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\begin{comment}
\title{Airline Fuel Costs: Hedging and Pass-Through\footnote{We would like to thank Yonghong An, Zhiqi Chen, Matt Weinberg and participants at Southern Economic Association Meeting (2016) and the Industrial Organization Workshop at University of Oklahoma for helpful comments and suggestions.}}

\author{Myongjin Kim\and Qihong Liu \and Long Shi\footnote{Address: Department of Economics, University of Oklahoma, 308 Cate Center Drive, Norman, OK 73019. E-mails: mjkim@ou.edu; qliu@ou.edu; Long.Shi-1@ou.edu.}}

\date{\today}
\end{comment}

\begin{document}
\setcounter{page}{82}

\begin{center}
\textbf{\large{Chapter Two Appendix - Tables}}
\end{center}

\begin{table}[!htbp]\centering
\caption{Summary statistics} \label{table:sumstat1}
\medskip

\begin{tabular}{l c c c c }\hline\hline
\multicolumn{1}{c}{\textbf{Variable}} & \textbf{Mean}
 & \textbf{Std. Dev.}& \textbf{Min.} &  \textbf{Max.} \\ \hline
average\_fare & 178.637 & 76.609 & 15 & 1033.33 \\
number\_of\_passengers & 1275.077 & 2272.718 & 1 & 65221 \\
share\_of\_roundtrip\_tickets & 0.803 & 0.205 & 0 & 1 \\
HHI & 0.699 & 0.287 & 0.151 & 1 \\
afc & 2.076 & 0.939 & 0.553 & 6.736 \\
average\_salary & 14.97 & 3.408 & 6.511 & 33.686 \\
merger & 0.071 & 0.256 & 0 & 1 \\
bankruptcy & 0.012 & 0.108 & 0 & 1 \\
bankruptcy\_duration & 0.091 & 0.288 & 0 & 1 \\\hline
\multicolumn{1}{c}{N} & \multicolumn{4}{c}{196,053}\\ \hline
\end{tabular}
\end{table}

