Testing Nowcast Monotonicity with Estimated Factors

This paper proposes a test to determine whether ‘big data’ nowcasting methods, which have become an important tool to many public and private institutions, are monotonically improving as new information becomes available. The test is the first to formalise existing evaluation procedures from the nowcasting literature. We place particular emphasis on models involving estimated factors, since factor-based methods are a leading case in the high-dimensional empirical nowcasting literature, although our test is still applicable to small-dimensional set-ups like bridge equations and MIDAS models. Our approach extends a recent methodology for testing many moment inequalities to the case of nowcast monotonicity testing, which allows the number of inequalities to grow with the sample size. We provide results showing the conditions under which both parameter estimation error and factor estimation error can be accommodated in this high dimensional setting when using the pseudo out-of-sample approach. The finite sample performance of our test is illustrated using a wide range of Monte Carlo simulations, and we conclude with an empirical application of nowcasting U.S. real gross domestic product (GDP) growth and five GDP sub-components. Our test results confirm monotonicity for all but one sub-component (government spending), suggesting that the factor-augmented model may be misspecified for this GDP constituent.

本文提出一种检验方法，以研判如今已成为众多公共与私营机构重要工具的大数据实时预测（nowcasting）方法，能否随着新信息的获取而实现单调提升。该检验首次将现有实时预测文献中的评估流程进行形式化处理。鉴于基于因子的方法是高维实证实时预测文献中的主流方法，我们尤其关注包含估计因子的模型，尽管本检验同样适用于桥梁方程与混合数据抽样（MIDAS）模型这类低维设定场景。我们的方法将近期用于检验多矩不等式的方法论拓展至实时预测单调性检验场景，该场景允许不等式的数量随样本量增大而增加。我们给出了相关结论，阐明了在使用伪样本外方法时，该高维设定下可同时容纳参数估计误差与因子估计误差的条件。我们通过大量蒙特卡洛模拟实验展示了所提检验的有限样本表现，并以美国实际国内生产总值（GDP）增速及GDP五大分项的实时预测作为实证应用案例完成全文收尾。检验结果显示，除政府支出分项外其余分项均满足单调性，这表明针对该GDP分项的因子增强模型可能存在设定偏误。