Estimating general equilibrium models: an application with labour market frictions

This handbook shows how to set up, approximate, and estimate a standard real business cycle model enriched with labour market frictions. The structural equations of the model are derived by maximizing the agents’ objective function subject to the structure of the economy. Given the complexity of the resulting equations, we show how to approximate the model around its long-run equilibrium. We then use the approximated equations to take the model to the data and estimate it using Bayesian techniques. To perform the analysis we use a simple real business cycle model for two reasons. First, due to its simplicity, we can primarily focus on the modelling and estimation techniques; second, this simple framework constitutes the backbone model on which central banks build microfounded models to support the policy analysis. A series of forthcoming Handbooks will document how to enrich this simple framework. To motivate the exercise we start from recent empirical evidence suggesting that a positive technology shock leads to a decline in labour inputs. The standard real business model fails to account for this empirical regularity. The question we analyze in this handbook is whether the presence of labour market frictions addresses this problem, without otherwise altering the functioning of the standard model. To this end, we develop and estimate a real business cycle model using Bayesian techniques that allows, but does not require, labour market frictions to generate a negative response of employment to a technology shock. The results of the estimation support the hypothesis that labour market frictions are the factor responsible for the negative response of employment. Given the pedagogical nature of this handbook, we provide documentation of the MATLAB codes used to implement the modelling and estimation techniques described. To make the programming simple, we used Dynare version 3. We thank Michel Juillard for making his routines publicly available.