Boldrin De Nardi and Jones 2015 — Fertility and Social Security

Summary

Estimates how much of the post-WWII fertility decline in developed countries and the persistent Europe–US total fertility rate (TFR) gap can be explained by the growth of public pension systems. Using cross-country and panel regressions plus two calibrated general-equilibrium models of fertility (Barro-Becker (BB) dynastic altruism vs. Boldrin-Jones (BJ)/Caldwell "old-age security" reverse altruism), the paper finds that a 10-percentage-point increase in Social Security (SS) spending as a share of gross domestic product (GDP) is associated with $0.7$–$1.6$ fewer children per woman. The BJ/Caldwell model quantitatively accounts for $55$–$65\%$ of the Europe–US TFR gap and over $80\%$ of cross-country variation; the BB model fails — its SS effect is near zero or perversely signed. Published in Journal of Demographic Economics 81(3): 261–299.

Key Claims

Empirical: Cross-Country and Panel Evidence

• Cross-section (104 countries, 1997): Social Security spending as a percentage of GDP (SST) coefficient $= -16.1$ ($t = -7.3$) in the simple regression; $-6.8$ ($t = -4.2$) after controlling for GDP and infant mortality rate (IMR). An increase in SST from $0\%$ to $10\%$ of GDP → TFR falls by $0.7$–$1.6$ children per woman. $R^2 = 0.34$–$0.77$ depending on specification.
• Panel (8 European countries, 1960–2000): SST coefficient $= -12.2$ to $-6.4$; robust to IMR controls and share of elderly. A 10-percentage-point increase in SST/labor earnings → TFR falls by $1.0$–$1.8$ children.
• Only 4 countries with SST $\geq 6\%$ of GDP have TFR above $2.0$ children per woman.
• Standard alternative explanations — female labor force participation (FLFP), infant mortality decline, per-capita income, education — cannot jointly account for both the time series decline within countries and the cross-sectional Europe–US gap. The TFR-FLFP correlation turned positive in the 1980s–90s (high-FLFP countries like the US have higher fertility than low-FLFP European countries), ruling out female employment as the driver.

The Two Models

Barro-Becker (BB) model: Parents value children because they perceive children's utility as a continuation of their own (forward altruism / dynasty planning). In a pay-as-you-go (PAYGO) system, the dynasty planner nets out the SS transfers, and the effect on fertility is near zero or slightly positive (if child costs are in time). The BB model is inconsistent with the empirical data.

Boldrin-Jones (BJ) / Caldwell model: Parents have children because children provide old-age support (reverse altruism — children care about parents' utility). SS directly substitutes for children as a retirement asset:

• In equilibrium, fertility depends on: preference parameters, the growth rate of technology, the return on capital, and the degree of capital market accessibility ($\xi$).
• In a general-equilibrium (GE) model, the effect of SS on fertility operates through the interest rate (not through direct substitution in partial equilibrium). Effects are thus absent under fixed prices but present in closed-economy GE.

Quantitative Model Results

• Calibrated to US 2000 data (TFR $= 2.0$, $K/Y$ ratio, intergenerational transfers from micro evidence).
• Comparing a world with no SS to the US 2000 baseline ($\tau = 10\%$ of labor income): the BJ model predicts a TFR increase of $\approx 0.4$–$0.6$ children — roughly $55$–$65\%$ of the observed Europe–US TFR gap.
• Comparing the US to high-SST European countries (SST/GDP $> 14\%$ vs. low-SST countries): the BJ model accounts for over $80\%$ of the observed cross-country TFR differences.
• Capital market accessibility ($\xi$) is the other major channel: societies where saving for retirement is harder (low return on capital, underdeveloped financial markets) have higher fertility. This accounts for most of the remaining half of the time series decline in developed countries.
• The BB model fails: fertility is either neutral or slightly increases with SS, opposite to the data.

Reverse Causality and the Feedback Loop

• Standard SS fiscal analysis treats low fertility as an exogenous demographic constraint threatening SS finances. This paper inverts the direction: SS generosity causes low fertility, which then worsens the old-age dependency ratio, which in turn increases fiscal pressure on SS.
• This "pension-fertility trap" is most severe in continental Europe, where SST/GDP exceeds $14$–$20\%$.
• Government pension systems are a larger share of retirement income for low-income families, consistent with the empirical finding that fertility has declined more steeply for lower-socioeconomic-status (SES) individuals.

Concepts Introduced or Extended

• Demographic Transition — SS as a driver of post-WWII fertility decline; BJ/Caldwell model vs. Barro-Becker model; pension-fertility feedback loop
• Stochastic Fertility Forecasting — identification of SS generosity as a structural determinant of long-run TFR; relevant for calibrating mean-reversion target $F^*$

Entities Mentioned

• Michele Boldrin
• Mariacristina De Nardi
• Larry Jones

Quotes

"An increase in government provided old-age pensions is strongly correlated with a reduction in fertility."

"The effect on fertility in the Boldrin and Jones model is sizeable and accounts for between 55 and 65% of the observed Europe–US fertility differences both across countries and across time and over 80% of the observed variation seen in a broad cross section of countries."

"Since children are perceived by parents as a component of their optimal retirement portfolio, any social or institutional change that affects the economic value of other components of the retirement portfolio will have a first order impact on fertility choices."

My Take

The paper's chief strength is the model-selection test: two plausible, well-calibrated models of fertility make sharply different predictions about the effect of SS, and the data decisively selects the Caldwell/BJ framework. The empirical correlation is striking and robust across many specifications. The main limitation is that the regressions are cross-sectional or short-panel and cannot fully address endogeneity — countries with generous pensions may have lower fertility for other correlated reasons (urbanization, secularization, female education). The paper acknowledges this but does not provide a convincing instrumental variable (IV). For the wiki, the most important connection is to the SS solvency literature: if the pension-fertility link is causal, then standard actuarial projections that treat fertility as exogenous systematically underestimate the long-run fiscal impact of generous pension systems — the policies assumed to help fix SS also reduce its long-run tax base.