How the (Econometric) Sausage is Made

Today I'm getting into the weeds a bit about how "finicky" (as I describe it) the IV estimator is. Before describing some of the downside to IV, I think it is worth saying that I think IV gets a very bad wrap. It's a great solution to a very common problem ... under the right assumptions. If those assumptions hold, don't be ashamed to use it. Clearly, that's a big "if" and, as they say, therein lies the rub. So, one thing that makes IV "finicky" is that it a consistent estimator, but it is not unbiased. I think most people know this (but I do see references to IV producing "unbiased causal effects" far too often). Perhaps less well known is that in exactly identified models t he expectation of the estimator does not exist! For those who perhaps don't recall, consistency is an asymptotic property based on taking plims. Bias is a finite sample property based on expectations. So, in finite samples (and I have yet to see an ...

Applied economists are often interested in models where a covariate enters in quadratic form. For instance, the Kuznets curve and Environmental Kuznets curve posit inverted-U relationships between inequality and pollution, respectively, and income. The Mincer wage equation includes a quadratic for age or experience. Many other theoretical models give rise to non-linear effects of a covariate on outcomes. How classical measurement error impacts the estimates is not given a lot of thought. But ... it should be. Suppose one estimates a quadratic model y = a + b1*x + b2*x^2 + e that satisfies all the assumptions of the CLRM except x suffers from classical measurement error. Griliches & Ringstad (1970) show that (under normality) the OLS estimates of b1 and b2 both suffer from attenuation bias. However, the bias of b2 is more severe; the plim for b2 is b2 times the squared reliability ratio. Since the reliability ratio (the ratio of the variance of the true x to the variance of ...

Classical ME results in attenuation bias. We all (hopefully) know that. But ... The bias depends on the ratio of the variance of the measurement error, μ, to the variance of the observed X not explained by other covariates. Formally, this is shown below where the degree of the attenuation bias depends on the R2 from a regression of X on the remaining covariates in the model. The implication is that even "small" measurement error (as captured by the variance of μ) can be enormously consequential in multiple regression. It is not sufficient IMHO to dismiss measurement error simply because you believe it to be "small." On top of that, ignoring measurement error in a covariate because it is not the "regressor of interest" is a common, but costly, mistake. Measurement error in a control variable in your regression model will (in all likelihood) bias your coefficient of interest if the regressor of interest is correlated with the mismeasured regresso...

I am somewhat reluctantly starting this blog on econometric stuff that applied people will hopefully find useful. I am wary to do so because I do not consider myself to be an econometrician; I am an applied econometrician. As such, I suffer from a bit of imposter syndrome in creating a blog on econometric topics. That said, my goal is to make applied types aware of some issues - in as nontechnical way as possible (as I said, I am not an econometrician) - that arise in typical applied (micro) research. The issues I find fascinating are the subtle parts of econometrics that individuals either may not have learned or may have forgotten. By diving a bit into how various econometric methods work in practice, we hopefully will all better understand how the econometric sausage is made. Perhaps ignorance is bliss, but as economists we tend to relish in the dismal. I am fortunate to teach econometrics at SMU and think all empirical types should teach econometrics. It's amazing what you ...