Estimation and Testing of Forecast Rationality with Many Moments

TL;DR

This paper introduces a P-GMM based method for estimating and testing forecast rationality that effectively handles invalid moments, improves efficiency, and enhances test power in high-dimensional settings, demonstrated through simulations and real data.

Contribution

It develops a P-GMM moment selection approach tailored for forecast rationality testing, allowing for invalid moments and improving estimation and testing accuracy.

Findings

P-GMM estimator performs comparably to the oracle estimator.

Reducing uninformative instruments increases test power.

Method effectively analyzes forecast rationality in real-world data.

Abstract

We in this paper utilize P-GMM (Cheng and Liao, 2015) moment selection procedure to select valid and relevant moments for estimating and testing forecast rationality under the flexible loss proposed by Elliott et al. (2005). We motivate the moment selection in a large dimensional setting, explain the fundamental mechanism of P-GMM moment selection procedure, and elucidate how to implement it in the context of forecast rationality by allowing the existence of potentially invalid moment conditions. A set of Monte Carlo simulations is conducted to examine the finite sample performance of P-GMM estimation in integrating the information available in instruments into both the estimation and testing, and a real data analysis using data from the Survey of Professional Forecasters issued by the Federal Reserve Bank of Philadelphia is presented to further illustrate the practical value of the suggested methodology. The results indicate that the P-GMM post-selection estimator of forecaster's attitude is comparable to the oracle estimator by using the available information efficiently. The accompanying power of rationality and symmetry tests utilizing P-GMM estimation would be substantially increased through reducing the influence of uninformative instruments. When a forecast user estimates and tests for rationality of forecasts that have been produced by others such as Greenbook, P-GMM moment selection procedure can assist in achieving consistent and more efficient outcomes.