We have a panel dataset on 2 variables $Y_{it}$ and $X_{it}$. Imagine that we know of another key variable $Z_{t}$ which is unobserved, correlated with both $Y$ and $X$, and varies over time but is constant across entities.
If we are interested in estimating the causal effect of $X_{it}$ on $Y_{it}$, we could estimate the following model with time fixed effects: $Y_{it}=\beta_1X_{it}+\lambda_{t}+u_{it}$ The time-fixed effects ($\lambda_{t}$) will allow us to control for ALL the unobserved variables that vary across time and are constant across entities; therefore time fixed effects will control for $Z_t$ among others. This may or not end up giving us the causal effect of interest; it will depend on the DAG but in the least the time fixed effects allowed us to control for $Z_t$ and let's suppose that gives us an estimate of the causal effect that is closer to the true causal effect than a model that does not control for $Z_t$.
Now, imagine that we are interested in predicting $Y_{it}$ using $X_{it}$. Is there any way we can leverage our knowledge that there is a key variable $Z_{t}$ correlated with both $Y$ and $X$ that varies over time but is constant across entities? For prediction purposes can we say anything about how the regression without time fixed effects $Y_{it}=\beta_0+\beta_1X_{it}+u_{it}$ will compare to the one with time fixed effects $Y_{it}=\beta_1X_{it}+\lambda_{t}+u_{it}$? Would we ever want to use the time fixed effects model for prediction?
Here is a link to a distantly related question.
