Different local projection (LP) estimators for structural impulse responses of proxy vector autoregressions are reviewed and compared algebraically and with respect to their small sample suitability for inference. Conditions for numerical equivalence and similarities of some estimators are...

A growing literature uses changes in residual volatility for identifying structural shocks in vector autoregressive (VAR) analysis. A number of different models for heteroskedasticity or conditional heteroskedasticity are proposed and used in applications in this context. This study reviews the...

This paper proposes a new non-parametric method of constructing joint confidence bands for impulse response functions of vector autoregressive models. The estimation uncertainty is captured by means of bootstrapping and the highest density region (HDR) approach is used to construct the bands. A...

A major challenge for proxy vector autoregressive analysis is the construction of a suitable external instrument variable or proxy for identifying a shock of interest. Some authors construct sophisticated proxies that account for the dating and size of the shock while other authors consider...

Johansen's reduced-rank maximum likelihood (ML) estimator for cointegration parameters in vector error correction models is known to produce occasional extreme outliers. Using a small monetary system and German data we illustrate the practical importance of this problem. We also consider an...

The literature on systems cointegration tests is reviewed and the various sets of assumptions for the asymptotic validity of the tests are compared within a general unifying framework. The comparison includes likelihood ratio tests, Lagrange multiplier and Wald type tests, lag augmentation...

In proxy vector autoregressive models, the structural shocks of interest are identified by an instrument. Although heteroskedasticity is occasionally allowed for, it is typically taken for granted that the impact effects of the structural shocks are time-invariant despite the change in their...

The cointegration revolution has had a substantial impact on applied analysis. The methods for conducting this analysis are sketched out, reminding the reader of the ideas underlying them and giving sufficient background for empirical work. The treatment can be used as a textbook for courses on...

We propose a new bootstrap for inference for impulse responses in structural vector autoregressive models identified with an external proxy variable. Simulations show that the new bootstrap provides confidence intervals for impulse responses which often have more precise coverage than and...

A major challenge for proxy vector autoregressive analysis is the construction of a suitable instrument variable for identifying a shock of interest. We propose a simple proxy that can be constructed whenever the dating and sign of particular shocks are known. It is shown that the proxy can lead...