Working Paper: U.S. Jewish Demographic Projections

Projecting future Jewish demographics in the United States: Whither the Jews? Edieal J. Pinker1

Abstract Drawing upon a recent comprehensive survey of the American Jewish population conducted in 2013 by the Pew Research Center, we estimate the trajectory of the population and its denominational segments, 50 years into the future. Our analysis relies upon estimates of the population in 2013, fertility rates, marriage behaviors, and denominational switching patterns as inputs into a model of population demographics. We project that over the next 50 years, the demographics of U.S. Jews will change dramatically. We project that the share of the population that is Orthodox will rise from 13% to 28%, with their share of the child population reaching 45%. Among Reform and Conservative Jews, the number of 30-69 year-olds is projected to drop by approximately 47% over this period. We also project a slight drop in the total Jewish population followed by a recovery propelled by the growing Orthodox population.

Introduction

The U.S. Jewish community is distinctive in several ways. Unlike other sizeable religious groups in the United States, Jews are also an ethnic group; and unlike almost all other American ethnic groups, Jews are also a religious group. In comparison with their religious and ethnic counterparts, Jews are unusually cohesive with a wide variety of institutions ranging across a diverse array of sectors including the religious, educational, cultural, philanthropic, political and human service domains, as well as a strong relationship with Israel. Marked by a pre- American history of autonomous institutions and communities, Jews lived for centuries socially apart from the larger societies in which they dwelled. There – in Eastern and Central Europe, the Mideast, and other areas of pre- American residence -- they sustained their distinctive religion, culture, language, geography, and economic pursuits, all of which were reinforced by a sense – albeit varying – of mutual separation, if not at times, disdain and outright hostility. Maintaining communal continuity is an ongoing challenge for the Jewish community and is one faced by other minority groups. How does a minority group maintain its distinctiveness while engaging successfully with the society around it? One could in fact argue that many of the benefits that the United States derives from the diversity of its population are dependent upon subgroups being able to maintain their distinctiveness while being fully engaged in society. Jews in the diaspora around the world have, at different times wrestled, with this challenge especially since the 18th century. In broad terms, Jews’ “survivalist ideology” (Glazer 1957) and distinctive group history have left their mark. While, over the last several decades, both Roman Catholics and Mainline Protestants in the U.S. have experienced significant numerical declines and defections (Putnam and Campbell 2010; Pew 2015a), the Jewish

1 School of Management, Yale University. Email: [email protected]

1 population numbers grew by approximately one million – or almost a fifth – from 1990 until 2013 (compare Kosmin et al 1991 with Pew 2013). This growth was due in part to immigration from the FSU and elsewhere, the growth of the Orthodox, and the children of the numerically large baby boom generation (those born between 1946 and 1964). While all late generation European-origin ethnic groups have experienced considerable assimilation -- seen by Herbert Gans as a transition from “twilight” to “darkness“ (Gans 2014; Gans 2015) – Jews have surely maintained social cohesiveness, as well as a notable cultural and political presence. The aforementioned growth indicates clearly that projections about the size and composition of this population requires taking into account standard demographic factors such as migration and fertility in addition to how much Judaism attracts and/or retains members. Indeed, it has been recognized by many researchers of religious groups that projections about the size of religiously affiliated populations require taking into account not just the switching in and out behaviors of the population but the differing fertility rates across religious groups (Skirbekk et al 2010; Scheitle et al 2011; Hout et al 2001). Yet, notwithstanding the historic and contemporary features that distinguish American Jews from comparable religious and ethnic groups in America, several developments point to changes afoot in the socio- demographic size and contours of American Jewry. Both local Jewish community studies (UJA Federation of New York 2013), as well as the Pew Research Center’s 2013 national study, report high rates of intermarriage, that is, Jews marrying non-Jews. Rates are particularly high among the non-Orthodox, which constitutes roughly 90% of the adult population. A high rate of intermarriage certainly influences the identities of offspring, but, as we will demonstrate, the impact of intermarriage on the number and the denominational distribution of American Jewry is mediated by other factors such as fertility. Another important shift has been to lower-than-replacement levels of fertility as reported in prior studies (Pew 2013; Pew 2015b). These demographic trends underscore the large gaps in socio-demographic and religious characteristics between the current 10% of adult Jews who are Orthodox and the vast majority who are not. In light of these and other considerations, this study makes projections into the future about the size, demographic make-up, and denominational distribution of the US Jewish community. We ask, if current trends continue, what will the community look like demographically decades into the future? These kinds of projections are fraught with uncertainty and come with many caveats. However, we will show that many aspects of the projections are quite robust and point to significant changes, assuming recent trends continue, if only approximately. Projected and prospective demographic and denominational changes among American Jews are significant in their own right, and have direct implications for the religious character of the Jewish community as well as its political leanings, a matter of some consequence for the broader society given the significant involvement of American Jews in political and social causes. Moreover, the study of American Jewry may also hold some implications for other religious, cultural and ethnic minorities. Demographic projections require knowledge of an initial state for a population – its size, fertility and mortality rates, as well as rates of migration into and out of the population be it geographically or by way of identity switching (e.g., conversion and apostasy). Our study seeks to not only project the overall Jewish

2 population size, but also that of the major Jewish religious denominations. Consequently, for the purposes of our study, it is also important to know how the critical demographic factors vary across denominations, the rates of transition from one denomination to another, and the impact of marriage with non-Jews. Our primary source for estimates of most of these parameters is respondent data from Pew (2013) based on interviews with 3,475 individuals whom Pew defined as currently self-identified as Jewish.

Relation to other studies This work is very much in the spirit of Hout et al (2001), Skirbekk et al (2010), and Scheitle et al (2011) in combining religious switching behavior with demographic forces to create a projection of a religious group’s population. With the exception of Skirbekk et al (2010) these studies have focused on the much larger Christian denomination populations. Few scholarly projections of the US Jewish population size and characteristics have been undertaken. Most notably, Della Pergola and Rebhun (1999) made projections regarding the Orthodox denomination alone using the 1990 National Jewish Population Study (NJPS) (Kosmin et al 1991). Pew (2015b), Rebhun et al (1990), Della Pergola (2013) and Skirbekk et al (2010) made projections of the entire U.S. Jewish population in the aggregate. Using data from the 1990 NJPS, Della Pergola (2013) carefully spells out the challenges in counting the Jews and in projecting the population into the future. He reviews the main previous data sources and presents a projection to 2020 for the total Jewish population in the US. While valuable and instructive, all of these projections aggregate all Jews without disaggregating by denomination, a critical point of differentiation. In particular, the Orthodox are so different demographically from the other subgroups of the Jewish population that failing to distinguish them as a distinct sub-population yields an imprecise projection of the total population. To be sure, for relatively short-term projections, aggregating Jewish denominations has little impact, especially when the Orthodox population was as small as it was in 1990, comprising just 7% of adult Jews and with an older age profile. However, today the Orthodox population is reaching a critical mass – particularly among children and teenagers -- and is much younger in age distribution than the other groups and has lower a rate of intermarriage and higher rate of inter-generational retention. Accordingly, the Orthodox subgroup must be distinguished in population projections to get a good read on where the US population is heading. Della Pergola and Rebhun (1999) analyze just the Orthodox using the 1990 NJPS data. Based upon their assumptions of fertility and marriage patterns for the Orthodox, which they note differ in significant ways from the other denominations, they make two projections for the Orthodox population in 2020. If the Orthodox have no defections, they project 550,000 Orthodox adults and children in 2020; and if their defections to other denominations remain at the same levels as documented in the 1990 NJPS, then they project 415,000 in 2020. In fact, the Pew (2013) survey points to more than 800,000 Orthodox Jews (adults and children), a large discrepancy owing to many possible deviations from the assumptions in Della Pergola and Rebhun (1999). Our analysis here differs from previous studies in that it makes population projections for different Jewish denomination categories simultaneously and does so in an integrated way that accounts for transitions between denominations and out of Jewish affiliation, taking into account differing patterns of marriage and fertility.

