}
\begin{tabular}[h]{l c c c  r l c c c}
    \hline \hline

\multicolumn{9}{c}{\rule[0mm]{0mm}{5mm}The Most Positive Manufacturer Price Responses}      \\
Cars &  Brand & mpg & $\widehat{\frac{\partial p}{\partial gp}}$ & \; & SUVs & Brand & mpg & $ \widehat{\frac{\partial p}{\partial gp}}$ \\
\hline
2003 SRT4  & Dodge &  32.85 & 0.9148 && 2006 Escape Hybrid     & Ford     & 30.25 & 0.6485   \\
2004 Prius & Toyota & 55.05 & 0.5268 && 2006 RX 400h           & Lexus   & 30.25 & 0.4304 \\
2006 Prius & Toyota & 55.05 & 0.5227 && 2006 Mariner Hybrid    & Mercury   & 30.80 & 0.3944 \\
2005 Prius & Toyota & 55.05 & 0.4971 && 2006 Highlander Hybrid & Toyota  & 30.25 & 0.3111   \\
2005 SRT4  & Dodge & 26.40 & 0.4661 && 2003 Wrangler          & Jeep & 19.10 & 0.1551  \\
2004 SRT4  & Dodge & 26.40 & 0.3740 && 2005 Wrangler          & Jeep & 19.65 & 0.1442  \\
2003 Prius & Toyota & 48.15 & 0.3414 && 2006 Liberty           & Jeep & 20.20 & 0.1284  \\
2004 Neon  & Dodge & 32.85 & 0.3305 && 2003 Liberty           & Jeep & 21.75 & 0.1246  \\
2003 Neon  & Dodge & 32.85 & 0.3244 && 2003 Durango           & Dodge & 16.75 & 0.1155  \\
2005 Neon  & Dodge & 32.85 & 0.2981 && 2006 Wrangler          & Jeep &  19.65 & 0.0691  \\
      \hline
      \multicolumn{9}{c}{\rule[0mm]{0mm}{5mm}The Most Negative Manufacturer Price Responses}      \\
Cars &  Brand & mpg & $\widehat{\frac{\partial p}{\partial gp}}$ && SUVs &  Brand  & mpg & $ \widehat{\frac{\partial p}{\partial gp}}$ \\
\hline
2003 XKR      & Jaguar & 19.85 &-2.0168 && 2003 H2        & Hummer  & 13.65 & -2.3293 \\
2004 GTO      & Pontiac & 18.75 &-2.0239 && 2006 H2 SUV    & Hummer & 13.65 & -2.3618 \\
2004 Marauder & Mercury & 20.30 &-2.0617 && 2004 H1        & Hummer & 13.65 & -2.3711 \\
2005 Viper    & Dodge & 16.95 &-2.1401 && 2003 9-7X      & Saab & 13.65 & -2.4298 \\
2003 Viper    & Dodge & 16.95 &-2.1462 && 2003 H1        & Hummer & 13.65 & -2.4511 \\
2004 Viper    & Dodge & 16.95 &-2.1880 && 2003 Escalade  & Cadillac & 13.65 & -2.5031 \\
2003 Marauder & Mercury & 20.30 &-2.2581 && 2006 H2 SUT    & Hummer & 13.65 & -2.5640 \\
2006 Viper    & Dodge & 16.40 &-2.4917 && 2005 H2 SUT    & Hummer & 13.65 & -2.578  \\
2005 GT       & Ford & 17.40 &-3.2390 && 2006 H1        & Hummer & 13.65 & -2.6173 \\
2006 GT       & Ford & 17.40 &-3.2552 && 2005 Envoy XUV & GMC & 13.65 & -2.6979 \\
\hline
\multicolumn{9}{p{7.8in}}{\footnotesize{\rule[0mm]{0mm}{0mm}Based on
Appendix Table \ref{tab:regs3} and Figures \ref{fig:regs3a} and
\ref{fig:regs3b}.}} \label{tab:lists}
\end{tabular}
\end{center}
\end{table}
\end{landscape}





