I intended to leave a comment but do not have the reputation. I have a set of comments for you and some suggestions.

Firstly, what exactly is the intended quantity of interest? You say you want to quantify the impact on $Y_{it}$ around these events, but the impact (or treatment) is not the event itself? If your theory is simply that the event allows for some other variable to affect $Y_{it}$, then it sounds like you have an interaction model: $$Y_{it}=\beta_0+\beta_1X_{it}+\beta_2 Z_{it}+\beta_3 X_{it}Z_{it}$$ where $Z_{it}$ is a dummy variable indiciating that the event happened in unit $i$ and time $t$ and $X_{it}$ is the variable you think has an effect on $Y_{it}$.

Secondly, if the event itself is the impact or treatment, you will have difficulty identifying the effect if the treatment is heterogenously applied to units and can occur multiple times. You can look at differences in differences (DiD) with multiple time periods but it is usually assumed that the treatment is applied similarly across units.

You can possibly look into using synthetic controls (e.g., Abadie 2021), where you essentially simulate control units (i.e., who did not experience event) that are similar to the treated units in all ways except the event(s) itself.

If you were insistent on DiD, you would need to include a term for time effects (e.g., $\gamma_t$) and be cautious that your standard errors will likely be incorrect if using more than two time periods (Bertrand et al. 2004). This vignette (Callaway and Sant'Anna 2023) seems particularly relevant for you and perhaps I would start there.

In general, $\underline{\text{Mostly Harmless Econometrics}}$ may be a useful source for you. If you can clarify your quantity of interest this book will help you estimate it and to be aware of the assumptions necessary for the estimate to be any good (Angrist and Pischke 2008).

Abadie, Alberto. 2021. "Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects." Journal of Economic Literature. https://www.aeaweb.org/articles?id=10.1257/jel.20191450

Angrist, Joshua and Jörn-Steffen Pischke. 2008. Mostly Harmless Econometrics. Princeton University Press. https://www.mostlyharmlesseconometrics.com/

Bertrand, Marianne, Esther Duflo, and Sendhil Mullainathan. 2004. "How Much Should We Trust Differences-in-Differences Estimates?" The Quarterly Journal of Econometrics. https://www.jstor.org/stable/25098683

Callaway, Brantly and Pedro H.C. Sant’Anna. 2023. "Introduction to DiD with Multiple Time Periods." https://bcallaway11.github.io/did/articles/multi-period-did.html

I intended to leave a comment but do not have the reputation. I have a set of comments for you and some suggestions.

Firstly, what exactly is the intended quantity of interest? You say you want to quantify the impact on $Y_{it}$ around these events, but the impact (or treatment) is not the event itself? If your theory is simply that the event allows for some other variable to affect $Y_{it}$, then it sounds like you have an interaction model: $$Y_{it}=\beta_0+\beta_1X_{it}+\beta_2 Z_{it}+\beta_3 X_{it}Z_{it}+\varepsilon_{it},$$ where $Z_{it}$ is a dummy variable indicating that the event happened in unit $i$ and time $t$ and $X_{it}$ is the variable you think has an effect on $Y_{it}$.

Secondly, if the event itself is the impact or treatment, you will have difficulty identifying the effect if the treatment is heterogenously applied to units and can occur multiple times. You can look at differences in differences (DiD) with multiple time periods but it is usually assumed that the treatment is applied similarly across units.

You can possibly look into using synthetic controls (e.g., Abadie 2021), where you essentially simulate control units (i.e., who did not experience event) that are similar to the treated units in all ways except the event(s) itself.

If you were insistent on DiD, you would need to include a term for time effects (e.g., $\gamma_t$) and be cautious that your standard errors will likely be incorrect if using more than two time periods (Bertrand et al. 2004). This vignette (Callaway and Sant'Anna 2023) seems particularly relevant for you and perhaps I would start there.

In general, $\underline{\text{Mostly Harmless Econometrics}}$ may be a useful source for you. If you can clarify your quantity of interest this book will help you estimate it and to be aware of the assumptions necessary for the estimate to be any good (Angrist and Pischke 2008).

Abadie, Alberto. 2021. "Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects." Journal of Economic Literature. https://www.aeaweb.org/articles?id=10.1257/jel.20191450

Angrist, Joshua and Jörn-Steffen Pischke. 2008. Mostly Harmless Econometrics. Princeton University Press. https://www.mostlyharmlesseconometrics.com/

Bertrand, Marianne, Esther Duflo, and Sendhil Mullainathan. 2004. "How Much Should We Trust Differences-in-Differences Estimates?" The Quarterly Journal of Econometrics. https://www.jstor.org/stable/25098683

Callaway, Brantly and Pedro H.C. Sant’Anna. 2023. "Introduction to DiD with Multiple Time Periods." https://bcallaway11.github.io/did/articles/multi-period-did.html

I intended to leave a comment but do not have the reputation. I have a set of comments for you and some suggestions.

