Modelling future air passenger demand

Chapter 6

Modelling future air passenger demand Typically, one of the main objectives of producing air transport forecasts is to predict future air passenger demand volume. Therefore in this chapter, we present an approach for estimating air passenger origin-destination (OD) flows and total air passenger flows, including transfer passengers, between countries as well as airports. The model is based on the fundamental theory of the gravity law. The results of the model form the basis for the forecasts in Part III of this book. Here, we are looking at air passenger demand from a perspective that does not include airport capacity constraints and their effects on demand volume and structure. Airport capacity and their limits are the topics of Chapter 7, Modelling future airport capacity and capacity utilisation, and Chapter 8, Modelling future airport capacity enlargements and limits, while modelling aircraft size, that is passengers per flight, is presented in Chapter 9, Modelling future development of the average number of passengers per flight. Finally, we integrate all the models presented in Part II, so that we can present an integrated forecast in Part III and discuss the mitigation strategies for limited airport capacity.

6.1

Background

Whilst variables relating to distance, population and gross domestic product (GDP) are rather common in gravity models, we expected further insights by including an airfare variable, which has been computed on the basis of Sabre AirVision Market Intelligence (MI) data. This includes, among other items, passenger flows and airfares between airports by airline. For better discrimination between different types of origin and destination, for example tourist destinations, we have included variables, such as tourism receipts and expenditures and population density. Furthermore, we have employed a Poisson pseudo maximum likelihood (PPML) estimator to produce better and more reliable forecast results, thereby enhancing the out-of-sample results, that is forecast efficacy. We begin this chapter with a brief literature review of gravity models in transport and economics and, before we turn to model parameter estimation and a test application, we present a brief section of Airport Capacity Constraints and Strategies for Mitigation. DOI: https://doi.org/10.1016/B978-0-12-812657-8.00006-3 © 2020 Elsevier Inc. All rights reserved.

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theoretical results that underline the importance of considering a PPML estimator for gravity models. The test application comprises the typical 20 years’ forecasts, such as those of Airbus and Boeing; however, this is not the actual model application of Part III of the book. So far, the gravity model has been employed in a wide range of disciplines in regional science (e.g. Mikkonen and Luoma, 1999), transportation (e.g. Evans, 1976) and trade (e.g. Bergstrand, 1985; Linnemann, 1966; Tinbergen, 1962). One of the first gravity models employed in air transport research was developed by Harvey (1951) to analyse airline traffic patterns in the United States. An overview of selected gravity models in air transport research can be found in Grosche et al. (2007) and Tusi and Fung (2016). In particular, the scope of work of Grosche et al. (2007) has some common ground with this work. They presented two gravity models to estimate the air passenger volume of city pairs without currently existing non-stop air services. Looking at the bigger picture, the gravity model has been applied to many different research objects in air transport research. For example Tusi and Fung (2016) analysed passenger flows at Hong Kong (HKG) airport and focused their research work on a single airport, whereas Matsumoto (2004) and Shen (2004) based their gravity models more upon network analysis. Matsumoto (2004) estimated a gravity model for passenger and cargo flows between a distinct number of large conurbations, such as Tokyo, London, Paris and New York. Shen (2004) estimated a gravity model to analyse intercity airline passenger flows in a 25node US network. Bhadra and Kee (2008) employed a gravity model to analyse demand characteristics, that is fare and income elasticities of the US OD market over time. Endo (2007) developed a gravity model to analyse the impact of the bilateral aviation policy between the United States and Japan on passenger air transport. Hazledine (2009) estimated a gravity model to analyse the border effects in international air travel. The gravity models listed have been estimated by the traditional ordinary least squares (OLS) method in their log-linearised form. Table 6.1 displays

TABLE 6.1 Selected gravity models for origin-destination air passenger demand (Gelhausen et al., 2018). References

Number of variables

R2 (%)

Endo (2007)

4
9

43
69

Harvey (1987)

6

76

Hazledine (2009)

9
11

53
56

Matsumoto (2004)

7
19

39
45

Tusi and Fung (2016)

13

74

Modelling future air passenger demand Chapter | 6

135

various models in terms of their number of parameters and R2 based on the estimation data set (Gelhausen et al., 2018). If the source paper comprises various models, for example in the case of different market segments, ranges of the values are given. The number of variables and R2 vary considerably and are determined by, for example the scope of work, problem structure and data availability. However, there are two caveats: first, R2 is typically computed on the basis of the log-linearised model. Second, R2 is based upon the estimation data set, which does not really assess the out-of-sample forecast efficacy. Therefore we have chosen a different approach, based upon Carson et al. (2011) and Gelhausen et al. (2018), to test the forecast efficacy of the model on 10% of the data sample that has not been used for parameter estimation before.

6.2

Model theory

In a very general form the stochastic gravity equation can be written as (Silva and Tenreyro, 2006) yOD 5 expðα0 Þ L xi;OD βi 1 εOD

ð6:1Þ

yOD 5 expðα0 Þ L xi;OD βi ηOD

ð6:2Þ

εOD expðα0 ÞLi xi;OD βi

ð6:3Þ

i

respectively,

i

with ηOD 5 1 1

The dependent variable yOD is the flow to be modelled between origin ‘O’ and destination ‘D’, expðα0 Þ represents a constant factor and xi;OD are explanatory variables. α0 and β i are the coefficients to be estimated. Here,

xi;OD 5 0 and εOD and η represent error terms with E ε OD
  OD E ηOD
xi;OD 5 1, respectively, which are assumed to be statistically independent of the explanatory variables (Silva and Tenreyro, 2006). Thus, the gravity model is basically a constant elasticity model, such as the Cobb
Douglas production function. Therefore we can create a forecast by multiplying the base year values with the corresponding growth factors. There have been many applications of the gravity model to explain regional or economic phenomena. However, obtaining consistent estimators of the model coefficients of the gravity model has always been an issue (see Goldberger, 1968; Manning and Mullahy, 2001); nevertheless, in many

