Historically, economics has fallen into the bad habit of thinking the fancier estimation method is closer to being "right" -- based on one sample of data. We used to think this of GLS vs OLS until we paid careful attention to exogeneity assumptions.
We used to think this of 2SLS vs OLS until problems with weak instruments were revealed.
We still seem to think matching methods are somehow superior to regression adjustment if they give somewhat different estimates.
And we now seem to think ML methods are to be preferred over basic methods. Perhaps a reckoning is on its way.
And when we simulate, it's common to rig the simulation methods in favor of the fancier method. Such as imposing strict exogeneity when comparing GLS when correcting for serial correlation to OLS, and usually assuming the serial correlation model is correct.
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Yesterday I was feeling a bit guilty about not teaching lasso, etc. to the first-year PhD students. I'm feeling less guilty today. How much trouble does one want to go through to control for squares and interactions for a handful of control variables?
And then it gets worse if I want my key variable to interact with controls. You can't select the variables in the interactions using lasso. I just looked at an application in an influential paper and a handful of controls, some continuous, were discretized.
Discretizing eliminates the centering problem I mentioned, but in a crude way. So I throw out information by arbitrarily using five age and income categories so I can use pdslasso? No thanks.
I was reminded of the issue of centering IVs when creating an example using PDS LASSO to estimate a causal effect. The issue of centering controls before including them in a dictionary of nonlinear terms seems it can be important.
The example I did included age and income as controls. Initially I included age, age^2, inc^2, age*inc. PDSLASSO works using a kind of Frisch-Waugh partialling out, imposing sparsity on the controls.
But as we know from basic OLS, not centering before creating squares and interactions can make main effects weird -- with the "wrong" sign and insignificant. This means in LASSO they might be dropped.
It seems like every week, if not more frequently, I learn something new about a basic estimation method -- OLS, 2SLS, and offshoots. My students seem skeptical when I tell them this but it's true.
This week: centering before creating squares and interactions.
Now, I've taught this in the context of OLS and 2SLS for a long time, and it comes up a lot in my introductory book. It's often needed to give main effects a sensible interpretation -- whether those are exogenous or endogenous, whether it's a pooled method or FE.
But one case where I've been too cavalier is with creating instruments out of squares and interactions of exogenous variables when, say, the structural equation includes w*xj where w is endogenous and xj is exogenous. We can use xj*zh as IVs.
I've decided to share a Dropbox folder containing a recent paper -- a sort of "pre-working" paper -- on panel data estimators for DID/event studies. I'm "in between" web pages (and could use recommendations on a simple, effective platform).
The paper starts with algebraic equivalence results -- hence the somewhat odd title -- and applies those to interventions with common entry time and staggered entry. I think it's useful to see the equivalence between TWFE with lots of heterogeneity and pooled OLS equivalents.
I think of it as a parametric regression adjustment version of Callaway and Sant'Anna (but using levels rather than differences) And, as in Sun and Abraham, I make a connection with TWFE (while allowing for covariates).
Speaking of two-way FE, it's been under fire for the last few years for estimating treatment effects in DID designs -- especially staggered designs. As many on here know. As an older person, I don't let go of my security blankets so easily.
Certainly the simple TWFE estimator that estimates a single coefficient can be misleading. We know this thanks to recent work of several talented econometricians (you know who you are). But maybe we're just not being flexible enough with treatment heterogeneity.
Now when I teach panel data interventions, I start with basic TWFE but note that, with multiple treatment periods and different entry times, we can easily include interactions that allow for many different average treatment effects (on the treated).
More on LPM versus logit and probit. In my teaching, I revisited a couple of examples: one using data from the Boston Fed mortgage approval study; the other using a balanced subset of the "nonexperimental" data from Lalonde's classic paper on job training.
In both cases, the key explanatory variable is binary: an indicator being "white" in the Fed study (outcome: mortgage approved?), a job training participation indicator in the Lalonde study (outcome: employed after program?)
In just adding binary indicator alone, the probit, logit, linear give similar stories but the estimates of the average treatment effects do differ. In the Lalonde case by 4 percentage points (19 vs 22 vs 23, roughly).
So, I decide to practice what I (and many others) preach ....