The dataset "US macro data".xls contains quarterly time series data for the US for the period Q1 2002 to Q4 2018. Here Q1 20xx stands for the first quarter of the year 20xx, and so on. The variables are: Year: 20xx Quarter: 1 to 4 lgdp: logarithm of US Real Gross Domestic Product, Billions of Chained 2012 Dollars, Quarterly, Not Seasonally Adjusted lcons: logarithm of US Real Personal Consumption Expenditures, Billions of Chained 2012 Dollars, Quarterly, Not Seasonally Adjusted (Source: Federal Reserve Bank of St Louis) (a) In taking logarithms of output and consumption, a Federal Reserve economist Anne wrote: "For several reasons, taking logarithms of macroeconomic aggregates is a good idea. First, it makes the distributions much closer to the normal distribution, and hence t and Fstatistics are better applicable. Second, a loglog regression allows interpreting the regression coefficient as an elasticity, which is a very useful and intuitive concept in economics and allied disciplines. Even a regression where the dependent variable is in logarithms but the regressor is not provides interpretation in terms of growth rates. Third, and finally, first difference in logarithms is very close to growth rates, and this offers nice interpretation as well." Critically discuss the above statement. (b) It is commonly thought that, because of Christmas and holiday spending, 4th quarter consumption expenditure is higher than the first three quarters. Evaluate the validity of the statement on the given data, using analysis of variance. Clearly state your assumptions, null and alternate hypotheses, test statistics and sampling distributions. Discuss the results fully. (c) Conduct regression analysis to evaluate the same statement as in (b). Discuss the dummy variable bias in this context. Are your findings similar to (b) or different? Fully discuss. Based on the estimated model, what are the average log real consumptions in Q1 and Q4? (d) Another Fed economist Bob thinks that the results in (b) and (c) could be misleading because of omitted variables. Surely, he argues, income (gdp) should be related to consumption. Regress lcons on lgdp and quarterly dummies to evaluate the hypotheses in (b) and (d). Fully discuss your findings.

What do your results suggest about consumption varying by quarter? What can you say about Bob's suggestion of omitted variable bias in (c)? (e) The above findings are presented to a senior Fed manager Carol. She is very worried about the high 2, arguing that there may be common trends in income and consumption which can then invalidate the findings in (b), (c) and (d). She suggests taking growth rates of consumption and income (year-on- year differences in lcons and lgdp) and reconducting the analysis. Follow her suggestions and estimate the model. Fully discuss your findings. Which is your preferred model and why? Hint: Construct growth rate variables = 4 = 4