Control Variables

I control for production costs and quality in the first model because they can influence fare levels. In addition, I control for dependence across dyads. All of these controls are at the dyad-time level.

I use three variables to capture production costs. These are:

Cost per available seat mile (CASM): I control for cost per available seat mile (CASM), which is a measure of the sum of the unit costs of the members of dyad i at time t, because I expect the sum of the average fare charged by the members of dyad i to increase as their production costs increase. Unit cost is defined as the ratio of total operating expense (TotalOpExpense) to available seat miles (AvailSeatMiles). TotalOpExpense is reported in Schedule P-7 of the Air Carrier Financial Reports and provides quarterly operating expenses by functional grouping for large certified U.S. air carriers. AvailSeatmiles is reported in T1: U.S. Air Carrier Traffic and Capacity Summary by Service Class. To calculate CASM at the dyad- time level, I first calculate unit cost at the carrier-time level by dividing the total operating expense (TotalOpExpense) of a given carrier at the time t to its available seat miles (AvailSeatMiles) at time t. Next, I sum the unit costs of the members of dyad i at time t to calculate CASM at the dyad-time level.

103 Productivity: I control for productivity because I expect a negative relationship between total productivity of the members of dyad i at time t and the sum of their average prices at time t. Dyad members can pass their efficiency on to customers in the form of lower fares. To calculate productivity at the dyad-time level, I first calculate it at the firm-time level and then sum the productivity scores of members of dyad i at time t. To calculate productivity at the firm-time level, I take the ratio of the total operating revenues (OpRevenues) of a given carrier at time t to its number of full time equivalent employees (FTEEmployees) at time t. OpRevenues is reported in schedule P-1.2 of Air Carrier Financial Reports. This schedule is a quarterly profit and loss statement for carriers whose annual operating revenues exceed $20 million and FTEEmployees is reported in Schedule P-1(a) Employees of Air Carrier Financial Reports, which is a monthly interim operations report of air carrier employment. After I calculate the individual productivity scores of the members of a given dyad at time t, I take their sum to compute productivity at the dyad-time level.

Stage Length: Stage length, which is the sum of the average distance flown by members of dyad i at time t, is expected to lead to higher ticket prices because distance has a positive impact on price (Borenstein, 1989). To calculate stage length at the dyad-time level, I will first calculate stage length at the firm-time level and then sum the stage length of the members of dyad i at time t. To calculate stage length at the firm-time level, I take the ratio of revenue miles flown (RevMilFlown) by a given carrier at time t to its revenue aircraft departures performed (RADPerformed) at time t. Both of these variables are reported in T1: U.S. Air Carrier Traffic and Capacity Summary by Service Class. After I calculate the stage length and thus the average length of all flights of the members of a given dyad at time t, I sum them to calculate stage length at the dyad-time level.

104

I also control for variables that influence both cost or service quality. To this end, I use the following variables:

Load Factor: Load factor, in general, reflects the proportion of airline output that is consumed and thus the percentage of filled seats. Airlines sell revenue passenger miles and produce available seat miles. Load factor is the ratio of the former to the latter and thus captures capacity utilization at the aircraft level. Since I define load factor at the dyad-time level, I sum the load factor levels of the members of dyad i at time t to calculate this control variable. Load factor influences fares in three ways (Borenstein, 1989), making its impact on fares indeterminate. First, it can reduce the sum of the average fare charged by the members of a given dyad because it reduces the per passenger cost of their flights. Members of a given dyad can pass on such cost savings to their passengers in the form of lower ticket prices. Second, load factor can increase the sum of the average fares charged by the members of a given dyad because it increases their opportunity cost of using their aircrafts due to demand peaking. Third, it can reduce the average fare level of a given dyad because of the reduction in perceived quality of their services due to their crowded planes.

To calculate load factor at the dyad-time level, I first compute load factor at the carrier- time level and then sum the load factor values of the members of dyad i at time t. To calculate load factor at the carrier-time level, I divide the revenue passenger miles flown (RevPaxMiles) by a given carrier at time t by its available seat miles (AvailSeatMiles) at time t. Both of these variables are available from T1: U.S. Air Carrier Traffic and Capacity Summary by Service Class. After I calculate the load factor at the carrier-time level, I sum the load factor values of the members of dyad i at time t.

