Introduction
The discourse surrounding post-pandemic learning recovery in Indonesia has long been trapped in an urban-centric visual bias. Lavish budgetary allocations for school digitalization and the widespread adoption of app-based learning frameworks are frequently hailed as benchmarks of national success. However, when massive longitudinal datasets are subjected to micro-level scrutiny through rigorous econometric modeling, a starkly different structural reality emerges.
This article intentionally shifts the spotlight to the bedrock of the national education landscape: rural communities. Far from being mere statistical filler on paper, these regions represent the true epicenter where the future cognitive capacity of the next generation is actively at stake. By isolating this specific sample, we unpack the hidden dynamics of foundational competencies in areas that have long been excluded from mainstream policy publications.
Methodological Framework: Fixed Effects (FE) and Urban Sample Exclusion
Before dissecting the empirical shifts within the data, it is crucial to clarify our methodological boundaries to prevent any misinterpretation of the findings. Specific sample filtering was conducted by evaluating the baseline distribution of the data, which revealed severe observational asymmetries. The valid, de facto longitudinal National Assessment (AN) dataset for primary education spanning the 2021–2025 period is heavily concentrated in rural areas, comprising 1,032 observations for rural public elementary schools (SD) and 63,525 observations for rural Islamic elementary schools (Madrasah Ibtidaiyah/MI).
Conversely, the urban subsample was virtually non-existent, yielding a meager 7 observations for urban public schools and 31 observations for urban madrasahs. Theoretically, a sample size this minuscule lacks the necessary inter-temporal variation required for panel modeling, causing it to be automatically omitted by the system due to perfect multicollinearity. Consequently, to maintain strict scientific validity, the urban cohort was formally excluded from our estimations. This ensures that all subsequent analyses objectively capture the distinct educational reality of rural Indonesia.
A Fixed Effects (FE) approach was deployed to control for all time-invariant school-level characteristics—such as permanent geographic constraints, baseline accreditation tiers, and deeply embedded institutional cultures. Through an internal within-transformation, this model isolates and observes the direct impact of policy interventions occurring within the schools themselves between 2021 and 2025. Finally, standard errors are strictly clustered at the school level to correct for potential serial correlation biases over time.
Determinant Factor Analysis: Public Rural Schools vs. Rural Madrasahs
To analyze how domestic household socioeconomic disadvantages compete with time-bound policy interventions at the grassroots level, we examine the estimation parameters yielded by our FE specification. The table below juxtaposes the elasticity parameters for numeracy and literacy performance across rural school ecosystems.
Table 1. Fixed Effects Panel Estimates: Spatial Impacts Across Rural Regions
| Variables | (1) NUM: SD Rural | (2) NUM: MI Rural | (3) LIT: SD Rural | (4) LIT: MI Rural |
|---|---|---|---|---|
| SES_siswa | -0.484** (0.151) |
-0.554*** (0.024) |
-0.907*** (0.191) |
-0.797*** (0.031) |
| SES_sekolah | -0.012 (0.077) |
-0.036** (0.013) |
-0.031 (0.076) |
-0.014 (0.016) |
| 2021.year | 0.000 (.) |
0.000 (.) |
0.000 (.) |
0.000 (.) |
| 2024.year | 10.815*** (1.053) |
14.874*** (0.181) |
1.316 (1.318) |
6.776*** (0.228) |
| 2025.year | 9.242*** (1.196) |
9.705*** (0.204) |
1.717 (1.444) |
2.254*** (0.253) |
| _cons | 57.836*** (8.398) |
64.520*** (1.458) |
93.378*** (10.900) |
87.436*** (1.873) |
| R-squared (Within) | 0.636 | 0.630 | 0.272 | 0.333 |
| Observations | 772,000 | 47,563,000 | 771,000 | 47,557,000 |
Note: Figures in parentheses represent robust standard errors clustered at the school level. Statistical significance levels are indicated by: * p < 0.05, ** p < 0.01, *** p < 0.001.
The parameters in Table 1 expose a highly concerning sociological anomaly. Within the literacy domain for rural public elementary schools (Column 3), the inter-temporal coefficients for the years 2024 (1.316) and 2025 (1.717) entirely lose their statistical significance (p > 0.05). This finding empirically verifies an absolute paralysis in literacy progress; rural reading programs at the public school level have completely stagnated, failing to yield any meaningful cognitive improvements since the 2021 baseline year.
Conversely, student-level Socioeconomic Status (SES_siswa) exerts an unrelenting grip across all model specifications with highly significant negative coefficients. This empirical phenomenon confirms that the primary bottleneck hindering cognitive recovery in rural regions does not stem from a deficiency in school physical infrastructure (the school-level socioeconomic variable, SES_sekolah, proved insignificant in most models). Rather, it is a direct consequence of entrenched, structural economic deprivation within the students’ own households.
Stability Versus Systemic Shocks
At first glance, reading the terminal coefficients for the 2025 numeracy model can be deceptive, as the coefficient for rural madrasahs (9.705) appears slightly higher than that of public elementary schools (9.242). However, to accurately evaluate the dynamic trajectory and pinpoint which institution bore the brunt of post-pandemic shocks, one must observe the magnitude of the year-over-year degradation. This momentum is clearly captured by the visualization of predictive marginal effects in the graph below:
The marginal effects graph provides absolute visual validation of a severe “cognitive hemorrhage” across rural landscapes. Measured by the rate of elasticity degradation (the net drop from 2024 to 2025), the rural madrasah ecosystem experienced a far more punishing trend reversal. The impressive recovery momentum achieved by rural madrasahs in 2024 (+14.874) suddenly cratered, plummeting by -5.169 points in a mere twelve-month window. By contrast, rural public elementary schools demonstrated a more resilient buffering mechanism, experiencing a much shallower correction of -1.573 points.
Furthermore, the visual spread of the confidence intervals (error bars) offers profound theoretical insights. The vertical lines for public schools (blue) span quite wide, illustrating that adaptive capacities among rural public schools are highly unequal and heterogeneous. Conversely, the interval bars for rural madrasahs (red) are tightly polarized, compressed, and highly precise. This hyper-consistent interval pattern signals a uniform structural mechanism at play. The collapse in 2025 numeracy performance was not an isolated case restricted to a few madrasahs; it reflects a systemic crisis ripping through the entire rural religious sector, driven by fragile, community-funded operational structures buckling as artificial, centralized stimulus interventions hit their saturation point.
Conclusion & Policy Recommendations
The pendulum of national education policy can no longer be driven by rigid, top-down macro standardization. For strategic decision-makers, the steep cognitive decline observed within rural madrasahs stands as an early distress signal: the local, faith-based social capital that historically sustained these institutions has officially hit its structural ceiling.
The government and its ministries must urgently reorient intervention frameworks toward targeted, affirmative fiscal assistance that directly addresses domestic family socioeconomic asymmetries (SES_siswa). This redistribution of cognitive assets is a far more pressing priority than continuing to sink capital expenditure into cosmetic digital hardware, which empirical data proves only sparks brief, artificial acceleration at the grassroots level.