Standard latent variable analysis in structural state space models decomposes latent variables into contributions of structural shocks (shock decomposition), or into contributions of the observable variables (data decomposition). We propose to link the shock decomposition of the latent variables and the data decomposition of the structural shocks in what we call the double decomposition. This decomposition allows us to better gauge the influence of data on latent variables by taking into account the transmission mechanism of each type of shock. We show the usefulness of the double decomposition by analyzing the role of observable variables in estimating the output gap in two models and by studying the role of news in revisions of the output gap.

结构状态空间模型中的标准潜在变量分析将潜在变量分解为结构冲击的贡献（冲击分解），或分解为可观察变量的贡献（数据分解）。我们建议将潜在变量的激波分解与结构激波的数据分解联系起来，称之为双重分解。这种分解使我们能够通过考虑每种冲击的传输机制来更好地评估数据对潜在变量的影响。我们展示了双重分解的用处 通过分析两个模型中可观察变量在估计产出缺口中的作用以及研究新闻在产出缺口修正中的作用。