Are you concerned with measurement error? Do you wanna know how partial identification can help you address this problem? This thread is for you! (@dlmillimet, I was inspired by your blog post!) 1/14
Many people think that binary variables are less likely to be mismeasured. But this is not the case! Education (bit.ly/2RqOBM7), Unionization (bit.ly/2OZPs4V) and Welfare Participation (bit.ly/34XNXJU) are all measured with error! 2/14
So, if you are trying to estimate a LATE, you should think about measurement error in your treatment variable. Ura (2018, bit.ly/2Pnyr3d) and Calvi, @lewbel and Tommasi (2019, bit.ly/34X0Js7) are there to help you! 3/14
Note that the mismeasured variable is binary! So no classical measurement error here! Life is much more complicated than attenuation bias! Bias can go anywhere! As Brazilians say, you are in the woods without a dog! (I like to translate some expressions literally.) 4/14
But, as Brazilians also say, he who doesn't have a dog hunts with a cat! Ura (2018) and Calvi et al (2019) offers you two different cats to go hunting with you! 5/14
In addition to the standard LATE assumptions, Ura imposes that the instrument is independent of the counterfactual mismeasured variable and sharply bounds the LATE parameter using the ITT and the total variability metric (doing a better job than simply using the Wald estimand). 6
For his empirical application, Ura analyzes the impact of 401(k) participation on financial savings (Abadie, 2003) using 401(k) eligibility as the instrument. He finds that the bounds around the LATE parameter are similar to the confidence intervals around the Wald estimand. 7/14
This finding suggest that the previous literature about the impact of 401(k) participation on financial savings is robust to measurement error. So everyone can sleep peacefully. 8/14
Calvi et al (2019) proposes a Mismeasurement Robust (MR-)LATE that explores two mismeasured treatment variables. On top of the LATE conditions, Calvi et al assumes that the counterfactual mismeasured treatment variables are independent of the potential outcomes for the compliers.
Then, they discuss under which conditions the MR-LATE is closer to the true LATE than the Wald Estimand. After that, they have a cool application that combines tools from structural econometrics and the treatment effects literature. 10/14
They are concerned with the effects of women's control over resources on family health. Their true treatment variable is whether the wife has primary control of resource allocation decisions in the household, which is unobserved. 11/14
They measure (with error) the treatment using a structural model. They use the MR-LATE to estimate the treatment effect of interest using changes in inheritance laws as an IV. The MR-LATE can get close to the true LATE even if the structural model behind it is misspecified. 12/14
They find that women’s control of household resources improves their and their children’s health at no cost to men’s health. In my opinion, this results provides an economic model to explain why CCT programs usually target mothers instead of fathers. 13/14
I hope this thread illustrated the usefulness of partial identification and similar tools to address measurement error. 14/14
