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@yudapearl I'll play! I assume you're asking for something other than a trivial case where randomization suffices for conditional ignorability. (1/8)
@yudapearl Let's say Y is the change in your consumption of prescription drugs from year t-1 to t, X is the change in cost sharing for the insurance plan you were enrolled in during year t-1, and Z = {controls for cost sharing and utilization in year t-1}. (2/8)
@yudapearl Let's say we can control nonparametrically for Z so that we can find plans with identical cost sharing and utilization in period t-1, some of which increase their cost sharing and others of which maintain their cost sharing at the current level. (3/8)
@yudapearl For simplicity, let's assume that cost sharing is entirely from copays. Their are a few ways conditional ignorability might fail. Plans might be changing their cost sharing provision in anticipation of future changes in enrollee utilization. (4/8)
@yudapearl We might argue that this is unlikely beccause actuaries don't set cost sharing rates using forecasting models of this type. Additionally, we might worry that the plans which change their cost sharing by more were systematically different to begin with. (5/8)
@yudapearl For example, plans A and B both have $5K utilization in period t-1. But plan A's population has been rapidly aging while plan B's population has been getting healthier. Plan A increases their copays each year in response to past trends. (6/8)
@yudapearl To argue against the plausibility of this story, we might graphically illustrate that prior to the change in copays, plans A and B have similar utilization trends and we see a sudden divergence when plan A increases its copays. (7/8)
@yudapearl Anyway, I could say more but hopefully this is enough for us to get started! (8/8)
