Consider the dividends and profits time series given in the U.S. economic time series data posted on the book’s website. Since dividends depend on profits, consider the following simple model:

LDIVIDENDS_t = β₁ + β₂LCP + u_t

a. Would you expect this regression to suffer from the spurious regression phenomenon? Why?

b. Are the logged Dividends and logged Profits time series cointegrated? How do you test for this explicitly? If, after testing, you find that they are cointegrated, would your answer in (a) change?

c. Employ the error correction mechanism (ECM) to study the short- and long-run behavior of dividends in relation to profits.

d. If you examine the LDIVIDENDS and LCP series individually, do they exhibit stochastic or deterministic trends? What tests do you use?

e. Assume LDIVIDENDS and LCP are cointegrated. Then, instead of regressing dividends on profits, you regress profits on dividends. Is such a regression valid?