Implements the iterative principal-components estimator of Bai (2009) for panel data with interactive fixed effects: $$y_{it} = \alpha_i + \beta' x_{it} + \lambda_i' f_t + u_{it},$$ where \(f_t\) is an \(r\)-vector of unobserved common factors and \(\lambda_i\) is unit \(i\)'s vector of factor loadings. Unlike CCE (which proxies \(f_t\) via cross-sectional averages), IFE estimates \(f_t\) and \(\lambda_i\) directly via principal components on the residual matrix.
The algorithm iterates between:
Given \((\hat\beta, \hat\alpha_i)\), compute residuals \(\hat e_{it}\) and extract the first \(r\) principal components as \(\hat f_t\), with loadings \(\hat\lambda_i\).
Given \((\hat f_t, \hat\lambda_i)\), re-estimate \(\hat\beta\) and \(\hat\alpha_i\) by pooled OLS on the defactored data.
until convergence. The number of factors \(r\) can be specified or selected by information criteria (BIC3 of Bai & Ng 2002).
Important: IFE estimates a common (pooled) \(\beta\), not heterogeneous unit-specific slopes. If you need heterogeneous slopes, use CCE/DCCE instead.