Survey Responses on Desired Fertility in Patriarchal Societies: Community Norms vs. Individual Views

The paper deals with a problem regularly faced by survey studies of patriarchal communities, i.e. communities with a high authority of senior generations and a low level of women’s autonomy. In such communities, female respondents might give untruthful answers to survey questions in order to fi t norms which are treated as obligatory or highly desirable in the community. The situation causes a "community bias" in survey results. The task of the paper is to show using the example of a survey concerning reproductive behaviour that the expected "community bias" can indeed occur in patriarchal communities. For this purpose, we suggest a relatively simple method of discovering "community bias" and apply this method to the results of a qualitative survey which we conducted in the rural part of the North Caucasus, a region of Russia where patriarchal social norms are quite strong. A characteristic of the North Caucasus which is important for our study is that its village communities, inhabited mainly by Muslims, differ considerably in the degree to which patriarchal norms are preserved there. The central idea of our method is to study the signifi cance of community parameters of patriarchy for individual answers to survey questions. Community parameters are calculated as averages of the individual parameters of women interviewed in the same village community. Multi-level regression models are run for both the actual and the desired number of children, which allow us to distinguish between individual and community effects. In agreement with the "community bias" hypothesis, community characteristics are found to be signifi cant for answers on desired, but not on actual, fertility. Based on this result, some tasks for future research of the "community bias" effect on answers to survey questions concerning reproductive behaviour are suggested.


Introduction
The paper deals with the survey behaviour of respondents to demographic surveys undertaken in communities with strong patriarchal family norms. By patriarchy, following, Lerch (2013), Szołtysek et al. (2017), we mean strict asymmetries of gender and generation roles in a family, which support the subordinate position of women and the empowerment of elder generations over younger generations (see section 2.1 for a more detailed treatment of the concept of patriarchy). In patriarchal communities, there are special reasons to assume that respondents to a survey will avoid expressing attitudes to some family matters if their attitudes fail to align with those prevailing in the community to which they belong. This tendency will be called "community bias" in this paper (see Krumpal 2013 for a general overview on literature on social desirability and community bias in answering survey questions, Milewski and Otto 2017 for social desirability of survey behaviour of international migrants, and section 2.1 for further details on this concept). We give empirical evidence that "community bias" is indeed observed in survey answers at least to one demographically important question, which concerns women's desired fertility. Although no studies concentrating on the relation between patriarchy and "community bias" are known to us, there are special reasons to expect this bias in patriarchal communities. It has been shown that if the power of the elderly is present in a community, family behaviour is one of the most probable objects of infl uence of elder generations, so that adherence to behaviour patterns imposed by elders becomes a kind of social duty (Mason 2001;Kaser 2008). In this context, it may be socially undesirable for a respondent to report facts of his/her family life or his/her attitudes to family issues when they contradict patterns approved by elders. Also, strict gender hierarchies and the subordinate position of women in patriarchal communities may put special constraints on the survey behaviour of women, making it especially diffi cult for them to give answers which do not fi t attitudes and values accepted in the community. A considerable number of studies have shown that strong generation and gender asymmetries of power can infl uence actual fertility behaviour, being related to a higher number of children or the mother's younger age at birth (cf. Dyson/Moore 1983and Malhotra et al. 1995for India, Lerch 2013 for Albania, Dommaraju/Agadjanian 2008 for some countries of Central Asia, and some others). If patriarchal norms in a community can be strong enough to infl uence actual family behaviour, it is quite natural also to expect that they can prevent a respondent to a survey from reporting something that does not align with those norms. In this case respondents may be caused to give untruthful answers. Our paper attempts to check this expectation. We study signifi cance of community parameters of patriarchy for individual answers to survey questions. Expressed in most general terms, the central idea behind our analysis is that the signifi cance of community parameters is an indicator of possible "community bias".
For our study, we have chosen a society where the level of patriarchy has been reported by existing studies to differ from one village community to another. As an example of a region with such variety, we take the rural part of the North Caucasus, an area of Russia mainly inhabited by indigenous peoples of Muslim origin (see sec-tion 2.2 for some characteristics of that region). We analyse the results of a survey of women of reproductive age which we conducted in this area in 2016. The analysis has shown a signifi cant positive relation of community patriarchy to desired fertility and a weaker relation to actual fertility. We give reasons why this difference between desired and actual fertility supports the view that "community" bias takes place during the survey.
The paper is organised as follows. In section 2.1, the concept of social desirability for survey answers is outlined. In this section, we also discuss the parameters which we use as indicators of patriarchy of a community, and explain why we expect that respondents in patriarchal communities are likely to give untruthful answers regarding desired fertility. In section 2.2, we introduce the area in which our study was undertaken. In section 3, we present our hypotheses, section 4 contains data and a method description, and section 5 demonstrates the results of the models. Section 6 discusses the results and suggests some goals for future research.

