Consider the following vector autoregressive model

(7.95)

where yt is a p × 1 vector of variables determined by k lags of all p variables in the system, ut is a p× 1 vector of error terms, β0 is a p× 1 vector of constant term coefficients and βi are p × p matrices of coefficients on the ith lag of y.

(a) If p = 2, and k = 3, write out all the equations of the VAR in full, carefully defining any new notation you use that is not given in the question.

(b) Why have VARs become popular for application in economics and finance, relative to structural models derived from some underlying theory?

(c) Discuss any weaknesses you perceive in the VAR approach to econometric modelling.

(d) Two researchers, using the same set of data but working independently, arrive at different lag lengths for the VAR equation (7.95). Describe and evaluate two methods for determining which of the lag lengths is more appropriate.