Although I saw a few similar threads, I don't believe I saw the specific answer to the following question: If your dependent variable is an average are any assumptions violated?

Let me give you some more details on what I plan to do: I am interested in detecting the effect of some policy (a treatment) on cheating in exams. A simple identification strategy would work as follows:

  1. Calculate the number of similar answers $Y$ for each pair of neighbors
  2. Consider each individual $i$. For example, individual $i=1$. This guy was sitting next to individuals $i=2$ and $i=3$. For each student $i$, calculate the average number of similar answers over both neighbors $\overline{Y}_i$.
  3. Run the following regression: \begin{equation} \overline{Y}_i = \beta_0 + \beta_1 Treatment\_Dummy_i + u_i, \end{equation} where $\beta_1$ identifies the treatment effect on the average number of similarly answered questions. Put differently, the treatment was randomized.

My question: I wonder whether this can be done? Would I get biased standard errors in this example? Are other assumptions violated?

Thank you very much!

  • $\begingroup$ Can you be more concrete about what your dependent and independent variables are and how you computed the average ? $\endgroup$ – user83346 Sep 21 '17 at 13:46
  • $\begingroup$ Thank you for this quesion. I will clarify my initial post. $\endgroup$ – bachelor Sep 21 '17 at 14:09
  • $\begingroup$ How do you define the dummy ? $\endgroup$ – user83346 Sep 22 '17 at 6:12
  • $\begingroup$ The dummy is 1 if an individual is part of the treatment group and zero otherwise. Individuals are randomly allocated to the treatment and control gruop. $\endgroup$ – bachelor Sep 25 '17 at 6:34

One assumption of linear regression is independence of errors. If Y1 is a function of neighbors Y2 and Y3, and Y2 is a function of neighbors Y1 and Y3, then the errors will be correlated. It is possible to use generalized linear regression methods to account for the correlation.

It would be difficult to randomize at the subject level to treatment groups since subjects are clustered into neighbors. If you define neighborhoods of several students and randomly allocate treatment to neighborhoods, then the model would include treatment and neighborhood effects as well as a subject effect. This will allow testing of whether the treatment has a significant impact on average sharing between neighbors given the effects of the neighborhood and individual.

  • $\begingroup$ Thank you very much. I also thought about that and planned to cluster s.e. on a row level. I think this would take care of this problem as long as students only copy answers from direct neighbors. Am I right? $\endgroup$ – bachelor Sep 21 '17 at 15:37

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