Petersen (2009)
The post discusses Petersen (2009) on estimating standard errors in finance panel data set.
Introduction
Two forms of dependence for a firm’s residuals
- time-series dependence (unobserved firm effect): correlated across years
- cross-sectional dependence (time effect): correlated across different firms
Estimating Standard Errors in the Presence of a Fixed Firm Effect
The standard regression for a panel data set
\[Y_{it} = X_{it}\beta+\varepsilon_{it}\]where $i$ represents firms and $t$ represents years.
We assume that $X$ and $\varepsilon$ to be independent of each other and to have a zero mean and finite variance. The OLS estimated coefficient is
\[\hat{\beta}_{OLS}=\frac{\sum_{i=1}^{N}\sum_{t=1}^{T}X_{it}Y_{it}}{\sum_{i=1}^{N}\sum_{t=1}^{T}X_{it}^{2}}\]