Analysing the impact of digital technology diffusion on the efficiency and convergence process of the commercial banking industry of Pakistan

The study addresses the role of digitalisation in transforming Pakistan’s banking sector and examines efficiency dynamics and convergence over 2006–2020. Technical efficiency is a widely used gauge of banking performance, decomposable into pure technical (managerial) and scale efficiencies. Prior DEA studies often lacked statistical properties, while SFA has limitations in handling multiple inputs/outputs and functional form assumptions. This study aims to provide bias-corrected efficiency estimates and robust econometric analysis. It formulates four research questions: RQ1: What is the technical efficiency of Pakistan's banking industry, and how has it changed over the period? RQ2: What is the impact of digitalisation on banking efficiency? RQ3: Does the efficiency of Pakistan’s banking industry exhibit absolute convergence? RQ4: What is the impact of digitalisation on the efficiency convergence process? The context includes growing competition from international banks, regulatory tightening, restructuring and deregulation, and rapid diffusion of digital technologies (internet, mobile, e-wallets). The purpose is to measure efficiency accurately (via bootstrap DEA), identify determinants including digitalisation (via Tobit and DPDSYS-GMM), and test absolute and conditional convergence, particularly the role of digitalisation in accelerating catch-up among less efficient banks. The study analyzes 29 banks covering roughly 90% of industry assets.

Prior research on the digitalisation–efficiency nexus in banking is mixed. Several studies (Ekinci, 2021; Li et al., 2021; Wang et al., 2021; Zuo et al., 2021; Le et al., 2022) find a positive link between digital technology adoption and efficiency, while others (Martín-Oliver & Salas-Fumás, 2008; Chen & Xie, 5) report negative associations. The evidence for Pakistan is scarce. Convergence literature in banking documents mixed results across regions: evidence of β- and σ-convergence in European Union banking (Weill, 2009; Casu & Girardone, 2010; Kasman et al., 2013; Degl’Innocenti et al., 2017), Latin America (Carvallo & Kasman, 2017), China (Matthews & Zhang, 2010; Chen et al., 2020), Arab countries (Olson & Zoubi, 2017; Mansour & El Moussawi, 2020), and India (Thota & Subrahmanyam, 2020). Conditional convergence in banking is less studied; Fung (2006) supports conditional (not absolute) convergence for US BHCs; Izzeldin et al. (2021) confirm convergence between Islamic and conventional banks; Casu & Girardone (2010) find cost-efficiency convergence but not profit efficiency; Casu et al. (2016) note long-run productivity gaps and lack of convergence in the EU. Gaps identified include limited empirical work on (i) the digitalisation–efficiency link in Pakistan, (ii) banking efficiency convergence in Pakistan, (iii) conditional convergence in banking, and (iv) the role of digitalisation in efficiency convergence. Conceptually, parallels and distinctions between macro growth convergence and micro-level banking efficiency convergence are discussed, including roles of structural reforms, technological diffusion, market integration, and human capital.

Design: Two-stage approach. Stage 1 estimates bank efficiency using DEA and bootstrap DEA; Stage 2 investigates determinants of efficiency and convergence using Tobit and two-step dynamic panel data system GMM (DPDSYS-GMM). Sample and data: 29 Pakistani commercial banks (SCBs, PSTBs, PSIBs, SPBs, FBs) from 2006–2020 (435 bank-year observations). Excludes DFIs, microfinance, and investment banks. Bank data from State Bank of Pakistan; ICT indicators (digitalisation) from ITU; macroeconomic indicators from World Bank. Stage 1 (DEA): Input-oriented CCR (CRS) and BCC (VRS) models estimate overall technical efficiency (OTE), pure technical efficiency (PTE), and scale efficiency (SE). Inputs (intermediation approach): total deposits (TD), interest expense (IE), fixed assets (FA), non-interest expense (NIE). Outputs: total loans (TL), interest income (II), non-interest income (NII). To address DEA’s statistical limitations, bootstrap DEA (Simar & Wilson 1998, 2000, 2007) with 1,999 replications provides bias-corrected efficiency scores and confidence intervals. Stage 2 (Determinants of efficiency): Second-stage regressions use panel Tobit (efficiency scores bounded between 0 and 1) and DPDSYS-GMM to account for dynamics, endogeneity, heteroskedasticity, and autocorrelation. Dependent variable: bootstrap bias-corrected efficiency (primarily BSBC-PTE for managerial efficiency). Key digitalisation variables: ATM-based transactions (ABTR), internet-based transactions (IBTR), POS-based transactions (POSBTR), and a PCA-based Digitalisation Index (DIG INDEX). Bank-specific controls: NIM, ROE, ROA, CIR, CAPT, SIZE (ln assets), AGE, ownership dummies (SCBs, PSBs, SPBs). Macroeconomic controls: INFRATE, INTRATE, GDPGR; year dummies. Convergence analysis: Absolute β-convergence: ΔlnEff_it = α + ϕ ΔlnEff_it-1 + β lnEff_it-1 + year dummies + ε_it (expected β<0). Absolute σ-convergence: ΔDEff_it = α + ϕ ΔDEff_it-1 + β DEff_it-1 + year dummies + ε_it, where DEff is deviation from cross-sectional mean; β<0 indicates σ-convergence. Conditional β-convergence: ΔlnEff_it regressed on lagged growth, initial efficiency, bank-specific digitalisation (lnABTR, lnIBTR, lnPOSBTR, DIG INDEX), countrywide digitalisation (DICTA index from fixed broadband subscribers per hundred; DICTU index from PCA of mobile subscribers per hundred and fixed telephone subscribers per thousand), additional bank controls (lnCIR, SIZE, LGR, LLPTNPL, NPLTTL, lnHR), macro controls (M2_GR, INFRATE, GDPGR), year dummies. Diagnostics: Arellano–Bond AR(1)/AR(2), Sargan/Hansen tests, instrument counts, and Wald tests reported. Robustness: Phillips and Sul (log-t) club convergence (reported in supplementary).

