An Alternative Perspective on the Changing Relationships between Fertility and Replacement Level in European Countries

This paper brings a new perspective to the population growth implications of the low fertility levels of European countries. For years between 2009 and 2018, whether constant fertility, mortality, and net migration would generate long-run population growth or population decrease is indicated simply and visually by comparison of the total fertility rate (TFR) to a migration-adjusted replacement level. The results show that, when considered in combination with concurrent net migration and mortality, the population growth implication of low fertility varies between countries and over time. For Sweden, Luxembourg, Belgium, and the United Kingdom for all the years considered the fertility–mortality–migration combination is coherent with long-run population growth. For the former two countries, long-run population growth would be sustained by net migration at current levels even if fertility were to fall to very low levels. In contrast, for every Eastern European country and year considered, unchanged fertility–mortality–migration combination would lead to population decrease. The need for an alternative view of low fertility in terms of whether the TFR is above or below a migration-adjusted replacement level and the need for a migration context-specific view, as distinct from a universal best view, of the desirability of fertility level are discussed.


Introduction
When describing fertility levels, it is routine for demographers to compare fertility levels to a "replacement level," which has a zero-population growth implication for a closed population under specified conditions (Dublin and Lokta 1925).In 2018 in every country in Europe, the total fertility rate (TFR) was below the replacement level 1 that in the absence of migration would prevent long-run population decline (Espenshade, Carlos Guzman, and Westoff 2004;Gietel-Basten and Scherbov 2020).The TFR was below 1.5 births per woman in two-fifths of Europe's countries (Eurostat 2021).McDonald (2006) and Demeny (2016) both cast the levels of migration which would be needed to offset the effects of such a fertility level on generational size as "massive" and argued a need to raise fertility levels to near replacement level.Between 2009 and 2018, the TFR fell in two-thirds of European countries and increased in the remaining, mostly Eastern European, countries (Matysiak, Sobotka, and Vignoli 2021;Sobotka 2017).According to Frejka and Sobotka (2008), Europe's fertility levels and trends are of "grave concern" and the "consensus" among scholars is that maintaining a fertility rate of 1.7-1.8would make population aging and eventual decline easier to manage.The associated possibility of population decrease is also regarded with concern, even alarm, by some commentators (Coleman and Rowthorn 2011;van Dalen and Henkens 2011;Demeny 2016).In 2019, just under half of the reports by European countries to the United Nations expressed "countering long-run population decline" as a population policy concern (UNPD 2019a).
A sustained low birth rate alone does not guarantee a decrease.In theory, sustained high net migration may drive long-run population growth even when fertility remains below the ("2.1") replacement level (Pollard 1973;Espenshade, Bouvier, and Brian Arthur 1982;Parr 2021Parr , 2023a)).Over the 2009-2018 period, this paper considers net migration was positive for roughly two-thirds of European countries (Eurostat 2021).This paper aims to assess the implications of the constant fertility, migration, and mortality for long-run population growth in European countries, and, in the light of the results, to offer alternative migration-context-specific perspectives on the population growth implications of their low fertility levels.

Migration, mortality, and population growth in Europe
A geographical divide in the pattern of net migration is apparent within Europe.Over 2009-2018 for all the countries of Northern, Western, andCentral Europe (except Ireland over 2009-2013), net migration was generally positive while for most Eastern European 2 countries (Czechia, Slovakia, Hungary, Belarus, and Russia are exceptions) net migration was generally negative (UNPD 2019b; Eurostat 2021).These patterns were influenced by the substantial flows of migration from Eastern Europe to Northern and Western Europe which followed the 2004 and 2007 enlargements of the European Union.There were also substantial net inflows of immigrants from outside Europe, mostly to wealthier countries in Northern, Western, and Central Europe (Van Mol and De Valk 2016;Trenz and Triandafyllidou 2016).
