DEA-DYNAMIC-NETWORK - Dynamic-Network DEA with Carryovers and Bad Outputs

Overview

DEA-DYNAMIC-NETWORK extends static two-stage network DEA over T time periods by incorporating (i) carryover assets c^t that link current-period choices to future production possibilities, and (ii) lagged bad inputs b^{t-1} (e.g. nonperforming loans from prior period) that constrain stage 1 capacity. Performance is measured via the weighted DN-directional distance function DN~D. Efficiency: DN~D=0. Productivity change: DNL indicator decomposed into efficiency change (DNEC) and technical change (DNTC). The nonlinear LP is linearised using Kuosmanen's (2005) variable substitution γ=φλ.

Output

Efficiency, lower is better

Data

Crisp

Size

10+ alternatives, N+Q+M+L+C ≤ J/3 per period criteria works best

Used for

Banking performance with nonperforming loans over time, multi-period two-stage production with carry-forward assets, financial institution efficiency with regulatory constraints, energy sector with accumulated emissions as bad inputs

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Assumptions to verify

• Two-stage network structure appropriate for the application
• Carryover assets measurable and clearly defined
• Bad inputs (lagged bad outputs) enter stage 1 under JWID
• Stage 2 bad outputs satisfy JWOD (jointly weak disposable with linked desirables)
• CRS frontier assumption (Σλ free); add Σλ=1 for VRS
• Initial conditions b^0 and c^0 exogenously available

Edge cases and pitfalls

• Treating carryover assets as exogenous rather than endogenously optimised choice variables causes suboptimal solutions - c^t for t=1,...,T are decision variables in the LP.

• Failing to enforce link constraints between stage 1 and stage 2 intermediate products (Eq.10.18) leads to inconsistent efficiency estimates.

• Using the nonlinear form (Eq.10.19) directly - always apply Kuosmanen linearisation substituting γ^{1t}=φ^t λ^{1t}, γ^{2t}=θ^t λ^{2t}.

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