U.S. air carriers and work-rule constraints – Do airlines employ an allocatively efficient mix of inputs?

Research in Transportation Economics 45 (2014) 9e17

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Research in Transportation Economics journal homepage: www.elsevier.com/locate/retrec

U.S. air carriers and work-rule constraints e Do airlines employ an allocatively efficient mix of inputs? John Bitzan a, *, James Peoples b a b

Department of Management and Marketing, North Dakota State University, 320 Richard H. Barry Hall, Fargo, ND 58108-6050, USA Department of Economics, University of Wisconsin-Milwaukee, Milwaukee, WI 53210, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Available online 6 August 2014

Past research on the allocation of factor inputs for the airline industry suggests an overutilization of labor relative to other inputs immediately following deregulation. This study argues rigid work rules in conjunction with productivity improvements of nonlabor inputs may create an incentive for carriers to under-invest in labor relative to nonlabor inputs. Findings derived from estimating a long-run shadow cost function for this industry suggest that airlines over-employ non-labor inputs relative to labor. Simulations suggest potential savings ranging from 13 to 14 percent derived from satisfying the conditions of allocative efficiency for carriers in the study's sample. © 2014 Elsevier Ltd. All rights reserved.

JEL classification: l93 D24 Keywords: Allocative efficiency Airline work rules Translog cost function

1. Introduction Deregulation of the airline industry in 1978 has been a major success in terms of generating lower prices and improved service for consumers, and productivity gains for airlines. Airline deregulation enhanced rivalry in the industry, forcing legacy carriers to pursue innovations such as introducing hub and spoke networks and investing in larger, more fuel efficient aircraft. Moreover, the productivity gains realized by airlines have continued well beyond the first few years of deregulation. Bitzan and Peoples (2014) estimate an average 2.5 percent productivity gain per year in the airline industry since 1993, largely as a result of higher load factors and increasing stage lengths. Despite the success of deregulation in enhancing the efficiency of the airline industry, the increased competitive pressure that has led to increased efficiency has also resulted in a number of bankruptcies in recent years. In the last 10 years, each of the four largest U.S. carriers has declared bankruptcy. While a number of factors may account for the lack of financial success of airlines, including reduced demand after 9/11 and rising fuel costs, many observers believe that one of the major problems is low labor productivity caused by restrictive work rules. Although some have argued that these problems have disproportionately affected legacy carriers,

* Corresponding author. E-mail addresses: [email protected] (J. Peoples).

(J.

http://dx.doi.org/10.1016/j.retrec.2014.07.002 0739-8859/© 2014 Elsevier Ltd. All rights reserved.

Bitzan),

[email protected]

recent evidence suggests these problems are not limited to legacy carriers. In arguing that legacy carriers face bigger problems in this area, Severin Borenstein cites less restrictive work rules as a major advantage realized by low-cost carriers, ‘“They get much more productivity out of their workers,” he argues. “The jobs are defined more broadly and their workers tend to be able to cover more of the work load”’ (Caitlin Kenney, NPR 2011). On the other hand, in a recent letter to employees, Southwest CEO Gary Kelly wrote: “The sloth like industry you remember competing against is now dead and buried. We fought them and we won. Now, the enemy is our own cost creep, our own legacy-like productivity, and our own inefficiencies” (Caitlin Kenney, NPR 2011). Moreover, other recent evidence suggests that labor costs between low cost carriers and legacy carriers are converging. Tsoukalas, Belobaba, and Swelbar (2008) find that the average difference in labor cost per available seat mile between legacy carriers and low cost carriers decreased from 1.2 cents in 2000 to 0.3 cents in 2006. The authors suggest that bankruptcy and the threat of bankruptcy has allowed legacy carriers to negotiate more favorable labor contracts, while increasing labor seniority and slower growth have contributed to higher labor costs for the low cost carriers. Even though legacy costs are converging to levels resembling those achieved by low cost carriers, as illustrated in the recent bankruptcy case of American Airlines, restrictive work rules and labor productivity are still major issues. Recently, in federal bankruptcy court, American Airlines requested that its labor contracts with unions be voided (Associated Press, March 27 2012). American

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J. Bitzan, J. Peoples / Research in Transportation Economics 45 (2014) 9e17