\newpage

\begin{table}[!htbp]
\centering
\caption{Fuel cost pass-through (afc)}\label{table:afc}
\medskip
\resizebox*{!}{.75\paperheight}{
\begin{tabular}{lcccccc} \hline
 & (1) & (2) & (3) & (4) & (5) & (6) \\
VARIABLES & lnfare & lnfare & lnfare & lnfare & lnfare & lnfare \\ \hline
$\ln afc$        &       0.199*** &       0.124***&       0.383***&       0.119***&       0.114***&       0.105***\\
&    (0.0149)         &    (0.0101)         &    (0.0211)         &    (0.0109)         &    (0.0209)         &    (0.0206)         \\
$lag \ln afc$    &      0.0899***&      0.0604***&      0.0620***&      0.0592***&      0.0542***&      0.0533***\\
&   (0.00628)         &   (0.00668)         &   (0.00889)         &   (0.00668)         &   (0.00707)         &   (0.00716)         \\
$lag2 \ln afc$    &    0.000544         &      0.0205**&      0.0486***&      0.0201***&      0.0174** &      0.0160* \\
  &   (0.00553)         &   (0.00602)         &   (0.00881)         &   (0.00605)         &   (0.00722)         &   (0.00720)         \\
$lag3 \ln afc$    &    -0.00958*  &      0.0488** &       0.101*** &      0.0479*** &      0.0621*** &      0.0606*** \\
            &   (0.00577)         &   (0.00587)         &   (0.00806)         &   (0.00588)         &   (0.00737)         &   (0.00736)         \\
$lag4 \ln afc$   &      0.0134*   &      0.0421*** &       0.119*** &      0.0406*** &      0.0348*** &      0.0322*** \\
            &   (0.00692)         &   (0.00736)         &    (0.0147)         &   (0.00735)         &   (0.00912)         &   (0.00903)         \\
lnsalary    &       0.272*** &       0.195*** &       0.314*** &       0.190*** &       0.164*** &       0.165*** \\
            &    (0.0141)         &   (0.00675)         &    (0.0162)         &   (0.00667)         &   (0.00887)         &   (0.00890)         \\
roundtrip\_share   &       0.319*** &      -0.143*** &       0.313*** &      -0.143*** &      -0.160*** &      -0.160*** \\
            &    (0.0205)         &   (0.00999)         &    (0.0214)         &   (0.00995)         &    (0.0150)         &    (0.0150)         \\
merger      &       0.105*** &      0.0633*** &       0.176*** &      0.0649*** &      0.0899*** &      0.0857*** \\
            &    (0.0103)         &   (0.00711)         &    (0.0104)         &   (0.00712)         &   (0.00782)         &   (0.00789)         \\
$merger\times \ln afc$&     -0.0279**  &     -0.0708*** &     -0.0941*** &     -0.0718*** &      -0.104*** &     -0.0992*** \\
            &    (0.0112)         &   (0.00710)         &    (0.0123)         &   (0.00711)         &   (0.00786)         &   (0.00793)         \\
Bankruptcy  &     -0.0778*** &     -0.0413*** &     -0.0522*** &     -0.0411*** &     -0.0535*** &     -0.0498*** \\
            &   (0.00644)         &   (0.00473)         &   (0.00721)         &   (0.00471)         &   (0.00576)         &   (0.00573)         \\
Bankruptcy\_Duration&       0.161*** &      0.0117**  &       0.152*** &      0.0103*   &     0.00857         &     0.00735         \\
            &    (0.0105)         &   (0.00578)         &    (0.0110)         &   (0.00577)         &   (0.00625)         &   (0.00626)         \\
{\footnotesize{Bankruptcy\_Duration}}$\times \ln afc$ &     -0.0136         &      0.0197*** &      0.0136         &      0.0225*** &      0.0196**  &      0.0221*** \\
            &    (0.0140)         &   (0.00668)         &    (0.0147)         &   (0.00670)         &   (0.00763)         &   (0.00769)         \\
HHI         &       0.291*** &       0.270*** &       0.279*** &       0.360*** &       0.669*** &       0.696*** \\
            &    (0.0261)         &    (0.0141)         &    (0.0292)         &    (0.0199)         &    (0.0622)         &    (0.0644)         \\
interaction&      -0.214*** &      0.0313*** &      -0.230*** &      0.0367*** &       0.126*** &       0.115*** \\
            &    (0.0185)         &    (0.0105)         &    (0.0202)         &    (0.0120)         &    (0.0385)         &    (0.0387)         \\
lnafc\_competitor&                     &                     &                     &                     &       0.110*** &                     \\
            &                     &                     &                     &                     &    (0.0161)         &                     \\
            &                     &                     &                     &                     &    (0.0161)         &                     \\
Observations  &      190600         &      190600         &      190600         &      188869         &      106726         &      106726  \\
R-squared & 0.11 & 0.33 & 0.14 & 0.33 & 0.34 & 0.35 \\
%clustered se & y & y & y & y & y & y \\
route-carrier FE & n & y & n & y & y & y \\
year-quarter FE & n & y & y & y & y & y \\
IV & n & n & y & y & y & y \\
Number of carrier\_route &  & 8,691 &  & 8,691 & 5,223 & 5,223 \\ \hline
\multicolumn{7}{c}{ Clustered standard errors by route in parentheses} \\
\multicolumn{7}{c}{ *** p$<$0.01, ** p$<$0.05, * p$<$0.1} \\
\end{tabular}}
\end{table}

