In economies with multi-level governments, why would a change in the fiscal rule of a government in one level lead to a fiscal response by a government in a different 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 fills 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 fiscal interactions. Second, we propose a novel strategy for identifying it, by considering an empirical design that confines the common-pool channel to specific 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 affecting the tax base of oil rich states specifically. This latter feature enables attributing the vertical fiscal reactions of the remaining states to the CS channel. Following this strategy, via a difference-in-differences approach, we decompose the sources of the vertical fiscal reactions arising from this federal tax change and find that those attributed to the CS channel: (i) account for approximately 38% of the overall vertical fiscal 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.