The State's grants to communes, at their thresholds

Evidence

The State gives communes grants whose eligibility follows a published rule. The dotation d'équipement des territoires ruraux (DETR) funds the investment projects the préfet selects: €1,015m, estimated in 2024, over 18,153, estimated projects. The fraction cible of the dotation de solidarité rurale (DSR) goes to the first 10,000 rural communes of a ranking on potentiel financier and income: €324m, estimated in 2019. The dotation de solidarité urbaine (DSU) goes to the first two thirds of the towns of 10,000 inhabitants or more, ranked on their resources and costs: €2.2bn, estimated in 2019. The question is what a euro of each does to a commune's budget: whether it raises investment by more than itself, as the State reports for the DETR, adds only itself, or is saved.

• The DETR cap. Communes of 2,001 to 20,000 inhabitants are eligible only while their potentiel financier per inhabitant is below 1.3 times the mean of all such communes. Each year's list is drawn from the previous year's criteria; rebuilt that way, the cap holds 99.3%, estimated of the communes that received the DETR in 2018-2020, and communes do not bunch under it (McCrary log ratio −0.06, estimated). Just under the cap a commune is 32, estimated percentage points more likely to receive the DETR in a year, and receives €5.3, estimated more per inhabitant: the comparison measures what eligibility, through that money, does to a commune's budget.
• The DSR cible rank. The first 10,000 communes of the ranking receive the fraction cible: among the communes ranked 4,001 to 16,000 in 2018 and 2019, the rank reproduces 100%, estimated of the payments. Just inside the cutoff a commune receives €35.3, estimated per inhabitant of fraction cible more than just outside, where 12.9%, estimated of the communes still receive money through guarantees. A commune's place near the cutoff changes from year to year, so each is compared with its own three previous years.
• The DSU two-thirds rank. The first two thirds of the ranked towns receive the DSU, and the rule reproduces 100%, estimated of the payments of 2018 and 2019. At the cutoff the DSU jumps by €5.6, estimated per inhabitant, and 25.5%, estimated of the towns past it still receive money through guarantees.

What each design can see. Before any jump was estimated, the variance of the accounts near each threshold set the smallest leverage each design detects four times in five with a test at 5%. At the DETR cap it is 13.3, estimated euros of equipment spending per euro of DETR over one year and 11.7, estimated over three: the design would only have the power to detect a leverage of at least about 12, not one of 3.6, the State's figure for 2025. At the DSR rank it is 1.0, estimated per euro of DGF, small enough to tell a euro spent from a euro saved; at the DSU rank, 9.9, estimated.

At the DETR cap, communes just under it spent €54, estimated per inhabitant more on equipment in the first year than those just over it (€6, estimated to €102, estimated); measured against each commune's own three previous years, the jump is €50, estimated (€14, estimated to €86, estimated). The two differ on the placebo: at a cutoff halfway into the eligible side, where no rule changes, equipment spending in level jumps by +€25, estimated, +€55, estimated and +€66, estimated per inhabitant over one to three years, about half the jumps at the cap, since spending curves with potentiel financier; measured against the commune's own past it moves by +€0.5, estimated in the first year. Over three years communes under the cap borrowed €68, estimated more in level (€9, estimated to €127, estimated), but only €9, estimated against their own past, an interval that holds zero.

Per euro of DETR, equipment spending in level rose by 10.3, estimated (1.3, estimated to 23.5, estimated) over one year, 8.0, estimated (−0.3, estimated to 17.8, estimated) over two and 6.9, estimated (−1.3, estimated to 15.6, estimated) over three. The DSIL, which communes above the cap may still receive, moved by −€7.0, estimated over three years, short of significance, so all the State's investment grants rise by less than the DETR: per euro of them, the first-year figure is 8.6, estimated (1.1, estimated to 34.0, estimated). Every interval per euro of DETR holds the State's 3.6, and those over two and three years also hold zero: the design neither confirms nor refutes the State's figure. The first-year figures are the most fragile: eligibility persists from one list to the next, so that year's spending may carry DETR granted in earlier years and paid as projects are completed, while the denominator counts one year's grant. New borrowing in level rose by 3.9, estimated (0.5, estimated to 8.1, estimated) euros per euro of DETR over three years.

