O10 | Macro Paper Warehouse

Revolutionary Transition: Inheritance Change and Fertility Decline

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

Gay, Gobbi, and Goñi test Le Play’s (1875) hypothesis that the French Revolution contributed to France’s early fertility decline by abolishing impartible inheritance. In 1793, a series of decrees culminating in the Loi de Nivôse (January 6, 1794) abolished testamentary rights and imposed equal partition of assets among all children — partible inheritance — across France, overriding the mosaic of local customs and written laws that had governed inheritance in the Ancien Régime.

The paper’s central argument is that this reform reduced the economic incentive to have children through indivisibility constraints in agricultural land. Under impartible inheritance, land passed to a single heir undivided, keeping plots above the subsistence productivity threshold even at high fertility. Under partible inheritance, each additional child fragments the land further, potentially pushing plots below the minimum productive size, so households face a strong incentive to limit fertility. A Stone-Geary production function with a minimum land threshold L̄ formalizes this mechanism: when landholdings fall in the binding range (L̄ < L < L̃), fertility is strictly higher under impartible than under partible inheritance.

The authors construct the first complete map of inheritance rules across France’s 435 judicial districts as of 1789, classifying each along two dimensions: partible versus impartible, and whether women were included or excluded. This atlas draws on Brette’s (1904) Atlas des Bailliages and the Nouveau Coutumier Général (Bourdot de Richebourg 1724), covering 141 distinct customs. Treatment is defined as municipalities under impartible inheritance before 1793 whose system was altered by the reforms; control municipalities were already under partible inheritance.

The main identification strategy is a difference-in-differences (DD) design comparing women with varying lengths of remaining fertile years after 1793 — from 0 for women aged 40+ at the reform to 25 for women aged 15 or younger — across treated and untreated municipalities. This is augmented by a regression-discontinuity difference-in-differences (RD-DD) design exploiting sharp discontinuities at judicial district borders. Two independent datasets are used: the Enquête Louis Henry (34,812 women in 39 rural municipalities, family-reconstitution method) and Geni.com crowdsourced genealogies (11,649 women across 2,966 locations after the Blanc 2023 horizontal restriction).

Each additional fertile year of exposure to the 1793 reforms reduced completed fertility by approximately 1 percent. Over the full 25-year fertile cycle, this corresponds to a reduction of roughly 0.7 children, or 24 percent relative to the pre-reform mean of 2.92 surviving children in treated areas. This magnitude equals the entire pre-reform fertility gap between impartible- and partible-inheritance areas (2.9 versus 2.2 children), meaning the reforms closed this gap entirely. DD and RD-DD estimates are similar and not statistically distinguishable from each other, and results replicate across both datasets. Results hold on both the extensive margin (childlessness) and intensive margin (fertility of mothers).

The mechanism is most relevant where smallholder landownership is widespread. France — where 40–80 percent of households owned land at the eve of the Revolution — meets this condition. England and Prussia, with more concentrated landownership, would not be expected to show the same response because the indivisibility constraint would not bind even after partition.

Q: What was France’s inheritance system before the Revolution, and how heterogeneous was it? A: Before 1793, inheritance was governed by 141 distinct customary and written laws applied within 435 judicial districts. The country was broadly divided between the customary-law north (Pays de droit coutumier) and the Roman written-law south (Pays de droit écrit), with substantial local variation within regions. Systems ranged from strictly partible (equal division among all offspring) to impartible (primogeniture, ultimogeniture, or unigeniture). Systems also varied in whether women could inherit or received only a dowry. This geographic variation — rooted in the laws of Germanic peoples after the fall of Rome in 476 CE — is exogenous to late eighteenth-century economic conditions and provides the identifying variation for the paper.

