Hill Kulu
email: hill.kulu@liverpool.ac.uk

Quantitative Methods, C39 -Other < C3 -Econometric Methods: Multiple/Simultaneous Equation Models < C -Mathematical and Quantitative Methods, J13 -Fertility|Family Planning|Child Care|Children|Youth

Keywords: fertility, urban-rural, event history analysis, Europe, Finland fertility, urban, rural, event history analysis, Northern Europe, Finland J13, C39, C41

In this study, we examine the causes of fertility variation across settlements. We use rich longitudinal data from Finland and apply event history analysis. Our analysis shows that fertility levels are the highest in small towns and rural areas and the lowest in the capital city, as expected. The socio-economic characteristics of women and selective migrations account for only a small portion of fertility variation across settlements. Housing conditions explain a significant portion of urban-rural fertility variation for first birth, but little variation for second and third birth. The analysis suggests that there are also significant contextual effects.

Introduction

For a long time, spatial fertility variation was an under-researched topic in the literature on low fertility in industrialised countries. However, recent contributions to the literature are evidence of the growing interest in spatial aspects of fertility, including urban-rural fertility differences [START_REF]Regional fertility differences in Western Germany: an overview of the literature and recent descriptive findings[END_REF][START_REF] Thygesen | Modelling regional variation of firsttime births in Denmark 1980-1994 by an age-period-cohort model[END_REF][START_REF] De Beer | An explanatory model for projecting regional fertility differences in the Netherlands[END_REF]KULU et al. 2007). Studies show that urban-rural fertility variation has decreased over time, but significant differences between various settlements persist. Fertility levels are higher in rural areas and small towns and lower in large cities. This pattern has been observed for the US [START_REF] Heaton | The timing of family formation: ruralurban differentials in first intercourse, childbirth, and marriage[END_REF][START_REF] Glusker | Differences in fertility patterns between urban and rural women in Washington State, 1983-1984 to 1993-1994[END_REF], England and Wales (TROMANS et al. 2008), France [START_REF] Fagnani | Fertility in France: the influence of urbanization[END_REF], the Netherlands [START_REF] Mulder | The connection between family formation and first-time home ownership in the context of West Germany and the Netherlands[END_REF][START_REF] De Beer | An explanatory model for projecting regional fertility differences in the Netherlands[END_REF], Italy [START_REF] Brunetta | Urban and rural fertility in Italy: regional and temporal changes[END_REF][START_REF] Michielin | Lowest low fertility in an urban context: the role of migration in Turin, Italy[END_REF], Germany and Austria [START_REF]Regional fertility differences in Western Germany: an overview of the literature and recent descriptive findings[END_REF][START_REF] Kulu | Fertility of internal migrants: comparison between Austria and Poland[END_REF], the Nordic countries [START_REF] Thygesen | Modelling regional variation of firsttime births in Denmark 1980-1994 by an age-period-cohort model[END_REF]KULU et al. 2007), the Czech Republic [START_REF] Burcin | Changes in fertility and mortality in the Czech Republic: an attempt of regional demographic analysis[END_REF], Poland and Estonia [START_REF] Vojtěchovská | Population development in Poland[END_REF][START_REF] Kulu | Migration and fertility: competing hypotheses re-examined[END_REF]2006) and Russia [START_REF] Zakharov | Regional fertility differentiation in Russia: 1959-1994[END_REF].

While studies on urban-rural fertility variation show broadly similar patterns (the larger the settlement, the lower the fertility levels are), it is far from clear why fertility levels are higher in smaller places and lower in larger settlements. Most research discusses two competing hypotheses regarding spatial fertility variation: the compositional and the contextual. The compositional hypothesis suggests that fertility levels vary between places simply because different people live in different settlements, whereas the contextual hypothesis suggests that factors related to immediate living environment are of critical importance. The role of selective migrations has also been discussed in the literature; couples with childbearing intentions may decide to move to smaller places that are better suited to childrearing, whereas those with no childbearing plans may migrate to larger settlements.

Although previous research has shed considerable light on spatial aspects of fertility, we argue that it suffers from important shortcomings. First, most studies have used aggregate data and respective indices (ASFR, TFR), which have been useful in outlining general patterns but less so for finding out the causes of urban-rural fertility variation. Second, urbanrural fertility variation has been a side-topic in most of those aforementioned studies that have examined disaggregated behavioural patterns using individual-level data. The causes of urban-rural fertility variation have been briefly discussed in these studies rather than being thoroughly analysed. Third, the role of selective migrations and housing conditions in urbanrural fertility variation has not been examined.

To investigate the causes of spatial fertility variation is important for demographic research. If the context turns out to be an important determinant of childbearing patterns, then research on urban-rural fertility variation will have the potential to significantly advance our understanding of the causes of fertility patterns and dynamics in Europe and North America.

The issue of whether and how the social context influences fertility behaviour of individuals has been an ingredient part of ongoing discussion on the causes of fertility dynamics and patterns [START_REF] Becker | A Treatise on the Family[END_REF][START_REF] Mcdonald | Gender equity in theories of fertility transition[END_REF][START_REF] Lesthaeghe | From the first to the second demographic transition: an interpretation of the spatial continuity of demographic innovation in France, Belgium and Switzerland[END_REF][START_REF] Neyer | Consequences of family policies on childbearing behaviour: effects or artifacts?[END_REF][START_REF] Thornton | Sweeping changes in marriage, cohabitation and childbearing in Central and Eastern Europe: new insights from the developmental idealism framework[END_REF]. If the composition of a population plays a critical role, then spatial fertility patterns and their dynamics might still be of interest for researchers working on regional population projections [START_REF] De Beer | An explanatory model for projecting regional fertility differences in the Netherlands[END_REF][START_REF] Wilson | Recent developments in population projection methodology: a review[END_REF].

In this study, we examine the causes of urban-rural fertility variation. We go beyond the traditional urban-rural dichotomy and distinguish settlement groups by the size of settlement (KULU et al. 2007). We investigate to what extent the socio-economic contribution to the literature on urban-rural fertility variation is twofold. First, we examine the contribution of selective migrations to urban-rural fertility differences. While recent research has investigated the role of the individual-level characteristics in spatial fertility variation (KULU et al. 2007;KULU et al. 2009), no study has examined the contribution of selective migrations to urban-rural fertility differences (on the role of selective residential moves in high suburban fertility, see KULU and BOYLE 2009). Second, and even more importantly, we include in the analysis information on the housing characteristics of couples to investigate how much these account for fertility differences by settlement. This is an important step in the analysis that has not been executed in previous studies on urban-rural fertility variation. While some recent studies have examined childbearing patterns by housing type and size (KULU and VIKAT 2007;[START_REF] Ström | Housing and first births in Sweden, 1972-2005[END_REF], none of these has explicitly focussed on urban-rural fertility variation. Further, to our knowledge, no recent study has modelled fertility and housing choices simultaneously to control for unobserved selectivity of individuals with different fertility plans into different housing types. This is a critical step for measuring the contribution of housing conditions to urban-rural fertility variation.

We use rich individual-level register data from Finland, a Northern European country, to examine patterns separately for first, second and third births. Parity-specific analysis allows us to gain a better understanding of the causes of urban-rural fertility variation than is possible via conventional studies based on aggregate data and indicators. We use data from Finland for two reasons. First, the Finnish register data contain a detailed information on the housing characteristics of individuals and couples. Second, information on residential and housing changes is provided to the accuracy of a month which is needed for a study of the effect of selective migrations and housing conditions on spatial fertility variation.

Competing views on the causes of urban-rural fertility variation

The idea of compositional factors suggests that fertility levels vary between places because different people live in different settlements. First, it is a well-known fact that the share of highly educated people is larger in cities than in small towns and rural areas. For many countries, fertility levels tend to differ by education level, with the lowest for universityeducated individuals and the highest for individuals with only compulsory education [START_REF] Hoem | Why does Sweden have such high fertility?[END_REF][START_REF] Andersson | Cohort fertility patterns in the Nordic countries[END_REF]. Therefore, lower fertility in larger places might simply be attributed to the higher proportion of highly educated people living there. Educational composition may thus be an important determinant of urban-rural fertility variation in many countries, particularly for spatial differences in childlessness. It is also likely that the role of education in urban-rural fertility differences varies between countries -it may be bigger in the countries where differences in fertility levels by education level are larger (e.g., Great Britain or Germany) and smaller in the countries where fertility levels vary little by level of education (e.g., the Nordic countries) [START_REF] Hoem | Why does Sweden have such high fertility?[END_REF][START_REF] Andersson | Cohort fertility patterns in the Nordic countries[END_REF]. Second, fertility variation by residence may also result from the larger share of students in cities and towns than in small towns and rural areas [START_REF]Regional fertility differences in Western Germany: an overview of the literature and recent descriptive findings[END_REF]KULU et al. 2007). Previous research shows that the likelihood of family formation is very small during the studies, even though some variation exists in Europe, particularly between the East and the West.

Third, the share of married people is larger in smaller places, and marriage is clearly related to childbearing. Thus, the over-representation of married people in small towns and rural areas may explain the higher fertility rates there and particularly the higher likelihood of family formation [START_REF]Regional social contexts and individual fertility decisions: a multilevel analysis of first and second births in Western Germany[END_REF]. However, the direction of causality between marriage and childbearing is not as clear as it may appear to be at first glance. It might be argued that childbearing could be seen as a reason to give a more "legal form" to a relationship [START_REF] Baizan | The interrelations between cohabitation, marriage and first birth in Germany and Sweden[END_REF]). This may be true even for the countries where childbearing in cohabitation is not rare (anymore). (For that reason marriage is left out from the models in this study.)

Selective migrations may also account for variations in spatial fertility. Couples who intend to have a child (or another child) may move from larger places to smaller ones because the latter are perceived as better suited to raising children. Indeed, recent studies show that selective moves take place between cities and neighbouring rural areas, many of which can be classified as suburbs of cities [START_REF]Regional fertility differences in Western Germany: an overview of the literature and recent descriptive findings[END_REF]KULU and BOYLE 2009). However, the factor of selective migrations may be less relevant to explaining urban-rural fertility variation if the areas around cities and towns have been included in the analysis as part of the urban region. Previous studies have shown that there are families who move from cities and towns to small towns and rural areas over long distances, potentially with the intention of having another (or a third) child, but the share of such couples is not very large [START_REF] Kulu | Fertility and spatial mobility in the life-course: evidence from Austria[END_REF].

