Macroeconometrics Assignment: ARMA Applications and Introduction to VARs

Solve all the problems that follow in a single Stata .do file called HW6CONTROL. You should submit this .do file, only, as your solutions to this homework.

1. The dataset HW6.dta contains the same data as for the midterm exam: ap1 (the average product of labor in the US); u (the level of unemployment in the US); 1f (the level of the labor force in the US); v (the level of vacancies in the US)¡ and quarcer (a time variable).

(a) Use the ac command to generate an autocorelation graph for the natural logarithm of u, which you shoul create and call 1ogu¡ call this graph ac1ogu and use the rep1ace and nodrau commands. Do the same using the pac command and naming the graph pac1ogu. Then, use the graph combine command to generate a combined graph with pac1ogu on the left-hand side and ac1ogu on the right-hand side. Call this last graph combineu1. Write down in your Stata code as comments your conclusions about stationarity. Explain your reasoning.

(b) Repeat part (a) but now for the growth rate of u, which you should create and name d1ogu (i.e., the first difference of 1ogu). Call the autocorrelations graph acd1ogu, the partial autocorrelations graph pacd1ogu, and the combined graph combineu2. (Write down in your Stata code as comments your conclusions about stationarity. Explain your reasoning.)

(c) Repeat part (a) but now for the cyclical component of the natural logarithm of u, which you should create and name C1ogu using an HP filter with smoothing parameter equal to 1600. Call the autocorrelations graph acC1ogu, the partial autocorrelations graph pacC1ogu, and the combined graph combineu3. (Write down in your Stata code as comments your conclusions about stationarity. Explain your reasoning.)

(d) Repeat part (c) but now using an HP filter with smoothing parameter equal to 1O5. Call the cyclical component C21ogu. Call the autocorrelations graph acC21ogu, the partial autocorrelations graph pacC21ogu, and the combined graph combineu4. (Write down in your Stata code as comments your conclusions about stationarity. Explain your reasoning.)

(e) Consider modeling 1ogu, d1ogu, C1ogu, and C21ogu as ARMA processes using the Box Jenkins approach. What would be your choice of starting order for each of these processes given your results in (a), (b), (c), and (d)? Write down in your Stata code your conclusions as comments and explain your reasoning.

(f) Model (i.e., write Stata code for) d1ogu and C1ogu as ARMA processes. For each of these variable use all the steps of the Box Jenkins approach, and control for ARCH and GARCH, modifying the specifications as needed for heteroskedasticity. Write down in your Stata code as comments your justification for each step that you take. Finally, given your preferred bottom-line specification for each process, decide which you would prefer to use. Please explain your reasoning as comments in your Stata code.

2. Model (i.e., write Stata code for) d1ogu and C1ogu using Stata‘s suite of VAR commands. The steps are: selecting an optimal lag order, checking for stability, etc. Write down using comments in your Stata code a justification for each of the steps that you take. You will now have 4 specifications for these variables: 2 from problem 1, and 2 from problem 2. Which of these would be your preferred specification? Explain your reasoning as comments in your Stata code.

3. Generate impulse response functions to a 1-unit shock for 30 periods for each of the 4 specifications you‘ve arrived at through problem 2 and plot each of these impulse responses in a single graph (i.e., 4 graphs total, all in a single graph). Also, generate one-step-ahead predictions for each of the 4 specifications you‘re arrived at and plot each of these predictions along with the empirical data series that each of these corresponds to in a single graph (i.e., 4 graphs total, all in a single graph). Write down in your Stata code as comments a description of what you observe in each of the impulse response function graphs and elaborate on the extent to which they differ. Do the same for the graphs pertaining to the one-step-ahead predictions. Also, please comment on the following: do the IRF and one-step-ahead predictions change in any way your conclusions about a preferred specification relative to problem (2)?

Attachment:- hw6.rar