Instrumental Variable - Example

Example

Informally, in attempting to estimate the causal effect of some variable x on another y, an instrument is a third variable z which affects y only through its effect on x. For example, suppose a researcher wishes to estimate the causal effect of smoking on general health (as in Leigh and Schembri 2004). Correlation between health and smoking does not imply that smoking causes poor health because other variables may affect both health and smoking, or because health may affect smoking in addition to smoking causing health problems. It is at best difficult and expensive to conduct controlled experiments on smoking status in the general population. The researcher may proceed to attempt to estimate the causal effect of smoking on health from observational data by using the tax rate on tobacco products as an instrument for smoking in a causal analysis. If tobacco taxes affect health only because they affect smoking (holding other variables in the model fixed), correlation between tobacco taxes and health is evidence that smoking causes changes in health. An estimate of the effect of smoking on health can be made by also making use of the correlation between taxes and smoking patterns.