I am a newcomer to Dynare and I am studying how to specify the variance and covariance of exogenous variables in a model. Dynare Reference Manual provides two ways of specifying the covariance/correlation of two exogenous variables as follows.
var VARIABLE_NAME, VARIABLE_NAME = EXPRESSION;
corr VARIABLE_NAME, VARIABLE_NAME = EXPRESSION;
Accordingly, I tried to replace
var e, u = phi0.0090.009;
in Example1.mod from Resources | Dynare with
corr e, u = phi;
While the variance-covariance matrix M_.Sigma_e of the shocks is the same under the two specifications, the matrix M_.Correlation_matrix are different. Under the first specification, M_.Correlation_matrix is the 2-by-2 identity matrix, while under the second specification, it is [1 phi; phi 1]. I am wondering what exactly M_.Correlation_matrix is. More generally, what are the differences between the two specifications?