Efficiency levels (Stage 1): • Mean original DEA OTE (CRS) = 0.87. • Mean bootstrap bias-corrected OTE (BSBC-OTE) = 0.74; BSBC-PTE = 0.77; BSBC-SE = 0.96. Managerial (pure technical) inefficiency (≈23%) is the dominant source of overall inefficiency; scale inefficiency is comparatively minor (≈4%). Annual variation: highest BSBC-OTE in 2018 (0.77) and lowest in 2020 (0.68). Determinants of efficiency (Stage 2): • Digitalisation has a significant positive effect on efficiency across indicators: ABTR, IBTR, POSBTR, and DIG INDEX are all positive and significant in Tobit and DPDSYS-GMM (e.g., DIG INDEX coefficient ≈ 0.009–0.014, p<0.05). • Bank-specific factors: ROA and SIZE are positive and significant; NIM shows mixed/insignificant results in DPDSYS-GMM; CAPT positive in Tobit but insignificant in DPDSYS-GMM; CIR results mixed (Tobit positive; DPDSYS-GMM negative but insignificant); AGE insignificant. • Ownership: State-controlled banks (SCBs) exhibit higher efficiency than PSBs and SPBs. • Macroeconomic factors: INTRATE and GDPGR positively and significantly associated with efficiency in DPDSYS-GMM; INFRATE effect is insignificant/ambiguous. Convergence: • Absolute β-convergence: significant convergence with catch-up speed reported around 41.43% (negative and significant β). • Absolute σ-convergence: significant (negative β on dispersion term), indicating declining cross-sectional dispersion, also at ≈41.43%. • Conditional β-convergence: adding digitalisation and controls markedly accelerates convergence; speeds improve from ≈41% (absolute) up to roughly 63%–82% across model variants. Digitalisation effects in convergence: • Bank-specific digitalisation (lnABTR, lnIBTR, lnPOSBTR, DIG INDEX) positively boosts efficiency growth and accelerates convergence. • Country-level DICTU index (communications utilisation) is positive and significant; DICTA index (broadband availability) is negative in several specifications (suggested digital divide). Interactions show DICTA × SCBs negative; DICTA × PSBs positive; SPBs/FBs interactions insignificant. Additional convergence drivers: • Lower lnCIR, larger SIZE, higher LGR, higher LLPTNPL, lower NPLTTL associate with faster efficiency growth and convergence. • Higher M2 money supply growth and GDPGR support higher efficiency growth; INFRATE typically insignificant.

The study’s findings directly address the research questions. RQ1: Bootstrap DEA reveals that Pakistan’s banks operate, on average, at 74% of the bias-corrected overall technical frontier, with most inefficiency arising from managerial practices (pure technical inefficiency) rather than scale. RQ2: Digitalisation—measured via ATM, internet, POS transactions and a PCA-based digitalisation index—significantly enhances efficiency, consistent with the cost-reduction and process-streamlining benefits of digital channels. SIZE and ROA also support efficiency, and macro conditions (interest rate and GDP growth) appear conducive to improved efficiency. RQ3: Evidence of absolute β- and σ-convergence indicates that less efficient banks have been catching up to more efficient peers, and cross-sectional dispersion has narrowed over 2006–2020. RQ4: Conditional β-convergence shows that digitalisation materially accelerates the speed of convergence, suggesting that technology adoption helps lagging banks close efficiency gaps faster. Heterogeneity in countrywide digital indicators suggests a digital divide—broadband availability (DICTA) may not uniformly benefit all banks; utilisation (DICTU) positively contributes, and ownership structures moderate these effects. Overall, the results underscore digitalisation’s system-wide role in raising efficiency and promoting a more uniform, resilient banking sector, with managerial practices and macro conditions further shaping performance.

This study contributes by: (i) providing statistically robust, bias-corrected efficiency estimates for Pakistan’s banks, showing managerial inefficiency as the primary source of overall inefficiency; (ii) demonstrating that digitalisation significantly improves bank efficiency; (iii) establishing evidence of absolute β- and σ-convergence; and (iv) showing that digitalisation accelerates conditional β-convergence, enabling lagging banks to catch up more rapidly. Policy implications include supporting digital infrastructure, incentivising bank-level digital innovation, promoting prudent risk management, and calibrating monetary policy to foster a conducive macro environment. Future research directions include: • Methodological extensions to parametric frontiers (e.g., SFA) and cost/profit efficiency to triangulate results. • Broader digitalisation metrics (e.g., IT investments, R&D, blockchain, AI, fintech partnerships) and richer micro data. • Longer time horizons to capture long-run convergence dynamics and structural breaks. • Cross-country or regional comparisons to assess external validity and heterogeneity in institutional contexts.

• Methodological scope: Efficiency estimated via DEA/Bootstrap DEA; alternative parametric approaches (e.g., SFA) and cost/profit efficiency were not implemented here. • Measurement scope: Digitalisation captured by transaction volumes and composite indexes (DIG INDEX, DICTA, DICTU); other technology indicators (IT spending, AI, fintech integration) were not included. • Time horizon: 2006–2020; banking efficiency convergence can be sensitive to short-term shocks, while longer spans may be needed to capture persistent trends. • Context specificity: Findings pertain to Pakistan’s commercial banking sector and may not generalise to other countries or financial segments without caution. • Potential nonlinearity and heterogeneity: Some determinants (e.g., NIM, CIR, DICTA) exhibit model-dependent or ownership-dependent effects, suggesting further exploration of nonlinearities and interaction effects.