202103 Aug

Understanding and Solving the Structural Vector Autoregressive Identification Problem

Summary

In this blog, we look closely at the identification problem posed by structural vector autoregressive models and its solution. Mathematically we can represent this in a two-equation system: This structural VAR model includes separate contemporaneous shocks to each variable, $\epsilon_{1,t}$ and $\epsilon_{2,t}$. To see this, lets combine the "shock" components of each equation such that we define: Now our two-equation system becomes becomes a reduced form VAR model: We can use OLS to estimate our unknown parameters in the reduced form VAR model However, the residuals from these estimates do not allow us to determine the impacts of the shocks $\epsilon_{1,t}$ and $\epsilon_{2,t}$ on $Y_1$ and $Y_2$. Recall my example earlier about, the economic theory of money neutrality and the implication that monetary policy has no long-run effects on output. and MSc in economics and engineering and has over 15 years combined industry and academic experience in data analysis and research.

Source: Aptech

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