Comparative Statics for Difference-in-Differences

Finn Christensen

No 2023-08, Working Papers from Towson University, Department of Economics

Abstract: In a model with spillovers, consider the difference in the impact of a positive shock on average outcomes among the treated and untreated, or the marginal average effect of treatment among the treated with spillovers (MATTS). MATTS is positive if, and only if, the negated Jacobian inverse of the equilibrium system is a B-matrix by columns. This condition is also sufficient to answer traditional comparative statics questions. I also give several sufficient, and sometimes necessary, conditions on the noninverted Jacobian–which correspond to common modeling assumptions-under which its inverse is a B-matrix by columns. Sign restrictions on MATTS are testable because the sample difference-in-differences is an unbiased estimator for MATTS from a superpopulation perspective. I also show that MATTS generalizes the ATT and the ATE when interference, or spillovers, are present. I apply the results to oligopoly and contests.

Keywords: Comparative statics; difference-in-differences; interference; spillovers; profit maximization hypothesis; B-matrix; symmetric games. (search for similar items in EconPapers)
JEL-codes: C31 C33 C65 C72 D21 L21 (search for similar items in EconPapers)
Pages: 46 pages
Date: 2023-11, Revised 2025-04
New Economics Papers: this item is included in nep-ecm
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