Too hot to give birth? Temperature shocks and general fertility rates in Japan

1 Introduction

Weather is a high-frequency environmental shock, but fertility is observed only after a long and partly endogenous sequence of decisions and biological events. A temperature realization can affect time use, sexual activity, conception, early pregnancy survival, gestational length, and delivery timing. Monthly births therefore combine several margins that need not move in the same direction or at the same horizon. This distinction matters for interpretation. A decline in births nine or ten months after a hot month may represent fewer conceptions, clinically unobserved pregnancy losses, or shifts in delivery timing. A subsequent increase may represent delayed conceptions, but it may also reflect ordinary seasonal dynamics or sampling variation. Aggregate birth counts alone cannot identify which families changed behavior or whether a birth occurred later.

The exposure measure creates a second interpretive problem. Daily maximum temperature captures the hottest point of the day, but it need not describe the thermal burden over the remaining hours. A short afternoon peak and a persistently hot day can enter the same maximum-temperature bin. Daily minimum temperature contains different information: a high minimum often indicates limited nighttime cooling. Daily mean temperature summarizes conditions over the day more directly, though it too remains an outdoor ambient measure rather than personal exposure. Because these metrics are correlated but not equivalent, focusing on one can attribute to a brief peak a relationship that is more closely associated with sustained heat.

This paper revisits the temperature-fertility relationship using all three metrics. I link monthly vital statistics for Japan’s 47 prefectures from January 2012 through December 2019 to daily maximum, minimum, and mean temperature reconstructed from raw Japan Meteorological Agency (JMA) station files. For each prefecture, I select the three stations nearest its geographic center, assign inverse-distance-squared weights, screen observations using the source quality flags, and renormalize weights over stations observed on each day. This procedure yields a balanced panel of 4,512 prefecture-months and permits the three temperature measures to be compared on a common raw-data foundation.

The outcome is the monthly general fertility rate (GFR): live births divided by the number of women ages 15–49, multiplied by 1,000. This denominator follows demographic practice more closely than a working-age total-population denominator. Annual female population enters at the prefecture-year level. In a log specification with prefecture-by-year fixed effects, that denominator is absorbed, so the temperature coefficients are numerically identical when log live births replaces log GFR. The GFR nevertheless remains preferable because it states clearly the population at risk and avoids describing the dependent variable as a total fertility rate.

The empirical design compares months within tightly defined location and time cells. Each regression includes a full vector of temperature-bin days for one exposure metric, lag-specific precipitation, the number of missing temperature days, year-month fixed effects, prefecture-by-calendar-month fixed effects, and prefecture-by-year fixed effects. The first set absorbs nationwide month-specific shocks. The second allows each prefecture to have its own seasonal pattern. The third absorbs slow-moving local conditions within a year, including the annual female-population denominator. Standard errors are clustered by prefecture. I also report two-way clustering by prefecture and year-month and Benjamini-Hochberg adjustments over the displayed dynamic path.

Three findings organize the paper. First, the estimated association with extreme daily maximum temperature is fragile. A day with maximum temperature at or above 35∘C is associated with a 0.229 percent reduction in GFR at lag nine (coefficient −0.002294, standard error 0.001140, p=0.05002), but the result is not significant under two-way clustering (p=0.114) and does not survive adjustment over the dynamic path (q=0.655). The lag-ten estimate is smaller and insignificant. When lags nine and ten enter the same model, the cumulative maximum-temperature estimate is −0.002784 (p=0.080). When complete daily-mean bins enter jointly, the cumulative maximum-temperature coefficient is essentially zero (−0.000004,p=0.998).

Second, high minimum and mean temperatures show more coherent negative associations at the gestational horizon. A day with minimum temperature at or above 25∘C is associated with 0.387 percent lower GFR at lag nine and 0.246 percent lower GFR at lag ten. The lag-nine estimate remains significant with two-way clustering and after the within-metric false-discovery adjustment. The cumulative lag-nine-plus-lag-ten estimate is −0.005837 (standard error 0.001048). For daily mean temperature, a day at or above 30∘C is associated with 0.495 percent lower GFR at lag ten (standard error 0.001522, p=0.0021); its two-way-clustered p-value is 0.0015, while the adjusted q-value is 0.060. The cumulative mean-temperature estimate is −0.006371 (standard error 0.001905), and it remains negative when maximum-temperature bins enter jointly.