Moreover, our work presents denominational breakdowns by age, both current and projected into the future, and this age-denomination breakdown drives our main results. This undertaking requires deciding how to aggregate the various denominations and how to assign individual respondents to denominations, with choices constrained by the quality of the data and the size of the data set (denomination descriptions appear in S1 Table). Creating too many categories will make the sub-group population estimates less reliable. Therefore, notwithstanding their demographic and cultural differences, we aggregated all the streams of Orthodox Jews (Haredi and Modern) into one group. Similarly, notwithstanding the differences in various measures of Jewish engagement between the Reform and Conservative populations (among them, the much higher rates of intermarriage among the Reform), we aggregated the Conservative and Reform movements – including both synagogue members and non-members -- into one group, Reform/Conservative. Notably, Reform/Conservative differ from the Orthodox not only with respect to their lower levels of observance and in-marriage. In addition, both self-identifying Reform and Conservative Jews, in aggregate, are older than the Orthodox with far fewer children in their households, and even fewer children who are being raised as Jews. Finally, all other respondents who identify as Jewish we classified as Jews of no denomination, although they do include very small numbers who identify as Reconstructionist, Renewal, Secular Humanist, and other very small groups. We also needed to characterize households and those of respondents’ parents by the Jewish and denominational identities to capture the impact of how children are raised on their ultimate adult denominational affiliation. The household types are defined by parental denominations (Orthodox, Reform/Conservative, other) and whether one or both of the parents or spouses are Jewish. The model we use to generate future projections is detailed in the Methods and Materials section below. Briefly, we characterize each adult by their age and denomination affiliation, and each child by age and household type. Each child, depending upon their family environment, will become an adult of one of the three denominational groups with a specific probability we estimate from the Pew (2013) data. Each adult will produce some number of children in a particular family environment at a rate that depends upon the adult’s denomination and marriage behavior.

Summary of main results 1. We project an initial rise in the total Jewish population over the next 10 years, then a decline that bottoms out in approximately 40 years, followed by a steady increase thereafter. 2. Denominations vary considerably in their projected trend lines. The Orthodox rise steadily during the entire period examined (from 2013 to 2063). The Reform and Conservative groups (they are analyzed jointly) drop steadily and significantly, while the number of Jews with No Denomination stays relatively flat and even begins to increase in later years. 3. Although Jews of No Denomination lose many of their number to total assimilation (leaving the Jewish population altogether), they are replenished by defections from the other groups. Eventually the growth in the Orthodox could lead to enough switchers to No Denomination that Orthodox defections sustain the No Denomination segment.

4. The key age group of 30 to 69-year old in the Reform/Conservative denominational segment faces a precipitous decline in the coming decades, with direct implications for these denominations’ congregational members and leaders, both of religious bodies and other institutions where such Jews heavily participate. 5. Among the non-Orthodox, the population dynamics are driven primarily by low birthrates and high intermarriage rates, as well as low retention of Jewish affiliation among children raised in No- Denominational families or single Jewish parent families (the intermarried). 6. The sharp drop in the population of Reform/Conservative, and in particular the 30-69 age group, is to a large degree locked in by the initial age distributions.

Results

Initial populations in 2013 Our primary data source is the raw data from the Pew 2013 study (Pew, 2013) (based on interviews with 3,475 individuals whom Pew defined as currently self-identifying as Jewish). The Pew 2013 data (Pew, 2013) allows for estimates of the number of adults in each denominational group in 10-year age bands as well as an estimate of the number of 18 to 19-year old in each denomination (S2 Table). We estimate the number of children from Pew (2013) based upon the number of children being raised Jewish and non-Jewish reported in each household and the type of household (S3 Table). These are reported in 0-9 and 10-17 age groups to which we append the 18-19 years old populations. We assume that the children are raised in the denomination of their parents and that there is only one adult respondent per household. One challenge is that those children in a household in which the responding parent is “non-married” are typically cases of divorce and we cannot know if we should characterize the environment within which the child is being raised as 1-Jewish parent or 2-Jewish parents. Our approach is to characterize the parentage of the children in the non-married households as 1 or 2 Jewish parents in the same proportions as the children in the married households. We have similar data on children ages 10-17 being raised as non-Jews in the S3 Table. We split 18 to 19-year old across 1 or 2 Jewish parent households in the same proportions as the 10 to 17-year-old and combine them with the children in the S3 Table in the 10-17 age range. Adopted children are accounted for in the initial population through the responses to questions on the number of children in a household. All of these estimates are based upon total population estimates from Pew (2013). We split these into female and male populations using gender ratios from the 2017 National Vital Statistics Report (USCDC 2017). Our model is constructed around the female population and in each age group it is assumed that the number of males corresponds to the female population using the age appropriate gender ratio. Using S2 and S3 Tables as inputs yields, for the initial conditions, a total estimated Jewish population of 6.4 million (5.0 million adults 20 years and older and 1.4 million children under 20 years). In addition, we track 0.3 million children being raised as non-Jews in households with at least one parent who identifies as Jewish. Pew (Pew, 2013) reports 5.3 million Jewish adults and includes 18-19 year olds as adults. Using that definition of

5 adult, we have 5.2 million. The Pew researchers reported 1.0 million children being raised as Jews by religion or no religion, 0.3 million being raised as Jewish and something else, and 0.4 million being raised not Jewish at all for a total of 1.8 million (with rounding) children being raised in a household with at least one Jewish parent. Using our approach to estimate these from their data, we come up with a total of 1.2 million children (age 0-17) being raised Jewish in some way, and 0.3 million children being raised non-Jewish for a total of about 1.5 million. The discrepancy between our estimates and those of Pew (2013) centers around how to count children who are not being raised Jewish at all or together with another religion. These children constitute a population with weak links to the Jewish community so we are not concerned that the difference between our approach and that of Pew (2013) will exert an appreciable impact on long run projections. Fig 1 shows the total population of Jews in ten-year age groupings, split into our three denominational classifications. If we look at the total Jewish population (upper left chart), we see a population bulge in the 50-69 ranges. These are the baby boomers. There is another population bulge in the 20 to 29-year old range; this “boomlet” is an echo of the baby boomers, their offspring.

