Economics Stack Exchange Archive

Estimating demand elasticity econometrically

• posted by: ben on 2012-03-09
• tagged: econometrics, elasticity, production
• score: 2

When specifying a production function for regression, it is well known that one of the features of using a log-log model is that the estimated coefficients are the output elasticities w.r.t. their respective independent variables.

My question is does it then follow that if one regresses log(production) on log(price), the coefficient on log(price) will be the demand elasticity?

That is, if we specify the production model as follows:

$$\ln q=\alpha_0 + \alpha_p \ln p$$

(where q is quantity of output and p is output price)

and then differentiate w.r.t. $\ln p$

$$\frac{d \ln q}{d \ln p}=\alpha_p$$

then isn’t this the demand elasticity?

If it is, then does the omission of other important variables in the production function bias the elasticity (if firms are not homogenous in those variables)?

Thanks

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