Cross Price Elasticity

[Kathrine Andersen]

Dear all,

I'm trying to estimate cross price elasticities of a non linear logtransformed model. Do any of you know how to estimate the cross price elasiticy in stata? In addition to the prices and number of quantity sold, I have six different dependent variables. The dataset includes 500 drugs divided into generic og original. I want to estimate the cross price for generic and original drugs in each of the 500 drugs types.

I'm forever grateful,

Kathrine

[Christophe Kolodziejczyk]

Maybe you could take a look at margins (see help margins).

I think your question is too general and the answer depends very much on the model you are estimating. We need more details to answer the question, which model you have estimated and what you want to do with the estimates. Not everyone here is an economist and knows what a cross-price elasticity and a non linear logtransformed model is a rather vague description of your model.

Does your model look like this?

E[ln Q_g|..] = a0 + a11 * ln(p_g) + a22* ln(p_o) + a12 *ln(p_g)*ln(p_o) + X*b

and you want to estimate for example

dE[lnQ_g]/E[lnQ_g] / dp_o/p_o ?

d : change

Q_g : quantity generic drugs
Q_o : quantity original drugs

p_g : price generic drugs
p_o : price

[Kathrine Andersen]

Thanks,


The model:

lnQ= β0 +β1ln(P)+β3+β4+e

Where lnQ is the demand, β0 is income, β1ln(P) is the price, β3 is population growth, β4 is a dummy and e is the error term


Our Panel data is divided into a number of different drugs, and all the drugs are categorized as generic or original.

I would like to estimate the percentage change in demand of the original drug with 1 % increase in the price of the generic drug for all the different drugs in the dataset.

The formula for cross price elasticity is:


Exy= ((Qx2-Qx1)/(Qx2+Qx1/2))) / ((Py2-Py1)/((Py2+Py1)/2))) = percentage change in Qx / Percentage change in Py

where Qx2 is the quantity for the generic drug and Qx1 is the quantity of the original drug, and Py2 is the price for the generic drug and Py1 is the price for the original drug


Thank you for your help

[Kathrine Andersen]

Correction of the model:
lnQ= β0 +β1ln(P)+β2X2+β3X3+e

[Christophe Kolodziejczyk]

The problem is that your model is on the log-scale whereas you want to compute the elasticity on the raw-scale. This is potentially a problem since E(Q) is not necessarily equal to exp(E[ln(Q)]) and in order to apply your formula you need to retransform the dependent variable to the raw-scale. Moreover β1 can be interpreted as the elasticity only if the model is homosedastic.

see also this post