Age Distribution Total Population Age Distribution Jewish with No Denomination

80-89 280,000 80-89 80,000 70-79 410,000 70-79 120,000 60-69 940,000 60-69 310,000 50-59 1,020,000 50-59 280,000 40-49 710,000 40-49 250,000 30-39 720,000 30-39 320,000 20-29 920,000 20-29 410,000 10-19 640,000 10-19 160,000 0-9 710,000 0-9 170,000

Age Distribution Reform/Conservative Age Distribution Orthodox

80-89 180,000 80-89 20,000 70-79 270,000 70-79 20,000 60-69 580,000 60-69 50,000 50-59 650,000 50-59 90,000 40-49 380,000 40-49 80,000 30-39 280,000 30-39 120,000 20-29 410,000 20-29 100,000 10-19 350,000 10-19 130,000 0-9 310,000 0-9 230,000

Fig 1. Initial populations by age and denomination In contrast with the population as a whole, the graph of the Reform/Conservative (lower left) portrays the boom (age 50-69), but not the boomlet (age 20-39). Where did it go? Looking at the Jews of No-Denomination (upper right), we see the 20 to 29-year old and 30 to 39-year old are unusually numerous relative to the older Jews in this grouping. This pattern suggests that the Reform and Conservative boomer generation see many of their young adult children identifying as No-Denomination rather than Reform or Conservative. To be sure, denominational affiliation among younger adults may be fluid and No-Denomination adult children of Reform/Conservative boomers may yet return to their childhood denominations, particularly when they marry and have children of their own. Nevertheless, at least for adult children under 40 years of age, the results point to significant departure from the two largest denominations outside of Orthodoxy.

Denominational transitions

Within our model, we define denomination transition as moving from the denomination of the household one is raised in to the denomination to which one identifies as an adult. We estimate transition rates based upon the respondents in the 30-49 age group (S4 Table). S4 Table thus gives our estimate of the probability that a child raised in a particular household will grow up to identify as a member of a particular denomination or not Jewish when they become adults forming families. We define the childhood household types by a denomination and whether one or both of the parents are Jewish. This age group (30-49) seems most appropriate to use to estimate denominational transitions because those even older represent behaviors of an earlier time that is likely less relevant to projecting into the future. (For example, Orthodox retention rates have grown over the years in part reflecting increasing levels of ritual observance, residential concentration and of Jewish day school and yeshiva education.) Those aged 18-29 would also be less useful in charting inter-generational transitions in denominational identities, because the vast majority are unmarried and have not yet settled into a denomination, if they ever will. Some definitional choices we made are worthy of mention and some explanation. Some households had a Jewish adult but reported not raising their children as Jewish at all. We did track the children being raised non- Jewish in those households because there was evidence that in the past some children raised in this way came to identify as Jewish in adulthood. Another choice we have made is not to distinguish between matrilineal and patrilineal descent, in contrast with the practice of traditional Jews to recognize only matrilineal descent. In our model, a child born into a family with either parent Jewish – mother or father -- is treated the same way. If they grow up into adults that identify as Jewish, we count them in the Jewish population. Thus, each child, depending upon their family environment, will become an adult of one of the three denominational groups with a specific probability derived from the Pew data. Each adult will produce some number of children in a particular family environment at a rate that depends upon the adult’s denomination (see below). Fertility and household creation rates To derive fertility rates, we used the data on how many Jewish-raised children the 40-49 year old respondents have ever had, as reported in S5 Table by the respondent’s current denomination and marital status. Each cell of the table corresponds to a household type. For example, the Jewish No Denomination respondent who is married to a non-Jewish spouse is creating a household that is, “One Jewish parent no-denomination.” On average, such a person will produce 2.3 children during their life (a seemingly high number reflecting the fact that these are the currently married respondents, in contrast with their age peers who are divorced, never-married, or widowed). Of these 2.3 children, 44% will be raised as having Jewish identity, while 56% will be raised as having no Jewish identity. Therefore, for our purposes, the effective Jewish fertility of such a household will be 1.02, while 1.28 is added to the pool of non-Jewish children we track. The 40-49 age group is more appropriate than younger cohorts to use for completed fertility rates because they have had more time to bear children. Pew (2013) reports completed fertility based upon the 40-59 age group. Upon inspection we found that the 50-59 age group tended to have lower total number of children ever had than the 40-49 age group across denominations and marital status. This suggests this older cohort has different fertility patterns. Therefore, we use the more fertile 40-49 age group

7 to estimate completed fertility looking forward. We do not account for adoption and thus the completed fertility is a slight undercount of the number of new children entering the population.

In S6 Table we report our estimates of the marital status for age groups 30-39 and 40-49. The possible marital status categories are “married to a Jewish spouse,” “married to a non-Jewish spouse,” and “Not married.” Some significant differences differentiate these two age groups. 1) In the No-Denominational and Reform/Conservative groups, the younger cohort has substantially more intermarriage, 2) the younger Reform/Conservative cohort has more unmarried, and 3) the younger Orthodox have many fewer unmarried. All of these differences weaken the potential contribution of the younger cohort of non-Orthodox to the Jewish- identified population relative to the older cohort while at the same time strengthening the contribution of the Orthodox. For our future projections we use the 30-39 age group as the base case as they are more likely to be representative of the behaviors of future Jews and also representative of the behaviors for first marriages. Table S6 reports the aggregate marital statuses rates for men and women combined as well as gender specific marriage and intermarriage rates. To project into the future, we do the following (as an example). For every female who is Reform or Conservative, we say 33% will, at the age 40-49 (S6 Table), be married to a Jewish spouse and will have produced 2.09 (S5 Table) children over her life, approximately 49% of whom are female. This 1.02 girl will be raised in a two-Jewish parent, Reform /Conservative household and will have a 63% chance (S4 Table) of growing up to be Reform/Conservative as well. On the other hand, 31% of the Reform/Conservative females will marry a non-Jewish spouse and will produce 1.70 Jewish children or .83 Jewish girls who are raised in a single- Jewish parent Reform/Conservative household and who will have a 50% chance of growing up Reform/Conservative. We use completed fertility rates based upon respondents in the 40-49 age group. For the 36% who are Not-Married, the fertility rate is much lower (1.03) for obvious reasons. Not- Married people include those who are widowed, divorced, never married, or living with a partner. For the other denominations that report cases of non-Jewish partners/spouses, we use the same approach we did for determining the household environments for the children. We assume that the not-married parents are split between raising children similarly to one versus two Jewish parents in the same proportions as those that are married. Therefore, for the Reform/Conservative not-married person, we assume that the household type the children experience will be Reform/Conservative one-Jewish or two-Jewish parent in the same proportions of intermarriage for the Reform/Conservative people who are married. That is, 33/(33+31) = 52% will be two-Jewish parent, and 48% will be a one-Jewish parent. The fertility rates we use for the non-Orthodox are not far off from the general US population and previous analyses of Jewish demographics. They are below replacement rates. The Orthodox fertility rates are so much higher than the others and this difference is so important to the projections that they deserve some additional discussion. Pew (2013) reports a completed fertility rate of 4.1 for the Orthodox women 40-59. Using the 1990 data from (Kosmin et al, 1991), Della Pergola and Rebhun (1999) use an average of 3.7 children per Orthodox woman. The implied increase in Orthodox fertility over a 23-year period, from the 1990 NJPS, is not

