A Spatial Truncated Autoregressive Regression Spline for Open Unemployment with Policy Thresholds and Spillovers in East Java

Abstract

High spatial variation is shown in East Java Open Unemployment Rates (OUR) variables, and there is a nonlinear relation with Regional Minimum Wages and Average Years of Schooling. However, two key features are often excluded from standard regression models, which are expressed policy thresholds and spatial dependency effects. They are excluded for a specific reason, namely that selecting knot locations jointly with the spatial parameter is a non-convex search that standard spatial packages do not implement, so that threshold locations in the regional policy literature are conventionally fixed at round numbers rather than estimated from the data. To address these challenges, this work introduces the Spatial Truncated Autoregressive Regression Spline (STARS) model that combines truncated spline flexibility to enable nonlinearities with a spatial autoregressive structure to measure regional dependence across regions. Knot locations are chosen using Generalized Cross Validation, but with the stipulation that candidate knots cannot occur in sufficiently sparse intervals, and parameters are estimated by concentrated Generalized Least Squares on the spatially filtered response. The analysis pools 2024 and 2025 data for the 38 regencies and cities of East Java into an estimation sample of 76 region year observations with a common year effect, and the spatial dependence is modeled by a row standardized weight matrix consisting of 5-nearest-neighbour. Two policy variables retain a threshold. The regional minimum wage bends upward at 20.2% above the provincial median, where the total effect of a wage increase rises from +0.44 to +2.12 percentage points, and average years of schooling bends at 7.97 years, where the total effect falls from +0.59 percentage points to a value indistinguishable from zero. The spatial autoregressive coefficient is ρ = 0.395 and indirect effects run at 0.604 of direct effects, so that roughly three eighths of the impact of a local policy is realized outside the jurisdiction that enacts it. STARS improves on a linear SAR benchmark in explanatory fit, in AICc and in leave one region out cross validation. A cluster bootstrap that re-runs the complete selection procedure in every replicate confirms that both thresholds are detected in a large majority of replicates, while showing that their locations are determined only within wide intervals, and we report both results.