Macroeconometrics Problems
Macroeconometrics Module 7: Graded Homework Problems This homework has two problems, but you should only solve one of them: your choice, and I will grade the problem that you submit. Please clearly indicate in your submission which problem you are solving. VERY IMPORTANT: You should not submit more than one solved problem. If you submit more than one solved problem then your grade on the entire assignment will be zero. 1. The dataset HW6.dta contains the following data: apl (the average product of labor in the US); u (the level of unemployment in the US); lf (the level of the labor force in the US); v (the level of vacancies in the US); and quarter (a time variable). Create a .do …le called HW7Control.do that models vacancies and unemployment as a recursive VAR. You are free to use whatever version of the data you like: levels, log levels, growth rates, etc. There is no need for you to try multiple speci…cations nor justify why you chose a particular type of version of the data to model. Just make sure that all your i’s are dotted and all your t’s are crossed, by which I mean that you should carefully follow the procedures gone over in the last two Lessons to model VARs. In addition, you should thoroughly annotate your code explaining your reasoning behind any one procedure that you implement and your results. Finally, please have your code generate in a single graph the 4 possible orthogonalized impulse response functions that will emerge from your modeling and annotate in your code your interpretation of these results. 2. Consider a VAR with two variables: y1;t and y2;t . In particular, assume Yt = y1;t y2;t ; 1 = ; “t = 2 “1;t “2;t ; and 1 = 1;11 1;12 0 1;22 , where “t is white noise and the s and s are parameters. Assume that the VAR is stable and that the system begins in steady state. Then, in period 0, y2 is pushed out of steady state given a non-orthogonalized one-time one-unit shock to “2 . Amid this backdrop, what is the period-2 non-orthogonalized impulse response function for y1 equal to (in response to the shock to “2 )? Please show your work and explain your 1 reasoning with careful detail. Also, the impulse response function should be stated explicitly in terms of parameters, only. HINT: The VAR is Yt = + 1 Yt 1 + “t : In steady state “t = 0 in all periods t and Y is constant across periods. Therefore, Y= + 1Y ! Y ! (I2 1Y = !Y= 1) Y = I2 , 1 since the process is stable (we don’t need the lag operator because in steady state by de…nition Y is constant across periods). In any period before time 0 the system is happy, at rest, or in other words, in literally in steady state. In period 0, though, a one-unit shock hits “2 (therefore, “2 = 1) and “activates”the system so that IRF0 Y0 = + 1Y 1 + {z } | = + 1Y = + 1 I2 1 = + 1 I2 1 = II22 11 + I2 1 1 = I2I2 11 + I2 1 1 = I2 11 + I2 1 1 = I2 1 =Y 0 1 = Y+ 2 . 0 1
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