  This paper proposes a novel method to estimate large panel data
error-correction models with stationary/non-stationary covariates and spatially
dependent errors, which allows for known/unknown group-specific patterns of
slope heterogeneity. Analysis is based on composite quasi-likelihood (CQL)
maximization which performs estimation and classification simultaneously. The
proposed CQL estimator remains unbiased in the presence of misspecification of
the unobserved individual/group-specific fixed effects; therefore, neither
instrumental variables nor bias corrections/reductions are required. This
estimator also achieves the `oracle' property as the estimation errors of group
memberships have no effect on the asymptotic distributions of the
group-specific slope parameters estimates. Classification and estimation
involve a large-scale non-convex mixed-integer programming problem, which can
then be solved via a new algorithm based on DC (Difference-of-Convex functions)
programming - the DCA (DC Algorithm). Simulations confirm good finite-sample
properties of the proposed estimator. An empirical application and a software
package to implement this method are also provided.