\newpage

\begin{table}[htbp]\centering \caption{Summary statistics\_Pass-through Rate \label{table:sumstat2}}
\begin{tabular}{l c c c c }\hline\hline
\multicolumn{1}{c}{\textbf{Variable}} & \textbf{Mean}
& \textbf{Std. Dev.}& \textbf{Min.} &  \textbf{Max.} \\ \hline
Revenue & 186779.839 & 293711.597 & 15 & 7573022.5 \\
Cost & 43064.203 & 74144.051 & 1.063 & 1361936.25 \\\hline

average\_fare & 191.155 & 77.898 & 15 & 844.04 \\
number\_of\_passengers & 1113.366 & 1908.071 & 1 & 57085 \\
share\_of\_roundtrip\_tickets & 0.782 & 0.217 & 0 & 1 \\
HHI & 0.655 & 0.291 & 0.151 & 1 \\
afc & 2.348 & 0.853 & 0.553 & 6.736 \\
merger & 0.073 & 0.26 & 0 & 1 \\
average\_salary & 15.172 & 3.559 & 6.511 & 33.686 \\
Bankruptcy & 0.009 & 0.095 & 0 & 1 \\
Bankruptcy\_Duration & 0.077 & 0.267 & 0 & 1 \\\hline
\multicolumn{1}{c}{N} & \multicolumn{4}{c}{76633}\\ \hline
\end{tabular}
\end{table}

\newpage

\begin{table}
\centering
\caption{Pass-through rate}\label{table:rate}
\medskip

\resizebox*{!}{.75\paperheight}{
\begin{tabular}{lcccc} \hline
 & (1) & (2) & (3) & (4)  \\
VARIABLES & Revenue & Revenue & Revenue & Revenue \\ \hline
 &  &  &  & \\
Cost    &            1.418***&       1.111***&       1.097***&       0.975***\\
            &       (0.307)         &     (0.130)         &     (0.347)         &     (0.199)           \\
lag\_Cost   &       0.306** &       0.253***&       0.326** &       0.259***      \\
            &      (0.150)         &    (0.0764)         &     (0.154)         &    (0.0796)             \\
lag2\_Cost  &          0.113         &      0.0192         &      0.0483         &      0.0130               \\
            &     (0.133)         &    (0.0953)         &     (0.141)         &    (0.0961)          \\
lag3\_Cost  &       0.275** &       0.243***&       0.431***&       0.235***    \\
            &     (0.139)         &    (0.0881)         &     (0.159)         &    (0.0871)              \\
lag4\_Cost  &        0.981***&       0.484***&       0.881***&       0.481***\\
            &      (0.164)         &    (0.0554)         &     (0.190)         &    (0.0556)             \\
roundtrip\_share   &     30013.6***&     25811.5***&      6855.0         &     23682.4***\\
            &     (6644.1)         &    (3500.4)         &   (10076.4)         &    (4400.1)               \\
merger      &       -4734.5*  &     -4215.7***&       513.4         &     -3839.8***\\
            &     (2576.8)         &    (1010.5)         &    (3545.0)         &    (1028.4)           \\
$ Merger\times Cost$ &       0.400** &      0.0575         &       0.304* &      0.0449               \\
            &      (0.157)         &    (0.0572)         &     (0.169)         &    (0.0602)            \\
Bankruptcy  &      2728.8         &     -2787.0** &     -1839.5         &     -3182.9**  \\
            &     (2158.0)         &    (1271.4)         &    (2124.2)         &    (1293.2)                 \\
Bankruptcy\_Duration&     5014.2*  &     11000.8***&      4104.9         &     11254.8***\\
            &     (2854.5)         &    (1156.6)         &    (3046.3)         &    (1222.3)               \\
\footnotesize{Bankruptcy Duration} $\times Cost$&        -0.785***&      -0.185***&      -0.644***&      -0.163** \\
            &     (0.160)         &    (0.0559)         &     (0.187)         &    (0.0647)              \\
HHI         &     -43205.0***&     13233.5         &    -23430.4** &     62809.7***\\
            &   (10184.1)         &    (8343.6)         &    (9767.1)         &   (13217.3)            \\
$HHI\times Cost$ &        0.883         &       0.654         &       2.142**&       1.059* \\
            &     (0.637)         &     (0.432)         &     (0.859)         &     (0.608)           \\
 &  &  &  & \\
Observations &  74066         &       74066         &       74066         &       72457  \\
R-squared & 0.71 & 0.63 & 0.71 & 0.62 \\
%clustered se & y & y & y & y   \\
route-carrier FE & n & y & n & y   \\
year-quarter FE & n & y & y & y \\
IV & n & n & y & y  \\
Number of carrier-routes &  & 5,806 &  & 5,806  \\ \hline
\multicolumn{5}{c}{ Clustered standard errors by route in parentheses} \\
\multicolumn{5}{c}{ *** p$<$0.01, ** p$<$0.05, * p$<$0.1} \\
\end{tabular}}
\end{table}

