Use the data in Exercise 9.37 to answer these questions:

a. Estimate the simple regression model with spending as the dependent variable and income as the explanatory variable.

b. Estimate the equation Y = α + βX + ε, where Y is income and X is the year. Use your estimates to calculate the predicted value of income each year, Y_ = a+bX. The residuals Y −Y_ are the detrended values of income.

c. Repeat the procedure in question b using spending as the dependent variable.

d. Estimate a consumption function where the dependent variable is detrended spending and the explanatory variable is detrended income.

e. Identify any important differences between your answers to questions a and d.

Exercise 9.37

Consider the hypothetical income and spending data in Table 9.14.

a. Identify any important differences in the patterns in these data compared to the data in Table 9.3.

b. Estimate the simple regression model with spending as the dependent variable and income as the explanatory variable.

c. Calculate the annual percentage changes in income and spending and estimate the simple regression model with the percentage change in spending as the dependent variable and the percentage change in income as the explanatory variable.

d. Identify any important differences between your answers to questions b and c.

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Table 9.14: Exercise 9.37 Hypothetical Income Hypothetical Spending 1929 100 90 1930 110 99 1931 121 107 1932 129 118 1933 132 115 1934 140 126 1935 148 135 1936 162 142 1937 173 151 1938 179 163 1939 194 169 1940 200 182