Autoregressive Distributed Lag
An autoregressive distributed lag (ARDL) model was
developed and used with OLS regression analysis. Traffic
was regressed onto similar explanatory variables as in prior
models, but also onto lagged values of traffic. The inclusion
of lagged values of the dependent variable (traffic) is
done to account for the slow adjustment of supply (in the
form of capacity) to changes in the explanatory variables.
The applicability of this assumption is less reasonable for
the U.S. domestic market as the barriers to expanding
capacity are fewer than on international routes; the U.S.
domestic market was therefore excluded from ARDL
estimation 16.
InterVISTAS experimented with the use of ‘prior period’
and ‘year over year’ lags. Although both showed some
degree of success in controlling for these factors, ‘year
over year’ lags had higher correlations with current traffic
levels than ‘prior period’ lags, and were determined to be
the preferred form of lagged variable.
The ARDL models used a formulation as follows:
ln(Traffic t ) =
Constant + b1 x ln(Traffic t-1 ) + b2 x ln(Price t )
+ b3 x ln(Var3 t ) + … + bn x ln(VarN t )
+ bn+1 xDummies t
Where:
• Traffic t is the dependent variable,
• Traffic t-1 is the traffic in the same month (or quarter)
of the previous year
• Price is the average economy or leisure air travel price.
• Var2 to VarN are other quantifiable explanatory
variables that affect traffic levels.
• ln( ) refers to the variables inside of the parentheses
transformed by the natural logarithm.
• The dummies are variables that take the form of 1
or 0 in any observation and capture any remaining
structural reasons for traffic differences between
routes.
Since traffic appears on both sides of the equation,
the coefficients on the explanatory variables cannot be
directly interpreted as long-run elasticities. The long-run
elasticities are defined as when traffic across time periods
stabilise. In general, the use of ARDL models tended to
produce more elastic price elasticity estimates with much
higher goodness of fit values.