Archive for ‘Econometrics’

October 8, 2013

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).

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October 31, 2012

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.

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October 7, 2012

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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November 29, 2011

Dairy supply management: Orphans versus yuppies

Yesterday Federal Agricultural Minister Gerry Ritz uttered insane lies about dairy supply management:

I would make the argument that I don’t see those inflated prices, certainly, depending on where you buy,” Ritz told a joint news conference with Alberta Agriculture Minister Evan Berger and Saskatchewan Agriculture Minister Bob Bjornerud.

I received a flyer in my mailbox last night when I got back to my apartment and I opened it up and it’s from Canadian Tire. They’ve got four litres of milk for $4.19. That’s completely comparable to the American price that we’re always being beat up over.

Canadian Tire Econometrics aside, consumers are of course harmed by high prices driven by quantity restrictions. Click here to see a graph showing how much higher our prices are than the EU, US, or New Zealand (all of which all of which except New Zealand [*] also have some sort of supply management, Canada’s is just more severe).

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October 24, 2011

Patient knowledge, antibiotic abuse, and impolite physicians

Antibiotic overuse causes great social harm yet is largely absent from public discussion of drug policy. There is a textbook external effect of an antibiotic prescription: the more antibiotics are used, the higher the risk we all face of resistant infections. As a result, there tends to be too much use of antibiotics. There have been ongoing efforts to reduce use of antibiotics, particularly in the context of treating respiratory infections, in part by educating GPs, the supply side of the relationship, on appropriate use.

In “Patient knowledge and antibiotic abuse: Evidence from an audit study in China” Janet Currie, Wanchuan Lin, and Wei Zhang consider the demand side of the relationship: what is the effect of patient knowledge on antibiotic use?

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October 12, 2011

Interaction terms in nonlinear regression models

Say you wish to estimate a model with a binary dependent variable. You recall that you ought not use OLS primarily because OLS will not bound your predicted values between zero and one. So you use a nonlinear variant, say, probit. But you also recall that it doesn’t matter much if you just use OLS and ignore the binary nature of your dependent variable so long as you are interested in estimating the effects of your covariates, not generating predicted values.

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October 5, 2011

Tips on estimating models and producing publication-ready tables using Stata

Frances Woolley has posted some great tips on how to clean data in Stata. This post follows up with some tips on how to quickly and robustly estimate models as you vary specifications, and on how to get your results in a publication-ready form. The .do file described in this post can be downloaded by clicking here, you must change the extension from .doc to .do.

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October 3, 2011

Will Yelp kill Applebee’s?

A new working paper by Michael Luca estimates the effect of Yelp reviews on Seattle restaurant revenues. Disentangling causality here is difficult, as even if reviews have no effect on revenues we would expect to observe reviews and revenues both moving with changes in underlying relative quality. Luca exploits a quirk in the way Yelp presents information: average scores are reported rounded in 0.5 star bins on a 5 star scale. For example, underlying average scores of 2.76 and 3.24 are both reported as “3 stars,” but a good review which bumps the average up to 3.25 bumps the reported score up to 3.5 stars. The estimates show that Yelp reviews do have a substantial effect on revenues.

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October 3, 2011

Propensity score matching: not magic

Nice quote from EconJeff on propensity score matching. The idea that somehow matching buys you causality in a situation in which you’d snicker at the idea that OLS does seems to be distressingly common.

Matching is not a design or an identifying assumption. Rather, it is one of several estimators that can be use when assuming selection on observed variables or unconfoundedness (or ignorability, or conditional independence, or whatever else your particular discipline or sub-field happens to call it this week). The key to evaluating an analysis based on an assumption of selection on observed variables is a careful consideration of the set of conditioning variables used in the analysis to deal with the problem of non-random selection into treatment. Estimator choice, e.g. matching versus linear regression versus inverse propensity weighting, is not unimportant, and can be very important for specific data generating processes, but what really matters in general is the set of conditioning variables.

October 1, 2011

Chetty, Friedman, and Saez on detecting knowledge differences with observational data

Models usually implicitly assume that people are aware of the incentives they face. People in a labor supply model, for example, usually make their decisions based on the actual schedule, not their subjective impression of the schedule. But many people may not even be aware of changes in income taxes schedules: how can they then respond to changes in the schedule? In current research, Raj Chetty, John Friedman, and Emmanuel Saez turn this apparent difficulty into an advantage. They estimate the causal effect of changes in an aspect of the income tax schedule on labor supply. Since the policy they study is Federal, there is not much variation to identify the effects of interest using traditional methods, but the authors show how to recover regional variation in knowledge of the schedule. The interaction of knowledge and the schedule then varies across regions and time even though the schedule only varies over time, so there’s lots more variation to identify the effect of the schedule on labor supply.

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