3. An alternative approach for determining air

The African Statistical Journal, Volume 14, May 2012 83

3. An alternative approach for determining air transportation costs in the International Comparison Program

Abdoulaye Adam1

AbstractIn the International Comparison Program (ICP) the cost of air transportation is compared across countries. The cost of air transportation between two cities varies depending on the quality of service and the air carrier. The quality of service (aircraft type, meals and refreshments, on-board entertainment, flight schedule, etc) is reflected in the price of the ticket. The date of issuing the ticket before travel is also a price-determining factor. Precisely capturing all the price-determining characteristics in the product description is difficult and may not be feasible. Therefore, airfare prices constitute a challenge for ICP price collection if like is to be compared like with like.

This paper examines air transportation structured product descriptions (SPDs) from the 2005 and in 2011 ICP rounds and notes their deficiencies for purposes of comparison. It proposes a number of improvements: (i) using a geographic coordinate system (latitude and longitude) to determine orthodromic distances between departure and destination points; and (ii) basing comparisons on unit (kilometer or mile) costs of these orthodromic distances. It would then be possible for air transportation price data to be collected directly by Regional Coordination teams or by the Global Office through travel agencies, using the major Computer Reservation System (CRS) vendors.

Key words: Airfare prices, Structured Product Descriptions, Latitude, Longitude, Orthodromic Distances, Computer Reservation System

RésuméLes coûts du transport aérien sont comparés entre les pays dans le Programme de comparaison internationale (PCI). Le coût du transport aérien entre deux villes varie en fonction de la qualité du service et de la compagnie aérienne. La qualité du service (type d’aéronef, les repas, les rafraîchissements et le divertissement à bord, l’horaire de vol, etc.) est répercutée sur le prix du billet. La date d’émission du billet avant le voyage est aussi un facteur déterminant le prix. Capter avec précision toutes les caractéristiques déterminant le prix dans la description du produit est difficile et peut ne pas être réalisable. En conséquence, les prix des billets d’avion constituent un défi pour la collecte des prix du PCI en vue de comparer des choses comparables.

1 Abdoulaye ADAM, International Statistical Consultant BP 12965 Niamey NIGER, Email:[email protected]

Journal statistique africain, numéro 14, mai 201284

Abdoulaye Adam

Ce document examine les descriptions structurées de produits (DSP) du transport aérien des deux cycles 2005 et 2011 du PCI et met en exergue leurs lacunes en termes d’exhaustivité pour des fins de comparaison. Il propose un certain nombre d’améliorations et recommande de: (i) utiliser les coordonnées géographiques (latitude et longitude) pour déterminer les distances orthodromiques entre les points de départ et de destination et ; baser les comparaisons sur les coûts uni-taires (km ou mile) de ces distances orthodromiques. Alors il est possible de faire la collecte des prix du transport aérien directement par les équipes régionales de coordination ou par le Bureau mondial à travers des agences de voyages en utilisant les systèmes informatiques majeurs de réservation.

Mots clés : Tarifs aériens, Descriptions structurées de produits, Latitude, Lon-gitude, Distances orthodromiques, Système informatique de réservation

1. INTRODUCTION

The qualityof Purchasing Power Parities (PPPs), which are used for country comparisons, depends on the capacity to separate pure price levels from other factors, and to measure them accordingly. One of the most difficult problems in constructing those indices is accurately describing products so as to capture and treat quality change and/or differences across countries. A product is the smallest entity on which price measurements may be made and compared. It should be defined by a “complete description.”

In the 2005 International Comparison Program (ICP) round, Structured Product Descriptions (SPDs) were used to describe products, the prices of which were collected and compared among countries. An SPD is a coherent and structured set of price-determining characteristics or parameters aimed at describing goods and services in a rationalized fashion in order to develop an item list and harmonize item identification for price surveys in different countries. SPDs provide all the relevant characteristics of products, whereby each product represents a particular configuration of those characteristics.

Airfare prices were collected during the 2005 ICP round from two main sources: (i) airline companies and (ii) travel agencies using Computer Reser-vation Systems and/or airlines. In addition to airfare, surcharges, and taxes, the price of a ticket includes the quality of the service (aircraft type, meals and refreshments, on-board entertainment, flight schedule, etc). The date of issuing the ticket before travel is also a price-determinant.



The air transportation products in 2005 were not directly comparable. The SPDs failed to capture differences in the quality of services. As well, the distances involved differed considerably.

