Z12 | Macro Paper Warehouse

Praying for Rain

Mon, 01 Jan 0001 00:00:00 +0000

This paper studies rainmaking as an instrumental religious belief. The central research question is: why do people believe that prayer can bring rain, even though it does not work? The authors develop a model of cultural evolution in which a religious leader prays for rain at an arbitrary time, and people update their beliefs about whether the leader can cause rainfall based on whether rain follows. The key mechanism is the local rainfall hazard function — the probability of rain conditional on how many days have passed since the last rainfall. In environments where the hazard is increasing (rain becomes more likely the longer a drought continues), a leader who prays during a drought will tend to be followed by rain, creating the illusion of efficacy. In environments with a flat or declining hazard, prayer cannot be systematically followed by rain in a persuasive way. The model yields five predictions: rain ritual traditions will select for prayers correlated with rainfall; the level of average rainfall does not determine persuasiveness; constant-hazard environments cannot support persuasive prayer; increasing-hazard environments are more likely to adopt rainmaking; and higher net benefits of rainfall (e.g., settled agriculture) further increase the likelihood of ritual.

The authors test these predictions with two empirical strategies. First, they use daily data from the Catholic church in Murcia, Spain, covering 1600 to 1836. Church records provide the daily timing of pro pluvia rogations (prayers for rain), while municipal council records — kept independently of the church — record notable rainfall events. Murcia’s rainfall hazard is estimated to be increasing after long dry spells: the hazard rate after a long drought is roughly double the hazard rate two months after the last rainfall. The main finding is that a prayer for rain in the last 30 days predicts a 0.144 percentage-point higher daily probability of notable rainfall (standard error 0.057 pp), relative to a baseline mean daily rainfall probability of 0.203 pp — a 71% increase in the predicted probability. Prayer also Granger-causes rainfall conditional on lags of recent rainfall, and the predictive power holds within a given calendar month, ruling out a purely seasonal coincidence.

Second, the authors construct an original dataset covering rainmaking practice for 1,208 ethnic groups drawn from the Ethnographic Atlas (Murdock, 1967), coded from 370 anthropological sources. They match each ethnic group to its nearest weather station and estimate the rainfall hazard function each group faces in its ancestral location. Of the 1,208 groups, 33% face an increasing rainfall hazard, and 39% of all groups practice rain ritual. The main global finding is that ethnic groups facing an increasing rainfall hazard are 14 percentage points more likely to practice rainmaking (standard error 3.7 pp), relative to a base rate of 30% among groups facing a non-increasing hazard — a 47% increase. This result is robust to continent fixed effects, geographic and climatic controls (longitude, latitude, elevation, distance to coast, ruggedness, mean temperature, mean rainfall, coefficient of variation of rainfall, maximum dry spell length, and the Giuliano-Nunn 2021 climatic variability measure), alternative hazard estimation methods, and linguistic family fixed effects. Crucially, lower average rainfall, longer droughts, and greater climatic variability are not associated with more rain ritual conditional on hazard shape — it is specifically the shape of the hazard function, not aridity or variability per se, that drives adoption.

A second global finding concerns demand: groups dependent on agriculture are 11 pp more likely to practice rainmaking; those dependent on intensive agriculture, 21 pp more likely; and those dependent on intensive irrigated agriculture, 32 pp more likely (on a base of 32%). The scope of the findings is the pre-modern or traditional period captured by the Atlas; the Murcia case covers 1600–1836. The authors conclude that some environments create an illusion of efficacy that sustains instrumental religious belief through cultural selection, without requiring that believers be irrational.

Q: What is the paper’s central theoretical claim about why rainmaking beliefs persist? A: The paper argues that in environments where the rainfall hazard is increasing during a drought, a leader who begins praying during a dry spell will tend to be followed by rain, because the probability of rain rises as the drought lengthens. People who cannot observe the counterfactual hazard (what rainfall would have been without prayer) interpret this coincidence as evidence that prayer works. Cultural selection then favors leaders whose prayer timing is more persuasive, causing the belief to persist across generations even though prayer does not actually cause rain.

Q: What is the rainfall hazard function, and why does its shape determine whether prayer can be persuasive? A: The hazard function h(t) gives the instantaneous probability of rain at time t days after the last rainfall. If the hazard is flat, the probability of rain is the same regardless of whether prayer was offered or not, so there is no systematic correlation between prayer and rainfall to exploit. If the hazard is declining, prayer during a drought will be followed by lower-than-average rainfall probability, undermining the leader. Only if the hazard is increasing does prayer during a long dry spell systematically coincide with a higher probability of rain, creating a persuasive correlation.

