Question 3 We have annual observations on housing investment and a housing price

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Question 3 We have annual observations on housing investment and a housing price index in New Zealand from 1947 through 2010. Let invpc denote real per capita housing investment (in thousands of dollars) and price denote a housing price index (equal to 1 in 1982). A simple regression in constant elasticity form, which can be thought of as a supply equation for housing stock gives (a) log(1nvpc)-0.31 5 + 1.034 log(price), n = 64, Rz-0.222 (0.023) (0.334) We know that both invpc and price have upward trends. Then we run another model including a inear trend. (b) log(mpc)-0.451-0.565 log(price) + 0.01 St, n = 64, R40.369 (0.136) (0.679) (0.0035) (Standard errors are given in the parenthesis) i) Test if log(price) is significant at 5% significance level in both (a) and (b). ii) Refer to the regression models above; please explain why the coefficient and significance of log(price) changes from model (a) to (b). Please specify and explain what is wrong with the first (a) model?

Explanation / Answer

i)

yes, in a model (a)-0.334 and (b)-0.679 p-value is >0.05 so reject the null hypothesis and value of log price is significant.

ii)

model (b) is preferred over the model (a) as adjusted R-squared is increased in a model (b).

hence variable "t" is really useful for the model prediction.

In model (a) one variable is less used. So full information about data is not used in model prediction(a) hence some information is missing, So model (b) is preferred over (a).

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