1. According to the real business cycle theory, productivity shocks are an important source of business cycles. Using the Cobb–Douglas production function (for example, Eq. 3.2, p. 62) and annual data since 1961, calculate and graph U.S. total factor productivity. Use real GDP for Y, the capital stock from the source listed in Table 3.1 for K, and civilian employment for N. Look for periods marked by sharp changes up or down in productivity. How well do these changes match up with the dates of business cycle peaks and troughs? (See Chapter 8.)