For some European countries, the level of net migration has been volatile.Following the 2007-2009 "Great Recession," immigration fell

Extension of the concept of replacement to incorporate migration
Extensions of the concept of cohort replacement fertility to consider agespecific rates of net migration or age-specific rates of emigration have been proposed by Hyrenius (1951), Ryder (1997), Preston and Wang (2007), and Espenshade (1982).However, none of these formulations represents the implication of immigration or net migration numbers which are unrelated to the number in the size of the corresponding age-sex group.Alho (2008) considers cohort replacement with net migration amounts by age formulated as a proportion of births.However, neither empirical evidence nor a theoretical justification for the proportionate relationship between net migration amount and the number of births is provided.
The concept of replacement has also been extended to migration, using a variety of methods.Espenshade, Bouvier, and Brian Arthur (1982) illustrate a (total) population replacement level (volume) for migration which, in combination with constant fertility and mortality rates, would generate a stationary population equal in size to the then current U.S. population.Parr (2023a) illustrates the variation in values of this measure for an extensive range of European countries over 2009-2018.For differing ranges of countries and time periods, UNPD (2000), Bijak, Kupiszewska, and Kupiszewski (2008), Bijak et al. (2013), andCraveiro et al. (2019) summarized trajectories for what they called "replacement migration," which could maintain constant population size over specified finite time periods.Alho (2008), Billari andDalla-Zuanna (2011), andWilson et al. (2013) analyze the replacement of birth cohort size to female reproductive ages by net migration.Recently, Parr (2021) proposed a new way of representing population replacement, involving a level of "replacement" fertility which in combination with constant net migration amount (as distinct from age-specific rate) and age-sex specific mortality rates would generate a stationary population equal in size to the current population size.The "same as current total population" replacement scenario which underpins the calculation of Parr's (2021) migration-adjusted replacement TFR parallels the approach to replacement migration of Espenshade, Bouvier, and Brian Arthur (1982) and may accord more closely with public perception of zero population growth than the zero growth of the female reproductive age population plus momentum-driven change to population at older ages which would occur under a birth cohort size replacement scenario (Alho 2008;Billari and Dalla Zuanna 2011;Wilson et al. 2013).Parr's (2021) results show wide variation in his migration-adjusted replacement level between countries for a single five-year wide time period (2011)(2012)(2013)(2014)(2015).However, the volatility over time of this measure and the related implication of constant fertility-mortality and net migration for long-run population growth is unclear.This paper assesses the stability or volatility and the trends over time in the long-run population growth implication of constant fertility-mortality-migration for a selection of European countries with positive net migration by comparing the TFR to Parr's (2021) replacement level and discusses the implications of the results for the discourse on the low fertility levels in European countries.

Method and data
The size of the stationary population (P) that is generated by constant below-replacement fertility 5 in combination with constant absolute amounts of net immigration by age and sex, age-sex specific mortality rates, and sex ratio at birth can be expressed as the sum of components corresponding to generations of migrants (Espenshade, Bouvier, and Brian Arthur 1982;Schmertmann 1992): where P denotes the total size of the stationary population, i is the migrant generation index, and P i is the size of the ith migrant generation.The size of the "first-generation" component in Equation ( 1) (P 1 ) is calculated by: where M denotes the annual total net migration, m x, j denotes the proportion of total net migration contributed by persons of age x (last birthday) and sex j (1 for female and 2 for male), e x, j is the (remaining) life expectancy for x and j, and ω is the maximum age of people in the population.
The "second generation" component (P 2 ) is calculated by where TFR denotes the total fertility rate, f x + t is the proportionate contribution to the TFR from the age-specific fertility for age x+ t, t p x,1 is the probability of a female surviving from x to x+ t, k the upper limit of the female reproductive age range, s j is the proportion of births of sex j, and e 0, j is life expectancy at birth for sex j.For all i ≥2, where NRR denotes the conventional (zero migration) net reproduction rate.Thus for NRR < 1, .