Firstly, what exactly is the intended quantity of interest? You say you want to quantify the impact on $Y_{it}$ around these events, but the impact (or treatment) is not the event itself? If your theory is simply that the event allows for some other variable to affect $Y_{it}$, then it sounds like you have an interaction model: $$Y_{it}=\beta_0+\beta_1X_{it}+\beta_2 Z_{it}+\beta_3 X_{it}Z_{it}$$ where $Z_{it}$ is a dummy variable indiciating that the event happened in unit $i$ and time $t$ and $X_{it}$ is the variable you think has an effect on $Y_{it}$.

Secondly, if the event itself is the impact or treatment, you will have difficulty identifying the effect if the treatment is heterogenously applied to units and can occur multiple times. You can look at differences in differences (DiD) with multiple time periods but it is usually assumed that the treatment is applied similarly across units.

You can possibly look into using synthetic controls (e.g., Abadie 2021), where you essentially simulate control units (i.e., who did not experience event) that are similar to the treated units in all ways except the event(s) itself.

If you were insistent on DiD, you would need to include a term for time effects (e.g., $\gamma_t$) and be cautious that your standard errors will likely be incorrect if using more than two time periods (Bertrand et al. 2004). $\underline{\text{Mostly Harmless Econometrics}}$ may be a useful source for you as well once you clarify what the intended quantity of interest is (Angrist and Pischke 2008). This vignette (Callaway and Sant'Anna 2023) also seems particularly relevant for you and perhaps I would start there.

Abadie, Alberto. 2021. "Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects." Journal of Economic Literature. https://www.aeaweb.org/articles?id=10.1257/jel.20191450

Angrist, Joshua and Jörn-Steffen Pischke. 2008. Mostly Harmless Econometrics. Princeton University Press. https://www.mostlyharmlesseconometrics.com/

Bertrand, Marianne, Esther Duflo, and Sendhil Mullainathan. 2004. "How Much Should We Trust Differences-in-Differences Estimates?" The Quarterly Journal of Econometrics. https://www.jstor.org/stable/25098683

Callaway, Brantly and Pedro H.C. Sant’Anna. 2023. "Introduction to DiD with Multiple Time Periods." https://bcallaway11.github.io/did/articles/multi-period-did.html

I intended to leave a comment but do not have the reputation. I have a set of comments for you and some suggestions.

Firstly, what exactly is the intended quantity of interest? You say you want to quantify the impact on $Y_{it}$ around these events, but the impact (or treatment) is not the event itself? If your theory is simply that the event allows for some other variable to affect $Y_{it}$, then it sounds like you have an interaction model: $$Y_{it}=\beta_0+\beta_1X_{it}+\beta_2 Z_{it}+\beta_3 X_{it}Z_{it}$$ where $Z_{it}$ is a dummy variable indiciating that the event happened in unit $i$ and time $t$ and $X_{it}$ is the variable you think has an effect on $Y_{it}$.

Secondly, if the event itself is the impact or treatment, you will have difficulty identifying the effect if the treatment is heterogenously applied to units and can occur multiple times. You can look at differences in differences (DiD) with multiple time periods but it is usually assumed that the treatment is applied similarly across units.

You can possibly look into using synthetic controls (e.g., Abadie 2021), where you essentially simulate control units (i.e., who did not experience event) that are similar to the treated units in all ways except the event(s) itself.

If you were insistent on DiD, you would need to include a term for time effects (e.g., $\gamma_t$) and be cautious that your standard errors will likely be incorrect if using more than two time periods (Bertrand et al. 2004). This vignette (Callaway and Sant'Anna 2023) seems particularly relevant for you and perhaps I would start there.

In general, $\underline{\text{Mostly Harmless Econometrics}}$ may be a useful source for you. If you can clarify your quantity of interest this book will help you estimate it and to be aware of the assumptions necessary for the estimate to be any good (Angrist and Pischke 2008).

Abadie, Alberto. 2021. "Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects." Journal of Economic Literature. https://www.aeaweb.org/articles?id=10.1257/jel.20191450

Angrist, Joshua and Jörn-Steffen Pischke. 2008. Mostly Harmless Econometrics. Princeton University Press. https://www.mostlyharmlesseconometrics.com/

Bertrand, Marianne, Esther Duflo, and Sendhil Mullainathan. 2004. "How Much Should We Trust Differences-in-Differences Estimates?" The Quarterly Journal of Econometrics. https://www.jstor.org/stable/25098683

Callaway, Brantly and Pedro H.C. Sant’Anna. 2023. "Introduction to DiD with Multiple Time Periods." https://bcallaway11.github.io/did/articles/multi-period-did.html