The State's 3.6 is a ratio of accounts: the cost of the projects the DETR funds over the DETR granted to them. It counts a project's whole cost as the grant's doing, whether or not the commune would have carried the project out without it. The same ratio from the DGCL lists, for every DETR project of a commune, was 3.42, estimated in 2020, its lowest since 2018, and 4.96, estimated in 2025. The cap measures the other quantity: what a commune invests because it is eligible.

At the DSR rank the grant comes and goes from year to year: a commune just inside the cutoff is only 18, estimated percentage points more likely than one just outside to have been inside it the year before. There, a euro of fraction cible raised the commune's self-financing capacity by 1.36, estimated (0.62, estimated to 2.10, estimated) euros in the first year against its own three previous years, and by 1.06, estimated (0.65, estimated to 1.48, estimated) in level: the first-year euro was saved. The first figure can exceed one because its interval holds one, and because it divides by the DGF the accounts record, which jumps by €32.1, estimated at the cutoff, against €35.3, estimated of fraction cible in the allocation criteria. In that year the intervals exclude more than 0.21, estimated euro of extra operating spending per euro, more than 0.66, estimated of extra equipment spending, and a cut in local taxes of more than 0.03, estimated. By the third year equipment spending per euro is 0.32, estimated, with an interval up to 1.63, estimated: investing the saved money later cannot be excluded. Debt moved by −0.64, estimated (−1.33, estimated to 0.03, estimated) euro per euro over two years, short of significance. The design measures communes at the cutoff, for whom the grant may be gone the next year; how communes that receive it every year use it, it cannot say.

At the DSU rank, per euro of DSU, equipment spending moved by 0.53, estimated (−10.59, estimated to 10.28, estimated) in the first year and operating spending by 1.00, estimated (−13.60, estimated to 11.97, estimated). The grant at the margin is too small against town budgets for the design to say anything about its use.

The estimates in level at the DETR cap also depend on the bandwidth: the three-year leverage is 10.1, estimated at half of it and 1.8, estimated at double (−2.8, estimated to 6.2, estimated). Of the 24 placebo jumps at the cap, 4 are significant at 95%, all on the eligible side and all in level. At the DSR rank, 1 of 24 is significant, about what chance gives; at the DSU rank, 4 of 24, all on the ineligible side, where guarantees move money. Communes do not bunch at the DSR rank (McCrary log ratio −0.04, estimated) or at the DSU rank (0.01, estimated).

At the DETR cap the design measures eligibility and observes the receipt it brings, each commune's DETR in the DGCL lists; at the DSR and DSU ranks it divides by the grant the accounts record as paid. The accounts are each commune's main budget, which leaves out its annexed budgets and what its intercommunality spends. Each jump is a local linear regression on each side of the threshold with a triangular kernel, at the Imbens-Kalyanaraman bandwidth for equipment spending, years pooled, with standard errors clustered by commune. A leverage divides the jump in the outcome by the jump in the grant, with an Anderson-Rubin interval, which stays valid when the jump in the grant is small; at the DSR and DSU ranks the grant is the DGF the accounts record, which carries it. Euros are per inhabitant, summed over windows of one to three years from the allocation. At the DETR cap eligibility persists from one year's list to the next: a commune just under the cap is 62, estimated percentage points more likely than one just over it to have been under the previous one, so its own past already carries part of the effect, and the page gives the jumps both in level and against that past. Nor can the cap separate the DETR from what eligibility signals to the préfet and to other funders. The criteria of 2020 and later are not on data.gouv.fr, so the DETR design covers the allocations of 2018 to 2020, the DSR design 2016 to 2019 and the DSU design 2018 and 2019. The criteria are in criteria.csv, the DGCL lists of funded projects in projects.csv, the communes' accounts in accounts.csv, every estimate with its minimum detectable effect in results.csv and the sources in SOURCES.md. The code is analysis/grants.ml, with the bandwidth and density test of lib/rdd.ml.