Q: What exactly did the 1793 reforms change, and were they enforced? A: The Loi de Nivôse an II (January 6, 1794) abolished testamentary rights entirely and mandated equal partition of assets among all children, including women, throughout France. The reforms came unexpectedly — only 8 of 571 cahiers de doléances analyzed by Goy (1988) mentioned inheritance — and were motivated by the equality principle, legal unification, and the fear that revolutionary sympathizers would be disinherited (Lataste et al. 1901). Offspring quickly asserted their new rights, and by the late 1790s inheritance disputes were the most common cases before family tribunals (Desan 1997; Poumarède 2011).

Q: What is the model’s core mechanism linking inheritance reform to fertility decline? A: The model uses a Stone-Geary production function with a minimum land threshold L̄ below which output falls to zero. Under impartible inheritance, land passes undivided to a single heir, keeping the farm above L̄ regardless of family size. Under partible inheritance, each child receives an equal share, so adding children risks fragmenting plots below L̄ — a powerful incentive to limit family size. The fertility gap between impartible and partible households is at its maximum when landholdings fall in the intermediate range (L̄ < L < L̃) where the constraint is binding. As land size increases, the constraint becomes less binding but the positive fertility differential persists.

Q: What is the paper’s main quantitative estimate of the reform’s effect on completed fertility? A: Each additional fertile year of exposure to the 1793 reforms reduced completed fertility by approximately 1 percent. Over the full 25-year fertile cycle (ages 15–40), this implies a reduction of roughly 0.7 children, or 24 percent relative to the pre-reform mean of 2.92 surviving children in treated areas. This is nearly identical to the pre-existing fertility gap between impartible- and partible-inheritance areas (0.7 children: 2.9 versus 2.2 surviving children), implying the reforms effectively eliminated the fertility differential.

Q: Are the DD and RD-DD estimates consistent with each other, and do both datasets agree? A: Yes. The DD and RD-DD estimates are similar and not statistically different from each other. The RD-DD design compares women born close to judicial district borders where inheritance rules differed, before and after 1793, exploiting the sharp spatial discontinuity at those borders. Consistency across these two designs — which rely on different identifying assumptions — strengthens causal interpretation. Results are also consistent across the Enquête Louis Henry (family-reconstitution) and Geni.com (crowdsourced genealogies) datasets, which are produced by fundamentally different methodologies.

Q: How do the authors verify the parallel trends assumption? A: Figure 6 shows that for cohorts who completed their fertile cycle before 1793, fertility trended downward in parallel across partible- and impartible-inheritance areas: a constant gap of approximately 0.7 children was maintained from women born in the early 1700s (3 versus 2.3 children) through women born in the early 1750s (2.7 versus 2.0 children), the last cohorts to complete fertility before the reforms. The convergence — from 0.7 to 0 children — only begins among cohorts fertile after 1793. The authors also include flexible trend controls interacted with municipality-level religiosity, political support for the Revolution, proximity to administrative centers, and wheat prices, and confirm the main estimate is robust.

Q: What role did the extension of inheritance rights to women play? A: The extension of rights to women was a companion mechanism distinct from abolishing impartible inheritance. Beyond increasing the number of heirs (which directly reduces land per heir), the right to inherit improves a woman’s outside option and postpones entry into marriage, following de Moor and van Zanden (2010). The DD and RD-DD estimates suggest that including women in inheritance and abolishing impartible inheritance had similar effects on fertility. The paper treats these as separate but reinforcing channels.

Q: How do the authors address potential confounders — mortality, migration, and economic conditions? A: On mortality: child mortality did not evolve differently after 1793 across areas with different inheritance rules (Appendix Table A3), and baseline adult mortality (age at death, probability of dying before completing the fertile cycle) was balanced across treated and control areas (Table 1). On migration: the authors explicitly rule out that results are driven by migration. On economic conditions: municipality-specific decade-average wheat prices (Ridolfi 2019) are included as controls for local Malthusian dynamics, and results are robust to their inclusion.