The context may influence fertility behaviour through economic opportunities and constraints or cultural factors. It is a well known fact that children are more expensive in cities than in rural areas [START_REF] Livi-Bacci M | Italian fertility: an historical account[END_REF][START_REF] Becker | A Treatise on the Family[END_REF]. First, food, commodities and services are more expensive in larger than in smaller places [START_REF] Becker | A Treatise on the Family[END_REF]. Secondly, we may also argue that children are expensive in cities because parents have to pay for each step of their children's education, be that sending the child to piano lessons after school or playing football in a sports club. Third, children in cities are more timeconsuming for their parents than those in rural areas; parents not only need to pay (or pay more) for post-school activities but also organise their children's journeys to and from home. This may become an extremely difficult task for couples with many children, particularly if school, home and post-school activities are in different places, which is often the case in cities [START_REF] Fagnani | Fertility in France: the influence of urbanization[END_REF]. The latter argument, however, is challenged by some recent studies, which argue that in a 'daily prism' of the same size, in fact, a greater variety of amenities can be reached in a city than in a rural area [START_REF] De Meester | Time spent in paid work by women and men in urban and less urban contexts in the Netherlands[END_REF]. Amenities are thus more concentrated in cities; therefore, children in cities are not necessarily more time-consuming than those in rural areas.

Finally, one could argue that urban environments as such encourage higher spending on children because of norms, proximity to shops (and other attractions) and a need to invest more in children through extra-curriculum activities (cf. BECKER 1991). All of these factors outweigh the (minor) difference in salaries between urban and rural areas. Life in small towns and rural areas is simpler in contrast to urban life: there are fewer attractions for children, and there is less normative pressure for parents; children may even contribute to the family economy, assisting their parents either in running a farm or in family-based tourism [START_REF] Caldwell | On net intergenerational wealth flows: an update[END_REF]. Also, it is important to emphasise that a spacious child-friendly housing is affordable for many couples in rural areas and small towns, but for a fewer couples in large cities (see our further discussion below on the possible effect of housing.)

Opportunities costs are also higher in cities and towns than in small towns and rural areas [START_REF] Becker | A Treatise on the Family[END_REF][START_REF] Michielin | Lowest low fertility in an urban context: the role of migration in Turin, Italy[END_REF]. Life in an urban context, particularly in large cities, offers various opportunities for work and leisure. For example, a teacher in a school may accept a job at other (and a better) school in the city; she may then become headteacher of the school and finally accept a managerial job at the department for education and children at the city government. Having children, however, means that the possibility of taking advantage of such opportunities is relatively small. In rural areas and small towns, in turn, where usually only one educational institution exists, fewer promotion opportunities exist for a school-teacher and the opportunities costs are thus significantly lower. There is also strong normative pressure to achieve in the work arena in cities, which may be further promoted by stronger competition in cities. Briefly, there is more to lose (and win) in cities than in small towns and rural areas, and this dynamic per se may constantly remind urban couples of the conflict between work and family.

The emphasis on economic factors should not necessarily imply that childbearing decisions are subject to purely individual rational calculation in its instrumental form (the maximisation of utility). Rather, economic factors may be the basis for a normative context for various decisions, including childbearing decisions; the context may discourage couples from having large families (in large cities) or encourage them to have many children (in rural areas).

Cultural factors may also explain urban-rural fertility variation. Research has shown that people in rural areas and small towns retain traditional attitudes and lifestyles, with a value orientation towards large families and a preference for extended families [START_REF] Trovato | Decomposing the urban-rural fertility differential: Canada[END_REF][START_REF] Heaton | The timing of family formation: ruralurban differentials in first intercourse, childbirth, and marriage[END_REF][START_REF] Snyder | Residential differences in family formation: the significance of cohabitation[END_REF][START_REF] Snyder | The role of contemporary family behaviors in nonmarital conception outcomes of nonmetro women: comments on Albrecht and Albrecht[END_REF]. A rural and small-town population can thus be considered a 'family-oriented' sub-culture within a country (cf. LESTHAEGHE and NEELS 2002;[START_REF] Sobotka | Religiosity and spatial depographic differences in the Netherlands[END_REF]. The 'family-oriented' sub-culture forms a normative context for couples to draw upon when they make various decisions. Cities, in turn, are the places where the 'second' demographic transition began and spread, and they also remain a stronghold of 'post-modern' values (cf. LESTHAEGHE and NEELS 2002). Cities promote individual autonomy and selfactualisation -and, thus, individual choices, which (despite their variety) usually means fewer children. There is also more heterogeneity in cities: while a 'family-oriented' subculture may exist there, particularly in the suburbs, cities are also places that support (or at least tolerate) the 'culture of singlehood and childlessness'. Finally, the physical and social dimensions of the residential environment should not be neglected. Life in rural areas and small towns involves living in the vicinity of nature. The lure of the rural and small town environment for many parents or prospective parents is related to the child-friendly environment they offer: green and quiet environment; a lot of open space. Rural and small town residents are also more likely to be surrounded by other families with children because of the higher fertility in these areas and possibly the migration of (some) families with small children from large cities to rural areas and small towns [START_REF] Courgeau | Interaction between spatial mobility, family and career life-cycle: a French survey[END_REF][START_REF] Mulder | First-time home-ownership in the family life course: a West German-Dutch comparison[END_REF][START_REF] Kulu | Fertility and spatial mobility in the life-course: evidence from Austria[END_REF].

While various compositional and contextual factors have received attention in the literature on spatial fertility variation, the role of housing conditions has been only briefly discussed. Housing type and size vary across residential contexts. Most people in rural areas and small towns live in detached or semi-detached houses, whereas in towns and large cities in particular, apartments are the dominant type of housing. Detached or semi-detached houses are usually larger than apartments and they also have a garden. Most importantly, fertility levels are higher in detached or semi-detached houses than in terraced houses or apartments (KULU and VIKAT 2007). However, studies show that selective residential moves on the part of couples intending to have a child (or another child) explain a significant portion of fertility differences between family houses and apartments, as expected (KULU and VIKAT 2007). Therefore moving from one type of housing to another type is not likely to cause a change in couple's fertility behaviour. An opportunity of making such a move or the lack of it, however, may shape couple's childbearing plans and patterns (cf. MULDER 2006). For example, fertility may be high in rural areas because the couples can move to larger housing (or a 'proper' housing) when planning to have a child (or another child); fertility in large cities, in contrast, may be low because of the lack of opportunities for many couples to improve housing conditions. The efforts required to obtain a 'proper' housing are much greater in large cities than in rural areas and small towns; a 'proper' housing (e.g. detached or semi-detached house, terraced house or large apartment) is a pre-condition of family formation in most industrialised societies [START_REF] Mulder | Population and housing: a two-sided relationship[END_REF]cf. BERNARDI et al. 2008). The spatially varying availability and affordability of housing may thus account for urban-rural fertility variation.

In this study, we examine the relative contributions of the socio-economic characteristics of a population, selective migrations, housing conditions and contextual factors to fertility differences between various settlements in Finland. We focus on the childbearing of partnered women. We do this for two reasons. First, childbearing outside a union is uncommon in the Nordic countries; if it occurs, it is mostly among teenagers who have unplanned pregnancies (cf. VIKAT 2004), and that phenomenon is not the focus of this study. Second, we investigate the contribution of housing conditions to spatial fertility variation. With a focus on childbearing in unions, we know with a relatively high level of precision what the housing conditions are at the moment when a couple decides to have a child. We disaggregate fertility patterns by separately analysing determinants of spatial variation in first, second and third birth. We use individual-level register data from Finland, which is necessary for examining the role of various factors in urban-rural fertility variation; our sample is also sufficiently large to obtain robust results.

Urban-rural fertility variation in Northern Europe

Before we proceed with a description of the hypotheses, a brief summary of the urban-rural fertility variation in Northern Europe is useful. Figures 1a to 1d settlements in all the four countries. Moreover, we observe a systematic inverse relationship between the fertility levels and the size of settlement -the larger the settlement is, the lower the fertility has been. Interestingly, the fertility variation has persisted over time and the differences between the countries have been minor. We also notice that in the beginning of the 21st century the TFR in rural settlements and small towns stayed close to replacement level, while the TFR in the capital city region remained at levels between 1.5 and 1.7 children per woman. The Finnish data thus provide us with a good opportunity to study the causes of urban-rural fertility variation in Northern Europe. Further, we are reassured that the findings of our study are valid for industrialised countries in more general.

FIGURES 1A, 1B, 1C AND 1D ABOUT HERE

Hypotheses on the relative contribution of various factors

First, we expect fertility levels to significantly vary by settlements, with the highest in small towns and rural areas and the lowest in large cities (see Figure 1b). We assume that we will observe differences for all three parity transitions [START_REF] Thygesen | Modelling regional variation of firsttime births in Denmark 1980-1994 by an age-period-cohort model[END_REF]KULU et al. 2007). Second, we expect the socio-economic characteristics of women to account for some fertility variation across settlements [START_REF]Regional fertility differences in Western Germany: an overview of the literature and recent descriptive findings[END_REF][START_REF] De Beer | An explanatory model for projecting regional fertility differences in the Netherlands[END_REF]. However, socio-economic factors may play a smaller role in explaining spatial fertility variation as shown in previous studies: the focus of this study is the childbearing of women in unions, and there are fewer in cities and towns who are still in school at this stage of life compared to when they were single. Also, fertility levels vary relatively little by education in Finland (and in other Nordic countries), which is where our data set comes from [START_REF] Andersson | Cohort fertility patterns in the Nordic countries[END_REF]. Third, we expect selective migrations to play little or no role in urban-rural fertility differences because we have controlled for the possible (confounding) effect of suburbanisation by including suburbs of cities and towns as a part of the urban region (cf. KULU and BOYLE 2009). Fourth, we expect housing conditions to explain some urban-rural fertility variation at least. The key question, however, is how much spatial fertility variation is attributed to housing conditions and how much to the remaining factors, and whether the patterns vary by parity. We assume that these remaining factors, if any, are related to the living environment for couples in both the economic and the cultural sense.

Data and definitions

Our data come from the Finnish Longitudinal Fertility Register. This is a database developed by Statistics Finland that contains linked individual-level information from different administrative registers (see [START_REF] Vikat | Women's labor force attachment and childbearing in Finland[END_REF]. The extract we used in the analysis included women's full birth and educational histories. Data on partnership, residential and housing histories, and annual measurements of characteristics of women's activity and income were collected for the period from 1987 to 2000. The extract used is a ten-percent random sample stratified by single-year birth cohort and drawn from records of all women who had ever received a personal identification number in Finland and were in the age range of 16-49 during the period between 1988 and 2000 (this includes cohorts born between 1938 and 1983). We focused on childbearing among women who were in unions and included in the analysis all co-residential unions that were formed between 1988 and 2000. Foreign-born women (three percent) were excluded from the analysis.

We studied the impact of settlement type on first, second and third births. We distinguished four types of settlements according to the size of the municipality of residence: 1) the capital city of Helsinki, with 500,000+ inhabitants; 2) other cities with a population of 14 50,000-250,000; 3) towns with 10,000-50,000 inhabitants; and 4) small towns and rural areas with less than 10,000 inhabitants. This was consistent with the fertility patterns we observed for various settlement groups at aggregate level (see Figure 1b). We also considered all cities and many towns to extend beyond their administrative borders and defined suburban municipalities (for cities and towns with more than 30,000 inhabitants) as part of the urban regions. We followed a definition developed by Statistics Finland and assigned a municipality to its respective urban region if at least 10% of its employed population commuted to work in the neighbouring city or town in 2000. Using commuting data to define labour-market regions is standard in migration and urbanisation research, although the threshold used varies across studies (see [START_REF] Champion | Urbanization, sub-urbanization, counterurbanization, and reurbanization[END_REF][START_REF] Hugo | Toward a new conceptualization of settlements for demography[END_REF][START_REF] Kupiszewski | Internal migration and regional population dynamics in Europe: Finland case study[END_REF].

