Shrinkage for Vector Autoregressions and Impulse Response Estimation

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The core of Macroeconomic policy analysis is understanding the impact of unexpected events, news, and variation on core economic variables including GDP, inflation, wages, investment, and employment. Applied macroeconomic research focuses on estimation of these impacts known as "impulse response functions". Current estimation methods are less precise than desirable, and are difficult to implement with a large number of variables. This project develops new methods which produce sharper and more precise estimates of these effects, allowing for more precise understanding of the macro economy and economic policy. The methods are based on combination (or ensembles) of simpler methods. The new method can be much more precise than existing simpler methods.This project explores impulse response function (IRF) estimation in vector auto-regressions (VARs) by model combination. Estimates from lower-dimensional models (VARs and ARs of lower order) will be combined by standard model averaging methods. The IRF is a non-linear function of the VAR coefficients. The investigator develops a large-sample (asymptotic) approximation to the distribution of the combination IRF. Using this asymptotic approximation, this research calculates the approximate mean-squared error (MSE) of the combination IRF, and shows how to estimate the MSE using an appropriate information criterion which is similar to a Mallows criterion or Focused information criterion. The combination weights can then be selected to minimize this criterion function, resulting in a practical combination estimator. The goal of the project is to study the statistical properties of this combination method and extend its application to high dimensional contexts.