A Score-Driven Filter for Causal Regression Models with Time- Varying Parameters and Endogenous Regressors

This paper proposes a score-driven model for filtering time-varying causal parameters through the use of instrumental variables. In the presence of suitable instruments, we show that we can uncover dynamic causal relations between variables, even in the presence of regressor endogeneity which may arise as a result of simultaneity, omitted variables, or measurement errors. Due to the observation-driven nature of score models, the filtering method is simple and practical to implement. We establish the asymptotic properties of the maximum likelihood estimator and show that the instrumental-variable score-driven filter converges to the unique unknown causal path of the true parameter. We further analyze the finite sample properties of the filtered causal parameter in a comprehensive Monte Carlo exercise. Finally, we reveal the empirical relevance of this method in an application to aggregate consumption in macroeconomic data.