Obtaining own price, cross price and income elasticities

[Muhammad Ibrahim Shah]

Dear all,

I want to estimate demand for chicken accounting for seasonal dummies (quarterly dummies). I have chosen log log functional form and the findings are below:

Ln(demand for chicken)= 17.05-0.50(lnpricechicken) -.167 (lnpricepork)+ .822 (lnpriceturkey)+ 0.217(lnpricebeef) -0.396 (lngdp) -.044Q1+ .0388Q2+.009Q3

Now, here, I want to estimate own price elasticity and cross-price elasticity. Is there any command in stata that gives me own or cross-price/income elasticity, perhaps something like margins or dydx?

I know this is not a discussion forum for this but in general, are the following calculation from the log-log functional form correct:

Own price elasticity of chicken=-0.50
Cross price elasticity with respect to pork=-0.167
Income elasticity=-0.396

Are the above elasticity calculation correct? Or in the case of cross elasticity, I have to add constant and -0.50 (own price coefficient) as well? Please guide.

[Clyde Schechter]

Your calculations are correct. In a more complicated situation, you might also use the -margins, dydx()- command to get elasticities. But as your equation is strictly linear in all of the log-transformed variables, you can just read the elasticities off as the coefficients (as you have done).

Note that your equation models the seasonal effects simply as seasonal shock to the demand for chicken, with the elasticity being the same all year around. Is that an economically realistic model? (Serious question--I have no idea, I'm neither an economist nor an agricultural expert.) I might be inclined to think that the elasticity of chicken with respect to own price or other prices might vary from quarter to quarter. That would require a different model, with the quarter indicators interacting with the other variables. In that case, it wold be advisable to use -margins, dydx()- rather than trying to hand calculate the elasticities from the regression output.

[Muhammad Ibrahim Shah]

Thank you so much for your help!