In order to employ vector autoregressions (VAR) for the analysis of causal relations between economic quantities - the underlying fundamental structure - researchers must overcome the omnipresent identification challenge. That means, the mutually uncorrelated structural shocks must be uncovered from the estimated reduced form residuals of the model. One possibility to achieve identification and to uncover structural innovations from the data is the use of statistical information extracted from time-varying volatility, which is present in many macroeconomic time series. This approach relies on a minimal set of identifying assumptions and is free of economically motivated restrictions. Chapters 1 and 2 of this dissertation concern model selection and inference in the context of models identified through time-varying volatility. Chapters 3 and 4 use this identification strategy to quantify the economic effects of different structural innovations and evaluate the compatibility of other identification approaches with the data. The first chapter, which is joint work with Helmut Lütkepohl, assesses the performance of information criteria and tests for residual heteroskedasticity for choosing between different models for time-varying volatility. Although it can be diffcult to find the true volatility model with the selection criteria, using them is recommended because they can reduce the mean squared error of impulse response estimates substantially relative to a model that is chosen arbitrarily based on the personal preferences of a researcher. Heteroskedasticity tests are found to be useful tools for deciding whether time-varying volatility is present but do not discriminate well between different types of volatility changes. The selection methods are illustrated by specifying a model for the global market for crude oil. The second chapter, resulting from joint work with Helmut Lütkepohl, reviews and compares different bootstrap methods and estimation techniques for inference for structural vector autoregressive models identified by generalized autoregressive conditional heteroskedasticity (GARCH) in a Monte Carlo study. Three bootstraps are considered: a wild bootstrap, a moving blocks bootstrap, and a GARCH residual based bootstrap. Estimation is done by Gaussian maximum likelihood, a simplified procedure based on univariate GARCH estimations and a method that does not re-estimate the GARCH parameters in each bootstrap replication. The latter estimation strategy is computationally more efficient than the other methods while still being competitive with the other estimation approaches and often leads to the smallest confidence sets without sacrificing coverage precision. An empirical model for assessing monetary policy in the US is considered as an example. The different inference methods for impulse responses lead to qualitatively very similar results. The third chapter, a single authored paper, assesses the interrelation of uncertainty and financial conditions and their impact on economic output in the US. Identification via heteroskedasticity offers a convincing alternative to conventional identification strategies in this context to uncover structural innovations because credible identifying assumptions based on economic mechanisms are hard to defend for the subject matter. Additionally, the use of the data-driven identification approach allows for formally testing linear restrictions imposed on structural parameters. This feature is employed to introduce a novel identification scheme using exclusion restrictions for different types of common uncertainty and financial shocks that is in line with the data. The causal dynamic analysis suggests that broad uncertainty shocks from different origins tighten financial conditions and the reverse is usually also true. Moreover, both, uncertainty and financial shocks are important drivers of real economic activity. However, quantitative effects depend on the specific type of uncertainty. The fourth chapter, based on joint work with Maximilian Podstawski and Malte Rieth, proposes a framework to combine identifying information from time-varying volatility and external instruments for the quantification of US monetary policy shocks. Exploiting both types of information is shown to sharpen structural inference, and allows for testing both the relevance and exogeneity condition of instruments. Moreover, the proposed framework alleviates weak instruments problem from the proxy-VAR approach. Building on this novel framework, surprise monetary contractions are documented to lead to a significant and medium-sized decline in economic activity. Models with external instrument neglecting the identifying information in heteroskedasticity are less effcient and tend to underestimate the effects of monetary policy.
