FILE The savings rate has declined dramatically over the past few decades (CNNMoney.com, June 30, 2010). While some economists are extremely concerned about this decline, others believe that it is a nonissue. Consider the following monthly data on the personal savings rate (Savings) and the personal disposable income (Income) in the U.S. from January 2007 to November 2010; the complete data set, labeled Savings Rate, can be found on the text website.

Date Savings (%) Income ($ billions)

2007–01 2.2 10198.2 2007–02 2.3 10252.9

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2010–11 5.5 11511.9 S OURCE: Bureau o f Economic Analysis.

a. Estimate and interpret a log-log model, In (Savings) =

β 0 + β1 In (Income) + ε . 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: In (Savings) =

β 0 + β1 In (Income) + β 2d + β 3 In (Income) × d + ε .

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 Ftest to determine whether or not β 2 and β 3 are jo in tly significant. Has there been a structural shift?