# Empirical set-up for measuring elasticity with respect to quality in an environment without price

I have data on the determinants of market share in an environment without prices. So, imagine, person A chooses technology C at time X of a certain size, speed, and resolution (all measurable). And I have data for thousands of people and the technologies they choose over a time period of about 10 years. So again, imagine, changes in quality (a newer high-quality technology is developed) and this shocks the system, therefore demand changes as technology A is replaced by technology B, and then a few years later, technology C is available, etc., in an environment where everything is free and only 3 technologies are available, for example.

How do I model elasticity with respect to quality?

The data is stored in MySQL and I typically use Stata for statistical regression. Can you link me to a good example of an empirical test for this type of problem, or, at least, a step-by-step description of what info I need?

• Do you have data on choice sets? That is, do you observe all the potential choices for person A and their attributes? – Dimitriy V. Masterov Oct 30 '15 at 0:10
• No. You might be able to assume that person A has the choice of all available technology on that date, but ultimately I just know that on day 1, person A chose Technology B with x size, speed, and resolution. But, I can see if person A chooses Technology C, for example, on day 2 or, conversely, if person A sticks with Technology B... – EconoQ Oct 30 '15 at 0:25

You might have to create your own set-up for a question like this. Elasticity of quantity with respect to some variable is can generally be measured by

$$\frac{\frac{\partial Q}{Q}}{\frac{\partial x}{x}}$$ where x is the variable you are measuring. In this case, you can do three separate elasticities w.r.t size, speed, resolution. Since you have data on thousands of people, just aggregate it all together and run a regression to measure the quantity of people who buy a tech with such and such size, speed, resolution across your whole time period. So you'll have something like

$$y = \beta_1 x_1 + \beta_2 x_2 + \beta_1 x_1 + \epsilon$$

Where $$x_1 = \frac{\frac{\partial Q}{Q}}{\frac{\partial \text{size}}{\text{size}}}, \quad x_2 = \frac{\frac{\partial Q}{Q}}{\frac{\partial \text{speed}}{\text{speed}}}, \quad x_3 = \frac{\frac{\partial Q}{Q}}{\frac{\partial \text{resolution}}{\text{resolution}}}, y = \text{total techs of all sorts sold}$$

Although you probably want to tweak that a bit, as I'm not sure why you'd want to specifically use elasticity.

If I am fundamentally misunderstanding the model you are trying to do, please let me know.

• Thanks Kitsune, that makes sense. And to see how these preferences change over time w.r.t. technology available, would I do a difference-in-differences or run this regression at each time period where a new technology emerges and subtract the coefficients of the regression to calculate the change? – EconoQ Nov 1 '15 at 13:07
• Run this regression and see if you find any structural breaks. Then you can adjust for that or try adding in some lag variables (something akin to the differences in differences, I think) – Kitsune Cavalry Nov 1 '15 at 15:58