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Fare impacts of Southwest Airlines: A comparison of nonstop and connecting flights
Journal of Air Transport Management 84 (2020) 101771
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Fare impacts of Southwest Airlines: A comparison of nonstop and connecting flights Junqiushi Ren * Research Institute of Economics and Management, Southwestern University of Finance and Economics, Chengdu, 611130, China
A R T I C L E I N F O
A B S T R A C T
Keywords: US airline industry LCC Southwest airlines Entry Connecting flights
This paper examines the effects of Southwest Airlines’ entry on its rivals’ pricing, with a focus on comparing nonstop and connecting flights. The results produce two important findings. First, Southwest’s nonstop entry depressed its rivals’ nonstop airfares and connecting airfares. Second, Southwest’s connecting entry depressed its rivals’ connecting airfares, but did not depress their nonstop airfares. Considering nonstop and connecting ser vices as differentiated products which differ in quality, the findings suggest that firms have quite different fare strategies upon the entry of different quality products.
1. Introduction Since the first low-cost carrier (LCC), Southwest Airlines, established in 1967, LCCs have reached a huge success in the U.S. and elsewhere in the world. Unlike traditional legacy carriers who operate on hub-andspoke structures, LCCs adopt a very different business model which in volves point-to-point structures, allowing for higher aircraft utilization. In addition, LCCs are well known for requiring employees to work multiple roles to cut personnel costs.1 Such cost-cutting strategy allows LCCs to sell tickets at a relatively low price and maintain competitive advantage. Over the past twenty years, LCCs have been growing rapidly in the US. In 2017, 49% of all domestic passengers travelled with LCCs. Southwest, the leading LCC, itself transported 27.9% of the domestic traffic, making it the largest carrier in the U.S. and the largest LCC worldwide.2 Given the fact that LCCs have been so successful, it is not surprising that they have attracted a lot of attention in the literature. Many re searchers have shown that LCCs, including Southwest Airlines, lowered airfares on the routes they entered.3
However, most of the studies either only looked at nonstop flights, or aggregated across the service types. According to Reiss and Spiller (1989) and Dunn (2008), this may lead to incorrect inference, since nonstop and connecting flights may be regarded as differentiated products in similar markets. This paper fills the gap by discussing Southwest’s effects in the context of both service types and comparing their differences. It should be noted that although Southwest is famous for its P2P routing, it does connect as well, only not to the same degree as tradi tional hub-and-spoke carriers, like Delta and American. For instance, in 2017, Southwest provided connecting service on 4801 domestic routes, and provided nonstop service on 2011 routes, while for Delta the numbers of routes were 5604 and 755 for connecting and nonstop ser vice, respectively. Passengers were open to use those connecting itin eraries as well, especially on mid-haul and long-haul routes, where connecting traffic comprised about 30% and 40% of the domestic traffic, respectively.4 The main objective of this work is to study how Southwest’s entry affects its rivals’ pricing, with a focus on comparing nonstop and
* Research Institute of Economics and Management, Southwestern University of Finance and Economics, Gezhi Building 1109, Wenjiang District, Chengdu, 611130, China. E-mail addresses: [email protected], [email protected]. 1 See Borenstein (1992) for a detailed discussion about the differences between LCCs and legacy carriers. 2 The rankings are based on passenger count. 3 Examples include Borenstein (1992), Whinston and Collins (1992), Dresner et al. (1996), Vowles (2000, 2001), Morrison (2001), Alderighi et al. (2004), Brueckner et al. (2013), and many others. 4 The numbers of routes and the percentages of traffic are identified from the DB1B data.
https://doi.org/10.1016/j.jairtraman.2020.101771 Received 30 August 2019; Received in revised form 21 January 2020; Accepted 23 January 2020 Available online 28 January 2020 0969-6997/© 2020 Elsevier Ltd. All rights reserved.
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Journal of Air Transport Management 84 (2020) 101771
connecting flights. All other (e.g. frequencies) being equal, the nonstop service is viewed as a higher quality product compared to the connecting service, and different connecting services also vary in quality using a measure of the extra flight distances.5 A set of price equations are esti mated using U.S. airline industry data from 1993 to 2017. The rest of the paper are composed as follows: Section 2 reviews related literature. Section 3 outlines the research method. Section 4 describes the data and the steps taken to construct the sample. Section 5 describes the main results. Section 6 concludes the paper.
ValuJet’s entry into Atlanta. They discovered that after ValuJet entered Atlanta, Delta lowered its fares on nonstop routes terminating in Atlanta and on connecting routes flying through Atlanta. Brueckner et al. (2013) measured the in-market, adjacent, and potential competition from LCCs, where both nonstop competitor indicators and connecting competitor indicators were included in the model. Nevertheless, the former work is more like a case study, and the latter work is based on a sample which spanned only four successive quarters and does not examine the dy namic trends of airfares. This paper differs from them by investigating the topic in more depth, using a much longer sample period, and tracking the patterns of price changes. The conclusions are also different. As a brief summary, this paper adds to the literature in three major ways. First, this paper is among the few works which take the type of services into account when studying LCCs’ impacts. Second, to the best of the author’s knowledge, this paper is the first work to show that service types significantly influence carriers’ decisions in response to LCCs’ entry. Third, the findings of this study indicate that airlines compete both within and across service types, which also extends pre vious theories on airline competition.