(5)  Parr (2021) shows a migration-adjusted replacement level for the TFR (which he termed "current migration replacement TFR") (abbreviated here as MAR_TFR), which in combination with the values of M, m x, j , e x, j, s j , f x+t , and t p x,1 for a specified population and time period generates a total stationary population size (P) of equal size to the size of the total population size (POP) can be calculated by 6,7   MAR_T Since MAR_TFR is the product of the (conventional) exact replacement level for A (i.e., T FR/NRR) and a "migration adjustment" index, derived from the sizes of the first generation (P 1 ) and second generation (P 2 ) components of the stationary population and the NRR, it is referred to in this paper as the "migration-adjusted replacement level" (hence the abbreviation MAR_TFR).When net migration is zero formula (6) replicates the value of the TFR that corresponds to an NRR of 1.0.It should be noted that, while MAR_TFR equates the total size of the stationary population to the current population size, the age-sex structure and annual births of the stationary population will generally differ from the current ("real") agesex structure and annual births. 8MAR_TFR is a period measure, and its value will fluctuate from year-to-year especially due to the year-to-year fluctuation in the scale (M) and age-sex distribution (m x, j ,) of net migration, and, less importantly, due to changes in age-sex specific mortality rates, the current population (POP), the proportionate distribution of the TFR by woman's age (f x ) 9 and the proportions of births that are male and female (s j ).
For some populations and years, it is not feasible to find a value of migration-adjusted replacement level (MAR_TFR) that can solve the stationary population size (P) equals the "real" population (POP) equation.It is not valid to calculate MAR_TFR for migration patterns which generate negative numbers of females of reproductive age in the "first-generation" component of the stationary population (P 1 ) (and hence negative numbers of births to the "first generation"). 10Furthermore, for some populations with very high net migration rates, specifically those for which the size of the current population (POP) is less than the size of the "first-generation" component of the stationary population (P 1 ), there is no feasible value for MAR_TFR. 11 The analysis in this paper is for individual years between 2009 and 2018.Wherever possible the data were sourced from the Eurostat website (Eurostat 2021). 12For some countries missing values of immigration or emigration by age and sex were imputed by applying observed average proportions for other years to the published totals on Eurostat (2021). 13For a few countries for which data on the distribution by age was unavailable for any of the years considered from Eurostat (2021), immigration and emigration by age and sex were imputed by applying international averages of these proportions to the country's published totals. 14 For Luxembourg for 2011-2018, Malta for 2014-2018, and Cyprus for 2009-2011 current population (POP) is less than the size of the "firstgeneration" component of the stationary population (P 1 ), and calculation of a migration-adjusted replacement level (MAR_TFR) is infeasible.In other words, in these countries, with constant migration and mortality the population would grow in the long term even if the TFR fell to and remained at zero.Clearly, the implication of constant fertility-mortality-net migration at the observed levels for these countries and years is long-run population growth.For a range of Eastern European countries for most or, in some cases, all the years considered and for Ireland, Greece, Portugal, Spain, and Cyprus for some years it was also infeasible to calculate MAR_TFR because of negative values for net migration. 15Clearly, when net migration is negative and the net reproduction rate is below one, under constant fertility-mortality-net migration the population will eventually decrease to zero.
In Figures 1-5 if the TFR (shown by the solid blue line) for a particular country and year is above the corresponding migration-adjusted replacement level (shown by the orange dashed line or marker 16 ), constant fertility, mortality, and net migration at the levels for that year will generate long-run population increase (and if below constant fertility, mortality, and net migration will generate long-run population decrease).Table 1 presents average values of the TFRs and migration-adjusted replacement TFR, and the average over 2009-2018 and 2018 ratios of stationary population (P) to actual population (POP).

Comparison of fertility to migration-adjusted replacement level
The results for the various countries considered are grouped along regional lines, in view of the marked regional contrasts in fertility and net migration (Salt and Almeida 2006;Frejka and Sobotka 2008;Rindfuss et al. 2016).Of the various countries for which its value could be calculated for all the years considered, the average migration-adjusted replacement TFR was highest for Hungary, France, and Slovakia and lowest for Sweden, Norway, and Switzerland (Table 1).The European countries with relatively high values for the TFR also tend to have relatively low values for the migration-adjusted replacement level.In other words, countries with higher fertility also tend to have combinations of net migration and mortality which are more conducive to long-run population growth, while those with lower fertility tend to have combinations of net migration and mortality which are more conducive to long-run population decrease.