Q: What do Propositions 2 and 3 of the model establish? A: Proposition 2 establishes that if the hazard rate is constant and a person’s prior belief that prayer works is below 0.5, then no prayer start time can persuade them to support the leader. Proposition 3 establishes the converse: if the hazard rate is increasing and the prior is below 0.5, there exists a meaningful belief for which a person will support the leader for any prayer start time. Together these propositions identify the increasing hazard as the necessary and sufficient structural condition for persuasive prayer.

Q: What is the main quantitative finding from Murcia, and what identification strategy supports it? A: A prayer for rain in the last 30 days predicts a 0.144 percentage-point higher daily probability of notable rainfall (standard error 0.057 pp) relative to a baseline mean of 0.203 pp, a 71% increase. The authors additionally demonstrate that prayer Granger-causes rainfall conditional on lags of recent rainfall, and that the effect holds within a given calendar month, ruling out the explanation that prayer simply tracks the rainy season. The prayer and rainfall records are kept by independent institutions (church and municipal council), reducing the risk of strategic recording.

Q: How does the hazard rate in Murcia behave, and does it satisfy the model’s key condition? A: The hazard of rainfall in Murcia is initially high just after rain, declines to a minimum roughly two months after the last rainfall, and then increases significantly thereafter, reaching or exceeding its initial level after a long drought. The fluctuations are large: the hazard after a long dry spell is roughly double the hazard two months after rainfall. This U-shaped pattern means the hazard is increasing during a prolonged drought, satisfying the model’s key condition for persuasive prayer.

Q: How was the global rainmaking dataset constructed, and what is its coverage? A: The authors used the Ethnographic Atlas (Murdock, 1967) as a template, covering 1,290 ethnic groups, and combed 370 anthropological sources — primarily group-specific ethnographic monographs — to code rainmaking practice for 1,208 groups. A group is coded as practicing rain ritual only if there is clear evidence of a practice specifically intended to bring rain through supernatural means. The authors treat their measure as a lower bound. They find that 39% of the 1,208 groups practice rainmaking, across every settled continent.

Q: What is the main global regression result and how robust is it? A: Ethnic groups facing an increasing rainfall hazard are 14 percentage points more likely to practice rain ritual (standard error 3.7 pp) relative to a base rate of 30%, a 47% proportional increase. This coefficient is positive and statistically significant across all specifications, including those adding continent fixed effects, a full battery of geographic and climatic controls (longitude, latitude, elevation, distance to coast, ruggedness, mean temperature, mean rainfall, coefficient of variation of rainfall, maximum dry spell length, and the Giuliano-Nunn 2021 climatic variability measure), alternative hazard estimation methods, linguistic family fixed effects, and restrictions to groups with high-quality rainfall data.

Q: Does aridity or climatic variability explain rainmaking adoption? A: No. Lower average rainfall, longer droughts, and greater climatic variability (measured using the Giuliano-Nunn 2021 index) are not associated with more rain ritual practice, conditional on the shape of the hazard function. This rules out the naive hypothesis that people pray for rain simply because they do not get enough, or because their rainfall is unreliable. It is specifically the shape of the hazard — whether it is increasing during a drought — that drives adoption, not the level or volatility of rainfall.

Q: How does demand for rainfall, proxied by agricultural subsistence, affect rainmaking adoption? A: Groups dependent on agriculture are 11 percentage points more likely to practice rainmaking relative to other subsistence modes. Groups dependent on intensive agriculture are 21 percentage points more likely, and groups dependent on intensive irrigated agriculture are 32 percentage points more likely, all on a base of 32%. This gradient is consistent with Proposition 5 and 6 of the model: settled, location-specific agricultural investment raises the net benefit of rainfall control, increasing support for rain ritual independently of the persuasion channel.

Q: What does the model’s cultural evolution mechanism (Proposition 4) predict about how prayer timing changes over generations? A: Proposition 4 states that rituals with high support are more likely to persist. In increasing-hazard environments, random variation in prayer timing means some leaders gain more support than others; those with more persuasive timing are more likely to persist. Each generation then adopts a policy at least as persuasive as the prior generation, so support rises over time and prayers gradually converge toward the timing that maximizes persuasiveness. This mechanism does not require deliberate optimization by any individual leader.

