Simultaneous equations model for passenger demand

Our purpose is to estimate how much more(less) air travel demand does an increase(decrease) in GDPs produce?
We use DOT data for the USA France travel market to show how this question can be answered by econometrics.

Demand, Traffic, Supply, Market shares. 
 
People in airlines make a distinction between:

- Demand (for travelling from A to B).
- Traffic or actual number of passengers carried between two points, by a given service.

Demand is like fisch in the sea. Airlines capture them using aircrafts as nets.
The bigger the net(aircraft), the higher the number of passengers. Chart below displays
the log of passengers' share for an airline, against log of percentage of seats
(Source: US Department Of  Transportation, Quarterly, 2003Q1 - 2010Q1).
Observations line up, displaying a stable relation over years:

For airlines, empty seats are useless costs, and turned down passengers are loss of income.
So it is better to know the market's potential to build a schedule, choosing the right size of
aircraft and number of flights.

Elasticity to GDP:

For the USA-France market, we expect  a positive correlation between the change in GDPs for France
and the USA, and the variation in demand for air travel between the two countries.
Actually, there is more than correlation but a causal relation exists, because GDP is an indicator of the available income.

We can write down a first equation (dummy variables, D1-D3 are here for seasonal effects,  for three quarters only since a constant Kd is already in the model):
D(t) = Kd . GDP(t)^a  . D1(t) . D2(t) . D3(t)

(We use only one parameter for the GDP, the average of France and USA, since we do not know the number of tickets sold in each country)
 
Multiplicative form is the standard form because (using the first order approximation) it simplifies into: 
[% change in Demand]  =  a x [% change in GDP]

This equation above is the reason for naming the "a" coeffcient an "elasticity".
Estimation of  "a", the GDP exponent can be done by mean of ordinary least squares (OLS or  linear regression), but two things prevents us from doing this.


Problem 1: No demand statistics for a country pair (A,B)

Airlines report carried  passengers to the DOT, but a passenger departing from CDG and connecting at Heathrow will appear as a passenger originating from the UK, not from France.
We might consider using traffic data, as an approximation, but then there is another problem.

Problem 2: Planners use GDP forecasts to design schedules.

Thus, a change in GDP causes a change in traffic via 2 different channels: Demand D, and Supply.  cannot use only traffic data to estimate the GDP demand factor.

Solution with multiple equations and conclusion.


Instead of using Demand , we should use traffic and supply to fit a simultaneous equations model. This enables us to make an unbiased  estimation of the demand exponent.

Nevertheless, we use another (reasonable) hypothesis : The average proportion of seats used by connecting passengers, i.e. people originating from other countries than France and the USA does not change dramatically in time. Otherwise, a specific airline would have to substract its own connecting passenger from the trafic, a much simpler operation anyway, compared to collecting data from all other carriers for the geographical origin of their passengers on a particular route.

Seats and traffic data for the USA-France market comes from DOT, and the OECD provides GDPs for France and USA.

Using this obviously too simple model,  elasticity to GDP exponent is.1.43

Here are results for single equation alternatives:
Using traffic data from a specific airline with a single equation :     1.93
Using aggregated traffic from all carriers with a single equation:     1.11

At least on this particular example, fitting a model using all the available data compensates for the absence of more relevant data.


Application: Predicting traffic for a single airline 

This model can also be used to predict traffic.Chart below illustrates the goodness of fit for a single airline. Forecasts would not necessarily be as good as this. A simple counterargument is that you'll need an accurate forecast for GDPs to build your forecast.