APPENDIX A: EXTENSIONSIN THIS APPENDIX, we consider three extensions to our main result derived in Section 2. The extensions are (i) supply-side instead of demand-side taxation, (ii) nonlinear, instead of ad valorum taxation, and (iii) a setting with multiple goods and multiple taxes.
A.1. Supply-Side TaxationTo extend our result to supply-side taxation, we again start out with the most general formulation of the supply-demand system given by equations (1), (2). However, we now assume the tax τ it is levied on the supply side. Because the tax is levied on the supply side, we need to slightly adjust the exclusion restrictions formulated in Section 2. In particular, in this setting, the logically equivalent SER is that the instrument can be excluded from the demand equation, because the tax is paid for by the supply side:
SUPPLY-SIDE STANDARD EXCLUSION RESTRICTION:If the tax τ it is levied on the supply side, then we set γ = 0.The logical equivalent of the RER with supply-side taxation is that supply depends only on the price net of the tax rate denoted by P −τ it = (1 − τ it )P it . The motivation for the supply-side RER is similar to the motivation of the demand-side RER: it follows from rational behavior of producers, and is a standard assumption in most models of taxation. Under the supply-side RER, the supply equation is given by y it = ε S p