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  • Experimental game and panel data: xtprobit or xtreg

    Hi,

    I'm currently using a dataset from an experimental game. I have 30 observations for each player, corresponding to 30 rounds played one after the other. My dependent variable is a dummy one, taking the value of 1 if the player cheated during the round, 0 otherwise.

    So far, I've been using the basic reg command, with players' fixed effects to account for time-invariant (observable/non-observable) players' characteristics.

    But I think my data are suitable to be considered as panel data (is it? Even if the observations are spread over a very short period of time (rather than days, months or years) ?). In that case, I was wondering whether it would be more appropriate to use xtprobit (without individual (players) fixed effects, as FE are not allowed using xtprobit), or xtreg (linear probability model) with players FE?

    Any thoughts?

  • #2
    Dear Marine,

    Considering that your dependent variable is binary, it would probably more appropriate to use another estimator (i.e. xtlogit, xtprobit) rather than OLS (xtreg). You can still use player fixed effects with the xtlogit command. As for considering the data as a panel, it seems that it would be appropriate since the games were played successively.

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    • #3
      In a well designed experiment, the participants are selected randomly into the different treatments. So accounting for players' fixed effects is not a concern. But you can use the Hausman test to check whether you'd be justified running a random effects model. There is no conditional probit fixed effects estimator, but there is a conditional logit fixed effects estimator. So if you have a binary outcome, take a look at xtlogit. Empirically, it matters little whether you use logit or probit. Both give very similar transformations from \(\beta^\prime x\) to \(Pr(\beta^\prime x)\).

      Code:
      help xtlogit
      Note: Crossed with #2.
      Last edited by Andrew Musau; 13 Sep 2023, 06:57.

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      • #4
        Marine:
        as others wisely suggested, I'd go -xtlogit,fe-, being aware, as Andrew explicitly mentioned, that, due to incidental parameter bias (PII: S0304-4076(99)00044-5 (brown.edu)), -xtlogit- offers a conditional fixed effect estimator.
        Kind regards,
        Carlo
        (Stata 19.0)

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