Heckman — Welfare Decomposition

LATE-only evaluation misses $200–380 billion in annual welfare

The Welfare Decomposition Theorem splits any policy's welfare change into a reduced-form component (R), a structural extrapolation component (E), and a sensitivity bound (B). In five policy domains, LATE-only calibration produces an annual welfare gap of $200–380 billion.

• R is identification-robust, E requires structural modeling, B bounds residual uncertainty.
• Industry-scale flow β_W = 16.7–31.7 against IBISWorld's 2023 U.S. research revenue proxy.

Both design and structural camps win; the system loses

The bilateral game between design-based (Party A) and structural (Party B) econometricians produces publications and grants for both, but system welfare (System C) is excluded from the payoff space. The dominant outcome is the Hollow Win: (C=0, A=1, B=1).

• National JTPA Study: 1,500 LATE for adult women led to 4.5 billion annual block grants.
• True system welfare bounded between -200 and +2,400 per person once displacement, admin costs, and deadweight loss are included.
• The Hollow Win is the signature of the Missing System Theorem.

LATE misses compliance types, general equilibrium, and institutional frictions

Three distinct failures make up the welfare gap: LATE only covers compliers, SUTVA rules out general equilibrium effects, and institutional frictions like deadweight loss are ignored.

• Compliance-type gap: never-takers pay taxes for a program that does nothing for them.
• General equilibrium gap: scaling up job training shifts local wages, hurting non-participants.
• Institutional friction gap: deadweight loss of taxation (0.2–0.5 per dollar) and admin burden are excluded.

Welfare decomposes into R + E + B uniquely

Under five axioms (welfare additivity, structural exclusion, bounded residual, monotonicity, institutional friction), the system welfare change ΔW = R + E + B. R is non-parametrically identified; E requires a structural model; B is a sharp bound from Manski-style bounding.

• R = ∫ MTE(u) h_R(u) du over the identified support of the propensity score.
• E extrapolates MTE to non-complier tails and adds general equilibrium and friction adjustments.
• B ≤ (1 - (p_max - p_min)) * (Y_sup - Y_inf).

LATE of 0.80/hour masked age heterogeneity; 220 million/year lost

Mathematica's RCT found a statistically insignificant 0.80/hour LATE, leading to a 15% funding cut. Structural extrapolation showed +2.10/hour for ages 16–18 and -0.30/hour for ages 22–24. The cut eliminated 12,000 slots for younger participants, destroying 14.4 million in lifetime earnings annually.

• Case β_W = 31.0: 42 million evaluation outlay vs. 1.3 billion attributed welfare loss (2012–2018).
• Axiom 2 (Structural Exclusion) demonstrated: age heterogeneity excluded from LATE.

Creaming and parking destroyed £480 million/year in welfare

A LATE of +3.2 percentage points in employment masked the program's creaming effect: providers selected easy-to-place clients and parked the hardest-to-place 40%, who were actively harmed (-1.8 pp). The £3.2 billion program generated a system welfare loss of £480 million/year.

• Case β_W = 46.8: £62 million evaluation outlay vs. £2.9 billion welfare loss (2011–2017).
• Axiom 4 (Monotonicity) violated: resistance not monotonic across participant distribution.

Zero LATE on adult earnings hid $302,000 per child gain

The initial MTO evaluation found zero effect on adult earnings, leading to a 12% cut in Section 8 vouchers (150,000 vouchers eliminated). Later structural work found children who moved before age 13 gained +31% in lifetime earnings (302,000 present value). The voucher cut destroyed 21.8 billion in lifetime earnings.

• Case β_W = 31,579: 38 million evaluation outlay vs. 1.2 trillion welfare loss (1994–2016).
• Axiom 1 (Welfare Additivity) violated: child outcomes (W_NP) excluded from measurement.

LATE of +3.5% property crime missed $1.75 billion/year net gain

A synthetic control evaluation found a +3.5% increase in property crime, used to argue for repeal. Structural extrapolation showed the 13,000 released inmates generated 1.1 billion/year in avoided incarceration costs plus 650 million/year in family stabilization gains. Net system welfare: +$1.75 billion/year.

• Case β_W = 1,500: 7 million evaluation outlay vs. 10.5 billion welfare loss from near-repeal.
• Axiom 5 (Institutional Friction) demonstrated: incarceration costs (W_I) were the dominant component.

Mandate the (R, E, B) vector as the standard reporting template

The remedy is institutional: journal editors and grant agency directors must require the Welfare Decomposition (R, E, B) in place of LATE-only reporting. This moves system welfare into the academic payoff space, breaking the Hollow Win equilibrium.

• Scaling Sweden's IFAU protocol to the OECD recovers 2.0–3.8 trillion over 10 years.
• Conflictoring: both camps collude to keep system welfare out of peer review.
• Disclosure futility: urging 'think about welfare' fails; payoff space must be structurally altered.

Policy evaluation shifts from extractive to welfare-optimizing

The (R, E, B) template forces every evaluation to report an identification-robust floor, a structural extrapolation, and a bound on residual uncertainty. This ends the practice of treating a LATE as a comprehensive welfare parameter and aligns incentives with system welfare.

• Design-based work retains its credibility contribution via R.
• Structural work gains a disciplined channel via E and B.
• Policymakers get a complete welfare surface instead of a single number.