ASYMPTOTIC DISTRIBUTIONS OF IMPULSE RESPONSES, STEP RESPONSES, AND VARIANCE DECOMPOSITIONS OF ESTIMATED LINEAR DYNAMIC-MODELS

Formulas are derived for computing asymptotic covariance matrices of sets of impulse responses, step responses, or variance decompositions of estimated dynamic simultaneous-equations models in vector autoregressive moving-average (VARMA) form. Computed covariances would be used to test linear restrictions on sets of impulse responses, step responses, or variance decompositions. The results unify and extend previous formulas to handle any model in VARMA form, provide accurate computations based on analytic derivatives, and provide insights into the structures of the asymptotic covariances.