Q: What do the balance tests show? A: Panel A of Table 1 shows that before the reforms, areas with impartible versus partible inheritance were balanced on 9 of 11 individual-level characteristics — including husband and wife age at death, probability of dying before completing the fertile cycle, probability that parents-in-law were alive at marriage, literacy, data accuracy, and age at marriage. The only systematic pre-reform difference was fertility itself (0.7 children). Municipality-level climatic variables, soil suitability, and proxies for mortality uncertainty were also balanced. This is consistent with the origins of these systems in post-Roman Germanic law, which are unrelated to late eighteenth-century economic conditions.

Q: What robustness checks are reported? A: The authors report: (1) permutation tests reshuffling treatment exposure across women and municipalities; (2) non-linear treatment effects across cohorts, showing the heterogeneity required to explain away the baseline estimate is implausibly large per de Chaisemartin and d’Haultfoeuille (2020); (3) exclusion of outlier municipalities; (4) a placebo test for cohorts who completed their fertile cycle before 1793; (5) robustness to alternative sample definitions, treatment definitions, outcome variables, and control groups; (6) Cummins (2020) first-name repetition technique to correct for under-reported child deaths in Henry; (7) terrain characteristics including climatic and soil suitability (Galor and Özak 2016) and ruggedness (Nunn and Puga 2012); (8) for RD-DD: alternative bandwidths, running variable specifications, kernel functions, samples, and border-segment fixed effects. All checks support the main finding.

Q: Why did France experience a fertility decline from inheritance reform while other countries with similar reforms did not? A: The model rationalizes this through landownership structure. The fertility-reducing mechanism operates through indivisibility constraints that bind only when landholdings are small and fragmented — as in France, where 40–80 percent of households owned their land and plots were small. Where landownership is concentrated (England, Prussia), land per heir remains above L̄ even after partible division, so the indivisibility constraint is non-binding and fertility is unaffected by the reform. This provides a structural reason why France’s particular agrarian structure made it uniquely susceptible to this mechanism.

Q: What is the broader historical significance for understanding France’s early demographic transition? A: France’s fertility decline began roughly 50 years before industrialization, making it anomalous relative to standard quantity-quality tradeoff theories linking fertility decline to technological progress and rising returns to human capital. The 1793 reforms provide a legal-institutional explanation for the sharp post-Revolution acceleration visible in Figure 1, which is difficult to attribute to slowly-evolving cultural factors or human capital considerations not yet operative. The estimates imply the reforms brought large impartible-inheritance areas to the low-fertility regime that already characterized partible-inheritance areas, thus sharply accelerating the national transition.

Impartible inheritance: A system under which parents could designate a single heir (through primogeniture, ultimogeniture, or unigeniture) to receive the bulk of the family estate, preventing fragmentation of wealth; in pre-revolutionary France this was associated with extended family households and higher fertility (2.9 surviving children on average) relative to partible areas (2.2).

Partible inheritance: A system under which family wealth was divided equally among all offspring upon death; in the paper’s model this creates an incentive to limit fertility to prevent land fragmentation below the subsistence productivity threshold L̄.

Indivisibility constraint (land threshold L̄): In the Stone-Geary production function, a minimum land input below which agricultural output falls to zero; this is the mechanism through which partible inheritance generates fertility-limiting incentives, since dividing a small plot among many heirs risks crossing L̄ into zero production.

Difference-in-differences (DD) exposure design: The paper’s main identification strategy, using remaining fertile years after 1793 as a continuous treatment-intensity variable (0 for cohorts past fertility at the reform date, up to 25 for cohorts entirely within their fertile years), compared between treated municipalities (impartible → partible) and control municipalities (already partible).

Regression-discontinuity difference-in-differences (RD-DD): An augmented design exploiting the sharp geographic discontinuity at borders between judicial districts with different pre-reform inheritance rules, comparing outcomes on both sides before and after 1793, to address smooth unobserved confounders.

