In economies with multi-level governments, why would a change in the …scal rule of a government in one level lead to a …scal response by a government in a di¤erent level? The literature focused primarily on the standard common-pool problem, while giving little attention to the potential role of complementarity or substitutability (CS) between the public goods supplied by the two governments. This paper …lls this gap by focusing on the latter channel. First, we illustrate its potential key role in determining the sign of the vertical reaction through a generic model of vertical …scal interactions. Second, we propose a novel strategy for identifying it, by considering an empirical design that con…nes the common-pool channel to speci…c locations. We implement this design through a quasi-natural experiment: the 1980 U.S. Crude Oil Windfall Act, which increased federal tax collections from sale of crude oil, thereby a¤ecting the tax base of oil rich states speci…cally. This latter feature enables attributing the vertical …scal reactions of the remaining states to the CS channel. Following this strategy, via a di¤erence-in-di¤erences approach, we decompose the sources of the vertical …scal reactions arising from this federal tax change and …nd that those attributed to the CS channel: (i) account for approximately 38% of the overall vertical …scal response; (ii) point at complementarity between state and federal public goods, most notably in transportation and welfare expenditures; (iii) are manifested primarily via changes in states'sales and income taxation.