Is US Fertility now Below Replacement? Evidence from Period vs. Cohort Trends

In this study, we contrast period and cohort approaches to answering the question: Is US fertility now below replacement? The answer would appear to be an unambiguous “yes” based on period trends in the total fertility rate (TFR). Since 2007, TFR has declined from 2.12, just above the replacement level set by demographic tradition at 2.10 births per woman, to 1.67 in 2022, leading many to speculate that the United States has now entered a sustained period of below-replacement fertility. A quite different picture emerges from cohort trends in the cumulative fertility rate (CFR), a cohort measure that is not subject to biases that can distort period TFRs. For older birth cohorts of US women—those born between 1959 and 1987 and who were thus age 33 or older in 2020—observed or projected CFRs at age 45 vary between 2.00 and 2.24 births per woman. For younger cohorts—those born between 1988 and 2010 and who were 10 to 32 as of 2020—we project CFRs at age 45 that are below 2.00, with these declines attributable to falling fertility at younger ages. We thus conclude that from a cohort perspective, the question “Is US fertility now below replacement” should be replaced by the question “Will lifetime fertility fall below replacement for the youngest cohorts of US women?”, with the answer to this latter question depending on the extent to which decreases observed at early ages in these cohorts will or will not be offset by future increases at later ages.


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In this study, we contrast period and cohort approaches to answering the question: Is US fertility now below replacement?The answer from period trends in the total fertility rate (TFR) would appear to be an unambiguous "yes."Official estimates compiled by the National Center on Health Statistics (NCHS) show that TFR has declined steadily from 2.12 births per woman to a record-low of 1.64 in 2020, increasing very slightly to 1.66 and 1.67 in 2021 and 2022 (Hamilton et al., 2023), with these TFRs well below the replacement level set by demographic tradition at 2.10 births per woman.This decline is also notable in that period TFRs in the United States had remained at or near 2.00 throughout the 1990s and 2000s, in contrast to countries such as Canada, France, and the United Kingdom that saw period TFRs fall below 1.70 during this same period (HFD, 2023).
This rapid decline in period TFRs in the United States has prompted widespread speculation by public commentators and some academics that the United States has now entered a sustained period of below-replacement fertility (see, e.g., Rampell, 2018;Medaris, 2020;Vollset et al., 2020;Murray 2021;Kearney & Levine, 2021;Kearney et al., 2022).And if true, the United States could begin confronting issues faced by countries with low and sometimes very low fertility-more rapid aging of the US population with declines in the working age population relative to older, retired individuals, which would, all else equal, place strains on pay-as-you-go programs such as Social Security and Medicare (De Nardi et al., 1999).At a more micro level, below-replacement fertility would be problematic if lower levels were due to barriers resulting in individuals and couples having fewer children than desired (Morgan & Rackin, 2010).
Although heavily used, demographers have long recognized that period TFRs have serious deficiencies, including the possibility of "tempo distortions" that can substantially bias estimated levels and trends in fertility when birth rates at different ages are trending over time (Bongaarts & Feeney, 1998, 2010).This possibility is particularly relevant in the US context, in which fertility has been declining at early ages but increasing at later ages.
In the analyses reported below, we contrast trends in period TFRs with cohort trends in the cumulative fertility rate (CFR).These two measures provide period and cohort analogs of one another and furthermore measure fertility using the same metric-births per woman.An important advantage of cohort CFRs is that they are, by construction, free of tempo distortions that can bias period TFRs.But a disadvantage of cohort CFRs is that they provide estimates of lifetime fertility only for cohorts that have completed their fertility or that are close to doing so.This issue can be addressed, at least in part, by combining observed cohort CFRs with projections of future fertility (Ryder, 1986;Frejka & Sardon, 2004;Andersson et al., 2009), with our analyses relying on a projection method proposed by Myrskylä et al. (2013).
