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I have a yearly panel data in which each observation is a pair of monitoring stations (stations measuring water quality in rivers) one located upstream and the other downstream, each station in the pair is in the same river and in a different but neighboring county. I am running the following regression:

$pollution^{downstream}_{i,t} = \beta_1 pollution^{upstream}_{i,t} + \beta_2 \text{county alignment}_{i,t} + \gamma_i + \lambda_t + u_{i,t}$

Where $pollution^{downstream}_{i,t}$ is the pollution measured by the downstream monitoring station in station pair $i$ at time $t$, $pollution^{upstream}_{i,t}$ is the pollution measured by the upstream monitoring station in station pair $i$ at time $t$, $\text{county alignment}_{i,t}$ is my "treatment" and is a dummy variable which equals 1 when the mayor in the neighboring municipalities where the pair of stations is located belongs to the same political party. Lastly, $ \gamma_i$ and $\lambda_t$ are station pair fixed effects and time fixed effects.

I am trying to figure out at what level should I cluster my standard errors and the intuition behind it in order to get the right conclusions about my treatment coefficient ($\beta_2$). Right now I am clustering at the station pair level, but I am not sure if I should cluster at the downstream station level, county pair level, or downstream county level? Which level do you think I should cluster on and why?

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  • $\begingroup$ Your model and data seem to be very interesting. I wonder why you do not control for the distance between upstream and downstream stations, and whether there is a tributary river flowing into the main river between two stations... I am afraid that the answer to your question depends upon missing variables in your model specification, which could create statistical dependence in the random terms (and estimation biases). $\endgroup$
    – Bertrand
    Nov 28, 2021 at 11:31
  • $\begingroup$ I believe that by adding station-pair fixed effects I am controlling for the distance between stations since the distance is constant across years $\endgroup$
    – Quinoba
    Nov 28, 2021 at 19:34
  • $\begingroup$ Yes, of course! I overlooked the fixed effects and the fact that such a distance is constant over time... (However, the interpretation in terms of environmental policies would be interesting.) $\endgroup$
    – Bertrand
    Nov 28, 2021 at 20:36

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