The Weighting Game: Formula Apportionment as an Instrument of Public Policy

We propose an explanation for why states choose different apportionment formulas for corporate income tax purposes. Based on a two-state equilibrium model of location choice by firms, we show that aggregate social welfare is maximized when both states use the same formula, regardless of which formula is chosen. However, at least one of the states can increase its welfare by deviating from this coordinated solution; thus, the Nash equilibrium features the states choosing different formulas. Importing states have incentives to increase the sales factor, whereas exporting states will tend to increase the input factors. An empirical test of which states have deviated from the traditionally equally-weighted three factor formula supports the predictions of the model.