B. Time Series Regression (50 points) One version of the permanent income hypothesis (PIH) of consumption is that the growth in consumption is unpredictable. Let gc₁ = log(ct) – log(ct-1) be the growth in real per capita consumption (of non-durable goods and services). Then the PIH implies that E[gct | It-1] E[gc], where It-1 denotes information known at time t - 1 (e.g., gc₁, ..., gc₁-1); in this case, t denotes a year. Use the data in CONSUMP.csv to answer the questions below. = (a) (5 points) Compute the first five autocorrelations of gc₁. (b) (8 points) Test the PIH by estimating gc₁ = Bo + B₁gc₁_1 + ut (2 points).¹ Clearly state the null and alternative hypotheses (4 points). What do you conclude (2 points)? (c) (7 points) Estimate AR(p) models for p = 1, ..., 5 and report regression results (5 points). What lag length is chosen by the BIC (1 point)? What lag length is chosen by the AIC (1 point)? (d) (12 points) Add variables gyt-1, 13t-1, and inft-1 to the AR model you chose in (c) by BIC.2 Report the new regression results (4 points). Are these new variables individually or jointly significant at the 5% level (8 points)? (e) (6 points) For the regression in (d), what happens to the p-value for the t-statistic on gct-1 (2 points)? Does this mean the PIH hypothesis is now supported by the data (1 point)? Explain your answer (3 points). (f) (7 points) For the regression in (d), what is the F-statistic and its associated p-value for joint significance of the four explanatory variables (3 points)? Does your conclusion about the PIH now agree with what you found in (b) (1 point)? Explain your answer (3 points). (g) (5 points) Explain what is the meaning of stationarity (3 points) and do we need to worry about it in this question? (2 points).