2. Literature review Many studies have documented the fare impacts of LCCs. Dresner et al. (1996) indicated that the presence of a LCC, especially Southwest Airlines, reduced average yields on that route and on adjacent routes. Vowles (2000) showed that the presence of LCCs is an important determinant of average airfares. Morrison (2001) found that the entry of Southwest influenced the average prices on Southwest’s actual, adja cent, and potential routes. Alderighi et al. (2004), Goolsbee and Syver son (2008), and Kwoka and Batkeyev (2019) examined LCCs’ entry threats on nonstop trips. Daraban and Fournier (2008) applied a spatial autoregressive model and confirmed LCCs’ effects on spatially-linked, adjacent routes. Tan (2016) demonstrated that incumbents’ decreased the mean, 10th percentile, and 90th percentile airfares in response to LCCs’ entry. Asahi and Murakami (2017) showed that on certain routes, incumbents reduced the average fare when Southwest entered the market, and reduced the average fare even more in several years after the entry. Bachwich and Wittman (2017) analyzed the ultra-low cost carriers and argued that their presence was associated with significant decreases in market average fares. Though these literature have made remarkable contributions, a common problem is that they either restricted the attention to nonstop flights, or aggregated across the service types. This may be regarded as not appropriate, because nonstop and connecting services may be regarded as differentiated products in similar markets. From consumers’ perspective, connecting trips are more time-consuming and less conve nient, but sometimes can be a lot cheaper. From airlines’ perspective, on the other hand, connecting flights increase the utilization of their air crafts from/to hub airports and may lead to economies of density.6 Moreover, even for Southwest who is well known for its point-to-point network, it makes use of “operating bases” or “focus cities” to connect as well, only not to the same degree as traditional hub-and-spoke car riers. Beginning in 2009, Southwest tried a program at Chicago Midway for a forceful push for passenger connections.7 Travellers, especially leisure travellers who are more price sensitive, are open to use such connecting services as well. As pointed out by Cook and Billig (2017), about 40% of Southwest passengers used the connecting services it provided network-wide, while at Chicago Midway, 55% of passengers connected to other flights. Hence, it may not be proper to neglect con necting itineraries or to simply aggregate across service types. Instead, one should incorporate both service types and at the same time discuss their differences. This may be important since Reiss and Spiller (1989) concluded that the type of services is an essential determinant of the level of competition, not just the carriers. Dunn (2008) also showed that service types are important factors influencing airlines’ decisions, add ing support to the approach taken in this paper. Windle and Dresner (1999) and Brueckner et al. (2013) are among the few papers on LCCs which attempted to discuss the differences in service types. Windle and Dresner (1999) examined Delta’s responses to
3. The econometric model Following the estimation strategy in Goolsbee and Syverson (2008) and Tan (2016), the author uses a two-way fixed effects model to identify the entry effect of Southwest. A couple of dependent variables are used, including the natural log of incumbents’ mean nonstop airfare (InNonstopPrice) and the natural log of incumbents’ mean connecting airfare (InConnectingPrice). The basic specification is as follows: Yijt ¼ α þ γij þ μit þ
4þ X
βτ Entryj;t0 þτ þ θInconvenienceijt þ εijt
(1)
τ¼ 8
where Yijt is either InNonstopPriceijt or InConnectingPriceijt for incum bent airline i on route j in quarter t. γij and μit are carrier-route and carrier-quarter fixed effects, respectively. They control for any unob served differences across carrier-route and carrier-quarter. α is the constant term. εijt is the error term. Inconvenienceijt measures the quality of the trip in terms of incon venience, and is calculated as the itinerary distance over the nonstop distance. For nonstop trip, this variable equals to 1. For connecting trip, this variable is larger than 1. As this variable increases, the quality of the connecting trip drops. The key variables of interest, Entryj;t0 þτ , are quarter dummies that specify the lag/forward surrounding Southwest’s entry into route j. Again, the entry events are classified into nonstop entry and connecting entry, according to the service that Southwest provided. For an entry event at time t0 , the author constructed thirteen dummy variables cor responding to thirteen quarters surrounding time t0 , namely, t0 þ τ, 8; …; 0; …; 4 þ . The estimates of the coefficients βτ where τ ¼ show the relative sizes of the dependent variable in the dummy periods versus its value in the reference period (the 9th to 12th quarters before entry). For example, suppose β0 ¼ 0:126. This means that, holding all else constant, the mean airfare for incumbent airlines is 11.8% lower,8 on average, in the quarter of entry (t0 ) relative to its value in the reference period (the 9th to 12th quarters before entry). The pre-entry quarter dummies capture the fare strategies of the incumbents before actual entry. They can reflect whether there is preemptive price cutting behavior or not. The post-entry quarter dummies show the dynamic patterns of airfares once entry has occurred. Most likely the airfare will adjust gradually, in which case the post-entry
5
Note that the layover time is also an important determinant of connecting flight quality. Nonetheless, the dataset adopted in this study does not provide such information. So the author only uses the detour distance to infer quality. 6 See Brueckner and Spiller (1994). 7 See Cook and Billig (2017) for a detailed discussion.
8 The percent change relative to the excluded period is calculated as exp (–0.126) 1 ¼ 0.118.
2
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Journal of Air Transport Management 84 (2020) 101771
time dummies will reflect the dynamic pattern for up until the 4th quarter after entry. Equation (1) is estimated separately for each of the following situations:
Delta in 2000 Quarter 1 is summarized into cell “JFK-SAN-Delta2000Q1-nonstop”. Within each cell, the author then computes the mean ticket price and flight distance, weighted by the number of passengers.11 4.3. Sample selection
(i) examine incumbents’ nonstop fare changes surrounding South west’s nonstop entry; (ii) examine incumbents’ nonstop fare changes surrounding South west’s connecting entry; (iii) examine incumbents’ connecting fare changes surrounding Southwest’s nonstop entry; and (iv) examine incumbents’ connecting fare changes surrounding Southwest’s connecting entry.
The sample used in this study includes data from the first quarter of 1993, through to the last quarter of 2017. That being said, this study is based on a panel dataset that covers 25 successive years. The author restricts the sample to routes where Southwest started flying between 1993 and 2017. The criteria to identify a nonstop entry is as follows: Southwest must not have operated nonstop flights on the route for at least 12 quarters preceding the quarter of entry, and must have operated nonstop flights on the route for no less than 3 successive quarters following the quarter of entry. The criteria to identify a con necting entry is defined likewise. The author further restricts carriers to the seven major airlines in the sample period, namely, American Airlines, Delta Air Lines, United Air lines, US Airways, Northwest Airlines, Trans World Airlines, and Con tinental Airlines. Ultimately, Southwest is identified to have nonstoply entered into 826 routes, and have connectingly entered into 802 routes. The final sample contains 59,147 observations (cells). Summary statistics for continuous variables are given in Table 1.
In all cases, the standard errors are clustered by carrier-route to ac count for possible correlations in the error terms. Besides, the author weights observations by the total number of passengers flying the carrier-route over the sample years, so that high-traffic carrier-route combinations have more influence on the parameter estimates and lowtraffic carrier-route combinations have less. 4. Data and sample construction 4.1. Data description The data employed in this study comes from the Airline Origin and Destination Survey (DB1B),9 which is collected by the Office of Airline Information of the US Bureau of Transportation Statistics. The data is a quarterly data that consists of a 10% random sample of all tickets sold and operated by US carriers. The author uses the itinerary-level information in DB1B data set. For each itinerary, the following information is collected: the reporting carrier, the transaction price, the number of passengers, the fare class, the airport sequence (origin and destination airports along with all transfer points), the actual flight distance, and the nonstop flight dis tance between the two endpoint airports. The following data restrictions are imposed: (i) drop itineraries that are part of international travel; (ii) drop itineraries that have more than four legs; (iii) drop itineraries with fares less than $25, due to the high probability that those may pertain to frequent-flyer programs where passengers redeemed accumulated travel points to offset the full fare of travel10; and (iv) drop code-share itineraries.