8 far-fetched, if only because the Haredi community has grown steadily and is known for very high birthrates. Taking into account the unmarried Orthodox fertility rate (.80) and unmarried rate of 28%, we get an average fertility rate of 4.3 for Orthodox women 40-49. The difference between our fertility rate and that reported in Pew (2013) is caused by the difference in age group used. Scenarios B and E in the projections below both include lower married Orthodox fertility (5.0) which would make the average fertility 3.8 thus testing the robustness of our results to a decline in Orthodox fertility contrary to the trends of the last decades. Migration to and from Israel While Israelis in America certainly stand out as a visible presence in the Jewish population and community, we find that recent migration to and from Israel exerts only a small impact upon the overall Jewish population size in the US. Taking 2010 as an illustrative example, using data from the Israeli Central Bureau of Statistics (CBS) (2011) there were 2,530 immigrants to Israel from the USA (CBS 2011, Immigration Table 4) and 1,613 immigrant Israeli citizens from the USA (CBS 2011, Immigration Table 25). In addition, 838 U.S. citizens came to Israel as “potential immigrants” (CBS 2011, Immigration Table 20). At the same time (US DHS 2010, Table 2), 5,172 Israelis received permanent legal residence status in the U.S. (average of 5,400 from 2000- 2009). During 2001-2010, an average of 2,719 Israelis were naturalized annually (US DHS 2010, Table 20). Of the departing Israelis, 70% were Jews, while 80% of returning Israelis are Jewish. This leads to a net annual influx of approximately 1,024 Israeli Jews to the US Jewish population. Given these considerations, we decided not to include this relatively small effect in our projections. After the last major emigration wave of Jews from the former Soviet Union in the 1990s, the major Jewish populations outside of Israel and the United States consisted of France, Canada and the United Kingdom, all of which have relatively low total immigration to the United States. From Pew (2013), we learn that from 2003 until 2012, the total number of adult Jewish immigrants averaged about 9,000 annually, or less than 0.2% of the population. At the same time, we have no way of estimating the number of returning migrants or the total number of American Jews who emigrate to countries other than Israel. For all these reasons, it seems plausible to assume that net migration exerts very little impact on overall Jewish population size. Conversion Conversion into Judaism – be it through a formal ceremony or, as is somewhat more common, personal identity choice -- is a form of migration into the Jewish community. We find that among 35-49 year old Orthodox, Reform/Conservative, and No-Denomination populations, there are respectively 1.4%, 7.0%, and 2.0% who report that neither of their parents were Jewish (they include rabbinic converts and personal switchers). This identity migration has two effects. First, it boosts fertility in two-Jewish parent families because some Jewish men are marrying women who have converted or switched to Judaism. Second, it boosts the number of adults in the population. We do not know when these conversions or identity changes are taking place in individual’s lives. Therefore, to model their impact we have to make some assumptions that are described in the methods section. Future Projections Using point estimates of parameter values derived from Pew (2013), Fig 2 shows projections until 2063 both for the total Jewish population and for the three denominational groupings. During the 40 years from the 9 time of the Pew (2013) study until 2053, the projected total Jewish population declines about 5% and then begins to grow. Beyond the slight shrinkage in the total population, the denominational distributions will change as well, moving toward a close to equal split between the three denominational groups of Orthodox, Reform/Conservative and No-Denomination. Throughout this period, the number in the No-Denominational category would remain relatively constant; but we project large declines in the Reform/Conservative group. While the No- Denominational group is losing population to the non-Jewish category, the group is also being fully replenished by defectors from the Orthodox and Reform/Conservatives. In contrast, the currently numerous Reform/Conservatives are not being replenished in a significant way from Orthodoxy or any kind of “return migration” from the No-Denomination group.

7 6 5

4 Total Jewish Population 3 2

Total (Millions) Population Total 1 0 2013 2023 2033 2043 2053 2063 Year Fig 2. Population projections for the total US Jewish population and each denomination grouping using point estimates for all parameters

We constructed a Monte-Carlo simulation of the evolution the Jewish population over time based upon the 95% confidence intervals for the following model inputs: fertility rates, intermarriage rates, initial populations (children and adults), and denominational switching rates. Each trial of the simulation is based on a different randomly generated parameter set that are held constant through the projection period. In Figure 3, we report the range of population size outcomes for the various denominations and age groups giving an indication of the uncertainty in the population projections. For these plots, we use the point estimates for the initial populations and thus ignore the uncertainty in those estimates. This approach allows us to see how uncertainty in the other parameters affects the projections over time. In Fig S1, we report the projections for year 2063 taking into account the uncertainty in the initial populations.

Population All Ages All Ages (Millions) Population 2

Ortho Low Ortho Med Ortho High Ref/Con Low Ref/Con Med Ref/Con High No Denom Low No Denom Med No Denom High Total Low Total Med Total High 0 2013 2023 2033 2043 2053 2063 Year Fig 3. Monte-Carlo simulation of total Jewish population using point estimate of initial population

In Fig 3, we observe that uncertainty in the projections grows over time. This feature is common to all projections and is to be expected as the uncertainty in parameters has a compounding effect over time. However, even taking into account the increased uncertainty over time, the “story” remains unchanged. We find a relatively stable total population through 2033, followed by a decline that reaches its nadir in 2053. This pattern is robust to the uncertainty in model parameters. Looking at the individual denominations, we can see that 50 years post the Pew (2013) study, the predicted ranges in size of the three denominational populations overlap considerably, indicating a high likelihood that their shares of the total population will converge. This pattern can be compared to the initial denomination population estimates in 2013 that are very different from one another, with a small Orthodox share and a majority identifying as Conservative or Reform. Their 95% confidence intervals in 2013 do not overlap (Fig S1). We can also see that the uncertainty ranges for the Orthodox population are wider than for the other denominations. This large variation is a direct result of the relatively larger fertility rates of the Orthodox. A similar percentage of uncertainty on a larger rate will have a bigger impact on the future population size than for a segment with a smaller fertility rate. Table 1 which reports the population and uncertainty ranges for 2063 shows the wide variation clearly. The 5th percentile to 95th percentile range of the Orthodox is 48 percentage points of the median population projection, while amounting to only 23% for the Reform and Conservative population. So, while the general observation that the Orthodox will significantly increase their share of the total Jewish population appears robust, the exact level they are projected to reach has quite a bit of uncertainty about it. Table 1. Uncertainty ranges for populations in year 2063 without uncertainty in 2013 population. 11

Percentile Population (Millions) 5th 50th 95th Range Range/Median

Total 5.65 6.07 6.54 0.89 15%

Ref/Con 2.12 2.37 2.63 0.51 22%

No Denom 1.75 1.98 2.21 0.46 23%

Orthodox 1.30 1.72 2.18 0.88 51%

Total (30-69) 2.44 2.56 2.70 0.26 10%

Ref/Con (30-69) 0.95 1.05 1.16 0.21 20%

No Denom(30-69) 0.81 0.92 1.02 0.21 23%

Orthodox (30-69) 0.46 0.59 0.71 0.25 42%

Fig 4 shows the evolution of the 30 to 69-year old population with uncertainty ranges. Most significantly, the decline in the size of the Reform/Conservative group is very sharp even under the rosiest scenarios, and so is a significant aging of the Reform/Conservative Jewish population. There is minimal variation in the next 30 years in large part because the future demographic trends for this age group are “baked in” already, a direct outcome of the initial age distributions for children and young adults depicted in Fig 1. At the time of the survey (Pew 2013), the 30+ year old Reform/Conservative Jews have already been born. Unless they are able to draw in many of the No-Denomination Jews or experience large numbers of conversions by non-Jews, there is little chance of seeing a numerical recovery of Reform and Conservative groups.