Northern Europe
In 2009, the TFR was relatively high (by European standards) and above the migration-adjusted replacement level in all four Northern European countries considered (Denmark, Finland, Norway, and Sweden) (Figure 1).The gap between the TFR and migration-adjusted replacement level was considerably greater for Sweden and Norway than for Denmark and Finland.Over 2009-2018, the TFR decreased in all four countries but to very differing degrees.The population growth implications of constant national fertility, mortality, and net migration diverged (Hellstrand, Nisen, and Myrskyla 2021).In 2018, only Sweden had above migration-adjusted replacement fertility.
For Sweden, the TFR exceeded migration-adjusted replacement level by a considerable margin throughout the period considered (Figure 1a and    Table 1).Despite a small decrease in the TFR between 2010 and 2018, the gap between the TFR and migration-adjusted replacement level generally increased, due to reductions in the latter caused by increased net migration and, less importantly, increased life expectancies, and ages at birth. 17,18 For most of the period considered, Sweden's migration-adjusted replacement level is in the "very low" fertility range (below 1.5) (Billari and Kohler 2004).The gap between fertility and migration-adjusted replacement has a substantial implication for long-run population growth.For example, if sustained over the long run, the fertility-mortality-net migration combination for 2018 would propel Sweden's population ultimately towards a stationary population size (P), which is triple its 2018 size (POP) (Table 1).Similar to Sweden, between 2008 and 2011 the TFR for Norway exceeded migration-adjusted replacement level by a wide margin (Figure 1b).However, after 2011 the gap between TFR and migration-adjusted    replacement narrowed considerably due to a combination of both a large reduction in the TFR and a large reduction in net migration (and, due to the latter, a large increase in migration-adjusted replacement level) (Hagelund 2020).In 2018, Norway's TFR was marginally below migration-adjusted replacement.
Primarily due to its more restrictive policies on immigration, the average migration-adjusted replacement level for Denmark is significantly higher than those for Sweden and Norway (Figure 1c and Table 1; Hagelund 2020).Even though the TFR for Denmark in 2009 was only slightly lower than those for Norway and Sweden, it was nonetheless only marginally above migration-adjusted replacement level.Figure 1c shows the considerable fluctuation in migration-adjusted replacement level for Denmark over 2009-2018, and that the TFR was below migration-adjusted replacement level in some years and above it in others.In 2018, net migration was close to zero and migration-adjusted replacement level exceeded 2.0.Throughout 2009-2018, the value of migration-adjusted replacement level for Finland was relatively stable and considerably greater than the corresponding values for Norway and Sweden (Figure 1a, 1b, and 1d; Table 1).Between 2009 and 2018, the reduction to the TFR for Finland was the second largest for a European country 19 (Eurostat 2021; Hellstrand, Nisen, and Myrskyla 2020).Finland's TFR was marginally above migration-adjusted replacement over 2009-2013, but post-2014 fell far below it.If sustained over time, the fertility-mortality-net migration combination for 2018 would propel Finland's population ultimately towards a stationary population size (P) that is only 36 percent of its 2018 size (POP) (Table 1).However, if combined with constant net migration (and mortality) at the levels for Sweden for the same year, the TFR for Finland for 2018 would generate long-run population growth (Figure 1a).

Western Europe
Between 2009 and 2018, the TFR decreased in all the Western European countries (Figure 2).Despite this, except for Ireland during a period of neg- The TFR for the United Kingdom was above its migration-adjusted replacement level in all the years considered (Figure 2a).The gap was widest over 2014-2015, a period during which net migration was especially high.Net migration was somewhat lower in the year of and the years following the 2016 Brexit referendum, due to lower net migration from the European Union (Portes 2022).The TFR also fell, but remained above migrationadjusted replacement, albeit narrowly.