says that its current labor contracts reduce its ability to pursue new markets and opportunities (D.R. Stewart, Tulsa World 2012). As an example, a “scope clause” in the current labor contract American has with its pilots limits the use of fuel efficient jets used by regional carriers (D.R. Stewart, Tulsa World 2012). These anecdotes suggest that it is likely that U.S. air carriers use an inefficient mix of factors of production as a result of such work rules. At first glance, it seems obvious that airline work rules promote a business environment such that airlines have an incentive to use too much labor relative to other inputs such as fuel, capital, and materials (Kumbhakar, 1992). By placing limits on the tasks a particular type of labor can perform, work rules force airlines to hire additional labor to perform the other tasks that a particular type of labor is restricted from doing. However, while work rules are likely to force airlines to use more labor than they would without such work rules with everything else constant, they do not necessarily result in airlines using more labor relative to other inputs. Whether airlines use more or less labor relative to other inputs is an empirical question. On the one hand, work rules may prevent airlines from substituting laborsaving technologies for labor, resulting in an overuse of labor relative to other inputs. On the other hand, by increasing the costs of utilizing labor due to reductions in labor productivity, work rules may force airlines to increase their substitution of other factors for labor, resulting in an underuse of labor relative to other inputs. This paper will examine the allocation of labor relative to other inputs to answer two questions: 1) do airlines employ an optimal mix of labor relative to other inputs? and 2) if not, do they employ too much labor or too little labor relative to other inputs? Section 2 of the paper presents a theoretical and empirical model of firm cost minimization that allows for the possibility that firms employ an allocatively inefficient mix of inputs. Specifically, we use an approach developed by Atkinson and Halvorsen (1984) that assumes firms minimize “shadow costs”, taking into account a different price paid for labor and non-labor services in comparison to their market prices. Moreover, we discuss airline work rules, and how such work rules are likely to alter the “shadow price” of labor and other inputs. Subsequently, we present empirical results, showing our test for allocative efficiency and comparing costs and input demands to efficient allocation of resources. Finally, we discuss the implications of these results for airlines and their prospects for success as work rules are changed. 2. Allocative efficiency in the airline industry A major challenge airline companies encounter in their attempt to provide efficient service is the constraint on their ability to use an optimal mix of labor relative to non-labor inputs. Constraints arise, in part, from government enforcement of scheduled hours of flight service and from adherence to union negotiated work rules. The US Federal Aviation Administration (FAA) enforces federal aviation regulations (FAR) on duty time for flight crews as a safety precaution.1 Limitations on consecutive hours of service for pilots and copilots are intended to avoid air accidents attributable to fatigue. Hours of service regulations also apply to flight attendants, as enforcement of required minimum flight attendant crew sizes is intended to assist in addressing cabin safety-related responsibilities. Regional and national airlines operate under FAR part 121. Rules outlined in that section of the FAR provide the framework for establishing maximum hours of scheduled flight service and duty

1 Duty time is the period of elapsed time between reporting for an assignment involving flight time and release time from that flight assignment.

time for pilots and flight attendants. For instance, in accordance with these regulations airline pilots are only permitted to fly 8 h in a 24 h period, 30 h in 7 days, 100 in a month, and up to 1000 h in a calendar year. FAA regulations limit airline flight attendants servicing domestic flights without assistance from additional attendants to no more than 14 consecutive hours of scheduled duty period, followed by a rest period of at least 9 consecutive hours. Long scheduled duty periods of more than 14 h and less than 16 h are allowed if the flight includes at least one additional attendant. Attendants can be assigned duty times of more than 18 h, but no more than 20 h if the scheduled duty period includes one or more flights that land or take-off outside the 48 contiguous states and the District of Columbia. The rest period for these restrictions require at least 12 consecutive hours. While FAA regulations impose maximum hours of flight duty restriction, unions can negotiate more restrictive rules for flight crews. For instance, newly negotiated work rules for Delta, Alaska, and American Airline pilots set maximum scheduled hours at 84, 85 and 87 h per month, respectively.2 In contrast, low-cost carrier Spirit enforces the maximum 100 h per month allowed by FAA regulations. Because the maximum number of hours a Delta, Alaska or American pilot can work in a month is relatively low compared to pilots at low cost carriers (LCCs) such as Spirit, these legacy carriers are required to hire more people to work in the cockpit for the same amount of actual flight time as smaller crews for Spirit. In addition to hours of service rules, other negotiated terms of collective bargaining agreements may also prevent air carriers from employing an efficient mix of flight-crew labor and other inputs. One of these is in the “scope provisions” that have been included in pilot collective bargaining agreements.3 Scope provisions often limit the number of large jets flown by regional partners or limit the ability of carriers to enter into code sharing agreements with other carriers. Such provisions may force carriers to operate services that would be performed more economically by other carriers. Finally, other rigid work rules for flight crews impose additional costs, including those associated with deadheading crews, costly and lengthy layovers, and employment of additional crews for long distance international flights. Deadheading refers to crew members that are not actively performing work duties being transported free of charge. This most often happens when airline crews are located in the wrong place and need to travel to take up their duties. In addition to the opportunity cost associated with displacing paying customers on a flight with non-paying personnel, carriers incur expenses associated with crews staying overnight in a location other than their home base. Reports indicate that pilots work an additional 150 h per month doing nonflight duties, showing that the actual wages paid to crews do not accurately depict their productivity (BLS, 2012).4 Rather, the excess cost accruing from work rules on staffing of crews and on rules governing travel expenses for flight personnel contribute to high pay relative to credit for hours flown.5 Not only do air carriers face constraints in their utilization of flight crew members, but they also face important constraints

2 Source, American Airlines, http://www.restructuringamr.com/our-people-apakt3.asp. 3 Source: http://www.restructuringamr.com/our-people-apa-kt2.asp. 4 Source: http://www.bls.gov/ooh/transportation-and-material-moving/airlineand-commercial-pilots.htm. 5 Gershkoff (1989) estimates non-duty flight pay relative to total flight hour reaching as high as 17 percent. FAR requirements on rotating crews for long ehaul domestic and international flights are another source of additional labor cost associated with work rules.