Our cohort analyses rely on annual data on births from US vital registers; the same data used by NCHS to construct official estimates of TFR.We used these data to obtain cohort CFRs for single-year birth cohorts, yielding CFRs for cohorts of US women born between 1959 and 2010.For older cohorts of US women-those born in 1959-1987 and who were thus 33 or older in 2020, observed or projected CFRs vary between 2.00 and 2.24 births per woman-levels that are at, just below, or just above replacement. 1For younger cohorts-those born between 1988 and 2010 and who were thus 10-32 as of 2020-our answer of how many children they will ultimately bear is "too early to tell."On the one hand, the decreasing trend in fertility at early ages means that younger cohorts have had fewer births in their teens and early 20s than their counterparts in older cohorts, raising the possibility that younger cohorts will have lower lifetime fertility.On the other hand, the increasing trend in fertility at later ages could lead to more births at those ages than was true in older cohorts.A cohort approach thus clarifies that lifetime fertility in these younger cohorts will depend on the extent to which the decreases observed at early ages will or will not be offset by future increases at later ages (Frejka & Calot, 2001).
The contribution of this paper is twofold.A first consists of our empirical estimates of observed and projected cohort CFRs for single-year birth cohorts of US women born during the 52-year period between 1959 and 2010, with our projected cohort CFRs accompanied by estimates of the uncertainty of these projections.A secondary contribution, intended for a wide audience, is to provide a concise summary of various key demographic issues, including how period TFRs and cohort CFRs provide answers to what are different questions and why below-replacement fertility, should it in fact occur, will almost certainly emerge gradually.

Period vs. Cohort Measures of Fertility
To understand how and why answers from period TFRs and cohort CFRs might differ, we begin by reviewing how TFR is constructed.Official NCHS estimates of TFR follow the standard demographic practice by forming age-specific fertility rates (ASFRs) at ages 10-14, 15-19,..., 45-49 in a given calendar year.For example, the ASFR at ages 10-14 in the calendar year 2010 will be given by the ratio of the number of births at ages 10-14 in 2010 to the number of women aged 10-14 in 2010, with this ratio thus giving the mean number of births per woman aged 10-14 in the calendar year 2010.TFR is then calculated by summing the ASFRs for ages 10-14, 15-19,..., 45-49 and multiplying by five to account for the width of the above 5-year age groups.
The metric for TFR is thus the mean number of births per woman in a given calendar year, but the precise interpretation of TFR is not straightforward and thus can be easily misunderstood.To see this, note that TFR for the calendar year 2010 will be constructed from the age-specific fertility rates observed for women who were: (1) aged 10-14 in 2010 and who were thus born in 1996-2000, (2) aged 15-19 and thus born in 1991-1995,..., and (8) aged 45-49 and thus born in 1961-1970.As a consequence, the TFR for calendar year 2010 refers to no 1 Historical estimates show that, as expected, there was a long-term decline in the lifetime fertility of cohorts of US women, with booms and busts during the post-WWII baby boom and the Great Depression.These historical estimates suggest, for example, that births per woman at ages 45-49 declined from 3.70 for those born in 1870-1874 to 2.95 for those born in 1925-1929(Heuser, 1976)), with births per woman at age 49 then increasing to a peak of 3.21 for those born in 1935 and then declining to 1.97 for those born in 1953 (HFD, 2023).
76 Page 4 of 22 real-world group of women, but rather to a hypothetical ("synthetic") cohort of women under a complicated counterfactual involving what lifetime fertility would be were this hypothetical cohort to have the age-specific fertility observed in 2010 consisting of: (1) the fertility at ages 10-14 observed in 2010 for those born in 1996-2000, (2) the fertility at ages 15-19 observed in 2010 for those born in 1991-1995,..., and (8) the fertility at ages 45-49 observed in 2010 for those born in 1961-1965.As a formal demographic matter, period and cohort measures will agree in a stationary fertility regime in which ASFRs are not subject to trends over time (Bongaarts & Feeney, 1998, 2010;Kohler & Ortega, 2002;Schoen, 2004Schoen, , 2022)).Stationarity does not hold in the United States, where fertility has been decreasing at early ages but increasing at later ages (Martin et al., 2017).
We next turn to two stylized examples that provide further insight into why period and cohort approaches differ.We begin by considering a stationary fertility regime in which the age schedule of fertility is given by ASFRs equal to 0.05 at ages 10-49, with this age schedule implying that period TFRs and cohort fertility at age 49 will equal 2.00.Then suppose there is a fertility shock in calendar year t * that causes ASFRs at ages 10-19 to decline from 0.05 to 0.02.