This paper examines the 2005 and in 2011 air transportation SPDs and notes their shortcomings for comparative purposes. To make the prices of air transportation more comparable, improvements are proposed for the 2011 ICP product list: (i) use of a geographic coordinate system (latitude and longitude) to determine orthodromic distances between the points of departure and destination, and (ii) basing the comparisons on the unit (kilometer or mile) cost of these orthodromic distances. This would make it possible for price data for air transportation to be collected directly by Regional Coordination teams or by the Global Office through travel agen-cies, using the major Computer Reservation System (CRS) vendors.

2. DEsCRIPTIONs UsED IN 2005 AND 2011 ICP-AfRICA ROUNDs

Structured Product Descriptions (SPDs) were used in 2005 to define prod-ucts in the ICP-Africa list, including transportation by air. An example is provided in Table 1.


Abdoulaye Adam

Table 1: Example of air transportation product description in 2005 ICP-Africa

Basic heading: Passenger transport by air

Position élémentaire : Transport de voyageurs par air

Product name: Airfare to johannesburg Product code: 088.01

Nom du produit : Tarif vol aérien pour johannesburg

Code du produit : 088.01

Preferred quantity and unit of meas-urement:

1 service Quantité de référence et Unité de Mesure :

1 Service

Product description:

• Quantity: 1 service

• Type : Scheduled service

• Discounts/Type of ticket : Weekend rule (night Saturday/Sunday must be spent at destination)

• Discounts/Type of ticket : Minimum stay (of _7__ days)

• Discounts/Type of ticket : Maximum stay (of __60_ days)

• Discounts/Type of ticket : Advance reservation ( _14_ days)

• Discounts/Type of ticket : Advance payment ( _14_ days)

• Taxes : Airport tax included

• Type of Trip : Round trip

• Luggage : Included up to_25_kg

• Other item features : Cheapest non-rebookable Economy class fare

• Other item features : Exclude airport or departure tax

A problem with the description in Table 1 is that a major price-determining factor—the distance between the points of departure and destination—is not considered, so the product is not directly comparable across countries. And because the data source (airline or travel agency) is not indicated, the difficulty of product comparability is compounded. Furthermore, as



pointed out earlier, the quality of the service, and thus, the cost depends on the airline. One of the characteristics of the product is “Cheapest non-rebookable Economy class fare,” but this does not cover other restrictive conditions like date fixity or date change penalties. A better way of taking conditions of ticket usage into account would be to include the type of Economy class ticket.

The descriptions of Transportation by air products have been improved in the 2011 ICP product list. An example is presented in Table 2.

Table 2: Example of air transportation product description in 2011 ICP-Africa

Basic heading 1107331 Passenger transport by air

Product 110733106 Flight, International, return ticket – Long Distance

Number of units: 1 Unit of measurement: Ticket

Product specifications:

Transportation Type: International flight; round trip

Ticket type: Return ticket; not changeable after issue; non refundable

Starting point: Major airpoirt of the country

Destination: Most popular international destination

Distance: Approximately 14,000 km

Class: Economy adult passenger

Departure date: On or about last Wedneysday of April

Issued before departure: 42 - 56 days

Payment: When issued

Price includes: All additional taxes, fees, surcharges and charges included in the ticket, e.g. departure tax, passenger service charge, fuel surcharge

Price excludes: Price reductions, e.g. discount or special offer only for best customers

Purchasing place: Travel agent

Comments: Specify destination

The 2011 SPD is an improvement over 2005, but the description still does not properly address the distance issue, which is a major price determinant. The most popular international destinations vary in different countries and can be far less than 14,000 km away. The 2011 SPD requires that the destination, distance in km, additional taxes, fees, surcharges and charges be


Abdoulaye Adam

specified. However, these data, all of which are important in determining the price of a ticket, may not be collected unless the it is clearly specified that they be included. Thus, the data collection instruments should have fields for these elements, just as there is for the price of the ticket. Also, it should be clear that distance refers to flying distance based on orthodromic distance.

3. sUggEsTED APPROACh fOR COllECTION Of AIR TRANsPORTATION PRICEs

3.1 Data sources

Airline companies and travel agencies are the two main sources of air trans-portation price data. Tariffs can be classified into two groups: (i) public domain information, which is accessible worldwide, provided by the three major global Computer Reservation System vendors—Amadeus, Sabre and Travelport (including Galileo and Worldspan); and (ii) market tariff, which is accessible in countries or regions only for the points of departure. For example, a travel agency in Tunis, Tunisia, does not have access to the U.S. market prices, and American travel agencies do not have access to price information for North Africa. To ensure comparability, it is essential that the same source be used to determine the price of air transportation products. This can be done if prices are determined globally.

