The Long –Run Dynamic Equilibrium
Between Air Carrier Capacity and Profitability*

Bahram Adrangi
University of Portland

Richard D. Gritta
University of Portland

Kambiz Raffiee
University of Nevada, Reno

*An earlier version of the paper was presented at the 77^th annual conference of the Western Economic Association International, June 29-July 3, 2002, Seattle, Washington.

I.   Introduction

   The U.S. airline industry is entering its fifth consecutive year of troubled times. From 2001 through 2003, the industry incurred losses of $23.2 billion. Losses in 2004 are expected to amount to $8 billion. Industry wide, losses may fall in 2005, perhaps to around $2 billion to $4 billion, according to John Heimlich, chief economist for the Air Transport Association, the industry trade group (Skertic, 2005). Five more air carriers enter 2005 under the cloud of bankruptcy (United, ATA, Aloha, Hawaiian, and US Airways). Some of the factors that may help them out of this situation such as economic growth, lower fuel costs and changes in labor contracts, are out of their control. Furthermore, low interest rates, a big help in keeping interest costs lower, could increase this next year and further worsen the already precarious financial situation of the carriers.

   In the midst of rising operating costs and tough economic conditions airlines have been slashing fares in hopes of raising revenues. However, most industry analysts believe that fares should be rising. According to Brian Hayward of Chicago’s Zacks Investment Research (Skertic, 2005), air fares in real terms are at their lowest in years and should increase. The same analyst attributes the low real airfares to an overcapacity in the industry that has benefited passengers while landing many air carriers in financial distress. The overcapacity in the industry is a legacy of pre-2001 years when air carriers were expanding by increasing order for new aircraft. This situation may be viewed as the buildup of inventories in other sectors of the economy. However, even air carriers under Chapter 11 continue to operate, contributing to continual overcapacity. In this paper, we examine the pre 2001 industry capacity and profitability.

   Airlines are no different than other firms. They are profit-maximizing entities. Prior to 1978, airlines faced a variety of regulations that insulated them from market competition and its attending benefits and challenges. Airlines tried to maximize profits within the regulatory constraints. The Airline Deregulation Act of 1978 changed this business environment. Since deregulation, carriers have faced intense competition in all aspects of their business decisions. Additionally, deregulation has brought new elements to the industry, such as the hub and spoke system, mergers and increased market power. The consequences of these new elements on costs, efficiency, pricing and profits of air carriers were studied by Adrangi et al. (1996), Borenstein (1989, 1990, 1992), Brown (1992), among others. And the increasingly oligopolistic market structure of air transport was examined by Bailey and Williams (1988), Barla (1999), Joseph and Zick (1991), Kim and Singal (1993), Liu and Lynk (1999), and McGinley (1989), among others.

   A salient characteristic of an oligopolistic or near-oligopolistic market structure is that generally a handful of large firms tend to dominate the market place. The growth in firm size is often achieved through horizontal mergers. A priori, air carriers hope that they gain economies of scale and scope by mergers, thus, reducing their unit costs. Furthermore, clearly, horizontal mergers increase market power of postmerger firms, which in turn may increase firm profitability. Scherer and Ross (1990) discuss market power as a motivation for horizontal mergers. Mergers may also be motivated by efficiency considerations. Some mergers enable more efficient firms to take control of less efficient ones. The American Airlines, for instance, recently absorbed TWA. Furthermore, air carrier mergers may lead to gains in efficiency by eliminating excess capacity in certain segments of market that a carrier serves. Regardless of the above-mentioned incentives, horizontal mergers add to air carrier firms’ capacity and may contribute to more efficient utilization of resources and better use of the management resources. Thus, carrier profitability improves through horizontal merger activities.

   In the process of increasing oligopolistic structure, carriers are also attempting to maximize profits over time by increasing size and growth potential. There has been an increase in merger activity over the past decade. It appears that air carriers believe that, by horizontal mergers, they can benefit from economies of scale and scope. It is plausible that increasing size through horizontal merger may impact a carrier’s market power, and thus contributes to profitability. Most carriers have argued in the popular financial media that mergers increase their access to new markets, resulting in productive and allocative efficiencies.

