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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}
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\begin{center}
\textbf{\large{Chapter Two Appendix - Constructing fuel cost measures}}
\end{center}

\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

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