J. Bitzan, J. Peoples / Research in Transportation Economics 45 (2014) 9e17

regarding non-flight crew labor. FAA regulations on maximum scheduled hours of service and minimum crew sizes do not apply to non-flight crew members such as aircraft mechanics and baggage handlers.6 However, union negotiated work rules do influence airlines' ability to enhance productivity. Labor negotiated settlements of work rules for mechanics and baggage handlers include hours of service rules, rules that identify over-time, rules that limit the ability of air carriers to out-source aircraft repairs, and rules that limit the ability of air carriers to out-source baggage handling or to allow management to assist in providing baggage handling services.

2.1. Theoretical underpinnings of the problem Given the price competitive nature of this industry, the challenge facing air carriers is reducing crew costs associated with rigid work-rules. Formally, the problem can be viewed as follows: In order to minimize costs, and employ an allocatively efficient mix of inputs, the firm will employ each until the marginal product of a dollar's worth of one input is equal to the marginal product of a dollar's worth of another. For example, if the firm is using labor and capital:

MPL MPK ¼ wL wK where MPL and MPK are marginal products of labor and capital that would exist without work rules, and wL and wK are input prices that would exist without work rules. However, work rules potentially impact the productivity of inputs and/or the costs of hiring additional units of each input. Thus, the true optimization problem faced by firms is to use an allocatively efficient mix of inputs, taking into account the impact of work rules on input productivities and prices. We label the actual marginal productivities and input prices faced by firms (those that exist with work rules) as shadow marginal productivities (MP*L and MP*K) and shadow input prices (w*L and w*K). Therefore, firms choose a mix of inputs such that:

MP*L MP*K ¼ * w*L wK If work rules reduce the productivity of labor and/or increase the cost of hiring another unit of labor, then the shadow marginal product of a dollar's worth of labor (actual) is less than the marginal product of a dollar's worth of labor that would exist without work rules (when hiring the same amount of labor):

MP*L MPL < wL w*L At the same time, if such work rules do not alter the marginal productivity of capital or the cost of hiring a unit of capital:

MP*K MPK ¼ wK w*K This suggests that if the firm were utilizing the allocatively efficient mix of labor and capital that would exist without work

6 Aircraft mechanics normally work forty hour weeks on eight-hour shifts around the clock Baggage handlers can work shifts between eight and eleven hours a day for a compressed week. This scheduling flexibility presents baggage handlers with the opportunity to work four days consecutively followed by three nonworking days. Source: http://www.avjobs.com/careers/.

11

rules, the shadow (actual) marginal product of a dollar's worth of labor is less than the shadow (actual) marginal product of a dollar's worth of capital:

MP*L MP*K < * w*L wK Because of the law of diminishing returns, as the firm hires less labor, the marginal product of labor will increase until equality is achieved. This suggests the firm would hire less labor than suggested by an allocatively efficient mix. On the other hand, however, it is quite possible that work rules could reduce the productivity of non-labor inputs instead of labor. If work rules reduce the productivity of non-labor inputs, we would expect an underutilization of those inputs relative to labor. Whether airlines employ an allocatively efficient mix of inputs, and which inputs are over/underemployed are empirical questions. A priori, a prediction of allocative efficiency in this service sector is not obvious given the potential challenges imposed by rigid work rules. However, it is likely that major carriers have had some success in reducing the impacts of such work rules through code sharing agreements and acquiring regional carriers. Code-sharing allows regional carriers the opportunity to service flights on behalf of a major carrier, while the major carrier markets and sells tickets for these routes using it own flight designator code (Forbes & Lederman, 2009). Operational flexibility for major carriers is derived from their ability to bypass rigid work rules and share revenue with regional low-cost carriers who are less likely to operate under burdensome rules. Major carriers' acquisition of regional carriers provides some of the same advantages of code-sharing. However, shortcomings associated with regional acquisitions include the possibility of regional employees requesting work rules resembling those provided to the major carrier's unionized work forces (Forbes and Lederman). Moreover, while code sharing and acquiring regional carriers have likely helped reduce inefficiencies for major airlines, “scope clauses” in labor contracts may limit their use in some cases. Other successes realized by carriers in contending with work rules include restructuring union contracts through bankruptcy and extensive use of linear programming to optimize input use.7 Graves, McBride, Gershkoff, Anderson, and Mahidhara (1993) estimate substantial savings accruing from airlines using integer linear programming to optimize flight crew scheduling.8 Past research examining the airline labor markets and carrier operating efficiency support the notion that following deregulation labor productivity gains in the US contributed to relatively efficient airline operations. For instance, Ng and Seabright (2001) estimate a

7 Rules for engaging in labor negotiations in the airline industry are required to follow rules and regulations stipulated by the Railway Labor Act. The intent of this act is to avoid service disruptions in this industry. Thus service operations must continue without strike during an assigned cooling-off period. Such legislation has contributed to lengthy negotiation periods that preclude carriers from achieving work rule changes in a timely fashion. Reliance on bankruptcy court offers a legal alternative to voiding union contracts to avoid long negotiation disputes. 8 An example of flight crew optimizing software is the integer linear programming approach proposed by Graves et al. (1993). This program consists of a setpartitioning problem, which is a spreadsheet where rows represent flights to be staffed and columns available crew trips. Simulations using this approach rather than enumeration methods previously used by American Airlines generates potential savings of $18 million. The use of linear programming by airline companies is not unique to American as Air France, Delta and US Airways use alternatives approaches developed by Lavoie, Minoix, and Edourad (1985), AT&T, and Unisys, respectively.

