1/5 - Are We Measuring Fertility Wrong?

A mathematical decomposition (breaking down) of TFR of 314 million mothers across 33 countries reveals governments worldwide have been treating the wrong fertility problem for decades

Photo by Dan Cristian Pădureț on Unsplash

Stephen J. Shaw's paper (On a microdemographic framework for decomposing contemporary fertility dynamics) in Scientific Reports (2025) proposed that the Total Fertility Rate (used by every government and UN agency) obscures two independent crises by combining them into one misleading aggregate.

The math: TFR = TMR × CPM

• TMR (Total Maternal Rate): Proportion of women becoming mothers

• CPM (Children per Mother): Average family size among mothers

• TCR (Total Childlessness Rate): 1 - TMR

The independence that shouldn't exist: These components show zero statistical correlation across 33 countries, a finding frankly so counterintuitive it challenges decades of demographic orthodoxy (love that word orthodoxy). Shaw tested this through:

• Wavelet coherence: No synchronization between TMR and CPM in any country, so you are going to get weird stuff like 13 distinct motherhood-family size combinations produce identical TFR when rounded

• Information theory: TMR alone contains more information (3.64 bits) than combined TFR (3.43 bits), which means that 48.9% of fertility information lost when using TFR alone. In practical terms, this means policymakers using TFR as their primary metric are missing nearly half the diagnostic information needed to design effective interventions (like trying to diagnose heart problems while ignoring half the EKG data).

• Breakpoint analysis: Components shift at different times, responding to different forces

• Statistical confirmation: Knowing one component tells you nothing about the other

What else Shaw found in the data:

The measurement crisis extends to global institutions:

• 2024 UN Population Fund report identified fertility gaps across 14 countries through resource-intensive surveys but lacks standardized measures for societal childlessness or family size

• Birth order data completely missing in some high-resource countries, significantly delayed in others, preventing real-time fertility decomposition

• Prior warnings ignored: Demographers Sobotka and Lutz argued TFR is "mainly useful for answering 'Did TFR increase?',and little else," yet it remains the dominant metric

• Terminology confusion: The study renames TFR₁ to TMR for clarity, following precedent of BMI replacing the Quetelet Index for public understanding

Country-Specific Patterns Revealed

United States

• 1980 vs 2016: Identical TFR of 1.82 masks completely different realities

• TMR crashed from 76.1% to 69.4% between these periods

• CPM rose from 2.39 to 2.63: mothers having more children

• Sharp breaks: TMR dropped in 1971 and again in 2008 (Financial Crisis)

• Current status (2021): 63.6% TMR, 36.4% childlessness, 2.61 CPM

Japan

• All 47 prefectures simultaneously showed TMR drops 1974-1975 (p<0.0001)

• Breakpoints clustered October-November 1974: exactly 12 months after Oil Shock media coverage peaked

• TMR fell from ~95% to current 58.7% (41.3% childlessness)

• CPM remarkably stable at 2.13-2.20 across five decades

• Current status (2022): Lowest TMR among baseline countries

Italy

• Sharpest early decline: TMR plummeted around 1974 Oil Crisis

• CPM shows rare decline among studied nations: slight but sustained drop

• TMR dropped from over 95% in 1968 to 59.5% by 2023

• Current status (2023): 40.5% childlessness, 2.02 CPM

United Kingdom

• Similar 1974 shock to Italy and Japan in TMR

• CPM stability maintained around 2.3-2.4 for decades

• TMR declined from ~95% to 70.5%

• Current status (2020): 29.5% childlessness, 2.23 CPM

France (2013-2023 Deep Dive)

• TFR fell from 2.0 to 1.68 (seemingly gradual decline)

• Hidden reality: CPM rock-steady at 2.3-2.4 children

• TMR collapsed from 85.0% to 72.8%: 12.2 percentage point drop

• Current status (2023): 27.2% childlessness despite stable family size

Additional Countries (Latest Available)

• South Korea (2020): 47.9% TMR, 52.1% childlessness, 1.75 CPM (lowest family size)

• Germany (2022): 68.3% TMR, 31.7% childlessness, 2.11 CPM

• Netherlands (2023): 66.0% TMR, 34.0% childlessness, 2.18 CPM

• Spain (2023): 57.5% TMR, 42.5% childlessness, 1.95 CPM

• Turkey (2022): 62.0% TMR, 38.0% childlessness, 2.60 CPM

Statistical Evidence

Independence confirmed through multiple methods:

• Cointegration testing: No long-term equilibrium relationship between TMR and CPM

• Breakpoint analysis (PELT): TMR and CPM shifts occur independently

• Wavelet coherence: No significant synchrony detected across any country

• Mutual Information: Only 5.68% dependence between measures

Information theory findings: TMR alone contains more information than the combined TFR metric. This means policymakers using TFR are systematically discarding nearly half the information they need.

Key Insights

Critical measurement caveat: TMR can temporarily exceed 100% during policy changes; not an error but a "tempo effect" when women shift timing of first births. These distortions self-correct but can mislead short-term analysis.

The "fertility gap" redefined:

• CPM aligns with women's stated ideal family sizes (2-2.5 children)

• Gap stems from rising childlessness, not mothers having fewer children

• "Unplanned Childlessness" (i.e. circumstantial barriers preventing intended parenthood) emerges as key driver

Policy implications by pattern:

• High childlessness, normal CPM (Japan, Spain): Focus on motherhood entry barriers

• Universal motherhood, low CPM (historical pattern): Support larger families

• Rising childlessness, rising CPM (US): Bifurcating fertility requiring dual strategies

The shock pattern: Economic crises appear to coincide with lasting TMR declines with notable consistency:

• 1973 Oil Crisis → 1974: All 47 Japanese prefectures show simultaneous motherhood decline (p<0.0001)

• 2008 Financial Crisis → 2009: US motherhood drops 6.7 percentage points

• Pattern observed: Consistent 12-month lag from shock to demographic impact

• Historical tendency: TMR rates show limited recovery even during subsequent economic growth

The Central Mystery This Raises

At this point, I already summarized what you need to know about Shaw's paper. As I read it myself, it brings up a (well many) question(s): If TMR and CPM are independent (meaning they respond to different forces and require different interventions) why haven't policymakers moved beyond cliches to address this nuance? Policymakers are sounding the alarm of lower birthrates, especially as the negative effects starting to impact the economy in a number of different ways. Shaw isn't the first one to be talking about this either.

Not to mention there are four (out of many) questions that came out of this paper

• Why are economic shocks permanently depressing fertility rates & total maternal rates? (August 27th)

• Why is child per mother is slowly eroding in developed economies (August 29th)

• Why does the United States' CPM on the rise to the point that it temporary compensated for the falling TMR? (September 2nd)

• What are the sort of pronatalist polices actually out there, and what needs to be done? (September 4th)

Four interconnected mysteries, when solved, reveal why we've been fighting fertility decline with incomplete diagnostic tools; missing the interventions that might actually work.

On that note, tomorrow we will also start with another "big" mystery of "Who wants manufacturing jobs" with other ""big" mysteries such as "Can we rebuild and scale 'State Capacity'", “How ‘Yes, and’ YIMBYism can help small and mid towns, and "Why young men support Obama, Bernie, Trump, and Mamdani?" planned in September.