Interpreting Time Effects in Fixed-Effects Panel Regression

Summary

This exchange explains why adding time indicators to a firm fixed-effects panel regression can sharply raise the within R-squared. Firm fixed effects remove time-invariant differences across firms, while time dummies capture common period-by-period movements. The reported example moves from a very low within R-squared to a substantially higher one after those indicators are included.

The interpretation offered is that the time indicators explain some of the variation within firms over time, reflecting aggregate movements shared across firms. In the example, those movements are associated with the cross-sectional mean of the outcome in each period. The increase in fit alone does not show that the regressor of interest has become more informative, nor does it by itself establish that cross-sectional dependence has been corrected. The exchange gives a brief interpretation rather than a full econometric treatment of inference, model specification, or diagnostics.

Key ideas

• Firm fixed effects account for persistent differences across firms.
• Time indicators capture movements shared across firms in each period.
• A higher within R-squared can reflect aggregate outcome variation over time.
• The change in R-squared alone does not establish improved causal identification or corrected inference.

Tags

# R-squared increase dramatically when including "time dummy" (STATA)


# R-squared increase dramatically when including "time dummy" (STATA)












Currently running a fixed effect panel using STATA. First, I declare data set as panel: Code: xtset id obs

Where id = 350 firms and obs = 125

Then I run a fixed effect regression:

Code: xtreg y x, fe

The within r-squared of the fixed effect regression is 0.001

However, since I want to control for cross sectional dependence. I run the same regression but with time dummy:

xtreg y x i.obs, fe

The within r-squared increases dramatically to 0.25

The question is why there is a significant increase in r-squared? Is the increase due to higher explanatory power after correcting for cross sectional dependence?

Thanks

## Answer by Matthew Gunn (score 2, accepted)

https://quant.stackexchange.com/a/35476

It means that about 25 percent of your within firm variation (i.e. the variation of a firm over time) is explained by your time-series dummies `i.obs` which pickup the period by period cross-sectional mean.

To phrase it another way, about 25 percent of a firm's variation in $y_{it}$ over time is explained by variation in the aggregate $\bar{y}_t$.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.