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All Journal EIGEN MATHEMATICS JOURNAL E-Jurnal Matematika
Ray Sastri
STIS Polytechnic of Statistics
Mathematics

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An Application of the Quantile Regression Model to the Relationship Between Digitalization and Productivity Growth in Indonesia Ray Sastri; Rofiq Nur Rizal
Eigen Mathematics Journal Vol 9 No 1 (2026): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v9i1.371

Abstract

Ordinary regression models are often inappropriate for economic performance metrics due to their tendency to have non-Gaussian distributions, heavy tails, and extreme outliers. This study analyzes the link between digitalization and provincial labor productivity growth in Indonesia using a Quantile Regression Model to capture the full, varied range of regional economic dynamics. The empirical framework assesses the combined influence of digital transformation and the underlying economic structures on productivity trajectories by using a panel data set of 34 provinces from 2017 to 2023. The baseline estimates suggest that the digital-productivity relationship is highly non-linear and more pronounced at the 50th quantile in which the direct effects of digital infrastructure, household consumption and sectoral value-added are statistically significant. Importantly, the inclusion of macro-digital interaction terms significantly changes the dynamics of the model. The results show that the marginal effect of digitalization on regional industrial upgrading is not marginal. Instead, it is highly conditional on a synergistic alignment between infrastructure, intensity of use, digital skills, and strong underlying economic baselines to effectively catalyze labor productivity gains.
AN APPLICATION OF GREY MODEL IN MODELLING SOCIO-ECONOMIC VARIABLES WITH LIMITED DATA IN NORTH KALIMANTAN RAY SASTRI; ARBI SETIYAWAN
E-Jurnal Matematika Vol. 15 No. 2 (2026)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2026.v15.i02.p508

Abstract

New administrative regions often face a severe data scarcity precludes the use of conventional econometric models and data-intensive machine learning techniques. This study evaluates the performance of Grey System Theory, specifically the classical GM(1,1) and the extended model EXGM(1,1) in modeling &forecasting socio-economics variables under limited data conditions. Utilizing official time-series data from 2013–2021, models were developed using an 8-year training set and validated against a 1-year testing set. Performance was measured using the Mean Absolute Percentage Error (MAPE). Mathematical findings reveal that both models achieve highly accurate performance with MAPE under 5% for variables with near-monotonic trends, such as Gross Regional Domestic Product (GRDP) and unemployment rate. While EXGM(1,1) demonstrated superior mathematical fit during the training phase due to optimized background values. The classical GM(1,1) proved more resilient during the testing phase, particularly for volatile indicators like poverty rates. Specifically, EXGM(1,1) exhibited a risk of overfitting to grey noise in non-monotonic datasets, leading to higher forecasting errors compared to the GM(1,1). It concludes that while EXGM(1,1) offers superior flexibility for tracking turning points in stable decaying trends, the classical GM(1,1) remains the more reliable tool for general policy interpolating due to its predictive stability and resistance to stochastic fluctuations.
Co-Authors ARBI SETIYAWAN Rofiq Nur Rizal