5. Empirical results The estimation results are summarized in Table 2. Recall that the estimates of the coefficients on the quarter dummies reveal incumbents’ pricing patterns around the entry event. Column (I) presents in cumbents’ nonstop price changes surrounding Southwest’s nonstop entry. Column (II) presents incumbents’ nonstop price changes sur rounding Southwest’s connecting entry. Column (III) shows incumbents’ connecting price changes surrounding Southwest’s nonstop entry. Col umn (IV) shows incumbents’ connecting price changes surrounding Southwest’s connecting entry. According to the estimates, every column except for column (II) exhibits a price drop in the quarter of entry (Entryt0 ) and the quarter after entry (Entryt0 þ1 ). The post-entry estimates are all significantly negative in these three columns, indicating that incumbents lowered prices compared to the reference period. The coefficients of Inconvenience are negative in the last two col umns. This means that, holding all else constant, as a connecting trip gets more inconvenient, its price will decrease.
4.2. Data aggregation Since the raw data is huge, for the convenience of analysis, the author aggregates the data into cells. Specifically, each cell is a “routecarrier-quarter-service type” combination, where “route” is a directional combination of the two endpoint airports, regardless of any intermedi ate transfer points; “carrier” refers to the reporting carrier of the itin erary; “quarter” refers to the year-quarter combination of the itinerary; and “service type” is either nonstop or connecting. To illustrate, a nonstop itinerary from New York John F. Kennedy International Airport to San Diego International Airport reported by
Table 1 Summary statistics for continuous variables.
9 Available at https://www.transtats.bts.gov/Tables.asp?DB_ID¼125&DB_Na me¼Airline%20Origin%20and%20Destination%20Survey%20%28DB1B% 29&DB_Short_Name¼Origin%20and%20Destination%20Survey. 10 This is common in the literature, see, for example, Tan (2016) and Gayle and Wu (2011).
Variable
Definition
Mean
St. Dev
NonstopPriceijt
Mean nonstop airfare for carrier i on route j in quarter t
212.75
70.67
ConnectingPriceijt
Mean connecting airfare for carrier i on route j in quarter t
206.21
57.69
Inconvenienceijt
The itinerary distance divided by the nonstop distance for carrier i on route j in quarter t
1.12
0.13
11
Within a nonstop cell, trips are likely to have the same flight distance; whereas within a connecting cell, trips may have different flight distances if they transfer at different airports. Hence, it is necessary to weight not only the ticket price, but also the flight distance by the number of passengers, in order to take into account the relative frequency of different transfer stations. 3
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Journal of Air Transport Management 84 (2020) 101771
Table 2 Incumbent price responses to Southwest’s different types of entry. (I)
(II)
(III)
(IV)
Dependent Variable:
lnNonstopPrice
lnNonstopPrice
lnConnectingPrice
lnConnectingPrice
Entry Event: Entryt0 8
SW’s nonstop service 0.011 (0.008)
SW’s connecting service 0.004 (0.012)
SW’s nonstop service 0.022** (0.010)
SW’s connecting service 0.002 (0.009)
Entryt0 Entryt0 Entryt0 Entryt0
Entryt0 Entryt0
0.013 (0.010)
7
0.018 (0.017)
4 3 2
0.002 (0.011)
0.044b (0.017)
0.016 (0.012)
0.018 (0.013)
0.057a (0.020)
0.019 (0.017)
0.044** (0.020)
Entryt0 þ1
0.147a (0.026)
Entryt0
0.062a (0.022)
0.126a (0.023)
0.060b (0.024) 0.081a (0.030)
0.031a (0.011)
0.027b (0.013)
0.027b (0.011) 0.046a (0.013) 0.067a (0.014)
0.055a (0.014)
0.170 (0.026) 0.168a (0.028)
0.066 (0.027)
0.076*** (0.014)
Entryt0 þ4þ
Inconvenience Constant Adjusted R2 N
0.069b (0.033)
5.974a (0.021) 0.823 13,051
6.095a (0.023) 0.847 9,418
0.013 (0.011) 0.004 (0.011) 0.005 (0.013)
0.059*** (0.014)
0.058** (0.026)
Entryt0 þ3
0.015 (0.012)
0.032** (0.013)
0.169*** (0.028)
b
0.012 (0.012)
0.068*** (0.015)
Entryt0 þ2
a
0.002 (0.010)
0.033a (0.011)
0.013 (0.017) 0.039b (0.019)
0.010 (0.011)
0.013 (0.015)
0.036b (0.017)
0.022 (0.015)
5
1
Entryt0
0.008 (0.014)
0.019c (0.012)
6
0.072a (0.015)
0.246a (0.088) 6.258a (0.103) 0.789 22,338
0.035b (0.015) 0.042a (0.015)
0.080 (0.081) 6.132a (0.092) 0.767 14,340
Notes: This table presents the results for the two-way fixed effects regression of the natural log of incumbent carrier’s mean airfare (either nonstop or connecting) in response to entry by Southwest Airlines (either nonstop or connecting). The Entry variables are the lag/forward time dummies, where Entryt0 is the quarter of entry. Observations are at the route-carrier-quarter-service type level. Standard errors, which are clustered by carrier-route, are reported in parentheses. Observations are weighted by the total number of passengers flying the carrier-route over the sample years. a Significant at the 1% level. b Significant at the 5% level. c Significant at the 10% level.
In order to visualize the incumbent responses to entry, the author plots price paths based on the coefficients of the quarter dummies in the two-way fixed effects models. For ease of interpretation, the coefficients of quarter dummies are transformed into percent changes in the dependent variable relative to the reference period. Figs. 1–4 are plotted out based on the estimates in columns (I) to (IV) in Table 2, respectively. In all figures, the entry event occurs at time period 0. Negative quarter values represent quarters before entry and positive quarter values represent quarters after entry. The red solid line is the
Fig. 2. Incumbents’ nonstop price path surrounding Southwest’s connect ing entry.