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PART | II Models for assessing mitigation strategies

cases, the OLS method has been employed to obtain coefficient estimators of a log-linearised version of (6.2): X     ln yOD 5 α0 1 β i xi;OD 1 ln ηOD

ð6:4Þ

i

However, due to Jensen’s inequality, EðlnðyÞÞ 6¼ lnðEðyÞÞ, the expected value of the logarithm of a variable is different to the logarithm of its expected value (Silva and Tenreyro, 2006). Thus, estimated model coefficients are biased if the gravity model is estimated via OLS in its loglinearised form, unless the error term has certain distributional properties that are rather unlikely to hold. Silva and Tenreyro (2006) showed that εOD 5 expðα0 ÞLi xi;OD βi υOD has to be met to obtain consistent coefficient estimates. Here, υOD is a random variable statistically independent of the explanatory variables. In this case, ηOD equals 1 1υOD  and 
thus is statistically independent of the regressors. As a result, E ln ηOD
xi;OD is a constant with a value of 0. For example, the estimated distance coefficient of a gravity model is typically too low (Siliverstovs and Schumacher, 2009). In connection with air travel, this leads to an overestimation of international long-distance travel. On the other hand, Silva and Tenreyro (2006) proposed a PPML estimator, based upon a Poisson distributed error term, to obtain unbiased coefficient estimates of the gravity model. Here, the model is estimated in its original multiplicative form. The Poisson distribution is characterised by the equality of conditional conditional variance, that is

  mean  and E yOD
xi;OD ~ V yOD
xi;OD . Therefore the conditional mean is a function of a number of explanatory variables: ! X
 E yOD
xi;OD 5 exp α0 1 β i xi;OD ð6:5Þ i

Thus the original multiplicative form of the gravity model (6.1) can be formulated as a Poisson regression model: ! X
  
β i ln xi;OD E yOD xi;OD 5 exp α0 1 ð6:6Þ i

The coefficients are estimated by the method of maximum likelihood. However, the structure of heteroscedasticity, that is the different variability between subsets of the data, implied by the Poisson distribution is rather restrictive, thus we employed the overdispersion tests developed by Cameron and Trivedi (1990) to check for its appropriateness. Here, overdispersion means the presence of greater variability of the data compared to a given statistical model, in this case the Poisson distribution. There are many more possible specifications of heteroscedasticity; however, without further

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137

information on the structure of heteroscedasticity, it seems plausible to give the same weight to all observations, as the PPML estimator does (Silva and Tenreyro, 2006). On the one hand, observations with a larger conditional mean have a larger variance (Silva and Tenreyro, 2006). On the other, larger countries often provide better data quality in the case of trade data and the like (Frankel, 1997; Frankel and Wei, 1993). Nevertheless, for the coefficients to be estimated by PPML as unbiased ones, the data does not have to be Poisson distributed at all (hence the word ‘pseudo’ in PPML). Here, all that is needed is the correct specification of the conditional mean (Gourieroux et al., 1984), although the more the data resembles a Poisson distribution, the more efficient the coefficient estimates are. Regarding the data for model parameter estimation and testing, we have chosen the year 2014 as the reference year. The demand data, that is OD flow per country pair, the number of airports per country and average airfares, have been retrieved from Sabre AirVision Market Intelligence (MI) (2016), whilst socio-economic data, such as GDP, population and tourism expenditures/receipts, have been taken from the World Development Indicators (WDI) of The World Bank (2014). Total migrant stock by origin and destination has been retrieved from the United Nations (UN) (2015b) and is a measure of dependencies between two countries due to international migration. Here, international migrants are defined as people who live in a different country to that where they were born. The full data set comprises 14,642 country pairs with corresponding OD flows, of which 13,178 data sets were used for model estimation and 1464 (10%) were employed for model testing. Most variables (see Table 6.2) are more or less self-explanatory; however, some variables may need further explanation. ‘Distance’ and ‘total airfare’ both represent average values between two countries of flow origin and destination. Raw data, on an airport and airline level, is retrieved from Sabre MI and is weighted by OD demand size of corresponding airport pairs to obtain ‘average’ values between two countries. Whilst the concept of average distances and, especially, average airfares between two countries may seem to be rather inaccurate, the approach works quite well, as we can see in the estimation results section. ‘Country ties’ is a dummy variable that takes a value of 1, if there is a profound relationship between two countries, for example because of former colonial or cultural ties, or being a member of a common political community, such as the Commonwealth or French overseas territories. Data has been retrieved by our own analyses of various sources. The dummy variables ‘domestic’ and ‘continental’ take values of 1 in the case of domestic and continental flights, respectively, and otherwise 0. ‘Passenger-km per rail-km (domestic)’ and ‘population density (domestic)’ take a value of greater than 0 only for domestic passenger
OD flows and 0 otherwise. These variables stand for the ‘need’ for domestic flights and their actual substitution potential by other modes of travel, for example train. The

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PART | II Models for assessing mitigation strategies

TABLE 6.2 Data employed for model estimation, model testing and example forecast 2035. Variable name

Data source

Data description

Category

Continental

Sabre MI

Value of 1, if it is a flight within one of the seven world regions (Africa, Asia, Europe, Middle East, North America, South America, Southwest Pacific), 0 otherwise

Fixed

Country ties

Own analysis

Value of 1, if there are significant ties between countries, for example the Commonwealth or former colonies

Semifixed

Distance

Sabre MI

Weighted mean flight distance in kilometres between countries. Weighted mean is based on airport pairs with OD demand as weights

Fixed

Domestic

Sabre MI

Value of 1, if it is a domestic flight, 0 otherwise

Fixed

GDP per capita (destination)

WDI/ OECD

GDP per capita in USD of the destination country

Variable

GDP per capita (origin)

WDI/ OECD

GDP per capita in USD of the origin country

Variable

Migration

UN

Total migrant stock by origin and destination

Semifixed

Number of airports (destination)