Table 1 presents the distribution of person-years (exposure) and events (occurrences) across various settlement groups. The former shows how partnered women and their durations of residence were distributed across various settlements in the period when they were at risk for their first, second or third birth. Thirty four percent of all person-years for the first birth were lived in the capital city, 36% in other cities, 20% in towns and 9% in small towns and rural areas. The figures for the second birth were 30%, 37%, 21% and 11%, and those for the third birth 27%, 37%, 23% and 13%. There were 14,258 first births for 35,391 women, 12,097 second births for 23,154 women and 4,120 third births for 17,246 women in the data. Childless women who formed a union between 1988 and 2000 made up the population at risk for first births; the data set for second and third births also included women who had their first or second conception (that led to a birth) in 1988 or later but before union formation and women who had their first or second conception (that led to a birth) before 1988 but formed another union in 1988 or later. We controlled for a set of demographic and socio-economic variables when examining fertility variation across settlements. Our demographic controls included union duration, the woman's age, and time since previous birth (if there were any births). The socio-economic controls included the woman's language (Finnish or Swedish), educational enrolment (enrolled or not enrolled), education level (lower secondary, upper secondary, vocational, lower tertiary or upper tertiary) and annual earnings (none, low, medium, high or very high) 1 . We also controlled for calendar time. In addition, we included in the analysis a variable showing whether a couple had changed its settlement of residence to control for the possible effect of selective migrations. During its first (common) residential episode, a couple was treated as a non-migrant couple (whatever the migration history of the partners before their marriage or cohabitation); they became a migrant couple after they had changed (together) their settlement of residence (i.e. crossed the border of a labour-market area). If a child was born after the migration, the couple was again treated as a non-migrant couple. For second and third births, therefore, we only considered migrations that had taken place after the birth of first or second child, respectively. This strategy (i.e. include only migrations before the current childbirth) was considered the best to capture the effect of selective moves; in our further analysis (results not shown), we also used different definitions for the migration variable (e.g. no return to 'non-migrant' category after the birth of a child / another child).

Finally, we included housing type in the analysis, distinguishing between detached (and semidetached) houses, terraced houses, and apartments. A dwelling for one or two families is defined as detached house (or 'single-family house'). Terraced house (or 'rowhouse') is a dwelling with three or more houses in a row of houses and sharing a wall with its adjacent

Methods and modelling strategy

We used an event-history analysis [START_REF] Hoem | Statistical analysis of a multiplicative model and its application to the standardization of vital rates: a review[END_REF]1993;[START_REF] Rohwer G | Techniques of Event History Modeling: New Approaches to Causal Analysis[END_REF], fitting a series of regression models for the hazard of first, second, and third births. We modelled the time to conception (subsequently leading to a birth) to measure the effect of the settlement of residence on childbearing decisions as precisely as possible. The basic model can be formalised as follows:

∑ ∑ ∑ + + + + = k j l il ij j ik k i t w x t u z t y t ) ( ) ( ) ( ) ( ln l β α µ , (1)
where µ i (t) denotes the hazard of the first, second or third conception for individual i and y(t) denotes a piecewise linear spline that captures the baseline log-hazard (union duration for first birth or time since previous birth for the second and third births). We used a piecewise linear spline specification instead of the widely used piecewise constant approach to pick up the baseline log-hazard and the effect of ( In our modelling strategy, we first investigated first, second and third birth risk by settlement type controlling for basic demographic characteristics (union duration, woman's age and time since previous birth, if any). We then also controlled for socio-economic characteristics of women to explore how much these characteristics explained urban-rural fertility variation. In the third model, we also included migrant status to examine whether selective migrations played any role in spatial fertility variation. Finally, we included housing type in the analysis to further explain fertility variation across settlements. The aim of stepwise modelling was to examine the relative contribution of socio-economic characteristics, selective migrations, housing conditions and contextual (or remaining) factors to urban-rural fertility variation.

Housing type was an endogeneous variable in the fertility equations; childbearing plans of women (or couples) were likely to influence their housing choices. To identify and control for endogeneity of housing type in the fertility process we built a simultaneousequations model to estimate jointly three equations for fertility and another three equations for housing choices according to the type of destination housing. The model can be formalised as follows: positive value of ρ BD suggests that women with an above-average risk of having a child (or another child), net of their observed characteristics, have also an above-average propensity of moving to detached or semi-detached housing. The same logic applies for ρ BT and ρ BA , which denote correlations between the residuals of the birth and terraced housing equations and the birth and apartment equations, correspondingly. The identification of the model was attained through within-person replication (see [START_REF] Lillard | Simultaneous equations for hazards: marriage duration and fertility timing[END_REF]LILLARD et al.1995;[START_REF] Kulu | Migration and fertility: competing hypotheses re-examined[END_REF]2006;STEELE et al. 2006). Many women gave several births, and some women made several moves to the same housing type. We also tested robustness of the results by including and excluding various socio-economic variables from the equations of the two processes; the results were robust to different specification. The model was estimated via maximum likelihood using aML [START_REF] Lillard | aML Multilevel Multiprocess Statistical Software, Version 2.0[END_REF] 3 .

∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ + + + + + = + + + + + = + + + + + = + + + + + = + + + + + = + + + + + = k j l A i iml A l imj A j imk A k A A im k j l T i iml T l imj T j imk T k T T im k j l D i iml D l imj D j imk D k D D im k j l B i il B3 l ij B3 j ik B3 k B3 B3 i k j l B i il B2 l ij B2 j ik B2 k B2 B2 i k j l B i il B1 l ij B1 j ik B1 k B1 B1 i t w x t
ε β α µ ε β α µ ε β α µ ε β α µ ε β α µ ε β α µ ) ( ) ( ) ( ) ( ln ) ( ) ( ) ( ) ( ln ) ( ) ( ) ( ) ( ln ) ( ) ( ) ( ) ( ln ) ( ) ( ) ( ) ( ln ) ( ) ( ) ( ) ( ln , ( 2
The model thus controlled for woman-level unobserved characteristics, which influenced both her fertility and housing choices by destination. These unmeasured characteristics were assumed to be constant during a woman's reproductive ages. The model did not control for potential time-varying unobserved characteristics, which were birth-or move-specific.

The competing risks framework assumes that the risks of moving to different housing types are independent of each other [START_REF] Hachen | The competing risks model: a method for analyzing processes with multiple types of events[END_REF][START_REF] Hill | Competing hazards with shared unmeasured risk factors[END_REF]. The assumption of Independence of Irrelevant Alternatives (IIA) is obviously not valid here: it is likely that the protection against the IIA assumption, however; by allowing the correlation of womenspecific residuals of the three housing choice equations we control for the (unmeasured) similarity of alternative housing types.

Parity-specific fertility across settlements

First birth

In the first model, we only controlled for union duration and the woman's age. Couples living in the capital city of Helsinki had the lowest risk of a first birth, while couples in rural areas and small towns had the highest risk (Table 2 and3). In the second model, we also controlled for the socio-economic characteristics of women. The differences between settlements largely persisted. In the third model, we also included migrant status to control for the effect of selective migrations. Couples who had changed their settlement of residence had a higher risk of a first birth than did couples who had not moved, suggesting that selective migration was indeed in operation (Table 3). The patterns did not change, however, because of the small share of selective migrants. This was expected because we had included suburban municipalities as part of the urban regions.

TABLES 2 AND 3 ABOUT HERE Next, we also controlled for housing type. The differences in the first birth levels diminished considerably and disappeared between rural areas (and small towns) and urban Still, interestingly, women living in the capital city had a significantly lower risk of first birth than did those living in other settlements, even after controlling for housing conditions, suggesting that socio-economic factors and housing conditions did not explain all spatial variation in levels of first births and that there were other factors, possibly contextual ones, at play.

Second birth

Women living in rural areas and small towns had a significantly higher risk of a second birth than did those in cities and towns, but the risk of a second birth was not lower for women living in Helsinki (Table 4 and5). In the second and third model, we controlled for the socioeconomic characteristics of women and migrant status. The initial differences between the settlements persisted, suggesting that compositional factors and selective migrations played no role in spatial variation in the risk of a second birth. In the fourth model, we also controlled for housing type. The differences between urban and rural areas decreased somewhat, but the birth levels remained higher in rural areas. The patterns for third births were also interesting. Couples living in Helsinki had the lowest risk of a third birth, while couples in rural areas and small towns had the highest risk (Table 6 and7). This was similar to what we observed for the first birth. Next, we controlled for the socio-economic characteristics of women and migrant status. Couples who had changed their settlement of residence had a higher risk of a birth than did couples who had not moved,

showing that selective migration was in operation for third births as well. However, the patterns did not change because of the small share of (selective) migrants. In the fourth model, we controlled for housing type. Spatial fertility variation decreased only slightly (if at all). The levels of third births remained significantly higher in rural areas and small towns than in urban areas, clearly indicating that other factors, possibly contextual ones, were responsible for the high risk of third births in smaller settlements.

TABLES 6 AND 7 ABOUT HERE

The results of the analysis supported that housing was an endogeneous variable in the fertility process; the correlations between the residuals of the respective equations were significantly different from zero (Table 8). Positive values suggested that women who were more likely to have a child (or another child), ceteris paribus, were also more likely to change housing, whatever the type of destination housing. Migration was also endogeneous in the fertility process, as expected; its 'effect' ceased in a joint model of the two processes (compare the results of Model 3 and 4 in Table 3, 5 and 7.)

Summary and discussion

The aim of this study was to investigate the causes of urban-rural fertility variation. Using rich longitudinal register data from Finland, we examined the relative contribution of socioeconomic characteristics of population, selective migrations, housing conditions and contextual factors to fertility variation across settlements. While research had investigated the role of the individual-level characteristics in spatial fertility variation, no previous study had examined the contribution of selective migrations and housing characteristics to urban-rural fertility differences. Further, we modelled fertility decisions and housing choices jointly, which was necessary to measure the net contribution of housing conditions to urban-rural fertility variation.

