A recent NBER working paper by Morck and Yeung outlines the perils of instrumental variables. In addition to the standard "weak instruments” and "lack of exogeneity” problems, the authors describe a third problem that received much less attention – that of latent variables. Others have written about this issue too, but this happened to be the first paper where I encountered it.
Suppose you use an instrument to identify the causal effect of education on earnings and someone else uses the same instrument to identify the causal effect of education on health. You both get amazing results and submit to the top journal of your choice. What should the journal think?
Well, if there’s no fundamental relationship between health and earnings, you’re both ok. It just happened that education affects both. However, if there is a causal relationship between the two, as there is likely to be, then neither of your analyses is valid. Healthier people probably have higher potential earnings because they are more productive and those who earn more may be healthier because they spend more on their health. You could try to control for health in the regression of education on earnings or for earnings in the regression of education on health, but then you need another instrument, which may have the same issues. How’s that for dismal?