Theoretical and methodological assumptions a) Sensitivity of survey questions
The sensitivity of a survey question which can lead to a bias in survey results can originate from different sources. Tourangeau and Yan (2007) indicate three major sources of sensitivity. First, a question can be sensitive when it touches upon items which are too private or taboo in the respondent's culture (such questions are also termed "intrusive"). In the case of "intrusive" questions, it is expected that the proportion of respondents who refuse to answer them is too high and therefore the subgroup of those providing an answer is too "selective" to be representative of the whole population. Second, a question can be sensitive due to a "threat of disclosure". In that case, the respondent acknowledges the risk that a truthful answer to a question concerning some aspect of his/her private life could become known to somebody outside the survey setting and this could cause harm, such as job loss, family upset or even prosecution. Third, a question can be sensitive when a respondent perceives a particular answer to the question as socially desirable, and some other answer(s) as socially undesirable. A socially undesirable answer reports some attitude or behaviour of a respondent which violates certain norms existing in the society. Due to this violation, a respondent may either refuse to answer or give an untruthful answer when the truthful one is considered to be socially undesirable. Discussing the concept of social desirability, Randall and Fernandes (1991) show that two sub-dimensions of this concept can be distinguished. One sub-dimension refers to social desirability as a stable personality characteristic, such as a constant need of a person for social approval and impression management. The second subdimension refers to social desirability as an item characteristic, considering various activities or attitudes to be socially undesirable for someone in a society. In other words, the former sub-dimension concerns a way of regular survey behaviour of respondents, whereas the latter concerns behaviour expected from a potentially broad number of respondents answering only certain questions. Another important expectation regarding social desirability is that the tendency to give socially desirable responses may vary across cultural orientations. It is more probable in collectivistic cultures, as they emphasise good relationships with other group members and thus strengthen the risks of a negative outcome of reporting a socially undesired attitude (Lalwani et al. 2006). b) The concept of patriarchy and its measurement Following Szołtysek et al. (2017) and Lerch (2013) to a large extent, we take two characteristics -unequal gender relations and power of senior generations -as the key characteristics of a patriarchal organisation of a society. 1 As indicators of gender hierarchies in a society, parameters can be considered which show to what extent women's activities outside the family and household are restricted by social norms. Such parameters are often considered among indicators of women's autonomy in a society (Morgan et al. 2002;Agarwala/Lynch 2006). Of a broad range of indicators of women's autonomy suggested in the aforementioned studies, in the present study we use parameters concerning women's studies after graduating from a secondary school and having a job outside the household. Both obtaining post-school education and taking a job are not expected to be common in a society in which a strict gender hierarchy that does not support women's extra-family activities is active. 2 Therefore, despite the fact that women's autonomy and patriarchy are quite separate concepts in current sociological literature, restriction on women's access to education and work outside the household are obvious indicators of gender asymmetries and therefore also of patriarchy under the defi nition above. It should be noted that the two parameters which we use are by far not the only ones suggested for detecting gender hierarchies. Thus, Morgan et al. (2002) suggest a much broader list of indicators of what they call woman's autonomy. These indicators cover several aspects of a (married) woman's position in her family, including freedom of physical movement without her husband's permission, a wife's say in economic decisions in the family, and control upon the woman exercised by her 1 In Malhotra et al. (1995) patrilineal transmission of status and property is acknowledged as another characteristic of patriarchy. We do not discuss this in the present study, nor do we discuss one other characteristic suggested by Szołtysek et al. (2017), namely son preference. Anthropological studies mentioned in section 2.2 report patrilineal transmission as almost ubiquitous in the regions under study, with the result that this parameter was not expected to produce signifi cant community differences. As far as son preference is concerned, measuring its "actual" level was hardly possible in our study, as it would probably require data on sex selectivity in abortions, which is not available for village communities of the North Caucasus. 2 In some societies even a lower level of women's education can be considered as a violation of patriarchal norms. We consider as such only education continued after secondary school because in the society we are dealing with in our study, completing secondary school is almost obligatory (see section 2.2).
husband. However, we use the education and labour parameters as the most "objective" ones, as the other parameters mentioned may be more dependent upon the woman's own assessment of her situation in the family and can thus themselves be biased.
As far as the generational hierarchies are concerned, we use arranged marriage as their key indicator. It has been argued in many studies that parental arrangement of marriage, or at least active parental involvement in children's marriage, is characteristic of societies where senior generations are empowered by a high degree of control over younger generations. Specifi cally, many scholars relate arranged marriage to patriarchy in Muslim societies (see e.g. Moghadam 2004;Cohen/Savaya 2003). Although it is widely assumed that arranged marriage will be gradually abandoned in the process of social modernisation, a number of studies demonstrate that arranged marriage may persist in some societies, even despite urbanisation and loss of the traditional economy (see Bekker et al. 1996 for Muslim migrants in the Netherlands and Zang 2008 for ethnic Uyghurs in a Chinese city).
An important reservation should be made here that we do not treat arranged marriage as an obligatory characteristic of patriarchy. Some recent studies have shown that frequency of arranged marriages may be related to rather complex conditions in different Muslim societies (see Hamel et al. 2012;Milewski/Huschek 2015;van Zantvliet et al. 2014). However, the complex distribution of arranged marriages across societies does not preclude its treatment as an indicator of empowerment of elder generations in those contexts where arranged marriage is present. Also, it must be noted that at least for some societies where arranged marriage has been studied, it has been shown that the arrangement of a marriage is more typical of parents of young women than of men (Zang 2008 for Uyghurs). Given this, arranged marriage can be an indicator not only of generational hierarchies but also of gender hierarchies. However, even when it is restricted to marrying women, it signals authority of senior generations for whom taking decisions for their daughters is culturally acceptable.
In our study, we therefore use three indicators of patriarchy: (1) low acceptability for women to get an education beyond a level which is considered obligatory; (2) low acceptability for women to have a job; (3) high acceptability of arranged marriages.

