Technical Efficiency of Albanian Banks (2021–2023)

A Dynamic Network DEA Approach

Author

Aristea Gjokthomi

Published

April 17, 2026

Abstract

We assess the technical efficiency of nine Albanian banks — BKT, Raiffeisen, Credins, Intesa Sanpaolo, OTP, Tirana Bank, Union Bank, Fibank, and ABI — over 2021–2023 using a Dynamic Network DEA model. The production process is split into two stages: (1) converting labour, branches, and deposits into intermediate products (investments, cards, loans), and (2) converting those products into final outcomes (net income, ROE). Carry-over effects propagate part of each year’s intermediate products into the next year’s input base. We report bootstrap confidence intervals (Simar & Wilson, 1998), the Malmquist productivity index (Färe et al., 1994), and a sensitivity analysis across carry-over parameter values.

1. Data

2. Network Efficiency by Year

Bank-level summary across all years

3. Two-Stage Decomposition

Stage 1 measures how well a bank turns resources into products; Stage 2 measures how well those products translate into revenue. Points above the 45° line indicate that Stage 2 dominates; below, Stage 1 dominates.

4. Bootstrap Confidence Intervals

The red point is the bias-corrected efficiency score; the blue × is the original DEA point estimate. Given the small sample (n = 9 per year), the intervals are wide, which is expected.

5. Malmquist Productivity Index

6. Sensitivity to Carry-Over Parameters

The baseline assumes 30% of investments, 50% of the card base, and 20% of the loan portfolio carry over. Rankings can be fragile to these choices — the figure below shows how average Network efficiency shifts as we sweep the investment carry-over rate.

7. Discussion

BKT, ABI, Fibank, OTP, and Raiffeisen consistently sit at or near the efficient frontier across 2021–2023. Credins, Intesa Sanpaolo, Tirana Bank, and Union Bank show uneven performance between the two stages — a useful diagnostic: where the bottleneck lives tells management what to fix. The bootstrap intervals argue for caution in reading small efficiency gaps as real.

References

Färe, R., Grosskopf, S. (2000). Network DEA. Socio-Economic Planning Sciences.
Färe, R., Grosskopf, S., Norris, M., Zhang, Z. (1994). Productivity growth, technical progress, and efficiency change in industrialized countries. American Economic Review.
Kao, C., Hwang, S.-N. (2008). Efficiency decomposition in two-stage DEA. European Journal of Operational Research.
Sealey, C. W., Lindley, J. T. (1977). Inputs, outputs, and a theory of production and cost at depository financial institutions. Journal of Finance.
Simar, L., Wilson, P. W. (1998). Sensitivity analysis of efficiency scores: how to bootstrap in nonparametric frontier models. Management Science.
Tone, K., Tsutsui, M. (2014). Dynamic DEA with network structure. Omega.

--- title: "Technical Efficiency of Albanian Banks (2021–2023)" subtitle: "A Dynamic Network DEA Approach" author: Aristea Gjokthomi date: today lang: en format: html: toc: true toc-depth: 3 toc-location: left theme: cosmo code-fold: true code-tools: true fig-width: 9 fig-height: 6 embed-resources: true execute: warning: false message: false echo: false --- ```{r setup} library(here) library(dplyr) library(ggplot2) library(plotly) library(DT) r_files <- sort(list.files(here("R"), pattern = "\\.R$", full.names = TRUE)) invisible(lapply(r_files, source)) data <- load_bank_data() results <- dynamic_network_dea(data, verbose = FALSE) summary_tbl <- summarize_bank_performance(results) mpi <- malmquist_index(data) sens_inv <- sensitivity_carry_rates(data, param = "investime") ``` ## Abstract We assess the technical efficiency of nine Albanian banks — BKT, Raiffeisen, Credins, Intesa Sanpaolo, OTP, Tirana Bank, Union Bank, Fibank, and ABI — over 2021–2023 using a **Dynamic Network DEA** model. The production process is split into two stages: (1) converting labour, branches, and deposits into intermediate products (investments, cards, loans), and (2) converting those products into final outcomes (net income, ROE). Carry-over effects propagate part of each year's intermediate products into the next year's input base. We report **bootstrap confidence intervals** (Simar & Wilson, 1998), the **Malmquist productivity index** (Färe et al., 1994), and a **sensitivity analysis** across carry-over parameter values. ## 1. Data ```{r} DT::datatable( data, options = list(pageLength = 9, scrollX = TRUE), rownames = FALSE, caption = "Nine Albanian banks — annual observations, 2021–2023." ) ``` ## 2. Network Efficiency by Year ```{r network-trend-plot} ggplotly(plot_network_trends(results)) ``` ### Bank-level summary across all years ```{r summary-table} DT::datatable( summary_tbl, options = list(pageLength = 9), rownames = FALSE ) ``` ## 3. Two-Stage Decomposition Stage 1 measures how well a bank turns resources into products; Stage 2 measures how well those products translate into revenue. Points above the 45° line indicate that Stage 2 dominates; below, Stage 1 dominates. ```{r stage-scatter} ggplotly(plot_stage_scatter(results, year = max(results$Year))) ``` ## 4. Bootstrap Confidence Intervals ```{r bootstrap-ci, cache=TRUE} boot_stage1 <- bootstrap_by_year(data, stage = "stage1", n_boot = 500) plot_bootstrap_ci(boot_stage1) ``` The red point is the bias-corrected efficiency score; the blue × is the original DEA point estimate. Given the small sample (n = 9 per year), the intervals are wide, which is expected. ## 5. Malmquist Productivity Index ```{r mpi} plot_malmquist(mpi) ``` ```{r mpi-table} DT::datatable(mpi, options = list(pageLength = 20), rownames = FALSE) ``` ## 6. Sensitivity to Carry-Over Parameters The baseline assumes 30% of investments, 50% of the card base, and 20% of the loan portfolio carry over. Rankings can be fragile to these choices — the figure below shows how average Network efficiency shifts as we sweep the investment carry-over rate. ```{r sensitivity} ggplotly(plot_sensitivity(sens_inv)) ``` ## 7. Discussion BKT, ABI, Fibank, OTP, and Raiffeisen consistently sit at or near the efficient frontier across 2021–2023. Credins, Intesa Sanpaolo, Tirana Bank, and Union Bank show uneven performance between the two stages — a useful diagnostic: where the bottleneck lives tells management what to fix. The bootstrap intervals argue for caution in reading small efficiency gaps as real. ## References - Färe, R., Grosskopf, S. (2000). *Network DEA*. Socio-Economic Planning Sciences. - Färe, R., Grosskopf, S., Norris, M., Zhang, Z. (1994). Productivity growth, technical progress, and efficiency change in industrialized countries. *American Economic Review*. - Kao, C., Hwang, S.-N. (2008). Efficiency decomposition in two-stage DEA. *European Journal of Operational Research*. - Sealey, C. W., Lindley, J. T. (1977). Inputs, outputs, and a theory of production and cost at depository financial institutions. *Journal of Finance*. - Simar, L., Wilson, P. W. (1998). Sensitivity analysis of efficiency scores: how to bootstrap in nonparametric frontier models. *Management Science*. - Tone, K., Tsutsui, M. (2014). Dynamic DEA with network structure. *Omega*.