Question about Cluster Standard Errors

[Mingyu Qi]

Hi everyone,

I have a question about using cluster standard errors. I have a panel data set on facility-month level of all 50 states in the US. The actual treatment is on facility-month level, however, I have to code the treatment variable on state-month level due to the lack of data on facility-month level treatment status. So, in this case, I am estimating the intent-to-treat effect rather than the true average treatment effect. Since I am using data of all 50 states and sampling all facilities in each state, according to Abadie et al. (2023), the conventional cluster standard errors are extremely conservative under these circumstances. However, because I do not have information on facility-month level treatment status, I am not able to use to new estimators (CCV and TSCB) suggested by Abadie et al. (2023). It is my understanding that, in my case, although robust standard errors clustered on facility level might underestimate the true variance of treatment effect, they are still much closer to the true variance compared with conventional cluster standard error on state level. Any suggestions or thoughts would be greatly appreciated!

Thanks!

[shukang xiao]

Hi, if I understand correctly, you are using an aggregate variable at state level to estimate the causal effect. Since the treatment is timing variaying, I think there is variation in treatment assignment within clusters (variation across time). So according to my understanding, maybe you can use the estimator proposed by Abadie et al. (2023).

[Jeff Wooldridge]

Because the assignment is at the state level, you don't have much choice but to cluster at the state level. The AAIW adjustment doesn't work when there is dependence within cluster of the sort implied by serial correlation over time. Plus, it's unlikely you have enough observations (time periods) within a cluster for CCV to be reliable. (It's not clear how one would apply the bootstrapping procedure). One hope is to follow Ruonan Xu's extension of AAIW (2020, Econometrica) on using exogenous variables to reduce the estimated variance of the score. But, in my (admittedly) limited experience, it's hard to find improvements.

[shukang xiao]

Because the assignment is at the state level, you don't have much choice but to cluster at the state level. The AAIW adjustment doesn't work when there is dependence within cluster of the sort implied by serial correlation over time. Plus, it's unlikely you have enough observations (time periods) within a cluster for CCV to be reliable. (It's not clear how one would apply the bootstrapping procedure). One hope is to follow Ruonan Xu's extension of AAIW (2020, Econometrica) on using exogenous variables to reduce the estimated variance of the score. But, in my (admittedly) limited experience, it's hard to find improvements.

Thanks professor. I have one more question: although the treatment happened at the same time in a province or state, the intensity of the treatment may be quiet different across counties within a province. In such a case, the timing of the policy is determined by province government, which is exogeneous for county government. should we aruge that the treatment is at county level, instead of at state level? so cluster at county level?

[Mingyu Qi]

Because the assignment is at the state level, you don't have much choice but to cluster at the state level. The AAIW adjustment doesn't work when there is dependence within cluster of the sort implied by serial correlation over time. Plus, it's unlikely you have enough observations (time periods) within a cluster for CCV to be reliable. (It's not clear how one would apply the bootstrapping procedure). One hope is to follow Ruonan Xu's extension of AAIW (2020, Econometrica) on using exogenous variables to reduce the estimated variance of the score. But, in my (admittedly) limited experience, it's hard to find improvements.

Thank you for your advice, Dr. Wooldridge!

[Mingyu Qi]

Hi, if I understand correctly, you are using an aggregate variable at state level to estimate the causal effect. Since the treatment is timing variaying, I think there is variation in treatment assignment within clusters (variation across time). So according to my understanding, maybe you can use the estimator proposed by Abadie et al. (2023).

Thanks for your reply!