Long-Run Equilibrium and Shock Transmission among Indonesian Major State-Owned Banks: Evidence from VECM, Generalized Variance Decomposition, and Impulse Responses

Abstract

This study investigates long-run equilibrium and shock transmission among Indonesian major state-owned banking equities, focusing on Bank Mandiri, Bank Negara Indonesia (BNI), and Bank Rakyat Indonesia (BRI). While existing research has examined government ownership, bank performance, lending behaviour, financial stability, and shock exposure, comparatively less attention has been given to the dynamic interdependence of state-owned banks through their equity-market valuations. Using 199 weekly stock-price observations from 25 September 2021 to 11 July 2025, this study examines whether the three banks share a common long-run equilibrium and how institution-specific shocks propagate across the system. The empirical strategy applies Augmented Dickey-Fuller, Phillips-Perron, and KPSS tests, followed by Johansen cointegration analysis, a Vector Error Correction Model (VECM), generalized forecast-error variance decomposition, and generalized impulse-response functions. The results show that the three stock-price series are non-stationary in levels but stationary after first differencing, supporting an I(1) specification. Johansen tests provide evidence of one long-run relationship, although the trace and maximum-eigenvalue statistics indicate different levels of strength, requiring cautious interpretation. The VECM reveals asymmetric equilibrium adjustment, with BNI displaying the clearest and statistically significant response to deviations from the long-run relationship. Generalized variance decomposition shows that forecast uncertainty is not purely institution-specific, as shocks originating in other state-owned banks explain meaningful proportions of future variation and their relative importance changes across horizons. BRI becomes increasingly influential in explaining longer-horizon variation in the system. Generalized impulse responses further confirm substantial cross-bank transmission, with shocks affecting all three equities before stabilising over time. Overall, the findings portray Indonesia's major state-owned banks as an interconnected but asymmetrically structured financial subsystem in which common long-run forces coexist with heterogeneous adjustment and horizon-dependent shock transmission.