Third, the data delimit what can be concluded. There is no broad pattern in recorded fetal-death incidence that maps cleanly onto the fertility results. Under the Japanese statistical definition, this aggregate begins at 12 completed weeks and may include spontaneous and induced fetal deaths; it is not a measure of spontaneous pregnancy loss alone. Its absence of a broad response is therefore not evidence against a physiological pathway. Nor can the birth-rate dynamics establish a behavioral pathway. In particular, Hajdu and Hajdu (2019) find no significant contemporaneous or lagged relationship between temperature and sexual activity in time-use data. Changes in conception-related behavior remain possible, but the present prefecture-month panel does not measure sexual activity, contraceptive use, intentions, or conception.

The paper contributes to research documenting delayed birth responses to weather shocks. Classic work relates temperature to seasonal fertility (Lam and Miron, 1996); more recent studies use high-frequency weather variation to trace conception and birth-rate responses in the United States, Europe, Hungary, Spain, and East Asia (Barreca et al., 2018; Wilde et al., 2017; Hajdu and Hajdu, 2022; Cho, 2020; Hajdu, 2024; Conte Keivabu et al., 2025). Related work examines gestational length, birth outcomes, and pregnancy loss (Deschênes et al., 2009; Basu et al., 2016; Barreca and Schaller, 2020; Chen et al., 2020; Hajdu and Hajdu, 2021, 2023). The present contribution is not a new claim that heat unambiguously lowers completed fertility. It is a measurement result: consistent reconstruction and comparison of maximum, minimum, and mean temperature changes which exposure carries the most stable signal in Japan.

This measurement emphasis also changes the policy interpretation. A coefficient on daily maximum temperature may reflect daytime outdoor activity, indoor protection, building conditions, behavior, adaptation, and physiology. A coefficient on daily minimum temperature may reflect overnight recovery as well as correlated daytime conditions. A coefficient on daily mean temperature may better summarize cumulative ambient conditions but remains an imperfect proxy for individual heat load. These coefficients are not laboratory parameters that rank the intrinsic physiological potency of alternative temperature metrics. They are reduced-form relationships between related outdoor measures and monthly fertility.

The remainder of the paper develops these points. Section 2 describes possible pathways without assigning the estimates to one mechanism. Section 3 documents the demographic and weather inputs, including the raw-station reconstruction. Section 4 presents the fixed-effects design and inference. Section 5 reports the main estimates, dynamics, and descriptive recorded-fetal-death check. Section 6 summarizes supplementary checks and the birth-count translation. Section 7 discusses interpretation, limitations, and implications.

2 Temperature and fertility: possible pathways

2.1 Biological timing and observed births

Ambient heat can enter the reproductive process before conception, during pregnancy, or near delivery. Experimental and clinical literatures describe temperature-sensitive processes in reproductive function, but translating those findings into population exposure is difficult (Hansen, 2009). Outdoor station temperature is not core body temperature, and exposure depends on work, housing, air conditioning, sleep, mobility, and avoidance behavior. A prefecture-level reduced-form coefficient therefore combines the biological response with the circumstances that determine who is exposed.

Preconception exposure could affect fecundability through male or female reproductive function. Postconception exposure could affect implantation or early pregnancy survival. Many such losses occur before clinical recognition and will not appear in the recorded fetal-death aggregate. Later in pregnancy, heat can affect maternal stress and delivery timing; Barreca and Schaller (2020), for example, show that high temperature can shift delivery forward. These pathways imply different dynamic signatures but are not separately observed here. A birth decline nine or ten months after exposure is compatible with fewer conceptions or early losses. Responses at shorter lags could reflect gestational length or late-pregnancy effects. Monthly aggregation blurs these horizons because gestation length varies and births are dated by month rather than exact conception.

The fetal-death analysis is consequently limited. Under Japanese Vital Statistics, a fetal death is recorded from 12 completed weeks of gestation, and the published total may include both spontaneous and induced fetal deaths (Ministry of Health, Labour and Welfare, 2026). The source tables used here provide only that aggregate total, so the components cannot be separated. The main outcome divides recorded fetal deaths by women ages 15–49, keeping the population denominator parallel to the GFR. The Supplement also reports recorded fetal deaths divided by live births plus recorded fetal deaths. Neither measure is directly comparable to international stillbirth outcomes defined from 22 or 28 weeks, and neither can be interpreted as spontaneous pregnancy loss alone. Temperature can also affect the number of pregnancies reaching a recorded gestational stage as well as their conditional risk. An insignificant coefficient cannot rule out physiological effects; an isolated significant coefficient cannot identify one.

2.2 Behavior and the timing of conception

Temperature also changes how people allocate time. Hot conditions can reduce outdoor activity and labor supply or shift activity across hours (Graff Zivin and Neidell, 2014). These adjustments make conception-related behavior a plausible link between weather and births. Yet plausibility is not identification. The direct evidence on sexual activity is mixed: using Hungarian time-use surveys, Hajdu and Hajdu (2019) find no statistically significant effect of hot days on sexual activity on the same or subsequent days. That evidence weighs against treating reduced intercourse as an established general mechanism.