\begin{table}
\begin{center}
\caption{Multiple Fuel Cost Lags -- Cars}
\begin{tabular}[h]{l c c c c c}
    \hline \hline
\rule[0mm]{0mm}{5.5mm}Variables & $\qquad$ Weeks Lagged$\qquad$       &  GM    &  Ford       &  Chrysler        & Toyota     \\
      \hline
\footnotesize{Fuel cost}        & \footnotesize{0}        & \footnotesize{-37.39}    & \footnotesize{-50.31}     & \footnotesize{-46.24}    & \footnotesize{-81.33***}  \\
\footnotesize{Fuel cost}        & \footnotesize{1}        & \footnotesize{-3.56}     & \footnotesize{-13.28}     & \footnotesize{5.21}      & \footnotesize{22.78*}     \\
\footnotesize{Fuel cost}        & \footnotesize{2}        & \footnotesize{-19.01}    & \footnotesize{-36.08**}   & \footnotesize{-78.41*}   & \footnotesize{-2.99}      \\
\footnotesize{Fuel cost}        & \footnotesize{3}        & \footnotesize{17.41}     & \footnotesize{-46.24**}   & \footnotesize{-18.12}    & \footnotesize{17.15}      \\
\footnotesize{Fuel cost}        & \footnotesize{4}        & \footnotesize{18.63}     & \footnotesize{-5.47}      & \footnotesize{-17.10}    & \footnotesize{-18.97}     \\
\footnotesize{Fuel cost}        & \footnotesize{5}        & \footnotesize{8.79}      & \footnotesize{7.48}       & \footnotesize{18.23}     & \footnotesize{11.85}      \\
\footnotesize{Fuel cost}        & \footnotesize{6}        & \footnotesize{-29.07***} & \footnotesize{21.31**}    & \footnotesize{66.43*}    & \footnotesize{-26.99***}  \\
\footnotesize{Fuel cost}        & \footnotesize{7}        & \footnotesize{13.72}     & \footnotesize{8.66}       & \footnotesize{29.70}     & \footnotesize{-0.59}      \\
\footnotesize{Fuel cost}        & \footnotesize{8}        & \footnotesize{9.20}      & \footnotesize{-55.16***}  & \footnotesize{-29.28}    & \footnotesize{-2.15}      \\
\footnotesize{Fuel cost}        & \footnotesize{9}        & \footnotesize{38.37**}   & \footnotesize{61.03***}   & \footnotesize{87.15}     & \footnotesize{15.40}      \\
\footnotesize{Fuel cost}        & \footnotesize{10}       & \footnotesize{-128.67***}& \footnotesize{-76.56*}    & \footnotesize{-186.37*}  & \footnotesize{-19.28}     \\

\footnotesize{Competitor fuel cost}        & \footnotesize{0}        & \footnotesize{62.56**}   & \footnotesize{96.30}      & \footnotesize{179.61**}  & \footnotesize{39.14**}    \\
\footnotesize{Competitor fuel cost}        & \footnotesize{1}        & \footnotesize{-6.61}     & \footnotesize{-50.99}     & \footnotesize{-33.56**}  & \footnotesize{-8.47}      \\
\footnotesize{Competitor fuel cost}        & \footnotesize{2}        & \footnotesize{14.27}     & \footnotesize{13.95}      & \footnotesize{-0.29}     & \footnotesize{4.88}       \\
\footnotesize{Competitor fuel cost}        & \footnotesize{3}        & \footnotesize{8.94}      & \footnotesize{-0.07}      & \footnotesize{-29.92}    & \footnotesize{-4.58}      \\
\footnotesize{Competitor fuel cost}        & \footnotesize{4}        & \footnotesize{-7.34}     & \footnotesize{-12.45}     & \footnotesize{17.16**}   & \footnotesize{-5.11*}     \\
\footnotesize{Competitor fuel cost}        & \footnotesize{5}        & \footnotesize{4.24}      & \footnotesize{-4.73}      & \footnotesize{0.70}      & \footnotesize{6.23}       \\
\footnotesize{Competitor fuel cost}        & \footnotesize{6}        & \footnotesize{-14.43}    & \footnotesize{-11.32}     & \footnotesize{3.00}      & \footnotesize{3.67}       \\
\footnotesize{Competitor fuel cost}        & \footnotesize{7}        & \footnotesize{11.55}     & \footnotesize{18.85}      & \footnotesize{-8.89}     & \footnotesize{1.24}       \\
\footnotesize{Competitor fuel cost}        & \footnotesize{8}        & \footnotesize{0.78}      & \footnotesize{-30.56}     & \footnotesize{39.08}     & \footnotesize{1.67}       \\
\footnotesize{Competitor fuel cost}        & \footnotesize{9}        & \footnotesize{-19.88}    & \footnotesize{38.13}      & \footnotesize{-48.17}    & \footnotesize{-5.92*}     \\
\footnotesize{Competitor fuel cost}        & \footnotesize{10}       & \footnotesize{24.95}     & \footnotesize{16.55}      & \footnotesize{53.38}     & \footnotesize{2.42}        \\