Sabre MI

Number of airports of the destination country

Semifixed

Number of airports (origin)

Sabre MI

Number of airports of the origin country

Semifixed

Passengers-km per rail-km (domestic)

WDI

Value of million passenger-km per total rail-km for domestic passenger flows, 0 otherwise

Semifixed

Population (destination)

WDI/ UN

Number of people of the destination country

Variable

Population (origin)

WDI/ UN

Number of people of the origin country

Variable

Population density (domestic)

WDI

Value of population density of a country for domestic passenger flows, 0 otherwise

Semifixed (Continued )

Modelling future air passenger demand Chapter | 6

139

TABLE 6.2 (Continued) Variable name

Data source

Data description

Category

Total airfare

Sabre MI

Weighted mean total airfare in USD between countries. Weighted mean is based on average total airfares between airports with OD demand as weights

Variable

Tourism expenditures (origin)

WDI

Tourism expenditures in USD of the origin country

Semifixed

Tourism receipts (destination)

WDI

Tourism receipts in USD of the destination country

Semifixed

MI, Market Intelligence; OD, origin-destination; OECD, Organisation for Economic Co-operation and Development; UN, United Nations; USD, US dollar; WDI, World Development Indicators.

United States, Canada and Australia, in particular, are examples of countries with a high propensity for domestic flights. Furthermore, the input variables have been subdivided into three categories: G

G

G

Fixed: this category comprises input variables, which are fixed over time; for example distance between countries, or whether a flight is a domestic or continental flight. These characteristics do not change in the future. Variable: this category comprises input variables, which are likely to change over time, such as GDP and airfares. These variables are especially important for forecast purposes. Semi-fixed: This category comprises input variables, which can basically change over time, but do so only very slowly or have a high likelihood of no significant change over time, that is the degree of change makes no significant contribution to the forecast. This category is more or less the middle ground between the first two, however, much closer to the first than the second category. Examples include ‘migration’, ‘passenger-km per rail-km’ and ‘country ties’. Nevertheless, these variables can be beneficial for specialised scenario analyses of issues, such as structural changes, like promoting high-speed trains in some countries. Furthermore, fixed and semi-fixed variables serve the purpose of differentiating between ‘types’ of countries and airport pairs, respectively.

For an example forecast of passenger flows for the year 2035, economic data, that means the GDP forecast, was retrieved from the OECD (2017) and the population data forecast from the United Nations (UN) (2015a). The Airbus Global Market Forecast (2016) and the Boeing Current Market

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PART | II Models for assessing mitigation strategies

Outlook (2016) have been taken as reference forecasts for comparison purposes. Table 6.2 summarises the data that has been used to estimate and test the models and to produce the example forecast for 2035. With the exception of tourism expenditures and receipts, we focused on input variables of the second category. As we will see later in this chapter, the impact of varying tourism expenditures and receipts on the forecast results is rather small, and reliable forecasts for this type of data are hard to obtain. Nevertheless, this kind of data is important for identifying countries where tourism plays a major role, both inbound and outbound. Fig. 6.1 shows the cumulative distribution of global country
country OD passenger flows for the year 2014, based upon our own computations from Sabre AirVision Market Intelligence (MI) (2014). Global OD demand at the country level is highly concentrated; the top ten OD flows, which exclusively consist of domestic travel, account for more than 50% of global OD demand. The largest flow, US domestic, accounts for almost 18% of the global OD demand. As a result, the Gini coefficient also has a high value of 0.9715. For the top ten flows, Fig. 6.1 displays whether they belong to the estimation (E) or test (T) data set. As mentioned, we have taken a 10% sample from the full data set for the purposes of model testing. This comprised every tenth data record of a sample that is ranked by OD passenger volume (ODP). Therefore the largest OD flow in the test data set is Canada domestic, which is much smaller than US domestic.

100% Gini coefficient: 0.9715

Share of global OD passenger volume 2014

90% 80% 70% 60% 50% 40% 30%

Mexico domestic (E) Canada domestic (T) Turkey domestic (E) Australia domestic (E) India domestic (E) Indonesia domestic (E) Brazil domestic (E) Japan domestic (E ) China domestic (E)

20% US domestic (E)

10% 0% 0%

10%

20%

30% 40% 50% 60% 70% Share of OD passenger flows worldwide

80%

90%

100%

FIGURE 6.1 Lorenz curve and Gini coefficient of global country
country OD demand [Sabre AirVision Market Intelligence (MI), 2014].

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Modelling future air passenger demand Chapter | 6

TABLE 6.3 Key statistics of estimation and test data set [Sabre AirVision Market Intelligence (MI), 2014]. Estimation data

Test data

Ratio

Mean

186,662

79,383

0.43

Standard deviation

5404,174

865,304

0.16

Minimum

0.68

El Salvador
Dem. Rep. Congo

0.92

Afghanistan
Jamaica

1.35

Maximum

461,189,820

US domestic

30,270,504

Canada domestic

0.07

Hence, we have compiled a table of key statistics of the estimation and test data sets, as shown in Table 6.3. Because of the high concentration of global ODP on a rather small number of flows, the mean, standard deviation, minimum and maximum values are much lower in the test data set as compared to the estimation data set. This is almost inevitable and important to know when we later interpret the results of model estimation and testing.

6.3

Model estimation and testing

The coefficient estimates of the gravity equation used here refer to the functional form:     ð6:7Þ E yOD jxi;OD 5 expðα0 Þ L exp αi zi;OD L xj;OD βj L xk;OD β k zk;OD i

j

k

where yOD is the annual passenger flow between origin ‘O’ and destination ‘D’. The first multiplicand is the model constant (variable 1 in Table 6.4), the second refers to the dummy variables (zi;OD ) ‘domestic’, ‘continental’ and ‘country ties’ (variables 2
4), that is dummies which can take only the values 0 and 1. The third relates to continuous variables xj;OD , such as GDP per capita, population and total airfare (variables 5
15). Finally, the fourth multiplicand applies to continuous variables xk;OD . However, they take values greater than 0 only in particular cases and, thus, are combined with a dummy variable zk;OD . This applies to the two variables ‘passenger-km per rail-km (domestic)’ and ‘population density (domestic)’ (variables 16
17). Coefficients to estimate are α0 ; αi ; β j and β k with corresponding indices’ ranges. Coefficients are estimated by log-linearisation of the gravity equation and applying OLS in the OLS approach as well as applying maximum

TABLE 6.4 Estimation results of the ordinary least squares (OLS) and Poisson pseudo maximum likelihood (PPML) approach. OLS

PPML

No.