   Several researchers in recent years have examined the capacity related issues in the air transport. Oum et al. (2000) study optimal carrier capacity and capital structure using a sample of ten U.S. major carriers for the years of 1985-92. They show that profit-maximizing carriers over expand beyond the optimum capacity necessary for minimum cost of operation. Furthermore, under the present oligopolistic environment, the social costs, which include passenger delay costs, are not minimized.

   Liu and Lynk (1999) examine mergers and increased concentration in the deregulated U.S. airline industry using a panel of observations for eleven carriers for the period of 1984-91. They show that in the post-deregulation era, there is evidence of economies of network size. Cost savings resulting form hub network system and other opportunities such as predatory scheduling are conducive to market dominance and market power. Their findings imply that by expanding their network of hubs, airlines may be able to exercise monopoly power in certain segments of the market.

   The present study examines the relationship between carrier capacity and profits in a dynamic framework. The objective is to investigate whether carriers benefit from increased size. If the long-run relationship between size and profits is positive, then there is a market incentive for carrier mergers and acquisitions and a move toward an oligopoly market structure. This is particularly important in the aftermath of 9/11 events. Today, two questions face the major air carriers. First, how do they survive in the market place given the financial conditions they now face? Second, are the economic conditions facing them after 9/11 more favorable to consolidation or internal growth as compared to pre 9/11? In the evaluation of proposals for major air carriers’ mergers, the considerations of maintaining competition in air transport and improving scale and scope economies are far more daunting, specially in the face of staggering losses that the U.S. airline industry is facing after the events September 11.

   The remainder of this paper is organized as follows. Section II outlines the methodology and data sources. Section III presents the empirical findings and discusses their policy ramifications. Section IV offers a summary and the conclusions.

II.   Methodology and Data

   The main econometric tool used in this paper is the vector autoregressive technique (VAR) to examine the relationship between capacity, CAP, measured by available seat miles, and profits, PRF, adjusted by CPI for the US airline industry. The data consist of quarterly observations on nine US carriers (Alaska, American, America West, Continental, Delta, Northwest, Southwest, Trans World and United) from 1983.3 to 1998.3. Data Base Products (Dallas, Texas) is the source of the raw data used in the study. The summary statistics on capacity and profits by airline are presented in Table 1. Our data covers pre-September 11, 2001. Since 9/11 the airline industry has experienced extraordinary conditions that may distort statistical tests. Sufficient post 9/11 data are not yet available to warrant a retest at this time.

   VAR models are the best tools to investigate shock transmission since they provide information on impulse response analysis. A series of vector error correction models (VECM) constitute the mainstay of our empirical analysis. VAR or VECM models are particularly suitable for this type of a study because they are dynamic and allow for examining the effects of a shock to one endogenous variable on the remaining endogenous variables of the model.

   A VAR consists of a system of dynamic simultaneous equations. In each equation, an endogenous variable is a function of exogenous as well as the lagged values of all endogenous variables. Thus, a VAR allows for the simultaneous and dynamic interaction of all endogenous variables. More importantly, a VAR provides an unrestricted approximation to the reduced form of an unknown structural system of simultaneous equations. Though the underlying structure is not specified, it is assumed to exist.

   Zellner and Palm (1974), Zellner (1979), and Palm (1983) show that any linear structural model can be written in the form of a vector autoregressive moving average multivariate time series model (VARMA) whose coefficients are combinations of the structural coefficients. These researchers show that under mild regularity conditions a VARMA model can be written as a VAR model. Therefore, a VAR model serves as a flexible approximation to the reduced form of any wide variety of simultaneous structural models. To paraphrase, the reduced forms of traditional simultaneous models are special cases of VAR models.

   The consensus among researchers is that VAR models are dynamic and capture the simultaneous interactions among all variables. They are suitable to describe the economic data-generation process. VAR models are typically smaller than structural models and therefore require less data. We use VAR models in conjunction with the Akaike’s (1974) Information Criterion (AIC) and Schwarz (1978) Information Criterion (SIC) to determine the dimensionality of equations of the system. The vector autoregressive models and impulse response functions used in the paper are presented in Appendix A.

