2. [Excel Problem] Assuming log utility, the basic consumption Euler equa- tion can be written: If we take logs of this, and use the approximation that the natural log of one plus a small number is approximately the small number, then we can write this as: 9'": Z 951 _ 1115 In other words, the real interest rate ought to equal the expected growth rate of consumption minus the log of the discount factor. (a) For the period 1947 through 2015, download annual data on the GDP price deator (here), annual data on real consumption growth (here), and data on the the 3-Month Treasury Bill rate (here, this series is available at a higher frequency than annual, so to get it in annual terms, click \"edit graph\" and modify frequency to annual using the average method). The approximate real interest rate is n = 3'; Tiff\". Measure 2', by the 3-Month T-Bill rate and assume expected ination equals realized ination one period ahead (i.e. the interest rate observation in 1947 will be the 3-Month T-Bill in 1947, while you will use realized ination in 1948 for expected ination in 1947). Compute a series for the real interest rate. Plot this series. What is the average real interest rate? How often has it been negative? Has it been negative or positive recently? (b) What is the correlation between the real interest rate series you create 331 and expected consumption growth (i.e. compute the correlation between consumption growth in 1948:2015 and the real interest rate between 1947:2014)? Is the sign of this correlation qualitatively in line with the predictions of the Euler equation? Is this correlation strong