\footnotesize{Same-firm fuel cost}        & \footnotesize{0}        & \footnotesize{-38.58}    & \footnotesize{-58.84}     & \footnotesize{-130.65}   & \footnotesize{24.22}      \\
\footnotesize{Same-firm fuel cost}        & \footnotesize{1}        & \footnotesize{10.12}     & \footnotesize{58.21***}   & \footnotesize{27.63}     & \footnotesize{-12.61}     \\
\footnotesize{Same-firm fuel cost}        & \footnotesize{2}        & \footnotesize{1.84}      & \footnotesize{18.16}      & \footnotesize{77.65}     & \footnotesize{-6.11}      \\
\footnotesize{Same-firm fuel cost}        & \footnotesize{3}        & \footnotesize{-27.85}    & \footnotesize{42.70*}     & \footnotesize{45.63}     & \footnotesize{-12.74}     \\
\footnotesize{Same-firm fuel cost}        & \footnotesize{4}        & \footnotesize{-13.41}    & \footnotesize{14.15}      & \footnotesize{1.77}      & \footnotesize{20.82}      \\
\footnotesize{Same-firm fuel cost}        & \footnotesize{5}        & \footnotesize{-15.89}    & \footnotesize{-9.79}      & \footnotesize{-20.53}    & \footnotesize{-20.91}     \\
\footnotesize{Same-firm fuel cost}        & \footnotesize{6}        & \footnotesize{41.49***}  & \footnotesize{-16.04}     & \footnotesize{-71.12*}   & \footnotesize{19.82**}    \\
\footnotesize{Same-firm fuel cost}        & \footnotesize{7}        & \footnotesize{-26.16}    & \footnotesize{-27.69}     & \footnotesize{-23.03}    & \footnotesize{-1.58}      \\
\footnotesize{Same-firm fuel cost}        & \footnotesize{8}        & \footnotesize{-13.21}    & \footnotesize{77.31***}   & \footnotesize{-6.22}     & \footnotesize{-2.72}      \\
\footnotesize{Same-firm fuel cost}        & \footnotesize{9}        & \footnotesize{-17.86}    & \footnotesize{-95.73***}  & \footnotesize{-44.45}    & \footnotesize{-8.20}      \\
\footnotesize{Same-firm fuel cost}        & \footnotesize{10}       & \footnotesize{93.18**}   & \footnotesize{36.61}      & \footnotesize{139.47}    & \footnotesize{5.50}       \\

    \hline
\multicolumn{6}{p{6.1in}}{\footnotesize{\rule[0mm]{0mm}{0mm}Results
from four OLS regressions.  The dependent variable is the
manufacturer price, i.e., MSRP minus the mean regional and national
incentives (in thousands). The units of observation are at the
vehicle-week-region level. All regressions include vehicle, time,
and region fixed effects, as well as third-order polynomials in the
vehicle age (i.e., weeks since the date of initial production), the
average age of vehicles produced by different manufacturers, and the
average age of other vehicles produced by the same manufacturer.
Standard errors are clustered at the vehicle level but omitted for
brevity. Statistical significance at the 10\%, 5\%, and 1\% levels
is denoted by *, **, and ***, respectively.}} \label{tab:lags1}
\end{tabular}
\end{center}
\end{table}

