Policy Design in Long-Run Welfare Dynamics

TL;DR

This work analyzes sequential welfare interventions by contrasting Rawlsian and utilitarian policy families within a stochastic dynamic model where individual welfare decays absent intervention and is boosted by targeted efforts. Under mild regularity, Matthew-effect monotonicity, and a survival condition preventing any welfare from vanishing, Rawlsian policies achieve higher asymptotic welfare than short-horizon utilitarian rules, with a complementary ruin condition where the reverse holds. The authors provide closed-form expressions for the long-run growth rates under each policy and validate the theory via simulations using real-world SIPP data, highlighting a delay in short-term gains but superior long-run performance for Rawlsian strategies. The results advocate incorporating long-horizon considerations into welfare policy design and evaluation, illustrating how simple, normatively grounded policies can outperform seemingly superior short-run strategies over time.

Abstract

Improving social welfare is a complex challenge requiring policymakers to optimize objectives across multiple time horizons. Evaluating the impact of such policies presents a fundamental challenge, as those that appear suboptimal in the short run may yield significant long-term benefits. We tackle this challenge by analyzing the long-term dynamics of two prominent policy frameworks: Rawlsian policies, which prioritize those with the greatest need, and utilitarian policies, which maximize immediate welfare gains. Conventional wisdom suggests these policies are at odds, as Rawlsian policies are assumed to come at the cost of reducing the average social welfare, which their utilitarian counterparts directly optimize. We challenge this assumption by analyzing these policies in a sequential decision-making framework where individuals' welfare levels stochastically decay over time, and policymakers can intervene to prevent this decay. Under reasonable assumptions, we prove that interventions following Rawlsian policies can outperform utilitarian policies in the long run, even when the latter dominate in the short run. We characterize the exact conditions under which Rawlsian policies can outperform utilitarian policies. We further illustrate our theoretical findings using simulations, which highlight the risks of evaluating policies based solely on their short-term effects. Our results underscore the necessity of considering long-term horizons in designing and evaluating welfare policies; the true efficacy of even well-established policies may only emerge over time.

Figures (7)

• Figure 1: Social welfare as the finite-time growth rate averaged over all individuals, for all policies (solid lines), as well as theoretical expected growth rate, asymptotically (dashed lines) for budget $M=1$ (a) and $M=10$ (b).
• Figure 2: Social welfare as the finite-time growth rate average over all individuals, for all policies (solid lines) under one set of heterogeneous bounds.
• Figure 3: (a) Percentage of iterations where min-U obtains better social welfare than max-U at time step $t=6000$, as the bounds $\{f_i^-, f_i^+, g_i^-, g_i^+\}_{i=1:N}$ vary according to parameters $b$ and $\sigma^2$; (b) Percentage of iterations where min-U obtains better long-term social welfare than max-U at time step $t=10$, as the bounds $\{f_i^-, f_i^+, g_i^-, g_i^+\}_{i=1:N}$ vary according to parameters $b$ and $\sigma^2$.
• Figure 4: Social welfare as the finite-time growth rate averaged over all individuals, for all policies (solid lines), as well as theoretical growth rate for min-U and max-U policies (dashed lines) under different combination of monotonicities of $\{f_i(\cdot)\}$, $\{g_i(\cdot)\}$. The monotonicities of $\{f_i(\cdot)\}$, $\{g_i(\cdot)\}$ corresponds to Table \ref{['tab:monotonicity_combination']}, e.g., the plot at row one column one is generated under the assumption of $\{f_i(\cdot)\}$ and $\{g_i(\cdot)\}$ are decreasing.
• Figure 5: We show social welfare as the finite-time growth rate averaged over all individuals, for all policies (solid lines), as well as theoretical expected growth rate (dashed lines) under the ruin condition.

Theorems & Definitions (42)

• Definition 1: Long-term social welfare
• Theorem 1: Main result
• proof : Proof sketch.
• Theorem 2: Policy comparison under a ruin condition
• Theorem 3
• Corollary 1
• proof : Proof sketch
• Theorem 4
• Corollary 2
• proof : Proof sketch