Fig. 1. Incumbents’ nonstop entry.
nonstop
price
path
surrounding
transformation of the point estimates from the model. The blue dotted lines are the associated 95% confidence interval. Fig. 1 illustrates incumbents’ nonstop price path surrounding Southwest’s nonstop entry. According to this picture, the price was stable until the quarter prior to entry (quarter 1). In this quarter, in cumbents reduced price by 3.8%. Their response reinforced to 11.8% in the quarter of entry (quarter 0) and continued to 13.6% in the quarter after entry (quarter þ1). Four quarters and more after entry, the price was down by 15.5% compared to the benchmark. These results
Southwest’s
4
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Fig. 3. Incumbents’ nonstop entry.
Journal of Air Transport Management 84 (2020) 101771
connecting
price
path
surrounding
Brueckner et al. (2013), whose results indicate that a connecting pres ence of Southwest reduces nonstop fares by 4%. Fig. 3 portrays incumbents’ connecting price path surrounding Southwest’s nonstop entry. According to this picture, there were some fluctuations in price before entry. By the quarter prior to entry, in cumbents set price to be 4.5% lower compared to the benchmark. The price gradually dropped to 6.5% lower in the quarter of entry and went to 6.9% lower in four quarters and more after entry. This suggests that Southwest’s nonstop entry induced incumbents to cut their connecting fares. In other words, changes in nonstop market have spillover effects on connecting market. This result is in contrast with Goolsbee and Syverson (2008) and Gayle and Wu (2011) who stated that connecting market and nonstop market should be treated separate markets. Instead, the finding here provides empirical evidence to support the theoretical conclusion of Reiss and Spiller (1989), namely, competition exists both within and across service types. Fig. 4 represents incumbents’ connecting price path surrounding Southwest’s connecting entry. There were no significant price changes before entry took place. In the quarter of entry, incumbents dropped their fares slightly by 0.5%. One quarter after entry, fares were down by 3.2% while four quarters and more after entry, fares reached 4.1% lower. The finding is partly consistent with Brueckner et al. (2013) which also demonstrates that an extra connecting presence would depress connecting prices on that route, although the estimated sizes of the effects are much smaller in this paper. From the above analysis, it is clear that incumbents decreased both nonstop and connecting fares in response to nonstop entry by Southwest, whereas they only decreased their connecting fares in response to con necting entry by Southwest. Viewing the nonstop service as a higher quality product compared to the connecting service, these results sug gest that firms have quite different fare strategies upon the entry of different quality products. Another interesting phenomenon is that incumbents exhibited preemptive price cutting in response to Southwest’s nonstop entry (Figs. 1 and 3), but did not have this type of pricing strategy when facing its connecting entry (Fig. 4). One possible reason could be that South west pre-announced its nonstop entry into a route but did not preannounce its connecting entry, leaving time for its rivals to perform pre-emptive price cutting ahead of the nonstop entry only.
Southwest’s
6. Conclusions This article studies the fare impacts of Southwest Airlines’ entry, with a focus on comparing nonstop and connecting flights. By separately investigating incumbents’ responses to each of the service types, the author obtains two important findings. First, Southwest’s nonstop entry depressed incumbents’ nonstop fares and connecting fares. Second, Southwest’s connecting entry depressed incumbents’ connecting fares, but did not depress their nonstop fares. Viewing the nonstop service as a higher quality product compared to the connecting service, these results suggest that firms have quite different fare strategies upon the entry of different quality products. This article adds to the literature in three major ways. First, it is among the few works which take the type of services into account when studying LCCs’ impacts. Second, to the best of the author’s knowledge, it is the first work to show that service types significantly influence car riers’ decisions in response to LCCs’ entry. Third, the findings indicate that airlines compete both within and across service types, which also extends previous theories on airline competition. The conclusions in this paper have policy implications for antitrust analysis. In airline antitrust practices, a disputable question is whether nonstop and connecting services are effectively competing with each other. The estimates suggest that nonstop products are effective com petitors to connecting products, but not the converse, hence shed light on this question. More generally, the results in this article provide some insight into
Fig. 4. Incumbents’ connecting price path surrounding Southwest’s connect ing entry.
corroborate previous findings in the literature, such as Goolsbee and Syverson (2008) and Tan (2016), namely, incumbents decreased their nonstop price in response to nonstop entry by Southwest Airlines. Fig. 2 shows incumbents’ nonstop price path surrounding South west’s connecting entry. According to this figure, the price kept rising over time. The coefficients corresponding to the post-entry quarters are all positive, indicating that incumbents did not cut nonstop prices at all in response to connecting entry by Southwest. In other words, the entry of a low-quality product does not depress the pricing decision of the high-quality incumbents. This finding is contrary to the theoretical prediction of Mathur and Dewani (2015), who argued that the incum bent firm should reduce prices no matter the entrant firm introduces a higher-quality or lower-quality product. It is also not consistent with 5
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Journal of Air Transport Management 84 (2020) 101771
what one might expect to find in other vertically differentiated product markets. When a new product is launched, the quality of the product should be a crucial factor determining rivals’ reactions. There are some limitations to this study. First, due to limitations of the data, the layover time of a connecting trip, which should be an important determinant of connecting quality, is unknown and thus not controlled for. Second, it excludes code-share itineraries in the sample. As code-sharing becomes popular,12 future research may want to investigate if the findings in this paper could extend to code-share flights. Third, it does not take adjacent competition from Southwest into account. Suppose Southwest’s service on one route has spillover effects on adjacent routes that involve neighboring airports in the same MSA,13 then the aggregate impact of Southwest should be greater than estimated. What’s more, it is likely that the spillover effect of a nonstop entry is different from that of a connecting entry, which may be taken as additional evidence to support the argument in this study, namely, service types matter in the analysis of LCCs’ entry. These topics are left for further research.
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Data availability The data used to support the findings of this study are available from the author upon request. Declaration of competing interest The author declares no conflicts of interest. CRediT authorship contribution statement Junqiushi Ren: Conceptualization, Methodology, Software, Formal analysis, Data curation, Writing - original draft, Writing - review & editing, Visualization, Funding acquisition. Acknowledgments This work was supported by the Fundamental Research Funds for the Central Universities (no. JBK1901042). In addition, the author would like to appreciate Professor Jason R. Blevins from the Ohio State Uni versity for his comments and assistance. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.