Other behavioral margins remain possible. Couples may change travel, social activity, sleep, contraceptive use, or planned timing without changing total sexual activity. Planned conception can also have seasonal content, and preferences over season of birth may generate dynamics that resemble responses to temperature (Buckles and Hungerman, 2013; Clarke et al., 2019). The present data contain none of these variables. Contemporaneous marriages are observed, but marriage in the birth month is not a clean control for conditions at conception: it may be jointly determined with fertility timing and can become a bad control. I therefore exclude marriage from the baseline and add it only as a sensitivity check.

2.3 Why maximum, minimum, and mean temperature can differ

The three exposure measures answer different questions. Maximum temperature is generally reached during daytime hours, when outdoor activity may be greatest. Its coefficient can therefore reflect high exposure opportunity. Minimum temperature is commonly reached overnight, when many people are indoors, but a high minimum also signals limited nocturnal cooling and a sustained hot episode. Mean temperature averages conditions over the day and is less sensitive to a brief peak. Indoor protection may attenuate any outdoor measure, and the degree of attenuation may differ by hour and setting.

These distinctions are empirical, not physiological rankings. A larger coefficient on maximum temperature could arise because more people are outside at the daily peak. A larger coefficient on minimum temperature could arise because nighttime heat disrupts recovery or because hot nights mark persistent heat. A larger coefficient on mean temperature could arise because the average better captures cumulative conditions. Correlation among the metrics also matters: if maximum and mean temperature rise together, a single-metric maximum model can load onto the broader hot-day episode. Joint models help describe conditional associations, but multicollinearity and common measurement error prevent a clean decomposition into independent biological doses.

2.4 Displacement, recovery, and completed fertility

The timing of later coefficients determines whether a short-run birth decline is followed by an offset in observed births. Barreca et al. (2018) document dynamic adjustment in the United States, and work in Europe and Hungary likewise emphasizes conception timing (Hajdu and Hajdu, 2022; Hajdu, 2024). A positive coefficient after the gestational horizon can be consistent with postponed conception, but it is not uniquely diagnostic. Likewise, the absence of a precisely estimated positive coefficient through 24 months cannot show that births never occur later. Sampling error, multiple testing, changes beyond the observed horizon, and heterogeneous household responses all matter.

This paper therefore distinguishes a gross short-run difference from a completed-fertility effect. The regressions track monthly births for at most 24 months after exposure and cannot link parents across time. Any birth-count translation is a model-implied difference around the gestational horizon, conditional on the estimated exposure response. It is not a forecast of lifetime births and does not establish that the same families ultimately have fewer children.

3 Data and measurement

3.1 Vital statistics and the general fertility rate

Monthly live births, recorded fetal deaths, marriages, deaths, and divorces come from the Vital Statistics of Japan (Ministry of Health, Labour and Welfare, 2020). The sample contains all 47 prefectures from January 2012 through December 2019. Two source files overlap in December 2016. I compare all demographic fields for the 47 duplicated prefecture-month records, confirm that the values agree, and retain one record per prefecture-month. The resulting vital-statistics panel is balanced: 47 prefectures by 96 months, or 4,512 observations. It contains 8,040,326 live births.

The population denominator comes from annual prefecture-by-age-by-sex estimates (Statistics Bureau of Japan, 2020). I sum the seven five-year female age groups from ages 15–19 through ages 45–49 and convert the source units from thousands to persons. For prefecture p, calendar month t, and year y(t), the monthly GFR isThe regression outcome is log(GFRpt). This is a monthly general fertility rate, not a total fertility rate: it does not sum age-specific rates and should not be interpreted as expected lifetime births per woman.

GFRpt=LiveBirthsptWomenp,y(t),15-49×1,000.(1)

Annual female population changes at the prefecture-year level. Because the main model contains prefecture-by-year fixed effects,has the same within-transformed temperature coefficients as a log-live-birth specification. The Supplement verifies equality to numerical precision. The GFR terminology and denominator are nevertheless substantively important: they define the population at risk and answer the reviewer’s demographic concern.

log(GFRpt)=log(LiveBirthspt)−log(Womenp,y(t),15–49)+log(1,000)

Recorded fetal-death incidence is defined analogously as recorded fetal deaths per 1,000 women ages 15–49. As an additional check, I calculate the fetal-death-to-total-birth ratio under the Japanese statistical definition,and report log-ratio estimates in the Supplement.