Completed fertility (net): The number of children surviving to age six, preferred over total births because child mortality before 1800 was high (1–1.5 children per mother did not survive to age six per Houdaille 1984), making net fertility the more economically meaningful measure for inheritance and bequest decisions.

Horizontal restriction: A sampling correction applied to crowdsourced genealogical data (Blanc 2023a) that retains an observation only if at least one of the four preceding generations has more than one recorded offspring, correcting for the over-representation of single-child families that arises because Geni users tend to record direct ancestors rather than collateral relatives.

What Do Policies Value?

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

This paper asks a fundamental question about policy design: when a program prioritizes one group over another, is that because the group benefits more from the intervention, or because the policy assigns them higher intrinsic welfare weight? Björkegren, Blumenstock, and Knight develop a two-stage method to decompose observed allocation decisions into their underlying components: (i) welfare weights assigned to different types of people, (ii) heterogeneous treatment effects of the intervention, and (iii) relative weights on different outcomes. The key insight is that the same allocation rule can be consistent with very different value systems depending on how much each group actually benefits.

The method works as follows. In a first stage, the analyst estimates heterogeneous treatment effects — how much each individual benefits on each outcome dimension — using OLS or machine learning methods (e.g., causal forests). In a second stage, the analyst reconciles the observed ranking of beneficiaries with an implicit welfare function using an exploded logit likelihood, recovering welfare weights (who is valued), impact weights (how different outcomes are valued), and a base value for treatment independent of measured outcomes. Identification requires an exclusion restriction: the covariates used to estimate treatment effect heterogeneity must include variables excluded from the welfare weight specification, allowing the analyst to compare households with similar welfare weights but differential treatment effects. Variants of the method that impose known welfare weights or known impact weights can be used without the exclusion restriction.

The paper demonstrates the method using PROGRESA, Mexico’s large conditional cash transfer program launched in 1997. PROGRESA ranked households by a proxy means test poverty score and transferred approximately 197 pesos per month (roughly $20 USD) to eligible poor households, conditional on school attendance and doctor visits. The analysis uses endline survey data on 7,767 households and focuses on three outcomes emphasized in program documents: log per-capita consumption, child sick days (ages 0-5), and school days missed (ages 6-16).

The program’s average treatment effects were: a 0.149 log point increase in monthly consumption (SE=0.015), a 0.165 reduction in sick days per child (SE=0.051), and a near-zero effect on school days missed (-0.0053, SE=0.028). These effects were heterogeneous: indigenous households, for instance, benefited substantially more from the program.

The paper’s central empirical finding inverts the naive interpretation of PROGRESA’s targeting. Indigenous households were ranked 60.6 log points higher in the program’s priority order. A simple regression suggests the program favored them. But after accounting for the fact that indigenous households benefit substantially more from treatment, the method finds that the program’s implied welfare weight on indigenous households is, if anything, lower by 17.4% relative to non-indigenous households — not higher. The program’s prioritization of indigenous households is thus explained by efficiency, not by preferential welfare weighting.

Because PROGRESA cash transfers relax household budget constraints and outcomes like consumption reflect household choices, the impact weights capture the difference between how the policy values outcomes and how households value them. The estimates strongly reject non-paternalism: the policy implicitly values consumption and potentially health differently from household decision-makers. Of the total welfare impact, approximately 55% is attributed to the base value of the transfer itself (independent of measured outcomes), approximately 45% to consumption impacts, and less than 1% to health and schooling impacts combined. The implied value of providing the transfer independent of outcomes corresponds to 0.16 log points of consumption, or about 23.1 pesos per person per month — slightly below the average transfer of 33.9 pesos per person per month.

The paper also runs counterfactual exercises showing how alternative preference structures would have changed the allocation. A policy maximizing only educational impacts would have prioritized richer, smaller households; one maximizing only consumption impacts would have further prioritized indigenous households. These counterfactuals are mapped onto a Pareto frontier across the three outcomes. The estimated welfare weights from the implemented policy align closely with preferences elicited in a 2023 survey of 429 Mexican residents, though residents placed higher value on child health relative to what the policy implied.