Our study showed, first, that fertility levels varied significantly across settlements for all three parity transitions. The levels were the highest in small towns and rural areas and the lowest in the capital city of Helsinki. Second, the study showed that the socio-economic characteristics of women accounted for only a small portion of fertility variation across settlements. Third, we discovered that selective migrations did not explain any of the variation in spatial fertility: couples who had changed their settlement of residence had higher birth rates, but the share of internal migrants was small. Fourth, housing conditions accounted for a significant portion of variation in first birth levels across settlements. Fifth, we observed significant fertility variation across settlements after controlling for compositional characteristics, selective migration and housing conditions, which suggested that there were also contextual effects. First-birth levels were relatively low in the capital city of Helsinki;

the second and, especially, third-birth rates were high in rural areas and small towns. status and partner's education and income, for example. The share of married people was smaller in the capital city, and this explained the lower first-birth rates there. However, the direction of causality between marriage and childbearing is far from clear, as we discussed earlier. People may simply decide to marry when they wish to have children, thus making marriage a consequence (or a part) of family formation rather than its cause [START_REF] Baizan | The interrelations between cohabitation, marriage and first birth in Germany and Sweden[END_REF]). Also, we controlled for marriage in our further analysis, but significant differences in first-birth rates persisted between the settlements (results not shown). The inclusion of information on partner's education and income would have not changed the patterns either.

Previous studies on the Nordic countries have shown that in the context of relatively high educational homogamy and given the prevalence of dual-earner couples, woman's educational and labour market characteristics are good proxies for a household's labour market performance and income and its association with childbearing (cf. [START_REF] Andersson | Childbearing dynamics of couples in a universalistic welfare state: The role of labor-market status, country of origin, and gender[END_REF]. We are thus confident that contextual factors contributed to low fertility rates in the capital city. However, the question remains of which of those factors were critical.

To begin with economic factors, one might argue that some couples are unable to afford a child in large cities because of the high costs of child-rearing. However, while this may be true in some contexts, it is unlikely the case for Finland and other Nordic countries, where generous welfare provisions by the state ensure that couples enjoy sufficient security when raising a child. We may continue by considering the argument that higher opportunity costs account for lower first-birth rates in large cities. Again, it is unlikely that this is a (potentially including long journeys to and from home) are also unlikely to lead a couple to decide not to have any children (cf. FAGNANI 1991).

Significantly lower first-birth levels in large cities may thus be related to culturalnormative factors: for example, to voluntary childlessness. Recent studies reveal the spread of voluntary childlessness in European countries [START_REF] Goldstein | The emergence of sub-replacement fertility ideals in Europe[END_REF], and it could be argued that large cities are the places where such behaviour emerged and spread first. A large city environment is a source of heterogeneity in behavioural patterns and supports the existence of various sub-cultures, including that of singles and couples who have decided not to have any children; in smaller places, in contrast, union formation (marriage) and childbearing are still expected to be closely connected [START_REF] Heaton | The timing of family formation: ruralurban differentials in first intercourse, childbirth, and marriage[END_REF][START_REF] Snyder | The role of contemporary family behaviors in nonmarital conception outcomes of nonmetro women: comments on Albrecht and Albrecht[END_REF]. It is also possible that people with different family plans move to different environments at some stage in their lives (e.g., those who plan to remain childless leave rural areas for cities after leaving high school) or stay where they are (e.g. those who plan to have children stay in rural areas), but research in other European countries has found no support for this argument [START_REF] Kulu | Migration and fertility: competing hypotheses re-examined[END_REF]2006).

We have deemphasised the role of economic opportunities and constraints in explaining low first-birth levels in large cities and emphasised the importance of culturalnormative factors instead. This view, however, is challenged by the fact that housing conditions explained a significant amount of spatial variation in the first-birth levels. Lower first-birth rates in urban areas were related to the fact that people in cities mostly live in apartments; higher first-birth levels in rural areas and small towns were associated with living in detached or semi-detached houses, which were larger than apartments. Living in spacious housing per se does not lead to birth of a (first) child. However, an opportunity of moving to a larger housing or the lack of it may shape couple's childbearing plans and patterns. The 25 results thus suggest that the limited availability (or, more precisely, affordability) of a 'proper' housing is a factor in lower first-birth rates in urban areas, particularly in large cities.

Access to 'proper' housing is a pre-condition of family formation in most industrialised societies [START_REF] Mulder | Population and housing: a two-sided relationship[END_REF]. This is a requirement that is more difficult to fulfil in large cities than in towns and rural areas. Postponement of childbearing, in turn, increases the chances that some women will end up having fecundity problems [START_REF] Mulder | Population and housing: a two-sided relationship[END_REF].

It seems reasonable to assume that economic opportunities and constraints play an important role in explaining spatial variation in higher-order childbearing. Raising a second and especially a third child is costly in cities, even in the context of the Nordic welfare state.

Further, despite generous policies that aim for the reconciliation of parenthood with employment, having a large family limits a woman's career opportunities, especially in a competitive city environment. It also takes a great deal of time and effort to organise the everyday activities of a large family in a city context (although some studies disagree with this argument). If these factors are pertinent to our study, however, we should expect levels of second and third births to be particularly low in the large cities where the constraints are the greatest. However, the main fertility differences that we observed occurred between urban areas, including both large cities and medium-sized towns, and between rural areas.

Furthermore, while housing explained a significant portion of spatial variation in first-birth rates, it did account for less urban-rural variation in the levels of second births and little variation for third births; one would have expected the opposite if opportunities and constraints had been critical factors.

What then (or what else) explains high third-birth levels in rural areas and small towns? Daily support is particularly important for parents with large families, and grandparents are a primary source in this respect. It is thus possible that higher third-birth rates in rural areas and small towns can be attributed to the better availability of shown that there is not much of difference between the urban and rural areas in this respect;

grandparents are (almost) equally available (or not available) in cities and rural areas (cf. [START_REF] Malmberg | Distance to elderly parents: analyses of Swedish register data[END_REF]. It might also be argued that the inter-generational transmission of fertility explains high third-birth levels in rural areas and small towns: many rural and small-town residents come from families with three children. Again, however, previous studies based on survey data have shown that significant spatial variation in thirdbirth levels remains after controlling for the number of siblings [START_REF] Kulu | Migration and fertility: competing hypotheses re-examined[END_REF]2006). We also controlled for the effect of unmeasured characteristics of women in our further analysis, but this did not change the results (see Model 4 in Table 7). It is thus likely that culturalnormative (contextual) factors account for particularly high third-birth levels in rural areas and small towns as compared to the levels in towns and cities. Rural and small town populations continue to constitute a subculture with a value orientation towards large families.

To sum up, there is evidence that the desired family size in small towns and rural areas is larger than that in urban areas. Further, the rural and small town environment provides opportunities that allow the couples to reach their desired family size in the reality.

In urban areas, in turn, the desired family size is smaller and, in large cities in particular, some couples never reach their desired family size because of the inability to afford (at right time) a 'proper' housing (and status) required for forming a family.

This study has shown significant fertility variation across settlements in a Northern European country. Its novelty lies in its decomposition of urban-rural fertility variation, which revealed that a substantial portion of spatial fertility variation could be attributed to housing conditions and contextual factors. This is a first study to show the importance of housing conditions in urban-rural fertility differences. The role of contextual factors in examine contextual effects on fertility behaviour is to apply multilevel models to data on individuals and their regions of residence [START_REF]Regional social contexts and individual fertility decisions: a multilevel analysis of first and second births in Western Germany[END_REF]. However, while this is an appropriate way to explore spatial fertility variation to its full extent and with all its nuances, it may not be the best way to examine urban-rural fertility variation, which is of a persistent nature and is difficult to explain using conventional contextual characteristics. Another (and perhaps more fruitful way to proceed) would be to interview a sample of (similar) couples living in various settlements to ascertain the socio-spatial context of their childbearing decisions.

Most recent research in the low-fertility contexts examines childbearing dynamics in a country or compares fertility trends in a number of countries [START_REF] Mcdonald | Gender equity in theories of fertility transition[END_REF][START_REF] Kohler H.-P | The emergence of lowest-low fertility in Europe during the 1990s[END_REF][START_REF] Morgan | Is low fertility a twenty-first-century demographic crisis?[END_REF][START_REF] Neyer | Consequences of family policies on childbearing behaviour: effects or artifacts?[END_REF][START_REF] Frejka | Childbearing Trends and Policies in Europe, Demographic Research[END_REF][START_REF] Goldstein | The end of lowest-low fertility?[END_REF][START_REF] Thornton | Sweeping changes in marriage, cohabitation and childbearing in Central and Eastern Europe: new insights from the developmental idealism framework[END_REF]. This study suggests that more attention should be paid to family and fertility dynamics in sub-national units, particularly in large cities were low fertility emerged a few decades ago and has dominated since then (cf. BECKER 1991;[START_REF] Lesthaeghe | From the first to the second demographic transition: an interpretation of the spatial continuity of demographic innovation in France, Belgium and Switzerland[END_REF] for n = 0, 1, 2 ..., where s n+1 is the slope of the linear spline over the interval [t n , t n+1 ]. To compute the linear spline function we thus need to define nodes and estimate from the data constant y 0 and slope parameters s 1 , s 2 , ... . 3 Another possibility to address the issue of endogeneity of housing in the fertility process is to include housing conditions in the analysis as a regional-level variable. This would require of setting up a multilevel model where individuals are nested within regions. However, this specification would allow us to include in the analysis a variable showing the size of settlement / region, but not simultaneously dummies for settlements (or a dummy for the capital city region) and a variable showing housing conditions in the region. For that reason, we decided to conduct a simultaneous analysis of fertility behaviour and housing choices. Notes: For linear splines we present slope estimates which show how the log-hazard increases or decreases over a certain duration; Likelihood ratio test statistic (LR) Model 2 versus Model 1: LR = 871.8, df = 11, p < 0.001; Model 3 versus Model 2: LR = 5.1, df = 1, p < 0.05; Model 4 versus Model 3: LR = 440.9, df = 10, p < 0.001; the likelihood of a simultaneous-equations model was compared to a sum of the likelihoods of models for births and those for housing changes by type.

  , selective migrations and housing conditions explain fertility variation between various settlements and to what extent contextual factors play a role. Our

  to marry because they wish to have children; the decision to begin

  present total fertility rate (TFR) across settlement groups for four Nordic countries: Denmark, Finland, Norway and Sweden in the 1990s and the early 2000s. We see that the TFR has varied significantly across

  ('flats') are housing units in a dwelling that have three or more residential units, with at least one unit being on top of another.

  to various housing types are related; more specifically, the residuals of the three housing equations are correlated. Our simultaneous-equations model offers (some)

  high risk of first birth in rural areas and small towns was thus largely attributed to the fact that detached / semi-detached and terraced houses are dominant housing type there, while in urban areas in Finland (and other Nordic countries), most people live in apartments.

  first-birth levels low in large cities? It could be argued that omitted individual or couple characteristics are the reason; these characteristics might include marital

  critical factor in the Nordic context. Generous maternity leave, the availability of high-quality childcare and flexible work arrangement for parents (in the public sector) should minimise opportunity costs for parents, particularly if they (only) raise one child. Difficulties associated with childcare in a large city because of time and space constraints

  Interestingly, however, recent studies in the Nordic context have

  rural fertility variation needs further investigation. A conventional way to

Figure 1d .