FDRatiopt=RecordedFetalDeathsptLiveBirthspt+RecordedFetalDeathspt×1,000,(2)

3.2 Raw weather-station reconstruction

The weather inputs are raw historical JMA station records (Japan Meteorological Agency, 2020). I use 560 station-metric files: 140 files each for daily maximum temperature, daily minimum temperature, daily mean temperature, and monthly precipitation. The 140 distinct stations arise because one station serves among the nearest three for two prefectures. The station crosswalk contains exactly three distinct station assignments per prefecture, or 141 prefecture-station rows.

For each prefecture, I begin with its geographic center and choose the three closest stations with the required measures. If station s is dps meters from prefecture p’s center, its baseline weight iswhere Sp contains the three selected stations. The weights sum to one within every prefecture to machine precision. JMA quality remark 8 denotes a normal value with no missing underlying observations; remark 5 denotes a quasi-normal value whose missing share remains within JMA’s acceptable range (approximately 80 percent or more of the underlying observations are available) (Japan Meteorological Agency, 2026). A station-day is accepted only when its source quality remark is 5 or 8 and the value is not the source missing code. The same rule is applied to maximum, minimum, and mean temperature. When one or two stations are unavailable, I renormalize the weights over stations observed for that prefecture-day. A missing station is never assigned a zero temperature. A prefecture-day is missing only when none of its selected stations has an accepted value.

wps=dps−2∑r∈Spdpr−2,(3)

The procedure reconstructs 137,334 prefecture-days, equal to 47 times the 2,922 calendar days in 2012–2019. Daily mean temperature has 3 missing prefecture-days; maximum and minimum temperature each have 40. For each metric and month, the sum of all bin counts plus the metric-specific missing-day count equals the number of calendar days. Monthly precipitation is reconstructed using the corresponding weights and has no missing prefecture-months.

3.3 Temperature bins

The nonlinear bins are fixed before estimation and used consistently in the code, figures, tables, and text. Maximum temperature is divided into <0, 0–5, 5–10, 10–15, 15–20, 20–25, 25–30, 30–35, and ≥35∘C; 20--25∘C is the omitted category. Minimum temperature is divided into <−5, −5–0, 0–5, 5–10, 10–15, 15–20, 20–25, and ≥25∘C; 0--5∘C is omitted. Mean temperature is divided into <0, 0–5, 5–10, 10–15, 15–20, 20–25, 25–30, and ≥30∘C; 20--25∘C is omitted. Intervals are left-closed and right-open except for the open-ended tails.

Figure 1 is generated directly from the reconstructed prefecture-day panel. It is a distribution figure, not a regression-coefficient figure. Panel A shows maximum temperature, Panel B minimum temperature, and Panel C mean temperature. There are 1,026 prefecture-days with maximum temperature at or above 35∘C, 2,696 with minimum temperature at or above 25∘C, and 316 with mean temperature at or above 30∘C. The small mean-temperature tail is a reason to report its uncertainty carefully rather than treat statistical significance as a sufficient measure of reliability.

Table 1 reports prefecture-month summary statistics. The average monthly GFR is 3.43 births per 1,000 women ages 15–49. Extreme-bin counts are highly seasonal and contain many zeros outside summer. The identifying variation therefore comes from deviations in the number of days within narrowly controlled prefecture and calendar cells, not from a comparison of the warmest prefectures with the coldest.

Table 1. Summary statistics.

The unit of observation is a prefecture-month. Population is the number of women ages 15–49; the source workbook reports thousands and is converted to persons. Under the Japanese Vital Statistics definition, recorded fetal deaths begin at 12 completed weeks and the aggregate used here may include spontaneous and induced fetal deaths. Temperature variables are reconstructed from raw station observations.

4 Empirical strategy

4.1 Single-lag specification

For temperature metric q∈{max,min,mean} and lag ℓ, I estimatewhere bq0 is the metric-specific reference interval. The coefficients are semielasticities with respect to one additional day in a temperature bin, holding the omitted-bin days and the other included bins implicit through the fixed number of days in a month. The primary coefficients are those on maximum ≥35∘C, minimum ≥25∘C, and mean ≥30∘C.

log(GFRpt)=∑b≠bq0βqbℓTempDaysp,t−ℓq,b+ρqℓPrecipp,t−ℓ+μqℓMissingDaysp,t−ℓq+δt+θp,m(t)+αp,y(t)+εpt,(4)

The year-month fixed effects δt absorb national shocks in every sample month, including national fertility trends and common macroeconomic conditions. Prefecture-by-calendar-month fixed effects θp,m(t) allow each prefecture to have its own recurring seasonal profile. Prefecture-by-year fixed effects αp,y(t) absorb annual local factors and the GFR denominator. This is demanding variation: the coefficients are identified from within-prefecture departures from its usual month-specific exposure, net of national month shocks and prefecture-year conditions.