c) Measurements of community patriarchy
Since our study concerns respondents' behaviour in patriarchal communities, we need some procedure to measure community patriarchy. The procedure we suggest seems to be the most straightforward one, as it treats indicators of community patriarchy as proportions of respondents with a given characteristic in a community. Given the set of patriarchy indicators introduced above, this would be the proportion of women who have not studied after graduating from secondary school, the proportion of women not working outside the household, and the proportion of women whose marriage was arranged. Note that average characteristics of some communities or areas have been applied as explanatory parameters in several stud-ies dealing with the relation between family organisation and fertility. Thus, Lerch (2013) considers some municipally specifi c indicators for Albania, including women's average age at marriage and percentages of economically active women in relation to fertility. Malhotra et al. (1995) study the relation between average patriarchy parameters and total fertility rates for regions of India. Balk (1994) considers the relation between a woman's fertility and the average of some parameters of women's status calculated for the village that she comes from.
To calculate community parameters in the proposed way, we need to defi ne the limits of communities. Given that our survey was undertaken only in the rural part of the North Caucasus, we will consider each rural settlement (village) covered by the survey as a separate community. This seems justifi ed because, as will be pointed out in section 2.2, in the region under study rural settlements, even close to one another geographically, may differ from one another in family norms.

d) Desired fertility: the concept and its problems
In our study we follow the well-known distinction between desired and intended fertility. By desired fertility, following McCleland (1983), we understand "the number of children parents would have if there were no subjective or economic problems involved in regulating fertility". Under intended fertility we understand a decision to have a certain number of births. In the infl uential Traits -Desire -Intentions -Behaviour theoretical framework of reproduction (Miller 2011), the desire and intentions correspond to different "steps" of the sequential process that begins from non-conscious motivational dispositions (traits) and ends up with actual fertility behaviour. Problems with distinguishing between desired and intended fertility in survey data are often acknowledged. For example, Hayford and Agadjanian (2012) point out that "demographic surveys rarely collect prospective measures of both intentions and desires and frequently use 'intentions' as a general term to refer to both concepts" (see also Kodzi et al. 2010). In the survey designed for our study, the question of desired fertility was put in a way which made it as separate as possible from the reproductive intentions of respondents, with respondents being asked about the number of children they "generally would like to have" (rather than "plans to have", "agreed to have with the spouse"). In this way an attempt was made to disconnect the question from any practical context and inquire about the number of children the respondent would consider the best one based on values and attitudes rather than relevant circumstances.
Studies of survey answers about desired fertility have shown that they tend to change over time for the same respondent depending upon age and current number of children (see e.g. Williams/Abma 2000). In our analysis below, we at least partly deal with this issue by controlling for age and parity of respondents. Another important observation on survey answers regarding desired fertility is that desired fertility stated by a woman in a survey can often have a certain dependency on her husband's views on reproduction, especially in male-dominated cultures (see e.g. Oyediran 2006). Since only female respondents were involved in our survey, we could not directly control for potential spousal infl uence upon a woman's desired fertility. In this way, our study is limited in that it cannot discover possible "family internal" mechanisms affecting women's answers on desired fertility. We limit our study to the relation of those answers to community parameters and leave open the question about possible ways in which this relation is implemented at "family internal" level (e.g. whether it is the case that fertility views dominant in a community infl uence women's survey answers on desired fertility more through their husbands or more in a direct way).

Regional characteristics
We have chosen the North Caucasus, a region in the southern part of Russia bordering with Azerbaijan and Georgia, for a fi eld study assessing the "community bias" in answers to sensitive questions in a patriarchal society. The North Caucasus comprises seven republics within Russia, situated to the north of the Caucasus mountain chain between the Black Sea and the Caspian Lake. Its total population is about seven million people, the largest republic in terms of population being Daghestan, situated in the most eastern part of the North Caucasus, and the smallest republic being Adyghea in the most western part of North Caucasus. Most of the republics are inhabited both by ethnic Russians and indigenous local peoples, but the proportion between the former and the latter varies from one republic to the other, ranging from 2 percent of ethnic Russians in the Republics of Chechnya and Ingushetia to 67 percent in the Republic of Adyghea according to the 2010 Russian population census. However, indigenous peoples form the majority in all the republics of North Caucasus except Adyghea.
In post-Soviet times, the North Caucasus has experienced a deep economic crisis and a serious political destabilisation which included a rise of inter-ethnic violence and a long-lasting war in Chechnya. Beginning in the 2000s, there has been some revival of the local economy, based mainly on subsidies from the Russian federal budget, and the political situation appears to have quietened. However, the population of the North Caucasus still has lower average incomes than the population of Russia as a whole, and registered unemployment in the republics of the North Caucasus is considerably higher than in the rest of the country (Zubarevich 2011).
Indigenous peoples of the North Caucasus are mostly Muslims (apart from Ossetians who make up 64.5 percent of the overall approx. 700,000 residents of the Republic of North Ossetia according to the 2010 Russian population census; among these people there is a considerable proportion of Christians, more than 50 percent according to some assessments; see Filatov/Lunkin 2002 for an overview of the religious situation in the North Caucasus). Local Muslim peoples adopted the Islamic religion at different historical points between the 10th and 19th centuries. Almost only Sunni Islam is present in the region. Following atheistic pressure in the time of the USSR (1930s -early 1980s), a revival of Islam has been observed in the North Caucasus since the 1990s, when freedom of religion "returned". Although the religious revival took place in all the republics, its intensity was remarkably higher in the North-East Caucasus (Republics of Daghestan, Chechnya and Ingushetia) com-pared to the North-West Caucasus (Republics of North Ossetia, Kabardino-Balkaria, Karachay-Cherkessia and Adyghea). One possible reason for these contrasts is that in the North-East Caucasus the Islamic tradition had a longer pre-Soviet history and was to some extent preserved "underground" during Soviet times. The intensive islamisation of the North-East Caucasus was indicated by an increase in the proportion of people observing Islamic norms and by a temporary revival of religious institutions such as informal Sharia courts (Kazenin 2017). At the same time, differences in religiosity are currently observed not just between republics but also between communities in the same republic. For example, it is quite common that rural settlements, even though geographically close to one another, differ considerably in the proportion of residents who attend the mosque and in the actual infl uence of religious leaders in public life (on the variety of religious contexts within one republic of the North Caucasus, Daghestan, see Ware/Kisriev 2000). Considerable differences in informal norms that dominate community life are also reported for rural settlements (ways of confl ict resolution etc.).
At the same time, the North Caucasus has recently experienced considerable changes in its overall social organisation, but such changes were neither of the same intensity nor occurred synchronously in all republics. Intensive urbanisation

