I would like to estimate the own-and cross-price elasticities of demand of a health product. Consider following model:
$Product_{ij}=\beta_0+\beta_1ln(priceA)_j+\beta_2ln(priceB)_j+\beta_3Insurance_{ij}+X\beta+\epsilon_i+\nu_j$
Where:
- The indices $i$ and $j$ represent the individual and village,
respectively - $Product$ is a binary variable which takes on the value of 1 if the
respondent chose Product B and 0 if the person chose Product A - $ln(priceA)$ is the average price of Product A in the village
- $ln(priceB)$ is the average price of Product B in the village, and
- $Insurance$ is a binary variable indicating whether the person has
health insurance coverage (1) or otherwise (0)
I fitted a probit model because the outcome variable is binary. I am unsure how to calculate the elasticity. Given that the prices of products A and B are both entered in the model with the log transformation, would I calculate the elasticity (EY/EX) of the log-transformed variable or a semi-elasticity (EY/DX)?
Best Answer
In Stata, you can calculate this like this:
This can be interpreted as saying that a 1% increase in miles per gallon is associated with a 0.007 reduction in the probability of the car being imported (on a [0,1] scale), holding the weights of the cars constant.