Variable

Coefficient

Standard error

p-value

Coefficient

Standard error

p-value

1

Constant

214.44461

0.37479

0.00000

28.00390

0.00268

0.00000

2

Domestic

2.48589

0.17201

0.00000

1.02496

0.00193

0.00000

3

Continental

0.00000




0.00000

0.09919

0.00022

0.00000

4

Country ties

3.01515

0.08860

0.00000

2.29920

0.00024

0.00000

5

Distance

20.62874

0.03126

0.00000

20.02307

0.00017

0.00000

6

Total airfare

21.18108

0.03928

0.00000

21.11258

0.00022

0.00000

7

GDP per capita (origin)

0.36591

0.02713

0.00000

0.44865

0.00017

0.00000

8

GDP per capita (destination)

0.44137

0.01792

0.00000

0.22858

0.00011

0.00000

9

Population (origin)

0.32521

0.02239

0.00000

0.35845

0.00015

0.00000

10

Population (destination)

0.52188

0.01327

0.00000

0.26970

0.00010

0.00000

11

Tourism expenditures (origin)

0.34429

0.02254

0.00000

0.08142

0.00013

0.00000

12

Tourism receipts (destination)

0.23082

0.01257

0.00000

0.24743

0.00009

0.00000

13

Number of airports (origin)

0.23094

0.01349

0.00000

0.11970

0.00009

0.00000

14

Number of airports (destination)

0.16442

0.01386

0.00000

0.13854

0.00009

0.00000

15

Migration

0.10384

0.00494

0.00000

0.04065

0.00002

0.00000

16

Passengers-km per rail-km (domestic)

20.54470

0.12864

0.00000

20.81636

0.00066

0.00000

17

Population density (domestic)

0.00000




0.00000

20.05032

0.00046

0.00000

2

R (log-linear model): 77.98%

2

McFadden pseudo-R : 99.24% Overdispersion test g 5 μ(i): 1.581 Overdispersion test g 5 μ(i)2: 0.841

The sum of

(7
10)

1.65437

1.30537

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PART | II Models for assessing mitigation strategies

likelihood estimation to the original multiplicative gravity equation in the PPML model. Table 6.4 displays the estimated model coefficients for the OLS as well as the PPML approach. All coefficient estimates included are highly significant (p-value ,0.001) and of the expected sign. The ‘continental’ and ‘population density (domestic)’ variables of the OLS model are not significant at the 10% significance level and of the wrong sign, respectively. However, while all coefficient estimates included in the final model setup are highly significant, their standard errors are much lower in the PPML model, by a factor of between 90 (‘domestic’) and almost 370 (‘country ties’), the average factor being around 175. The R2 of the OLS approach is 77.98%, based upon the log-linearised version of the gravity model as typically reported in the literature. Compared to the models of Table 6.1, this is a rather satisfactory value of the R2. McFadden’s pseudo-R2 of the PPML approach is 99.24%. However, McFadden’s pseudo-R2 is not the same as R2 and is defined as (Hensher et al., 2005) pseudo-R2 5 1 2

LL ðestimated modelÞ LL ðbase modelÞ

ð6:8Þ

LL is the value of the log-likelihood function. The reason for using two different statistics for evaluating model fit is that one model is estimated by using OLS, while the other model is estimated using a maximum likelihood method, PPML. However, Domencich and McFadden (1975) have established an approximate relationship between McFadden’s pseudo-R2 and R2 of OLS: 30% pseudo-R2 equals around 65% R2, 40% pseudo-R2 is around 78% R2, 50% pseudo-R2 is about 90% R2 and 60% pseudo-R2 corresponds to more than 95% R2. To test for overdispersion, we employed the regression-based tests developed by Cameron and Trivedi (1990). Here, the null hypothesis   ð6:9Þ H 0 :Var yi 5 μi ðmean-variance equalityÞ is tested against the alternative hypothesis     ð6:10Þ H 1 :Var yi 5 μi 1 αg μi ðoverdispersionÞ   We have specified g μi to be equal to μi and μ2i , to test for different forms of overdispersion. The test statistics report values of 1.581 and 0.841, respectively, thus failing to reject the null hypothesis of no overdispersion. The critical value from the chi-squared table for one degree of freedom is 3.84 at the 5% significance level (Econometric Software, 2007). This is in line with the empirical simulations of King (1988) that the coefficient estimates of the Poisson regression are consistent and somewhat efficient, especially in large data samples. Furthermore, Table 6.4 reports the sum of coefficients of GDP per capita and population (both for origin and

*1012

Modelling future air passenger demand Chapter | 6

145

3,000,000 2,597,193 2,500,000

2,000,000

1,500,000

1,000,000

500,000 238,165 6848 0 In-sample residual sum of squares OLS

145

Out-of-sample residual sum of squares PPML

FIGURE 6.2 Residual sum of squares of the OLS and PPML approaches. OLS, ordinary least squares; PPML, Poisson pseudo maximum likelihood.

