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Do I always have to include time fixed effects or is there also a good reason not to include them? No. The first model includes state effects, which adjust for factors that differ across states but are constant over time. The second model introduces the time effects, which now adjust for any unobserved factors that change over time but are constant across ...

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You can apply the "double machine learning" of Chernozhukov et al. (2017) outlined in this paper. To fit your problem into their framework it is useful to write it in the following notation $$Y_i = D_i\theta + X_i'\beta + \varepsilon_i$$ The variable $D_i$ is your primary variable of interest, $X_i$ are additional controls (including an intercept),...

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This is not so much an answer to your question as it is an explanation of how causal inference and the $do$ calculus can help. Let's examine a simpler model $$y = \hat{\beta}_0 + \hat{\beta}_1 X_1 + \hat{\beta}_2 X_2$$ Unless you've generated the data $X_1, X_2$ via a controlled experiment, the data may be correlated and the effects confounded by ...

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I figured out that if one of x or y don't "move" (i.e. the value is the same through the entire series) it gvies this error. I fixed it by just dropping units that have this property and the model works fine.

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I was wrestling with this issue myself, and then discovered this article by Garcia et al., where they show how traditional definition of the VIF does in fact lead to values less than unity in the case of ridge regression. They subsequently propose an alternate definition, involving the ridge parameter $k$, which leads to VIFs bounded which are bounded from ...

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