There are several types of generating processes to consider (spatial autoregressive, spatial durbin, spatial error model, etc.) so things can be changed accordingly. Let me know if you want some R code an I can furnish some for you.
January 8, 2026 at 5:37 PM
There are several types of generating processes to consider (spatial autoregressive, spatial durbin, spatial error model, etc.) so things can be changed accordingly. Let me know if you want some R code an I can furnish some for you.
You can simulate from the reduced form if you want:
Y = (I - \rho W)^{-1})(X\beta + \epsilon)
W can be constructed by randomly distributing your observations over the unit square and using objective of choice (queen/rook, k-nn). Make sure \rho \in (-1,1) and W is row-normalized.
Y = (I - \rho W)^{-1})(X\beta + \epsilon)
W can be constructed by randomly distributing your observations over the unit square and using objective of choice (queen/rook, k-nn). Make sure \rho \in (-1,1) and W is row-normalized.
January 8, 2026 at 5:36 PM
You can simulate from the reduced form if you want:
Y = (I - \rho W)^{-1})(X\beta + \epsilon)
W can be constructed by randomly distributing your observations over the unit square and using objective of choice (queen/rook, k-nn). Make sure \rho \in (-1,1) and W is row-normalized.
Y = (I - \rho W)^{-1})(X\beta + \epsilon)
W can be constructed by randomly distributing your observations over the unit square and using objective of choice (queen/rook, k-nn). Make sure \rho \in (-1,1) and W is row-normalized.
In short I think Sylvia's paper is really good and a companion to our paper. They seem to compliment each other and I will make sure I address that in our next draft!
January 8, 2026 at 4:48 PM
In short I think Sylvia's paper is really good and a companion to our paper. They seem to compliment each other and I will make sure I address that in our next draft!
Finally, we point out that the original parallel trends assumtpion cannot hold mechanically in the face of heterogeneous autocovariance structures. This means that there are policies that go unstudied because they don't "look parallel" when they are.
January 8, 2026 at 4:48 PM
Finally, we point out that the original parallel trends assumtpion cannot hold mechanically in the face of heterogeneous autocovariance structures. This means that there are policies that go unstudied because they don't "look parallel" when they are.
Our results show that you can disentangle the treatment effect from the propagation directly under these modified assumptions and improve external validity and still estimate the cumulative dynamic path if that is the object a practioner is interested in.
January 8, 2026 at 4:48 PM
Our results show that you can disentangle the treatment effect from the propagation directly under these modified assumptions and improve external validity and still estimate the cumulative dynamic path if that is the object a practioner is interested in.
We focus on reformulating the identifying assumptions to make them robust to this dynamic setting, which nests the static environment as a special case. Unlike this paper, we do not develop a new estimator but rather argue that things like Arellano and Bond can be used accordingly.
January 8, 2026 at 4:48 PM
We focus on reformulating the identifying assumptions to make them robust to this dynamic setting, which nests the static environment as a special case. Unlike this paper, we do not develop a new estimator but rather argue that things like Arellano and Bond can be used accordingly.
We go on to point out that what is identified under the standard assumptions in a dynamic setting is the cumulative dynamic path of the treatment, a function of both the treatment effect and its propagation through time. This has implications for external validity as the propagation remains hidden.
January 8, 2026 at 4:48 PM
We go on to point out that what is identified under the standard assumptions in a dynamic setting is the cumulative dynamic path of the treatment, a function of both the treatment effect and its propagation through time. This has implications for external validity as the propagation remains hidden.
We show that the identifying assumptions of DiD (NA and PT) implicilty require that the autocovariance structures be equal to zero to identify the object of inference as a measure of first moments only.
January 8, 2026 at 4:48 PM
We show that the identifying assumptions of DiD (NA and PT) implicilty require that the autocovariance structures be equal to zero to identify the object of inference as a measure of first moments only.
I hadn't seen this, so thank you for bringing it to my attention. I think they are related by recognizing time series attributes in panel settings. Our paper differs in the focus; rather than focusing on the estimator we focus on the object of interest and estimand.
January 8, 2026 at 4:48 PM
I hadn't seen this, so thank you for bringing it to my attention. I think they are related by recognizing time series attributes in panel settings. Our paper differs in the focus; rather than focusing on the estimator we focus on the object of interest and estimand.
If you would like to learn more I will be presenting this at the ASSA Conference this Monday January 5th at 8:00am in room 303-A of the Philadelphia Convention Center as part of the sessions organized by the @sgeecon.bsky.social. Feel free to reach out as well!
January 2, 2026 at 9:29 PM
If you would like to learn more I will be presenting this at the ASSA Conference this Monday January 5th at 8:00am in room 303-A of the Philadelphia Convention Center as part of the sessions organized by the @sgeecon.bsky.social. Feel free to reach out as well!