The baseline does not include current marriages. Marriage counts occur in the outcome month rather than the exposure month and can co-move with planned fertility timing. Treating them as predetermined would be difficult to defend. The Supplement adds contemporaneous marriages as a robustness check and shows that the main minimum- and mean-temperature patterns remain.

I estimate Equation 4 separately for leads −3,−2,−1 and lags 0 through 24. A lag of nine, for example, matches births in month t to temperature in t−9. A negative lag is a future-temperature placebo: at lag −3, temperature occurs three months after the birth month. Because the model is re-estimated for each lag, sample size declines near the panel boundaries. Lag nine uses 4,089 observations and lag ten uses 4,042.

4.2 Cumulative and joint exposure models

Single-lag coefficients describe the response at a particular horizon, but summing coefficients from two separately estimated regressions would ignore their covariance and use different samples. I therefore estimate a distributed-lag specification that includes complete bin vectors, precipitation, and missing-day controls at lags nine and ten in the same regression. For metric q, the cumulative extreme-bin coefficient iswhere e is the extreme bin and V^q is the clustered covariance submatrix for the two coefficients.

βqcum=βq,e,9+βq,e,10,Var(β^qcum)=1′V^q1,(5)

To assess whether a short maximum-temperature peak contains information beyond the broader thermal environment, I also estimate maximum-mean joint models. The single-lag version includes all nonreference maximum and mean bins at the same lag. The distributed-lag version includes both complete vectors at lags nine and ten. The conditional coefficients should not be interpreted as experimentally isolated physiological effects. They ask whether one outdoor metric predicts fertility after conditioning flexibly on the other.

4.3 Inference and interpretation

The baseline covariance matrix clusters by prefecture, allowing arbitrary serial correlation and heteroskedasticity within each of the 47 prefectures. As sensitivity checks, I implement two-way clustering by prefecture and year-month following Cameron et al. (2011) and Conley spatial–temporal HAC inference (Conley, 1999). The Conley calculation allows Bartlett-weighted spatial covariance among prefectures in the same year-month and serial covariance within prefecture for up to 12 months. The prespecified primary spatial bandwidth is 250 km; 100 and 500 km are also reported. Because Figure 2 presents 28 lead/lag estimates for each metric, I calculate Benjamini-Hochberg q-values within each metric’s dynamic path (Benjamini and Hochberg, 1995). These inferential summaries answer different questions and are displayed together rather than selected according to favorability.

Weather variation is plausibly exogenous conditional on the fixed effects, but causal language still requires care. Station measurements are proxies for personal exposure; local mobility can produce measurement error; temperature metrics are correlated; and monthly births can respond through multiple margins. I interpret Equation 4 as a reduced-form short-run relationship under the stated controls. I do not use it to identify intercourse frequency, conception, pregnancy loss, or a physiological dose-response parameter.

5 Results

5.1 Maximum, minimum, and mean temperature

Table 2 reports the extreme-bin coefficients at lags nine and ten. Each cell comes from a separate full-bin regression. The first column provides limited evidence for maximum temperature. At lag nine, one additional day at or above 35∘C has a coefficient of −0.002294 (standard error 0.001140). The prefecture-clustered estimate is marginally above the conventional 5 percent threshold (p=0.05002); the two-way-clustered p-value is 0.114, and the within-metric BH q-value is 0.655. At lag ten, the coefficient is −0.000934 (standard error 0.000900, p=0.305). The point estimates are negative, but the evidence is too sensitive to horizon and inference to support a robust independent maximum-temperature effect.

Table 2. Extreme temperature and the log general fertility rate.

The dependent variable is log monthly GFR. Each column and lag is estimated separately. All nonreference bins for the indicated temperature metric enter jointly, together with lagged precipitation and missing-weather-day counts. Models include year-month, prefecture-by-calendar-month, and prefecture-by-year fixed effects. Standard errors are clustered by prefecture; the third row reports p-values under two-way clustering by prefecture and year-month. Benjamini–Hochberg q-values adjust over lags −3 through 24 separately within each metric. The reference bins are 20--25∘C for maximum and mean temperature and 0--5∘C for minimum temperature.

*** denote p<0.10, p<0.05, and p<0.01, respectively, based on prefecture-clustered standard errors.

The minimum-temperature results are more consistent. At lag nine, a day with minimum temperature at or above 25∘C has a coefficient of −0.003866 (standard error 0.000973, p=0.00025), corresponding to approximately 0.39 percent lower GFR. Its two-way-clustered p-value is 0.00009 and its BH q-value is 0.0069. At lag ten, the coefficient is −0.002456 (standard error 0.000800, p=0.0036); two-way clustering gives p=0.0051. Its q-value is 0.0502, which is close to but not below the 5 percent false-discovery threshold. Thus the lag-nine high-minimum estimate is the strongest individual coefficient on the full displayed path, while the lag-ten estimate is robust to clustering but marginal under multiple-testing adjustment.

