A researcher tells you s/he ran a regression estimating the following relationship for the inflation rate : T=Bot Bit+Bet2 tn S/he found that: 3o = -0.5; 3 = 0.7; and 3 Bo = 0.6. Does these estimates make sense in characterizing the behavior of inflation? To check, please find the equation's homogeneous solution using the researcher's parameter estimates (please show your work), and also set up a Stata do file called "HWProblem3" that does the following. Sets observations equal to 280. Implements a seed equal to 1. Generates the estimated process for inflation assuming that T = 0.02, 72 = 0.02, and thereafter follows the noted difference equation with parameter estimates and a disturbance term that has mean zero and standard deviation equal to 0.001 (note that the first two inflation observations will be equal to the Federal Reserve's target of 2 percent). Please graph your results. With your homogeneous equation's solution in hand as well as your graph, the last step is to argue intuitively why or why not the estimated process makes sense.