In this paper we develop a consistent and asymptotically efficient GMM estimator of average partial effects in correlated random coefficients panel data models with a small number of time series observations, T. The problem of identification and estimation is studied without imposing the restriction that T is larger than the number of covariates, which is a necessary condition for mean group type estimators. In addition, our approach allows for a rich form of correlated unobserved heterogeneity in the residuals, based on a multi-factor error structure. Finite sample evidence shows that the proposed estimator performs well, both in terms of bias and RMSE, as well as size. The methodology is applied to a large sample of bank holding companies, operating in the US, over the period 2004-2012. We find constant returns to scale in the production of value added bank services. By contrast, inference based on standard methods indicates decreasing returns to scale.