12 13
See Ito and Lee (2007) and Goetz and Shapiro (2012). See Morrison (2001). 6
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Journal of Air Transport Management journal homepage: http://www.elsevier.com/locate/jairtraman
Fare impacts of Southwest Airlines: A comparison of nonstop and connecting flights Junqiushi Ren * Research Institute of Economics and Management, Southwestern University of Finance and Economics, Chengdu, 611130, China
A R T I C L E I N F O
A B S T R A C T
Keywords: US airline industry LCC Southwest airlines Entry Connecting flights
This paper examines the effects of Southwest Airlines’ entry on its rivals’ pricing, with a focus on comparing nonstop and connecting flights. The results produce two important findings. First, Southwest’s nonstop entry depressed its rivals’ nonstop airfares and connecting airfares. Second, Southwest’s connecting entry depressed its rivals’ connecting airfares, but did not depress their nonstop airfares. Considering nonstop and connecting ser vices as differentiated products which differ in quality, the findings suggest that firms have quite different fare strategies upon the entry of different quality products.
1. Introduction Since the first low-cost carrier (LCC), Southwest Airlines, established in 1967, LCCs have reached a huge success in the U.S. and elsewhere in the world. Unlike traditional legacy carriers who operate on hub-andspoke structures, LCCs adopt a very different business model which in volves point-to-point structures, allowing for higher aircraft utilization. In addition, LCCs are well known for requiring employees to work multiple roles to cut personnel costs.1 Such cost-cutting strategy allows LCCs to sell tickets at a relatively low price and maintain competitive advantage. Over the past twenty years, LCCs have been growing rapidly in the US. In 2017, 49% of all domestic passengers travelled with LCCs. Southwest, the leading LCC, itself transported 27.9% of the domestic traffic, making it the largest carrier in the U.S. and the largest LCC worldwide.2 Given the fact that LCCs have been so successful, it is not surprising that they have attracted a lot of attention in the literature. Many re searchers have shown that LCCs, including Southwest Airlines, lowered airfares on the routes they entered.3
However, most of the studies either only looked at nonstop flights, or aggregated across the service types. According to Reiss and Spiller (1989) and Dunn (2008), this may lead to incorrect inference, since nonstop and connecting flights may be regarded as differentiated products in similar markets. This paper fills the gap by discussing Southwest’s effects in the context of both service types and comparing their differences. It should be noted that although Southwest is famous for its P2P routing, it does connect as well, only not to the same degree as tradi tional hub-and-spoke carriers, like Delta and American. For instance, in 2017, Southwest provided connecting service on 4801 domestic routes, and provided nonstop service on 2011 routes, while for Delta the numbers of routes were 5604 and 755 for connecting and nonstop ser vice, respectively. Passengers were open to use those connecting itin eraries as well, especially on mid-haul and long-haul routes, where connecting traffic comprised about 30% and 40% of the domestic traffic, respectively.4 The main objective of this work is to study how Southwest’s entry affects its rivals’ pricing, with a focus on comparing nonstop and
* Research Institute of Economics and Management, Southwestern University of Finance and Economics, Gezhi Building 1109, Wenjiang District, Chengdu, 611130, China. E-mail addresses: [email protected], [email protected]. 1 See Borenstein (1992) for a detailed discussion about the differences between LCCs and legacy carriers. 2 The rankings are based on passenger count. 3 Examples include Borenstein (1992), Whinston and Collins (1992), Dresner et al. (1996), Vowles (2000, 2001), Morrison (2001), Alderighi et al. (2004), Brueckner et al. (2013), and many others. 4 The numbers of routes and the percentages of traffic are identified from the DB1B data.
https://doi.org/10.1016/j.jairtraman.2020.101771 Received 30 August 2019; Received in revised form 21 January 2020; Accepted 23 January 2020 Available online 28 January 2020 0969-6997/© 2020 Elsevier Ltd. All rights reserved.
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Journal of Air Transport Management 84 (2020) 101771
connecting flights. All other (e.g. frequencies) being equal, the nonstop service is viewed as a higher quality product compared to the connecting service, and different connecting services also vary in quality using a measure of the extra flight distances.5 A set of price equations are esti mated using U.S. airline industry data from 1993 to 2017. The rest of the paper are composed as follows: Section 2 reviews related literature. Section 3 outlines the research method. Section 4 describes the data and the steps taken to construct the sample. Section 5 describes the main results. Section 6 concludes the paper.
ValuJet’s entry into Atlanta. They discovered that after ValuJet entered Atlanta, Delta lowered its fares on nonstop routes terminating in Atlanta and on connecting routes flying through Atlanta. Brueckner et al. (2013) measured the in-market, adjacent, and potential competition from LCCs, where both nonstop competitor indicators and connecting competitor indicators were included in the model. Nevertheless, the former work is more like a case study, and the latter work is based on a sample which spanned only four successive quarters and does not examine the dy namic trends of airfares. This paper differs from them by investigating the topic in more depth, using a much longer sample period, and tracking the patterns of price changes. The conclusions are also different. As a brief summary, this paper adds to the literature in three major ways. First, this paper is among the few works which take the type of services into account when studying LCCs’ impacts. Second, to the best of the author’s knowledge, this paper is the first work to show that service types significantly influence carriers’ decisions in response to LCCs’ entry. Third, the findings of this study indicate that airlines compete both within and across service types, which also extends pre vious theories on airline competition.