destination), which serves as an indicator of how GDP-responsive the model is. Here the OLS model is slightly more GDP-responsive than the PPML approach (1.65 vs 1.31). Before discussing the estimated elasticities of both models, we take a closer look at forecast efficacy, evaluated by means of the test data set. Fig. 6.2 displays the in-sample and out-of-sample residual sum of squares (RSS) of the OLS and PPML approaches. The values are very high, due to the large sample sizes, (especially the estimation data set) and the fact that both approaches are evaluated by means of the multiplicative form of the gravity model. For comparison, in its log-linearised form, the OLS model produces, for the RSS, a value of 32,221.22 for the estimation data set. In contrast, in both cases, the estimation and test data sets, the PPML model produces a significantly lower RSS and, thus, performs much better insample and out-of-sample than the OLS model. Figs 6.3 and 6.4 show the in-sample and out-of-sample mean absolute forecast error and the standard deviation of the absolute forecast error for both approaches; the interpretation of the results is basically the same as in the case of Fig. 6.2. The PPML model produces much better results than the OLS approach. Finally, Fig. 6.5 displays the corresponding ratios compiled from Figs 6.2 to 6.4. The PPML model performs better than the OLS approach in any case, especially out-of-sample. Whilst the RSS of the PPML model is lower by a factor of about eleven (1/0.09) in-sample, it increases to a value of 50 (1/ 0.02) out-of-sample. The mean absolute forecast error of the PPML model is

146 *103

PART | II Models for assessing mitigation strategies 300

285

250

200

150

144

138

100

50

39

0 In-sample mean absolute forecast error OLS

Out-of-sample mean absolute forecast error PPML

*103

FIGURE 6.3 Mean absolute forecast error. OLS, ordinary least squares; PPML, Poisson pseudo maximum likelihood.

16,000 14,000

14,036

12,000 10,000 8000 6000 4249 4000 2158 2000 313 0 In-sample standard deviation of absolute Out-of-sample standard deviation of absolute forecast error forecast error OLS PPML

FIGURE 6.4 Standard deviation of the forecast error. OLS, ordinary least squares; PPML, Poisson pseudo maximum likelihood.

lower by a factor of two (1/0.48) in-sample and almost four (1/0.27) out-ofsample. Finally, the standard deviation of the absolute forecast error of the PPML model is more than three times (1/0.30) lower in-sample and about seven times (1/0.14) lower out-of-sample. As a result, we can conclude that the PPML approach has a much better out-of-sample forecast efficacy.

Modelling future air passenger demand Chapter | 6

147

0.6

0.5

0.48

0.4

0.30

0.3

0.27

0.2 0.14

0.1

0.09

0.02

0.0 In-sample residual sum of squares (PPML/OLS)

In-sample Out-of-sample Out-of-sample In-sample mean Out-of-sample standard standard residual sum of absolute forecast mean absolute deviation of deviation of squares error (PPML/OLS) forecast error (PPML/OLS) absolute forecast absolute forecast (PPML/OLS) error (PPML/OLS) error (PPML/OLS)

FIGURE 6.5 Ratio of forecast efficacy evaluation statistics (PPML/OLS). OLS, ordinary least squares; PPML, Poisson pseudo maximum likelihood.

However, compared to various other models (Table 6.1), even the OLS model performs rather well in terms of R2, but, because of log-linearisation, R2 of gravity models should be taken with a pinch of salt. The out-of-sample forecast efficacy of the OLS approach is typically lower than the in-sample statistics of the log-linearised version might suggest. Fig. 6.6 visualises the model elasticities of the OLS and PPML approaches. Distance, in particular, plays a bigger role in the OLS approach than in the PPML model. On the other hand, ‘domestic’ factors are more important in the PPML approach. As a result, the OLS model is much more distance-responsive. Tourism expenditures, and the number of airports and migration are more important in the OLS model than in the PPML approach. Tourism receipts are more or less equally important in both models. However, in the example forecast presented in this chapter we will focus on GDP per capita, population and airfare. The remaining variables tend to be more stable over time and mainly serve to discriminate between different types of origins and destinations, for example leisure versus business destinations and large and thinly populated countries with a less developed railway network versus small and densely populated countries with a highly developed railway network. Fig. 6.7 compares the values of the constants as well as domestic, continental and country ties dummy variables of the OLS and PPML approaches. The absolute values of these variables (with the exception of the continental variable, which is not significant in the OLS model) are significantly greater

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PART | II Models for assessing mitigation strategies

0.8 0.6 0.4 0.2 0.0 –0.2 –0.4 –0.6 –0.8 –1.0 –1.2 –1.4 OLS

PPML

FIGURE 6.6 Comparison of the estimated model elasticities of the OLS and PPML approaches. OLS, ordinary least squares; PPML, Poisson pseudo maximum likelihood. 4 2 0 Constant

Domestic

Continental

Country ties

–2 –4 –6 –8 –10 –12 –14 –16 OLS

PPML

FIGURE 6.7 Comparison of the estimated constants, domestic, continental and country ties dummy variables of the OLS and PPML approaches. OLS, ordinary least squares; PPML, Poisson pseudo maximum likelihood.

in the OLS model when compared to the PPML approach. We interpret these findings as follows: the OLS model penalises the increasing distance much more than the PPML approach. This is partly offset by the large absolute value of the constant and a high value of the ‘domestic’ and ‘country ties’

Modelling future air passenger demand Chapter | 6

149

dummy variables to account for domestic traffic and special relationships between countries, especially in the United States and China. An advantage of the gravity model is the constant elasticity property, which means that growth factors can be employed to produce a forecast. The base year value multiplied by the growth factor equals the forecast value. For example, a GDP growth rate of 2% per year (CAGR) over a 20-year time horizon and a GDP elasticity of 1.5 equals a growth factor of 1.0320 5 1.81, thus, the forecast value is 1.81 times the base value. The advantage of applying growth factors is that potential erroneous estimates of base year flows have no effect on forecast values. Next we need to compute total passenger volume (TP) growth rates, including transfer passengers, from ODP growth rates. Fig. 6.8 illustrates OD and total passenger volume growth rates for the period 2003
16. According to Sabre MI, ODP increased between 2003 and 2016 on average by 6.1% per year (2011
16: 9.6%) and TP, including transfer passengers, grew on average by 5.4% per year (2011
16: 9.1%). However, whilst being more volatile in recent years, the difference between these two growth rates is more or less stable over time, as Fig. 6.8 shows. Furthermore, as discussed in Chapter 4, Constrained and under-utilised airports, of Part I of this book, the concentration of flights on airports worldwide has more or less stagnated over the period 2000
16. Thus the long-term difference in average annual growth rates of ODP and TP has been about 0.5%
0.7% points on a global scale.