3.2 Class types

In addition to the different data sources, prices vary within the same class depending on the class type:

• First Class: F, A and P• Business Class: J, C, D and Z• Economy Class: Y, L, K, Q, V, T, H, S and B

Each class type has different own conditions of ticket usage (e.g., date fixity, date change penalties, reimbursement, and validity).

3.3 geographic coordinate system

A location can be identified based on its latitude and its longitude, which Wikipedia defines as:



• The latitude of a location is the angular distance of that location south or north of the Equator. It is an angle and is usually measured in degrees. The Equator has a latitude of 0°, while the North and South Poles have, respectively, a latitude of 90° north (written 90° N or +90°), and a latitude of 90° south (written 90° S or −90°). The latitude of point A is the angle φ between the normal of the point and the Equator.

Figure 1: Definition of the latitude of a point A

• longitude specifies the east-west position of a point on the Earth’s surface. Points with the same longitude lie in lines running from the North to the South Pole, known as meridians. By convention, the position of zero degrees longitude is the position of the Prime Meridian, which passes through the Royal Observatory, Greenwich, England. The longitude of other places is measured as an angle east or west of the Prime Meridian. Specifically, it is the angle between a plane containing the Prime Meridian and a plane containing the North Pole, South Pole and the location in question. It ranges from 0° at the Prime Meridian to +180° eastward and −180° westward.

To precisely locate points on Earth, latitude and longitude are expressed in degrees, minutes, and seconds. A one-degree variation in latitude is about 69 miles; a minute of latitude, approximately 1.15 miles; and a second of latitude, approximately 0.02 miles. The magnitude of a difference induced by a longitude variation depends on the latitude. At the Equator, it is ap-proximately 69 miles, the same as a degree of latitude. At latitude of 45 degrees, a degree of longitude is approximately 49 miles. The size gradually decreases to zero as the meridians converge at the poles.

North Pole

φ Equator

Normal

Tangent

A


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3.4 Central angle

A central angle is an angle whose vertex is the center of a circle and whose sides pass through a pair of points on the circle. The sides subtend an arc between the two points whose angle is (by definition) equal to the central angle itself.

Figure 2: Definition of a central angle

The angle AOB forms a central angle, with center O and sides OA and OB.

Let ffss λφλφ ,;, be the geographical latitude and longitude of the two points A and B (a point of departure and a point of destination of a journey), and let λφ ΔΔ , be, respectively, their differences; then , the central angle be-tween them, is given by the spherical law of cosines defined in Wikipedia as:

)coscoscossincos(sinˆ λφφφφσ Δ+=Δ fsfsar (1)

When the distance is small (the two points are not far apart), the above formula can have large rounding errors. In that case, the harversine formula below is more numerically stable.

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛ Δ+⎟⎠

⎞⎜⎝

⎛ Δ=Δ2

sincoscos2

sinarcsin2ˆ 22 λφφ

φσ fs (2)

If the points are on opposite ends of the sphere (antipodal points), the following more complicated formula, which is accurate for all distances, should be used:

O

B A



⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

Δ+

Δ−+Δ=Δ

λφφφφ

λφφφφλφσ

coscoscossinsin

)coscossinsin(cos)sin(cosarctanˆ

22

fsfs

fsfsf

(3)

3.5 Orthodromic distance

In Euclidean geometry, the shortest distance between two points is the straight line joining them. In spherical geometry, distances are generally measured along a path on the surface of a sphere. The orthodromic distance, or the great-circle distance, between two points is the shortest distance between the two points on the surface of a sphere.

Geodesics/Great circles are defined as circles on the sphere whose centers are coincident with the center of the sphere. Geodesics/Great circles possess two essential features of Euclidean geometry:

• A point that moves along the surface of a sphere without turning will follow a great circle.

• The shortest distance between two points on a sphere lies along a great circle.

