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posted on 2022-07-25, 00:10 authored by Abigail FriedmanAbigail Friedman

This figure depicts a scenario where researchers might use a difference-in-differences (DD) research design to estimate a policy's effect. Here, a hypothetical policy went into effect in some regions in 2015 but was not adopted in other regions. A DD research design can be applied to estimate the impact of this policy on the y-axis variable if certain assumptions are met, specifically (a) policy exogeneity and (b) parallel pre-trends. The latter assumption is depicted here: time trends in the outcome variable in adopting vs. non-adopting jurisdictions were parallel before the policy went into effect. In other words, there is reason to believe that non-adopting jurisdictions’ trends provide a reasonable counterfactual for adopters' trends if the latter had not implemented the policy. When those assumptions hold, subtracting the pre-policy difference between adopters' and non-adopters' outcomes (⍺) from the post-policy difference (β) estimates the policy's effect (β - ⍺). 

Note that this is a simplification meant to build intuition. Empirical estimation typically involves multivariable regressions where covariates adjust for time invariant differences between adopting and non-adopting jurisdictions,  fixed effects for the period before vs after the policy went into effect (to absorb common time trends), population characteristics that may differ between locations over time and affect responses to the policy, and concurrent policies or other time varying jurisdictional factors that might be correlated with the policy in question and outcome. If the policy of interest goes into effect at different points in time in different jurisdictions, additional assumptions and tests are needed.