   We also test for the long-run equilibrium relationship among capacity and profits employing Johansen and Juselius (1990) cointegration test. Cointegration refers to the possibility that non-stationary variables may have a linear combination that is stationary. Such a linear combination, the cointegrating vector, implies that there is a long-run equilibrium relationship among variables, i.e., variables will not wander off apart from one another over extended periods of time. Therefore, cointegration between capacity and profits implies a long-run relationship between these variables. The test of cointegration employed in this paper. A brief description of the test is provided in Appendix B.

III.   Empirical Results

   Table 2 reports the results of the stationarity tests in Dickey and Fuller (1979). Unit roots tests indicate that capacity and profit variables for most airlines are not stationary when augmented Dickey-Fuller (ADF) regressions are estimated without trend and several are stationary with a trend variable included in the estimated regressions. Therefore, although regression analysis of the two variables may provide spurious results, we may be able to employ cointgration tests to investigate the long-run equilibrium and the short-run dynamic relationships between the two variables. To this end, we perform Johansen-Juselius cointgration test. The Johansen-Juselius test is based on the appropriate VAR model between the two variables. Therefore, In order to test for the long-run equilibrium relationship between the variables PRF and CAP by the Johansen and Juselius methodology, the lag order of the VAR should be determined. To this end, we estimate several VAR models by varying the lag order of the variables. Up to twelve lags are examined. Maximizing the Akaike and Schwarz Information Criteria (AIC and SIC, respectively) suggest VAR models with the appropriate lag orders for each air carrier company.

   Table 3 records the maximum AIC and SIC statistics necessary to determine the optimum lag values in VAR models. The lag structure ranges from 1 to eleven for the nine carriers under study. Therefore, the lag orders specified in this table are the basis of estimated VAR models for the remaining empirical investigation. In the following, we estimate VAR models with a lag orders reported in Table 3.

   Having estimated the VAR models with appropriate lag orders, we may investigate causality between the two variables for all air carrier firms employing the Granger causality test. The Granger causality tests show that in all cases the hypothesis that the available capacity does not Granger cause profits is rejected with ninety nine percent confidence. This finding sets the stage for the investigation of the long-run equilibrium relationship between these two variables. Table 4 summarizes the causality tests. In the next table we report the outcome of the Johansen-Juselius cointegration test.

   The Johansen-Juselius cointegration test results reported in Table 5 indicate that in six out of nine airlines, profits and capacity are cointegrated at the ninety one percent level of confidence. The six airlines with cointegrated profits and capacity are Alaska, American, America West, Continental, Delta and Trans World. Thus, for the remainder of the empirical investigation, cointegrting vectors and error-correction estimation are only reported for these six airlines. Combined with the Granger causality test results, we conclude that there is strong evidence in support of the hypothesis that the available capacity of a carrier positively affects its profitability.

   This finding is noteworthy for both analysts who study air carrier firms and investment opportunities in air transportation, airline executives, and policy makers. There seems to be a strong incentive for air carrier firms to merge and form larger carriers with increased profitability. Therefore, while the deregulation has prompted entry by many new firms in this sector of the transportation industry, the surviving firms have an incentive to enhance capacity in order to remain profitable. In light of this finding it should not be surprising that the market place has witnessed some highly publicized mergers among major carriers. These findings may also be supporting the view that the economies of scale impose an economic constraint on the number of major carriers that could remain profitable in the U.S. transportation industry.

   We also estimate the cointegrating vectors with exactly identifying restrictions.¹ According to the estimation results, there is a positive long-run equilibrium relationship between profits and capacity for all carriers. However, only in two cases the relationship is statistically significant. The conclusion is that the evidence in support of the long-run relationship between the capacity and profits is not very strong. However, as Granger causality tests indicate, the evidence for the short-run positive relationship between the two variables is more plausible. Therefore, in the remaining section, we discuss the short-run dynamic relationship between the two variables.

   Adopting the reported cointegrating vectors, we now return to the short-run dynamic analysis of the model. For this purpose error-correction models of the profit equation are estimated.² The lag order in each error-correction equation is determined by the order of the appropriate VAR in the cointegrating relationship. It is appropriate to focus on the coefficient of the error-correction term, which indicates the speed of adjustment in the system in the presence of shocks. The error-correction term exhibits the expected sign and is statistically significant in all cases but one. The speed of adjustment to shocks is quite high in all cases and similar for three out of five remaining cases. American Airlines is shown to demonstrate the highest speed of adjustment. This finding may be showing that the American Airline has developed a great deal of flexibility in reacting to changing market conditions. This airline is also a relatively high profit carrier with one of the lowest profit distribution skewness.