Q: What is the core identification challenge the paper addresses? A: When a policy prioritizes a group, it could be because the group benefits more (efficiency) or because the policy assigns them intrinsically higher value (preference). These two explanations are observationally equivalent from the allocation alone. The paper separates them by first estimating heterogeneous treatment effects and then inverting the allocation to recover residual welfare weights.

Q: What is the exclusion restriction required for full identification? A: The covariates used to estimate treatment effect heterogeneity (x-tilde) must include at least some variables excluded from the welfare weight specification (x). This allows the analyst to compare households with similar welfare weights but different predicted treatment effects, pinning down how much of the ranking reflects efficiency versus preference. Without this restriction, one can still recover conditional preferences by imposing known values for either welfare weights or impact weights.

Q: How does the exploded logit likelihood work in this setting? A: The analyst observes a single full ranking of all households, rather than partial orderings from multiple decision-makers. The welfare impact of treating household i is modeled as a linear function of predicted treatment effects scaled by welfare and impact weights, plus an extreme-value-distributed shock. The likelihood of observing household i ranked above household i-prime is the ratio of their exponentiated welfare scores, summed over all households ranked below i. Maximum likelihood recovers the welfare weights, impact weights, and base value simultaneously.

Q: What were PROGRESA’s average treatment effects on the three focal outcomes? A: Average treatment increased log monthly consumption by 0.149 (SE=0.015), reduced child sick days by 0.165 (SE=0.051), and had a near-zero effect on school days missed (-0.0053, SE=0.028). The consumption and health effects are statistically significant; the schooling effect is not distinguishable from zero.

Q: What does the analysis find about the welfare weight assigned to indigenous households? A: In the raw ranking regression, indigenous households are ranked 60.6 log points higher, suggesting the program favored them. After accounting for the fact that indigenous households benefit substantially more from treatment, the method finds the implied welfare weight on indigenous households is lower, not higher — specifically, about 17.4% lower than non-indigenous households. The program’s higher ranking of indigenous households is explained entirely by their larger treatment effects, not by preferential weighting.

Q: How are the impact weights on consumption, health, and schooling interpreted given that outcomes reflect household choices? A: Because PROGRESA relaxes household budget constraints and outcomes like consumption result from household optimization, the estimated impact weights capture the difference between how the policy values outcomes relative to how households value them (internalities), rather than the absolute policy valuation. A nonzero weight implies the policy disagrees with household preferences — paternalism. The positive coefficient on log consumption implies the policy values this outcome more than households do.

Q: How much of PROGRESA’s welfare impact comes from the base transfer value versus measured outcomes? A: The base value of the transfer (independent of measured impacts on consumption, health, and schooling) accounts for approximately 55% of total implied welfare impact. The impact on consumption accounts for approximately 45%. Impacts on health and schooling together account for less than 1%. The implied value of the base transfer corresponds to 0.16 log points of consumption per capita, or about 23.1 pesos per person per month — somewhat below the average transfer amount of 33.9 pesos per person per month.

Q: Does the analysis reject egalitarian welfare weights and non-paternalism? A: Yes, using Wald tests with bootstrapped covariance matrices. The hypothesis of egalitarian weights (all gamma equal to one) is rejected. Non-paternalism (all beta equal to zero) is strongly rejected. The joint hypothesis of egalitarianism and non-paternalism is also rejected across all specifications tested.

Q: How do the estimated welfare weights compare to stated preferences of Mexican residents? A: The 2023 survey of 429 Mexican residents elicited preferences using multiple price lists over how to prioritize different household types. The welfare weights implied by the implemented policy are broadly similar to resident preferences, but the policy places relatively higher welfare weight on indigenous households than the median survey respondent does. Survey respondents value child health impacts more than household decision-makers and more than the implemented policy does, consistent with support for paternalism.

