The data set Housing_Start contains monthly data on housing starts and other related macro economic variables described below. Economists and practitioners have long found that housing starts (the numbers of new houses being built) is a very good leading indicator for economic growth in the next six to twelve months. Thus, we are interested in finding the important factors affecting housing starts. Suppose that we specify the following model for housing starts:

log(HS_t)=₀ +₁cconf_t +₂cexpect_t +₃csent +₄long_t +₅SP500_t +₆ log(HS_t1) + u _t

where, t indexes month t, HS_t is the new housing start in month t, cconf_t is a consumer confidence index in month t, cexpect_t is a consumer expectations index in month t, csent_t is a consumer sentiment index in month t, long_t is long-term interest rate in month t, SP500_t is the average S&P 500 stock index in month t, and HS_t-1 is the new housing start in the previous month (t-1).

a. Estimate the model by LS and report your estimation output table.

b. Does the model above suffer from multicollinearity (using 5% significance level)? Explain your answer.

c. If the model above suffers from multicollinearity, can you modify and re-estimate the model above so that the new model no longer suffers from multicollinearity?