We next consider two scenarios.In a first "pure delay" scenario, the declines in ASFRs at ages 10-19 are offset by increases 15 years later, yielding a new stationary age schedule in calendar year t * + 15 in which ASFRs at ages 25-34 rise from 0.05 to 0.08.Under "pure delay," lifetime fertility for all birth cohorts will be unchanged, remaining at 2.00.By contrast, TFR will drop to 1.70 for 15 years and then will rise abruptly back to 2.00.This "pure delay" scenario is an example of what Bongaarts and Feeney (1998) have termed a "tempo" effect, in which declines in births at earlier ages are offset by births at later ages, with the delay in births thus representing a change in the "tempo" of fertility.
In a second "pure decline" scenario, the above decrease in ASFRs at ages 10-19 is all that happens, implying in turn that period TFRs will decrease abruptly and will remain at 1.70 starting in calendar year t * .Under this scenario, the lifetime fertility of successive birth cohorts of women will likewise decline to 1.70, but this decline will take place gradually.To see this, note that the age 49 CFRs will remain at 2.00 for all cohorts of women who were 20 or older in calendar year t * .For younger cohorts-those 19 or younger in calendar year t * -CFRs at age 49 will undergo a gradual decline, falling to 1.97 for those who were age 19 in calendar year t * , 1.94 at age 49 for those age 18 in calendar year t * ,..., and 1.70 at age 49 for those age 10 in calendar year t * .This "pure decline" scenario is an example of what Bongaarts and Feeney have termed a "quantum" effect, in which declines in births at earlier ages consist of births that are not offset by births at later ages, thus generating a decline in the "quantum" of lifetime fertility.
Although stylized, these two scenarios suggest very different future paths for US fertility given continuing declines at younger ages.Under a "pure decline" scenario, US fertility could indeed fall below replacement, but this decline would occur gradually, in sharp contrast to the abrupt decline seemingly implied by period TFRs.Under a "pure delay" scenario, the lifetime fertility of successive birth cohorts of US women could remain unchanged if the lower ASFRs currently observed at early ages for younger cohorts were to be offset by corresponding future increases at later ages.
How realistic are these two scenarios?A standard demographic argument holds that a birth that is prevented from occurring at an early age can be expected to be replaced by k births in the future, with k ∈ [0, 1] ."Pure decline" thus corresponds to k = 0 and "pure delay" to k = 1 , but one might more realisti- cally expect k to lie between these two extremes.
We now turn to an example constructed from actual ASFRs for the United States.Table 1 reproduces published NCHS estimates of TFR and ASFRs for the calendar years 1970, 1975, … , 2019(Martin et al. 2017;;Hamilton et al., 2022).The non-stationary nature of US fertility is clear from Table 1, with fertility decreasing at younger ages but increasing at older ages.
Table 2 rearranges the NCHS estimates in Table 1 to obtain cohort CFRs.We used ASFRs at ages 10-14 in 1970, 15-19 in 1975, … , and the 45-49 in 2005 to obtain cohort CFRs for women born in 1956-1960.We then repeated this procedure to obtain cohort CFRs for women born in 1961-1965, … , 1996-2000.The resulting cohort CFRs, obtained from the same ASFRs used by NCHS to construct period TFRs, thus provide a picture of cohort trends in the mean number of births observed over time for successive birth cohorts of US women.
The period TFRs and cohort CFRs in Tables 1 and 2 provide quite different accounts of trends in US fertility, with the abrupt swings in period TFRs contrasting sharply with the far more gradual changes portrayed by the cohort CFRs.These differences reflect the fact that period TFRs and cohort CFRs answer different questions, with period TFRs answering what fertility would be for a series of hypothetical cohorts and cohort CFRs answering what fertility has been for actual birth cohorts.