\newpage

\begin{table}[!htbp]
\centering
\caption{Sunk Cost Fallacy - Southwest Airlines}\label{table:fallacy1}
\medskip

\def\sym#1{\ifmmode^{#1}\else\(^{#1}\)\fi}
\begin{tabular}{l*{3}{c}}
\hline
            &\multicolumn{1}{c}{(1)}&\multicolumn{1}{c}{(2)}&\multicolumn{1}{c}{(3)}\\
            &\multicolumn{1}{c}{lnfare}&\multicolumn{1}{c}{lnfare}&\multicolumn{1}{c}{lnfare}\\
\hline
$Low\_WN90_t \times WN$&     -0.0602\sym{***}&                     &     -0.0589\sym{***}\\
            &   (0.00395)         &                     &   (0.00409)         \\
$Low\_WN75_t \times WN$&                     &     -0.0432\sym{***}&    -0.00276         \\
            &                     &   (0.00330)         &   (0.00261)         \\
HHI         &       0.375\sym{***}&       0.384\sym{***}&       0.375\sym{***}\\
            &    (0.0190)         &    (0.0191)         &    (0.0190)         \\
lnsalary    &       0.205\sym{***}&       0.204\sym{***}&       0.205\sym{***}\\
            &   (0.00805)         &   (0.00802)         &   (0.00804)         \\
roundtrip\_share   &      -0.129\sym{***}&      -0.129\sym{***}&      -0.129\sym{***}\\
            &    (0.0121)         &    (0.0121)         &    (0.0121)         \\
merger      &      0.0165\sym{***}&      0.0171\sym{***}&      0.0164\sym{***}\\
            &   (0.00289)         &   (0.00289)         &   (0.00289)         \\
Bankruptcy  &     -0.0362\sym{***}&     -0.0422\sym{***}&     -0.0365\sym{***}\\
            &   (0.00461)         &   (0.00464)         &   (0.00463)         \\
Bankruptcy\_Period&      0.0273\sym{***}&      0.0314\sym{***}&      0.0273\sym{***}\\
            &   (0.00382)         &   (0.00386)         &   (0.00382)         \\\hline
Carrier-route FE       &         Yes         &         Yes         &         Yes         \\
Year-quarter FE       &         Yes         &         Yes         &         Yes         \\
IV &    Yes         &         Yes         &         Yes         \\
\hline
N           &      160907         &      160907         &      160907         \\
carrier\_route&                     &                     &                     \\
\hline\hline
\multicolumn{4}{l}{\footnotesize Standard errors in parentheses}\\
\multicolumn{4}{l}{\footnotesize \sym{*} \(p<0.1\), \sym{**} \(p<0.05\), \sym{***} \(p<0.01\)}\\
\end{tabular}
\end{table}

\newpage

\begin{table}
\centering
\caption{Sunk Cost Fallacy - Delta Airlines}\label{table:fallacy2}
\medskip

