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.

#metricstotheface
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.
When I did the example, age was dropped but age*inc was kept. Then I centered to instead use (age - agebar)*(inc - incbar) (and also in the squares). Now both level terms are kept. The causal effect estimate changed nontrivially.
I couldn't find anywhere where this is discussed with LASSO generally. I'd appreciate a citation if anyone has one. I haven't done a simulation, but this one example and my intuition tell me centering controls in nonlinear functions when using LASSO might be important.
With OLS and forcing all controls to remain, it doesn't matter whether we center the controls or not; the estimated causal effect is invariant when assumed constant. But LASSO is different because it's a selection method.

• • •

Missing some Tweet in this thread? You can try to force a refresh
 

Keep Current with Jeffrey Wooldridge

Jeffrey Wooldridge Profile picture

Stay in touch and get notified when new unrolls are available from this author!

Read all threads

This Thread may be Removed Anytime!

PDF

Twitter may remove this content at anytime! Save it as PDF for later use!

Try unrolling a thread yourself!

how to unroll video
  1. Follow @ThreadReaderApp to mention us!

  2. From a Twitter thread mention us with a keyword "unroll"
@threadreaderapp unroll

Practice here first or read more on our help page!

More from @jmwooldridge

24 Apr
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?

#metricstotheface
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.
Read 8 tweets
24 Apr
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.

#metricstotheface
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.
Read 6 tweets
7 Apr
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).

#metricstotheface
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).
Read 6 tweets
24 Mar
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.

#metricstotheface
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).
Read 13 tweets
13 Mar
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.

#metricstotheface
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 ....
Read 5 tweets
13 Mar
A somewhat common device in panel data models is to lag explanatory variables when they're suspected as being "endogenous." It often seems to be done without much thought, as if lagging solves the problem and we can move on. I have some thoughts about it.

#metricstotheface
First, using lags changes the model -- and it doesn't always make sense. For example, I wouldn't lag inputs in a production function. I wouldn't lag price in a demand or supply function. In other cases, it may make sense to use a lag rather than the contemporaneous variable.
Under reasonable assumptions, the lag, x(i,t-1) is sequential exogenous (predetermined). You are modeling a certain conditional expectation. But, logically, it cannot be strictly exogenous. Therefore, fixed effects estimation is inconsistent with fixed T, N getting large.
Read 5 tweets

Did Thread Reader help you today?

Support us! We are indie developers!


This site is made by just two indie developers on a laptop doing marketing, support and development! Read more about the story.

Become a Premium Member ($3/month or $30/year) and get exclusive features!

Become Premium

Too expensive? Make a small donation by buying us coffee ($5) or help with server cost ($10)

Donate via Paypal Become our Patreon

Thank you for your support!

Follow Us on Twitter!