Suppose that a city is interested in increasing the per-capita rate of recycling among its citizens while decreasing the city’s operating costs.

To encourage this, the city allows individuals to discontinue curbside recycling pickup and instead opt into a rebate program. The city wants to evaluate whether or not this rebate program increases the amount of recycling in the city.

The city compiles the following variables in a dataset to evaluate the success of the rebate program:

`recycled`

: amount recycled (kg/person).`rebate`

: participation in rebate program (curbside vs. rebate).`distance`

: distance from recycling center (5 miles vs. > 5 miles). An individual who lives less than five miles from a recycling center might be more likely to opt into the rebate program than someone who lives more than five miles from a center. However, distance to a recycling center should not directly impact the amount of waste each person recycles.

We are going to use Instrumental Variables to answer the city’s question, but before we dive into that, we need to establish some more tools.

The first is **conditional exchangeability.**

One key assumption made in causal inference methods like weighting or stratification is *conditional exchangeability*. This assumption states that there are no unmeasured confounding variables that have a causal effect on both the treatment assignment and the outcome.

Randomization of the treatment assignment ensures that both measured and unmeasured confounding variables are evenly balanced between treatment groups. In a non-randomized setting, balance is NOT guaranteed. The assumption of conditional exchangeability cannot be tested or verified — in most cases, the best we can do without randomization is to identify and measure as many potential confounding variables as possible.

Instrumental variable (IV) estimation is a causal inference technique that help us estimate the causal effect of the treatment even in the presence of unmeasured confounding variables. In this lesson, we will learn about the assumptions and potential applications of IV estimation.

### Instructions

Take a look at the diagram in the learning environment. This diagram depicts the causal relationships between the treatment, the outcome, and confounding variables in a typical non-randomized study.