The main contribution of network DEA deals with the dual role of deposits in the bank production process. Deposits are first viewed as an intermediate output, produced by, e.g., fractions of labor and capital. This intermediate output is next used as an input in the second process, together with the remaining labor and capital, to produce output combinations. A problem occurs in that network DEA suffers from the difficulty of determining the fractions of labor and capital used in the first process. This research thus develops an economic model to characterize the underlying multi-stage technologies and proposes a copula-based econometric model to identify parameters of the structural equations, including the fractional parameters, by the maximum likelihood. Our model also estimates technical efficiencies of the stochastic production and cost frontiers. We collect data from U.S. banks in 2009 to illustrate the feasibility and usefulness of our modeling, and the results are promising.