3.8 Estimation
Although it was theoretically possible to estimate the reduced form VAR model with five lags, the selection of lag length was restricted to between one and four, owing to difficulty in estimating a non-singular variance-covariance matrix. On the basis of both the Akaike Information criterion (AIC) and the Bayesian Information criterion (BIC), the sample evidence for the entire reduced form VAR system suggested a lag length of one. A series of sequential likelihood ratio tests for a shorter lag length versus a longer lag length, suggested a lag length of two. A lag length of one or two is quite short compared with other New Zealand VAR studies. For example, Evans and Wells (1985) chose a lag length of three and Conway (1998) a lag length of four. Moreover, there was evidence of serial correlation in some of the reduced form residuals, when the VAR was estimated using lags of both one and two.
Given these considerations, we estimated the reduced form VAR with three lags. This was done using Seemingly Unrelated Regression (SUR), rather than Ordinary Least Squares (OLS), owing to the inclusion of zero restrictions on some lagged variables (which results in inefficient OLS estimators when the residuals are correlated across equations). The Durbin H statistic suggested that the reduced form VAR with three lags was absent of serial correlation.
The contemporaneous matrix, 
, was estimated using maximum likelihood. Initial starting values for were found using the genetic algorithm. The estimates from the genetic algorithm were then used as starting values to find the final parameter estimates for using the Broyden, Fletcher, Goldfarb and Shanno (BFGS) algorithm. As part of the sensitivity analysis, the model was estimated over sample sub periods to test the robustness of coefficient estimates. The estimation results from different sub periods suggested the model was robust to changes in the sample period. Sensitivity analysis of the model to alternative identifying restrictions was also done.