105 Seating Density: Seating Density captures economies of density of the members of dyad i at time t. It is the sum of the average size of an aircraft on flights of the members of dyad i at time t. The sign of the impact of seating density on fare level is indeterminate due to its two opposing impacts (Borenstein, 1989). On the one hand, seating density is expected to reduce the sum of the average fare charged by the members of a given dyad by reducing their cost per-seat mile cost. On the other hand, seating density can have a positive impact on the sum of the average fares of the members of a given dyad by increasing the perceived quality of their products and value proposition as larger planes are perceived as more comfortable and safer. To calculate seating density at the dyad-time level, I first calculate it at the carrier-time level by dividing the available seat miles (AvailSeatMiles) of carrier i at time t by its revenue miles flown (RevMiles Flown) at time t. Both of these variables are available from T1: U.S. Air Carrier Traffic and Capacity Summary by Service Class. Next, I sum the respective seating density values of the members of dyad i at time t to capture seating density at the dyad-carrier level.

Frequency: Frequency is defined as the sum of the revenue aircraft departures performed (RADPerformed) by the members of dyad i at time t. This variable is reported in T1:U.S. Air Carrier Traffic and Capacity Summary by Service Class. The sign of the effect of frequency on the dependent variable is indeterminate due to its two opposing impacts (Borenstein, 1989). On the one hand, there is a positive relationship between frequency and aircraft utilization, lowering per flight costs of the members of dyad i, which can be passed on to passengers in the form of lower prices. On the other hand, greater flight frequency reduces the total number of delays of the members of a dyad. This in turn improves the perceived quality of their services, enabling them to increase their ticket prices.

106 Network Effect: Network effect is a dyad specific auto regressive term that controls for firm effects across dyads. Since level of analysis is unordered pairs of rivals, observations on dyads that have common members are not independent of one another, which leads to cross- sectional interdependence. A given airline may be a member of multiple dyads at any given time period and observations that come from dyads that have a common member are not independent. For example if firm i has an aggressive pricing policy, errors from dyads that have airline i as the common actor will be correlated due the general propensity of this firm to cut prices. Such cross- sectional interdependence is called common actor effect (Baum and Korn, 1999; Lincoln, 1984) and, if not corrected, can lead to inefficient parameter estimates and difficulty to rigorously examine the statistical significance of results (Gulati, 1995).

There are various solutions offered in the literature to control for this kind of unobserved heterogeneity. The first solution is to consider common actor effect as a model misspecification and include controls for all firm-level attributes that influence fare levels to eliminate all unmeasured effects of common firms (Gulati, 1996; Stuart, 1998). However it is difficult to identify and control for all of the relevant firm level variables, which limits the effectiveness of this solution, especially when the model is not completely specified (Korn and Baum, 1999). The second solution is to consider membership of a given firm in multiple dyads as an oversampling problem and discount oversampled cases in proportion to their extent of oversampling (Baum and Korn, 1996; Gulati, 1995). However this solution does not solve the problem of cross- sectional interdependence and the resulting correlation of errors from dyads that have common actors (Fuentelsaz and Gomez, 2006). The third solution is to use firm dummy variables and code them as one for each firm that is a member of a particular dyad in a particular time period (Stuart, 1998). However, this solution consumes too many degrees of freedom.

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A fourth solution to control for unobserved heterogeneity and the method that I use in my empirical model is to include a network autocorrelation term (Lincoln, 1984; Lincoln et al., 1992; Park, 2007). I use the “network effect” as the dyad specific autoregressive term to control for biases that stem from unobserved similarities and dependence among dyads with a common firm (Lincoln et al., 1992; Park, 2007; Keister, 1999). “Network effect” is a variable that is defined for the ijth dyad and refers to the mean of the dependent variable across all dyads that that include firm i or firm j ( excluding ij) ( Lincoln et al., 1992 ). The purpose of this variable is to capture within quarter firm effects that are not otherwise included in the model (Stuart, 1998). It cleans the coefficients on other independent variables of the unobserved propensities of the two airline companies in a dyad to charge a particular level of ticket price within each time period. Hence “network effect” is an additional control for unobserved heterogeneity and including it in the empirical model is similar to the mean differencing strategy that is used to control for cross-sectional and time specific interdependence in panel data analysis (Lincoln et al., 1992).“Network effect” is constructed by multiplying a W matrix by . W is a square matrix (45 by 45) with all potential dyads listed as rows and columns. For example, for three airlines, “the rows and columns are the dyads 1-2, 1-3, and 2-3. If the row and column dyads share a common node, then a 1 is entered in the matrix; otherwise a 0 is entered. The rows are then normalized by dividing each element by the sum of the row” (Wholey and Huonker, 1993, p: 360).