   As expected, the long-run equilibrium is quickly restored in almost all of the cases studied. The implication of this finding may be that the post deregulation Airline industry has become quite efficient in responding to market conditions and is equipped to deal with economic shocks to the capacity and profits. The adjustment process, however, may bring about bankruptcies and layoffs in this sector as in most other competitive industries.

IV.   Summary and Conclusions

   The present study examines the long-run dynamic relationship between an indicator of air carrier firms’ capacity measured by the available seat miles and their profits. The objective is to investigate whether carrier size as measured by the firms’ capacity is related to profitability. If size and profits demonstrate a positive long-run relationship, then there is a market incentive for carrier mergers and acquisitions and a move toward an oligopoly market structure. Thus further concentration in this sector of the economy may be inevitable.

   Employing vector autoregressive models (VAR) and cointegration tests, we show a long-run positive relationship between the available seat miles and profits. Granger causality tests verify that for all carriers the capacity variable Granger causes profits. These findings imply that there is a market incentive for carrier mergers and acquisitions and a move toward an oligopoly market structure and further concentration in this sector of the economy.

   Another ramification of our findings is that air carriers had expanded capacity in the pre 9/11 era with the objective of increasing profits. The post 9/11 era has presented an unpredictable set of challenges to air carriers. The economic slow-down, geopolitical uncertainties, erratic fuel costs, combined with labor contracts that are incompatible with the current industry climate lead to financial distress that currently many carriers are facing. For instance, John Heimlich, the chief economist for Air Transport Association estimates that every 1$ increase in the price of a barrel of oil results in $440 million more in annual fuel expenses for the industry. On January 5, 2005 Delta Airlines announced a new fare structure that most experts believe may lead to a new round of fare wars. While low fares and a rise in fuel costs or any other adverse development may force some carriers out of business and benefit surviving carriers, the long–run solution may hinge on improved efficiency. For instance carriers may want to retire their old and inefficient fleet in some routes and replace them with more modern and fuel efficient smaller jets. This two-pronged solution would reduce capacity and improve fuel efficiency. Fuel efficiency in 2005 will be critical as oil prices rose from $31 a barrel in 2003 to $42 in 2004.

   The findings of this paper is particularly important in the aftermath of 9/11 events giving weight to the future proposals for air carrier mergers. Given the current economic conditions of the industry, it appears that the economic conditions facing the majors after 9/11 are also favorable to consolidation in the airline industry compared to pre 9/11. The implications for policy purposes may be that future mergers between major air carriers should be evaluated in such a way by allowing air carriers to take advantage of the long-run co-movement between their capacity and profits, ensuring them market survival. This approach is different from the usual considerations in evaluation of major carrier mergers based on only efficiency, scale and scope economies and carrier profitability.

   Two questions flow from this analysis: What are the ramifications of this research for the carriers and for governmental policies and will the relationship found hold in the future? The last several years have been the most difficult in the history of the U.S. airline industry. Because of 9/11 and the start of a slowdown in air travel in early 2001, the U.S. commercial aviation industry lost $7.7 billion in 2001, in spite of federal compensation for the September system shutdown and its related losses. Losses have continued to mount during the following two and a half years, and according to one report now total of over $30.0 billion (Skertic, 2005). The debt/equity ratios of the majority of the major carriers in this industry have always been excessively high and now have deteriorated to the extent that the very continued existence of many of the large carriers is clearly in doubt. The bankruptcy rate is this industry was atrocious before 9/11. Over 130 carriers had failed prior to that tragic date, and the total number of carrier failures has since increased to 144 and counting.

   The ramifications for the airlines themselves are clear, especially given the continuing financial problems in mid-2004. They must adopt strategies that will ensure survival in the increasingly unfavorable environment fostered by high fuel prices, increasing labor unrest, and the destabilizing effects of terrorism on the already unstable demand for the industry’s product. The airlines must also determine whether the economic conditions facing them after 9/11 would make consolidation more favorable post 9/11, as compared to pre 9/11. That may mean that growth may not be a priority for the next several years.