Q: How does the paper’s finding relate to the long-standing anthropological debate between the traditional and revisionist schools on rainmaking? A: The traditional school (following Frazer 1890) holds that belief is instrumental — people engage in rainmaking to make rain, and belief responds to empirical evidence. The revisionist school (Wittgenstein, Durkheim) argues that religious belief and rationality are fundamentally separate, and religious practice is performative rather than evidence-responsive. The paper’s finding that rainmaking is more prevalent precisely where it is more persuasive — i.e., where the environment makes prayer appear to work — supports the traditional, instrumental interpretation that belief responds to evidence of efficacy.

Q: What are the scope conditions for the paper’s conclusions? A: The Murcia case study covers the period 1600–1836, ending when the abolition of tithes reduced the church’s funding and influence; it applies to a sophisticated Catholic institutional context. The global analysis covers traditional practices of pre-modern ethnic groups as recorded in the Ethnographic Atlas and anthropological literature; it does not speak to modern religious practice or to religions after substantial modernization. The persuasion mechanism requires that people cannot directly observe what rainfall would have been without prayer, a condition satisfied in pre-scientific contexts.

Rainfall hazard function: In this paper’s usage, the function h(t) = f(t)/(1-F(t)) giving the instantaneous probability of rainfall at time t days since the last rainfall. Its shape — whether flat, declining, or increasing during a drought — determines whether prayer can be persuasive, not the overall level of rainfall.

Increasing hazard: A hazard rate that rises as the length of a dry spell increases, so that rain becomes more likely the longer the drought has continued. The paper defines this specifically as the derivative of the hazard function evaluated at the 99th percentile of spell length. This is the necessary structural condition for prayer to seem efficacious.

Instrumental religious belief: Belief directed at achieving a worldly outcome (here, rainfall), as opposed to purely expressive or social belief. The paper treats belief as instrumental if it responds to perceived evidence of efficacy and is adopted where it appears to work.

Persuasion (in the model): The process by which a leader’s prayer timing causes people to update their belief that prayer works, by generating a correlation between prayer and subsequent rainfall that exceeds what people expect from the background hazard rate. Persuasion is possible only when the hazard is increasing.

Pro pluvia rogations: The Catholic church’s formal prayers for rain, practiced in Murcia since at least the 14th century. In the paper’s data, these prayers follow a pattern of escalation — increasing in number and intensity — during prolonged droughts, consistent with the model’s prediction about prayer timing.

Cultural evolution: The paper’s framework (drawing on Henrich 2015) in which religious leaders act as cultural entrepreneurs; leaders whose prayer timing happens to be more persuasive gain greater support and are more likely to survive across generations, so prayer traditions drift toward more persuasive timing without deliberate design.

Rain ritual (global measure): A binary indicator coded as one for an ethnic group if the anthropological literature contains clear evidence of a practice specifically intended to bring rain through supernatural means, including dances, sacrifices, prayers, and petitioning of rain deities. Treated by the authors as a lower bound on actual prevalence.

Religion, Education, and the State

Mon, 01 Jan 0001 00:00:00 +0000

This paper studies how Indonesia’s Islamic education sector responded to one of the largest state-driven mass schooling expansions in history — the SD INPRES program (Sekolah Dasar Presidential Instruction) launched in 1973 — and whether that program achieved its secular nation-building objectives. The research question is three-part: Did Islamic schools enter or exit markets where the state built more primary schools? How did religious school choice shift across cohorts? And did the program advance secular identity formation among exposed individuals?

The empirical setting is Indonesia in the 1970s onward. Under SD INPRES, the government used windfall oil revenues to build more than 61,000 primary schools between 1973 and 1980, allocating construction across districts proportional to the non-enrolled primary-school-age population. Because Islamic schools were historically more prevalent in underserved areas, this rule produced a strong positive correlation between SD INPRES intensity and pre-existing Islamic school density — the same markets where the state expanded were precisely those with the greatest Islamic education presence.

The authors use several novel data sources: administrative registries covering nearly 220,000 secular and 160,000 Islamic schools with establishment dates; six rounds of the National Socioeconomic Survey (Susenas) from 2012–18; the Indonesia Family Life Survey (IFLS, 1993–2014); a 2018–19 curriculum timetable registry (SIAP) covering nearly 20% of madrasa; and a 2016 political/religious attitudes survey. Identification relies on difference-in-differences (DID) exploiting cross-district variation in SD INPRES intensity, the synthetic DID approach of Arkhangelsky et al. (2021) for robustness to violations of parallel trends, and a staggered village-level event study using the Borusyak et al. (2024) estimator.

