nicomarto
commented
3 years ago Main Idea:
Propose PCA/Factors models as a way to tackle the attenuation bias originated by variables measured with classical errors, as an alternative to the usage of IV as widely applied in the literature.
Stage 1: Theoretical formulation and derivation of the proposed estimator and its properties
Stage2: Simulation. 1) We define a certain DGP: we take our 'x' variable and construct 'y' according to the value of the coefficients that we determine. We know the real DGP.
2) We create a bunch of proxies for 'x', by adding different random shocks of mean zero and different variance to our variable 'x'. We can show by Monte Carlo simulation that regressing 'y' on any of the proxies will give us an biased estimators.
3) We take our bunch of proxies an apply PCA/Factor models to 'extract' (estimate) 'x', and then simulate OLS of 'y' in our extracted 'x'. Hopefully we show how the bias goes away. We could do different simulations comparing the amount of proxies we used in the PCA/Factor models and hopefully find (as I believe) that the more variables you have for 'x', the less bias we have
Stage 3: Having shown theoretically and fictionally that our idea works, we do an empirical approach resting in the foundations we built in S1 and S2 so we are not doing random regressions
ijyliu
We aim to put forward a new approach to handling measurement error in regression and deal with attenuation bias. We will use a factor model/method to extract a new explanatory/independent variable, rather than take an instrumental variables approach, then proceed with regressing a dependent variable on this extracted variable.
This will be mostly a theory based project. The main focus will be a Monte Carlo simulation showing good performance, but after that we will discuss or implement an application.
Prior paper: https://warwick.ac.uk/fac/soc/economics/staff/knagasawa/PartialEffects.pdf