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translog cost function for the US and EU airline industries to simulate airline costs for EU carriers assuming they operated at the higher post-deregulation labor productivity levels achieved by US carriers. Findings show that from 1990 to 1995 European airline costs were approximately 26 percent higher than levels they could have attained with the same competitive structure in the US. At issue, though, is whether US air carriers have been able to satisfy the conditions of allocative efficiency when operating in a business environment still requiring adherence to rigid work rules, even with the post-deregulation adoption of efficiency enhancing approaches mentioned above. Evidence on allocative efficiency immediately preceding and immediately following 1978 airline deregulation in the U.S. indicates that carriers employed an inefficiently high level of labor relative to capital and fuel (Kumbhakar, 1992). However, there is some evidence to suggest that carriers' employment of labor relative to other inputs may have changed since the period immediately following deregulation. Bitzan and Peoples (2014) find that airline productivity increased by an average of 2.5 percent per year between 1993 and 2010. Moreover, they find that these productivity gains are labor saving, suggesting less use of labor in comparison to other inputs. An example of potential productivity gains from investing in non-labor inputs is highlighted by Baltagi, et al (1995), who find large gains in fuel efficiency due to carrier investment in larger, more fuel efficient aircrafts. To the extent that work rules have decreased labor productivity, the adoption of labor saving technologies may have been enhanced. Section 3 presents an empirical approach to measuring allocative efficiency, applying the approach to U.S. air carriers from 1993 to 2010. 3. Empirical approach and results 3.1. Model and data We estimate a long-run cost function for the airline industry using individual airline Form 41 financial reports and T-100 traffic data reported by large certificated U.S. air carriers to the U.S. Department of Transportation for the years 1993e2010. Table A1 of the Appendix shows all variable definitions and data sources. Table A2 provides descriptive statistics for these variables. The airline cost function includes four factor prices, two outputs, four technological characteristics and a time trend. The generalized airline cost function is:


 C ¼C wl ;wf ;wk ;wo ;QP;QF;LOAD;LOAD2;StgLength;PtsServed;T where: wl ¼ price of labor wf ¼ price of fuel wk ¼ price of capital wo ¼ price other9 QP ¼ passenger output (revenue passenger miles) QF ¼ freight/mail output (revenue ton-miles) LOAD ¼ load factor passengers (rev. pass-miles/avail. passmiles) LOAD2 ¼ load factor freight (rev. ton-miles/avail. ton-miles) Stg Length ¼ average stage length Pts Served ¼ number of airports served T ¼ time trend

Technological variables included in our cost function include an average passenger load factor, an average freight load factor, average stage length, and the number of airports served. Passenger load factor is defined as revenue passenger miles divided by available passenger miles, while freight load factor is defined as revenue ton-miles divided by available ton-miles. These are included to take into account the fact that many costs of operating a flight (e.g., flight crew, maintenance, fuel) do not increase proportionally with the number of passengers and tons on a flight. Average stage length, or the average segment length, is included to account for the fact that many costs are a function of the number of takeoffs or landings (e.g., maintenance, fueling, boarding, security, landing fees) and do not vary proportionally with distance. The number of points served is included as a proxy for firm size. Finally, we include firm fixed effects (i.e. firm dummy variables, including merger variables) variables to account for unmeasured firm characteristics, and a time trend to account for technical change. As previously shown by Atkinson and Halvorsen (1984) and Oum and Zhang (1995), we can test for allocative efficiency by estimating the firm's cost function with an embedded ‘shadow cost’ function. If work rules alter the costs of using various inputs, the effective price of using an input will vary from it's market price. Firms are expected to base their input hiring decisions on these unobserved shadow prices, and therefore, minimize total shadow costs. We can specify the firm's shadow cost function as:


 CS ¼ CS Q ; W *; T

Where CS are the firm's shadow costs, Q is a vector of outputs, W* is a vector of shadow prices, and T is a vector of technological characteristics. Input shadow prices (wi*) are equal to the market input price multiplied by a factor of proportionality (Lau and Yotopoulos, 1971):

wi * ¼ ki wi

The price of other includes the price of all inputs other than labor, capital, and fuel. It is calculated as a residual per hour of operation.

(2)

This factor of proportionality (ki) shows the relationship between the true input prices and market prices paid by firms for inputs:

wi * wi

ki ¼

(3)

If ki is greater that one, it suggests that the firm's shadow price for this input is greater than the market price. This would suggest an underutilization of this input. Alternatively, if ki is less than one, overutilization of the input is suggested. Atkinson and Halvorsen (1984) show that applying Shephard's Lemma to the shadow cost function yields input demands:

vC S ¼ xi vwi *

(4)

Total actual cost is:

C¼

X

wi xi ¼

i

X i

wi

vC S vwi *

(5)

As shown by Atkinson and Halvorsen (1986), the share of shadow costs accounted for by input i is:

SSi ¼ 9

(1)

ki wi xi CS

This implies that input xi is:

(6)

J. Bitzan, J. Peoples / Research in Transportation Economics 45 (2014) 9e17

xi ¼

0

SSi C S ki wi

(7)

ln C ¼a0 þ

X

X B C X ai ln@ki wi A þ bo ln Qo þ gn ln tn o

i

0

The total actual cost function is:

C¼

X

wi

i

þ

(8)

þ

SSi ki

ln

i

S

ln C ¼ a0 þ

0

!