   The implications for public policy would appear to revolve around two possible diametrically opposed strategies. Governmental authorities could follow a laissez-faire approach. Policy could default to the marketplace and let the industry seek equilibrium on its own in spite of any costs. This could mean continued labor unrest, the possible disruption of service in some markets, and the likelihood of the future bankruptcy of several other major carriers. The implications of this study for public policy may be that, in the face of the staggering losses suffered because of the events of September 11, future mergers between major air carriers could be examined in the context of allowing the majors to take advantage of the long-run relationship between their capacity and profits to ensure them survival, rather than the usual considerations of efficiency, scale and scope economies and carrier profitability.

   A final point must be made. While this study has demonstrated statistically that carrier capacity, measured by available seat miles, has been the key to profitability in the past, the reality may be changing. The rise of the low cost carriers such as Southwest, JetBlue, AirTran, etc., together with the morphing of America West into a low cost carrier after its bankruptcy filing, may be a sign that the past is not an indicator of the future. Changing aircraft technology in the form of the new regional jets has made the smaller regional carriers more efficient allowing them to under price the majors, and in the process crippling the large carriers. Given their much lower costs, as low as 6.9 cents per available seat miles for Jet Blue, and the excess capacity in the market, these airlines can under price the major carriers and still make money while the large carriers bleed more red ink. The percent of the US domestic market served by these so-called “low-cost” carriers has grown to over 25%, and some major carriers may be rethinking their traditional hub-and-spoke and “fortress-hub” strategies. American, for example, has considered moving to a “rolling hub” concept and has cut back at several major hubs, such as Dallas/Ft.Worth. US Airways is reducing it hub in Pittsburgh. Delta is rumored to be considering dropping many short-haul (feeder) routes into its hubs, and selling of its subsidiary-Comair to raise money, in order to concentrate on the long-haul markets with a higher level of service (at higher prices). Northwest exemplified this latter strategy in its prime during the 1970s and 1980s, when its profitability was second to none in the industry.³ The major carriers may be able to survive by abandoning growth in favor of consolidation strategies.

   It may also be that, as the low cost carriers grow larger, and as competition intensifies in this market, these carriers will experience significant increases in their cost structures and lose the competitive advantages they now hold over the major carriers. Since the data in this study covers the period up to 1999, this analysis may not have picked up the effects of these changes. Future research over the next several years may shed light on this, but as noted above, sufficient data is not yet available to answer this question.

Footnotes:

1. The estimation results on cointegrating vectors with exactly identifying restrictions are available from the authors upon request.
2. The estimation results of the error-correction equations are available from the authors upon request.
3. During the years of the 1960-70s, the larger airlines were known as “trunklines.” Later they were called “majors,” which in now defined as those carriers with revenues of $1.0 billion or more. Of the large carriers that existed back then and those that grew into “majors,” (Alaska, America West, and Southwest), six (America West, Braniff, Continental, Eastern, PanAm, TWA,) declared bankruptcy one or more times prior to 9/11 and three have disappeared forever (Braniff, Eastern and Pan Am). Since 9/11, both United and US Airways filed bring the total to eight. That’s a failure rate of 50%. The threat in 2004-2005 by American and Delta to file for court protection would raise the total to ten or 62.5%, an abysmal statistic. No other economic sector, including domestic steel and textiles, has experienced that high a rate of failure.

