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I would like to run the following model: $Y_{ij}=\beta_0+\beta_1 X_{ij}+ f(controls) + e_{ij}$ where observations are collected from several individuals ($i\in[1,N]$) following several events ($j\in[1,E]$). Moreover, for each individual $i$, I have $X_{i1}=X_{i2}=\cdots=X_{iE}$.

As a concrete example suppose that $Y$ is an individual's approval rating of a politician recorded after each public speech of that politician and $X$ is the age of the individual. Also suppose that the data was collected over the course of a short period such that the age of each individual was constant.

Clearly I cannot run an OLS. Would fixed effects be appropriate in this situation (e.g., "regress approval age i.individual" run in Stata)?

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  • $\begingroup$ How bit is E, both in absolute and relative to N? Why exactly do you think OLS is inappropriate? Are you worried that the epsilons are correlated across i or j or both? $\endgroup$ – Dimitriy V. Masterov Oct 24 '17 at 19:31
  • $\begingroup$ There are 353 individuals (N=353) and 214 events (E=214), and individuals give responses in some but not all of the events. I am worried that epsilons are correlated primarily across i. Overall, I feel that OLS is inappropriate because I have multiple observations for individuals and for each individual age (the main X variable) is constant. $\endgroup$ – financial theory Oct 24 '17 at 19:52
  • $\begingroup$ I would think about clustering the errors over individuals to avoid the Moulton problem. $\endgroup$ – Dimitriy V. Masterov Oct 24 '17 at 19:54
  • $\begingroup$ Thank you for pointing towards the Moulton problem. I was unsure whether clustered errors would be sufficient as a solution but after doing some research following your comment it seems it will work for me. $\endgroup$ – financial theory Oct 24 '17 at 21:19

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