Fig 4. Monte-Carlo simulation of 30-69 year old Jewish population by denomination Deterministic Scenario Sensitivity Analyses Table 2 reports the results of sensitivity analysis we conducted, on some of the key parameters, to reduce concern that the qualitative characteristics of our results are driven by specific parameter values. The first three

12 columns show two time points, the initial (2013) conditions and +50 years using base case (Scenario A) assumptions. We can see the rapid growth of the Orthodox, both in their absolute numbers and in their share of the population. We also see that most of the decline in the Jewish population in that period can be linked to a numerical collapse in the Reform/Conservative 30-69 population. Columns 3 to 7 show how the 50-year projection changes with modifications to the model’s assumptions (scenarios B-F). Table 2. Population Projections and Sensitivity Analysis. Initial Populations in State Aa Bb Cc Dd Ee Ff Gg Millions 2013 2063 2063 2063 2063 2063 2063 2063 Total Jews (All Ages) 6.41 6.19 5.92 6.19 6.32 6.04 7.11 5.74 Orthodox (All Ages) 0.86 1.84 1.62 1.88 1.85 1.67 2.44 1.70 Reform and Conservative (All Ages) 3.44 2.33 2.31 2.30 2.65 2.59 2.37 2.12 No Denomination (All Ages) 2.12 2.02 2.00 2.01 1.82 1.78 2.30 1.93 Reform and Conservative Ages 30-69 1.89 1.03 1.02 1.03 1.14 1.12 1.07 0.97 Orthodox Fraction of all Children 27% 44% 40% 46% 44% 41% 50% 45% Orthodox Fraction of all ages 13% 28% 25% 28.5% 27% 26% 32% 28%

aBase Case. bLower Married Orthodox Fertility (5.0). cMarital Status for non-Orthodox based on Ages 40-49. d50% of the No-Denomination aged 20-29 become Reform/Conservatives. eCombination of scenarios b, c, and d. fDenomination switching of all segments based on ages 20-29. gMarital behavior is gender specific.

In Scenario B, we reduce the completed fertility rate of married Orthodox women to 5.0 which would put it more in line with that reported in (Kosmin et al, 1991). This reduction will of course depress the total Jewish population and to some degree the populations of the non-Orthodox as well as the Orthodox share of the total population. In the 20+ years since (Kosmin et al, 1991), the more traditional wings of the Orthodox have grown significantly, producing both higher fertility and retention than was estimated then. So, it is unlikely that the Orthodox fertility is as low as modeled in Scenario B. Scenario C uses the marriage status parameters of the 40 to 49 year-olds for the non-Orthodox segments rather than ages 30-39 as is done in the base case. The major differences with the base case are that intermarriage rates for the no-Denomination and Reform/Conservative segments are reduced and their overall marriage rates are

13 greater. One would expect that both these factors would lead to larger non-Orthodox populations, but this is not the case. The change in marriage status parameters produce a very slight decrease in the non-Orthodox population and a slight increase in the Orthodox population. In theory, intermarriage can increase the population because marriages of Jewish men to non-Jewish women on average increase the number of fertile females associated with the Jewish population. The offspring of intermarried couples are less likely to identify as Jewish when they become adults, but the two opposing effects balance each other leading to very little impact on the total population size. This finding may seem surprising, but it is not because intermarriage is not influential on individuals or an important phenomenon. Rather, our modeling assumptions, specific parameter values, other effects, and the perspective of the entire population all work together to reduce the impact of intermarriage. We return to this further in the discussion section. Scenario D considers what would happen if 50% of no-Denomination Jews aged 20-29 ultimately identify as Reform/Conservative Jews (an unlikely eventuality, to be sure). This assumption produces a very slight increase in the total number of Jews and a noticeable increase in the number of Reform/Conservatives aged 30-69. However, in the long run, this increase barely compensates for the structural declines in the Reform/Conservative population. Scenario E combines all the factors in B-D, which creates a worst-case situation from the perspective of the Orthodox share of the total population. Yet, even in this case, the Orthodox still more than double their share of the total Jewish population. Scenario F represents the case in which the rates at which children become adults of the various denominations is based upon the data on ages 20-29 which tends to have much higher retention rates for each group. We see that with greater retention, all denominations do better, and the total population grows by more than 700K people. Yet the Reform/Conservative segment still sees a very large decrease in both the total population and in the 30 to 69-year-old groups. This decrease is because much of the change in this segment over the next few decades is built into their current age structure, that is, the smaller numbers of Conservative and Reform Jews under age 30. The marriage behaviors of Jewish males and females differ (Sheskin and Hartman 2015) and (Phillips 2017). Our base case aggregates these and assumes the behaviors are the same for both genders. Scenario G considers what would happen if these differences persisted into the future. In Scenario G, women are less likely to be in-married than men in all denominations. The result is 450,000 fewer Jews in 50 years relative to the base case. Most of this reduction comes at the expense of the Reform/Conservative and Orthodox populations. S2 Fig is the same as Fig 2 but is recalculated for the gender specific marriage behavior parameters used in Scenario G. The population nadir in 2053 is smaller and the recovery is slower. Intermarriage by females has a different effect then intermarriage by men. Therefore, distinguishing between the genders leads to a different result than Scenario C. Increasing the in-marriage rates of non-Orthodox Jewish females will lead to a larger Jewish population. In contrast, increasing the in-marriage rates of non-Orthodox Jewish males will reduce the Jewish population.

Materials and methods Our primary data source is the raw data from the Pew (2013) study (based on interviews with 3,475 individuals whom Pew defined as currently self-identifying as Jewish). This data set is publicly available. The

Pew researchers used the Rao-Wu-Yue survey bootstrap methodology (Rao et al 1992) to create appropriate weightings for the data (see (Pew 2013) pages 138-143). Thus, to generate estimates of parameters and confidence intervals for these parameters from this survey requires using these weights and the complex survey estimation functions in the statistical software package Stata (Kolenikov 2010) (we used version 15.1). We estimate initial populations in each age group by denomination, along with fertility rates, intermarriage patterns and denominational transitions, as well as mortality and migration in and out of the population. We combine these estimated parameters in a matrix population model to make future projections. The algorithms we used to classify respondents into denominations using the Pew (2013) variables appear in the supplementary materials.