Data and Methods
Our analyses of cohort CFRs exploit annual data on births from the US vital registration system, the same data used by NCHS to construct TFR.We used these data to identify single-year birth cohorts of US women born in 1959-2010, with these cohorts thus spanning a 52-year period.We used data on the age of the mother (to the nearest year) to infer her year of birth, from which we obtained the number of births to women in cohort c who were age a in calendar year t.Our analyses also require data on the number of women who were age a in calendar year t, which we obtained from the National Cancer Institute's program on Surveillance, Epidemiology, and End Results (SEER).We used public-use versions of both data sources.We constructed CFRs for single-year birth cohorts as follows.For calendar year t, we estimated single-year age-specific fertility rates (ASFRs) by taking the ratio of the number births to women aged 10, 11, … , 49 in calendar year t to the number of women in each single-year age group in calendar year t.This step yielded a rectangular matrix of ASFRs at ages 10, 11, … , 49 for the calendar years 1969-2020.We then rearranged the single-year ASFRs in the above rectangular matrix using the fact that those born in 1959 were 10 in 1969, 11 in 1970, … , and 49 in 2008.The resulting triangular matrix, consisting of the Lexis diagonals of the above rectangular matrix, thus provides estimated ASFRs at ages 10, 11, … , 49 for US women born in the calendar years 1959, 1960, … , 2010.We then estimated cumulative fertility rates (CFRs) for women in birth cohort c by summing the ASFRs for cohort c from age 10 to age a.The resulting CFRs thus give the mean number of births observed for US women in cohort c when they were age a.This yields estimated CFRs at single ages for single-year birth cohorts and, following NCHS, we regard fertility as completed at age 49.1956-1960, 1961-1965, … , 2006-2010. Source Table 4, Martin et al. (2017); Hamilton et al. (2022) Because CFRs give the mean number of births that have occurred by age a in cohort c, they provide stylized facts that social scientists and policy makers can regard with a very high degree of confidence when, as is the case here, the quality of data is high.For cohorts too young to have completed their fertility, we used a projection method proposed by Myrskylä et al. (2013).A comprehensive survey of over 150 projection methods, conducted by Bohk-Ewald et al. (2018), found that this simple method outperformed others, including complex Bayesian methods.
Figure 1 provides an illustrative example of the Myrskylä et al. method for projecting future values of ASFRs at age 20.In Fig. 1, five observed ASFRs at age 20 are plotted for US women born in 1996-2000, the five most recent birth cohorts to have attained age 20 by 2020, the last year for which we have data.The method then projects future values of the next five age 20 ASFRs for the 2001-2005 birth cohorts using the projected values from an ordinary least squares regression, after which ASFRs at age 20 are "frozen" for cohorts born in 2006 or later.The procedure is then repeated for other ages, yielding a series of projected ASFRs in which recent trends in observed ASFRs are used to obtain projections for the next 5 years, after which ASFRs are frozen, yielding a stationary fertility regime for all subsequent calendar years.For each cohort of women in our data, we then summed the observed and projected ASFRs to obtain observed and projected CFRs.In results reported below, we have also accompanied estimates of projected CFRs with 95% prediction intervals for the uncertainty in estimated projections.See Appendix 1 for additional details.

Results
Figure 2 reproduces official estimates of period trends in TFR for 1970-2022(Martin et al. 2017;;Hamilton et al., 2023).TFR was 2.48 in 1970, then declined very rapidly to 1.74 in 1976, for an apparent decrease of 0.74 births per woman over this short 7-year period. 2 TFR then increased to 2.08 in 1990, fell slightly to 1.97 in 1997, then rose again, reaching a peak of 2.12 in 2007 after which it declined steadily, falling below 2.00 in 2010 and reaching a record-low of 1.64 in 2020 before rising slightly to 1.66 in 2021 and 1.67 in 2022.TFR was 2.10 or higher in only 4 years -in 1970, 1971, 2006, and 2007. 3 Table 3  These decreases in cohort CFRs at early ages contrast with increases at later ages.CFRs at age 39 rose from 1.96 for the 1959 birth cohort to a peak of 2.18 for the 1976 birth cohort, while CFRs at 49 rose from 2.00 for the 1959 birth cohort to 2.14 for the 1971 birth cohort, for increases of 0.22 and 0.14 at ages 39 and 49, respectively.