The main findings are as follows. First, Islamic schools did not exit markets where the state expanded — they entered in greater numbers. A one standard deviation increase in SD INPRES construction led to 1.4 additional Islamic school entries per district above a mean of 1.9 per district in 1972. Entry was competitive at the primary level, where new madrasa (MI) entered at twice the baseline annual rate in the years immediately following INPRES construction, and strategic at the secondary level, where Islamic junior secondary schools (MTs) peaked 6–9 years after INPRES entry as graduates sought continued education. The Islamic sector financed this expansion through waqf (inalienable religious endowments), informal taxation (infaq, zakat), and revenues from a concurrent rice price spike; entry responses were stronger in villages with above-median waqf endowments and above-median potential rice yields.

Second, rather than converging toward secular curricula, newly established Islamic schools in high-INPRES districts devoted more time to religious content. Each additional SD INPRES is associated with a 1.2 percentage point increase in the religious curriculum share among newly created madrasa, with increases of 1.3 and 2.4 percentage points at the primary and junior secondary levels respectively — the latter equaling 82% of the cross-school standard deviation. Some of this increase came at the expense of Pancasila/civic education and national language instruction.

Third, while SD INPRES reduced Islamic primary school enrollment by roughly 7%, it increased overall Islamic school attendance: each additional SD INPRES increased the likelihood of attending any Islamic school by approximately 5%, as demand for secondary education outweighed substitution at the primary level. Female students exhibited stronger secondary-level demand effects, amplified in districts with a concurrent state ban on the Islamic veil in public schools.

Fourth, SD INPRES did not advance its ideological objectives. In the 1977 and 1982 elections, Golkar’s vote share fell and the Islamic PPP’s rose by 0.5–1.0 percentage points per SD INPRES school in high-INPRES districts. Among exposed cohorts, SD INPRES did not increase Pancasila proficiency, national language use at home, or support for secular governance, but did increase Arabic literacy by approximately 3% per additional SD INPRES. Exposed cohorts also prayed more frequently, fasted more during Ramadan, gave more to charity, and expressed greater pilgrimage intentions. These religious patterns were transmitted to children of exposed cohorts, who were more likely to attend Islamic schools themselves.

Q: What was the allocation rule for SD INPRES and why did it create confrontation with Islamic schools? A: Presidential Instruction No. 10/1973 allocated school construction across districts proportional to the non-enrolled primary-school-age population in 1971. Because Islamic schools historically served underserved populations, this rule meant the state built more schools precisely where Islamic education was most prevalent. The paper shows graphically and in Table 1 that the number of SD INPRES schools built is strongly correlated with the pre-existing stock of Islamic schools, conditional on district population and enrollment.

Q: How large was the Islamic sector’s entry response to SD INPRES at the district level? A: In the standard DID specification (Table 2, panel a), a one standard deviation increase in SD INPRES schools led to 0.013 more Islamic schools per district-year per 1,000 children, equivalent to 1.4 additional Islamic school entries in the average district relative to a mean of 1.9 Islamic schools per district in 1972. The synthetic DID (panel b) delivers positive and slightly larger estimates, indicating the result is not an artifact of diverging pre-trends.

Q: What was the timing of the Islamic sector entry response at the village level? A: Using the Borusyak et al. (2024) estimator on a balanced panel from 1960 to 1999, the paper finds (Figure 4) that INPRES construction is followed by a jump in Islamic school entry. Primary madrasa (MI) entered at twice the baseline annual rate in the years immediately following INPRES construction and this elevated rate persisted for six years before reverting to baseline. Islamic junior secondary entry (MTs) peaked around years 6–9 after SD INPRES construction, consistent with newly graduated primary students seeking continued schooling.

Q: How did the Islamic sector finance its expansion? A: The sector relied on waqf endowments (inalienable religious land assets), informal faith-based contributions (infaq), and obligatory alms (zakat). Fortuitously, the initial year of SD INPRES coincided with a large spike in the global price of rice, Indonesia’s main agricultural commodity, boosting harvest revenues channeled through informal Islamic taxation. Table 3 shows that entry responses were significantly stronger in villages with above-median waqf endowments and above-median potential rice yields, and these heterogeneous effects did not arise in non-INPRES periods or for non-Islamic private schools. Survey data from 2007–13 further show higher rates of informal taxation in villages with Islamic schools built during this period.

