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synth-inference / synthdid

Synthetic difference in differences
https://synth-inference.github.io/synthdid
BSD 3-Clause "New" or "Revised" License
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Question about group specific control group #99

Closed Jeonghyeok-Kim closed 1 year ago

Jeonghyeok-Kim commented 1 year ago

Hello all,

I want to assign specific control groups (C_a, C_b) to different treatment groups (T_a, T_b). For instance, the donor pool of T_a is only C_a. I think I can have two options. For both cases, I need some help.

One is running sdid by group level and get average. I think ATT will be weighted averge of tau_a and tau_b. But I don't know whether and how in this way I can get standard error properly.

Second would be to modify sdid code to give weights only certain units. I have no idea where to start. It would be great if someone can help me out :)

Thank you so much, JK

davidahirshberg commented 1 year ago

Go for the first approach. The root-mean-square of the standard errors you get for your two (or more) groups should be a standard error for the average you’re taking.

Jeonghyeok-Kim commented 1 year ago

Go for the first approach. The root-mean-square of the standard errors you get for your two (or more) groups should be a standard error for the average you’re taking.

I really appreciate your prompt answer! Just to make sure, is following what you meant? RMSE = (w_1sigma_1^2 + ... + w_nsigma_n^2)^(1/2), where w_1 + ... +w_n =1

Best, JK

davidahirshberg commented 1 year ago

When calculating the standard error of the weighted average of effects, you're going to want to weight by w_1^2 ... w_n^2.

The idea behind this is that your group-specific treatment effect estimators should be well-approximated by independent normal random variables with means equal to the group-specific treatment effect. The standard error we estimate for each group are is an estimate of the standard deviations of the corresponding normal.

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*Jeonghyeok-Kim @.> started the conversation "[synth-inference/synthdid] Question about group specific control group (Issue #99)" with synth-inference/synthdid @.> and Subscribed @.**>.

On Tue, Feb 7, 2023 at 11:55 AM, Jeonghyeok-Kim wrote:

Hello all,

I want to assign specific control groups (C_a, C_b) to different treatment groups (T_a, T_b). For instance, the donor pool of T_a is only C_a. I think I can have two options. For both cases, I need some help.

One is running sdid by group level and get average. I think ATT will be weighted averge of tau_a and tau_b. But I don't know whether and how in this way I can get standard error properly.

Second would be to modify sdid code to give weights only certain units. I have no idea where to start.

Thank you so much, JK

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On Tue, Feb 7, 2023 at 1:45 PM, David Hirshberg wrote: Go for the first approach. The root-mean-square of the standard errors you get for your two (or more) groups should be a standard error for the average you’re taking.

Jeonghyeok-Kim commented 1 year ago

I am really grateful for your answer and explanation.

I'll use the squared weights for the standard error.

JK