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I am new to R, so I apologize in advance if the question may sound inappropriate.

I have a sample of 484 M&A deals (each deal is unique) and I ran a regression to understand if multiples paid for companies with a specific characteristic differ from those paid for targets that do not have it. After reviewing the literature regarding the topic, I included some control variables, but I don't understand the following: in previous papers, authors running a similar regression to the one I'm currently working on included fixed effects for "Entry Year", "Country" and "Industry" of the M&A targets. However, after looking for R codes/packages suggestions on how to do this, it seems to me that fixed effects are always used in panel data and not in samples like the one I have, where each deal is unique and I don't have N observations of the same individual over time.

How do I include fixed effects in R in the regression I'm trying to run? Is there a way to do so or am I missing some information? Maybe authors of the research papers I read are using the terminology "fixed effects" referring to some other treatment?

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If I understand correctly your dataset, you have 484 observations (rows). These observations are structured in a way such that there is:

  • at least one categorical variable such as ID_doer which is a name of someone doing something
  • at least a factor (ordinal) variable as exposure, which is the feature that some doers have and others have not (or, they have it on different levels of exposure).
  • an outcome variable which is your dependent variable

If this is the case, given the formula

outcome ~ exposure + ID_doer

you can look at the relationship between the exposure feature and your outcome feature, de-biasing the estimate of the concept express in exposure from the hidden, circumstantial, features fixed in the identity of who is doing stuff in your dataset.

This formula would work for regressions in the stats package but not for other packages like plm or lme4. Anyway, those are still quite intuitive; I think they require proper panel data to work, too.

Basically you only have a hierarchical categorical variable, so you could be interested to further investigate hierarchical/multilevel models depends by the structure of your database.

I would discourage to adopt fixed effects ("within estimation") if the average of observations per ID_doer is not sufficiently high, i.e. if there are more than 150 unique ID_doer in your dataset of 484 observations.

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