Poor identification of individual impulse response coefficients does not necessarily mean that an impulse response is imprecisely estimated. This paper introduces a three-pronged approach on how to communicate uncertainty of impulse response estimates: (1) withWald tests of joint significance; (2)...

A covariance-stationary vector of variables has a Wold representation whose coefficients can be semiparametrically estimated by local projections (Jordà, 2005). Substituting the Wold representations for variables in model expressions generates restrictions that can be used by the method of...

This paper investigates the finite sample properties of confidence intervals for structural vector error correction models (SVECMs) with long-run identifying restrictions on the impulse response functions. The simulation study compares methods that are frequently used in applied SVECM studies...

A path forecast refers to the sequence of forecasts 1 to H periods into the future. A summary of the range of possible paths the predicted variable may follow for a given confidence level requires construction of simultaneous confidence regions that adjust for any covariance between the elements...

We introduce a new hybrid approach to joint estimation of Value at Risk (VaR) and Expected Shortfall (ES) for high quantiles of return distributions. We investigate the relative performance of VaR and ES models using daily returns for sixteen stock market indices (eight from developed and eight...

A covariance-stationary vector of variables has a Wold representation whose coefficients can be semi-parametrically estimated by local projections (Jordà, 2005). Substituting the Wold representations for variables in model expressions generates restrictions that can be used by the method of...

Measuring and displaying uncertainty around path-forecasts, i.e. forecasts made in period T about the expected trajectory of a random variable in periods T+1 to T+H is a key ingredient for decision making under uncertainty. The probabilistic assessment about the set of possible trajectories that...

In many countries the demand for health care services is of increasing importance. Especially in the industrialized world with a changing demographic structure social insurances and politics face real challenges. Reliable predictors of those demand functions will therefore become invaluable...

Real-time estimates of output gaps and inflation trends differ from the values that are obtained using data available long after the event. Part of the problem is that the data on which the real-time estimates are based is subsequently revised. We show that vector-autoregressive models of data...

Many questions of economic interest in structural VAR analysis involve estimates of multiple impulse response functions. Other questions relate to the shape of a given impulse response function. Answering these questions requires joint inference about sets of structural impulse responses,...