Fig. 1:
Location map including villages Note: The map was created with QGIS 2.18 version package using the Layer Russia_ geojson_wgs84, from the resource. Note that location of the villages was added to the map by the authors.
Source: Own design in the republics of the North-West Caucasus took place as early as the 1960-1970s, whereas in the North-East Caucasus its peak was reached only in the 1990s (for details on rural-to-urban migration in the North Caucasus, see Eldarov et al. 2007;Belozerov 2004). As argued by anthropologists studying the region, rather tight relations between members of rural communities are preserved in the North Caucasus despite intensive out-migration processes in many rural communities (see Karpov/ Kapustina 2011 for a comprehensive analysis of qualitative fi eld data on family and community norms and their dynamics in the recent decades in the North Caucasus). This is manifested, for example, in a high proportion of marriages between members of the same rural community, preferences of many people to maintain business relations with members of their rural community even in the case of outmigration, and regular informal meetings of elder community members where decisions on various aspects of life of the community are taken. Anthropological studies on the North Caucasus have also revealed that patriarchal norms are generally well preserved there, but with noticeable local differences (Molodikova/Watt 2014). One generalisation that available qualitative surveys permit is that in the North-East Caucasus women's autonomy is lower overall and the authority of senior generations is higher than in the North-West Caucasus. However, the qualitative studies summarised in Karpov/Kapustina 2011 as well as our own unpublished fi eld data suggest a large amount of evidence that even village communities in the same region differ in terms of patriarchal characteristics. Specifi cally, village communities may be very different in the proportion of women having a job outside the household, in the average educational level of women and in the frequency of arranged marriages. Qualitative surveys have discovered villages that are geographically close to one another but differ considerably with regard to these parameters. To conclude, the North Caucasus is a region where relations between members of rural communities generally remain tight, and elements of patriarchy are observed in the rural communities, although to different degrees from one community to another. This makes the region an adequate case for studying "community bias" in answers to sensitive survey questions. Given that the "community bias" is expected in patriarchal communities, the North Caucasus gives an opportunity to measure it in communities with different degrees of patriarchy.
Republics of the North Caucasus differ considerably in their current fertility. The differences are especially marked between republics of the North-East Caucasus (Daghestan, Chechnya, and Ingushetia) and those of the North-West Caucasus (North Ossetia, Kabardino-Balkaria, Karachay-Cherkessia, and Adyghea). In the rural part of the North-West Caucasus, which is the object of our study, fertility has been below the reproduction level (2.2) for more than two decades, whereas in the North-East Caucasus current rural fertility is still well above that level. It can be concluded that the First Demographic Transition has been completed in the rural part of the North-West Caucasus (as in most other parts of Russia) but not of the North-East Caucasus, where signs of the First Demographic Transition stalling are currently observed (Kazenin/Kozlov 2016). 3