The reductions in TFRs for Belgium and the Netherlands were somewhat steeper than that for the United Kingdom (Figures 2b and 2c).The TFR for Belgium consistently exceeded that for the Netherlands.In both countries, the migration-adjusted replacement level was relatively high over 2013-2014, due to a dip in net migration.However, whereas for Belgium the TFR remained above migration-adjusted replacement, for the Netherlands it was marginally below this replacement level.Figure 2b shows a noticeable dip in migration-adjusted replacement for Belgium in 2015, a year in which net migration was of unusually high.For the Netherlands, a post-2015 reduction in migration-adjusted replacement level to below the TFR is evident, as immigration, mainly from within the European Union, increased (OECD 2019) 20 .
Luxembourg is internationally distinctive for having one of the world's highest rates of net migration (UNPD 2019b).Indeed, for eight of the years considered the net migration rate was so high that even a TFR of zero could not balance the stationary population that equals the current population equation.The values of the migration-adjusted replacement level for 2009 and 2010 (the only years for which it could be calculated) are very low and far below the corresponding values of the TFR (Figure 2d).
Despite being one of the highest in Europe, the TFR for France for 2009 barely exceeded migration-adjusted replacement level (Pison 2020; Figure 2e).Due to France's low rate of net migration, the migration-adjusted replacement level was similarly close to (zero migration) replacement level.Both the TFR and the migration-adjusted replacement fell slightly over 2009-2018.However, due to the reduction in the latter being slightly greater, in 2017 and 2018 the TFR was marginally below migration-adjusted replacement.
The TFR for Ireland also decreased (Figure 2f).However, despite this, the transformation of Ireland's net migration from negative over 2009-2013 to positive over 2014-2018 also transformed the implication of constant fertility-mortality-net migration from one of population extinction for the years over 2009-2013 to one of population growth for 2014-2018.For 2018, a year in which net migration was especially high, the migration-adjusted replacement TFR for Ireland fell into the "very low" range and far below the TFR.Constant fertility-mortality-net migration at the levels for 2018 would lead to its population tripling over the very long run.

Central Europe
There is broad similarity in the trends for Germany and Austria over 2009-2018 and wide year-to-year variation in the migration-adjusted replacement level (Figures 3a and 3b).In both countries, between 2009 and 2012 the TFR fell in the "very low" range and was considerably below migration-adjusted replacement.Over 2009-2015, both TFRs increased while migration-adjusted replacement fell.Consequently, in both countries over 2014-2017 the TFR exceeded migration-adjusted replacement.The particularly low migration-adjusted replacement levels for 2015 are due to the very high net migration, driven by very large inflows of refugees (Pew Research Centre 2016).For 2018, the TFR was marginally below migrationadjusted replacement for Austria and marginally above it for Germany.
The trends for Switzerland are very different from those for Germany and Austria (Figure 3c).Switzerland's TFR remained more-or-less constant at around 1.5 births per woman throughout 2009-2018.Despite its low level, over 2009-2016 Switzerland's TFR was above migrationadjusted replacement.This was primarily due to its high rate of net migration, one of the highest worldwide (UNPD 2019b).The net migration rate fell considerably between 2009 and 2014, the year in which a referendum proposing to limit immigration from the European Union was narrowly approved, and even further between 2014 and 2018 (Randall 2016).These reductions to net migration explain the narrowing gap between and eventual crossover of the TFR and the migration-adjusted replacement level (Figure 3c).For Liechtenstein, the TFR fluctuated from-yearto-year and was generally slightly below migration-adjusted replacement (Figure 3d).

Southern Europe
The Southern European countries exhibit a combination of very low fertility and very volatile net migration.For the countries in this region with larger populations, the implication of constant fertility-mortality-net migration was generally one of long-run population decrease.