Daily mean temperature shows a different allocation across the two lags. The lag-nine coefficient on mean temperature at or above 30∘C is −0.001986 (standard error 0.001439, p=0.174). The lag-ten coefficient is −0.004950 (standard error 0.001522, p=0.0021), or about 0.50 percent lower GFR per additional threshold day. The estimate remains significant under two-way clustering (p=0.0015), but its BH q-value is 0.060. The combination of a rare exposure bin and a broad dynamic search calls for emphasis on the pattern across specifications rather than on a single star.

Table 3 compares maximum and mean temperature in separate and joint models. In the separate distributed-lag models, the cumulative lag-nine-plus-lag-ten coefficient is −0.002784 for maximum temperature (standard error 0.001553, p=0.0796) and −0.006371 for mean temperature (standard error 0.001905, p=0.0016). The corresponding minimum-temperature cumulative coefficient, reported in the Supplement, is −0.005837 (standard error 0.001048, p<0.00001).

Table 3. Maximum and mean temperature in separate and joint specifications.

Separate models contain the complete nonreference bin vector for one temperature metric. Joint models contain complete maximum- and mean-temperature bin vectors simultaneously. Lag-9 and lag-10 rows are single-lag regressions; the cumulative row comes from a regression that enters both lags and uses their covariance to form the standard error. All specifications use the baseline fixed effects, lag-specific precipitation and missing-day controls, and prefecture-clustered standard errors.

*, , and * denote p<0.10, p<0.05, and p<0.01, respectively, based on prefecture-clustered standard errors.

Conley spatial–temporal HAC inference supports the cumulative minimum- and mean-temperature estimates at the 250-km bandwidth (p<0.0001 and p=0.0003, respectively). The separate maximum-temperature cumulative estimate is borderline (p=0.0491), but maximum temperature remains essentially zero when the complete mean-temperature bins enter jointly (p=0.9979), while the conditional mean-temperature estimate remains negative (p=0.0130). The 100- and 500-km results are similar (Supplementary Table S11).

Conditioning the two exposure vectors on each other changes the maximum result sharply. In the joint distributed-lag model, the cumulative maximum coefficient is −0.000004 (standard error 0.001985, p=0.998), while the cumulative mean coefficient is −0.005252 (standard error 0.002553, p=0.045). The data therefore do not support treating a brief maximum-temperature peak as a stable independent exposure once the distribution of daily mean temperature is held constant. By contrast, the mean-temperature association retains a negative conditional signal, albeit with wider uncertainty.

This comparison should not be read as proof that mean temperature has a stronger intrinsic physiological effect. Maximum temperature typically occurs during daytime hours, when outdoor exposure can be high; minimum temperature generally occurs at night, when indoor protection may be greater; and high nighttime temperature can mark an episode with little opportunity for cooling. Mean temperature summarizes the full day more directly. The estimates combine these exposure opportunities with building conditions, activity, adaptation, and biology. The defensible conclusion is about measurement and statistical stability: sustained heat measures carry a more consistent signal in these data than the brief maximum peak.

5.2 Dynamic adjustment

Figure 2 plots the complete path from three future-temperature placebo leads through 24-month lags. The shaded region marks lags nine and ten. Confidence intervals use prefecture-clustered standard errors, and black markers identify estimates with BH q<0.05 within a metric. The negative horizontal values are not pre-exposure fertility effects; they are future-temperature tests included to reveal chance alignment or residual seasonality.

The graph reinforces the difference across metrics. The maximum-temperature path has a negative point at lag nine but no concentration of precise negative estimates across the gestational window. The minimum-temperature path reaches its most negative and most precisely estimated point at lag nine, with a smaller negative estimate at lag ten. The mean-temperature path is negative at lags nine and ten, with the more precise estimate at lag ten. Under the three separate within-metric Benjamini–Hochberg adjustments, only the minimum-temperature lag-nine estimate has q<0.05.

Later positive estimates do not form a stable or complete offset. Some coefficients after the gestational horizon are positive, but none provides a basis for identifying the same households or pregnancies. Conversely, the absence of a cumulative statistically significant rebound through lag 24 does not show that the initial gross difference persists indefinitely. Compensation may occur after the observed horizon, across calendar months with limited power, or through heterogeneous timing shifts that aggregate imperfectly. The estimates identify a short-run reduction or displacement around the gestational horizon, not a permanent decline in completed fertility.