 1d Figure 1d. TFR by Settlement Type in Sweden, 1990-2003. Note: the category of large city regions includes Stockholm and Gothenburg. Source: Calculations based on the population registers of Denmark, Finland, Norway, and Sweden.

  based on Finnish Longitudinal Fertility Register, 1988-2000. Significance: '*'=10%; '**'=5%; '***'=1%.

TABLE 1 ABOUT

 1 HERE

  other) time-varying variables that change continuously. Parameter estimates are thus the slopes for linear splines over user-defined time periods. With sufficient nodes (bend points), a piecewise linear-specification can capture any log-hazard pattern in the data (for further details, see LILLARD and PANIS 2003) 2 . z k (u ik + t)denotes the spline representation of the effect of a time-varying variable that is a continuous function of t with origin u ik (the woman's age, calendar time and union duration for the second and third births). x ij represents the values for a time-constant variable (language), and il (t) represents a time-varying variable whose values can change only at discrete times (place of residence and all other variables).

	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

w

  (t) represent the risk of mth move of individual i to detached housing, terraced housing and apartment in the competing risk framework. ε i B , ε i are person-specific time-invariant residuals for the fertility, moving to detached housing, terraced housing and apartment equations, respectively. The residuals are assumed to follow a multivariate normal distribution with correlations ρ BD , ρ BT , ρ BA , ρ DT , ρ DA and ρ TA . A

	where µ i	B1 (t), µ i	B2 (t), µ i	B3 (t) denote the hazard of the first, second and third birth of individual
	i, respectively, and µ im D (t), µ im T (t), µ im A D ,
	ε i	T and ε i	A
				F o r
					P
					e
					e r
					R
					e
					v i e
					w
					O n l
					y
					)

TABLE 8

 8

	ABOUT HERE

  . Research on childbearing dynamics in large cities would deepen our understanding of the determinants of low fertility in Europe and other industrial countries. Research on fertility dynamics in smaller places, in turn, may lead us to a better understanding of the factors that promote a relatively high fertility in the lowfertility settings. While most researchers assume that selective migrations explain much spatial fertility variation within countries, this study showed that this is not the case. Clearly, We thank Andres Vikat for preparing a command file for calculation of earnings in the Finnish context. The value of the linear spline function between the points (t n , y n ) and (t n+1 , y n+1 ) is computed as follows:

	1 ) ( ) ( 1 n n n t t s y t y -+ = +
	F o r F o r F o r F o r F o r F o r F o r F o r
	P P P P P P P P
	e e e e e e e e
	e r e r e r e r e r e r e r e r
	R R R R R R R R
	e e e e e e e e
	v i e v i e v i e v i e v i e v i e v i e v i e
	w w w w w w w w
	O n l O n l O n l O n l O n l O n l O n l O n l
	y y y y y y y y
	residential context matters.
	35

2

Table 1 : Person-years and Births by Place of Residence.

 1

		Person-years		Births
		Number Percent	Number Percent
	First birth
	Capital city	33716.34	34	4494	32
	Other cities	35395.34	36	5228	37
	Towns	19849.82	20	2998	21
	Rural areas and small towns	8980.05	9	1538	11
	Total	97941.56	100	14258	100
	Second birth
	Capital city	15324.76	30	3446	28
	Other cities	18705.52	37	4447	37
	Towns	10706.93	21	2648	22
	Rural areas and small towns	5561.81	11	1556	13
	Total	50299.01	100	12097	100
	Third birth
	Capital city	13760.01	27	957	23
	Other cities	18694.41	37	1476	36
	Towns	11451.49	23	970	24
	Rural areas and small towns	6779.79	13	717	17
	Total	50685.70	100	4120	100
	Source: Calculations based on Finnish Longitudinal Fertility Register, 1988-2000.

Table 2 : Relative Risks of Conception Leading to First Birth.

 2

	Place of residence	Model 1	Model 2	Model 3	Model 4
	Capital city	0.88 ***	0.86 ***	0.86 ***	0.89 ***
	Other cities	1	1	1	1
	Towns	1.04 *	1.02	1.02	0.99
	Rural areas and small towns	1.18 ***	1.14 ***	1.14 ***	1.02
	Source: Calculations based on Finnish Longitudinal Fertility Register, 1988-2000.
	Significance: '*'=10%; '**'=5%; '***'=1%.
	Model 1: controlled for union duration and the woman's age.
	Model 2: additionally controlled for language, educational level and enrolment, earnings and calendar time.
	Model 3: additionally controlled for migration.
	Model 4: additionally controlled for housing type.

Table 3 : Log-risks of Conception Leading to First Birth.

 3

	Variable	Model 1	Model 2	Model 3	Model 4
	Place of residence
	Capital city	-0.126 ***	-0.151 ***	-0.150 ***	-0.120 ***
	Other cities	0	0	0	0
	Towns	0.042 *	0.024	0.021	-0.007
	Rural areas and small towns	0.167 ***	0.133 ***	0.128 ***	0.018
	Demographic variables
	Union duration (baseline)
	Constant	-2.506 ***	-0.555 **	-0.544 **	-0.902 ***
	0-1 years (slope)	-0.165 ***	-0.172 ***	-0.175 ***	-0.153 ***
	1-3 years (slope)	0.069 ***	0.079 ***	0.078 ***	0.094 ***
	3-5 years (slope)	-0.005	0.002	0.001	0.024
	5+ years (slope)	-0.137 ***	-0.125 ***	-0.125 ***	-0.110 ***
	Age
	-24 years (slope)	0.086 ***	0.050 ***	0.050 ***	0.054 ***
	25-29 years (slope)	0.072 ***	0.045 ***	0.045 ***	0.051 ***
	30-34 years (slope)	-0.072 ***	-0.069 ***	-0.069 ***	-0.072 ***
	35+ years (slope)	-0.270 ***	-0.274 ***	-0.273 ***	-0.288 ***
	Socio-economic variables
	Year
	1988-2000 (slope)		-0.017 ***	-0.017 ***	-0.015 ***
	Language
	Finnish		0	0	0
	Swedish		0.103 **	0.104 **	0.095 **
	Educational enrolment
	Not enrolled		0	0	0
	Enrolled		-0.568 ***	-0.568 ***	-0.570 ***
	Educational level
	Lower secondary		0.109 ***	0.110 ***	0.140 ***
	Upper secondary		0	0	0
	Vocational		0.093 ***	0.092 ***	0.088 ***
	Lower tertiary		0.283 ***	0.281 ***	0.297 ***
	Upper tertiary		0.253 ***	0.249 ***	0.270 ***
	Earnings
	None		-0.394 ***	-0.395 ***	-0.384 ***
	Low		-0.020	-0.022	-0.008
	Medium		0	0	0
	High		0.067 ***	0.067 ***	0.051 **
	Very high		0.106	0.106	0.072
	Migrations
	No migrations			0	0
	One or two migrations			0.090 **	0.014
	Housing conditions
	Housing type
	Detached house				0.377 ***
	Terraced house				0.237 ***
	Apartment				0
	Source: Calculations based on Finnish Longitudinal Fertility Register, 1988-2000.
	Significance: '*'=10%; '**'=5%; '***'=1%.

Table 4 : Relative Risks of Conception Leading to Second Birth.

 4

	Place of residence	Model 1	Model 2	Model 3	Model 4
	Capital city	0.98	0.98	0.98	1.00
	Other cities	1	1	1	1
	Towns	1.02	1.02	1.02	1.00
	Rural areas and small towns	1.15 ***	1.15 ***	1.14 ***	1.09 ***
	Source: Calculations based on Finnish Longitudinal Fertility Register, 1988-2000.
	Significance: '*'=10%; '**'=5%; '***'=1%.
	Model 1: controlled for the age of the first child, union duration and the woman's age.
	Model 2: additionally controlled for language, educational level and enrolment, earnings and calendar time.
	Model 3: additionally controlled for migration.
	Model 4: additionally controlled for housing type.

Table 5 : Log-risks of Conception Leading to Second Birth.

 5

	Variable	Model 1	Model 2	Model 3	Model 4
	Place of residence
	Capital city	-0.020	-0.020	-0.019	-0.002
	Other cities	0	0	0	0
	Towns	0.024	0.022	0.019	-0.005
	Rural areas and small towns	0.143 ***	0.137 ***	0.134 ***	0.088 ***
	Demographic variables
	Time since first birth (baseline)
	Constant	-3.130 ***	-1.968 ***	-1.945 ***	-1.976 ***
	0-1 years (slope)	2.493 ***	2.563 ***	2.561 ***	2.651 ***
	1-3 years (slope)	-0.160 ***	-0.110 ***	-0.113 ***	-0.016
	3-5 years (slope)	-0.298 ***	-0.298 ***	-0.299 ***	-0.292 ***
	5+ years (slope)	-0.089 ***	-0.081 ***	-0.081 ***	-0.089 ***
	Union duration (baseline)
	0-1 years (slope)	-0.108 *	-0.106 *	-0.111 *	-0.031
	1-3 years (slope)	-0.024	-0.028	-0.029	-0.078 ***
	3-5 years (slope)	-0.015	-0.020	-0.020	-0.009
	5+ years (slope)	-0.049 ***	-0.048 ***	-0.048 ***	-0.030 **
	Age
	-24 years (slope)	0.029 ***	-0.008	-0.008	-0.017 *
	25-29 years (slope)	-0.004	-0.024 ***	-0.024 ***	-0.022 ***
	30-34 years (slope)	-0.054 ***	-0.061 ***	-0.061 ***	-0.063 ***
	35+ years (slope)	-0.218 ***	-0.219 ***	-0.219 ***	-0.234 ***
	Socio-economic variables
	Year
	1988-2000 (slope)		-0.009 ***	-0.010 ***	-0.012 ***
	Language
	Finnish		0	0	0
	Swedish		-0.029	-0.029	-0.051
	Educational enrolment
	Not enrolled		0	0	0
	Enrolled		-0.357 ***	-0.361 ***	-0.384 ***
	Educational level
	Lower secondary		-0.218 ***	-0.217 ***	-0.206 ***
	Upper secondary		0	0	0
	Vocational		0.152 ***	0.151 ***	0.164 ***
	Lower tertiary		0.247 ***	0.245 ***	0.262 ***
	Upper tertiary		0.236 ***	0.231 ***	0.249 ***
	Earnings
	None		-0.338 ***	-0.339 ***	-0.334 ***
	Low		0.041 *	0.040 *	0.050 **
	Medium		0	0	0
	High		0.029	0.031	0.019
	Very high		0.175 **	0.175 **	0.151
	Migrations
	No migrations			0	0
	One or two migrations			0.082 **	0.010

Table 6 : Relative Risks of Conception Leading to Third Birth.