Despite falling in the "very low" range, in 2009 and 2010 the TFR for Italy was almost identical to the migration-adjusted replacement level (Figure 4a; Vitali and Billari 2017).The low value of the latter is primarily due to Italy's high rate of net migration, then among the highest worldwide (UNPD 2019b).Post-2011, Italy's TFR fell progressively lower while large For Spain, Portugal, and Greece, the TFR decreased slightly between 2009 and 2013 and recovered slightly between 2013 and 2018.Even following the return to positive net migration, the TFRs for Greece and Portugal remained below migration-adjusted replacement (Figure 4b and 4c). 21 However, the particularly high net migration 22 for Spain in 2018 propelled the migration-adjusted replacement level marginally below its very low TFR (Figure 4d).
For Malta, while the TFR decreased slightly to even lower levels over 2009-2018, net migration increased considerably.The increase in net migration resulted in constant fertility-mortality-net migration having a positive population growth implication over 2012-2018 (Figure 4e).Indeed, over 2014-2018 the rate of net migration is so high that estimation of the migration-adjusted replacement level is infeasible.For Cyprus, the TFR also decreased (Figure 4f).The rate of net migration was extremely volatile.Constant fertility-mortality-net migration would generate positive population growth even with a TFR of zero over 2009-2011, population extinction over 2012-2015, partial population reduction for 2016, and population growth for 2017-2018.

Eastern Europe
For Eastern European countries for years between 2009 and 2018 invariably the long-run implication of constant fertility-net migration-mortality is population decrease.Under the negative patterns of net migration observed in a majority of these countries and years of constant fertility-net migration-mortality would result in the population eventually decreasing to zero.However, even for those Eastern European countries and years for which net migration was positive, invariably the TFR is below the migration-adjusted replacement level.The following text covers only those countries and years in which net migration was positive.
The increase in TFR for Hungary between 2009 and 2018 was the largest of any European country (Eurostat 2021; Stone 2018).Despite this, the TFR remained below the migration-adjusted replacement level (Figure 5a).A reduction in migration-adjusted replacement between 2014 and 2018 also contributed to a narrowing of its gap to the TFR.Over this period, net migration increased due to a combination of an increase in returning Hungarian citizens and their foreign-born children and an increase in immigration by foreign citizens (Gödri 2018) 23 .Increases in life expectancy, the largest of any of the countries considered in this paper, also contributed to the reduction to migration-adjusted replacement level (Parr, Li, and Tickle 2016;Eurostat 2021).Even with the narrower gap between fertility and migration-adjusted replacement, the long-run implication of continuation of the 2018 fertility-mortality-net migration combination is a more than halving of Hungary's population size (Table 1).
For Slovakia, reported net migration was positive and small in every year between 2009 and 2018. 24The migration-adjusted replacement TFR fluctuated between 1.78 and 2.02 (Figure 5b).The TFR also fluctuated but invariably was considerably below migration-adjusted replacement.For neighboring Czechia, net migration was negative over 2010-2012 and positive and generally increasing over 2013-2018.The TFR for Czechia fell between 2009 and 2011 and then rose between 2012 and 2018.Despite this recovery, the TFR remained below migration-adjusted replacement, albeit only slightly so over 2016-2018 (Figure 5c).Over 2015-2018, Estonia also recorded positive net migration.Like Czechia and Slovakia, over 2013-2018 its TFR increased.Despite this increase, the TFR remained below migrationadjusted replacement level, albeit only slightly so for 2018 (Figure 5d).

Bringing a new perspective to the fertility levels of European countries
This paper's comparison of fertility levels to a migration-adjusted replacement level provides a range of new perspectives on the fertility levels of European countries.First, contrary to UNPD (2019b), it illustrates that sustained average lifetime fertility of 2.1 live births per woman is not required for populations with low mortality to have a growth rate of zero in the long run.Rather, the implication of a below 2.1 TFR for long-run population growth is interdependent on net migration and mortality levels.This paper's results provide a range of examples of European countries and years for which a TFR below 2.1, in combination with the concurrent net migration and mortality, is coherent with long-run population growth.Sweden, Belgium, Luxembourg, and the United Kingdom are examples of countries for which the fertility-mortality-net migration combination is "above migration-adjusted replacement" for every year over the 2009-2018 period and thus has a long-run population growth implication.Equally, positive net migration alone does not guarantee long-run population growth.Slovakia and Hungary are examples of countries with positive recorded net migration for which the fertility-mortality-net migration combination is consistently below "migration-adjusted replacement" (with an associated implication of long-run population decrease).