0

1

X o

1 0

bo ln Qo þ

X

io

gn ln tn

1

ai þ SA i (10)

Imposing symmetry and homogeneity conditions yields the following parameter restrictions:

i

i

X

j

i

fio ¼

X

fin ¼ 0; fij ¼ fji

(11)

i

To get the shadow cost share equations, we use Shephard's lemma and differentiate the translog shadow cost function with respect to shadow prices as follows:

  vln C S vln C S vC vðki wi Þ 1 ¼ ¼ k ¼ SSi x w i i i vlnðki wi Þ vC S vðki wi Þ vlnðki wi Þ C S

SSi ¼ ai þ

X j

(12)

X   X ∅ij ln kj wj þ ∅io ln Qo þ ∅in ln tn o

(15)

Substituting from Equation (12):

nl

fij ¼ 0;

(14)

i

1X þ fnl ln tn ln tl 2

X

wi xi C

. SSi ki
.  SA i ¼P S Si ki

X 1X þ ∅op ln Qo ln Qp þ fon ln Qo ln tn 2 op on

fij ¼

fon ln Qo ln tn þ

As shown by Atkinson and Halvorsen (1984), we can put this in terms of shadow share equations by using Equations (7) And (8):

n

in

X

X

As in other applications of the translog cost function, we jointly estimate total costs with factor share equations in a seemingly unrelated system of equations. In order to obtain factor share equations, note that the share of expenditures on factor i is:

SA i ¼

1X f ln@ki wi Aln@kj wj A 2 ij ij 0 0 1 1 X X fio ln@ki wi Aln Qo þ fin ln@ki wi Aln tn þ

ai ¼ 1;

1X B C fin ln@ki wi Aln tn þ ∅op ln Qo ln Qp 2 op

(13)

þ

X

X

i

(9)

ai ln@ki wi A þ

i

io

1

1X fnl ln tn ln tl 2 on nl   P P P 0 1 ai þ ∅ij ln kj wj þ ∅io ln Qo þ ∅in ln tn X o o j B C þln@ A ki þ

Thus, we can estimate the shadow cost function as an embedded part of the total cost function. Using the translog functional form for the shadow cost function:

X

1

ij

in

When we take the logarithms, we get:

X

n

1 0

0 1 X B B C B C C fij ln@ki wi Aln@kj wj A þ fio ln@ki wi Aln Qo 0

X SS SSi C S i ¼ CS ki wi k i i

ln C ¼ ln C S þ

1X 2

13

1

o

From Equations (9), (10) And (12) we can get the total cost function:

¼

P

  P P ∅ij ln kj wj þ ∅io ln Qo þ ∅in ln tn o

j

P i

ai þ

P j

!,

o

  P P ∅ij ln kj wj þ ∅io ln Qo þ ∅in ln tn o

ki , !

o

ki (16)

The total cost function (Equation (13)) is estimated jointly with factor share Equations (16) using Zellner's Seemingly Unrelated Regressions. Since the factor shares sum to 1, one of the cost share equations is deleted to obtain a nonsingular covariance matrix. Because the total cost function is homogeneous of degree zero in factors of proportionality, one of the factors of proportionality (the one for labor) is normalized to one. Thus, all other factors of proportionality are measured relative to that for labor.10 3.2. Cost function parameter estimates and tests of allocative efficiency Table 1 presents the nonlinear seemingly unrelated regression results for total airline costs. As the table shows, all first-order terms except one have their expected signs, and most are

10 We estimated this same cost function several times, each time normalizing a different factor of proportionality to one. We did this to check our methodology, and did get consistent results. We also estimated a cost function that used the additive specification of the relationship between shadow price and market price (Eakin & Kniesner, 1988), and got the same qualitative results.

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J. Bitzan, J. Peoples / Research in Transportation Economics 45 (2014) 9e17

Table 1 Nonlinear seemingly unrelated regression estimation of airline costs 1993e2010. Variable

Parameter estimate

Standard error

Intercept Shadow price  Labor Shadow price  Fuel Shadow price  Other Shadow price  Capital Factor of proportionality  Labor Factor of proportionality  Fuel Factor of proportionality  Other Factor of proportionality  Capital Revenue passenger miles Revenue ton-miles Average stage length Load factor (Passengers) Load factor (Freight) Airports Time ½ Shadow labor2 ½ Shadow fuel2 ½ Shadow other2 ½ Shadow capital2 Shadow labor  Shadow fuel Shadow labor  Shadow other Shadow labor  Shadow capital Shadow fuel  Shadow other Shadow fuel  Shadow capital Shadow other  Shadow capital Shadow Labor  Pass-miles Shadow fuel  Pass-miles Shadow other  Pass-miles Shadow capital  Pass-miles Shadow Labor  Ton-miles Shadow fuel  Ton-miles Shadow other  Ton-miles Shadow capital  Ton-miles Shadow labor  Stage Shadow fuel  Stage Shadow other  Stage Shadow capital  Stage Shadow labor  Load (pass) Shadow fuel  Load (pass) Shadow other  Load (pass) Shadow capital  Load (pass) Shadow labor  Load (freight) Shadow fuel  Load (freight) Shadow other  Load (freight) Shadow capital  Load (freight) Shadow labor  Airports Shadow fuel  Airports Shadow other  Airports Shadow capital  Airports Shadow labor  Time Shadow fuel  Time Shadow other  Time Shadow capital  Time ½ Rev pass-miles2 ½ Rev ton-miles2 ½ Stage length2 ½ Load (pass)2 ½ Load (freight)2 ½ Airports2 ½ Time2 Rev pass-miles  Rev Ton-Miles Rev pass-miles  Stage Length Rev pass-miles  Load (pass) Rev pass-miles  Load (freight) Rev pass-miles  Airports Rev pass-miles  Time Rev ton-miles  Stage Length Rev ton-miles  Load (pass) Rev ton-miles  Load (freight) Rev ton-miles  Airports Rev ton-miles  Time Stage length  Load (pass) Stage length  Load (freight) Stage length  Airports