 6

	Place of residence	Model 1	Model 2	Model 3	Model 4
	Capital city	0.92 **	0.93 *	0.93 *	0.95
	Other cities	1	1	1	1
	Towns	1.05	1.06	1.05	1.04
	Rural areas and small towns	1.22 ***	1.22 ***	1.21 ***	1.19 ***
	Source: Calculations based on Finnish Longitudinal Fertility Register, 1988-2000.
	Significance: '*'=10%; '**'=5%; '***'=1%.
	Model 1: controlled for the age of the second child, union duration and the woman's age.
	Model 2: additionally controlled for language, educational level and enrolment, earnings and calendar time.
	Model 3: additionally controlled for migration.
	Model 4: additionally controlled for housing type.

Table 7 : Log-risks of Conception Leading to Third Birth.

 7

	Variable	Model 1	Model 2	Model 3	Model 4
	Place of residence
	Capital city	-0.085 **	-0.077 *	-0.072 *	-0.054
	Other cities	0	0	0	0
	Towns	0.047	0.054	0.049	0.039
	Rural areas and small towns	0.201 ***	0.199 ***	0.191 ***	0.174 ***
	Demographic variables
	Time since second birth (baseline)
	Constant	-2.498 ***	-2.676 ***	-2.620 ***	-2.664 ***
	0-1 years (slope)	1.928 ***	1.977 ***	1.965 ***	2.019 ***
	1-3 years (slope)	-0.084 ***	-0.044	-0.049	-0.013
	3-5 years (slope)	0.009	0.004	0.003	0.019
	5+ years (slope)	-0.066 ***	-0.059 ***	-0.059 ***	-0.054 ***
	Union duration (baseline)
	0-1 years (slope)	-0.246 **	-0.249 **	-0.262 **	-0.187 *
	1-3 years (slope)	-0.068 *	-0.074 *	-0.078 **	-0.124 ***
	3-5 years (slope)	-0.168 ***	-0.178 ***	-0.177 ***	-0.207 ***
	5+ years (slope)	-0.060 ***	-0.062 ***	-0.061 ***	-0.056 ***
	Age
	-24 years (slope)	-0.058 **	-0.067 **	-0.068 **	-0.064 **
	25-29 years (slope)	-0.045 ***	-0.059 ***	-0.058 ***	-0.053 ***
	30-34 years (slope)	-0.037 ***	-0.042 ***	-0.041 ***	-0.041 ***
	35+ years (slope)	-0.247 ***	-0.252 ***	-0.251 ***	-0.262 ***
	Socio-economic variables
	Year
	1988-2000 (slope)		0.002	0.002	-0.002
	Language
	Finnish		0	0	0
	Swedish		-0.106	-0.101	-0.110
	Educational enrolment
	Not enrolled		0	0	0
	Enrolled		-0.289 ***	-0.299 ***	-0.301 ***
	Educational level
	Lower secondary		-0.123 ***	-0.123 ***	-0.085 *
	Upper secondary		0	0	0
	Vocational		0.053	0.052	0.050
	Lower tertiary		0.310 ***	0.306 ***	0.322 ***
	Upper tertiary		0.145 **	0.136 **	0.150 **
	Earnings
	None		-0.159 ***	-0.163 ***	-0.150 **
	Low		0.150 ***	0.146 ***	0.149 ***
	Medium		0	0	0
	High		-0.008	-0.010	-0.028
	Very high		0.257 **	0.255 **	0.234 *
	Migrations
	No migrations			0	0
	One or two migrations			0.223 ***	0.140 **

Table 8 : Standard Deviations and Correlations Between Person-specific Residuals (Model 4).

 8

	Standard deviations
	Fertility	0.463 ***
	Move to detached housing	0.590 ***
	Move to terraced housing	0.371 ***
	Move to apartment	0.324 ***
	Correlations
	Fertility and move to detached
	housing	0.339 ***
	Fertility and move to terraced
	housing	0.716 ***
	Fertility and move to apartment	0.536 ***
	Move to detached housing and move
	to terraced housing	0.652 ***
	Move to detached housing and move
	to apartment	0.400 ***
	Move to terraced housing and move
	to apartment	0.486 ***
	Source: Calculations based on Finnish Longitudinal Fertility Register, 1988-2000.
	Significance: '*'=10%; '**'=5%; '***'=1%.

TFR by Settlement Type in Denmark, 1990-2003.

		2.4
	Total Fertility Rate	1.8 2.0 2.2
		1.6
		1.4
		1990	1992	1994	1996	1998	2000	2002
					Year
			Capital city region		City regions
			Towns			Medium-sized towns
			Small towns		Rural areas
		Figure 1b.

TFR by Settlement Type in Finland, 1990-2003.

		2.4
	Total Fertility Rate	1990 1.4 o 1992 r 1.6 F 1.8 2.0 2.2	1994	1996	1998	2000	2002
		P Capital city region Towns e Small towns e r Figure 1c.	Year	City regions Medium-sized towns Rural areas
			R
			e
				v i e
					w
					O n l
						y
				47

TFR by Settlement Type in Norway, 1990-2003.

		2.4
	Total Fertility Rate	1.8 2.0 2.2
		1.6
		1.4
		1990	1992	1994	1996	1998	2000	2002
					Year
			Large city regions		City regions
			Towns			Medium-sized towns
			Small towns		Rural areas

Acknowledgements

I am grateful to two anonymous referees for their valuable comments and suggestion on a previous version of this paper. I would also like to thank Statistics Finland for providing me with the register data used in this study, and Marianne Johnson for valuable suggestions when preparing the data order. The analyses of this study are based on the Statistics Finland Register Data at the Max Planck Institute for Demographic Research (TK-53-1662-05).

Variable


Zsolt Csók

Tamás Kégl

László Párkányi

Ágnes Varga

Sándor Kunsági-Máté

László Kollár

Facile, high yielding

Keywords: Supramolecular chemistry, Host-guest systems, Cavitands, Pi interactions Supramolecular chemistry, Host-guest systems, Cavitands, Pi interactions .manuscriptcentral.com/

published or not. The documents may come

Introduction

The "molecule within a molecule" concept was first introduced by Donald J. Cram. [1] Since then, there has been an ever growing interest in molecular containers having expanded inner cavities capable of housing sizable or multiple guests. Molecular containers are of particular interest in separation science, drug delivery systems, and molecular sensing and recognition. [START_REF] Cram | Container Molecules and their Guests[END_REF] Host molecules are able to shield their guests from the exterior solution, which might cause radical changes in their physical and/or chemical properties. This phenomenon was nicely demonstrated e.g. in the stabilization of short-lived reaction species such as cyclobutadiene. [START_REF] Cram | [END_REF] Furthermore, the encapsulation of guest molecules within an extended cage and subsequent release of the products may result in their use as nanosized reactor chambers. [4] Several synthetic methodologies were developed in order to increase the inner volume of molecular containers. The covalent synthesis of the first closed-surface carcerand and its carceplex [5] has inspired a number of researchers to prepare structurally well-defined container compounds and determine their host-guest binding properties. [6] However, these synthetic procedures mostly involve intricate reaction routes that are frequently combined with low isolated yields, which make their application rather limited. Recently, dynamic covalent chemistry has been effectively utilized to overcome such difficulties. [7] Self- assembly through metal-ligand interactions, van der Waals forces and, mainly, hydrogen bonding also plays an important part in constructing large molecular capsules with increased internal cavities. [8] On the other hand, these non-covalent systems often suffer from relative instability, functional group intolerance and insolubility in organic solvents.

First-generation cavitands [9] based on resorcin [4]arenes [10] are conformationally rigid, bowl-shaped molecules, and thus, are ideal platforms for accommodating small molecules, ions or both. Various synthetic strategies have been developed to produce deepened cavitands with an open-end. The depth of the cavitands was increased either by Suzuki cross-coupling reactions [11] or by bridging the resorcinarene hydroxyl groups with 1,4-diazine derivatives. [12] This latter family of cavitands was developed further into one of the largest synthetic hosts, which are able to complex extended adamantane and pyridine derivatives of up to 19 Å in length. [13] Surprisingly, only a few studies utilize the convenient Williamson etherification on the rim of the cavitand skeleton. [14] Herein, we report a facile, high yielding synthetic procedure and full characterization of a novel family of deepened cavitands.

Results and discussion

Synthetic studies

This series of deepened cavitands was synthesized in four simple, high yielding steps; starting from 2-methylresorcinol and acetaldehyde (Scheme 1). The obtained tetrakis(methyl)resorcin [4]arene [15] (1) was bridged by BrCH 2 Cl (2), [16] and selectively brominated according to Sorrell and Pigge [17] using azobisisobutyronitrile (AIBN) as a catalyst to afford tetrakis(bromomethyl)cavitand (3) in 80% combined yield. Cavitand 3 was then reacted with an excess of various aliphatic alcohols and phenols in the presence of an adequate base to give the corresponding tetrakis(alkoxymethyl) (5, 6, 10) and tetrakis(aryloxymethyl) cavitands (7-9) in high (60-78 %) isolated yields. These reactions proceeded well at room temperature; however, full etherification was only seen at 70 °C after 16 hours. Sodium hydroxide was used to deprotonate phenol derivatives, while K 2 CO 3 was sufficient to carry out the reaction with methanol. Sodium hydride was employed for the preparation of 10. All these cavitands turned out to be pure after performing a simple work-up procedure, except for compound 8 that required further purification. Cavitand 3 was also reacted with PhB(OH) 2 under typical Suzuki-reaction conditions to yield tetrabenzylcavitand (11). The presence of an unidentified minor component made purification by column chromatography inevitable, which dramatically decreased the yield to 24% in this coupling We also describe a simple method for the synthesis of tetrakis(hydroxymethyl)cavitand (4). This key intermediate was previously prepared either by LiAlH 4 reduction of tetraesters [5,18] or by hydrolysis of the tetra(acetoxymethyl)cavitand. [19] Here, we propose NaOH hydrolysis of 3 that affords 4 in excellent yield (81%). Tetrol 4 was employed to synthesize 10 using the easily available benzyl bromide derivative (see Experimental Section, Method B.).

All compounds possess a high degree of symmetry (C 4 ) due to the complete, four-fold etherification, which is reflected in their simple 1 H-NMR spectra. The formation of the alkyl(aryl)oxymethyl cavitands was best followed by the unique downfield shifts of the methylene-spacer (ArCH 2 O) protons (Figure 1). Upon performing the Suzuki cross-coupling reaction, this singlet resonance was upfield shifted to 3.71 ppm in cavitand 11. The chemical shifts of the methyleneoxy-bridge (OCH 2 O) protons are also characteristic; they appear as a sharp pair of doublets indicating the inherent rigidity of the cavitand framework. All signals of the "parent" cavitand skeleton are broadened in CDCl 3 in the 1 H-NMR spectrum of compound 6, while the resonances of the C 12 alkyl chain remain sharp (Figure 1). However, the observed line broadening disappears upon changing the NMR solvent to dmso-d 6 .

Compound 6 bearing long alkyl chains resembles the cavitand obtained by ROMP of caprolactam. [20] The structural assignments of this cavitand family were also confirmed by 1).