Q: Did Islamic schools converge toward secular curricula under competitive pressure from SD INPRES? A: No. Table 4 shows that madrasa established in high-INPRES districts after 1972 devote more time to religious content, not less. Each additional SD INPRES is associated with a 1.2 percentage point increase in the share of classroom time devoted to religious subjects among newly created Islamic schools, with increases of 1.3 percentage points at the primary level and 2.4 percentage points at the junior secondary level — the latter equal to 82% of the cross-school standard deviation. Similar patterns hold for Arabic instruction, and the junior secondary increase comes partially at the expense of Pancasila/civic education and national language instruction.

Q: Did curriculum differentiation responses vary with local religious ideology? A: Yes. Appendix Table A.14 shows a stronger curriculum differentiation response in markets with greater historical support for conservative Islam, proxied by Islamic political party vote shares in the 1950s elections. The paper also constructs a school-name-based predicted ideology index using a ridge shrinkage estimator and finds (Appendix Table A.15) that madrasa entering high-INPRES districts after the program onset have a more religious ideology on this measure.

Q: What happened to the formalization of the Islamic sector? A: Figure 5 and Appendix Table A.6 show that formal madrasa entry increased as a share of all new school entry, while informal Islamic schools (pesantren, diniyah) declined as a share of all new schools and all new Islamic schools. This formalization mirrors the organizational structure of state schools (primary-to-secondary progression), facilitating switching between public and religious schools and providing option value to moderate but still religious families. Crucially, the newly entering formal madrasa introduced more religious curriculum than incumbent madrasa, so formalization did not reduce religious instruction.

Q: What was the net effect of SD INPRES on Islamic school attendance? A: Table 5 shows that SD INPRES reduced the likelihood of attending Islamic primary school by roughly 7% per additional SD INPRES school but increased Islamic secondary attendance, with the net effect being a roughly 5% increase in the likelihood of attending any Islamic school (column 4). This finding holds in both DID and synthetic DID. The IFLS validation (Appendix Table A.18) confirms decreased Islamic elementary attendance and increased Islamic junior secondary attendance, consistent with the Susenas results.

Q: How does selection into secondary education affect the religious schooling results? A: The authors address selection using parametric (Heckman 1976) and semiparametric (Newey 2009) selection-correction procedures, using exposure to a 1960s pilot compulsory schooling program as an exclusion restriction. Table 6, panels (c) and (d), show that selection-adjusted estimates are broadly consistent with unadjusted estimates, with similar signs and magnitudes. The selection-corrected estimates approximately identify a local average treatment effect among compliers: those induced to attend elementary school were less likely to attend Islamic elementary; those induced to continue to secondary were more likely to attend Islamic secondary.

Q: How did gender shape the effects of SD INPRES on religious school choice? A: Table 7 shows that SD INPRES had more limited impacts on total schooling for women than men (consistent with Duflo 2001) but that the secondary-level demand effect toward Islamic schools was stronger for women. Table 8 shows that within high-INPRES areas, the SD INPRES-induced increase in Islamic secondary education is three times larger for women in districts with greater exposure to the 1982 state ban on the Islamic veil in public schools, and this differential is specific to Islamic schooling rather than total schooling.

Q: Did SD INPRES strengthen or weaken the secular ruling regime’s political standing? A: It weakened it. Table 10 shows that in the 1977 and 1982 elections, Golkar’s vote share decreased and the Islamic PPP’s vote share increased in high-INPRES districts, in the range of 0.5–1.0 percentage points per SD INPRES school. This represents a 1.5–3.0% change in PPP vote share and a 0.5–1.0% change in Golkar vote share per standard deviation in SD INPRES intensity. The PPP gained most in areas where SD INPRES had the greatest potential to draw students away from Islamic schools.

Q: Did SD INPRES produce a secular ideological shift among exposed cohorts? A: No. Table 11 shows that SD INPRES did not increase self-reported Pancasila proficiency, national language use at home, national language literacy, or attitudes in favor of secular governance. By contrast, Arabic literacy increased by approximately 3% per additional SD INPRES among exposed cohorts, indicating that Islamic schooling exposure rather than secular schooling drove literacy gains in that language.