Second, this paper's results show the heterogeneity of the population growth implications of differing fertility levels across Europe tends to be amplified by concurrent differences in net migration and, less importantly, mortality.The (mostly Northern and Western European) countries of Europe with a TFR above 1.5 tend to have lower migration-adjusted replacement levels whereas the countries in the (mostly Eastern and Southern European) countries with very low fertility (i.e., TFR below 1.5) tend to have either a relatively high migration-adjusted replacement level or else negative net migration.
Third, this paper's results illustrate the heterogeneity of the population growth implication of the same fertility level in the context of different patterns of net migration.For example, a TFR in the 1.7-1.8range, mentioned by Frejka and Sobotka (2008), would lead to population reduction if combined with constant net migration (and mortality) at the levels of Slovakia or Denmark for 2018 and to smaller reduction to population size if combined with those for Hungary, Finland, France, or Italy for 2018.Yet the same fertility would generate considerable growth, with the population ultimately increasing to several times its current size, if combined with constant net migration (and mortality) at the levels of Sweden, Spain, Ireland, or Luxembourg for 2018 and to smaller percentage increases in population if combined with those for Germany, Norway, Switzerland, or the United Kingdom for 2018.Such widely differing population growth implications of the same level of fertility in the context of differing migration would bring very different population-related challenges.In view of this, a "one size fits all" consensus view on "optimum" range for fertility would appear illogical (Van Dalen and Henkens 2021).Rather a "horses for courses" country and migration-context-specific view of the preferred national fertility level is warranted.
Fourth, this paper's results cast a new perspective on the migration levels which could prevent population decline under sustained "very low" (TFR below 1.5) fertility.This paper's results show that constant very low fertility combined with levels of migration (and mortality), which were "average" in Norway, Sweden, Switzerland, or Luxembourg over 2009-2018 would lead to increased population.Viewed through the prism of the recent demographic patterns in these countries (or (not shown) in Australia or Canada), the requisite net migration rate to prevent population decrease under very low fertility would be seen as "typical," in contrast to its portrayal as unusually, even implausibly, large ("massive") by Demeny (2016).
Fifth, unlike Parr (2021), this paper's results show the year-to-year change in the population growth implication of constant fertility-mortalitymigration for the same country over time, and differences between countries.For some countries (including Sweden, most of the countries in Western Europe, and most of the countries in Eastern Europe) the population growth implication of constant fertility-mortality-migration remained broadly similar across 2009-2018.The results for some other countries show a generally unidirectional pattern of change over the 2009-2018 period.In particular, the direction of the implication of constant fertility-mortalitymigration changed from growth to decrease in Finland, Switzerland, and Norway.However, the main driver of such changes differs between countries.The change was primarily due to reduced fertility for Finland, primarily due to reduced net migration for Switzerland, and due to a combination  a substantial reduction to fertility and a substantial reduction to net migration for Norway.In contrast, for Germany, the implication of constant fertility-mortality-migration changed from decrease to growth.Particularly for the Southern European countries, Ireland, Austria, and Germany, net migration was extremely volatile over 2009-2018.Except for Ireland, these countries generally had very low fertility.For these countries, the answer to whether replacement migration is actually taking place in low fertility countries may be seen as "sometimes," rather than in binary "yes" or "no" terms (Billari and Dalla-Zuanna 2011;Wilson et al. 2013).
