As a statistics enthusiast, I’ve often come across the terms R² and Within R² in panel event studies. But what do they really mean, and how do we interpret them?
When running a panel event study with unit and time fixed effects, our output often reports both overall R² and Within R². While the intuition behind Within R² – variance explained after de-meaning by unit and time – is clear, it’s essential to have a solid understanding of these metrics to make informed decisions.
The Difference Between R² and Within R²
R², or the coefficient of determination, measures the proportion of variance in the dependent variable explained by the independent variables. In other words, it tells us how well our model fits the data. However, in panel event studies with unit and time fixed effects, we’re dealing with multiple observations for each unit (e.g., individuals, firms, or countries) across different time periods.
This is where Within R² comes in. Within R² calculates the variance explained after controlling for unit and time fixed effects. It’s like de-meaning the data by unit and time, and then calculating the R² value. This provides a more accurate picture of the variance explained by our model, as it accounts for the differences between units and time periods.
Interpreting Within vs. Overall R² in TWFE Event-Study Specs
When interpreting R² and Within R² in TWFE (Two-Way Fixed Effects) event-study specifications with leads and lags, it’s essential to keep the following in mind:
- Overall R²: This value gives us an idea of the overall fit of the model. However, it can be misleading, as it doesn’t account for the unit and time fixed effects.
- Within R²: This value provides a more accurate representation of the variance explained by our model, as it controls for unit and time fixed effects. A higher Within R² value indicates a better fit of the model.
Citable Sources
For those interested in diving deeper, I recommend checking out:
- Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data. MIT Press.
- Cameron, A. C., & Trivedi, P. K. (2005). Microeconometrics: Methods and Applications. Cambridge University Press.
These sources provide a comprehensive introduction to panel event studies, TWFE models, and the interpretation of R² and Within R².
By understanding the difference between R² and Within R², we can better analyze our panel event study data and make more informed decisions.
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Further reading: Panel Data Analysis