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).
The equivalence results suggest how to extend to heterogeneous trends to allow violation of common trends, and also some simple strategies for nonlinear models: exponential mean, Poisson QMLE (FE or pooled) if y(i,t) >=0, logit or probit if y(i,t) is binary or fractional.
Happy to get public and private comments. Interpreting and extending DID seems to have become almost an economics community project. It's written at a level I can understand, which makes it a bit tedious. Some of you might think it's "DID for dummies."
Anyway, here is the link to the paper and Stata files:


Probably several typos and thinkos lurking ....

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More from @jmwooldridge

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.

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.

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.

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
10 Mar
In 2018 I was invited to give a talk at SOCHER in Chile, to give my opinions about using spatial methods for policy analysis. I like the idea of putting in spatial lags of policy variables to measure spillovers. Use fixed effects with panel data, compute fully robust ses.
For the life of me, I couldn't figure out how putting in spatial lags of Y had any value. After preparing a course in July 2020, I was even more negative about this practice. It seems an unnecessary complication developed by theorists.
As far as I can tell, when spatial lags in Y are used, one always computes the effects of own policy changes and neighbor policy changes, anyway, by solving out. This is done much more robustly and much more easily modeling spillovers directly without spatial lags in Y.
Read 6 tweets
8 Mar
I taught a bit of GMM for cross-sectional data the other day. In the example I used, there was no efficiency gain in using GMM with a heteroskedasticity-robust weighting matrix over 2SLS. I was reminded of the presentation on GMM I gave 20 years ago at ASSA.

The session was organized by the AEA, and papers were published in the 2001 JEL issue "Symposium on Econometric Tools." Many top econometricians gave talks, and I remember hundreds attended. (It was a beautiful audience. The largest ever at ASSA. But ASSA underreported the size.)
In my talk I commented on how, for standard problems -- single equation models estimated with cross-sectional data, and even time series data -- I often found GMM didn't do much, and using 2SLS with appropriately robust standard errors was just as good.
Read 4 tweets
7 Mar
I think frequentists and Bayesians are not yet on the same page, and it has little to do with philosophy. It seems some Bayesians think a proper response to clustering standard errors is to specify an HLM. But in the linear case, HLM leads to GLS, not OLS.

Moreover, a Bayesian would take the HLM structure seriously in all respects: variance and correlation structure and distribution. I'm happy to use an HLM to improve efficiency over pooled estimation, but I would cluster my standard errors, anyway. A Bayesian would not.
There still seems to be a general confusion that fully specifying everything and using a GLS or joint MLE is a costless alternative to pooled methods that use few assumptions. And the Bayesian approach is particular unfair to pooled methods.
Read 5 tweets

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