Elasticities and percentage change
Problem
Data: http://media.nek.lu.se/data/elasticities.xlsx
In this problem, we will confirm that \(β_2=\left( ∂y/∂x_2 \right)(x_2/y)\) is approximately equal to the percentage increase in y when \(x_2\) increases by 1%. We also confirm that \(β_2=∂log y/∂log x_2\) which is approximately equal to the change in log y over the change in log x2.
In the excel file Part 6 you have the following (see previous problem for notation)
Column D/E calculates y, log x2, log x3 and log y. You set start values x2 and x3 (check formulas in E3)
Column G/H calculates y, log x2, log x3 and log y. You set end values x2 and x3.
B7 has the percentage change in y (start in E2 end in H2)
B8/B9/10 has the change in log x2, log x3 and log y
B11/B12 has the ratios (set to zero if infinite)
- Increase end value of x2 by 1%, that is, enter 1.01 in cell H1. What is the percentage change in y? Confirm that it is close to beta2. Do the same for x3.
- What is the change in log y over the change in log x2? Confirm that it is close to beta2.
- Do the same thing, increasing x2 by 0.1%. What is the percentage change in y? What is the change in log y over the change in log x2.
- Now change beta2 to -0.3 and do a-c again.