Matrix population model We created 5-year age groupings from [0-4] to [95-99]. Within each age group, different subgroup types and behaviors are age-dependent. For children 0-19, we assigned them the same denominations as their parents, even though the more mature children may have offered denominational identities different from those of their parents. We further subdivided the non-Orthodox children by whether they are in a household with a single Jewish parent or with two Jewish parents. We also track children being raised as non-Jews. When the children transition into adulthood, they also can transition into different denominations (S3 Fig). Once someone transitions to non-Jewish they are no longer counted, although a small number of them may return to the Jewish population, as may have some of their children. The age group 20-49 is considered the fertile adult population. Our model makes the simplifying assumption that they do not switch denominations. The assumption that denomination is fixed at age 20 and remains the same throughout life is clearly false in practice. It is done for computational convenience when making projections that are focused on tracking fertility. The population in ages 50-99 is considered non-fertile and do not switch denominations in our model. Age specific mortality rates apply for all groups in the model, but are not depicted in the accompanying diagram. In S4 Fig, we illustrate the dynamics of the model with the case of a child raised in a Reform/Conservative household with one Jewish parent. When such a child turns 20, he/she transitions to one of the denominations. The thickness of the arrows represents the likelihood of each outcome. For example, the data show that a Reform/Conservative child with one Jewish parent is most likely to become an adult who does not consider him/herself Jewish. The dotted line from the box for 20-24 year old Reform/Conservative Jews indicates that for such adults some fraction of the offspring will be children raised as Reform/Conservative with one Jewish parent. It is also possible for Reform/Conservative adults to create two Jewish parent Reform/Conservative households when in-marrying. The right side of S4 Fig depicts our modeling assumption that once the adult denomination is set, it does not change. We are also assuming that if an adult identifies himself or herself as a Reform/Conservative Jew, then if they marry a non-Jew, they will raise their children as Reform/Conservative.

Mathematically, we can represent the model in matrix notation. Let Xt be the vector of populations in a particular 5-year time period t. The vector Xt is composed of three sub-vectors Xc,t, Xf,t, and Xnf,t representing

15 respectively the populations of children, adults of fertile age, and adults of non-fertile age. We can also define a population projection matrix P as follows.

c f Nf

P = c Ac T 0 0

f F 0 Af

nf 0 0 Anf

The submatrices Ac, Af, Anf respectively represent the aging and mortality processes for the three main age groups. These submatrices also account for converts joining the population. The submatrix T represents the transition rates of children into the various denominations as they enter adulthood. It also accounts for mortality. The submatrix F represents the household formation and fertility processes. The fertility rates are boosted to account for Jewish males forming two-Jewish parent household with non-Jewish females who have converted. We can then project population forward in time using the following calculation,

, = = , (1) 𝑋𝑋𝑐𝑐 𝑡𝑡 , 𝑋𝑋𝑡𝑡+1 𝑷𝑷𝑋𝑋𝑡𝑡 𝑷𝑷 � 𝑋𝑋𝑓𝑓 𝑡𝑡 � 𝑋𝑋𝑛𝑛𝑛𝑛 𝑡𝑡 Note that the projection matrix P is not subscripted by time, implying that we are assuming that all the parameters governing population evolution do not change over time. S3 Fig provides a high-level depiction of the projection model structure. Every adult is characterized by his/her age and denomination, while each child is characterized by his/her age and household type. Thus, each child, depending upon his/her family environment, will become an adult associated with one of the three denominational groups (or disassociated from the Jewish community) with a specific probability estimated from (Pew 2013). Each adult will produce some number of children in a particular family environment at a rate that depends upon the adult’s denomination. The Pew 2013 data (Pew, 2013) allows for estimates of the number of adults in each denominational group in 10-year age bands as well as an estimate of the number of 18 to 19-year old in each denomination (S1 Table). For the population 20 years and older, we generate estimates for the numbers in five-year age bands by equally splitting the numbers in the 10-year bands. This step of course introduces some inaccuracy in the initial and future age distributions for each denomination, albeit a simplification that has an insignificant impact on the main thrust of the results. We conducted sensitivity analysis on this assumption and find insignificant differences. For the purposes of our model, we also have to allocate the estimated total fertility rate across the 5-year intervals of the fertile years. Lacking data on the timing of each child’s birth, we make rough assumptions. There is evidence that among college-educated white American women, childbirth is happening later (Pew, 2018). There

16 is also considerable evidence that Orthodox Jewish women start having children earlier than the non-Orthodox, if only because they marry far earlier than the non-Orthodox, as in the Pew data. To capture these phenomena, we spread the fertility across ages for each denomination as follows. The five age intervals considered fertile are 20- 24, 25-29, 30-34, 35-39, and 40-44. The percent of births in each of those intervals for the No-Denomination and Reform/Conservative groups are respectively: 0%, 20%, 20%, 40%, and 20% and for the Orthodox: 15%, 20%, 20%, 25%, and 20%. Conversion We introduce the impact of conversion (including switching by personal choice) to the above model in two ways. First, we boost the fertility rates during ages 20-45 to represent the women joining the Jewish population through conversion thus increasing the number of children being born into two Jewish parent households. Second, we add a flow of adults to the 45-49 year old age groups in the varying denominations. The result of this approach is that in theory, a woman converting to Judaism at the age of 25 will not be counted as part of the Jewish population until she is 45, but will contribute to the number of Jewish children born in the years she is 20-44 years old. We say “in theory” because we do not actually track individuals. We have run the analysis without including conversion effects at all. The results do not change significantly and thus we do not believe our modeling assumptions about conversion are distorting the results. Mortality rates We use mortality rates for white Americans reported in (US CDC 2017). Because the Jewish community is generally wealthier and better educated than average compared to the general US population, these US mortality rates are probably higher than for Jews, and therefore lead to an underestimate of the future total size of the Jewish population. We also do not model increases in lifespan that may occur in the future, a choice that further underestimates the future population. That said, the mortality rates are already so low for people below 50 years of age that the underestimates of mortality in our model will primarily influence our estimates of the more elderly part of the population while having little impact on fertility estimates. We also do not believe that increases in life expectancy will affect different denominations of Jews in significantly different ways; thus, our projections of the relative sizes of the denominational groups should be unaffected by the small discrepancies in estimated versus actual mortality rates. Uncertainty analysis using Monte-Carlo simulation We simulate 1000 randomly generated draws of the model parameter values thus generating 1000 values for the various demographic outcome measures of interest. With 1000 trials the 90% confidence intervals generated for simulation samples means were typically less than 1% of the means for the outcomes of greatest interest. We generate the random parameters once for each of the 1000 simulation trials and then hold constant for each time period in that trial. All of these parameters are of course correlated with each other. For example, if the true Orthodox fertility is actually lower than the mean value derived from the Pew survey, then it could be that it is more likely that the true Reform/Conservative fertility is also lower than the mean value in the Pew sample. We do not have a way to determine these correlations. For parameters that are essentially probabilities in