The hypotheses
We now turn to the hypotheses which we expect to be confi rmed if "community bias" induced by patriarchy is observed in the survey results. We hypothesise that survey answers by women to questions about desired fertility are infl uenced by the degree of patriarchy in the communities to which respondents belong. There are clear reasons to assume that in a patriarchal society a woman may consider it socially undesirable to report her intention to have a number of children which is perceived as low in that society. Strong gender asymmetries make children a woman's main reason to constitute her own social status in a society where such asymmetries are active (see Mason 2001;Folbre 1983). Disclosing a low desired number of children may make a woman an outsider among her relatives and neighbours. This is highly expected particularly when an inclination by women towards education and career is not welcomed in the society. Besides, the power of senior generations in patriarchal communities often results in the intensive imposition of the family life norms of elder generations on younger generations. This can also cause a woman to follow the opinions of her senior family members, neighbours and other community members rather than her own opinion when she answers survey questions on family life. The reason why we have chosen answers to the question on desired fertility for our analysis is exactly the expectation that in patriarchal communities "community bias" can be substantial in answers to that question.
As mentioned above, to measure community patriarchy we use the percentages of women in a community with education higher than secondary school, of women with a job, and of women whose marriage was arranged. Our fi rst hypothesis will be confi rmed if these percentages have a signifi cant negative relation to the desired number of children reported by a woman. Furthermore, if the community characteristics infl uence answers to survey questions on desired fertility, we expect that their infl uence will not depend on the respective personal characteristics of respondents as regards the woman's personal education, job experience and parental role in her marriage. Therefore, we additionally hypothesise that the community parameters will remain signifi cant even when these personal parameters of the respondent women are included in the model. However, discovering a relation between answers about desired fertility to the community characteristics of patriarchy does not allow us to distinguish between two distinct scenarios which could underlie that relation. One is the scenario we argue for, where a woman may give untruthful answers on the number of children she wants to have because of the social undesirability of having too few children in a patriarchal community. This scenario fi ts the idea of "community bias". The other scenario, however, is that patriarchal values of a community are adopted by a woman as her own personal values and this increases the number of children she actually wants to have. In this case, answers on desired fertility are related to community patriarchy, but they are not expected to be untruthful, thus providing no reasons to support the existence of "community bias". Note that the possibility of the latter scenario is strengthened by the fi ndings on social interaction as a possible mechanism for community infl uence on fertility behaviour (Bongaarts/Watkins 1996;Montgomery/Casterline 1996;Rossier/Bernardi 2009). According to these fi ndings, gaining knowledge on the fertility values of people from her network and observing their fertility behaviour can cause a woman to adopt the fertility preferences of her community. This scenario cannot be excluded in patriarchal communities, of course.
Although it is hardly possible to completely exclude each of these scenarios in any given study, we suggest an approach which can demonstrate a higher probability of the "community bias" scenario over the scenario of social interaction. This involves a study of the relation of the actual fertility of a woman, apart from the desired fertility she reports, to the patriarchal community parameters. If, via social interaction in her community, a woman adopts patriarchal values in her actual fertility behaviour rather than merely in answering survey questions, she is expected not only to report higher desired fertility but also to adjust her actual fertility to those values. In that case, the community parameters of patriarchy will be signifi cant not just for desired fertility but also for actual fertility. If, however, the patriarchy of a community causes a woman who is a member of the community to give untruthful answers about her desired fertility rather than to actually adopt values of the community in her fertility behaviour, the community parameters of patriarchy are expected to be more signifi cant for desired than for actual fertility.
To conclude, we assume that the "community bias" is probable in survey answers about desired fertility if the following two hypotheses are borne out: Hypothesis 1: Level of community patriarchy is positively related to the reported desired number of children.
Hypothesis 2: Level of community patriarchy is insignifi cant for the actual number of children or is less signifi cant than for the desired number of children.

4
The data and methods

The survey
Our study is based on a survey conducted among married women aged 16-39 in the North Caucasus region between June and December 2016 and covered a to-tal of 1555 women in the respective age group. We limited the survey to married women because the gender hierarchy, an essential component of patriarchy, mainly concerns the position of women in marriage. Besides, one of the key indicators of patriarchy which we apply − i.e. arranged marriage − is defi ned only for women who have ever been married. Before we proceed with the characteristics of the survey, a general note addressing the survey designed for our particular study is needed. Obviously, another possibility for studying "community bias" in survey answers was to use existing country-level sample surveys like the DHS or MICS. The majority of such surveys randomly choose primary sampling units which include households located close to one another. Moreover, studies exist which, similar to the analysis proposed in this paper, measure certain characteristics of DHS sampling units as averages of some individual parameter (e.g. years spent in school) for women of that unit, and then consider the signifi cance of such community parameters for individual answers to other questions of the survey (cf. Kravdal 2002). However, we had the following reasons to undertake a separate survey for our study rather than use existing country-level surveys. First, the DHS and other similar surveys usually involve a rather limited number of parameters which are related to gender and generation relations, e.g. they normally do not include information on whether the marriage of a woman was arranged by her elder relatives, which is an important indicator of empowerment of the elder generation in the family. Second, primary sampling units in such surveys do not necessarily correlate with settlements. In our survey, we made rural settlements (villages) survey units (see below for the procedure to select villages for the sample). This solution appears justifi ed at least for the region where rural settlements − even those situated in close proximity to one another − may be very different from one another in terms of culture and norms (see section 2.2).
The survey was undertaken in two regions of the North Caucasus: Daghestan and Karachay-Cherkessia. Daghestan is part of the North-East Caucasus, and Karachay-Cherkessia is part of the North-West Caucasus. As mentioned in section 2.2, the two parts of the North Caucasus differ considerably in current fertility levels. The regions chosen for the survey represent the two contrasting parts of the North Caucasus.
Daghestan (population over 3,085,000 on 1 January 2019 according to Rosstat) is the region in the very eastern part of the North Caucasus. Mountains constitute almost half of its territory and about 25 percent of its population reside there, although migration from the mountains to the valley has been very intensive in the last 3-4 decades, especially migration to the republic's capital Makhachkala (Eldarov et al. 2007). Daghestan is one of the most multi-ethnic regions of Russia: of its approximately 30 indigenous peoples, no single ethnic group constitutes more than 15 percent of the population.
Karachay-Cherkessia (population over 465,500 on 1 January 2019 according to Rosstat) is a region in the east of the North Caucasus. Like in Daghestan, nearly half of its territory lies in the mountains, but a large part of its mountains is almost depopulated. Migration to the valley and to local towns was already intensive during the Soviet time. Karachay-Cherkessia has a higher proportion of Russian popula-tion compared to Daghestan (31.6 percent according to the Russian census 2010 compared to 5 percent in Daghestan). Apart from Russians, major peoples are Karachays (38.5 percent in 2010) and Circassians (11 percent in 2010). Several ethnic minorities related to one of these peoples are also present in the region.
The survey was conducted face-to-face in rural settlements in the two republics. The survey was undertaken in Russian (despite the wide linguistic diversity of the North Caucasus, Russian is known by most of its population along with native languages). Women were interviewed in privacy by trained residents of their region, but not of their communities. The survey questions mainly concerned items on women's biography (date and place of birth, education, job experience, migration history) and marital/reproductive behaviour (current marital status, number of children, age at marriage and at child birth, desired number of children), as well as woman's personal religiosity (performing daily prayer, practising fasting, attitude to