Theoretical studies

The geometry of compound 7 was optimized at the PBEPBE/6-31G(d,p) level of theory and the resulting structure is shown in Figure 3. The minimum-energy structure exhibits symmetry very close to C 4 . Most of the computed structural parameters (bond length, bond angles and torsion angles) are in reasonable agreement with the X-ray structure of 7.

The deviation from C 4v symmetry to C 4 is a consequence of the deviation of dihedral angle (C6-C1-C7-O4) from -90° to -77.8° (-76.4° in the X-ray structure). The rotation of the phenoxy groups around the C1-C7 axis (and the analogous carbon-carbon bonds) results in a subtle change in the bond lengths as well as in the natural (NPA) charges of the aromatic rings and the OCH 2 O bridges of the cavitand skeleton. The C-C distances in the aromatic rings are somewhat elongated compared to 1.403 Å in benzene, optimized at the same level of theory as 7.

The main difference between the computed and the experimental structures is the significantly closer arrangement of the four phenoxymethyl groups which can be attributed to weak interactions of the neighbouring rings causing a slight contraction of the C12-C13 bond.

In contrast to the T-shaped π-π interactions described in the literature, [21] where the first ring is oriented towards the center of the second one, these intramolecular interactions can be attributed mainly to the interactions between the inner ortho(or meta)-positioned hydrogen and the ortho (or meta) carbon of the perpendicularly orientated neighbouring ring (see Figure 3). These non-contact distances are estimated to be 3.522 Å and 3.141 Å, respectively.

The molecular graph of 7 (Figure 4) obtained within the framework of the Quantum Theory of Atoms In Molecules (QTAIM) analysis exhibits a cage critical point (CCP) revealing a cage formed by the aromatic rings of the phenoxymethyl substituents. This cage is outlined by the H•••C interactions between the perpendicular rings forming a four-sided wall, and additionally, an upper and a lower plane having one ring critical point (RCP) for each.

Figure 5 shows the Laplacian distribution ∇ 2 ρ(r) in the plane of the T-shaped interaction.

Several other ring structures are predicted within 7 with another CCP in the center of the cavitand backbone. Espinosa and co-workers proposed a simple formula expressing the relationship between the hydrogen bond energy and the local potential energy density V(r) in the bond critical point [22] with the proportionality factor being in volume atomic units:

) ( 2 1 CP HB V E r = (1)
The local potential energy density V(r CP ) can be obtained from the topological parameters using the local form of the virial equation:

) ( 2 ) ( 4 ) ( 2 2 CP CP CP G m V r r r - ∇ = ρ h ( 2
)
where G is the local electronic kinetic energy density.

Using Eq. 1 the interaction energy is estimated to be 0.7 kcal/mol and 1.5 kcal/mol for the C•••H interactions with distances 3.522 Å and 3.141 Å, respectively. Thus, the overall stabilization energy for the T-shaped interactions of the upper aromatic walls is less than 10 kcal/mol; suggesting that an incoming, appropriate guest molecule can enter the cavity with a low activation barrier.

Host-guest complexation studies

As preliminary studies, the host-guest complex formation ability of two deepened cavitand molecules (7 and 8) towards 4-chloro-benzotrifluoride (13) was investigated with photoluminescence (PL) method in chloroform (see Experimental). The Benesi-Hildebrand method combined with the van't Hoff theory was applied to calculate the thermodynamic parameters of the molecular association. The results justified the presence of the host-guest complexes in solution with considerable concentration and possessing 1:1 stoichiometry.

Figure 6 shows the Job's plot of the interaction of host 8 with 13. However, our experiments show significantly different thermodynamics for the complex formation. Although these host -guest interactions associated with almost the same Gibbs free energy changes at room temperature (∆G=-26.8 kJ/mol for 7:13 and ∆G=-27.2 kJ/mol for 8:13, respectively), the enthalpy change is much higher when the complex of 7 is formed (∆H=-36.8 kJ/mol for 7:13

and ∆H=-29.2 kJ/mol for 8:13, respectively). The entropy changes were found to be considerably different (∆S=-33.5 J/K•mol for 7:13 and ∆S=-6.7 J/K•mol for 8:13, respectively). The well-known enthalpy-entropy compensation may be responsible for this unexpected phenomenon, which is probably due to the steric hindrance of the methyl groups located on the upper phenyl rings of compound 8. The stability constants K ass at room- temperature were determined to be 4.9x10 5 dm 3 /mol for 7:13, and 5.8x10 5 dm 3 /mol for 8:13 complexes, respectively.

Conclusions

In sum, Williamson etherification provides easy access to a wide variety of deepened cavitands from readily available, inexpensive alcohols. The synthesized cavitands exhibit great stability and good solubility in most organic solvents. The upper aromatic walls are attached to a rigid cavitand platform through CH 2 , CH 2 O and CH 2 OCH 2 spacers. Hence, this "upper cavity" of the molecule possesses some flexibility, which allows potential guest molecules to enter and to be more or less surrounded by the walls of the host. In this way, the entrapment of guest molecules and their isolation from the bulk medium can be more effective. Theoretical calculations suggest that the formation of a host-guest complex might take place via a small activation barrier. This novel series of deepened cavitands may be useful for complexing electron-poor aromatics, such as nitroaromatics, benzotrifluorides, etc.

due to the presence of a flexible binding pocket with tunable electron-density. Indeed, two of these deepened cavitands (7 and 8) behave as hosts and show the formation of 1:1 complexes with 4-chloro-benzotrifluoride as a guest. Furthermore, cavitand 9, bearing four aryl iodide moieties, may serve as a potential intermediate for further functionalization of this cavitand family, as demonstrated in the synthesis of cavitand 12.

Experimental Section

General procedures and materials

All reagents and solvents were purchased from Aldrich. For the synthesis of 10, THF was distilled from sodium/benzophenone under argon atmosphere, and the reaction was carried out under Ar by using standard Schlenk-techniques. General work-up procedure is as follows: the reaction mixture was partitioned between CH 2 Cl 2 (30 ml) and water (30 ml). The organic phase was separated, and the aqueous phase was extracted with another portion of CH 2 Cl 2 (30 ml). The combined organic phases were washed with water (2x30 ml), dried over MgSO 4 , and evaporated to dryness. The residue was treated with MeOH, and the resulting precipitate was collected by filtration. Data collection: Intensity data were collected on a Rigaku R-Axis Rapid diffractometer with Mo-K a radiation (λ = 0.71075 Å) at room temperature. 46012 reflections were collected of which 1602 were unique, R int = 0.067. Numerical absorption correction [START_REF] Higashi | NUMABS[END_REF] was applied to the data (the minimum and maximum transmission factors were 0.975 and 0.986). The crystals diffract poorly, the resolution of the data is limited to 1 Å.

Structure solution and refinement: The structure was solved with direct methods and refined by anisotropic full-matrix least-squares refinement [START_REF] Sheldrick | [END_REF] on F 2 . Hydrogen positional coordinates were calculated from assumed geometries and were not refined. Difference electron density maps indicate the presence of highly disordered solvent molecules. The SQUEEZE procedure of program PLATON [25] was applied and the solvent-free data were used in further x,1/2-y,z and y,1/2-x,z symmetry operations (Fig. 2).

Synthetic Procedures

Tetrakis(hydroxymethyl)cavitand (4).

To the THF (30 ml) solution of 1 g (

Tetrakis(methoxymethyl)cavitand (5).

To the THF (15 ml) solution of 300 mg (0.31 mmol) of 3 10 ml of MeOH and 689 mg (4.96 mmol) of K 2 CO 3 was added. The reaction mixture was stirred at 70 °C for 16 hours.

General work-up procedure, white solid (m=185 mg, 78%).

Tetrakis(dodecanoxymethyl)cavitand (6).

To the THF (10 ml) solution of 881 mg (4.73 mmol) of 1-dodecanol 5 ml of 0.95 M aqueous NaOH solution was added, and was left stirring for 30 min. This solution was then slowly added to the THF (10 ml) solution of 285 mg (0.3 mmol) of 3. The reaction mixture was stirred at 70 °C for 16 hours. General work-up procedure, white solid (m=249 mg, 60%).

Tetrakis(phenoxymethyl)cavitand (7).

To the THF (10 ml) solution of 200 mg (0.21 mmol) of 3 2 ml of 1M aqueous solution of NaOPh (freshly prepared from phenol and NaOH) was added. The reaction mixture was stirred at 70 °C for 16 hours. General work-up procedure, white solid (m=160 mg, 75%).

F

Tetrakis(4-iodo-phenoxymethyl)cavitand (9).

To the THF (10 ml) solution of 740 mg (3.36 mmol) of 4-iodophenol 10 ml of 0.34 M aqueous NaOH solution was added, and was left stirring for 30 min. This solution was then slowly added to the THF (10 ml) solution of 200 mg (0.21 mmol). The reaction mixture was stirred at 70 °C for 16 hours. General work-up procedure, white solid (m=215 mg, 67%).

Tetrabenzylcavitand (11).

To the toluene (60 ml) solution of 1.04 g (1 mmol) of 3, under Ar atmosphere 12 mg (0.05 mmol) of Pd(OAc) 2 , 28 mg (0.1 mmol) of PPh 3 , 1.15 g (8.3 mmol) of K 2 CO 3 and 760 mg (6.2 mmol) of PhB(OH) 2 was added. The reaction mixture was vigorously stirred at 100°C for 16 hours. After cooling, it was filtered through a layer of Celite, and evaporated to dryness. Column chromatography (silica gel; eluent: benzene/n-hexane=4:1, R f =0.64) yielded the product as white solid (229 mg, 24%).

Tetrakis(4-phenyl-phenoxymethyl)cavitand (12).

To the toluene (20 ml) solution of 380 mg (0.25 mmol) of 9, under Ar atmosphere 2.9 mg (0.013 mmol) of Pd(OAc) 2 , 6.8 mg (0.026 mmol) of PPh

Computational details

The geometry of 7 was calculated without any symmetry constraints using the gradient-corrected exchange functional developed by Perdew, Burke and Ernzerhof in combination with a correlation functional, developed also by the same authors, and denoted as PBEPBE. [26] The 6-31G(d,p) basis set [27] was employed throughout this study. For the stationary point, the Hessian was evaluated in order to characterize the genuine minima (no imaginary frequency). Natural population analysis (NPA) and natural bond orbital (NBO) analysis [28] were performed at the same level of theory as the one used for geometry optimization. For the calculations, the Gaussian 03 suite of programs was used [START_REF] Gaussian | Gaussian[END_REF] . QTAIM (Quantum Theory of Atoms In Molecules) analysis of the wave function was carried out with the AIM2000 software [START_REF] Biegler-König | AIM2000[END_REF] to investigate the electron density of the optimized structure.

