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I'm just learning econometrics, so I would like to know if I can use fixed effects/random effects on cross-sectional data. I have read many papers where they use these model with data panel, but my data is cross-sectional. I study the effects on students performance.

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  • $\begingroup$ You may add the fixed effects or individual dummies by using penalized regression, such as, Lasso or ridge regression. There is a blog that proposes this approach $\endgroup$ Oct 8 '18 at 19:07
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The basic fixed effect model is something like:

$$y_{ij} = \boldsymbol{\beta} \cdot \mathbf{x}_{ij} + u_j + \epsilon_{ij}$$

Typically, either $j$ or $i$ is indexing over time, but there's no reason it can't be anything else. The math doesn't care. $i$ could index over students and $j$ could index classroom.

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The second dimension does not need to be time, or even ordered. You could have pairs of twins, students within classrooms, or exams of individuals where the second dimension is questions. However, whether FE or RE or FD makes sense, depends on your research question and the type of heterogeneity that you want these effects to represent.

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You may add the fixed effects or individual dummies by using penalized regression, such as, Lasso or ridge regression. There is a blog that proposes this approach

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  • $\begingroup$ At present this is more of a comment than an answer. You could expand it, perhaps by giving a summary of the information at the link, or you could convert it into a comment. $\endgroup$ Oct 8 '18 at 17:00

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