Calculating the price elasticity and income elasticity of demand The demand function for air travel between the U.S. and Europe has been estimated to be
$$\ln Q = 2.737 - 1.247 \ln P +1.905 \ln I$$
where $Q$ denotes number of passengers (in thousands) per year, $P$ the (average)
ticket price and $I$ the U.S. national income.
Determine the price elasticity and income elasticity of demand.
 A: The estimated equation is \begin{equation}\ln Q = a + b \cdot \ln P + c \cdot \ln I.\end{equation} Take the derivative of both sides with respect to $P$. Very roughly, the estimated parameters $a,b,c$ are constants and $I$ is an exogenous variable (we've assumed the price change is so small that it does not change national income). Variables $Q$ and $P$ are functions of $P$. This gives you \begin{equation} \frac{1}{Q} \cdot \frac{\partial Q}{\partial P} = 0 + b \cdot \frac{1}{P} \cdot \frac{\partial P}{\partial P} + 0.\end{equation} Rearranging terms to get the price elasticity:
\begin{equation}\varepsilon_{Q,P} = \frac{\partial Q}{\partial P} \cdot \frac{P}{Q} = b\end{equation}
A: Thanks to all who have presented here on the powerful and efficient manner showing how elasticity can be computed when one has a simple OLS model relating Q to P. This may be an interesting topic for textbooks but lacks generality needed in practice. Often Q is not only a function of P but one or more lags of P and sometimes future expectations of P. Additionally there may be the need to incorporate ARIMA structure in addition to P and its lags. More generally there may be unobservable input variables in the mix which can often be proxied by level/step shifts, time trends, seasonal pulses, or one-time pulses.  Other structures often needed in practice include holiday effects/day-of-week effects, promotions etc. The reason for identifying and incorporating these kinds of effects is to render the error process Gaussian, leading to valid tests of significance for all estimated coefficients. 
With this in mind, a more general/robust approach to calculating an elasticity is to form a useful model and generate a forecast (baseline forecast) using an expected P (user-specified) for the next period. Take that same model and the same parameters and increase P by 1%. Compute the difference in the forecasted Q and convert the difference in the two forecasts to a percent change from the baseline forecast. In this way you have not sacrificed model form, but you can still compute elasticity. The advantage of the double log approach is speed, but this may entail using a sub-standard model.
Transformations of any kind should be viewed as possibly helpful BUT possibly harmful. The whole idea is to keep the model as simple as possible, but not too simple. Some analysts think that incorporating pulse indicators is kitchen-sink modelling, but they are only point adjustments for proven unusual values, much like the value 5 in the process {1,9,1,9,1,9,1,9,1,9,5,9,1,9,1,9,1,9,1,9}. The 5, if untreated, will bias the characterization of the process.
