Instrumental Variables Estimation

Instrumental Variables (IV) estimation is a tool economists and social scientists use when they want to deduce a cause-and-effect relationship between two variables—specifically when there's a problem, and hidden factors are messing with results. 

Imagine you're trying to see how pet ownership affects people’s long-term health. The challenge is that factors like income level or personality traits, for example, could influence both an individual’s likelihood to adopt a pet and their long-term health. This creates a problem because these hidden factors make it difficult to know whether it’s actually the pet ownership that’s affecting health, or if baseline health and wealth impact whether someone is more likely to own a pet in the first place. 

That’s where IV estimation comes into play. Instead of directly trying to link pet ownership to health, researchers use an ‘instrument’—a third variable that’s related to pet ownership but doesn’t directly affect health. The key is finding something that influences whether someone adopts a pet, without being influenced by the same hidden factors.

For example, one potential instrument could be the presence of pet adoption campaigns in a specific neighborhood. A greater number of pet adoption advertisements won’t have an impact on the health of the people in the area, but it would likely increase someone’s willingness to adopt. Using this outside variable of adoption campaigns as an instrument helps to isolate the effect of pet adoption on health, stripping away the noise from the hidden factors. 

In more technical terms, the number of pet adoption campaigns is considered an exogenous variable because it’s unrelated to the health outcomes of people in the area (they influence pet adoption rates but don't directly affect health). On the other hand, if we tried to use something like income as a predictor of pet adoption, we might face endogeneity because income could also influence health outcomes, creating a correlation with both adoption and health which leads to biased results. 

To recap, the instrumental variable (the adoption campaigns) helps overcome this bias by isolating the effect of pet adoption on health. Thus, exogeneity ensures the variable only impacts the predictor (adoption rates) and not the outcome (health) and endogeneity occurs when a variable impacts both, confounding the analysis.