17 multinomial distributions, e.g., marital status and denomination switching, we have additional dependencies between the parameters. These challenges inform our approach to random generation of the parameters. For fertility rates and initial population values, we draw parameter values from their 95% confidence intervals using a uniform random variable. This approach ignores any central tendency in the parameter estimates and thus exaggerates the uncertainty to some degree. For marital status, for each denomination, we randomly generate a value for the in-married status and then split the remaining probability across intermarried and unmarried according to the same relative proportion they have at their mean values. For denomination switching we use a similar approach. For each family environment, we randomly generate the probability of staying within one’s denomination and then distribute the remaining probability across the other denominations. In the Results section, we reported the projected total population in each of the denomination sub-groups from 2013 to 2063, and the population in the 30-69 age group in Figs 3 and 4. For each outcome measure we reported the 5th (low), 50th (medium), and 95th (high) percentiles. For those plots we used the point estimates for the initial populations and ignore the uncertainty in those estimates. This allowed us to see how uncertainty in the other parameters affects the projections over time. In S1 Fig, we plot the all-ages population projections including uncertainty in the initial populations.

Discussion We have presented projections of the future demographic size and denominational makeup of the U.S. Jewish community using the best available national-level data and reasonable assumptions regarding fertility, household formation, denominational switching, migration and mortality. Our approach constructed a demographic model customized to the particular structure of the U.S. Jewish community, i.e., one with interacting denominational subpopulations. Our results are NOT a prediction, but a projection. They represent a set of possible trajectories given the current state and trends and the inevitably imprecise assumption that current behaviors will continue into the future. This is a quantitative demographic analysis of the population and we do not claim to project the future quality of Jewish life in America or how that quality will impact demographics. Despite the great uncertainty that we should have about any future projections, the key projections of our model are robust, relatively unaffected by reasonable possible variations in the several components that go into creating the projections. The initial conditions that provide the current populations by age and denomination have been directly measured by (Pew 2013) and have not been strongly challenged. Lacking good estimates of Jews’ mortality, the older age groups are the ones with greatest uncertainty; but they have the least significance for the future projections. The current age distributions contain the seeds for the next 50 years of the adult populations. Unless a large-scale denominational switching by adults takes place -- with many of the Orthodox and/or the non- denominational becoming Reform and Conservative -- we should not expect outcomes very different than the projections herein. We addressed uncertainty about factors such as fertility rates and denominational switching through Monte Carlo simulation and deterministic sensitivity analysis. We have characterized American Jews as belonging to one of three major denominational groups -- Orthodox, Reform/Conservative, and No-Denomination, corresponding to respondents’ subjective identity. That said, we are not

18 certain that these labels will be as relevant in the future. The Jewish community may well shed these labels as new generations abjure defining themselves as members of particular denominational movements, especially outside of Orthodoxy (Wertheimer 2018). For the purposes of our demographic model and projections, the imprecision of denominational identities and the fluctuation in their meanings over time do not present a major problem. Most relevant are the behavioral patterns in terms of marriage patterns, fertility rates, child rearing and denominational retention. From (Pew 2013), we can see three major denominationally aligned constellations of behaviors: Subgroup 1 (Orthodox) is heavily in-marrying, has high fertility, and has relatively high retention rates. Subgroup 2 (Reform/Conservative) exhibits a lot of out-marrying, low fertility with even lower effective Jewish fertility, and relatively high retention among its in-married families. Subgroup 3 (the No- Denomination) exhibits high levels of out marrying, low fertility, and poor retention, with many leaving the Jewish population entirely. Our projections assume that these three distinct clusters of behaviors will persist for the near future, even if they do not continue to use the same denominational labels into the future. We make no assumption that everyone in the Reform/Conservative category is an actual member of those movements, especially in light of the fact that only a minority (33%) of self-defined Reform identifiers are synagogue members, as are about half (50%) of the Conservative identifiers (Pew 2013, page 60). Nor do we claim that those movements will continue to exist as we know them today. While modeling the distinct denominations and their interactions is a strength of this work it is also a weakness. The segmentation into denominations should be more detailed with distinctions between Modern and Haredi Orthodox and between Reform and Conservative streams. Unfortunately, the data did not support that level of detail. Another limitation of our modeling approach is that we assume that denomination choice takes place once and remains fixed from the age of 20, even though it is based on denomination transition behavior of 30-49 year olds. This approach ignores the fact that over their lives people change their denominational identification more than once. We make this simplifying assumption to enable us to track child production. For example, a person who has settled on Reform/Conservative at age 40 may have had children when they were 30. We need to have them producing those children at the rate at which the average 40 year old identifying as Reform /Conservative would have. By basing individual total fertility on people’s identification when they are 40-49 as we do, it takes into account the fact that they took many paths to get there. For denomination transition, we are using the denominational identifications of people 30- 49, potentially distorting our estimates of the 20-29. If, for example, many Jews spend their twenties as No-denomination before settling into a different group, then in any particular year we might be undercounting No-denomination people because we have already counted them as at their final destination denomination. While this imprecision in the model may have implications for the denominational breakdown of the 20-29 year old population, it should not have a significant impact on the total population or the long-term projections. Our model ignores several factors that may influence population dynamics. For example, we ignore the positive externalities that members of the community provide for others. A critical mass of thriving communal institutions makes it easier and more attractive for Jews to participate in the community. In addition, religious or cultural innovations may help construct a more appealing Judaism and Jewish community. For example, Jewish philanthropists may well substantially increase investment in Jewish educational endeavors – both formal and informal – that have been shown to increase rates of in-marriage and effective Jewish fertility (Fishman and

Cohen 2017; Cohen 2018; Saxe et al 2017). Another possibility is that over time, the offspring of intermarriage will increasingly identify as Jews, augmenting the population (Sasson 2014;Sasson et al 2017). Indeed, others – interpreting the same data set -- see a quite different future for American Jewry (Saxe et al 2015). Societal gender roles and Jewish communal attitudes about intermarriage are also evolving (McGinity 2014; Sheskin and Hartman 2015). For this reason, we have not distinguished between matrilineal and patrilineal descent, have assumed a common intermarriage rate for males and females, and assumed that denomination-switching rates are the same for children in single Jewish parent households regardless of which parent identifies as Jewish. These modeling choices lead to projections that probably overestimate the future size of the Jewish population. These alternate eventualities may lead to higher rates of Jewish identification, more in-marriage, and less defection, as well as more non-Jewish spouses and children choosing to engage in Jewish life. At the same time, our model shows that the combination of low fertility, high intermarriage, and low retention among the non- Orthodox, coupled with the steady growth and greater retention of the Orthodox, has led the U.S. Jewish community to a demographic inflection point with significant changes in size and even more in composition. We are well aware that projections are not predictions. So many unknown changes in the larger society’s culture, religious life, politics, and marriage and fertility patterns can and will affect the outcomes we chart above, as will changes in Jews’ denominational structure and transition, responses to intermarriage, family formation patterns, and communal policy. At least for the short run – the next ten, twenty, or thirty years – we do feel confident in projecting the major demographic trends outlined above: small declines in the total population size, sharply growing Orthodoxy, and dramatically declining Conservative and Reform numbers. Our projections thirty or more years hence point to conceivable scenarios if present trends continue. To the extent that they are accurate, they indicate that Jews in America will not disappear or even diminish much. However, the U.S. community will experience substantial growth in the two poles of Jewish engagement – the Orthodox and the most nominally Jewish, even as the middle – as represented here by self-identified Reform and Conservative Jews – shrinks in number. This unfolding shift in denominational demographics will undoubtedly have many consequences for the institutions and collective life they populate and support.