In contrast to Parr's (2021) illustration of the measure used in this paper using data averaged over a five-year period, this paper considers annual data across multiple time periods.By doing so, it is able to present a much more detailed and richer picture, including the steady unfolding of regular trends in the TFR and migration-adjusted replacement over time (e.g., for Finland, Norway, and Switzerland), large changes to migration-adjusted replacement over short periods of time (even in some cases between consecutive years) due to one-off crises (e.g., for Germany and Austria due to the 2015 asylum-seeker crisis), and the potential for averages over five-year periods to be distorted by the effects of these "outlier" years.This paper's method has the potential to provide a model-based explanation of the projected considerable future growth in the population sizes of some countries.For example, the growth projected for Sweden, Norway, Switzerland, Luxembourg and the United Kingdom, Australia, and Canada by United Nations population projections could be portrayed in terms of the outcome being consistent with the assumptions involving "above migration-adjusted replacement fertility," rather than the seemingly inconsistent portrayal of such growth as occurring under fertility assumption involving "below replacement level" (UNPD 2019a(UNPD , 2019b)).This paper's method facilitates assessment of whether projected growth is more than a matter of the population momentum generated by the age structure of the population and whether it is more than a matter of assumed reductions over future time in the projection's mortality levels.The formulation of migration-adjusted replacement TFR in this paper corresponds to the measurement of net migration in absolute terms (as opposed to age-specific rates).This measure of migration is widely used in population projections (including by UNPD 2019b).The formulation of migration-adjusted replacement TFR in this paper may be modified to accommodate measurement of emigration as age-specific rates, a formulation which relates emigration to the size of the population which is exposed to the risk of emigration 25 (Rogers 1990;Parr 2022).
National-level population growth is the product of fertility, mortality, and migration.The application of the concept of replacement to national populations should consider all three processes.
15 The countries and years included Bulgaria, Croatia, Latvia, Lithuania, and Poland for all years over 2009-2018, Ireland over 2009-2013, Greece over 2010-2015, and 2017, Spain over 2010-2015, Portugal over 2011-2016, and Cyprus over 2012-2015. 16 For countries with net migration such that valid values of MAR_TFR can only be calculated for some but not all the years considered the valid values are indicated by orange markers (and values of MAR_TFR for the other years are missing).17 With older ages at birth a higher proportion of TFR accrues after immigration.Hence the number of births which forms the second (and higher order) generation components is greater.
18 The latter two trends are common to all the countries considered in this paper.
19 Only Iceland had a larger decrease in TFR between 2009 and 2018.20 All else equal, younger net migration increases the life expectancy after mi-gration (hence the first-generation component of the stationary population P 1 ) and the number of births in the destination country post migration (hence the second-generation component of the stationary population P 2 ).
21 For Spain for 2010-2015, Portugal for 2011-2016, and Greece for 2010-2015 and in 2017 the migration-adjusted replacement level could not be estimated due to negative net migration.

FIGURE
FIGURE 5 TFR and migration-adjusted replacement TFR for (a) Hungary, (b) Slovakia, (c) Czechia, and (d) Estonia 2009-2018 17284457, 2023, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/padr.12559 by National Health And Medical Research Council, Wiley Online Library on [19/07/2023].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License reductions in net migration increased the migration-adjusted replacement level further and further above the TFR. of 17284457, 2023, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/padr.12559 by National Health And Medical Research Council, Wiley Online Library on [19/07/2023].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 17284457, 2023, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/padr.12559 by National Health And Medical Research Council, Wiley Online Library on [19/07/2023].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 17284457, 2023, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/padr.12559 by National Health And Medical Research Council, Wiley Online Library on [19/07/2023].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 17284457, 2023, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/padr.12559 by National Health And Medical Research Council, Wiley Online Library on [19/07/2023].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/padr.12559 by National Health And Medical Research Council, Wiley Online Library on [19/07/2023].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

TABLE 1 Mean values of total fertility rate (TFR), migration-adjusted replacement total fertility rate (MAR_TFR) and the mean ratio of stationary population size to actual 2018 population (P/POP) for 2009-2018 1 and for 2018 for selected European countries
a 2010-2018 for Belgium.SOURCE: Author's calculations based on Eurostat (2021).
17284457, 2023, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/padr.12559 by National Health And Medical Research Council, Wiley Online Library on [19/07/2023].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License ative net migration over 2009-2013 and the Netherlands during a period of relatively low net migration over 2012-2014, the TFRs of Western European countries remained either similar to or above the corresponding migrationadjusted replacement levels.