2. Literature review Many studies have documented the fare impacts of LCCs. Dresner et al. (1996) indicated that the presence of a LCC, especially Southwest Airlines, reduced average yields on that route and on adjacent routes. Vowles (2000) showed that the presence of LCCs is an important determinant of average airfares. Morrison (2001) found that the entry of Southwest influenced the average prices on Southwest’s actual, adja cent, and potential routes. Alderighi et al. (2004), Goolsbee and Syver son (2008), and Kwoka and Batkeyev (2019) examined LCCs’ entry threats on nonstop trips. Daraban and Fournier (2008) applied a spatial autoregressive model and confirmed LCCs’ effects on spatially-linked, adjacent routes. Tan (2016) demonstrated that incumbents’ decreased the mean, 10th percentile, and 90th percentile airfares in response to LCCs’ entry. Asahi and Murakami (2017) showed that on certain routes, incumbents reduced the average fare when Southwest entered the market, and reduced the average fare even more in several years after the entry. Bachwich and Wittman (2017) analyzed the ultra-low cost carriers and argued that their presence was associated with significant decreases in market average fares. Though these literature have made remarkable contributions, a common problem is that they either restricted the attention to nonstop flights, or aggregated across the service types. This may be regarded as not appropriate, because nonstop and connecting services may be regarded as differentiated products in similar markets. From consumers’ perspective, connecting trips are more time-consuming and less conve nient, but sometimes can be a lot cheaper. From airlines’ perspective, on the other hand, connecting flights increase the utilization of their air crafts from/to hub airports and may lead to economies of density.6 Moreover, even for Southwest who is well known for its point-to-point network, it makes use of “operating bases” or “focus cities” to connect as well, only not to the same degree as traditional hub-and-spoke car riers. Beginning in 2009, Southwest tried a program at Chicago Midway for a forceful push for passenger connections.7 Travellers, especially leisure travellers who are more price sensitive, are open to use such connecting services as well. As pointed out by Cook and Billig (2017), about 40% of Southwest passengers used the connecting services it provided network-wide, while at Chicago Midway, 55% of passengers connected to other flights. Hence, it may not be proper to neglect con necting itineraries or to simply aggregate across service types. Instead, one should incorporate both service types and at the same time discuss their differences. This may be important since Reiss and Spiller (1989) concluded that the type of services is an essential determinant of the level of competition, not just the carriers. Dunn (2008) also showed that service types are important factors influencing airlines’ decisions, add ing support to the approach taken in this paper. Windle and Dresner (1999) and Brueckner et al. (2013) are among the few papers on LCCs which attempted to discuss the differences in service types. Windle and Dresner (1999) examined Delta’s responses to
3. The econometric model Following the estimation strategy in Goolsbee and Syverson (2008) and Tan (2016), the author uses a two-way fixed effects model to identify the entry effect of Southwest. A couple of dependent variables are used, including the natural log of incumbents’ mean nonstop airfare (InNonstopPrice) and the natural log of incumbents’ mean connecting airfare (InConnectingPrice). The basic specification is as follows: Yijt ¼ α þ γij þ μit þ
4þ X
βτ Entryj;t0 þτ þ θInconvenienceijt þ εijt
(1)
τ¼ 8
where Yijt is either InNonstopPriceijt or InConnectingPriceijt for incum bent airline i on route j in quarter t. γij and μit are carrier-route and carrier-quarter fixed effects, respectively. They control for any unob served differences across carrier-route and carrier-quarter. α is the constant term. εijt is the error term. Inconvenienceijt measures the quality of the trip in terms of incon venience, and is calculated as the itinerary distance over the nonstop distance. For nonstop trip, this variable equals to 1. For connecting trip, this variable is larger than 1. As this variable increases, the quality of the connecting trip drops. The key variables of interest, Entryj;t0 þτ , are quarter dummies that specify the lag/forward surrounding Southwest’s entry into route j. Again, the entry events are classified into nonstop entry and connecting entry, according to the service that Southwest provided. For an entry event at time t0 , the author constructed thirteen dummy variables cor responding to thirteen quarters surrounding time t0 , namely, t0 þ τ, 8; …; 0; …; 4 þ . The estimates of the coefficients βτ where τ ¼ show the relative sizes of the dependent variable in the dummy periods versus its value in the reference period (the 9th to 12th quarters before entry). For example, suppose β0 ¼ 0:126. This means that, holding all else constant, the mean airfare for incumbent airlines is 11.8% lower,8 on average, in the quarter of entry (t0 ) relative to its value in the reference period (the 9th to 12th quarters before entry). The pre-entry quarter dummies capture the fare strategies of the incumbents before actual entry. They can reflect whether there is preemptive price cutting behavior or not. The post-entry quarter dummies show the dynamic patterns of airfares once entry has occurred. Most likely the airfare will adjust gradually, in which case the post-entry
5
Note that the layover time is also an important determinant of connecting flight quality. Nonetheless, the dataset adopted in this study does not provide such information. So the author only uses the detour distance to infer quality. 6 See Brueckner and Spiller (1994). 7 See Cook and Billig (2017) for a detailed discussion.
8 The percent change relative to the excluded period is calculated as exp (–0.126) 1 ¼ 0.118.
2
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Journal of Air Transport Management 84 (2020) 101771
time dummies will reflect the dynamic pattern for up until the 4th quarter after entry. Equation (1) is estimated separately for each of the following situations:
Delta in 2000 Quarter 1 is summarized into cell “JFK-SAN-Delta2000Q1-nonstop”. Within each cell, the author then computes the mean ticket price and flight distance, weighted by the number of passengers.11 4.3. Sample selection
(i) examine incumbents’ nonstop fare changes surrounding South west’s nonstop entry; (ii) examine incumbents’ nonstop fare changes surrounding South west’s connecting entry; (iii) examine incumbents’ connecting fare changes surrounding Southwest’s nonstop entry; and (iv) examine incumbents’ connecting fare changes surrounding Southwest’s connecting entry.
The sample used in this study includes data from the first quarter of 1993, through to the last quarter of 2017. That being said, this study is based on a panel dataset that covers 25 successive years. The author restricts the sample to routes where Southwest started flying between 1993 and 2017. The criteria to identify a nonstop entry is as follows: Southwest must not have operated nonstop flights on the route for at least 12 quarters preceding the quarter of entry, and must have operated nonstop flights on the route for no less than 3 successive quarters following the quarter of entry. The criteria to identify a con necting entry is defined likewise. The author further restricts carriers to the seven major airlines in the sample period, namely, American Airlines, Delta Air Lines, United Air lines, US Airways, Northwest Airlines, Trans World Airlines, and Con tinental Airlines. Ultimately, Southwest is identified to have nonstoply entered into 826 routes, and have connectingly entered into 802 routes. The final sample contains 59,147 observations (cells). Summary statistics for continuous variables are given in Table 1.
In all cases, the standard errors are clustered by carrier-route to ac count for possible correlations in the error terms. Besides, the author weights observations by the total number of passengers flying the carrier-route over the sample years, so that high-traffic carrier-route combinations have more influence on the parameter estimates and lowtraffic carrier-route combinations have less. 4. Data and sample construction 4.1. Data description The data employed in this study comes from the Airline Origin and Destination Survey (DB1B),9 which is collected by the Office of Airline Information of the US Bureau of Transportation Statistics. The data is a quarterly data that consists of a 10% random sample of all tickets sold and operated by US carriers. The author uses the itinerary-level information in DB1B data set. For each itinerary, the following information is collected: the reporting carrier, the transaction price, the number of passengers, the fare class, the airport sequence (origin and destination airports along with all transfer points), the actual flight distance, and the nonstop flight dis tance between the two endpoint airports. The following data restrictions are imposed: (i) drop itineraries that are part of international travel; (ii) drop itineraries that have more than four legs; (iii) drop itineraries with fares less than $25, due to the high probability that those may pertain to frequent-flyer programs where passengers redeemed accumulated travel points to offset the full fare of travel10; and (iv) drop code-share itineraries.
