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Data for this exercise are available on the textbook website under the link for Chapter 9( Before starting the exercise, please review the relevant portions of the Guide to Working with Economic Data, including sections G.1-G.5, G.10-G.14, and G.16. Please remember that for this question you must provide a (1) Table (2) Graph (3)a comprehensive written answer that is a minimum of 500 words.

1. Detrend quaterly data for labor productivity in the United States from 1948 to the present(use the Bureau of Labor Statistics productivity index; see the Guide, section G.12, on detrending data. Explain your choice of detrending method.)
(a) Before attempting any data analysis, think about the business cycle using the models of this chapter. Explain how you might expect labor productivity to vary with the business cycle(e.g., do you expect productivity to be a leading, lagging, or coincident indicator; pro-cyclical or countercyclical?). State your reasoning carefully.
(b) Plot detrended labor productivity and indicate NBER recession dates using shading.
(c) Create a graph showing the typical cyclical behavior of labor productivity. First identify the segment of the data that run from 8 quarters before to 16 quarters after each of the last seven business-cycle peaks(excluding the most recent if there are not enough data). Convert each segment into an index taking the value 100 at the business-cycle peak. Average across all seven cycles. Plot the resulting series on a vertical axis against the values -8, -7,....,0,1,2,....16(horizontal axis) - that is, aginst the number of quaerters after the peak. ( Your graph should be similar to Figure 5.8 and 5.9.)
(d) Based on your graphs, is there a clear cyclical pattern of either productivity series? comment on the nature of the pattern. How well do these patterns agree with those you hypothesized in (a)? What might account for the differences between your expectations and the data?

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