Population and Welfare: Measuring Growth when Life is Worth Living

Layer 1: Overview

The paper asks how much economic progress looks different when one applies a total utilitarian welfare criterion — counting every person’s flow utility — rather than the standard per-capita consumption measure. The motivation is both philosophical and practical: philosophers have long debated whether the number of people matters for social welfare alongside average living standards, yet growth economists have almost exclusively used the per-capita approach. The authors do not adjudicate the debate; they quantify its stakes across a broad cross-country sample.

The framework is parsimonious. Under total utilitarianism, flow social welfare is W = N·u(c). Consumption-equivalent (CE) welfare growth is gλ = v(c)·gN + gc, where gN is population growth, gc is per-capita consumption growth, and v(c) = u(c)/[u’(c)·c] is the value of a year of life in units of per-capita consumption. Diminishing marginal utility guarantees v(c) > 1: each percentage point of population growth is worth more than a percentage point of per-capita consumption growth. The baseline utility function is u(c) = ū + log(c). The key parameter ū is calibrated to the U.S. Environmental Protection Agency’s Value of Statistical Life (VSL) of $7.4 million (2006 prices): dividing by remaining life expectancy (~40 years) and U.S. per-capita consumption of $38,000 gives v(c_US,2006) ≈ 4.87. Normalizing U.S. 2006 consumption to 1 sets ū = 4.87. Under log utility, v(c) = ū + log(c) rises with living standards: it averaged roughly 2 in 1820 for the U.S. and nearly 5 by 2019, and ranges from about 2 (Ethiopia) to 5 (U.S.) across countries in 2019. The world-sample average of v(c) over 1960–2019 is 2.7.

Applying the formula to Penn World Table 10.0 data for 101 countries over 1960–2019 yields the following main findings. CE welfare growth averages 6.2% per year versus 2.1% per year for per-capita consumption growth; at 2.1% growth per-capita consumption doubles every 33 years, but under the CE measure social welfare doubles every 12 years. Population growth (averaging 1.8% per year) accounts for 66% of CE welfare growth unweighted across countries, and 51% weighting by country population (which gives China a large weight). For the United States specifically, CE welfare growth averages 6.5% per year versus 2.2% for per-capita consumption growth. Country rankings shift dramatically. Mexico rises from the 35th to the 88th percentile (CE welfare growth: 8.6% per year; population contribution: 79%). South Africa and Kenya similarly move up sharply. Germany falls to the 11th percentile, Japan to the 32nd, and China to the 44th — all below the United States. The cross-country correlation between CE welfare growth and per-capita consumption growth is 0.51; with population growth, 0.29. Over the very long run (1500–2018, Maddison data), per-capita consumption rose 20-fold (0.6% per year) while CE welfare rose 3,700-fold (1.6% per year) due to population growing at 0.5% per year scaled by v(c).

Robustness checks confirm the core result. Halving the baseline VSL (setting ū = 2.4) still leaves population contributing 38% of CE welfare growth on average. Incorporating within-country consumption inequality under a log-normal distribution lowers CE welfare growth by an average of just 10 basis points (from 6.1% to 6.0% for 1980–2007). Attributing migrants to source rather than destination countries produces a correlation of 0.92 between adjusted and baseline CE welfare growth rates. Decomposing population growth, roughly three-quarters of actual population growth in a 24-country subsample reflected increases in the number of lives lived (i.e., births), not longevity extension — so the welfare contribution of births exceeds that of rising longevity.

An extended model adds leisure, parental altruism toward children’s consumption and human capital, and endogenous fertility. Using time-use data from six countries (U.S. 2003–2019; Netherlands 1975–2006; Japan 1991–2016; South Korea 1999–2019; Mexico 2006–2019; South Africa 2000–2010), the extension modestly reduces the population share of CE welfare growth in most countries. The main reason is that parental altruism “double-counts” children’s consumption in the social welfare function, making consumption growth relatively more valuable and thus scaling down the weight on population growth. Rising quality of children (human capital) roughly offsets falling fertility in most countries, leaving net CE welfare growth little changed. Mexico is the sharpest exception: under extended preferences, CE welfare growth falls from 6.5% to 3.3% because of sharply declining leisure and little offsetting gain in children’s quality. Japan and South Korea also see smaller population shares under the extended model. The qualitative conclusion — that population growth is a major contributor to CE welfare growth — survives across all specifications.