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Appendix A

The test of cointegration employed in this article is from Johansen (1988) and Johansen, and Juselius (1990). This method is a multivariate generalization of the methodology suggested by Engle and Granger (1987). A brief description of the test is as follows. Let

(A.1) Δ x_t  =  p x_t-l+ e_t

where x_t and  e_t are (n_*1) vectors and p is an (n_*n) matrix of parameters.   The Johansen (1988) methodology requires estimating  the system of equations in (9) and examining the rank of matrix p.  If rank (p) = 0, then there is no stationary linear combination of the {x_it} process, the variables are not cointegrated.  Since the rank of a matrix is the number of non-zero eigenvalues (l) , the number of l>0 represents the number of cointegrating vectors among the variables.  The test for the non-zero eigenvalues is normally conducted using the following two test statistics:

(A.2) l_trace  ( r ) = -T ln (1- λ_i )

(A.3) l_max (r, r+1) = -T ln (1- λ_r+1)

where λ_i is the estimated eigenvalues, and T is the number of valid observations.  Note that

l_trace statistic is simply the sum of l_max statistic.   In equation (A.3), l_max tests the null hypothesis that the number of distinct cointegrating vectors is less than or equal to r against a general alternative. l _max statistic tests the null hypothesis of r cointegrating vectors against r+1 cointegrating vectors.  Johansen and Juselius (1990) derive the critical values of  l_trace  and l_max by simulation method.

Appendix B

The vector autoregressive (VAR) models and impulse response functions used in the paper are presented below. The VAR system of equations can be written in compact matrix notation as follows:

(B.1)             +  =                                   

where α₁₁(L) through α₂₂(L) are n-th order scalar polynomials in the lag operator L, where α_ij(L) = , and L^k is the lag operator of order k of variables PRF_t and CAP_t, and m is the lag length specified. Variables PRF_t and CAP_t represent profits (adjusted by CPI) and capacity (available seat miles), respectively, β_i, model constants,  and u_t= [u_lt u_2t] is a vector of white noise residuals process.

A final consideration in using the VAR model is the choice of the order of the process, p.  Without a formal method, the selection of lag order in a VAR model will be arbitrary and could lead to specification error, see Fair and Schiller (1990) and Funke (1990).  Several criteria, similar to those used in the distributed lag models, are suggested to determine the model dimension, see Lutkepohl (1985). It can be shown that the GLS estimators of the coefficients are identical to the OLS estimators under the above assumption regarding the residuals.

VAR models are routinely used to perform impulse response analysis, which allow us to measure the various period impact of the U_t-i on each variable. Impulse response analysis requires a vector moving average (VMA) representation of a VAR.  The VMA allows us to trace out the time path of the various shocks on the variables of the VAR system.  Consider the VMA process given by

(B.2)    =  +      

The sets of coefficients Ø_kj(i) are called the impulse response functions.  For example Ø₁₂(0) is the instantaneous impact of a one-unit change in ε _CAPt on PRF_t.  Similarly, Ø₁₂(1)is the one period response of PRF_t to one unit change in ε _CAPt-1.  The accumulated effect of unit impulses in ε _CAPt on PRF_t for example, can be computed by summing the coefficients of the impulse response function.  Thus, the effect of ε _CAPt on the PRF_t after n periods is given by .

To produce reliable VAR estimates and impulse response analysis, variables of the model are required to be stationary, i.e., not have unit roots. 

Table 1. Summary Statistics 

                                                           Capacity                                                    Operating Profit

                                               Mean                    S.D.                                  Mean                       S.D.

Alaska                              2,125,734               962,832                        10,686,943             23,441,645             

American                       23,429,716             5,375,458                     122,553,459           138,239,855

America West                  3,606,405             1,761,802                       11,636,349              26,762,448

Continental                     10,619,399             3,337,194                       11,489,717             66,489,738

Delta                              21,087,879             5,504,189                     107,071,114          147,616,065

Northwest                      10,839,447             3,390,765                       62,464,672          116,837,626

Southwest                        5,534,606             3,241,608                        50,583,710             49,520,151

Trans World                     7,494,779                901,327                      (10,799,706)            49,289,754

United                            22,198,865             3,199,548                       64,634,642           146,317,721

Notes:  Capacity is available seat miles (ASM) in thousands. Operating profit is adjusted for inflation using the CPI.  The data consist of quarterly observations on the nine airlines from 1983.3 to 1998.3.  US Airways was not included in the sample due to incomplete data.  The data were provided by Data Base Products of Dallas, Texas. Based on the quarterly average of available seat miles, the top three airlines in the sample are American, United and Delta, respectively.  Based on the quarterly average of adjusted profits, the top three airlines in the sample are American, Delta and United, respectively.