Q: Did SD INPRES increase religiosity among exposed cohorts? A: Yes. Table 12 shows that SD INPRES increased prayer frequency, fasting during Ramadan, charitable giving, and pilgrimage intentions among exposed cohorts. These effects on prayer and fasting are stronger among women, consistent with the stronger shift toward Islamic secondary schooling found in Table 7. These outcomes are consistent with greater exposure to Islamic education increasing religiosity rather than the secular curriculum reducing it.

Q: Were the effects on religious identity and Arabic literacy transmitted to the next generation? A: Yes. Table 13 shows that SD INPRES increased Arabic literacy among the children of exposed cohorts, and that children of exposed cohorts were more likely to attend Islamic schools themselves. These intergenerational results confirm that the preference for Islamic education instilled during the SD INPRES era persisted into the next generation rather than converging toward secular norms over time.

Q: What are the key robustness checks for the school entry results? A: Several checks support causal interpretation. The Roth and Rambachan (2022) procedure finds no systematic pre-trends in the standard DID. Historical Podes data from 1980, 1983, 1990, and 1993 confirm the post-1973 increase in Islamic school entry, addressing survival bias in the 2019 registry. Results are robust to allowing differential trends in waqf endowments, Muslim population share, Islamic party vote shares, historical Arab immigration, Islamist insurgency, and Transmigration resettlement. The heterogeneous entry responses by waqf and rice yield do not appear in non-INPRES periods or for non-Islamic schools.

Q: What do the results imply for the political economy of education reform more broadly? A: The paper argues that state capacity to homogenize culture through education is limited when strong non-state actors can mobilize their own resources and provide differentiated alternatives. Rather than crowding out religious schools, state expansion triggered competitive entry, curriculum differentiation, and formalization in the religious sector, producing an equilibrium where both sectors expanded simultaneously with distinct clienteles. The findings imply that the long-run cultural effects of education programs cannot be evaluated without accounting for equilibrium responses by competing non-state providers.

SD INPRES (Sekolah Dasar Presidential Instruction): Indonesia’s 1973 mass public primary school construction program, financed by oil windfalls, which built more than 61,000 elementary schools between 1973 and 1980 by allocating schools to districts proportional to the non-enrolled child population; the program’s explicitly secular nation-building objectives brought it into direct confrontation with the Islamic education sector.

Waqf: Inalienable Islamic religious endowments — of land, agricultural assets, or other property — that under Islamic law can only be used for religious or charitable purposes and cannot be seized or repurposed by the state; in this paper, the pre-existing waqf base in a village serves both as a long-run financing mechanism for Islamic school construction and as an index of Islamic sector organizational capacity.

Madrasa: Formal day Islamic schools operating at the same primary-to-secondary grade levels as secular state schools, teaching standard academic subjects alongside a religious curriculum (including Islamic law, doctrine, ethics, Qur’an, Arabic, and history of the Prophets) that averages 26% of total instruction hours; distinct from the more informal pesantren (boarding schools) and madrasa diniyah (afternoon Qur’anic study schools).

Curriculum differentiation: The strategy by which newly entering madrasa in high-INPRES districts increased the share of classroom time devoted to religious and Arabic instruction rather than converging toward the secular state curriculum; measured as classroom hours devoted to Islamic subjects, Arabic, Pancasila/civic education, and national language instruction from 2018–19 SIAP timetable data.

Pancasila: The official secular nationalist ideology of the Indonesian state, consisting of five principles (monotheism, humanitarianism, national unity, democracy, and social justice) intended to transcend ethnic and religious divisions; SD INPRES sought to transmit Pancasila through civic education and national language instruction as part of its homogenizing nation-building agenda.

Synthetic difference-in-differences (SDID): The Arkhangelsky et al. (2021) estimator used throughout the paper, which reweights and matches pre-INPRES trends in Islamic school construction across high- and low-INPRES exposure districts to deliver estimates more robust than standard DID to violations of parallel trends; applied with a binary treatment indicator (districts above the 51st percentile in INPRES intensity).

Formalization: The documented shift in the composition of the Islamic sector after SD INPRES, whereby formal madrasa (organized along the same grade-level progression as state schools) increased as a share of all new Islamic school entry while informal pesantren and diniyah declined as a share; interpreted as a competitive response that expanded parental option value without sacrificing religious instruction intensity.