Layer 2: Deep Dive

What is the paper’s identification strategy and what does it rely on?

This is a welfare accounting exercise rather than a causal identification exercise. There is no identification problem in the traditional econometric sense: the authors are computing a welfare index given a social welfare function and observed data on population and consumption. The two key inputs are (1) data on population and consumption per capita from the Penn World Table 10.0 for 101 countries over 1960–2019, and (2) a calibrated value of the parameter ū, which is the value of a year of life measured in units of per-capita consumption. The calibration of ū is anchored to external VSL estimates (EPA’s $7.4 million in 2006 prices), divided by life expectancy and per-capita consumption. The paper is explicit that it cannot make causal policy recommendations because it says nothing about the production side of the economy or externalities (pollution, ideas, human capital spillovers).

What is v(c) and why does it matter so much for the results?

v(c) = u(c)/[u’(c)·c] is the value of a year of life measured in consumption-equivalent units — specifically, how many years’ worth of per-capita consumption an individual would require as compensation for losing one year of life. Under log utility u(c) = ū + log(c), v(c) = ū + log(c), so it rises with the log of consumption. The key implication is that each percentage point of population growth is worth v(c) percentage points of per-capita consumption growth. Since v(c) empirically ranges from about 2 (Ethiopia) to 5 (rich countries), and averages 2.7 over 1960–2019 across 101 countries, population growth receives a substantial weight in the CE welfare measure. Without this amplification (i.e., if v = 1 so CE welfare equals aggregate consumption growth), population would still account for 36% of all growth.

How does the paper distinguish its approach from simply using aggregate (total) consumption growth?

Using aggregate consumption growth is equivalent to setting v(c) = 1 in the CE welfare formula — that is, weighting population growth and consumption growth equally. The paper shows that, under a total utilitarian welfare function with diminishing marginal utility, the correct weight on population growth is v(c) > 1, not 1. So aggregate consumption growth systematically understates the contribution of population growth to welfare: in a country with average v(c) = 2.7, a percentage point of population growth should receive 2.7 times the weight of a percentage point of consumption growth, not equal weight.

What threats to the baseline calibration of v(c) does the paper address?

The paper addresses four main threats. First, VSL uncertainty: it considers halving and raising the baseline VSL by 50%, yielding ū = 2.4 and ū = 7.3 respectively. Population’s share of CE welfare growth remains 38% even under the low VSL. Second, functional form: it considers CRRA utility with risk-aversion γ = 2 rather than log (γ = 1), which lowers the population share to 40% (from 53% baseline, population-weighted). Third, whether v(c) should be constant rather than income-varying: rows 7–9 of Table 3 test constant v = 4.87, v = 2.7, and v = 1. Even v = 1 (aggregate consumption growth) gives population a 36% share. Fourth, whether the marginal VSL used to calibrate the model overstates the average value of a birth (since a birth produces a new life from the start, not an added year for a middle-aged person). The paper acknowledges this concern but treats the calibration as a natural baseline and explores lower ū as a robustness check.

How does within-country inequality affect the results?

Under log utility and a log-normal distribution of individual consumption, CE welfare growth becomes gλ = [ū + log(c_t) - (1/2)σ²_t]·gN + gc - σ²_t·gσ, where σ² is the cross-sectional variance of log consumption. Inequality enters in two ways: it reduces the weight on population growth (because average utility is lower than utility of average consumption under concavity), and increases in inequality directly reduce CE welfare growth. Implementing this for 90 countries over 1980–2007, the mean adjustment is -10 basis points (6.1% to 6.0%), with a mean absolute deviation of 18 basis points. The adjustment is sizable for South Africa (−0.83 pp, due to very high inequality relative to U.S. 2006 baseline) and small or positive for Brazil (falling inequality over the period) and Ethiopia.

How does the paper treat migration, and does it matter?