Host-guest complexation experiments

The host-guest complex formation ability of two deepened cavitands (7 and 8) towards 4-chloro-benzotrifluoride (13) was investigated with photoluminescence (PL) method in chloroform. Samples containing 10 -4 M of 7 or 8 were prepared for these experiments, and the PL spectra of the host molecules were recorded both in the absence and in the presence of 4chloro-benzotrifluoride as a guest. The concentration of the guest was varied from 1x10 -4 M up to 9x10 -4 M through 1x10 -4 M steps. The samples were excited at 395 nm and the PL peak of the host obtained at 430 nm was used for data evaluation. A highly sensitive Fluorolog τ3 spectrofluorometric system (Jobin-Yvon/SPEX) was used, for data collection; a photon counting method with 0.2 s integration time was applied. Excitation and emission bandwidths were set to 1 nm. 1 mm layer thickness of the fluorescent probes with front face detection was used to eliminate the inner filter effect. The stoichiometry of the formed complexes was checked by the Job's method. The Benesi -Hildebrand method was employed to determine the stability constants at all temperatures. [START_REF] Benesi | [END_REF] The van't Hoff theory was applied to calculate the thermodynamic parameters of the interactions.

F

  9, bearing four aryl iodide moieties, was used to further extend the aromatic walls of the cavity in a Suzuki cross-coupling reaction (Scheme 2). This reaction provided cavitand 12 with a considerably large, hydrophobic pocket in good yield (59%).

  refinement cycles (solvent accessible volume 1309.0 Å 3 , total electron count 162 e). Atoms of the C8...C13 phenyl ring were fitted to a regular hexagon and treated as a rigid group throughout the refinement. 1602 reflections were used for the refinement of 158 parameters (R = 0.1043, wR2 = 0.2403 for all intensity data; R = 0.0798, wR2 = 0.2189 for 1332 [I>2s(I)], GOOF = 1.10). The minimum and maximum final residual electron density was -0.23, 0.18 eÅ -3 . A cavity of 2.34 Å radius is inside the cavitand moiety (the centre of the sphere is at 0.250, 0.250, 0.400). The whole molecule was generated by the 1/2-y,x,z; 1/2-

Figure 1 .

 1 Figure 1. Partial 1 H-NMR spectra of 5-9 and 11, o and x denote the spacer methylene and CHCH 3 protons, respectively (* stands for the residual protons of CH 2 Cl 2 ).

Figure 2 .

 2 Figure 2. a.) Molecular diagram of 7 with the atomic numbering (hydrogen atoms are omitted for clarity). Atomic displacement ellipsoids represent 40% probabilities. b.) Top-view of the molecule. Symmetry generated parts are drawn in green, blue and red colours. Carbon atoms are denoted by bare numbers.

Figure 3 .

 3 Figure 3. Structure of 7 computed at the PBEPBE/6-31G(d,p) level of theory.Selected bond distances are in Å. NPA charges are written in italics.

Figure 4 .

 4 Figure 4. Molecular graph of 7 (top view). The color scheme identifying the critical points is as follows: red for bond critical points (BCPs); yellow for ring critical points (RCPs) and green for cage critical points (CCPs). The nuclear maxima are denoted by larger spheres.

Figure 5 .

 5 Figure 5. Laplacian distribution of 7 illustrating the "T-shaped" interaction between two phenyl rings. Solid lines indicate charge concentrations (∇ 2 ρ(r) <0) whereas

Figure 6 .

 6 Figure 6. Job's plot of the interaction of host 8 with 4-chloro-benzotrifluoride (13).

Scheme 1 .Scheme 2 .Figure 1 .Figure 2 Figure 2 Figure 3 .Figure 3 .Figure 4 .Figure 4 .Figure 5 .Figure 6 .

 12122334456 Scheme 1. Synthetic route for the deepened cavitands.

  1 H and 13 C-NMR spectra were recorded at 25°C in CDCl 3 on a Varian Inova 400 spectrometer at 400.13 MHz and 100.62 MHz, respectively.

	(Bruker Daltonics) in positive ion modes, using a 337 nm pulsed nitrogen laser (accelerating
	voltage: 20.0 kV, matrix: 2,5-dihydroxybenzoic acid).
	4.2. Crystallography
	CCDC-795580 contains the supplementary crystallographic data for this paper. These
	data can be obtained free of charge from The Cambridge Crystallographic Data Centre via
	www.ccdc.cam.ac.uk/data_request/cif.
	Crystal data: C 64 H 56 O 12 ; MW: 1017.09; colourless; block size: 0.37x0.35x0.35 mm;
	tetragonal space group P 4 /ncc (No. 130); a = 15.4744(13) Å; c = 25.423(2) Å; V = 6087.7(9) F r o Å 3 ; Z = 4; D x = 1.110 gcm -3 ; µ = 0.076 mm -1 ; F(000) = 2144.
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

The 1 H and 13 C chemical shifts (δ), reported in parts per million (ppm) downfield, are referenced to residual CHCl 3

(7.26 ppm)

and to the carbon resonance of CDCl 3 (77.00 ppm), respectively. MALDI-TOF spectra were obtained on an Autoflex II TOF/TOF spectrometer

  separated, and the aqueous phase was extracted with another portion of CH 2 Cl 2 (30 ml). The combined organic phases were washed with 0.5% aq. HCl solution (30 ml), water (60 ml) and dried over MgSO 4 . Evaporation of the solvent yielded a light yellow solid (m=600 mg, 81%). 1 H-NMR (CDCl 3 ): 1.77 (d, J=6.9 Hz, 12H, CH 3 CH); 4.44 (d, J=6.8 Hz, 4H, inner of

	OCH 2 O); 4.54 (s, 8H, ArCH 2 O); 5.03 (q, J=6.9 Hz, 4H, CHCH 3 ); 5.91 (d, J=6.8 Hz, 4H, outer
	of OCH 2 O); 7.26 (s, 4H, Ar). 13 C-NMR (CDCl 3 ): 16.02 (CH 3 CH); 31.09 (CH 3 CH); 55.36
	(CH 2 OH); 99.67 (OCH 2 O); 119.61; 126.25; 139.03; 153.10. MS: 735.17 [M+22] + .
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

1.04 mmol) of 3 30 ml of 1M aqueous NaOH solution was added. The reaction mixture was stirred at 70 °C for 48 hours. The reaction mixture was partitioned between CH 2 Cl 2 (60 ml) and water (30 ml). The organic phase was

  was stirred at 70 °C for 16 hours, and it was poured into 30 ml 0.1 N HCl. 30 ml of CH 2 Cl 2 was added, the organic phase was separated, and the aqueous phase was extracted with another portion of CH 2 Cl 2 (30 ml). The combined organic phases were washed with water (2x30 ml), dried over MgSO 4 , and evaporated to dryness. The residue was treated with

	MeOH, and the resulting precipitate was collected by filtration. White solid, m=230 mg
	(69%).
	Method B: To the THF (10 ml) solution of 200 mg (0.28 mmol) of 4 90 mg (2.24
	mmol) of 60% NaH was added, and the mixture was left stirring for 30 min. Then 0.27 ml F (2.24 mmol) of benzyl bromide was slowly added. The reaction mixture was stirred at 70 °C for 16 hours. Work-up as described in Method A. White solid, m=160 mg (53%). o r 1 H-NMR (CDCl 3 ): 1.74 (d, J=7.3 Hz, 12H, CH 3 CH); 4.28 (m, 12H, ArCH 2 O
	overlapped with inner of OCH 2 O); 4.47 (s, 8H, OCH 2 Ph); 5.00 (q, J=7.3 Hz, 4H, CHCH 3 ); P 5.60 (d, J=7.1 Hz, 4H, outer of OCH 2 O); 7.20-7.40 (m, 24H, Ar and Ph). 13 C-NMR (CDCl 3 ): e 16.10 (CH 3 CH); 31.11 (CH 3 CH); 61.72 (ArCH 2 O), 72.85 (OCH 2 Ph), 99.53 (OCH 2 O); e 119.88; 123.84; 127.76; 128.32 (double intensity); 130.09; 138.71; 153.72. MS: 1095.53 r R [M+22] + .
	e
	v i e
	w
	1 H-NMR (CDCl 3 ): 1.81 (d, J=7.4 Hz, 12H, CH 3 CH); 4.59 (d, J=7.3 Hz, 4H, inner of O n l OCH 2 O); 4.86 (s, 8H, ArCH 2 O); 5.07 (q, J=7.4 Hz, 4H, CHCH 3 ); 5.73 (d, J=7.3 Hz, 4H, outer of OCH 2 O); 6.66 (d, J=8.7 Hz, 8H, Ar); 7.38 (s, 4H, Ar); 7.54 (d, J=8.7 Hz, 8H, Ar). 13 C-y
	NMR (CDCl 3 ): 16.13 (CH 3 CH); 31.20 (CH 3 CH); 60.62 (OCH 2 ); 83.30; 99.95 (OCH 2 O);
	116.84; 120.71; 122.31; 138.39; 138.95; 153.93; 158.44. MS: 1542.77 [M+22] + .
	4.3.7. Tetrakis(benzyloxymethyl)cavitand (10).

Method A: To the THF (10 ml) solution of 0.26 ml (2.5 mmol) of benzyl alcohol 100 mg (2.5 mmol) of 60% NaH was added, and the mixture was left stirring for 30 min. Then, THF (10 ml) solution of 300 mg (0.31 mmol) of 3 was slowly added. The reaction mixture

  at 80 °C for 2 days. After cooling, it was filtered through a layer of Celite, and evaporated to dryness. The residue was treated with MeOH, and the resulting precipitate was collected by filtration (195 mg, 59%). 1 H-NMR (CDCl 3 ): 1.85 (d, J=7.4 Hz, 12H, CH 3 CH); 4.73 (d, J=7.3 Hz, 4H, inner of

	OCH 2 O); 4.97 (s, 8H, ArCH 2 Ph); 5.12 (q, J=7.4 Hz, 4H, CHCH 3 ); 5.82 (d, J=7.3 Hz, 4H,
	outer of OCH 2 O); 6.99 (d, J=8.5 Hz, 8H, Ph); 7.27-7.53 (m, 32H, Ar and Ph). 13 C-NMR
	(CD 2 Cl 3 ): 16.20 (CH 3 CH); 31.26 (CH 3 CH); 60.66 (ArCH 2 O); 100.17 (OCH 2 O); 114.89;
	120.62; 122.78; 126.65; 128.17; 128.70; 134.12; 138.95; 140.55; 154.08; 158.25. MS: F r o 1343.41 [M+22] + .
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

3 , 276 mg (2 mmol) of K 2 CO 3 and 183 mg (1.5 mmol) of PhB(OH) 2 was added. The reaction mixture was vigorously stirred

Table 1 .

 1 Characteristic bond distances (Å) and torsion angles (°). Atoms marked with a

	o r
	P
	e
	e r
	R
	e
	v i e
	w
	O n l
	y

Acknowledgments

This work was supported by Science, Please! Research Team on Innovation (SROP-4.2.2/08/1/2008-0011). Z. C. and T. K. thank the Bolyai Grants of the Hungarian Academy of Sciences. The authors also thank to the the Supercomputer Center of the National Information Infrastructure Development (NIIF) Program, and to L. Márk (University of Pécs) for performing the MS experiments.