Regression models that describe macroeconomic properties in the United States often have to deal with large amounts of collinearity. For example, suppose we want to use as explanatory variables the...

Regression models that describe macroeconomic properties in the United States often have to deal with large amounts of collinearity. For example, suppose we want to use as explanatory variables the disposable income and the amount of household credit debt. Because the economy in the United States continues to grow, both of these variables grow as well. Here’s a scatterplot of quarterly data, from 1960 through 2011. Both are measured in billions of dollars. Disposable income is in red and credit debt is green.

(a) This plot shows timeplots of the two series. Do you think that they are correlated? Estimate the correlation.

(b) If the variables are expressed on a log scale, will the transformation to logs increase, decrease, or not affect the correlation between these series?

(c) If both variables are used as explanatory variables in a multiple regression, will you be able to separate the two?

(d) You’re trying to build a model to predict how changes in the macroeconomy will affect consumer demand. You’ve got sales of your firm over time as the response. Suggest an approach to using the information in both of these series in a multiple regression that avoids some of the effects of collinearity.