Interpreting parameters in the log-log model

Problem

In the model

\[\log{y_i} = β_1+β_2\log{x_{i,2}}+β_3 \log{x_{i,3}}+ε_i\]

\(b_3=2\) . Select the best option:

  1. E(y|x) increases by approximately 2 units when x3 increases by 1 unit
  2. E(y|x) increases by approximately 2% when x3 increases by 1 unit
  3. E(y|x) increases by approximately 2 units when x3 increases by 1%
  4. E(y|x) increases by approximately 2% when x3 increases by 1%

Solution

Answer: d