The baseline credits population growth to the country of residence. The migration-adjusted measure reassigns migrants to their country of birth: it adds the flow utility of out-migrants (at destination-country consumption levels) and subtracts the flow utility of in-migrants (at destination-country consumption levels) from each country’s welfare. Using the World Bank Global Bilateral Migration Database for 81 countries over 1960–2000, migration-adjusted and baseline CE welfare growth rates have a correlation of 0.92. The adjustment matters most for specific countries — it raises welfare growth for net out-migrant countries like Mexico and the Philippines (since their emigrants consume more abroad) and lowers it for net in-migrant countries — but it does not alter the broad conclusion that population growth matters greatly.

What is the decomposition of population growth into fertility and longevity effects?

For a 24-country subsample (from the Human Mortality Database combined with World Bank migration data), the authors compute counterfactual population growth holding age-specific death rates constant at their initial-period values. Population-weighted, actual annual population growth is 0.72% versus a counterfactual of 0.53% with fixed longevity. So roughly three-quarters of population growth (and therefore three-quarters of the CE welfare contribution of population growth) reflected an increase in the number of lives lived (births minus deaths under fixed mortality), not gains in longevity. Italy and Japan are outliers: falling death rates (i.e., longevity gains) account for about three-quarters of their population growth. For context, Jones and Klenow (2016) attribute ~1% per year of CE welfare growth to rising longevity for 128 countries over 1980–2007; the total population growth contribution here (~3% per year, population-weighted from Table 1) substantially exceeds the longevity-only benchmark.

What does the extended model with parental preferences add, and what are its main results?

The extended model incorporates adult leisure, parental altruism toward children’s consumption and human capital, endogenous fertility, and children’s utility as separate welfare contributors. Social welfare is W = N_p·u(c_p, l, c_k, h_k, b) + N_k·ũ(c_k), where b is fertility per adult, l is adult leisure, and h_k is children’s human capital. CE welfare growth is computed using first-order conditions from parents’ utility maximization — specifically, the MRS between leisure/fertility/human capital and consumption can be measured from time-use data, which provides the welfare weights on each term. Key parameters: parental altruism weight α = 2/3 (calibrated to USDA household spending data), diminishing-returns-to-fertility parameter θ = 0.8, and children’s human capital elasticity η = 0.21 (from Mincer estimates in Lee, Roys, and Seshadri 2024). Main results: (1) Population growth remains an important contributor to CE welfare growth in most countries. (2) The population share falls somewhat because parental altruism double-counts children’s consumption, raising the relative weight on consumption growth. (3) Rising children’s quality (human capital, measured via real wage growth) roughly offsets falling fertility in most countries. (4) Mexico is the main exception: CE welfare growth drops from 6.5% to 3.3% due to falling leisure and little offset from rising children’s quality. (5) Japan’s population share falls further, turning slightly negative in some specifications.

What is the philosophical foundation and what is the ‘repugnant conclusion’ objection?

The total utilitarian social welfare function W = N·u(c) follows from three axioms: same-number Pareto (welfare ordering respects Pareto improvements for fixed populations), non-anti-egalitarianism (society does not prefer inequality), and mere addition (adding a person who values living, holding others’ utilities constant, does not reduce welfare). These axioms, as surveyed by Kuruc, Budolfson, and Spears (2022), together imply total utilitarianism and rule out diminishing-returns-to-population approaches (e.g., W = N^α·u(c) for α < 1). The repugnant conclusion (Parfit 1984) holds that total utilitarianism could justify very large populations of people whose lives are barely worth living. The authors respond that their calculations are local — reflecting only actual births and deaths over 1960–2019 — not arbitrary expansions. They also note that 29 philosophers and economists (Zuber et al. 2021) have argued the repugnant conclusion is not a reason to reject totalism. The per-capita approach has its own problems: it implies one should remove people whose utility is valuable but below average (and implies the ‘sadistic conclusion’ under certain conditions).

How does this paper relate to Jones and Klenow (2016)?

