Solving Linear Difference Systems with Lagged Expectations by a Method of Undetermined Coefficients

This paper proposes a solution method to solve linear di§erence models with lagged expectationsin the form of AEtSt+1 +PNi=1iEtiSt+1= BSt +PNi=1iEtiSt+ CZt; where N is the order of lagged expectations. Variables with lagged expectations expand the modelís state space greatly when N is large; and getting the system into a canonical form solvable by the traditional methods involves substantial manual work (e.g., arranging the state vector St and the associated coe¢ cient matrices to accommodate EtiSt, i = 1; 2; :::; N), which is prone to human errors. Our method avoids the need of expanding the state space of the system and shifts the burden of analysis from the individual economist/model solver toward the computer. Hence it can be a very useful tool in practice, especially in testing and estimating economics models with a high order of lagged expectations. Examples are provided to demonstrate the usefulness of the method. We also discuss the implications of lagged expectations on the equilibrium properties of indeterminate DSGE models, such as the serial correlation properties of sunspots shocks in these models.