The future-temperature leads are generally centered around zero and none survives the within-metric false-discovery adjustment. This is reassuring but not dispositive. With only eight years and strong seasonal exposure, placebo power is limited, and the high-dimensional fixed effects absorb much of the variation. The full coefficient and inference table is therefore reported in Supplementary Table S1 rather than summarized selectively.

5.3 Descriptive recorded fetal-death check

Recorded fetal-death outcomes are retained only as a descriptive check; complete estimates appear in Supplementary Tables S4a, S4b. The Japanese aggregate begins at 12 completed weeks, combines spontaneous and induced fetal deaths in the available source, and omits earlier losses. It shows no broad pattern corresponding to the fertility estimates. An isolated negative lag-eight coefficient for high minimum temperature cannot be interpreted as protective or as evidence for any mechanism: it may reflect multiple comparisons, selection into the recorded risk set, timing shifts, or sampling variation. The check therefore neither supports nor rules out behavioral or physiological pathways.

6 Supplementary and descriptive analyses

The Supplement reports the full nonlinear response at lags nine and ten, all 84 dynamic coefficients, two-way clustered inference, separate within-metric BH adjustments, robustness specifications, leave-one-prefecture-out results, full fetal-death results under both Japanese aggregate definitions, and detailed birth-count calculations. Several patterns are worth noting here.

First, adding contemporaneous marriages does not account for the main minimum- or mean-temperature estimates. At lag nine, the high-minimum coefficient becomes −0.003992; at lag ten, the high-mean coefficient becomes −0.005549. Omitting precipitation also leaves these patterns similar. The maximum-temperature lag-nine estimate is more sensitive: it changes from −0.002294 to −0.002113 when precipitation is omitted and has p=0.0567. This asymmetry is consistent with the main conclusion that the maximum result is fragile.

Second, the minimum lag-nine and mean lag-ten estimates remain negative when Hokkaido, Tokyo, or Okinawa is excluded. Leave-one-prefecture-out estimates show that no single prefecture generates the sign. Removing prefecture-by-year fixed effects attenuates several coefficients, illustrating the importance of controlling for annual local conditions rather than treating alternative fixed-effects structures as interchangeable. The baseline specification remains preferred because it absorbs the annual population denominator and slow-moving prefecture-year confounding.

Third, replacing log GFR with log live births reproduces every reported temperature coefficient up to numerical precision. This is an algebraic implication of the prefecture-by-year fixed effects, not evidence that the demographic denominator is irrelevant. It confirms that the revised GFR definition changes interpretation and scale reporting without mechanically manufacturing the temperature result.

Finally, I translate the distributed-lag estimates into gross short-run birth differences. The calculation uses the lags-nine-and-ten coefficients estimated jointly, their full covariance matrix, and the exact semilog transformation. The model implies that observed mean-temperature exposure was associated with 5,418 fewer births relative to the reference-bin counterfactual over 2013–2019 (95 percent delta-method interval 2,122 to 8,713). This is an in-sample accounting exercise; exposure for 2012 cannot support both lags for all early outcomes, hence the 2013–2019 window.

An illustrative scenario with one additional day per prefecture-year at mean temperature at or above 30∘C implies 533 fewer births per year (95 percent interval 213 to 854). Five and seven additional days imply 2,665 and 3,728 fewer births, respectively. The scenario is threshold-matched to daily mean temperature; it is not obtained by applying a projection for maximum-temperature days to the mean-temperature coefficient. It is not a 2040 climate forecast, and it does not measure completed fertility. The Supplement reports corresponding calculations for each exposure metric, including the near-zero conditional maximum-temperature result.

6.1 Exploratory GRDP heterogeneity

Detailed GRDP results are confined to the Supplement. The only cumulative daily-mean signal does not meet the 5 percent wild-bootstrap false-discovery threshold and weakens under alternative GRDP timing; comparable cumulative interactions are unsupported for minimum and maximum temperature. The analysis therefore does not establish robust economic moderation or identify household income or adaptation capacity.

7 Discussion and conclusion

The principal result is that exposure measurement changes the substantive conclusion. A specification based only on daily maximum temperature gives a borderline lag-nine estimate that is not robust to two-way clustering, multiple-testing adjustment, the neighboring lag, or joint control for daily mean temperature. High daily minimum and daily mean temperature show more coherent negative associations around lags nine and ten. This pattern is consistent with sustained heat and limited nighttime cooling carrying information that a brief peak does not, but it does not reveal why.

