Macro-Econometrics Assignment -

This assignment is based on the data in the Excel worksheet HW_Data_Period_9.xlsx, which is attached. The data set contains 100 observations for three simulated data series - W, Z and Y - used in the text and illustrated in the lecture.

(a) The data are plotted in Figure 6.2. The data do not appear to be stationary. Based on what you see in the plots, what sort of non-stationary model(s) would you consider as possible candidates - trend stationary, unit root with drift, or unit root without drift?

(b) Conduct an augmented Dickey-Fuller test (as below) for each variable, using lag lengths (p) of 0 (no lags) and 4 (four lags). Report your results for the γs in a short table. What do you conclude?

Δy_t = α₀ + γy_t-1 + _i=1∑^p β_iΔy_t-1

Now, impose the null of a unit root and test for the significance of the constant. What are your results? Finally, re-test for a unit root but do not include a constant. What are your results? Do they match with your assessments in (a)?

(c) Estimate the following long-run cointegrating relationships (estimated separately):

y_t = α₀ + β₁z_t + β₂w_t + e_yt

z_t = α₀ + β₁y_t + β₂w_t + e_zt

w_t = α₀ + β₁y_t + β₂z_t + e_wt

Report your results for the βs in a table, along with the t-statistics. Why can't you conduct inference using these t-statistics?

(d) Using the 3 sets of residuals from part (c), test for stationarity (you do not need to report your results). Why can't we use the usual DF tables to make inferences about stationarity? Which table is appropriate for finding the correct critical values? Using a 5% critical value, what is the correct critical value? What do you conclude?

(e) Now, estimate an error correction model using the error-term from the 1^st equation in part (c) and 1 lag of Δy, Δz, and Δw. The easiest way to do this is estimate a VAR model, and enter the equilibrium errors as "exogenous variables". Remember to lag them! Present your results for the adjustment coefficients in a concise table with coefficient estimates and t-statistics. Which error-correction coefficients are statistically different from zero? What critical value did you use? Are there any pitfalls in using that critical value?

(f) Are the estimated error-correction coefficients consistent with LR convergence to your estimated cointegration vectors in (c)? Why or why not? Please be specific in your answer by carefully matching up the adjustment coefficients with the appropriate coefficients in the LR relationship that you estimated in part (c).

Attachment:- Data Set.rar