The distance d between two points on a sphere of radius r, and central angle σ̂Δ (expressed in radians) is given by:

σ̂Δ= rd (4)

The shape of the earth resembles a flattened sphere. The average radius for that approximation is 6371.01 km, while the quadratic mean or root mean square approximation of the average great circle circumference gives a radius of about 6372.8 km

Example of the computation of the orthodromic distanceTo calculate the orthodromic distance between Niamey, Niger and Paris, their latitudes and longitudes are converted into decimal degrees:

Niamey (Lat: 13.5167 / Long: 2.1167)

Paris (Lat: 48.8667 / Long: 2.3333)


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Based on the above notation and the first equation:

φN = 13.5167 λN = 2.1167 φP = 48.8667 λN = 2.33333 Δφ = - 35.35 Δλ = - 0.2166 Cos φN = 0.9723 Cos φP = 0.6580 Cos Δλ = 0.9999 Sin φN = 0.0368 Sin φP = 0.0407

σ̂Δ = arcos{(0.2337)(0.7532) + (0.97237)(0.65780)(0.9999)} = 0.616981789

Orthodromic Distance Niamey-Paris = (0.616981789)(6372.8) = 3,931.9 km

Other orthodromic distances calculated using the above three expressions are presented in Annex 1. The same values of σ̂Δ , and thus, of distances were found with all three expressions.

An easier way to find the orthodromic distance between two cities is through Internet websites:

www.travelmath.com www.mapcrow.info www.infoplease.com www.globefeed.com www.worldatlas.com

However, because the latitude and longitude and the formulae used differ slightly from one site to another, these sites do not give exactly the same distances. For the ICP, it is important to use the same source for distances on which prices will be determined in order to control variations that are not due to price differences.

4. PROCEDURE TO DETERMINE ORThODROMIC AND CRs-BAsED AIRfARE PRICE

The price of air transportation products can be determined by ICP regional or global coordinates using orthodromic distances between points of depar-ture and destination and prices obtained from one of the main Computer Reservation System (CRS) vendors—Amadeus, Sabre and Travelport (in-cluding Galileo and Worldspan). The procedure is:

1. For each participating country, determine the geographical coordinates of the departure and destination points of the air transportation products and calculate orthodromic distances between them using one of the



central angle formulae. These distances can be obtained from one of websites listed above. However, it is important to use the same method to determine all the distances.

2. Obtain the cost of such journeys from one of the main CRS vendors. These prices are more comparable than those from airline companies, which differ globally and across categories like airfare, surcharges and taxes.

3. Calculate the price per kilometer (km) of each product. These prices will then be used to compute PPPs for the basic headings after converting them in local currencies if necessary.

For ICP-Africa, the air transportation PPPs could be calculated based on the price per km of round-trip tickets from the capital cities of participat-ing African countries to selected destinations—London, Washington DC, New York, Johannesburg, Nairobi, Cairo and Dakar—and to cities where the implementing agencies for other ICP regions are located—Tunis (ICP-Africa), Manila (ICP-Asia), Moscow (CIS-Rosstat), Santiago, Chile (ICP-LAC), Beirut, Lebanon (ICP-Western Asia), and Paris (OECD). The final list of destinations for Africa may be decided based on the information in Amadeus, which is the most common CRS in Africa.

Orthodromic distances between each capital city and the above destina-tions, obtained from www.worldatlas.com, are presented in Annex 2. Prices of an Economy class Y, one-way ticket from African capital cities to those destinations were obtained by the World Bank Travel Agency (American Express) from the Amadeus database. These prices were converted into costs per km, as presented in Annex 3. The prices per km of all products will be converted into local currencies and used to compute the PPPs.

5. CONClUsION

Air transportation between any two cities is a product whose quality (aircraft type, meals and refreshments, on-board entertainment, flight schedule, etc.) depends on the services the air carrier offers. The quality of the serv-ice is reflected in the price of the ticket and is not entirely captured in the product description. Consequently, products of different qualities are being compared. In addition, the distance between the departure and destination points should be considered in the comparison. This study demonstrates that it is possible to collect airfare prices globally, or at least regionally, us-


Abdoulaye Adam

ing one of the major CRS vendors, and to take the distance of the trip into consideration. Ideally, distance should be orthodromic, and comparisons should be based on prices per unit distance (kilometer or mile).

REfERENCE

African Development Bank (2005), Product Catalogue for ICP Price Survey in African Countries Vol 2.

Gade, K (2004), NavLab, a Generic Simulation and Post-processing Tool for Navigation- European,” Journal of Navigation 2 51-59

Longley, PA Goodchild, M.F, Maguire,D.J and Rhind,D.W (2003). Geo-graphic Information Systems and Science, John Wiley and Sons 2nd Edition

The World Bank, ICP Global Office, DECDG (2011). Product Catalogue for ICP Price Surveys Global Core List 2011

Wikipedia, the free Encyclopedia. Available at: http://en.wikipedia.org/wiki/Great-circle_distance



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6

Documents

3. An alternative approach for determining air