Table 2. Unit Root Tests                                                                                                                  

                                                                                ADF                                                                 ADF (t)        

                                                      Capacity                                Profit                                Capacity                          Profit

Alaska                                               0.25                                    -5.35^***                            -3.60^**                           -6.02^***

American                                         -1.07                                    -1.04                                 -1.43                              -0.94

America West                                  -1.70                                    -2.09                                 -2.11                              -2.95

Continental                                       -1.10                                    -3.08                                 -1.70                              -3.78^**

Delta                                                -0.50                                    -6.65^***                            -2.18                              -9.71^***

Northwest                                        -1.22                                    -7.14^***                            -2.03                              -7.17^***

Southwest                                        -2.17                                    -4.09^**                              -1.79                              -3.98^**

Trans World                                     -2.14                                    -7.13^***                            -2.75                              -7.17^***

United                                              -1.23                                    -4.58^**                              -2.08                              -5.20^** 

Note:  ADF and ADF (t) are the Augmented Dickey Fuller statistics with and without trend and intercept.  The lag length in ADF equations are determined by the Akaike Information Criterion.

^***and ^**  significant at the 1 and 5 percent levels, respectively. 

Table 3. Test Statistics and Choice Criteria for Selecting the Order of the VAR Model

                                                                                 AIC                                         SIC                                Lag Order                      

Alaska                                                            -1803.8                                      -1853.7                                     11

American                                                        -2439.7                                      -2462.3                                      4

America West                                                 -1868.3                                     -1880.8                                       2

Continental                                                      -2420.3                                     -2429.3                                      1

Delta                                                               -2469.2                                     -2478.3                                      1

Northwest                                                       -2458.6                                      -2476.7                                      3

Southwest                                                       -1876.5                                     -1897.3                                      4

Trans World                                                    -2452.1                                    -2470.2                                       3

United                                                             -2531.9                                     -2559.0                                      5

Note:  VAR orders of 12, which include intercepts and trend variables are estimated, and the lag length for the cointgrating VAR is determined based on the maximum Akaike and Shwarz Information Criteria, AIC and SIC, respectively. 

Table 4. Likelihood Ratio Test of Block Granger Non-Causality in the Unrestricted VAR 

Airline                                                                      c²                                                                                                            

Alaska                                                                77.98 ^***

American                                                            26.52^***

America West                                                    124.97^***

Continental                                                         28.06^***

Delta                                                                  19.71^***

Northwest                                                            2.04^***

Southwest                                                          69.72^***

Trans World                                                       25.28^***

United                                                                12.35^***

Note:  The block causality tests are performed within the VAR framework.  VAR lag structure is determined and reported in Table 2.
  c² is the Chi-squared statistic.

 ^*** significant at 1 percent level.

Table 5. Cointegration Tests with Unrestricted Intercepts and Unrestricted Trends in the
VAR Models                                                                                                                                    
                        H0                   Ha                                            H0                   Ha                               

                        r=0                 r=1                                            r = 0                 r  1

                       r£1                 r=2                                             r  1                 r  2

                                                        l_max                                                                                                    l_trace

Alaska                                            63.77^***                                                                        68.94 ^***
                                                        5.16                                                                              5.16

American                                       21.70^**                                                                          23.20^**
                                                        1.50                                                                               1.50

America West                                20.52^**                                                                           24.54^**                             
                                                        4.02                                                                               4.02

Continental                                     23.46^**                                                                          25.59^**
                                                        2.13                                                                               2.13

Delta                                               19.03^**                                                                        22.53^**
                                                        3.50                                                                              3.50

Northwest                                         5.31                                                                              9.60
                                                        4.30                                                                               4.30

Southwest                                       10.55                                                                            11.38                                          
                                                        0.83                                                                               0.83

Trans World                                   27.46^**                                                                          31.91^**
                                                          4.45                                                                             4.45

United                                               9.88                                                                           11.19
                                                         1.31                                                                             1.31

Note:  The Johansen-Juselius cointegration test results indicate that in six out of nine cases, profits and capacity are cointegrated at the ninety one percent level of confidence.  The six airlines with cointegrated profits and capacity are Alaska, American, America West, Continental, Delta and Trans World.

^{*** and  **}  significant at the 1 and 5 percent levels, respectively.