We propose to add ranking restrictions on impulse‐responses to sign restrictions to narrow the identified set in vector autoregressions (VARs). Ranking restrictions come from micro data on heterogeneous industries in VARs, bounds on elasticities, or restrictions on dynamics. Using both a fully Bayesian conditional uniform prior and prior‐robust inference, we show that these restrictions help to identify productivity news shocks in the data. In the prior‐robust paradigm, ranking restrictions, but not sign restrictions alone, imply that news shocks raise output temporarily, but significantly. This holds both in an application with rankings in the form of heterogeneity restrictions and in another applications with slope restrictions as rankings. Ranking restrictions also narrow bounds on variance decompositions. For example, the bound of the contribution of news shocks to the forecast error variance of output narrows by about 30 pp at the one‐year horizon. While misspecification can be a concern with added restrictions, they are consistent with the data in our applications.

中文翻译：

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识别和推断排名限制

我们建议在冲激响应上添加排名限制，以限制符号，以缩小向量自回归（VAR）中的已标识集合。排名限制来自VAR中的异构行业的微观数据，弹性范围或动态限制。使用完全贝叶斯条件一致的先验和先验鲁棒推断，我们表明这些限制有助于识别数据中的生产率新闻冲击。在先前健壮的范式中，排名限制（但不是符号限制）本身意味着新闻冲击会暂时（但显着）提高产量。这在以异质性限制形式进行排名的应用程序中以及在具有斜率限制作为排名的另一个应用程序中都适用。排名限制还缩小了方差分解的范围。例如，在一年的时间范围内，新闻冲击对输出的预测误差方差的影响范围缩小了约30 pp。虽然可能会因附加规范而担心规格不正确，但它们与我们应用程序中的数据一致。