I would like to estimate the own-and cross-price elasticities of demand of a health product. Consider following model:
- 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)?