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
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.