Question

Suppose that you are studying the relationship between average housing price of communities and other community characteristics. Consider the conditional mean model

log(price) = β₀ + β₁ log (nox) + β₂rooms + β₃ rooms² + β₄stratio + U, E (U|nox, rooms, startio) = 0
where price is the average price of houses in the community, nox is an air pollution index that measures nitrogen oxide in the air in parts/million, rooms is average number of rooms in house, and stratio is the student-teacher ratio in the primary school in the community.
Give an interpretation for β₁ that is appropriate for the model. (Hint: 0.01 unit of change in log(nox) can be interpreted as 1% change in nox level.

Answer 1

In the given conditional mean model, the coefficient β₁ represents the elasticity of the average housing price concerning the level of air pollution index.

The model is specified in logarithmic form, so the interpretation of β₁ is expressed in percentage terms. Specifically, if the nox level (air pollution index) increases by 0.01 units, holding other variables constant, the expected percentage change in the average housing price is given by β₁.

Therefore, β₁ can be interpreted as the percentage change in the average housing price associated with a 1% increase in the nox level. In simpler terms, if β₁ is, for example, 0.05, it would mean that a 1% increase in the air pollution index (nox) is associated with a 5% increase in the average housing price, assuming all other variables remain constant.