Birth cohort
Table 4 presents cohort trends in births per woman between ages 10 and 14, 15 and 19,..., 45 and 49, showing, as expected, decreases in births at early ages and increases at later ages.Births continue to be infrequent at the very youngest and very oldest ages, with births between ages 10 and 14 or 45 and 49 accounting for at most 0.01 births per woman across all birth cohorts.By contrast, births between ages 15 and 19 increased from 0.26 births per woman for the 1959 cohort to a peak of 0.30 for the 1973 and 1974 cohorts.They then declined to 0.08 for the 2001 cohort, the most recent cohort to reach age 19 in 2020, the last year for which we have data.Births between ages 20 and 24 fluctuated between 0.51 and 0.57 for those born between 1959 and 1985 but then declined, reaching 0.34 for the 1996 cohort.Births between ages 25 and 29 fluctuated between 0.53 and 0.59 for those born between 1959 and 1984, but then also began declining, reaching 0.47 for the 1991 cohort.
These declining trends at earlier ages contrast with increasing trends at later ages.Births between ages 30 and 34 increased modestly from 0.40 to 0.46 between the 1959 and 1970 cohorts, then fluctuated between 0.48 and 0.51 for those born in 1971 or later.Similarly, births between ages 35 and 39 rose from 0.17 to 0.26 between the 1959 and 1981 cohorts and births between 40 and 44 rose from 0.04 to 0.06 between the 1959 and 1976 cohorts.
Table 5 presents observed and projected CFRs at age 45, which, as was seen in Table 4, is the age at which fertility is largely completed.Table 5 also reports 95% prediction intervals for projected CFRs in two ways-with and without a Bonferroni correction. 5or the 1959-1975 cohorts, age 45 CFRs are observed as of 2020 and vary in a narrow range from 2.00 to 2.22 births per woman-just below, at, or just above the replacement level of 2.10.For the 1976-1988 cohorts, the age 45 CFRs require projecting up to 13 years into the future, with the age 45 CFRs declining from 2.24 to 2.00.For cohorts born in 1989 or later, age 45 CFRs begin declining more rapidly, from 1.96 to 1.43, but the 95% prediction intervals also become wider.Thus, on the one hand, the projected CFRs at age 45 decline substantially, from 2.24 births per woman for the 1975 cohort ( Δ = 1, age 44 in 2020) to 1.43 births per woman for the 2010 cohort ( Δ =35, age 10 in 2020).On the other hand, the increasing uncertainty of projected CFRs means that we cannot reject the null hypothesis that projected age 45 CFRs will remain at roughly 1.70 based on the Bonferroni-adjusted 95% prediction intervals.
As a general rule, one might expect projections to be reasonably accurate when projecting somewhat into the future but increasingly less so when projecting very far into future.And as shown in Fig. 1, the method used to obtain the projections in Table 5 assumes that fertility trends will cease 5 years into the future.This, combined with the fact that 2020 is the most recent year for which we have data, means that the projections in Table 5 assume that US fertility will transition to a stationary fertility regime beginning in the calendar year 2025.Freezing rates after 5 years can be seen as sensible by preventing projected ASFRs from increasing or decreasing indefinitely, as would be the case if one were using linear extrapolation to project future ASFRs.Nevertheless, stationarity is likely to be an increasingly strong assumption when projecting very far into the future, as is the case for the very youngest cohorts in Table 5.
Table 6 provides suggestive evidence on the plausibility of stationarity by examining change in the age structure of US fertility.In Table 6, we have reported selected values of observed ASFRs at ages 15-49 using the minimum and maximum ASFRs, and the ASFRs for the calendar years 2010, 2015, and 2020.Then to provide a rough sense of the magnitude and pace of change in observed ASFRs, the last three columns report three age-specific ratios: the ratio of the maximum and minimum ASFR ("max/min"), the ratio for the most recent 5 years ("2020/2015"), and the ratio for the most recent 10 years ("2020/2010").
