Panel Data Models with Grouped Factor Structure Under Unknown Group Membership

Abstract

This paper studies panel data models with unobserved group factor structures. The group membership of each unit and the number of groups are left unspecified. The number of explanatory variables can be large. We estimate the model by minimizing the sum of least squared errors with a shrinkage penalty. The regressions coefficients can be homogeneous or group specific. The consistency and asymptotic normality of the estimator are established. We also introduce new C p -type criteria for selecting the number of groups, the numbers of group-specific common factors and relevant regressors. Monte Carlo results show that the proposed method works well. We apply the method to the study of US mutual fund returns under homogeneous regression coefficients, and the China mainland stock market under group-specific regression coefficients.

Sparse estimation of huge networks with a block‐wise structure

“…Although there are many examples in economics where the membership is given, in many others this is not true, making the assumption that the block structure is known a priori too restrictive. One interesting extension of this work would be to determine endogenously the inclusion of a unit in a group as well as the size and number of the groups, following the work by Lin and Ng (2012), Bonhomme and Manresa (2015) and Ando and Bai (2016). Future work should also consider a block-wise structure for the covariance matrix of a VAR model, within the setting proposed by Barigozzi and Brownlees (2016) and Abegaz and Wit (2013).…”

“…It is important, however, to remark that our approach requires a priori information on the block structure. If this is not available, then one could exploit methods from the clustering literature that allow us to determine endogenously the optimal grouping of cross-sectional units, such as the k-means algorithm (Forgy, 1965) extended to allow for covariates in the model; see, in particular, Lin and Ng (2012) and Bonhomme and Manresa (2015), and also Ando and Bai (2016). Our approach also has potential application in the area of spatial econometrics.…”

“…When the grouping is not fully known a priori, we could use methods that allow us to determine endogenously the optimal grouping of cross-sectional units, by employing techniques from the clustering literature; see, e.g. Lin and Ng (2012), Bonhomme and Manresa (2015) and Ando and Bai (2016).…”

Multi-level factor analysis of bond risk premia

“…This is meant to find out those variables with predictive power independent of an already known predictor, Cochrane and Piazzesi's factor. 3 Recently, Ando and Bai (2016) analyze a similar model. Their model allows a set of observed variables as well as group factors.…”

Econometric Analysis of Large Factor Models

“…Bai & Wang (2015) Panel regression models with heterogenous slop coefficients and with a block factor error structure are studied by Ando & Bai (2015a), where each block is referred as a group. The case of unknown group membership is examined by Ando & Bai (2016a), where common slope coefficients across individuals or group-dependent coefficients are assumed. Heterogenous slope coefficients with unknown group memberships are studied by Ando & Bai (2016b).…”