# Econometrics

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## Inequality, poverty, and health: Comments on the Globe’s coverage

Canada’s Globe and Mail newspaper has been running a series of articles on income inequality. This post presents some comments on the coverage of income inequality and health in Wealth begets health: Why universal medical care only goes so far by André Picard.

I make three points. First, that the article is much more consistent with the literature if one reads “poverty” every time the article uses the word “inequality.” Second, that the fact that income and health are correlated across people or across regions does not tell us that income causes health. And finally, that the research does suggest that decreasing poverty will increase health, but that we should not expect substantial reductions in health care expenditures as a result. I close with some notes on policy implications.

## U.S. voters more likely to support marijuana legalization than non-voters

Much has been made of a recent Gallup poll showing a majority of Americans now support marijuana legalization. But if a majority support legalization, why do politicians seem so reluctant to support drug law reform?

One explanation for this puzzle is that Americans who vote are less likely to support legalization than those who do not vote. Voters tend to be older, and possibly have other characteristics which are associated with opposition to drug policy reform.

## GMM and its application outside finance

The 2013 Nobel prize in economics was won by Fama, Shiller, and some other dude, according to most media accounts. Fama and Shiller were pretty easy to explain: one of them is at Chicago and is associated with a theory called “efficient markets,” so he’s the free market guy. Shiller criticized the Chicago guy, so we know where to put him on the political spectrum. But this third guy, Hansen, well, he’s at Chicago, but he does some sort of theoretical econometrics, so if we’re the Guardian we’ll just assume he’s “ultra-conservative” and then ignore him, or if we’re anyone else we’ll skip to just ignoring him (even the Economist gives up, complaining they can’t explain his work without “writing all sorts of equations in our newspaper.”) This post attempts to provide a relatively gentle, albeit with all sorts of equations, introduction to part of the third guys’s research, focusing on applications in causal modeling in microeconomics rather than the examples from finance or macroeconomics.

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## Remarks on Chen and Pearl on causality in econometrics textbooks

Bryant Chen and Judea Pearl have published a interesting piece in which they critically examine the discussions (or lack thereof) of causal interpretations of regression models in six econometrics textbooks. In this post, I provide brief assessments of the discussion of causality in nine additional econometrics texts of various levels and vintages, and close with a few remarks about causality in textbooks from the perspective of someone who does, and teaches, applied econometrics. Like Chen and Pearl, I find some of these textbooks provide weak or misleading discussion of causality, but I also find one very good and one excellent discussion in relatively recent texts. I argue that the discussion of causality in econometrics textbooks appears to be improving over time, and that the oral tradition in economics is not well-reflected in econometrics textbooks.

The Chen and Pearl paper has been around for a while in working paper form and recently came out in the Real World Economics Review, also available here from the authors with much clearer typesetting.

The additional textbooks I discuss below are: Amemiya (1985), Kmenta (1986), Davidson and MacKinnon (1993), Gujarati (1999), Hayashi (2000), Wooldridge (2002), Davidson and MacKinnon (2004), Deilman (2005), and Cameron and Trivedi (2005).

## The intuition of robust standard errors

Commonly econometricians conduct inference based on covariance matrix estimates which are consistent in the presence of arbitrary forms of heteroskedasticity; the associated standard errors are referred to as “robust” (also, confusingly, White, or Huber-White, or Eicker-Huber-White) standard errors. These are easily requested in Stata with the “robust” option, as in the ubiquitous

reg y x, robust

Everyone knows that the usual OLS standard errors are generally “wrong,” that robust standard errors are “usually” bigger than OLS standard errors, and it often “doesn’t matter much” whether one uses robust standard errors.  It is whispered that there may be mysterious circumstances in which robust standard errors are smaller than OLS standard errors. Textbook discussions typically present the nasty matrix expressions for the robust covariance matrix estimate, but do not discuss in detail when robust standard errors matter or in what circumstances robust standard errors will be smaller than OLS standard errors. This post attempts a simple explanation of robust standard errors and circumstances in which they will tend to be much bigger or smaller than OLS standard errors.

## What do we know about the effect of income inequality on health?

This post briefly surveys some of the methods and results in the literature on health and income inequality, closing with some remarks on problems with the existing literature and where future research may take us. It is not intended as anything resembling a comprehensive survey; Lynch et al (2004) provides a useful review of the empirical literature up to that time.

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