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Abstract

In this paper, we propose a simple approach to estimate impulse response function through smoothed local projections, thereby utilizing the flexibility of local projections, while creating smooth and economically plausible impulse response functions as provided by VARs. The approach allows to determine the appropriate degree of smoothing endogenously through a standard information criterion. This also avoids oversmoothing and provides an estimator that is generally more efficient than standard local projections.

Abstract

The importance of expectations in modern macroeconomic models and in particular of policy makers expectations for forward looking policy rules has generated a lot of interest in time series of professional forecasts (including central bank staff forecasts). This has spawned a large literature on the evaluation of forecasts that are not model based or where the model is unknown. Although, the available time series of historical forecasts are typically short, this literature has so far mostly disregarded the small sample properties of the proposed tests and estimators. In this paper we fill this gap in the literature, focusing on a set of recently proposed rationality tests for unstable environments. Using a Monte Carlo study we demonstrate that the asymptotic tests are substantially oversized in finite samples including any sample size that is practically available. We provide finite sample adjusted critical values, that allow those tests to be properly applied to sample sizes of typically available forecasts such as the Survey of Professional Forecasters, the Federal Open Market Committee. The critical values we provide will help to avoid false rejections using those data.