# Simulation with a priori elasticity: how do I calculate elasticity of the simulated data?

I'm building a simulation with an a priori elasticity estimate, and building a simulation to see how many samples I need until I converge to the correct elasticity estimate based on that simulated data. How do I calculate the elasticity of the simulated data?

Some more detail: Let's assume a priori elasticity of -2. I randomly generate a dataset where each "person" has 10% chance of buying the product. Each person gets a random value between .95 and 1.05 that changes the price for them (let's call this p). Then I calculate how likely each person is to buy the product with 10% * p-2 = z. Now I randomly generate whether this person buys the product with IF(rand()*z>0.9,1,0).

Now I have a column of price change, original expected probability of buying (10%) for everyone, and a column of 1's and 0's representing which people bought the product.

Now, I want to know how many "people" I need to simulate before my data converges to the population elasticity (or close to it) with some level of certainty.

I expect the number of samples required for convergence to be related to the width of the price change factor. That is, if p is [0,2] it would require less samples than if p is [0.95,1.05] or [.99,1.01].

• You want to recover own-price elasticity of demand from a binomial choice model? – BKay Apr 9 '18 at 20:49
• @BKay yes, exactly! Specifically, I want to know how many simulated samples to achieve a specific standard error for a given width of random price change factor. – Caleb Apr 11 '18 at 0:40