Q: What do counterfactual allocations reveal about the relationship between policy goals and targeting priorities? A: A policy maximizing only consumption impacts would further prioritize indigenous households with lower income. A policy maximizing only educational impacts would instead prioritize richer, smaller households. A policy maximizing only health impacts would largely preserve indigenous household prioritization while placing less emphasis on lower-education households. These three extreme policies map to the corners of a Pareto frontier, and the implemented PROGRESA policy lies close to the allocation consistent with surveyed resident preferences.

Q: What changed when Mexico reformed PROGRESA’s poverty score in 2003? A: The 2003 reform increased the priority of older and smaller households. Applying the method to the new poverty score reveals that it implicitly switched to assigning a positive welfare weight to indigenous households (compared to the negative implied weight under the original score), and placed less welfare weight on lower-income and younger households relative to the original design.

Q: What are the main limitations and scope conditions of the method? A: Full identification requires an exclusion restriction (some treatment effect heterogeneity predictors excluded from welfare weights) and sufficient variation in treatment effects across household types. If treatment effects are homogeneous, welfare weights and impact weights cannot be separately identified. If correlated unobservables drive the ranking but are not modeled, the method recovers preferences consistent with included variables only, analogous to omitted variable bias in OLS. The method also requires a way to estimate treatment effect heterogeneity, which is most credible with a randomized pilot, though non-experimental methods are in principle applicable.

Q: How does this paper relate to the inverse optimum public finance literature? A: The inverse optimum literature (Bourguignon and Spadaro 2012; Saez and Stantcheva 2016; Hendren 2020) recovers the redistribution preferences consistent with income tax schedules, conditioning on a single covariate (pre-tax income) affecting a single outcome (net-of-tax consumption). This paper generalizes that framework to arbitrary allocation policies conditioning on a vector of covariates and affecting a vector of outcomes, and extends it to settings beyond income taxation where heterogeneous treatment effects can be estimated.

Q: Can the method be applied when only a binary allocation is observed rather than a full ranking? A: Yes. A binary allocation corresponds to a ranking with only two levels, and the same exploded logit procedure applies, though with reduced statistical power. The paper provides an empirical illustration of this setting in Section 5.2.1.

Welfare weights (w(x_i)): The policy’s differential valuation of one household’s utility relative to another, expressed as a multiplicative function of household characteristics. Distinct from how much a household benefits — two households may be ranked identically despite different benefits if their welfare weights differ proportionally.

Impact weights (beta_j): The policy’s relative valuation of different outcome components (consumption, health, schooling). For outcomes that are household choices, impact weights capture the difference between how the policy values the outcome and how the household values it — an internality or paternalistic preference.

Base value (alpha): The value a policy assigns to providing a treatment independent of its measured impact on any specific outcome. Captures either a direct utility benefit of treatment or the value of relaxing household budget constraints when outcomes are choices.

Exclusion restriction: The requirement that the set of covariates used to estimate treatment effect heterogeneity includes at least some variables excluded from the welfare weight specification. Enables separate identification of efficiency-based and preference-based components of a ranking by comparing households similar in welfare weight but different in predicted treatment effects.

Exploded logit likelihood: The econometric procedure used in the second stage, adapted for a single complete ranking of all alternatives rather than partial orderings. Treats the observed ranking of household i as a choice from the set of all households ranked below it, with likelihood given by the softmax of welfare scores.

Value audit: A retrospective application of the method that reads the implicit values encoded in an implemented policy’s allocation decisions, enabling comparison against stated policy objectives, constituent preferences, or normative benchmarks.

Paternalism (in this paper’s sense): A policy is paternalistic if it assigns nonzero impact weight (beta_j ≠ 0) to outcomes that are household choices — meaning the policy values those outcomes differently from the households making the choices. The envelope theorem implies a non-paternalistic policy would place zero weight on choice outcomes beyond the general constraint relaxation.