a. Using observations on the change in consumption \(D C_{t}=C_{t}-C_{t-1}\) and the change in income \(D Y_{t}=\) \(Y_{t}-Y_{t-1}\) from 1959Q3 to 2015Q4, obtained from the data file cons_inc, estimate the following two models

b. Use each model estimated in part (a) to forecast consumption \(C\) in 2016Q1, 2016Q2, and 2016Q3.

c. Use the mean-square criterion \(\sum_{t=2016 Q 1}^{2016 Q}\left(\hat{C}_{t}-C_{t}\right)^{2}\) to compare the out-of-sample predictive ability of the two models.

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DC, 8+0,DC + 80DY, + DC, a+BoDY, + B3DY-3 +21 =