Jones and Klenow (2016) is the closest predecessor. That paper computes CE welfare measures incorporating consumption, leisure, life expectancy, and inequality, but in a per-capita framework — it measures individual living standards, not aggregate social welfare. The key difference here is moving from per-capita utility to total utilitarian welfare by multiplying individual utility by population, which introduces the v(c)·gN term. The current paper’s baseline is also simpler (consumption only) with an extended version that adds leisure and parental preferences. Jones and Klenow attribute ~1% per year of CE welfare growth to rising longevity for 128 countries over 1980–2007; the present paper shows total population growth (birth + longevity channels combined) contributes ~3% per year (population-weighted), substantially more.

What are the policy implications and their scope conditions?

The paper explicitly states it cannot make policy recommendations because it says nothing about the production side of the economy or about externalities (pollution, ideas externalities, human capital spillovers). Whether fertility rates are ’too low’ or the demographic transition raised or reduced social welfare requires estimating these externalities, which is beyond the paper’s scope. The paper is a measurement exercise, not an optimal policy analysis. Nonetheless, the results have implications for policy questions that depend on which welfare criterion is adopted: optimal fertility policy, the welfare cost of HIV/AIDS or other mortality shocks, the assessment of China’s One Child Policy, the welfare calculus of climate change mitigation, and the social returns to nonrival knowledge (which benefit a larger future population under totalism). The scope condition throughout is that the paper evaluates actual births and deaths over a historical period; the results do not directly speak to the desirability of population expansion beyond what occurred.

What are the main robustness checks run and what do they show?

1. VSL calibration: halving (ū = 2.4) or raising by 50% (ū = 7.3) the baseline VSL — population share falls to 38% or rises to higher levels, but population remains important in all cases. 2. CRRA utility with γ = 2 (more concave): population share falls to 40% population-weighted (from 53%). 3. Constant v(c): results with v = 4.87 (U.S. 2006 level), v = 2.7 (world average), and v = 1 (aggregate consumption growth) all confirm that population growth matters, with v = 1 still giving a 36% population share. 4. Inequality: mean absolute adjustment of 18 basis points; largest adjustment for South Africa (−0.83 pp). 5. Migration: correlation 0.92 between adjusted and baseline. 6. Birth vs. longevity decomposition: ~75% of population growth (population-weighted) is from net new lives, not longevity. 7. Extended preferences (time-use data): qualitative results survive; population share falls modestly except for Japan, South Korea, and Mexico.

What heterogeneity across countries and time periods is documented?

Cross-country: CE welfare growth ranges from just above 2% per year for the slowest-growing countries to more than 10% per year for the fastest. The correlation between CE welfare growth and per-capita consumption growth is 0.51; with population growth, 0.29. The value of v(c) ranges from about 2 (Ethiopia) to 5 (U.S.) in 2019, tracking consumption levels. Countries with high population growth (Mexico, Brazil, South Africa, Kenya, Sub-Saharan Africa more broadly) move up sharply in the growth rankings; countries with slow population growth (Germany, Japan, China) fall sharply. Within time: Japan shows CE welfare growth falling from 9.7% per year in the 1960s to −0.3% in the 2010s as both consumption growth and population growth slowed and then turned negative. China’s CE welfare growth fell more modestly from a 7.0% peak in the 1990s to 5.7% in the 2010s because rising v(c) partly offset slower population growth. Sub-Saharan Africa maintained stable population growth (~2.5% per year across all decades) and saw rising consumption in the 2000s and 2010s, producing CE welfare growth above 8% in the 2010s. Extended-model results (six-country sample): Mexico is a major outlier with falling leisure driving CE welfare growth down to 3.3% (from 6.5% baseline); Japan and South Korea have very small or near-zero population shares under extended preferences.

What does the very long-run historical exercise show?

Using Maddison Project data (de Pleijt and van Zanden 2020) from 1500 to 2018 for the world as a whole, per-capita consumption rose by a factor of 20 (0.6% per year) and aggregate consumption rose by a factor of 163 (1.1% per year). CE welfare rose by a factor of 3,700 — a 1.6% per year average annual growth rate. The power of compounding over 500 years causes a difference of only 1 percentage point per year between CE welfare growth (1.6%) and per-capita consumption growth (0.6%) to produce a ratio of 185:1 in cumulative outcomes (3,700-fold versus 20-fold). Population growth accounts for 61% of CE welfare growth over this very long run.

