Saturday, December 5, 2015

Do Friends Let Friends Do IV...or is all of that unobserved heterogeneity and endogeneity all in your head?

A few weeks ago, there was a post that caught my attention at the 'Kids Prefer Cheese' blog titled "Friends don't let Friends do IV" which was very critical of instrumental variable techniques. Around that same time, Marc Bellemare posted a contrasting piece, titled "Friends do let Friends do IV".

For some reason, I've written a number of posts recently related to instrumental variables, discussing different intuitive approaches to understanding them, or connections with directed acyclic graphs (DAGs).   In the past, I have discussed them in the context of omitted variable bias and unobserved heterogeneity and endogeneity.

Now some colleagues have introduced me to a few papers authored by Quin that really question the validity of using instruments in this context. In the first paper, Resurgence of the Endogeneity-Backed Instrumental Variable Methods, Quin states:

“Essentially, the paranoia grows out of the fallacy that independent error terms exist prior to model specification and carry certain ‘structural’ interpretation similar to other economic variables…..In fact, it is practically impossible to validate the argument of endogeneity bias on the ground of correlation between a regressor and the error term in a multiple regression setting, especially when the model fit remains relatively low. Notice how much the basis of the IV treatment for ‘selection on the unobservables’ is weakened once 'e' is viewed as a model-derived compound of unspecified miscellaneous effects. In general, error terms of statistical models are derived from model specification. As such, they are unsuitable for any ‘structural’ interpretation, e.g. see Qin and Gilbert (2001)”

Quin goes deeper into this in a later working paper, Time to Demystify Endogeneity Bias.

From the abstract-

"This study exposes the flaw in defining endogeneity bias by correlation between an explanatory variable and the error term of a regression model. Through dissecting the links which have led to entanglement of measurement errors, simultaneity bias, omitted variable bias and self
 -selection bias, the flaw is revealed to stem from a Utopia mismatch of reality directly with single explanatory variable models."


The paper gets pretty heavy in details, despite promises to keep the math at a minimum. One of the central arguments they make about "endogeniety bias syndrome" is to point out an apparent misunderstanding or misinterpretation of error terms in multivariable vs single variable regression that is often used in applied work to set the stage for doing IV:

"Error terms or model residuals have been long perceived as sundry composites of what modellers are unable and/or uninterested to explain since Frisch’s time....Since cov(z,e)≠ 0 is single variable based, the contents of the error term have to be adequately ‘pure’, definitely not a mixture of sundry composites, to sustain its significant presence.  Indeed,  textbook  discussions  of  endogeneity  bias,  be  it  associated  with  SB (simultaneity bias), measurement errors, OVB(omitted variable bias) or SSB (self-selection bias), are all built on simple regression models. As soon as these models are extended to multiple ones, the correlation becomes mathematically intractable. In a multiple regression, all the explanatory variables are mathematically equal. Designation of one  as  the  causing  variable  of  interest  and  the  rest  as  control  variables  is  purely  from  the substantive  standpoint.  The  premise, cov(x,e)≠ 0, implies  not  only cov(z,e)≠ 0 for  the entire  set  of control  variables,  but  also  the  set  being  exhaustive.  Both  conditions  are  almost impossible to meet in practice."

Quin also has an applied paper related to wage elasticities where some of these ideas are put into context. See the references below.

References:

Duo Qin (2015). Resurgence of the Endogeneity-Backed Instrumental Variable Methods. Economics: The Open-Access, Open-Assessment E-Journal, 9 (2015-7): 1—35. http://dx.doi.org/10.5018/economics-ejournal.ja.2015-7 

QIN, D. (2015) “Time  to  Demystify  Endogeneity  Bias” SOAS
Department  of  Economics  Working
Paper Series, No. 192, The School of Oriental and African Studies
192 Time to Demystify Endogeneity Bias (pdf)

Qin, D., S. van Huellen and QC. Wang. (2014), “What Happens to Wage Elasticities When We  Strip  Playometrics?  Revisiting  Married  Women  Labour  Supply  Model”, SOAS Department  of  Economics  Working  Paper  Series,  No.  190,  The  School  of  Oriental  and
African Studies  https://www.soas.ac.uk/economics/research/workingpapers/file97784.pdf 




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