4. Solve the linearized version of the model for the of model’s recursive law motion. - recursive law of motion gives the values of the variables determined in the model conditional on past values and the values of exogenous variables. 5. Simulations: calculate impulse responses and moments (variances and correlations). - impulse? a shock (change in a parameter or exogenous variable) - impulse response? dynamic response of the model’s endogenous variables to the shock. Describes their adjustment to the shock. - moments? moments of the variables. model’s endogenous - how variable are they? how are they correlated? - interest? how do these moments compare to moments in data for real-world economies? - We want to illustrate the procedure with an example. A Simple Model from Uhlig: Growth Model with Optimization - Uhlig sets this up as a planner’s problem (pp. 6-10). - Fundamental theorems of welfare economics: planners solution can be achieved by a competitive equilibrium. (Uhlig shows this for this model: pp. 11-12) - Notation: C consumption; K capital; N labour; Y output; F – – – – – production function; Z factor; –productivity random productivity shock variable.  – - The model uses specific forms for the utility function and the production function. This is necessary if the model is to be used in simulations.
4. Solve the linearized version of the model for the model’s recursive law of motion. - recursive law of motion gives the values of the variables determined in the model conditional on past values and the values of exogenous variables. 5. Simulations: calculate impulse responses and moments (variances and correlations). - impulse? a shock (change in a parameter or exogenous variable) - impulse response? dynamic response of the model’s endogenous variables to the shock. Describes their adjustment to the shock. - moments? moments of the model’s endogenous variables. - how variable are they? how are they correlated? - interest? how do these moments compare to moments in data for real-world economies? - We want to illustrate the procedure with an example. A Simple Model from Uhlig: Growth Model with Optimization - Uhlig sets this up as a planner’s problem (pp. 6-10). - Fundamental theorems of welfare economics: planners solution can be achieved by a competitive equilibrium. (Uhlig shows this for this model: pp. 11-12) - Notation: C – consumption; K – capital; N – labour; Y – output; F – production function; Z –productivity factor;  – random productivity shock variable. - The model uses specific forms for the utility function and the production function. This is necessary if the model is to be used in simulations.