Tab: 1:
The descriptive statistics of the villages in the survey Source: Data of the survey practices prescribed or prohibited by Islam) and cultural characteristics of her family (as an indicator of the authority of senior generations in their families, women were asked whether they took the decision to get married on their own or whether the marriage was arranged by their senior relatives). Our method of discovering "community bias" used community averages of parameters that indicate patriarchy. Therefore, the number of respondents in each community had to be large enough to obtain statistically signifi cant averages. We included 12 rural communities of Daghestan and 7 of Karachay-Cherkessia in our survey (the higher number of communities from Daghestan corresponds to its higher population). The number of respondents in each community varied between 25 and 125 depending on the number of residents, which ranges from about 800 to 5000. In each republic, rural settlements were selected randomly within three geographical zones (mountains, foothills, valley). If a zone was multi-ethnic (which was the case for all the zones in Daghestan and for all the zones except the mountains in Karachay-Cherkessia), rural settlements in that zone were divided into groups so that in each of the groups one people constituted the majority (this procedure was possible because most of the villages in the region are mono-ethnic or at least have more than 50 percent of residents of one ethnic origin; the groups were only built for 2-3 major peoples of each area). Then one settlement was randomly chosen from each of those groups. For each geographical zone, the sample of rural settlements included in the study refl ected the ethnic variety which is present in that zone.

Model design
The desired number of children was used as the dependent variable in the fi rst group of models. In the second group of models, the actual number of children was the dependent variable.
According to our theoretical assumptions outlined in section 2.1, we involved two groups of independent variables in the model. One group involved parameters which we treat as indicators of the authority of senior generations in a respondent's family. We use arranged marriage as the indicator of this authority. Answers to two survey questions concerning a woman's marriage were included in the models: whether the woman was acquainted with her future husband before the marriage ceremony and whether it was her own decision to marry that person or a decision of her parents. The second group of independent parameters included indicators of gender hierarchy in the woman's family. Based on our reasoning in section 2.1, we involved answers to questions on the woman's continuation of education after secondary school and on work outside the household as parameters relevant for this issue.
We also included a number of control parameters in our models. These were the woman's age at the time of the survey and her current parity (the former only in the models for desired fertility). Another group of control parameters included the level of wealth of the household to which a woman belongs. It involved a parameter of family wealth (whether a woman reported that incomes of her family are suffi cient for food; for clothing; for purchase of technical items for home use; for purchase of a new car; for purchase of a new house) and a parameter of residence (whether a woman's family lives in their own house, or in a rented house, or owns or rents a fl at). The latter two parameters were insignifi cant in all the models and are therefore not included in the tables for reasons of space.
Each survey question regarding patriarchal norms produced two parameters in the model: the individual one (dichotomic) and the community one. Community parameters were calculated as the mean for the respective individual parameter in a given village community. In this way, each woman included in the sample was ascribed the same number of community parameters as she was ascribed individual parameters.
Missing values in our survey ranged from 5 percent to 10 percent for different questions. We excluded these cases and calculated the models only for those respondents who had answered all the relevant questions (listwise deletion). As Table 2 shows, the question on desired fertility has the highest number of missing answers compared to other questions on which parameters of the model were calculated. Therefore, our fi nal sample includes 1248 respondents for all the models. The descriptive statistics for the sample excluding missing variables is presented in Table 3. The comparison of Table 2 and Table 3 shows that there is almost no difference between the means and dispersion of the variables before and after the exclusion of the missing cases. Source: Data of the survey both, while the desired fertility is higher in Daghestan than in Karachay-Cherkessia. Also Daghestan has higher mean values for the parameters indicating patriarchy. We used linear regression in our models. To assess the effects of individual and community parameters together, we used multi-level regression. We built two-level models and clustered community level (2 nd ) and individual level (1 st ) parameters. The randomisation for the model is used only for the intercept while the slopes are kept fi xed. To test our hypotheses under the limited number of villages included in the analysis (only 19), we used the Markov Chain Monte Carlo (MCMC) estimation with 5,000 iterations for the 2-level model in the statistical package MLwiN2.36. Before applying the MCMC for diagnostic reasons, we used the iterative generalised least squares (IGLS) algorithm.
The general equation for the models is shown in (1): In this equation β 0 is the intercept (or constant in the tables) demonstrating the mean number of children (actual or desired) for all the villages, and β 1 represents the estimation of the individual effect. The β 2 coeffi cient shows the effects of the community mean on the second level. Also, β 3 shows the effect of the control variables listed above. Finally there are components: u i − random effect at the village level and e ij − is the residual error at the respondent level.

