Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 18

The following equation describes the median housing price in a community in terms of amount of pollution (nox for nitrous oxide) and the average number of rooms in houses in the community (rooms):

log(price) =?0+?1log(nox) +?2rooms + u.

(i) What are the probable signs of ?1 and ?2? What is the interpretation of ?1? Explain.

(ii) Why might nox [or more precisely, log(nox)] and rooms be negatively correlated? If this is the case, does the simple regression of log(price) on log(nox) produce an upward or a downward biased estimator of ?1?

(iii) Using the data in HPRICE2.RAW, the following equations were estimated:

= 11.71 - 1.043 log(nox), n = 506, R2 = .264.

= 9.23 - .718 log(nox) + .306 rooms, n = 506, R2 = .514.

Is the relationship between the simple and multiple regression estimates of the elasticity of price with respect to nox what you would have predicted, given your answer in part (ii)? Does this mean that -.718 is definitely closer to the true elasticity than -1.043?

Step 1 of 6

(i)

The possible signs of regression coefficients are described as follows:

?₁ < 0 because more pollution can be expected to lower housing values as people would not want to buy homes which are in polluted areas.

?₂ > 0 because rooms roughly measures the size of a house and bigger the house, higher will be its price.