Annual growth rate of OD and total passenger volume

25%

20%

15%

10%

5%

0% 2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

2016

–5%

–10%

Annual growth rate of OD passenger volume (in %), AGROD Annual growth rate total passenger volume (in %), AGRTP AGRTP - AGROD

FIGURE 6.8 Comparison of annual growth rates of global OD passenger and total passenger volume (including transfer passengers) for the period 2003
16 [Sabre AirVision Market Intelligence (MI), 2016].

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PART | II Models for assessing mitigation strategies

Modelling airport choice based upon individual passenger decisions (e.g. Gelhausen, 2011; Gelhausen et al., 2008 for German case studies) is a rather complex and data-intensive endeavour, especially if access mode, flight route, airline or destination choice are also included. Therefore the majority of models and case studies are limited to a small number of airports of a particular region, for example the San Francisco Bay area, because of good data availability (see, e.g. Harvey, 1987; Pels et al., 2001, 2003; Basar and Bhat, 2004; Hess and Polak, 2005, 2006). Expanding this approach to a global perspective with more than 4000 airports seems to be a more or less insurmountable task on grounds of data availability alone. Therefore we have chosen a more parsimonious and less sophisticated model for transforming growth rates of ODP into growth rates of TP. Based upon Sabre MI data of almost 4000 airports worldwide in 2015, we linked TP to ODP and ODP share (ODPS) in a nonlinear way. Therefore the equation, which we call a variable gravity model because of the variable exponent of ODP, can be written as TP 5 1:01 ODP1:0420:13ODPS

ð6:11Þ

where ‘TP’ is the total passenger volume, ‘ODP’ is the OD passenger volume and ‘ODPS’ is OD passenger volume share. The ‘ODP’ is defined as the number of passengers flying from airport A to B on non-stop and stopover routes, whereby airport A is the one of the trip origin and airport B is the one of the trip destination. The ‘TP’ is, in contrast, the number of passengers on board all direct flights between these two airports. The ‘ODPS’ is the ratio of ODP to TP between these two airports. The ODP elasticity of TP is defined as @TP ODP 3 5 1:04 2 0:13 ODPS @ODP TP

ð6:12Þ

As a result, the rather simple functional relationship is not a drawback, as the estimation results in Table 6.5 underline. The model has been estimated by PPML. The ODP elasticity is not constant but depends on the ODPS, hence, we have a gravity model with a variable exponent. The higher the ODPS, the lower the TP growth rate. The coefficients are all highly significant (p-value ,0.001) and model fit is very good (McFadden pseudoR2 5 99.96%). However, the values of the overdispersion tests are not as good as in the case of the more complex OD demand model, but still satisfactory. Fig. 6.9 illustrates the model results graphically and shows how the ODP and TP are interrelated. If the share of ODP is below 32.1%, then TP will grow faster than ODP and vice versa. The ODP and TP models can be employed on different spatial levels. These include the following: G G G G

Global Regional Country Airport

Modelling future air passenger demand Chapter | 6

151

TABLE 6.5 Estimation results of the total passenger forecast model. No.

Variable

Coefficient

Standard error

p-value

1

Constant

1.01238

0.00116

0.00000

2

OD passenger volume

1.04142

0.00013

0.00000

3

OD passenger volume share

20.13310

0.00006

0.00000

McFadden pseudo-R2

99.96%

Overdispersion test g 5 μ(i)

5.065

Overdispersion test g 5 μ(i)

8.571

2

1.05

1.00

0.95

0.90

0.85

96%

91%

86%

81%

76%

71%

66%

61%

56%

51%

46%

41%

36%

31%

26%

21%

16%

11%

6%

0.80 1%

Total passenger volume growth/OD passenger volume growth

OD, origin-destination.

OD passenger volume/Total passenger volume

FIGURE 6.9 OD passenger volume elasticity of total passenger volume as a function of OD passenger volume share. OD, origin-destination.

At the regional and airport level the main limiting factor for applying the ODP flow model is the availability of forecast data of the input factors, such as GDP and population. Therefore typically, this model can be applied on a country level (or on a sub-country level for large countries, such as the United States or Russia), and the TP model on airport level, with the ODPS being the differentiating factor between individual airports. Thus our basic setup for Part III of this book is, first, to run the ODP model on the country level and then the TP model on the airport level, which we have found to work very well. Forecast ODP growth rates for each country pair are the

152

PART | II Models for assessing mitigation strategies Population (destination) 0.27% GDP per capita (origin) 0.45%

GDP per capita (destination) 0.23%

Total airfare –1.11%

Population (origin) 0.36%

OD passenger demand

Tourism expenditures (origin) 0.08%

Population density (domestic) –0.05%

Tourism receipts (destination) 0.25%

Total passenger demand FIGURE 6.10 Variable input factor elasticities of the total passenger demand model.

basis for the forecast TP growth rates for each airport pair, which are applied to the corresponding passenger volumes of the year 2016 to obtain forecast TP for each airport pair for the years 2030 and 2040. However, in the next section, both models are run on the global level, as we are primarily only interested in global forecast values. Here, we found no significant difference between running the models on a lower level and aggregating the results up to the global level and directly running the models on the global level. To prepare for the next section, Fig. 6.10 illustrates the impact of the input factors on ODP, which underlie the forecasts. For example, if airfares rise by 1%, ODP declines by 1.11%. On the other hand, if GDP per capita increases in the origin country by 1%, then ODP demand rises by 0.45%. Total passenger demand growth depends on the ODPS. If ODPS is less than 32.1%, then TP growth is marginally higher than OD demand growth; in the case that ODPS is higher than 32.1%, TP growth is marginally lower than OD demand growth. After modelling OD demand volume and TP demand volume (on already existing flight connections), we turn to the topic of new direct flight services between airport pairs where currently no non-stop flight exists. Here, we looked at non-stop connections that are viable in the long run given a particular flight frequency between two airports. Of course, many direct flight services open and close each year, but here we have taken a long-term view. Furthermore, we have already developed a similar model to assess the