\def\sym#1{\ifmmode^{#1}\else\(^{#1}\)\fi}
\begin{tabular}{l*{3}{c}}
\hline
            &\multicolumn{1}{c}{(1)}&\multicolumn{1}{c}{(2)}&\multicolumn{1}{c}{(3)}\\
            &\multicolumn{1}{c}{lnfare}&\multicolumn{1}{c}{lnfare}&\multicolumn{1}{c}{lnfare}\\
\hline
$High\_DL90_t \times DL$&     -0.0205\sym{**} &                     &     -0.0285\sym{***}\\
            &    (0.0101)         &                     &    (0.0106)         \\
$High\_DL75_t \times DL$&                      &    -0.00260         &      0.0198\sym{*}  \\
            &                     &    (0.0117)         &    (0.0114)         \\
HHI         &       0.408\sym{***}&       0.408\sym{***}&       0.408\sym{***}\\
            &    (0.0233)         &    (0.0233)         &    (0.0233)         \\
lnsalary    &      0.0571\sym{***}&      0.0580\sym{***}&      0.0569\sym{***}\\
            &    (0.0104)         &    (0.0103)         &    (0.0104)         \\
roundtrip\_share   &      -0.131\sym{***}&      -0.131\sym{***}&      -0.131\sym{***}\\
            &    (0.0151)         &    (0.0151)         &    (0.0151)         \\
merger      &      0.0218\sym{***}&      0.0174\sym{***}&      0.0218\sym{***}\\
            &   (0.00415)         &   (0.00387)         &   (0.00415)         \\
Bankruptcy  &     -0.0282\sym{***}&     -0.0290\sym{***}&     -0.0282\sym{***}\\
            &   (0.00489)         &   (0.00488)         &   (0.00489)         \\
Bankruptcy\_Period&      0.0332\sym{***}&      0.0339\sym{***}&      0.0333\sym{***}\\
            &   (0.00390)         &   (0.00387)         &   (0.00390)         \\\hline
Carrier-route FE       &         Yes         &         Yes         &         Yes         \\
Year-quarter FE       &         Yes         &         Yes         &         Yes         \\
IV &    Yes         &         Yes         &         Yes         \\
\hline
N           &      112979         &      112979         &      112979         \\
carrier\_route&                     &                     &                     \\
\hline
\multicolumn{4}{l}{\footnotesize Standard errors in parentheses}\\
\multicolumn{4}{l}{\footnotesize \sym{*} \(p<0.1\), \sym{**} \(p<0.05\), \sym{***} \(p<0.01\)}\\
\end{tabular}
\end{table}

\begin{comment}
\section{Conclusion}\label{sec:conclusion}

Airline fuel cost is a significant component of airline operating cost and fuel cost has been volatile in recent decades. In this paper, we analyze how fuel costs affect airlines' pricing decisions and how this impact varies with market structure. We find significant and lasting impact of fuel cost on fuel prices. We also find that fuel cost pass-through is more than 100\%, realized over multiple periods. We then investigate the issue of sunk cost fallacy, in particular, when fuel hedging nets the airline a lump sum financial gain or loss without affecting its true fuel cost, whether its price decision will depend on its hedging position. We find evidence of sunk cost fallacy in the case of Southwest -- it lowers its price further relative to other major airlines when its fuel cost dips significantly below other major airlines (due to hedging). However, the evidence is mixed for Delta when its fuel cost is significantly higher than other major airlines due to hedging.

There are a few directions which we can explore next. First, we want to refine the construction of fuel cost measures at the carrier-route-year-quarter level. We have made the simplifying assumption that fuel consumption is linear in payload and distance. If this is not the case, then our fuel cost measure will be biased and the direction of bias may depend on payload (which will depend on load factor) and distance. This is a tricky issue. For example, ticket price affects passengers' choice among flights, so prices will affect load factor which in turn affects fuel costs. As a result, we have fuel price affecting fuel cost (on the right hand side) as well as fare revenue (on the left hand side) - a simultaneity problem. Second, we are interested in looking at asymmetric adjustment, distinguishing between the case of fuel cost increase and decrease. Since we have micro-level airfare data, we can also analyze how fuel cost changes affect the distribution (not just the mean) of airfare. This would require careful construction of the price distribution measure. Given that one does not observe how exactly the round trip fare would break for each component, we could interpolate the break of the round-trip fare based on one-way fare within a route and measure the price distribution.