Overall I think we make the case that time series properties are important for identification in the DiD framework and should be considered by practioners going forward. Afterall, we live in a dynamic world where economic activity is not memoryless.
January 2, 2026 at 9:29 PM
Overall I think we make the case that time series properties are important for identification in the DiD framework and should be considered by practioners going forward. Afterall, we live in a dynamic world where economic activity is not memoryless.
Using these results we argue that one should adopt robust identifying assumptions that explicitly allow for varying autocovariance functions. This can be done through a pre-whitening step or including lags (and interactions) in the estimating equation. See the DR-PT estimates in prior images.
January 2, 2026 at 9:29 PM
Using these results we argue that one should adopt robust identifying assumptions that explicitly allow for varying autocovariance functions. This can be done through a pre-whitening step or including lags (and interactions) in the estimating equation. See the DR-PT estimates in prior images.
It is important to note that in all three of these cases the sequences of innovations are fixed and the deterministic trend is common across groups. All that we vary is the group level autocovariance function.
January 2, 2026 at 9:29 PM
It is important to note that in all three of these cases the sequences of innovations are fixed and the deterministic trend is common across groups. All that we vary is the group level autocovariance function.
The outcomes appear much farther apart (unconditionally) and do not appear to be parallel. The event study backs this up with a difference clearly showing up in the pre-treatment periods and an ever growing difference in the post-treatment periods.
January 2, 2026 at 9:29 PM
The outcomes appear much farther apart (unconditionally) and do not appear to be parallel. The event study backs this up with a difference clearly showing up in the pre-treatment periods and an ever growing difference in the post-treatment periods.
Additionally, you can see that the assumed counterfactual, which is a function of the treated groups autocovariance function, diverges from the true counterfactual. Meaning that even if we had no difference in the pre-trends, our counterfactual is poorly constructed for the DiD estimate.
January 2, 2026 at 9:29 PM
Additionally, you can see that the assumed counterfactual, which is a function of the treated groups autocovariance function, diverges from the true counterfactual. Meaning that even if we had no difference in the pre-trends, our counterfactual is poorly constructed for the DiD estimate.
This is the more pernicious case since these groups are in fact parallel, the shocks used to create these graphs are the exact same ones as before, but the groups differ in how they process those shocks through their autocovariance function.
January 2, 2026 at 9:29 PM
This is the more pernicious case since these groups are in fact parallel, the shocks used to create these graphs are the exact same ones as before, but the groups differ in how they process those shocks through their autocovariance function.
3. If the control and treated groups have heterogeneous, non-zero autocovariance functions, then parallel trends cannot hold by construction, even if the groups are parallel in truth.
January 2, 2026 at 9:29 PM
3. If the control and treated groups have heterogeneous, non-zero autocovariance functions, then parallel trends cannot hold by construction, even if the groups are parallel in truth.
Here we see a smoother transition for the treated group from the pre- to post-treatment periods with a wider distance between them despite the same innovation sequence. The event study shows a smooth transition for the treated group with the final points near the long-run value.
January 2, 2026 at 9:29 PM
Here we see a smoother transition for the treated group from the pre- to post-treatment periods with a wider distance between them despite the same innovation sequence. The event study shows a smooth transition for the treated group with the final points near the long-run value.
2. If the control and treated groups have homogenous, non-zero autocovariance functions, then the object identified is only a function of the treatment. This cumulative dynamic treatment effect converges to the long-run representation of the treatment and not the treatment effect itself.
January 2, 2026 at 9:29 PM
2. If the control and treated groups have homogenous, non-zero autocovariance functions, then the object identified is only a function of the treatment. This cumulative dynamic treatment effect converges to the long-run representation of the treatment and not the treatment effect itself.
Note that the treatment (orange) and control (blue) are parallel in the pre- and post-treatment periods with an immediate shift indicating the treatment in question. The event study coefficients support this with no difference pre- and a constant difference post-treatment.
January 2, 2026 at 9:29 PM
Note that the treatment (orange) and control (blue) are parallel in the pre- and post-treatment periods with an immediate shift indicating the treatment in question. The event study coefficients support this with no difference pre- and a constant difference post-treatment.
1. In order for No Anticipation and Parallel Trends to identify a treatment effect (time varying or time invariant) it must be the case that the treated and control groups both exhibit zero autocovariance; that is they are processes without memory. You might see something like this:
January 2, 2026 at 9:29 PM
1. In order for No Anticipation and Parallel Trends to identify a treatment effect (time varying or time invariant) it must be the case that the treated and control groups both exhibit zero autocovariance; that is they are processes without memory. You might see something like this:
My mixtape is all artists that have asphyxiated on their own vomit man...
a man is screaming in a car and saying `` hack the planet '' .
ALT: a man is screaming in a car and saying `` hack the planet '' .
media.tenor.com
December 8, 2025 at 2:22 AM
My mixtape is all artists that have asphyxiated on their own vomit man...