# Price Elasticity with real monthly data

Is it possible to calculate the Price elasticity based on the following set of data? I tried with the formulas widely available, but looks like the results are not correct. No, it is not possible. The reason for that is that to calculate price elasticity of demand you first have to estimate parameters of demand function. You might think that you have data on demand, but you don't. You have data on equilibrium supply-demand intersection across time.

Hence, the data you have are insufficient to estimate elasticity. If you would regress log of volume on log of price you would get biased estimates of price elasticity. What you should do is to expand your dataset in a way that allows you to use some simultaneous equations model that can handle the fact that there is endogeneity in the data (due to supply-demand interaction).

For example, you could estimate elasticity by running following 2SLS (all variables are in logs):

$$y_t = \alpha + \beta \hat{p}_t + \epsilon_t \\ p_t = \gamma + \omega c_t + e_t$$

where you use costs as an instrument for price (which is valid assuming cost based pricing or high degree of competition).

If you estimate the system above $$\beta$$ will be the elasticity of demand. However, in your table as it is now costs (or other instruments) are missing, so to answer your original question, no with data you have it is not possible to calculate/estimate price elasticity.

• Does this hold also in a scenario in which I would like to estimate the price elasticity of demand for goods in a shop? If I do not know the costs for selling certain products, does this mean I can never truly observe the right elasticity of demand? Mar 2 at 9:50
• @Athaeneus 1. yes it does hold for a shop. 2. No, you can observe/estimate the two elasticity by using 2SLS or any other advanced 'fancy' econometric technique as long as you collect data on some instrument such as firm cost. All this means is that you cannot just do it in a direct 'naive' way where you try to calculate it just from data on quantity and price. But it can be done, you just need much more data to estimate some structural model (e.g. 2SLS, GMM or whatnot - there is large amount of ways how this can be structurally modeled).
– 1muflon1
Mar 2 at 9:57