Results
The potential of the multi-level analysis for the sample is quite high. For the desired number of children, the Variance Partition Coeffi cient (VPC) that represents the percentage variance explained by the higher level (villages) is 23.6 percent (for more details about VPC, see Leckie/Charlton (2013)). In our case the fi gure can be interpreted as 23.6 percent of the variation in the child preferences between villages, also the Chi-square difference between 2-level and 1-level null-models is 418.66 (p=0.00). The results for the model with the desired number of children as the dependent variable of interest can be found in Table 4. As seen from Table 4, the community education indicator demonstrates a signifi cantly negative effect on the desired number of children in the models where the actual number of children is controlled for. This means that higher education at the community level ceteris paribus leads to a lower desired number of children. By contrast, the individual effect for education demonstrates a positive, but significant only at the 10 percent level relation with the desired number of children. For labour market participation (work), we fi nd no signifi cant effect on desired fertility at both the community and the individual level. If a woman was acquainted with her future husband before the marriage ceremony, desired fertility drops at both the community and the individual level with a 5 percent signifi cance (for the community level we get this relation only in MCMC models). This means that one of the characteristics of arranged marriage, namely lack of acquaintance of future spouses before marriage, is signifi cantly related to higher desired fertility. Parental decision on marriage, another indicator of the marriage being arranged, was not signifi cant for desired fertility neither at the individual nor at the community level. Models that did not control for the actual number of children were also fi tted for desired fertility (Table 4A). Here, most of the effects observed in the models with this control were retained. Specifi cally, the signifi cant effect of community education level persisted, as did the effect of the individual and community level of pre-marriage acquaintance of spouses. In addition, both individual and community levels of women working outside their household were signifi cant without control for actual fertility, being related to lower desired fertility. The community effect, however, was signifi cant only at the 10 percent level. We conclude that the community effects attested with control for actual fertility were confi rmed in models without such control. However, we do not touch upon the possible signifi cance of the community level of women's employment in the discussion below since it was low in the models without the control and non-existent with control for actual fertility.
The results for the actual fertility (number of children) are shown in Table 5. At the individual level there is a very pronounced negative effect of education on the number of children borne by the respondent. By contrast, at the community level the educational parameter was insignifi cant for the actual number of children. The parameter of labour force participation also showed a negative effect at the individual level. At the community level, this parameter also showed a signifi cant negative effect, but only in the regressions without the education variable. Among the indicators of arranged marriage, only the parental decision on marriage was signifi cant at the individual level for actual fertility. None of the indicators of arranged marriage was signifi cant at the community level in the models analysing actual fertility. 4 The models were checked for possible bias created by difference between the means calculated for the sampled respondents from a community and the means for all women in that community. The possibility of such bias is considered by Kravdal 2006 who shows that in studying community effects on fertility behaviour there is always a risk that the average of some parameter calculated for sample members in a particular community differs from the "true" average for that community. This of course could result in biased assessments of community effects on fertility. The same could be expected for community effects on survey behaviour as well. Having analysed simulations based on large-scale sample studies from sub-Saharan Africa, Kravdal argues for some conditions under which the risk of this bias can be considered as non-serious in studies of community effects ("not higher than about 10 percent", in his assessment). He puts forward two conditions for this. First, the number of respondents coming from each community should not be less than 25. Second, the intra-class correlation (ICC) for the variables for which the community effects are studied should not be lower than 0.2. The ICC is defi ned as the betweencommunity variance of a variable divided by its total variance. In order to study the possibility of this kind of bias for our models, we have calculated the ICCs for the models with the community parameters considered above. They are shown in the bottom lines of Tables 3 and 4. In the models for the desired number of children, the ICCs range between 0.189 and 0.280, being above 0.2 and thus meeting Kravdal's condition in 7 of 10 models. For models with actual fertility as the dependent parameter, the ICCs were lower than 0.2 in all the models, thus violating Kravdal's condition. As far as sample sizes for communities are concerned, they were all between 25 and 125 and thus were higher than Kravdal's level of 25 persons in each community. It therefore transpires that, following Kravdal's guidance, the effect of possible difference between sample and "true" community variables is not critical for desired fertility, but can be more serious for actual fertility in our study. Given that the community effect which we have identifi ed was more signifi cant and consistent for desired fertility than for actual fertility anyway, the tests suggested by Kravdal do not seem to undermine the results of our analysis.