As robustness checks, we further investigate the specifications in use by alternating the sample data. That is, we would drop the returning flight to adjust the standard errors as in Gerardi and Shapiro (2009). In addition, we would redefine the market as the non-directional as in Kim and Shen (2016) and confirm if our findings are consistent.

\begin{comment}\textit{First}, the BTS record of energy intensity of certificated air carriers, which we use to calculate the yearly fuel efficiency level, was no longer updated after 2012. As a result, we lose observations in the most recent 2 years in this study.\textbf{(QL: I am not sure why. If they don't update, some aircraft models remain in use, right? Or are we using energy efficiency measures that vary across time for the same aircraft type? But earlier we just said that they remain constant over time.)} \textbf{(LS: I drop the point above. We no longer use BTS information to construct the fuel cost.)}\textit{First}, this specification is based on the assumption that fuel consumption is linear in payload (weight) and distance. In particular, one may argue that the marginal cost of flying an additional passenger is close to zero. \textbf{(LS: The second drawback is that we can not update the fuel efficiency for each aircraft type over time.)}



\newpage

\section*{Appendix}

\textbf{Constructing fuel cost measures}
\medskip

We construct fuel cost measures, using data from multiple sources.
\medskip

\textbf{From external source:  https://www.aircraftcompare.com}

%\textbf{(QL: Can we say something about the reliability of this data? Also, what about the case where an aircraft with the same model-series has better efficiency over time?)} \textbf{(LS: The website does not leave direct information to show the reliability of their data, but there's contact information for inquiries and commercial cooperation. That's possibly better than nothing. Unfortunately, we may not be able to find it if an aircraft with the same model-series improves its efficiency over time.)}

\bi

\item Fuel efficiency ($FE^k$) at the aircraft ($k$) level

For each aircraft type $k$, we collect its fuel efficiency data (at gallon per nautical mile level) from the Internet. The website AircraftCompare.com reports basic characteristics like size, weight and fuel economy for each aircraft type, which remain constant over time. Aircraft type is at the model-series level, for example, Boeing 737- 600 / 700 / 800 / 900 are separately reported. The same source also gives payload data (in thousand pound) for each aircraft type. We divide the gallon/mile value by the payload to obtain fuel efficiency (at the unit of gallon per thousand pound per mile) to obtain fuel efficiency for aircraft type $k$, $FE^k$. Note that this variable depends only on aircraft type $k$, not on $i$, $j$ or $t$.
\ei

\textbf{From T-100 data}

\bi

\item Passenger share at the ($ijt,k$) level

For T-100 data, for each $ijt$, we count the number of passengers transported under each aircraft type, $passenger_{ijt}^k$.  Let $K$ denote the set of $k$'s for which we have $FE^k$ data. If
$$\frac{\sum_{k\in K} passenger_{ijt}^k}{\sum_k passenger_{ijt}^k}\ge 80\%,$$

then we keep this $ijt$ (otherwise we drop it). We then calculate the passenger share among all known aircraft types
\be psg\_share_{ijt}^k=\frac{passenger_{ijt}^k}{\sum_{l\in K} passenger_{ijt}^l}.\ee

\item Average fuel efficiency at the $ijt$ level

We then calculate the average fuel efficiency
$$AFE_{ijt}=\sum_{k\in K} \left(psg\_share_{ijt}^k\times FE^k\right),$$

still at the gallon (of fuel) per thousand pound per mile unit.\footnote{For $k\notin K$, we do not have fuel efficiency data for these aircraft types. When calculating average fuel efficiency at the $ijt$ level, we drop these aircraft types. If smaller aircraft types are both less likely to report fuel efficiency data and less efficient, then the actual $AFE_{ijt}$ may be larger since we are dropping the least efficient aircraft types. We want to control this bias somewhat, which is why we impose the constraint that only $ijt$'s for which at least 80\% of the passengers are transported by aircraft type $k\in K$.}