22.04396* 0.502208* 0.167535* 0.192998* 0.13726* 1.00000 0.658419* 0.316845* 0.345076* 0.976366* 0.004602 0.27938* 0.65218** 0.31711*** 0.01537 0.004123 0.039034* 0.065149* 0.064897* 0.072458* 0.05181* 0.010864* 0.001914 0.00736* 0.00597* 0.0684* 0.012266* 0.01515* 0.003138 0.00026 0.008594*** 0.009114** 0.01187* 0.00584* 0.05974* 0.053277* 0.001729 0.004734*** 0.02412 0.018771 0.000237 0.005109 0.03168*** 0.061903* 0.01327 0.01695** 0.00045 0.00342 0.001214 0.002662 0.00217* 0.005494* 0.00217* 0.00115* 0.212408* 0.171269* 0.141448** 0.50768*** 0.66299* 0.123515* 0.00224* 0.14561* 0.05378*** 0.120666 0.093882 0.12095* 0.02574* 0.117529* 0.25123** 0.14807 0.026029 0.023645* 0.026284 0.097936 0.10148*

0.0786 0.0160 0.00928 0.00979 0.00616 0.0677 0.0266 0.0301 0.1362 0.1351 0.0796 0.2712 0.1900 0.0484 0.00559 0.00627 0.00492 0.00326 0.00336 0.00392 0.00288 0.00225 0.00169 0.00132 0.00401 0.00427 0.00355 0.00203 0.00174 0.00483 0.00388 0.00234 0.00190 0.00638 0.00578 0.00346 0.00263 0.0176 0.0149 0.00927 0.00752 0.0177 0.0140 0.00894 0.00683 0.00443 0.00350 0.00228 0.00168 0.000712 0.000549 0.000387 0.000282 0.0431 0.0675 0.0651 0.2687 0.1627 0.0192 0.000541 0.0394 0.0295 0.0782 0.1046 0.0436 0.00375 0.0361 0.0986 0.1183 0.0454 0.00403 0.1094 0.0763 0.0259

Table 1 (continued ) Variable

Parameter estimate

Standard error

Stage length  Time Load (pass)  Load (freight) Load (pass)  Airports Load (pass)  Time Load (freight)  Airports Load (freight)  Time Airports  Time

0.00598** 1.02733* 0.326531* 0.038535** 0.03016 0.01973** 0.000699

0.00294 0.3719 0.1201 0.0160 0.0737 0.00981 0.00260

*significant at the 1 percent level **significant at the 5 percent level. ***significant at the 10 percent level. All variables except factors of proportionality are in natural logarithms. Parameter estimates for airline dummies not shown. They are available upon request from the authors. Adjusted R-Square: Cost ¼ 0.9949, Fuel Share ¼ 0.6223, Other Share ¼ 0.7340, Capital Share ¼ 0.7892. # of Observations ¼ 613.

significant at conventional levels.11 Moreover, adjusted R2s suggest a good statistical fit of the cost and share equations. The translog cost function is specified by normalizing all independent variables by their means. Therefore, first-order term parameter estimates can be interpreted as the elasticity of costs with respect to each variable when all variables are at mean levels. As the table shows, shadow cost shares of labor, fuel, other, and capital are 50, 17, 19, and 14 percent, respectively for the average airline. The table also shows interesting results related to returns to density, returns to firm size, and technical change. The sum of parameter estimates for revenue passenger miles and revenue tonmiles suggests approximately constant returns to density at the point of means, as output elasticity is 0.97. The parameter estimate for the number of airports served is approximately zero and not statistically significant, suggesting that returns to firm size are also constant at the point of means. Although the parameter estimates in Table 1 seem to suggest no technical change over time (insignificant parameter estimate on time), the large negative (and significant) parameter estimates for stage length and load factors suggest that technical change has been embodied in increasing flight distances and loads carried (See Bitzan and Peoples, 2014). Of particular interest are the estimated factors of proportionality. As the table shows, the factors of proportionality for fuel, other, and capital are all less than one.12 This suggests that airline firms do not employ an allocatively efficient mix of inputs. Moreover, the factors of proportionality of less than one suggest that the shadow prices of these inputs relative to their market prices are low in comparison to labor. Based on our hypothesis that labor rules inflate the price of labor above its market price, we interpret this to mean that the shadow price of labor is above its market price, under the assumption that all other factors' shadow prices are equal to market prices. As a result of this divergence between the shadow price of labor and its market price, airline firms use less labor relative to other inputs than they otherwise would. More insight into the decision facing airline firms can be seen by comparing shadow cost shares of inputs with actual cost shares. As Table 2 shows, the shadow cost share of labor is 0.50, while actual cost share of labor is 0.29 at the mean of all variables. Thus, airline firms that are minimizing shadow costs realize a much larger

11 The number of airports served has an unexpected negative sign. However, it is not significant at conventional levels. 12 The factor of proportionality for labor is normalized to one. Tests reject the hypothesis that the factors of proportionality are all equal to 1 (as they would be with allocative efficiency). These same results were obtained when using a different normalized factor of proportionality. Moreover, in estimating a cost function with the additive specification of shadow price, we get the same qualitative result.

