t This paper investigates the productivity and
efficiency of large bank holding companies (BHCs) in the
United States over the period 2004–2013, by estimating a
translog stochastic distance frontier (SDF) model with timevarying
heterogeneity. The main feature of this model is
that a multi-factor structure is used to disentangle timevarying
unobserved heterogeneity from inefficiency. Our
empirical results strongly suggest that unobserved heterogeneity
is not only present in the U.S. banking industry, but
also varies over time. Our results from the translog SDF
model with time-varying heterogeneity show that the
majority of large BHCs in the U.S. exhibit increasing
returns to scale, a small percentage exhibit constant returns
to scale, and an even smaller percentage exhibit decreasing
returns to scale. Our results also show that on average the
BHCs have experienced small positive or even negative
technical change and productivity growth.

• Productivity and efficiency at bank holding companies in the U.S.: a time-varying heterogeneity approach