The following table shows a portion of monthly data on the personal savings rate (Savings) and the personal disposable income (Income) in the U.S. from January 2007 to November 2010.

Date.................... Savings (%).................... Income ($ billions)

2007-01......................... 2.2................................. 10198.2

2007-02......................... 2.3................................. 10252.9

⋮................................................ ⋮........................................................ ⋮

2010-11.......................... 5.5................................ 11511.9

a. Estimate and interpret a log-log model, ln (Savings) = β0 + β1 ln (Income) + ɛ. What is the predicted percentage change in savings when personal disposable income increases by 1%?

b. Suppose we want to test whether or not there has been a structural shift due to the financial crisis that erupted in the fall of 2008. Consider a dummy variable d that assumes a value 0 before August 2008 and a value of 1 starting August 2008 onwards. Estimate: ln (Savings) = β0 + β1 ln (Income) + β2d + β3 In (Income) × d + ɛ. What is the predicted percentage change in savings when personal disposable income increases by 1% prior to August 2008? What is the predicted percentage change starting in August 2008 onward?

c. At the 5% significance level, conduct the partial F test to determine whether or not β2 and β3 are jointly significant. Has there been a structural shift?