Some striking aspects of change in the age structure of US fertility are evident in the second and third columns of Table 6, which report the minimum and maximum values of observed ASFR by age.For ages 15-29, the ASFR minima all occurred in the calendar year 2020, the last year for which we have data, while for ages 30-49, the ASFR minima occurred for the cohorts of US women born in 1959, 1960, or 1961, the three earliest cohorts in our data.By contrast, the ASFR maxima at ages 15-29 occurred during the calendar years 1990 and 1991, the maxima at ages 29-31 occurred in 2007, and the maxima at ages 32-49 occurred in the years 2016-2019.Thus, the ASFR minima and maxima occurred in particular periods and cohorts, with early and later age minima occurred in very recent years or in the oldest cohorts, while ASFR maxima occurred in the early 1990s (ages 15-29), mid-2000s (ages 29-31), and late 2010s (ages 32-49).
A rough sense of how much ASFRs have changed can be seen in the ratio of ASFR maxima and minima.At ages 15-29, the ASFR maxima occurred in earlier calendar years than the ASFR minima, thus implying a decreasing trend in ASFRs during these ages.At age 15, the largest observed ASFR was more than 7 times greater than the smallest observed ASFR at this age, with the max/min ratio declining monotonically between ages 15 and 29 (italicized max/min ratios).At ages 30-49, the ASFR maxima occurred in later calendar years than the ASFR As expected, trends in the max/min ratio reveal fertility declines at early ages and increases at later ages, but also illustrate vividly the very sizable magnitude of change in the age structure of US fertility.
Italicized and non-italicized values in column 7 ("max/min") refer to decreasing and increasing trends in age-specific fertility rates, respectively It is also important to emphasize a more subtle but equally critical point, which is that the projection method that we have used assumes that the large declines in ASFRs observed at early in younger cohorts will be offset only by the far more modest increases in ASFRs at later ages based on the short-term trends as observed for older cohorts at these ages.That is, because the Myrskylä et al. projection method freezes rates after 5 years, it is in effect imposing a quantum effect for these cohorts, hence ruling out the possibility of a tempo effect in which the lower fertility at early ages observed in younger cohorts is offset by higher fertility at later ages.
What might be the broader implications if the lifetime fertility of younger cohorts of US women were in fact to fall below replacement?Any answer to this question will be inherently speculative, but one can nevertheless give some answers under a "what if" scenario in which fertility is assumed to remain at a particular sub-replacement level for a long time in a closed population in which there is no in-or outmigration.Table 7 shows how long it would take for a closed population to decrease in size by a factor of two under a stationary sub-replacement fertility regime.Halving times vary in a highly non-linear way with the level of sub-replacement fertility, with a decrease from 2.10 to 2.00 implying a halving time of over 900 years, while 1.8, 1.6 and 1.4 imply halving times of 161, 84, and 54 years, respectively.
The halving times in Table 7 refer to the consequences for a stationary fertility regime in which fertility is assumed to remain at some permanent sub-replacement level.But in actual populations, reaching stationarity is itself a population process paralleling what was seen in the stylized"pure decline" scenario in which the transition of a population from one stationary regime to another takes place only gradually.A cohort perspective thus makes clear that the consequences for phenomena such as population aging will emerge only gradually even were the fertility declines at early ages observed for the youngest cohorts of US women not to be offset by future increases later ages.6

Discussion
US fertility continues to evolve in ways both similar to, and different from, fertility in Europe and Asia.Teen births have declined substantially, yet the overall level of teen fertility in the United States remains markedly higher than in much of Europe and Asia.Births to cohabiting couples now comprise a substantial fraction of all US births, but cohabiting unions in the United States continue to be fragile relative to their Nordic counterparts (Kiernan, 2004).The once robust negative gradient between fertility and education found in the US and in many other rich countries-that women with college degrees had fewer births, on average, than those with less education-may no longer hold (Doepke et al., 2022).Fertility preferences appear to have been little affected by the recent large and plausibly exogenous shocks posed by the Great Recession of 2009-2010 and the ongoing COVID-19 pandemic (Hartnett & Gemmill, 2020;Behrman, 2023).And the United States has been an exception to the low and sometimes very low fertility in much of Europe and Asia, at least in recent decades (HFD, 2023).The emergence of low and sometimes very low fertility has given rise to debates over the degree to which low fertility might be of concern.On the one hand, the population contexts of most nations and regions is such that low fertility and population aging have occurred in tandem, reflecting how the age structure of populations respond to ongoing changes in fertility and mortality.This link between low fertility and population aging will then affect dependency ratios, with consequences for the sustainability of programs such as Social Security and Medicare, but changes in the age structure of populations may also carry consequences for younger population members (Preston, 1984).For individuals, the transition to a low fertility regime may signal a mismatch between fertility preferences and achieved fertility, but may also result in parental investments allocated to fewer offspring (Lee, forthcoming).But these issues, clearly relevant in contexts in which fertility is low, are arguably less pressing in contexts in which fertility remains near or at replacement levels.
