Estimating Multi-Equational Lqac Models with I(1) Variables : A VAR Approach

This paper extends the existing literature on linear quadratic adjustment cost (LQAC) models under rational expectations to the inferential issues arising when: (i) agents optimise with respect to a vector of endogenous variables; (ii) the behavioural equations stemming from the agent's optimisation problem are specified as 'exact' rational expectations models; (iii) the stochastic processes involved are integrated of order one. We discuss estimation both in a 'limited-information' and in a 'full-information' framework. In the first case we show that consistent estimation of the structural parameters may be achieved by focusing on the open-form solution to the model, and implementing existing procedures. In the second case, by focusing on the unique and stable forward-looking solution to the model, we propose a likelihood-based inferential procedure in time domain. The key assumption is that agents form expectations through a cointegrated vector autoregression (CVAR) system representing the joint data generation process for both the endogenous and exogenous variables