The result also illustrates a broader lesson for environmental demography. Temperature metrics are not interchangeable labels for a single treatment. Maximum temperature emphasizes the peak and potentially daytime activity. Minimum temperature emphasizes the overnight trough and recovery environment. Mean temperature summarizes the day but can hide short extremes. If behavior and buildings mediate exposure, the mapping from ambient conditions to personal heat load varies across people and hours. Comparing coefficients without reconstructing all metrics consistently can conflate data construction with biology.

These measurement findings have limited but concrete implications for climate-resilient reproductive-health planning. Heat-health surveillance should not rely on daytime maxima alone: minimum and mean temperature can flag sustained exposure and limited overnight cooling. The study does not estimate a clinical threshold or the effect of any intervention. It instead motivates evaluating whether heat plans, preconception and antenatal communications, and maternity-service continuity account for sustained and nocturnal heat. Equity-oriented targeting should use directly measured vulnerability—safe indoor cooling, energy cost, housing quality, occupational exposure, and access to reproductive-health services—rather than prefectural GRDP, because the GRDP analysis cannot identify household resources or adaptation capacity (World Health Organization, 2023).

The analysis has several limitations. First, the unit is a prefecture-month. Exact conception dates, gestational age, maternal residence during pregnancy, parity, age-specific fertility, and individual characteristics are unavailable. The mapping from lag nine or ten to conception is approximate, and migration or travel can misclassify exposure. Second, weather stations measure outdoor ambient conditions. Indoor temperature, humidity, air-conditioning use, work environment, sleep conditions, and time outdoors are unobserved. The inverse-distance reconstruction improves spatial comparability but cannot recover personal exposure. The exploratory GRDP analysis does not establish robust economic moderation or identify specific adaptation mechanisms; future work should use direct measures of household income, air-conditioning access, housing quality, occupational exposure, and reproductive-health services.

Third, the sample covers 2012–2019. Eight years provide a balanced national panel but limited independent hot seasons. The highest daily-mean bin contains only 316 prefecture-days. The fixed effects are intentionally demanding, so confidence intervals are often wide. Dynamic analysis adds 28 tests per metric; reporting both nominal and adjusted inference is essential. The rare-tail evidence should be replicated over longer periods and with exposure measures such as wet-bulb temperature or indoor heat when available.

Fourth, the Japanese aggregate fetal-death data begin at 12 completed weeks, may include spontaneous and induced fetal deaths, and do not permit those components to be separated. They therefore neither measure early or clinically unobserved pregnancy loss nor correspond directly to later-threshold international stillbirth definitions. An absence of a broad response in this outcome cannot distinguish conception behavior from physiology. Hajdu and Hajdu (2021, 2023) show why unobserved loss can matter for temperature-fertility relationships, while Hajdu and Hajdu (2019) cautions against presuming that sexual activity is the central behavioral pathway. Linking weather to clinical pregnancy records, gestational age, assisted reproduction, and time-use or contraceptive data would permit a more discriminating test.

Fifth, monthly dynamics do not identify completed fertility. A positive later coefficient could reflect postponed conceptions, but a noisy or absent rebound through month 24 is not evidence that births never occur later. The data cannot follow a household that delays one conception or adjusts the timing of a later birth. Cohort fertility and longitudinal household records are needed to distinguish postponement from a change in eventual family size.

The corrected birth-count translation should be read within these limits. It applies the jointly estimated lag-nine and lag-ten semielasticities to observed or illustrative exposure and uses the covariance between coefficients. The calculation is useful for showing scale, but it is a gross short-run accounting difference. It is not an extrapolation from one hot-day threshold to another and not a prediction of lifetime births under a future climate scenario.

Japan is a valuable setting because climatic conditions vary substantially across a common national statistical system, and demographic aging makes short-run fertility responses salient. Yet the study does not establish that Japan has a uniquely inelastic response relative to the United States or Europe. Cross-country differences in rebound patterns could reflect power, exposure measurement, planned conception, physiology, institutions, or sample period. A credible comparison would require harmonized temperature metrics, outcomes, fixed effects, and observation horizons across countries.

The paper’s narrower conclusion is also its more defensible one. In this panel, high minimum and mean temperatures are associated with lower monthly GFR around the gestational horizon, whereas the independent maximum-temperature association is weak. The comparison suggests that persistent heat and limited overnight cooling deserve attention in future fertility research. It does not identify a particular reproductive mechanism or establish a decline in completed fertility. Progress on those questions requires individual conception and pregnancy histories, gestational timing, early-loss measurement, indoor exposure, and direct measures of adaptation.

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Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fhumd.2026.1899647/full#supplementary-material.

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Footnotes

Edited by: Goran Miladinov, Independent Researcher, North Macedonia

Reviewed by: Bing Chen, Yunnan University, China

Khondoker M. Akram, The University of Sheffield, United Kingdom

Petar Vasic, University of Belgrade, Serbia