5. Empirical results The estimation results are summarized in Table 2. Recall that the estimates of the coefficients on the quarter dummies reveal incumbents’ pricing patterns around the entry event. Column (I) presents in cumbents’ nonstop price changes surrounding Southwest’s nonstop entry. Column (II) presents incumbents’ nonstop price changes sur rounding Southwest’s connecting entry. Column (III) shows incumbents’ connecting price changes surrounding Southwest’s nonstop entry. Col umn (IV) shows incumbents’ connecting price changes surrounding Southwest’s connecting entry. According to the estimates, every column except for column (II) exhibits a price drop in the quarter of entry (Entryt0 ) and the quarter after entry (Entryt0 þ1 ). The post-entry estimates are all significantly negative in these three columns, indicating that incumbents lowered prices compared to the reference period. The coefficients of Inconvenience are negative in the last two col umns. This means that, holding all else constant, as a connecting trip gets more inconvenient, its price will decrease.
4.2. Data aggregation Since the raw data is huge, for the convenience of analysis, the author aggregates the data into cells. Specifically, each cell is a “routecarrier-quarter-service type” combination, where “route” is a directional combination of the two endpoint airports, regardless of any intermedi ate transfer points; “carrier” refers to the reporting carrier of the itin erary; “quarter” refers to the year-quarter combination of the itinerary; and “service type” is either nonstop or connecting. To illustrate, a nonstop itinerary from New York John F. Kennedy International Airport to San Diego International Airport reported by
Table 1 Summary statistics for continuous variables.
9 Available at https://www.transtats.bts.gov/Tables.asp?DB_ID¼125&DB_Na me¼Airline%20Origin%20and%20Destination%20Survey%20%28DB1B% 29&DB_Short_Name¼Origin%20and%20Destination%20Survey. 10 This is common in the literature, see, for example, Tan (2016) and Gayle and Wu (2011).
Variable
Definition
Mean
St. Dev
NonstopPriceijt
Mean nonstop airfare for carrier i on route j in quarter t
212.75
70.67
ConnectingPriceijt
Mean connecting airfare for carrier i on route j in quarter t
206.21
57.69
Inconvenienceijt
The itinerary distance divided by the nonstop distance for carrier i on route j in quarter t
1.12
0.13
11
Within a nonstop cell, trips are likely to have the same flight distance; whereas within a connecting cell, trips may have different flight distances if they transfer at different airports. Hence, it is necessary to weight not only the ticket price, but also the flight distance by the number of passengers, in order to take into account the relative frequency of different transfer stations. 3
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Journal of Air Transport Management 84 (2020) 101771
Table 2 Incumbent price responses to Southwest’s different types of entry. (I)
(II)
(III)
(IV)
Dependent Variable:
lnNonstopPrice
lnNonstopPrice
lnConnectingPrice
lnConnectingPrice
Entry Event: Entryt0 8
SW’s nonstop service 0.011 (0.008)
SW’s connecting service 0.004 (0.012)
SW’s nonstop service 0.022** (0.010)
SW’s connecting service 0.002 (0.009)
Entryt0 Entryt0 Entryt0 Entryt0
Entryt0 Entryt0
0.013 (0.010)
7
0.018 (0.017)
4 3 2
0.002 (0.011)
0.044b (0.017)
0.016 (0.012)
0.018 (0.013)
0.057a (0.020)
0.019 (0.017)
0.044** (0.020)
Entryt0 þ1
0.147a (0.026)
Entryt0
0.062a (0.022)
0.126a (0.023)
0.060b (0.024) 0.081a (0.030)
0.031a (0.011)
0.027b (0.013)
0.027b (0.011) 0.046a (0.013) 0.067a (0.014)
0.055a (0.014)
0.170 (0.026) 0.168a (0.028)
0.066 (0.027)
0.076*** (0.014)
Entryt0 þ4þ
Inconvenience Constant Adjusted R2 N
0.069b (0.033)
5.974a (0.021) 0.823 13,051
6.095a (0.023) 0.847 9,418
0.013 (0.011) 0.004 (0.011) 0.005 (0.013)
0.059*** (0.014)
0.058** (0.026)
Entryt0 þ3
0.015 (0.012)
0.032** (0.013)
0.169*** (0.028)
b
0.012 (0.012)
0.068*** (0.015)
Entryt0 þ2
a
0.002 (0.010)
0.033a (0.011)
0.013 (0.017) 0.039b (0.019)
0.010 (0.011)
0.013 (0.015)
0.036b (0.017)
0.022 (0.015)
5
1
Entryt0
0.008 (0.014)
0.019c (0.012)
6
0.072a (0.015)
0.246a (0.088) 6.258a (0.103) 0.789 22,338
0.035b (0.015) 0.042a (0.015)
0.080 (0.081) 6.132a (0.092) 0.767 14,340
Notes: This table presents the results for the two-way fixed effects regression of the natural log of incumbent carrier’s mean airfare (either nonstop or connecting) in response to entry by Southwest Airlines (either nonstop or connecting). The Entry variables are the lag/forward time dummies, where Entryt0 is the quarter of entry. Observations are at the route-carrier-quarter-service type level. Standard errors, which are clustered by carrier-route, are reported in parentheses. Observations are weighted by the total number of passengers flying the carrier-route over the sample years. a Significant at the 1% level. b Significant at the 5% level. c Significant at the 10% level.
In order to visualize the incumbent responses to entry, the author plots price paths based on the coefficients of the quarter dummies in the two-way fixed effects models. For ease of interpretation, the coefficients of quarter dummies are transformed into percent changes in the dependent variable relative to the reference period. Figs. 1–4 are plotted out based on the estimates in columns (I) to (IV) in Table 2, respectively. In all figures, the entry event occurs at time period 0. Negative quarter values represent quarters before entry and positive quarter values represent quarters after entry. The red solid line is the
Fig. 2. Incumbents’ nonstop price path surrounding Southwest’s connect ing entry.
