Macro-Econometrics Assignment

This assignment is based on data in the Excel worksheet HW_Data_Period_10.xlsx, which is attached. The data set contain monthly observations on interest rates on various financial instruments from July 1954 to October 2017. This exercise uses three of these interest rates: tbill (interest rate on 3-month Treasury bills), r3 (interest rate on 3-year Treasury securities), and r10 (interest rate on 10-year Treasury securities). A subset of these data were used in the lecture to illustrate the Engle-Granger methodology. This exercise asks you to estimate an error-correction model using the Johansen approach.

(a) What is your prior about these interest rates based on an economic theory, such as the term structure of interest rates? Specifically, how many common trends would you expect? How many cointegrating vectors?

(b) Estimate the model using the Johansen methodology. I suggest that you order the variables as such: r10, r3, tbill. Use 12 lags in your model, and choose the cointegration option that allows for a constant in the cointegrating vector but NOT in the VAR. What sort of behavior are you eliminating by restricting the constant to the CV and not the VAR? What behavior is being captured by the constant in the CV?

(c) What are the eigenvalues associated with this model?

(d) Focusing first on the trace statistic, can you reject the null that there are "no cointegrating vectors"? Explain your answer. What would it mean for the behavior of the interest rates, if you could not reject the null hypothesis?

(e) Can you reject the null that there is "one or less cointegrating vectors"? What about the null that there are "two or less cointegrating vectors"? What would it mean for the behavior of interest rates, if you rejected the null that there is "two or less cointegrating vectors" in favor of the alternative of three cointegrating vectors?

(f) Do your results change if you use the max statistic?

(g) Suppose that we decide that there are TWO cointegrating vectors. Do the normalized coefficients (slopes and constants) make sense to you? Keep in mind that most software packages present the coefficients as if they were "picked off" the following representation: X + a*Y + b*Z = e(t). If that is the case, you will find it useful to rearrange them as follow: X = -a*Y + -b*Z + e(t).

(h) Analyze the adjustment coefficients. Which are significant from zero, and do they have the "right" sign? That is, do the adjustment coefficients make sense relative to your results in part (g)? Please be clear about matching up each adjustment coefficient with the appropriate coefficients in the estimated cointegration equations.

Attachment:- Assignment Files.rar