Modelling future air passenger demand Chapter | 6

153

potential for intercontinental low-cost flights (Wilken et al., 2016) and the model presented in this book is based upon this approach. However, we have improved the model in several respects. First, we have enlarged the model’s scope. Therefore it comprises flights of all distances worldwide and, thus, is not only limited to long-haul travel from Europe. Second, we have employed a PPML estimator for model estimation. The purpose of this model is to forecast the number of air passengers flying directly on a link between two airports, assuming the existence of direct services in future. The forecast is based upon the following explanatory variables of the model: G G

G

Annual flight volume between two airports to model flight frequency. OD passenger volume between two airports, which includes both passengers flying non-stop and those passengers taking a stopover flight. Flight distance in kilometres between two airports.

Certainly, for our purposes, the OD passenger volume variable is the main driver of new direct connections between airports in the future. However, service frequency is also important to make a non-stop service more attractive from the passengers’ perspective as compared to a stopover flight. For example, passengers might be more likely to take a stopover flight, which is served twice daily compared to a non-stop flight twice a week. In turn, given a particular OD demand, flight frequency depends on aircraft size, that is passengers per aircraft, if load factors are economically viable. Therefore based on our forecast of OD passenger volume, we want to find out which stopover connections might be viable for non-stop flights in the future and what share of OD passenger volume choose the direct service. Therefore we have identified different types of routes between airports: G

G

G

G

‘Hub routes’ (Hub), defined as having a share of less than 50% OD demand between two airports compared to all passengers. In this case the number of transfer passengers at that airport pair exceeds the number of OD travellers taking a non-stop flight between those two airports. ‘Point-to-point (P2P) routes’, defined as having a share of between 95% and 105% OD demand between two airports compared to all passengers. These are routes where the majority of OD passengers are typically travelling non-stop. ‘Low-frequency (LF) routes’, defined as having a share of more than 150% OD demand between two airports compared to all passengers. These are routes where the majority of OD passengers takes a stopover flight. Some routes do not belong to any of the aforementioned categories, as they have an OD passenger volume share of 50% to less than 95% and more than 105% up to 150%, respectively.

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PART | II Models for assessing mitigation strategies

We have tested various route definitions empirically and have found that these categories produce good results in terms of model fit and parameter significance. However, ultimately, the definitions remain more or less arbitrary. The model has been estimated by PPML. The dependent variable is the ‘TP’ on direct flights between two airports. Table 6.6 presents the estimation results. ‘Hub’, ‘P2P’ and ‘LF’ are dummy variables that take a value of 1, if the route belongs to the category, and 0 otherwise. All coefficients show the expected sign and are highly significant (p-value ,0.01). McFadden’s pseudo-R2 of the model is 98.3%. The values of the overdispersion tests are very good; hence, the PPML estimator is fine for model estimation. All model elasticities are positive, although less than 1. Passenger volume flying non-stop is rather inelastic with regard to supply and demand characteristics, such as an increase of annual flights, OD demand and flight distance. Increasing OD demand between two airports by 1% increases the number of non-stop air passengers of that OD demand between those two airports by only 0.628%. This is because stopover flights on alternative routes are typically cheaper than non-stop flights. Increasing annual flight volume by 1% only raises the number of non-stop travellers on a route by 0.385%. Flight distance has a rather small effect on passenger volume on a route, thus, the elasticity is 0.132%. However, there are large differences in passengers on a route if we look at route categories. Ceteris paribus, a hub route has almost twice as many passengers as a P2P route (exp(0.6442)/exp (20.0562) 5 2.01). An LF route has only about 56% compared to a P2P

TABLE 6.6 Estimation results of the new direct connections model. No.

Variable

Coefficient

Standard error

p-value

1

Constant

0.86632

0.00029

0.00000

2

Hub

0.64420

0.00007

0.00000

3

P2P

20.05615

0.00005

0.00000

4

LF

20.64248

0.00020

0.00000

5

OD passenger volume

0.62771

0.00004

0.00000

6

Annual flight volume

0.38505

0.00005

0.00000

7

Flight distance

0.13150

0.00003

0.00000

2

98.31%

McFadden pseudo-R

Overdispersion test g 5 μ(i)

1.430

Overdispersion test g 5 μ(i)

0.000

2

LF, low frequency; OD, origin-destination; P2P, point-to-point.

Modelling future air passenger demand Chapter | 6

155

OD passenger demand volume forecast

Existing routes

Non-stop flights model

New routes

Total passenger demand volume and flight network structure forecast

FIGURE 6.11 The air passenger demand model.

route. Altogether, these results show the importance of airline network strategies and, here especially, of consolidating traffic at hubs in long-haul air travel (Alderighi et al., 2005; Hooper, 2005). Therefore the route categories and dummy variables are important to account for airline network strategy effects in estimating the number of passengers on a route between two airports. Finally, Fig. 6.11 summarises the air passenger demand model graphically. First, for each airport pair, OD and TP are forecast. Then, each airport pair, including existing as well as potentially new direct services, is checked in view of viable non-stop connections.