\item Average payload per passenger at the $ijt$ level

T-100 reports total payload and freight payload at the $ijt,k$ level. We treat the difference between total payload and freight as passenger payload. Dividing it by the total numer of passengers, we obtain average payload per passenger ($APP_{ijt}^k$) at the $ijt,k$ level. Aggregating over $k$'s on $ijt$, we have
$$APP_{ijt}=\sum_{k\in K} \left(psg\_share_{ijt}^k\times APP_{ijt}^k\right).$$

\ei

\textbf{From DB1B data}

\bi

\item Number of passengers at the $ijt$ level, $Passenger_{ijt}$.

DB1B data does not report aircraft type information and $Passenger_{ijt}$ includes passengers transported through all aircraft types. This is not to be confused with $passenger_{ijt}^k$ (with superscript $k$) from the T-100 data.

\item Sum over all passenger fares at the $ijt$ level, we obtain $Revenue_{ijt}$.

\ei

\textbf{Combining data}

\bi

\item Combining fuel efficiency, T-100 and DB1B data to calculate fuel consumption a the $ijt$ level
$$fuel\_consmption_{ijt}=Passenger_{ijt}\times APP_{ijt} \times AFE_{ijt} \times Distance_{ij},$$

gives gallons of fuel consumed to transport the passengers on $ijt$.

We have made a simplifying assumption that fuel consumption is linear in payload and distance. In practice, take off and landing are more like fixed cost so we would expect fuel consumption to increase with distance slower and slower. On the other hand, the longer the distance, the more fuel will be needed to travel that distance and carrying the extra fuel requires more fuel as well. This suggests the longer distance is less fuel efficient. We are implicitly assuming that the two opposite impacts cancel out each other.

\item Fuel cost is the product of airline fuel cost ($afc_{it}$) and fuel consumption
$$Cost_{ijt}=afc_{it}\times fuel\_consmption_{ijt}.$$

We also introduce one quarter lag of the fuel cost variable as follows:
$$Lag\_Cost_{ijt}= afc_{i,t-1}\times fuel\_consmption_{ijt}.$$

Other lags (2, 3 or 4-quarter lags respectively) are constructed similarly.

\ei

\newpage


\begin{thebibliography}{99}

\bibitem{} Al-Najjar, N., S. Baliga and D. Besanko (2005). ``The sunk cost bias and managerial pricing practices," Working paper.

\bibitem{} An, Y. and W. Zhao (2016). ``Dynamic merger efficiencies of the 1997 Boeing-McDonnell Douglas Merger," Working paper.

\bibitem{} Augenblick, N. (2015). ``The sunk-cost fallacy in penny auctions," Working paper.

\bibitem{} Borenstein, S. (1989). ``Hubs and High Fares: Dominance and Market Power in the U.S. Airline Industry," \textit{RAND Journal of Economics} 20(3), 334--365.

\bibitem{} Borenstein, S. and N. Rose (1994). ``Competition and price dispersion in the U.S. airline industry," \textit{Journal of Political Economy} 102, 653--683.

\bibitem{} Brueckner, J., N. Dyer and P. Spiller (1992). ``Fare Determination in Airline Hub-and-Spoke Networks," \textit{RAND Journal of Economics} 23(3), 309--333.

\bibitem{} Carter, D., D. Rogers and B. Simkins (2004). ``Fuel heding in the airline industry: The case of Southwest Airlines," Working paper.

\bibitem{} Ciliberto, F. and C. Schenone (2012) ``Bankruptcy and product-market competition: Evidence from the airline industry," \textit{International Journal of Industrial Organization} 30, 564--577.

\bibitem{} Ciliberto, F. and C. Schenone (2012) ``Are the bankrupt skies the friendliest?" \textit{Journal of Coporate Finance} 18, 1217--1231.