What data sources are used and what are the sample restrictions?

Baseline: Penn World Table 10.0 (Feenstra, Inklaar, and Timmer 2015) for 101 countries over 1960–2019 (starting from 111 countries and dropping those flagged as outliers in any year). Consumption is private plus government consumption. Inequality data: Jones and Klenow (2016), 90 countries, 1980–2007. Migration data: World Bank Global Bilateral Migration Database (1960, 1970, 1980, 1990, 2000), 81 countries. Birth/death decomposition: Human Mortality Database combined with World Bank migration data, 24 countries. Long run: Maddison Project (de Pleijt and van Zanden 2020), 1500–2018, with consumption proxied as 0.8 times per-capita GDP. Extended model: time-use surveys for U.S. (2003–2019), Netherlands (1975–2006), Japan (1991–2016), South Korea (1999–2019), Mexico (2006–2019), South Africa (2000–2010); Penn World Table for population, consumption, and hours worked; World Bank for number of children (0–19 years); USDA spending-on-children data (Lino 2011) for parental altruism calibration; Lee, Roys, and Seshadri (2024) Mincer estimates for human capital elasticity.

Key Concepts

Consumption-Equivalent (CE) Welfare Growth: The rate at which per-capita consumption would need to grow, holding population constant, to produce the same increase in total utilitarian social welfare as the observed combination of population growth and per-capita consumption growth. Formally gλ = v(c)·gN + gc. It is analogous to GDP in being a flow measure (not a present-discounted sum across generations).

Value of a Year of Life, v(c): The ratio u(c)/[u’(c)·c], equal to individual utility divided by the marginal utility of consumption times consumption. It converts the value of being alive for one year into consumption-equivalent units. Under log utility u(c) = ū + log(c), v(c) = ū + log(c), so it rises with living standards. It is calibrated from Value of Statistical Life estimates: v(c_US,2006) ≈ 4.87, meaning a year of American life in 2006 was worth approximately 4.87 years’ worth of per-capita consumption.

Total Utilitarian Social Welfare Function: W = N·u(c): social welfare is the sum of all individuals’ flow utilities. It treats every person’s utility symmetrically and linearly in population, so adding a person who values living always increases welfare. This contrasts with the per-capita (average utilitarian) approach (which implicitly sets the welfare weight on population to zero) and intermediate approaches that weight population with diminishing returns (W = N^α·u(c), α < 1).

Mere Addition (Axiom): One of three axioms (with same-number Pareto and non-anti-egalitarianism) whose conjunction implies the total utilitarian social welfare function for variable populations. It states that, holding the utilities of existing persons constant, adding a new person who values living does not reduce social welfare. The axiom directly rules out the average (per-capita) utilitarian criterion.

Repugnant Conclusion: Parfit’s (1984) critique of total utilitarianism: maximizing the sum of utilities could in principle justify an extremely large population of people whose lives are just barely worth living (positive but tiny utility), since total utility could exceed that of a smaller population with high per-capita welfare. The paper responds that its welfare calculations are local (reflecting actual historical births and deaths), not global maximization exercises, and cites the Zuber et al. (2021) consensus that this is not a decisive objection.

Parental Altruism Weight (α, θ): Parameters governing how parents value children’s consumption relative to their own in the extended model. Under Assumption 1, u includes the term αb^θ·log(c_k): α governs the overall weight on children’s consumption and θ governs diminishing returns as the number of children rises. Calibrated to α = 2/3 (from USDA household spending ratios with two children) and θ = 0.8 (from cross-family variation in per-child spending). Parental altruism causes double-counting of children’s consumption in the social welfare function, upweighting consumption growth and reducing the relative contribution of population growth to CE welfare.

Double-Counting of Children’s Consumption: When parents are altruistic, their utility depends on children’s consumption as well as their own; and children receive direct utility from their consumption too. In the CE welfare growth formula, this means a rise in children’s consumption raises welfare through two channels simultaneously (parental and child utility), so each unit of consumption growth is ‘worth more’ relative to population growth. This is why the extended model’s population term is smaller than the baseline’s: consumption growth is valued more heavily under parental altruism, scaling down the consumption-equivalent weight on population growth.