<p>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:</p>
<p><span class="math-container">$pollution^{downstream}_{i,t} = \beta_1 pollution^{upstream}_{i,t} + \beta_2 \text{county alignment}_{i,t} +  \gamma_i + \lambda_t + u_{i,t}$</span></p>
<p>Where <span class="math-container">$pollution^{downstream}_{i,t}$</span> is the pollution measured by the downstream monitoring station in station pair <span class="math-container">$i$</span> at time <span class="math-container">$t$</span>, <span class="math-container">$pollution^{upstream}_{i,t}$</span> is the pollution measured by the upstream monitoring station in station pair <span class="math-container">$i$</span> at time <span class="math-container">$t$</span>, <span class="math-container">$\text{county alignment}_{i,t}$</span> is my &quot;treatment&quot; 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, <span class="math-container">$ \gamma_i$</span> and <span class="math-container">$\lambda_t$</span> are station pair fixed effects and time fixed effects.</p>
<p>I am trying to figure out at what level should I cluster my standard errors and the intuition behind it in order to get the right conclusions about my treatment coefficient (<span class="math-container">$\beta_2$</span>). 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?</p>

CC BY-SA 4.0
2021-11-28T11:31:46.667Z
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).
Bertrand
CC BY-SA 4.0
2021-11-28T19:34:10.110Z
I believe that by adding station-pair fixed effects I am controlling for the distance between stations since the distance is constant across years
Quinoba
CC BY-SA 4.0
2021-11-28T20:36:51.277Z
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.)
Bertrand
<econometrics><regression><externalities><fixed-effects><empirical-methods>
At what level should I cluster my standard errors and why?
Quinoba
# At what level should I cluster my standard errors and why?

(Asked by: username_0 on 2021-11-24)

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?

**Tags:** econometrics, regression, externalities, fixed-effects, empirical-methods

> **Comments:**
> **username_1**: 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).  
> **username_0**: I believe that by adding station-pair fixed effects I am controlling for the distance between stations since the distance is constant across years  
> **username_1**: 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.)  

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## 0 answers

