Vector Autoregression (VAR) models for stationary random variables are reduced form models. Structural interpretations of VAR models require restrictions on structural form models. When random variables are unit root nonstationary, Error Correction Models (ECM) are widely used. We argue that the standard ECMs are reduced form models just as VAR models are.
We consider a structural ECM with restrictions which are based on economic theory. In particular, we consider structural ECMs in which at least one variable adjusts slowly to its long-run equilibrium level, with a constant speed of adjustment. We discuss sufficient conditions under which the structural speed of adjustment coefficient is consistently estimated by standard estimation methods for ECMs. We show that these conditions are not satisfied by an exchange rate model with slow price adjustment. We then propose an instrumental variable (IV) method to estimate the structural speed of adjustment coefficient.
First, we perform a single equation method, where an IV method is applied to a slow adjustment equation. We obtain positive estimates for the structural speed of adjustment coefficient in most cases. Second we employ a system method, where Hansen and Sargent's method that applies GMM to linear rational expectation models is combined with our single equation method. The speed of adjustment coefficient is estimated from a) the slow adjustment equation for the domestic price and b) the rational expectations equation for the exchange rate. We form a specification test by comparing the estimates for the speed of adjustment coefficient from these two equations.
So far we have assumed that the unbiased interest parity holds. As a first step towards combining risk premium models with the sticky price exchange rate model, we compare risk premium models nested in a generalized factor pricing model to discover which model is more consistent with the forward exchange rate data. With various instruments, the traditional CAPM usually fits the data better than the simple consumption CAPM. However, whether the CAPM or the habit formation model fits the data better depends on the choice of instruments.