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Panel estimators such the one implemented in the R package plm allow to estimate "individual", "time" or "twoways" effects.

See page 11.

When do I use which of the three possible specifications?

KT12
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majom
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2 Answers2

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The canonical two-way model is $$ y_{it}=x_{it}'\beta+\alpha_i+\theta_t+\epsilon_{it} $$ Here, the individual effect is $\alpha_i$, and $\theta_t$ is the time effect. It is a two-way model if both are present. Thus, $\alpha_i$ captures effects that are specific to some panel unit but constant over time, whereas $\theta_t$ captures effects that are specific to some time period but constant over panel units.

So, whether you need both will, as @Ben pointed out, depend on your research question. For example, if have a panel of firms, $\theta_t$ might represent business cycle effects, whereas $\alpha_i$ would contain firm specific effects that can be argued to be constant over time, such as the "culture" of the firm.

Christoph Hanck
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  • Thank you for this explanation and example! I understood both the interpretation of the individual effect and the time effect in a fixed-effects-model. However, I am unsure about the interpretation of a Two-way-fixed-effects-model with individual as well as time effects. How should I interpret this Two-way-model? Are there business cycle effects for every firm (or firm cultures)? Or do both effects exist without interacting? – TobKel Apr 07 '21 at 08:16
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    The effects enter additively, so there is no interaction between the effects, so all business cycle effects, say, affect firms, say, equally. Factor models, that however require large $T$, relax the requirement that each firm is affected equally. – Christoph Hanck Apr 08 '21 at 16:17
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It depends on your research, in some cases time effects could solve the cross-sectional problem. An article that is very useful is "Estimating Standard Errors in Finance Panel Data Sets: Comparing Approaches" by Mitchell A. Petersen, 2009.

In fact, twoways here means both individual and time effects, so it is just two specifications

hope this helps

Ben
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