Discussion
Our analysis suggests that "community bias" can be real in survey answers to sensitive questions and that it can correlate with community patriarchy.
With the example of a survey we have seen that parameters which indicate the level of patriarchy of the village to which a respondent belongs may indeed have a signifi cant infl uence upon answers to sensitive questions in such surveys. Moreover, for some parameters of patriarchy the signifi cance at the community level is higher than at the individual level, also when both the individual and the community level parameters are included in the model. At the same time, we have seen that the signifi cance of the community parameters for actual fertility is much lower in the case of our survey. This therefore confi rms both hypotheses which we expected to be true if "community bias" really exists in the survey which we study. Our fi ndings also imply that community and individual preferences may be of independent signifi cance for respondents' answers to sensitive questions. Finally, we have seen that particular parameters of community patriarchy may infl uence answers to sensitive questions to different degrees.
Among the parameters which we treat as indicators of gender hierarchies, desired fertility has been shown to have a strong negative correlation to post-school education. Under our assumptions, this means that the less women's education is approved in a village community where a respondent lives, the higher the desired number of children reported by that respondent. Individual parameters concerning women's education are of low signifi cance for desired fertility when included together with community parameters in the models. Community-level labour market involvement also showed signifi cance for desired fertility in one type of the models, but did not outrank the respective individual parameter in its signifi cance.
Among the parameters used as indicators of generational hierarchies, the percentage of women who were personally acquainted with their future husband before the marriage ceremony in the village community is negatively signifi cant for reported desired fertility. The same relation was found for the individual parameter indicating acquaintance of the respondent with her future husband. In this case, therefore, the community and individual parameter are quite similar in how they relate to desired fertility. This means that generational hierarchy operating in the village community and in the family of a particular woman both signifi cantly increase the desired fertility reported by the woman.
Another parameter which we considered as an indicator of arranged marriage − parental decision on respondent's marriage − is not signifi cant for desired fertility at the community level, but has a weak positive signifi cance at the individual level. The insignifi cance of the marriage decision process accepted in a community must be explained against the background of the signifi cance of acquaintance of future spouses before marriage. One possible explanation could suggest that contacts between future spouses are a public matter in a community and fall under community regulations more than marriage decision-making, which is a more family-internal matter. If so, acceptance of premarital acquaintance of future spouses in a village community is a more effective indicator of the prevalence of arranged marriage and hence women's dependency upon elder relatives in that community. It does not then come as a surprise that acquaintance of future spouses is of higher significance for answers to sensitive questions at the community level than parental role in marriage decisions.
Although the results of our analysis agree with the existence of "community bias", an alternative approach must be considered for the parameters concerning women's education. This approach relates a low educational level of women in a village community to poor economic conditions in that community rather than to gender hierarchies in it. Given that parents in today's North Caucasus most often have to pay, either formally or informally, for the post-school education of their children, a low percentage of women receiving post-school education in a village community can be a consequence of poverty rather than of norms accepted in the community. This is in line with the often acknowledged positive relation of higher actual fertility to poverty (see e.g. Birdsall et al. 2001). It is less understandable, however, how desired fertility could be related to individual poverty, especially because, to the best of our knowledge, no relation of this kind has been reported in current studies on desired fertility in different parts of the world. Another question which arises under this approach concerns the discovered community effects on desired fertility, because it does not seem clear how the economic status of the community could infl uence fertility attitudes independently of the individual economic status. Note also that for acquaintance before marriage an explanation viewing it as an indicator of economic conditions rather than of family norms is hardly possible. Therefore, possible "economic" explanations for some of the relations discovered in our analysis cannot substitute the "patriarchy" explanation for all the effects observed.
The different impact of different community parameters on desired fertility points to the need to treat each such parameter separately as a potential determi-nant of "community bias". A goal of future research will be to compare the significance of different community parameters for answers to sensitive questions. This comparison would defi nitely be more reliable when it is based on a set of surveys undertaken in different communities where patriarchal norms are expected.
In addition, an important question for future research would concern conditions under which the patriarchal features of a community have a stronger or weaker effect on community behaviour. It would be important to know whether parameters making a community more or less "closed" from the outer world (such as the level of temporary out-migration of community members, percentage of inter-marriages between community members among all marriages in the community) infl uence "community bias" in answering survey questions.

Summary
In the present paper we have undertaken an analysis of data of a survey which has demonstrated that "community bias" can indeed be observed in survey answers to sensitive survey questions given by women who belong to patriarchal communities. The central idea of the method we used was to consider the relation of answers to such questions both to individual and community indicators of patriarchal family norms. The individual indicators refl ect gender and generational hierarchies operating in the family of a respondent, and the community indicators are calculated as averages of individual parameters for the community (a village, in our case) to which a respondent belongs. On the basis of a survey undertaken among women of reproductive age in a part of Russia where patriarchal family norms are preserved to a large extent, we have shown that individual and community parameters of patriarchy have separate impacts on respondents' answers to sensitive questions. We have calculated multi-level models with answers to selected survey questions as dependent parameters, individual patriarchy parameters (a woman's education, her work experience outside her household, and whether her marriage was arranged by her senior relatives) as independent variables of the personal level and the community means of the same parameters as independent variables of the community level. The signifi cance of the community parameters in the multi-level models points to the possibility that community norms can infl uence the behaviour of respondents when answering sensitive questions. We have seen that the community means are more signifi cant for answers to questions concerning a respondent's attitudes or intentions (desired number of children) than for questions concerning easily verifi able facts (actual number of children). This can be accounted for on the obvious assumption that it is easier to give an untruthful answer to a question of the former than of the latter type. We have also seen that the relative signifi cance of individual mean values and community mean values can vary for different independent parameters. This makes it necessary to study the community effect separately for each parameter for which this effect can be expected. The "community bias" can vary in intensity not just from one survey sample to another, but also for different parameters studied within a single sample.
The suggested directions for future research concern the relative potential of different community level parameters of patriarchy to infl uence the survey behaviour of respondents, creating "community bias".