J. Bitzan, J. Peoples / Research in Transportation Economics 45 (2014) 9e17 Table 2 Estimated shadow cost share and actual cost share at the means of all variables.a Input

Shadow cost share

Actual cost share

Labor Fuel Other Capital

0.5022 0.1675 0.1930 0.1373

0.2848 0.1443 0.3454 0.2256

Shadow cost share for input i is ai, while actual cost share for input i is P ai w1 ai w1 i = i . a

i

financial burden from using labor than they would if the market price were the actual price they faced. The table also shows that fuel shadow cost share is slightly higher than its actual cost share, while shadow cost shares are much lower than actual cost shares for other and capital. This supports the idea that the true price of these inputs is low relative to their market price in comparison to labor and fuel. Given the allocative inefficiency and the underutilization of labor relative to other inputs, an obvious question one might ask is: How much of a difference does this make to airline firms? To obtain insight into this question, we compare costs the typical firm would realize with allocative efficiency to what they realize with allocative inefficiency. Specifically, costs realized under allocative efficiency are simulated using the mean of all independent variables (and for every firm in the sample) and the fitted cost function with all factors of proportionality set to one.13 Costs realized under allocative inefficiency are simulated using the fitted cost function with the estimated factors of proportionality. In a similar way, we simulate the quantity demanded of each input under allocative efficiency and make a comparison to the quantity demanded under allocative inefficiency. As shown previously, actual cost shares of inputs are specified as:

SA i ¼

wi xi CA

This suggests that:

xi ¼

A SA i C wi

Quantity of input i demanded under allocative efficiency is simulated using the above equation with factors of proportionality set equal to one. For allocative inefficiency, the same equation is used with estimated factors of proportionality used. Table 3 shows simulated percentage changes in costs and inputs used as a result of the allocative inefficiency. These are calculated using a simulation that is done at the means of all independent variables, and as the mean simulated percentage changes for individual firms. As the table shows, allocative inefficiency is simulated to result in a 13 to 14 percent increase in costs for the typical firm. Given estimated costs ranging from $13 million to $28 billion for the firms in our sample, these cost increases are substantial. The table also shows that the number of full time employees hired is about 35 percent less than with allocative efficiency and the amount of fuel used is about 9 percent less than with allocative efficiency, while the amounts of other materials and capital used are 105e107 percent and 92-96 percent higher than they would be with allocative efficiency, respectively. Combined with the findings of cost increases from allocative inefficiency, this seems to suggest that relaxing work rules could be a winewin situation for labor and management e that is, increased numbers of employees and lower costs.

13 This was also done for electric power generation by Atkinson and Halvorsen (1984).

15

Table 3 Simulated impacts of allocative inefficiency on costs and quantities of inputs used.a

Means of all Vars Means of Indiv. firm impacts

Percent change in cost

Percent change in FTEs

Percent change in fuel

Percent change in other materials

Percent change in capital

14.04% 13.35%

34.56% 34.96%

9.26% 8.50%

104.98% 106.50%

92.45% 96.03%

a The simulated changes in costs and inputs as a result of allocative efficiency are performed for the mean of all variables in the sample, and for all firms in the sample. The simulations assume that all firms realize the same degree of allocative efficiency.

However, caution must be used in this interpretation. The simulated impacts shown in Table 3 are based on a cost function estimation that assumes technical efficiency. It is important to keep in mind that the reason unions insist on restrictive work rules is to enhance employment. The idea is that if workers are so specialized that only some types of workers can perform specific tasks, the airline will be required to hire more workers to perform the tasks that the other workers are restricted from doing. To the extent that work rules are effective in forcing airlines to hire more workers to perform the tasks where other inputs are not easily substituted for labor, the allocative inefficiency findings may suggest that airlines use too much of all inputs. That is, they use an inefficiently high amount of labor and an even more inefficiently high amount of other inputs. If this is the case, the cost increases simulated in this study would vastly understate the cost increases that result from restrictive work rules. 4. Implications for the airline industry and future research Using estimates from a generalized cost equation for domestic US air transportation services this study computes input price distortion indices to examine whether US airlines employ an optimal mix of labor relative to non-labor inputs. Testing for allocative efficiency is significant in part because US carriers face operational constraints associated with restrictive work rules. Previous studies examining allocative efficiency immediately following deregulation suggests an overutilization of labor relative to non-labor inputs (Kumbhakar, 1992). Analysis using more current information is warranted, however. Recently, airline companies have invested in more productive non-labor inputs such as regional jets for short-haul routes and larger more fuel efficient aircraft for high density long-haul routes. Our findings suggest airlines use an inefficiently high amount of non-labor inputs (e.g. capital and fuel) relative to labor, supporting the idea that the higher cost of labor resulting from inefficient work rules leads to substituting other factors of production for labor. We note that in contrast to findings examining allocative efficiency immediately following deregulation, the incentive to under utilize labor is enhanced by technological improvements of non-labor inputs. Simulations revealing excess cost attributable to the underutilization of labor suggest a significant competitive disadvantage for those carriers that are unable to negotiate more flexible work rules. Cost-savings derived from the industry's movement toward less stringent work rules depicts a potential source of increased welfare gains to airline customers. While the results seem to suggest that carriers employ an inefficiently low amount of labor and an inefficiently high amount of non-labor inputs, an alternative interpretation is possible. Because work rules are designed to enhance employment by decreasing substitutability among different types of labor and substitutability of non-labor inputs for labor, it is unlikely that they result in an overall underutilization of labor. Instead, the finding that airlines employ an inefficiently low amount of labor relative to other inputs seems more consistent with the idea that airlines employ too much of all inputs. This can only be known through further study.

