Dear all,
I am currently working on my thesis and implementing a staggered Difference-in-Differences (DID) design. In my research, I am studying the impact of merger and acquisition events (M&A) on firm productivity, specifically measured by Total Factor Productivity (TFPQ). To address the issue of negative weighting, I am adopting the stacked regression approach proposed by Cengiz et al. (2019). This involves grouping M&A deals that occur in the same year into one cohort, creating a traditional 2*2 DID design for each cohort, and then combining them to estimate the treatment effect ($\delta_q$ in the following model).
My simplified model is as follows, where Treat is a dummy variable indicating the treatment status, EventYear is a dummy if the event happens in a certain year, $\theta$ represents cohort-unit fixed effects, q represents the time window I have selected for analysis, the time window I choose is (-3,3), and \epsilon is the error term(Note: I have simplified the notation by removing specific indices to make it more general):
\[TFPQ = \sum_{q=-3}^{+3}\delta_q\mathbb{I}\mathbb{I}\left \{ t-EventYear=q \right \}\times Treat+\theta+\epsilon \]
Based on my understanding, the final estimate of the treatment effect($\delta_q$) is a weighted average of estimates from different cohorts. However, I have a concern regarding the interpretation of the overall estimate. Let's consider an extreme case: if M&A has no effect on firm productivity, but another policy implemented in 2004 (e.g., a productivity-boosting policy that only affects the treatment group) leads to a significant $\delta_q$ in the 2004 cohort, would this result in a significant overall estimate?
To address this concern and determine if the observed significant $\delta_q$ is specific to a certain cohort rather than a general pattern, I am considering a robustness check. I would like to ask if you think this robustness check makes sense and is also necessary: I plan to repeat the stacked DID analysis, each time removing one cohort from the analysis. If the significant $\delta_q$ estimate disappears when eliminating a specific cohort, it would suggest that something specific to that cohort is driving the results, rather than the impact of M&A. On the other hand, if the results remain significant across all iterations, it would strengthen the robustness of my conclusion.
Thank you for your attention and any guidance you can provide.
I am currently working on my thesis and implementing a staggered Difference-in-Differences (DID) design. In my research, I am studying the impact of merger and acquisition events (M&A) on firm productivity, specifically measured by Total Factor Productivity (TFPQ). To address the issue of negative weighting, I am adopting the stacked regression approach proposed by Cengiz et al. (2019). This involves grouping M&A deals that occur in the same year into one cohort, creating a traditional 2*2 DID design for each cohort, and then combining them to estimate the treatment effect ($\delta_q$ in the following model).
My simplified model is as follows, where Treat is a dummy variable indicating the treatment status, EventYear is a dummy if the event happens in a certain year, $\theta$ represents cohort-unit fixed effects, q represents the time window I have selected for analysis, the time window I choose is (-3,3), and \epsilon is the error term(Note: I have simplified the notation by removing specific indices to make it more general):
\[TFPQ = \sum_{q=-3}^{+3}\delta_q\mathbb{I}\mathbb{I}\left \{ t-EventYear=q \right \}\times Treat+\theta+\epsilon \]
Based on my understanding, the final estimate of the treatment effect($\delta_q$) is a weighted average of estimates from different cohorts. However, I have a concern regarding the interpretation of the overall estimate. Let's consider an extreme case: if M&A has no effect on firm productivity, but another policy implemented in 2004 (e.g., a productivity-boosting policy that only affects the treatment group) leads to a significant $\delta_q$ in the 2004 cohort, would this result in a significant overall estimate?
To address this concern and determine if the observed significant $\delta_q$ is specific to a certain cohort rather than a general pattern, I am considering a robustness check. I would like to ask if you think this robustness check makes sense and is also necessary: I plan to repeat the stacked DID analysis, each time removing one cohort from the analysis. If the significant $\delta_q$ estimate disappears when eliminating a specific cohort, it would suggest that something specific to that cohort is driving the results, rather than the impact of M&A. On the other hand, if the results remain significant across all iterations, it would strengthen the robustness of my conclusion.
Thank you for your attention and any guidance you can provide.