6.4

Model application: comparing different forecasts

For this brief case study, we have chosen GDP and population forecasts, which are available to the public. However, for the more elaborated forecasts of Part III of this book, we needed more detailed data. Therefore in this chapter, forecast data has been retrieved from OECD (2017) for global real GDP growth from 2016 until 2035. The medium variant of the UN World Population Prospects [United Nations (UN), 2015a] has been chosen as a forecast of global population growth for the period from 2016 to 2035. Thus, we have taken a value of 3.2% per annum (p.a.) for global real GDP growth and 0.092% p.a. for global population growth. In the matter of real airfares, we distinguish between three scenarios: G G G

Constant real airfares 1% decline p.a. of real airfares 2% decline p.a. of real airfares

A long-term decline of real airfares seems plausible, due to the growth of the low-cost carrier segment and legacy carriers pushing their own low-cost subsidiaries. Furthermore, there is market potential in the long-haul segment

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PART | II Models for assessing mitigation strategies

350

14

300

12

250

10

200

8

150

6

100

4

50

2

0

Average yield (US cent/km)

OD average base fare (USD)

(e.g. Wilken et al., 2016). Even nominally stagnant airfares mean declining real airfares, due to inflation. Fig. 6.12 shows the development of the OD average base fare, that is the average fare excluding taxes and other charges, in USD and the average yield in US cents per km for the period 2002
16, as total airfares, including taxes and other charges, are only available from 2014 to 2016 [Sabre AirVision Market Intelligence (MI), 2016]. Between 2002 and 2016 the nominal OD average base fare and average yield declined by 0.7% per year [compound annual growth rate (CAGR)]. The highest nominal values for the OD average base fare and average yield were reached in 2012. For this period, CAGR was 3.6% and 3.7%, respectively. Thereafter, from 2012 to 2016, as well as the years 2009 and 2010, OD average base fare and average yield declined rapidly by 10.6% and 10.8% per year on average, respectively, accompanied by a large decline in jet fuel prices and increasing lowcost competition. The period with the largest CAGR is 2002
08. Here, we find values of 4.7% and 3.5% for the OD average base fare and the average yield, respectively. Whilst airfares are volatile over time, the long-term assumption of stagnating or slightly declining nominal airfares seems to be realistic.

0 2002

2004

2006

2008

OD average base fare (USD)

2010

2012

2014

2016

Average yield (US cent/km)

FIGURE 6.12 Development of OD average base fare in USD and yield in US cent worldwide for the period 2002
16 [Sabre AirVision Market Intelligence (MI), 2016]. OD, origindestination.

Modelling future air passenger demand Chapter | 6

50% 40%

3.0 30% 2.5

20% 10%

2.0

0% 1.5

–10% –20%

1.0

Year-to-year price change

US kerosene-type jet fuel retail sales by refiners in USD/gallon

3.5

157

–30% 0.5 –40% 0.0

–50% 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 US kerosene-type jet fuel retail sales by refiners in USD/gallon

Year-to-year price change

FIGURE 6.13 Development of US kerosene-type jet fuel retail sales by refiners USD/gallon (US Energy Information Administration, 2017).

Fig. 6.13 displays the development of US kerosene-type jet fuel retail sales by refiners in USD/gallon and the year-to-year price changes in percentages. There was a large decline in 2009 and, since 2012, jet fuel prices have continued to decline. Furthermore, jet fuel prices and airfares are highly correlated. The value of the correlation coefficient for the data sample is 0.9; hence, jet fuel prices and airfares move more or less in the same direction. However, whilst the OD average base fare and average yield declined by 0.7% per year during the period 2002
16, jet fuel prices increased by 4.4% per year on average, despite large fluctuations. On the other hand, during the 2012
16 period, jet fuel prices fell on average by 19% per year, whilst the OD average base fare declined by 11% per year. Figs 6.12 and 6.13 illustrate that jet fuel prices are much more volatile than airfares but generally tend to move in the same direction. Against this background the scenario assumptions seem realistic. The average inflation rate of consumer prices in the Euro area was 2.2% between 1995 and 2015 and 4.4% worldwide (The World Bank, 2015). However, airfares could also nominally increase, but less than the inflation rate, which also leads to a depreciation of real airfares. Still, these assumptions remain more or less arbitrary; however, from our point of view, a further decline of real airfares is rather likely.

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PART | II Models for assessing mitigation strategies

7% 5.9% 5.5%

Annual growth rate (CAGR)

6%

5% 4.0%

4%

5.1% 4.8%

4.6% 4.3%

4.5%

3.9% 3.7% 3.4% 3.2%

3%

2.7% 2.6%

2%

1%

0% Airbus

Boeing

OLS (constant real air fares)

PPML (constant real air fares)

CAGR total passenger volume

OLS (1% PPML (1% OLS (2% PPML (2% real air fares real air fares real air fares real air fares decline p.a.) decline p.a.) decline p.a.) decline p.a.) CAGR OD passenger volume

FIGURE 6.14 Comparison of different forecast scenarios in terms of airfare development with Airbus Global Market Forecast and Boeing Current Market Outlook (CAGR, 2016
35). CAGR, compound annual growth rate.

Fig. 6.14 shows the three different scenarios of the annual global total passenger demand volume growth rate forecast for the period from 2016 to 2035 and the corresponding forecasts of Airbus (2016) and Boeing (2016). Forecast values for Airbus are 4.5% p.a. and 4.0% p.a. for Boeing. Depending on the scenario chosen, the OLS model produces forecast values between 3.2% p.a. for constant real airfares and 5.5% p.a. for a 2% decline of real airfares. The PPML approach produces somewhat lower forecast values, which are in a range of 2.6% p.a. and 4.8% p.a. Overall, a decline of real airfares seems to be more likely than constant real airfares, especially compared to the Airbus and Boeing forecasts. Furthermore, Fig. 6.14 shows the corresponding ODP growth rate forecasts (excluding Airbus and Boeing, since they are not available to the public). As already explained earlier in this chapter, they are slightly higher and are in a range of 2.7% and 5.1% for the PPML model, depending on the assumptions about the future development of airfares. Correspondingly, the OLS model produces values that are about 0.7%
0.8% points higher. However, there is a caveat: as much as forecast results depend on forecast methodology, input data and (model) assumptions play a very important role as well. Therefore we have aimed for as much transparency as possible.

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159

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