Understanding Multi‐horizon Forecasts: Identification, Estimation and Testing

The properties of multi‐horizon forecasts are investigated by specifying and estimating a model nesting rational forecasts, as well as deviations from rationality resulting from horizon‐specific biases and idiosyncratic errors. Identification of the model's parameters is achieved by combining information on forecasts for a given point in time with different information sets, and forecasts at different points in time based on the same information set. Both sets of forecasts are used to estimate the model's parameters by generalised method of moments. A test of rationality is proposed with the twin advantages of circumventing parameter identification and boundary issues. The finite sample properties of the GMM estimator and the rationality test are also investigated. Applying the approach to US GDP growth forecasts of the Survey of Professional Forecasters, the empirical results show that forecasts deviate from rationality over all forecast horizons, with the strength of the deviations from rationality increasing with the forecast horizon.