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J. Bitzan, J. Peoples / Research in Transportation Economics 45 (2014) 9e17

APPENDIX Table A1: Variable definitions and data sources Variable

Source

Cost and input shares Total cost Operating expense Opportunity cost of capital Net property and equipment Before tax cost of capital

(Operating Expense þ Opportunity Cost of Capital) Form 41, Schedule P-6, Line 00360 e Total for the Year Net Property and Equipment x Before Tax Cost of Capital Form 41, Schedule B-1, Line 16750 e Annual Average over 4 Qtrs Calculated by Authors e Data are from Aswath Damodaran, New York University, Damodaran Online: http://pages.stern.nyu.edu/~adamodar/- these include: (1) historical U.S. Treasury Bond rates, before tax cost of debt for U.S. Airlines, effective tax rates for U.S. Airlines, U.S. Market Risk Premiums, historical betas for U.S. Airlines, historical debt and equity shares for U.S. Airlines e from 1993 to 1998, airline beta, tax rate, cost of debt, and equity/debt shares are unavailable e thus, 1999e2010 averages of these variables are used in calculating the cost of capital for 1993-1998. (Opp. Cost of Capital þ Rentals þ Deprec.þAmort.)/Total Cost Form 41, Schedule P-6, Line 00310 e Total For the Year Form 41, Schedule P-6, Line 00320 e Total For the Year Form 41, Schedule P-6, Line 00330 e Total For the Year Fuel/Total Cost Form 41, Schedule P-5.2, Line 51451 e Total For the Year Salaries and Benefits/Total Cost Form 41, Schedule P-6, Line 00140 e Total For the Year 1 e Capital Share e Fuel Share e Labor Share

Capital share Rentals Depreciation Amortization Fuel share Fuel Labor share Salaries and benefits Other share Input prices Capital price Air hours Fuel price Gallons Labor price Full time equiv. employees Other price

(Opp. Cost of Capital þ Rentals þ Deprec.þAmort.)/Air Hours T-100 Segment, Air Time Minutes/60 — Total for the Year Fuel/Gallons Form T-2, Aircraft Fuel Gallons e Total for the Year Salaries and Benefits/Full Time Equivalent Employees From 41, Schedule P-1(a), FTE Employees e Annual Average over 12 months (Total Cost e Opp. Cost of Capital e Rentals e Deprec. e Amort. e Fuel e Salaries and Benefits)/Ramp-to-Ramp Hours T-100 Segment, Ramp-to-Ramp Minutes/60 — Total for the Year

Ramp-to-ramp hours Output variables Revenue passenger miles Revenue ton-miles

T1 Summary Data e Total for the Year T1 Summary Data e Total for the Year

Technological characteristics Average stage length Load factor (passengers) Available seat miles Load factor (Freight) Available ton-miles Airports served Time

T-100 Segment, Average Distance (weighted by number of departures) d Average for the Year Revenue Passenger Miles/Available Seat Miles T1 Summary Data e Total for the Year Revenue Ton-Miles/Available Ton-Miles T1 Summary Data e Total for the Year T3 U.S. Air Carrier Airport Activity Statistics e Total Number of Airports Year e 1993

Costs and input prices are placed in 2005 prices using the GDP Implicit Price Deflator.

References Table A2: Descriptive statistics Variable

Mean

Standard deviation

Total Cost Capital Share Fuel Share Labor Share Other Share Capital Price Fuel Price Labor Price Other Price Revenue Passenger Miles Revenue Ton-Miles Average Stage Length Load Factor (Passengers) Load Factor (Freight) Airports Served

$3,421,006,938 0.2135 0.1736 0.2674 0.3455 $3537.72 $1.2492 $65,468.25 $4515.79 19,824,503,768 2,321,169,159 900.5417 0.6852 0.5563 89.6663

$5,831,860,082 0.0733 0.0880 0.0690 0.0913 $17,345.45 $0.7108 $22,841.24 $17,571.90 33,720,028,822 3,967,464,908 720.5464 0.1059 0.1016 57.8179

Costs and Input Prices are in 2005 Dollars using the GDP Implicit Price Deflator. 613 Observations.

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