\begin{table}
\begin{center}
\caption{Multiple Fuel Cost Lags -- SUVs}
\begin{tabular}[h]{l c c c c c}
    \hline \hline
\rule[0mm]{0mm}{5.5mm}Variables & $\qquad$ Weeks Lagged$\qquad$       &  GM    &  Ford       &  Chrysler        & Toyota    \\
      \hline
\footnotesize{Fuel cost}        & \footnotesize{0}        & \footnotesize{-71.20**}  & \footnotesize{-43.14*}    & \footnotesize{-83.16**}  & \footnotesize{-53.31***}  \\
\footnotesize{Fuel cost}        & \footnotesize{1}        & \footnotesize{19.08*}    & \footnotesize{14.33}      & \footnotesize{57.27**}   & \footnotesize{8.93}     \\
\footnotesize{Fuel cost}        & \footnotesize{2}        & \footnotesize{-7.88}     & \footnotesize{-26.46}     & \footnotesize{24.12}     & \footnotesize{-3.87}      \\
\footnotesize{Fuel cost}        & \footnotesize{3}        & \footnotesize{-17.00}    & \footnotesize{1.86}       & \footnotesize{7.55}      & \footnotesize{-0.311}      \\
\footnotesize{Fuel cost}        & \footnotesize{4}        & \footnotesize{15.59}     & \footnotesize{-10.92}     & \footnotesize{22.44**}   & \footnotesize{5.93}     \\
\footnotesize{Fuel cost}        & \footnotesize{5}        & \footnotesize{-11.67}    & \footnotesize{9.79}       & \footnotesize{3.11}      & \footnotesize{-8.23**}      \\
\footnotesize{Fuel cost}        & \footnotesize{6}        & \footnotesize{14.21}     & \footnotesize{-5.77}      & \footnotesize{3.41}      & \footnotesize{-26.99***}  \\
\footnotesize{Fuel cost}        & \footnotesize{7}        & \footnotesize{12.78}     & \footnotesize{4.16}       & \footnotesize{0.93}      & \footnotesize{6.12}      \\
\footnotesize{Fuel cost}        & \footnotesize{8}        & \footnotesize{-26.82**}  & \footnotesize{-2.80}      & \footnotesize{-3.14}     & \footnotesize{-2.73}      \\
\footnotesize{Fuel cost}        & \footnotesize{9}        & \footnotesize{16.32}     & \footnotesize{9.02}       & \footnotesize{11.18}     & \footnotesize{7.51}      \\
\footnotesize{Fuel cost}        & \footnotesize{10}       & \footnotesize{-26.35}    & \footnotesize{-31.32}     & \footnotesize{13.24}     & \footnotesize{-31.48***}     \\

\footnotesize{Competitor fuel cost} & \footnotesize{0}    & \footnotesize{54.88***}  & \footnotesize{51.93**}    & \footnotesize{-47.89}    & \footnotesize{19.78}    \\
\footnotesize{Competitor fuel cost} & \footnotesize{1}    & \footnotesize{-17.24***} & \footnotesize{-2.81}      & \footnotesize{26.82}     & \footnotesize{7.39}      \\
\footnotesize{Competitor fuel cost} & \footnotesize{2}    & \footnotesize{13.70**}   & \footnotesize{-1.54}      & \footnotesize{5.40}      & \footnotesize{1.49}       \\
\footnotesize{Competitor fuel cost} & \footnotesize{3}    & \footnotesize{0.64}      & \footnotesize{1.41}       & \footnotesize{-4.15}     & \footnotesize{-8.32}      \\
\footnotesize{Competitor fuel cost} & \footnotesize{4}    & \footnotesize{-10.06}    & \footnotesize{-12.30}     & \footnotesize{7.75}      & \footnotesize{6.37}     \\
\footnotesize{Competitor fuel cost} & \footnotesize{5}    & \footnotesize{1.93}      & \footnotesize{3.82}       & \footnotesize{-14.28}    & \footnotesize{-4.54}       \\
\footnotesize{Competitor fuel cost} & \footnotesize{6}    & \footnotesize{-1.86}     & \footnotesize{4.04}       & \footnotesize{16.51}     & \footnotesize{10.18**}       \\
\footnotesize{Competitor fuel cost} & \footnotesize{7}    & \footnotesize{-3.10}     & \footnotesize{13.56*}     & \footnotesize{-9.35}     & \footnotesize{4.41}       \\
\footnotesize{Competitor fuel cost} & \footnotesize{8}    & \footnotesize{5.59}      & \footnotesize{3.78}       & \footnotesize{-7.94}     & \footnotesize{12.13**}       \\
\footnotesize{Competitor fuel cost} & \footnotesize{9}    & \footnotesize{7.89}      & \footnotesize{6.02}       & \footnotesize{22.83}     & \footnotesize{-10.01}     \\
\footnotesize{Competitor fuel cost} & \footnotesize{10}   & \footnotesize{23.06*}    & \footnotesize{0.60}       & \footnotesize{-36.55}    & \footnotesize{6.40}       \\

