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evaluating the health consequences of large-scale public policy

The DD approach necessitates two critical assumptions: parallel trends and common shocks. The parallel trends assumption is that trends in the outcome of interest before the policy are similar in both the policy-affected and -unaffected communities. It is tested by running a second regression using the above equation, where time is a continuous variable (e.g., years) and the regression is isolated to the pre-policy period. If β3 is significant, the parallel trends assumption is violated, suggesting that the two states significantly differ in their pre-policy health outcome trends over time and presenting the need for a control group other than Colorado. If the β3 is insignificant, then Colorado is considered a valid comparator.

The common shocks assumption is, by contrast, untestable; it states that events occurring simultaneously or after the policy will affect both groups equally (e.g., the national economy may affect unemployment and associated cigarette sales but will affect Californians and Coloradoans equally). If, on the other hand, such shocks influence these states differently, this assumption is violated, and a source of confounding is potentially introduced. By taking the difference between the states’ data before and after the policy, the unobserved confounders that influenced Californians but not Coloradoans to pass the proposition are assumed to be “differenced out.” But, the DD approach cannot account for time-varying unobserved confounders (e.g., economic changes that affected one state more than the other), making the common shocks assumption often challenging to justif