Where:
• Traffic is the dependent variable,
• 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.
The regression analysis estimates the value of the
parameters (constant, a1 , a2, a3, a4, a5, etc.) on each of the
variables, which reflect the relative impact of each of the
variables on traffic levels. As log formulations approximate
percentage changes in impacts, the parameters of the
logged independent variables can be directly interpreted
as elasticities.
Two-Stage Least Squares
Two-stage least squares (2SLS) is a regression technique
that is used when explanatory variables are believed to be
correlated with the regression model’s error term used to
obtain consistent estimators15. One or more instrumental
variables (IVs) that are correlated with the endogenous
explanatory variable, but uncorrelated with the dependent
variable are used to isolate the effects of the endogenous
explanatory variable. This process increases consistency
(relative to OLS), at the expense of increasing sample
variance.
InterVISTAS experimented with the use of two-stage
least squares techniques to improve the consistency of
elasticity estimates. The natural logarithm of distance
and the natural logarithm of fuel prices were used
separately and combined as potential IVs. In some
data sets, distance was found to be a worthwhile IV,
exhibiting high correlations with travel prices and low
correlations with traffic. However, there is some concern
that distance should be used as an explanatory variable
instead of an instrument (if route distance is believed
to have an impact on traffic). Fuel prices were found to
be poor IVs. Fuel prices exhibited low correlations with
traffic and travel prices.