In this study, we have contrasted period and cohort approaches to answering the question, Is US fertility now below replacement?The picture of US fertility painted by period TFRs is one in which fertility has declined rapidly to levels well below replacement.But this apparently simple picture is complicated by the fact that what this period portrait depicts is the fertility of a hypothetical ("synthetic") cohort of women were they exposed to the age-specific fertility rates observed in a given calendar year.By contrast, the picture provided by a cohort approach is one that refers to actual, as opposed to hypothetical, cohorts of women.But a difficulty is that this cohort picture will be incomplete for the youngest cohorts of US women given that they will continue to have births over the next 20 or 30 years.Although period TFRs and cohort CFRs will agree in a stationary fertility regime, US fertility has continued to evolve, with the resulting non-stationary nature of US fertility providing a near-textbook example of how period TFRs and cohort CFRs differ when fertility is declining at early ages but increasing at later ages.Put another way, period TFRs and cohort CFRs in fact answer different questions-a point understood by demographers but sometimes less so by others.
A cohort approach also makes clear that declines observed in period TFRs correspond to the substantial and ongoing decline in fertility at early ages that, as of 2020, has depressed the fertility for younger but not older cohorts of US women.These analyses further show that the lifetime fertility is (or can be projected to be) at or near replacement levels for the oldest cohorts of US women in our data-the 30 cohorts born between 1959 and 1988 who were 32 or older in 2020.For the 76 Page 18 of 22 remaining 22 birth cohorts in our data-those born in 1989 or later and who were 10-31 in 2020-projections fall below replacement.But the projections for these younger cohorts rest on implicit assumptions that we regard as increasingly problematic when projecting further and further into the future, as is needed when estimating the lifetime fertility of the very youngest cohorts of US women.
The cohort approach we have taken thus leads us to conclude that the answer for the youngest cohorts of US women is that it is simply too early to tell.These cohorts-those in their teens and early 20s-have only begun their childbearing, but what their future fertility will be can be monitored by following them over time, with data in the future providing a clearer picture as these cohorts pass into later childbearing ages.Similar clues for these cohorts can be obtained by monitoring their future fertility intentions and desires, which to date continue to follow a twochild norm and thus closely resemble those in older cohorts (Morgan & Rackin, 2010;Hartnett & Gemmill, 2020;Behrman, 2023).Data over the next decade can thus be used to provide a more concrete sense regarding the degree to which the lower fertility at early ages currently observed in these cohorts will or will not be offset by fertility increases at later ages.
A final insight from a cohort perspective addresses the concerns of those who see trends in the period TFR as evidence that US fertility has now fallen below replacement.A cohort approach together with our cohort estimates clarifies that were below-replacement fertility in fact to emerge, it will be driven by the youngest cohorts of US women if their future fertility at older ages does not offset the current low levels fertility observed when these cohorts were in their teens and 20s.But because these lower levels pertain to younger but not older cohorts, any potential transition of US fertility to a below-replacement regime will almost certainly occur gradually, not suddenly, with gradual change typical of the evolving nature of many demographic processes.
