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Q5. (10 points) Consider the following two models that relate personal consumption (C), savings (S) and disposable personal income (Y): Model 1: St = [30 + [3119+ ut; Model 2: C, = a0 + alYf + at. Using the US annual data for 19701995, we estimate the rst model (savings function) as E. =62.42 + 0. 0376 11; (12.76) (0.0042) standard errors of the estimated coefcients are given in parentheses. Note that C. = Yr St and the true coefcients in Model 2 are linear functions of the coefcients in Model 1. By replacing S, in Model 1 with Y. C. and rearranging the terms, we get YrC; = 0+ lYt'l' u, or Cr = o + (1 [31)Yr 11;. By matching this model to Model 2, we can see that do = o and (11 = 1131. Question. Use the estimated coefcients for [30 and [31 from the savings function to construct estimators of a0 and a1. Report a; and 6]\" and derive their standard errors