am greatly indebted to Barbara Rossi for all the invaluable support, advice and encouragement I received. I would also like to thank M. Al-Sadoon for his great insights that led to major improvements of the present paper, and
Surveys of professional forecasters produce precise and timely point forecasts for key macroeconomic variables. However, the accompanying density forecasts are not as widely utilized, and there is no consensus about their quality. This is partly because such surveys are often conducted for "fixed events". For example, in each quarter panelists are asked to forecast output growth and inflation for the current calendar year and the next, implying that the forecast horizon changes with each survey round. The fixed-event nature limits the usefulness of survey density predictions for policymakers and market participants, who often wish to characterize uncertainty a fixed number of periods ahead ("fixed-horizon"). Is it possible to obtain fixed-horizon density forecasts using the available fixed-event ones? We propose a density combination approach that weights fixed-event density forecasts according to a uniformity of the probability integral transform criterion, aiming at obtaining a correctly calibrated fixed-horizon density forecast. Using data from the US Survey of Professional Forecasters, we show that our combination method produces competitive density forecasts relative to widely used alternatives based on historical forecast errors or Bayesian VARs. Thus, our proposed fixed-horizon predictive densities are a new and useful tool for researchers and policy makers.
In this paper we propose methods to construct confidence intervals for the bias of the two-stage least squares estimator, and the size distortion of the associated Wald test in instrumental variable models. Importantly our framework covers the local projections -instrumental variable model as well. Unlike tests for weak instruments, whose distributions are non-standard and depend on nuisance parameters that cannot be estimated consistently, the confidence intervals for the strength of identification are straightforward and computationally easy to calculate, as they are obtained from inverting a chi-squared distribution. Furthermore, they provide more information to researchers on instrument strength than the binary decision offered by tests.Monte Carlo simulations show that the confidence intervals have good small sample coverage.We illustrate the usefulness of the proposed methods to measure the strength of identification in two empirical situations: the estimation of the intertemporal elasticity of substitution in a linearized Euler equation, and government spending multipliers.
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