Both the first difference model and the fixed effect models are used when there is time-invariant unobserved heterogeneity, right? Then how can one select one of them?
According to Chat GPT,
"It is true that both the first difference model and fixed effects models are used when there is time-invariant unobserved heterogeneity, rather than time-variant unobserved heterogeneity.
In deciding between the first difference model and fixed effects models, it is important to consider the nature of the unobserved heterogeneity and the research question at hand.
The first difference model is useful when the researcher is primarily interested in the short-term effects of changes in the independent variables on the dependent variable. This model can also help control for unobserved time-invariant individual-specific effects that may bias the results.
On the other hand, fixed effects models are useful when the researcher is primarily interested in the long-term effects of the independent variables on the dependent variable. This model allows the individual-specific effects to vary across time, but assumes that they are constant across individuals.
Fixed effects models control for unobserved time-invariant individual-specific effects, but not for time-variant unobserved heterogeneity.
Therefore, the choice between the first difference model and fixed effects models depends on the specific research question and the nature of the unobserved heterogeneity.
If the unobserved heterogeneity is time-invariant and the research question pertains to short-term effects, then the first difference model may be appropriate. If the unobserved heterogeneity is time-invariant and the research question pertains to long-term effects, then fixed effects models may be more suitable."
I need insight from the experts :)
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