A Note on Error Correction Mechanisms and Steady-State Error
where x* is the exogenous desired value of xt and A(L) is a rational polynomial in the lag operator. Here xt is any variable which responds to disequilibria in the manner of equation (i). Part of Salmon's interest is in the steady-state error e" = X*8-x88, where x*8 follows a dynamic equilibrium path: his analysis emphasises that this error depends both on the nature of this path and on the adjustment polynomial A(L). Defining the type of (i) to be the number of unit denominator roots in A(L), he obtains the simple result that an error correction model of type s is required to guarantee a zero steady-state error when x*8 is following a polynomial of degree s I; this has recently been interpreted in terms of growth coefficients by Patterson and Ryding (I984). Because Salmon employs z-transforms his paper is not readily accessible to many economists, but we analyse the problem in the familiar terms of linear difference equations. Since Section I shows that Salmon's condition is necessary but not sufficient, this part of the note serves both to complement and to complete his study; although growth coefficients are not pursued here, it should be noted that Patterson and Ryding also overlook the stability requirement for their analysis. The extension to stochastic models in Section II is straightforward, and the results of Kloek (I984) for this case are seen to be essentially those obtained by Salmon. Our final section discusses the representation appropriate for these models.