Fig. 1. Incumbents’ nonstop entry.
nonstop
price
path
surrounding
transformation of the point estimates from the model. The blue dotted lines are the associated 95% confidence interval. Fig. 1 illustrates incumbents’ nonstop price path surrounding Southwest’s nonstop entry. According to this picture, the price was stable until the quarter prior to entry (quarter 1). In this quarter, in cumbents reduced price by 3.8%. Their response reinforced to 11.8% in the quarter of entry (quarter 0) and continued to 13.6% in the quarter after entry (quarter þ1). Four quarters and more after entry, the price was down by 15.5% compared to the benchmark. These results
Southwest’s
4
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Fig. 3. Incumbents’ nonstop entry.
Journal of Air Transport Management 84 (2020) 101771
connecting
price
path
surrounding
Brueckner et al. (2013), whose results indicate that a connecting pres ence of Southwest reduces nonstop fares by 4%. Fig. 3 portrays incumbents’ connecting price path surrounding Southwest’s nonstop entry. According to this picture, there were some fluctuations in price before entry. By the quarter prior to entry, in cumbents set price to be 4.5% lower compared to the benchmark. The price gradually dropped to 6.5% lower in the quarter of entry and went to 6.9% lower in four quarters and more after entry. This suggests that Southwest’s nonstop entry induced incumbents to cut their connecting fares. In other words, changes in nonstop market have spillover effects on connecting market. This result is in contrast with Goolsbee and Syverson (2008) and Gayle and Wu (2011) who stated that connecting market and nonstop market should be treated separate markets. Instead, the finding here provides empirical evidence to support the theoretical conclusion of Reiss and Spiller (1989), namely, competition exists both within and across service types. Fig. 4 represents incumbents’ connecting price path surrounding Southwest’s connecting entry. There were no significant price changes before entry took place. In the quarter of entry, incumbents dropped their fares slightly by 0.5%. One quarter after entry, fares were down by 3.2% while four quarters and more after entry, fares reached 4.1% lower. The finding is partly consistent with Brueckner et al. (2013) which also demonstrates that an extra connecting presence would depress connecting prices on that route, although the estimated sizes of the effects are much smaller in this paper. From the above analysis, it is clear that incumbents decreased both nonstop and connecting fares in response to nonstop entry by Southwest, whereas they only decreased their connecting fares in response to con necting entry by Southwest. Viewing the nonstop service as a higher quality product compared to the connecting service, these results sug gest that firms have quite different fare strategies upon the entry of different quality products. Another interesting phenomenon is that incumbents exhibited preemptive price cutting in response to Southwest’s nonstop entry (Figs. 1 and 3), but did not have this type of pricing strategy when facing its connecting entry (Fig. 4). One possible reason could be that South west pre-announced its nonstop entry into a route but did not preannounce its connecting entry, leaving time for its rivals to perform pre-emptive price cutting ahead of the nonstop entry only.
Southwest’s
6. Conclusions This article studies the fare impacts of Southwest Airlines’ entry, with a focus on comparing nonstop and connecting flights. By separately investigating incumbents’ responses to each of the service types, the author obtains two important findings. First, Southwest’s nonstop entry depressed incumbents’ nonstop fares and connecting fares. Second, Southwest’s connecting entry depressed incumbents’ connecting fares, but did not depress their nonstop fares. Viewing the nonstop service as a higher quality product compared to the connecting service, these results suggest that firms have quite different fare strategies upon the entry of different quality products. This article adds to the literature in three major ways. First, it is among the few works which take the type of services into account when studying LCCs’ impacts. Second, to the best of the author’s knowledge, it is the first work to show that service types significantly influence car riers’ decisions in response to LCCs’ entry. Third, the findings indicate that airlines compete both within and across service types, which also extends previous theories on airline competition. The conclusions in this paper have policy implications for antitrust analysis. In airline antitrust practices, a disputable question is whether nonstop and connecting services are effectively competing with each other. The estimates suggest that nonstop products are effective com petitors to connecting products, but not the converse, hence shed light on this question. More generally, the results in this article provide some insight into
Fig. 4. Incumbents’ connecting price path surrounding Southwest’s connect ing entry.
corroborate previous findings in the literature, such as Goolsbee and Syverson (2008) and Tan (2016), namely, incumbents decreased their nonstop price in response to nonstop entry by Southwest Airlines. Fig. 2 shows incumbents’ nonstop price path surrounding South west’s connecting entry. According to this figure, the price kept rising over time. The coefficients corresponding to the post-entry quarters are all positive, indicating that incumbents did not cut nonstop prices at all in response to connecting entry by Southwest. In other words, the entry of a low-quality product does not depress the pricing decision of the high-quality incumbents. This finding is contrary to the theoretical prediction of Mathur and Dewani (2015), who argued that the incum bent firm should reduce prices no matter the entrant firm introduces a higher-quality or lower-quality product. It is also not consistent with 5
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Journal of Air Transport Management 84 (2020) 101771
what one might expect to find in other vertically differentiated product markets. When a new product is launched, the quality of the product should be a crucial factor determining rivals’ reactions. There are some limitations to this study. First, due to limitations of the data, the layover time of a connecting trip, which should be an important determinant of connecting quality, is unknown and thus not controlled for. Second, it excludes code-share itineraries in the sample. As code-sharing becomes popular,12 future research may want to investigate if the findings in this paper could extend to code-share flights. Third, it does not take adjacent competition from Southwest into account. Suppose Southwest’s service on one route has spillover effects on adjacent routes that involve neighboring airports in the same MSA,13 then the aggregate impact of Southwest should be greater than estimated. What’s more, it is likely that the spillover effect of a nonstop entry is different from that of a connecting entry, which may be taken as additional evidence to support the argument in this study, namely, service types matter in the analysis of LCCs’ entry. These topics are left for further research.
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Data availability The data used to support the findings of this study are available from the author upon request. Declaration of competing interest The author declares no conflicts of interest. CRediT authorship contribution statement Junqiushi Ren: Conceptualization, Methodology, Software, Formal analysis, Data curation, Writing - original draft, Writing - review & editing, Visualization, Funding acquisition. Acknowledgments This work was supported by the Fundamental Research Funds for the Central Universities (no. JBK1901042). In addition, the author would like to appreciate Professor Jason R. Blevins from the Ohio State Uni versity for his comments and assistance. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.
12 13
See Ito and Lee (2007) and Goetz and Shapiro (2012). See Morrison (2001). 6