We now turn to standard errors for the projected ASFRs.A convention in the time-series literature is to use the term "confidence interval" for the error bars for observed y's in an OLS regression and "prediction interval" for the error bars for future y's obtained from projections off support.The standard errors for predicted y's will likewise differ from the more conventional standard errors for observed y's by including a term reflecting the uncertainty of the estimated OLS slope, with standard software packages allowing estimation of prediction standard errors.Then for the prediction intervals in the Table 5, let se(c + k, a) denote the prediction stand- ard error corresponding to the projected age-specific fertility rate ASFR(c + k, a) when projections k = 1, … , K years into the future.Because the MGC projection method freezes ASFRs after 5 years, the k = 6, … , K years, the resulting seriesof constrained ASFRs for can then be viewed as equivalent to the time-series problem in which a single constant value is used to predict all future values.These future standard errors then can be shown to increase linearly and hence that The above expression gives the standard errors for projected ASFRs but not for the age 45 CFR reported in Table 5. Recall that in Table 5, the age 45 CFRs are observed for the 1959-1975 cohorts but require projecting for the 1976-2010 cohorts.For the latter, let a * denote the age of cohort c in 2020, the last calendar year for which we have data; then We then invoke the strong assumption that the projected ASFRs for cohort c are independent.Then from probability theory, the variance of the sum of independent random variables X i is given by Then assuming independence These prediction intervals are derived from standard statistical theory, but their real-world performance will depend heavily on the degree to which various assumptions do or do not hold.These include not only the independence assumption noted above, but the strong and largely untestable assumptions implicit in the MGC projection method regarding future forecasts including: (1) local linearity, that future cohort ASFRs can be forecast in a locally linear way using past ASFRs for adjacent cohorts, and (2) stationarity, that the age structure of US fertility will stop evolving after 5 years, thus becoming stationary as of 2025.

Appendix 2
In Table 8, we compare official NCHS estimates of TFR with TFRs calculated from our estimates of the age-specific fertility rates at single ages.The two sets of TFRs are in close agreement.

Table 2
Cumulative fertility by age and birth cohort.US women born in presents CFRs for single-year birth cohorts, with rows giving CFRs for the 1959-2005 birth cohorts and columns giving CFRs at ages 15, 17, … , 49.4Color gradations indicate changes in the fertility of successive birth cohorts, with darker blues and reds indicating larger decreases and increases, respectively, relative to the CFRs observed for the 1959 birth cohort.CFRs at age 19 rose from 0.27 births per woman for those born in 1959 to a peak of 0.31 for those born in 1974, then fell steadily to a low of 0.08 for those born in 2001, the most recent cohort to reach the age of 19 in 2020.Thus by the end of the teen years, fertility declined from peak to trough by 0.23 or by 0.19 births when comparing those born in 1959 and 2001.CFRs at age 29 rose from 1.39 for those born in 1959 to a peak of 1.44 for those born in 1976, then fell to 1.07 for those born in 1991, thus declining from peak to trough by 0.37 or by 0.32 when comparing those born in 1959 and 1991.
2The decline in TFR between 1970 and 1976 was part of a longer-term fertility decline from the high levels of baby boom fertility in the 1950s.3SeeAppendix 2 for a comparison of NCHS estimates of TFR with TFRs calculated from our estimates of the age-specific fertility rates at single ages.The official and replicated TFRs are in close agreement.4CohortCFRs at ages 10-49 for the 1959-2010 cohorts are available upon request.

Table 3
Cumulative fertility by birth cohort and age.US women born in 1959-2005

Table 5
Observed and projected cohort CFRs at age 45 by birth cohort.US women born in 1959 to 2010 CFRs at age 45 are observed if Δ = 0 and projected otherwise with Δ giving the number of years needed to obtain projected CFRs at age 45.Numbers in parentheses provide 95% prediction intervals that give the uncertainty of projected CFRs under the assumption that the statistical model used to obtain future projections is correct.Intervals without a Bonferroni correction give the statistical uncertainty of the projected CFR for a single cohort, while intervals with a Bonferroni correction give the statistical uncertainty for a null hypothesis about all cohorts for which age 45 CFRs are projected

Table 6
Change in selected age-specific fertility rates, ages15-49.US women born in 195915-49.US women born in  -2010

Table 7
Years until a closed population declines by a factor of two under a stationary fertility regime with sub-replacement fertility.Source Calculations using an expression ofKohler and Ortega (2002)

Table 8
Total fertility rate:Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material.If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.To view a copy of this licence, visit http:// creat iveco mmons.org/ licen ses/ by/4.0/.