\bibitem{} Colon, C. (2016) ``Wholesale Prices, Retail Prices and the Lumpy Pass-Through of Alcohol Taxes," Working paper.

\bibitem{} Colon, C. and N. Rao (2016) ``Discrete Prices and the Incidence and Efficiency of Excise Tax," Working paper.

\bibitem{} Cornia, M., K. Gerardi and A. Shapiro (2011) ``Price Discrimination and Business-Cycle Risk," Working paper.

\bibitem{} Dai, M., Q. Liu and K. Serfes (2014). ``Is the Effect of Competition on Price Dispersion Non-Monotonic? Evidence from the U.S. Airline Industry," \textit{Review of Economics and Statistics} 96(1), 161-170.

\bibitem{} Fabra, N. and M. Reguant (2013). ``Pass-Through of Emissions Costs in Electricity Markets," Working paper.

\bibitem{} Federal Aviation Administration (2014). ``The Economic Impact of Civil Aviation on the U.S. Economy."

\bibitem{} Forbes, S. (2008). ``The effect of air traffic delays on airline prices," \textit{International Journal of Industrial Organization} 26, 1218--1232.

\bibitem{} Friedman, D., K. Pommerenke, R. Lukose, G. Milam, and B. Huberman (2007). ``Searching for the sunk cost fallacy," \textit{Experimental Economics} 10(1), 79�-104.

\bibitem{} Gerardi, K. and A. Shapiro (2009). ``Does competition reduce price dispersion? New evidence from the airline industry," \textit{Journal of Political Economy} 117, 1--37.

\bibitem{} Goldberg, P. and M. Knetter (1997). ``Goods Prices and Exchange Rates: What Have We Learned," \textit{Journal of Economic Literature} 35(3), 1243--1272.

\bibitem{} Gron, A. and D. Swenson (2000). ``Cost Pass-Through in the U.S. Automobile Market," \textit{Review of Economics and Statistics} 82(2), 316--324.

\bibitem{} Ho, T., I. Png and S. Reza (2015). ``Sunk cost fallacy in driving the world's costliest cars," Working paper.

\bibitem{} Kim, D. and R. Cotterill (2008). ``Cost pass-through in differentiated product markets: The case of U.S. processed cheese," \textit{Journal of Industrial Economics} 1, 32--48.

\bibitem{} Kim, M. and L. Shen (2016). ``Market Definition Changes the Story: Competition and Price Dispersion in the Airline Industry Revisited," Working Paper.

\bibitem{} Lavoie, N. and Q. Liu (2007). "Pricing-to-market: Price discrimination or product differentiation?" \textit{American Journal of Agricultural Economics} 89, 571--581.

\bibitem{} Lim, S. and Y. Hong (2014). ``Fuel hedging and airline operating costs," \textit{Journal of Air Transport Management} 36, 33--40.

\bibitem{} Linn, J., L. Muehlenbachs and Y. Wang (2015). ``Can sunk costs matter?"  Working paper.

\bibitem{} Liu, Z., P. Ghosh and Q. Liu (2017). ``An Application of Genetic Matching to US Airlines Merger," working paper.

\bibitem{} McAfee, R., H. Mialon and S. Mialon (2007). ``Production shifting and cost pass-through: Implications for electricity prices and the environment,"  Working paper.

\bibitem{} Marion, J. and E. Muehlegger (2011). ``Fuel Tax Incidence and Supply Conditions," \textit{Journal of Public Economics}, 95(9):1202--s1212.

\bibitem{} Miller, J., L. Bird, J. Heeter and B. Gorham (2015). ``Renewable Electricity Use by the U.S. Information and Communication Technology (ICT) Industry," National Renewable Energy Laboratory.

\bibitem{} Prince, J. and D. Simon (2017). ``The Impact of Mergers on Quality Provision: Evidence from the Airline Industry," forthcoming, \textit{Journal of Industrial Economics}.

\end{thebibliography}
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