Title: Mixed causal-noncausal autoregressions with strictly exogenous regressors for structural expectations equations
Authors: Sean Telg - Maastricht University (Netherlands) [presenting]
Alain Hecq - Maastricht University (Netherlands)
Joao Victor Issler - Getulio Vargas Foundation (Brazil)
Abstract: Some authors have proposed mixed autoregressive causal-noncausal (MAR) models to estimate economic relationships involving expectations variables. Indeed, when linearly solved, those structural equations usually imply explosive roots in their autoregressive part but have stationary solutions when the future of the realized variable is considered instead. In previous work, possible exogenous variables in economic relationships are substituted into the error term and are assumed to follow an MAR process to ensure the MAR structure of the variable of interest. Following this procedure, one loses the impact of exogenous variables that are very important for understanding economic phenomena. For that reason, we instead consider a MARX representation which allows for the inclusion of strictly exogenous regressors. We develop the asymptotic distribution of the MARX parameters. We assume a Student's $t$-likelihood to develop closed form solutions of the corresponding standard errors. Remarkably, our method does not involve tedious numerical methods. By means of Monte Carlo simulations, we evaluate the merit of our approach as well as the accuracy of a model selection based on information criteria after estimating models by non-Gaussian MLE. Several present value specifications empirically illustrate our analysis.