Revisiting the narrative approach of estimating tax multipliers

A number of recent studies regress a "narratively" identified measure of a macroeconomic shock directly on an outcome variable. In this note, we argue that this approach can be viewed as the reduced-form regression of an instrumental variable approach in which the narrative time series is used as an instrument for an endogenous series of interest. We construct confidence bands for the case in which the narrative shock and the endogenous variable of interest are only weakly correlated. We apply the method to four narrative tax measures recently constructed by Romer and Romer (2010), Cloyne (2013), and Mertens and Ravn (2012). These variables turn out to be weak instruments for cyclically adjusted tax revenues. Compared to the single-equation estimation, we find that using any of the considered narrative tax measures as an instrument for cyclically adjusted tax revenues yields estimates of multipliers that are statistically indistinguishable from zero after correcting the confidence bands for weak instruments.