\footnotesize{Same-firm fuel cost}  & \footnotesize{0}    & \footnotesize{14.05}     & \footnotesize{-10.78}     & \footnotesize{132.23*}   & \footnotesize{22.83}      \\
\footnotesize{Same-firm fuel cost}  & \footnotesize{1}    & \footnotesize{-3.03}     & \footnotesize{-11.78}     & \footnotesize{-86.08*}   & \footnotesize{-15.56}     \\
\footnotesize{Same-firm fuel cost}  & \footnotesize{2}    & \footnotesize{-6.04}     & \footnotesize{27.00}      & \footnotesize{-29.04}    & \footnotesize{0.12}      \\
\footnotesize{Same-firm fuel cost}  & \footnotesize{3}    & \footnotesize{15.90}     & \footnotesize{-3.69}      & \footnotesize{-4.66}     & \footnotesize{8.66}     \\
\footnotesize{Same-firm fuel cost}  & \footnotesize{4}    & \footnotesize{-7.62}     & \footnotesize{21.91}      & \footnotesize{-29.28*}   & \footnotesize{-15.09*}      \\
\footnotesize{Same-firm fuel cost}  & \footnotesize{5}    & \footnotesize{8.73}      & \footnotesize{-14.59}     & \footnotesize{10.42}     & \footnotesize{10.50}     \\
\footnotesize{Same-firm fuel cost}  & \footnotesize{6}    & \footnotesize{-13.94}    & \footnotesize{1.12}       & \footnotesize{-21.26}    & \footnotesize{-9.30}    \\
\footnotesize{Same-firm fuel cost}  & \footnotesize{7}    & \footnotesize{-10.22}    & \footnotesize{-17.76}     & \footnotesize{8.46}      & \footnotesize{-10.77}      \\
\footnotesize{Same-firm fuel cost}  & \footnotesize{8}    & \footnotesize{20.09}     & \footnotesize{2.19}       & \footnotesize{11.08}     & \footnotesize{-11.27}      \\
\footnotesize{Same-firm fuel cost}  & \footnotesize{9}    & \footnotesize{-8.55}     & \footnotesize{-14.54}     & \footnotesize{-34.20}    & \footnotesize{4.19}      \\
\footnotesize{Same-firm fuel cost}  & \footnotesize{10}   & \footnotesize{-1.68}     & \footnotesize{26.61}      & \footnotesize{24.88}    & \footnotesize{17.74}       \\

    \hline
\multicolumn{6}{p{6.1in}}{\footnotesize{\rule[0mm]{0mm}{0mm}Results
from four OLS regressions.  The dependent variable is the
manufacturer price, i.e., MSRP minus the mean regional and national
incentives (in thousands). The units of observation are at the
vehicle-week-region level. All regressions include vehicle, time,
and region fixed effects, as well as third-order polynomials in the
vehicle age (i.e., weeks since the date of initial production), the
average age of vehicles produced by different manufacturers, and the
average age of other vehicles produced by the same manufacturer.
Standard errors are clustered at the vehicle level but omitted for
brevity. Statistical significance at the 10\%, 5\%, and 1\% levels
is denoted by *, **, and ***, respectively.}} \label{tab:lags2}
\end{tabular}
\end{center}
\end{table}

\end{document}