Acknowledgements Steven M. Cohen provided valuable assistance in accessing and interpreting the data from (Pew 2013) as well as helpful feedback on earlier drafts of the paper. Sergio Della Pergola, Alan Cooperman, Conrad Hacker, Edward Kaplan, Alex Weinreb, and Alan Gerber all provided helpful feedback on earlier drafts. All remaining errors are my own.

References

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Supplemental Figures and Tables

S1 Fig. Monte-Carlo simulation of total Jewish population by denomination with uncertainty in initial populations.

S2 Fig. Population projections for the total US Jewish population and each denomination grouping using point estimates for all parameters and gender specific marriage behavior.

S3 Fig. High Level Schematic of the flows in the demographic model.

S4 Fig. Detailed example of population flows.

For respondents who identified as Jewish we define a new childhood religion variable “chrelig2” which takes on values 1,2,3 and 4. Where 4=”Orthodox”, 3= “Ref/Cons”, 2= “No-Denom”, 1= “Non-Jewish”. Code to generate chrelig2 variable: generate chrelig2 = 4 if (chdenom1cmbrec == 2 & chrelig==5) // Define as raised Orthodox anyone who said both raised Orthodox and Jewish. replace chrelig2 = 3 if (( chdenom1cmbrec == 1 | chdenom1cmbrec == 3| chdenom1cmbrec == 40| chdenom1cmbrec == 41| chdenom1cmbrec == 42 | chdenom1cmbrec == 43| chdenom1cmbrec == 44| chdenom1cmbrec == 45 |chdenom1cmbrec == 46) & chrelig==5) // Define as raised Reform/Conservative anyone who said either raised Reform or Conservative, or a mix of conservative or reform and some other Jewish stream. replace chrelig2 =2 if (chrelig2 !=3 & chrelig2 != 4 & (chrelig ==5 | chrelig==15 | chrelig==16| chrelig==17)) //Define as raised No- Denomination if they say they were raised as Jewish and something else that is not Messianic Judaism. replace chrelig2 = 2 if (qh15==2 & (chrelig == 9 |chrelig == 10 |chrelig == 12 |chrelig == 43 |chrelig ==44 | chrelig == 45)) // Define as raised No-Denomination if they say raised partially Jewish and Atheist, Agnostic, Nothing, Non-Denominational. Own beliefs or Believer. replace chrelig2 = 1 if (chrelig2 != 2 & chrelig2 !=3 & chrelig2 !=4) // Define all others as raised Non-Jewish. replace chrelig2=2 if( chrelig2==1 & (chrelig==9 | chrelig== 10 | chrelig==12 |chrelig== 43 |chrelig== 44| chrelig== 45 | ((chrelig==98 | chrelig==99)& qh15==3))) // Those who said not raised Jewish not even partly but picked a childhood religion that was not a well-defined other religion we reclassify them as No-Denomination. replace chrelig2=2 if( chrelig2==1 & qh15==1) // Those raised Jewish aside from religion. replace chrelig2=3 if (chrelig2==2 & (chdenom1cmbrec == 1 | chdenom1cmbrec == 3) ) & (qh19b==1 | qh19c==1) //Went to fulltime Jewish school or part-time Jewish school and said not raised Jewish but said childhood identification was Reform or Conservative replace chrelig2=2 if( chrelig2==1 & chrelig==98)// If respondent did not specify any childhood religion but has identified as Jewish.

RaiseHow is a new family environment variable taking values from 1 to 6 with 6= “Orthodox with two-Jewish Parents”, 5= “Reform/Conservative with two-Jewish Parents”, 4 = “Reform/Conservative with one-Jewish parent”, 3= “No-Denomination with two-Jewish parents”, 2= “No-Denomination with two-Jewish parents”, 1= “Not Jewish with one or two Jewish parents”

Code to create RaiseHow variable: generate RaiseHow=6 if (( ( chrelig2==4) & (qh16 == 3) )) replace RaiseHow = 5 if (( ( chrelig2==3) & (qh16 == 3) )) replace RaiseHow =4 if ((qh16 < 3) & (chrelig2 >2) ) //one Jewish parent and said raised orthodox defined as Ref/Con 1JP. replace RaiseHow = 3 if ((qh16 == 3) & (chrelig2==2 )) replace RaiseHow = 2 if ((qh16 <3) & (chrelig2==2 )) replace RaiseHow =1 if (qh16< 4 & chrelig2==1)

NowHow2 is a new variable for the current affiliation of a respondent. Only consider those with finalanalysistype < 3 so are either identifying as Jewish by religion or Jewish not by religion. Among these all who are Orthodox including both Modern and Haredi are combined into one group. I.e. anyone with qh1cmbrec=2

Anyone with qh1cmbrec= 1,2, 33, 40-46 are in the Reform/Conservative grouping and anyone with other values for qh1cmbrec or are Jews not by religion are classified as No-Denomination.

Code to create new variable NowHow2: generate Haredi=(qh2rec==10 | qh2rec==11 |qh2rec==12 |qh2rec==13 ) generate Orthodox = (qh1cmbrec==2) label define Ortholbl 0 "All other" 1 "Orthodox" label values Orthodox Ortholbl generate Denomination=qh1cmbrec label define Denomlbl 1 "Haredi" 2 "Modern Orthodox" 3 "Conservative" 4 "Reform" 5 "No denomination, other" 9 "Missing" label values Denomination Denomlbl recode Denomination (2=2)(3=4)(33=4) (1=3)(40/42=3)(45/46=3)(10/32 =5) (34/38 =5) (49=5) (99=5) (else=5) label variable Denomination "DenomNow" generate RJewishPew = (finalanalysistype <3) generate NowHow2=RJewishPew replace Denomination =1 if (Haredi ==1 & Denomination==2) replace NowHow2= 6 -Denomination if (NowHow2 == 1 & Denomination <=4) recode NowHow2 (3=2) (4/5 =3) label define NHowlbl 0 "Non Jewish" 1 "Jewish no denom" 2 "Reform or Conserv" 3 "Orthodox" label values NowHow2 NHowlbl

S5 Fig. Denomination Classification Logic and Code.

Denomination Description Haredi Jews 6% of Jewish adults, and are the most sectarian and religiously observant denominational category. Often referred to as “ultra-Orthodox,” the Haredim (plural) consist of two streams – Hassidic and Yeshivish – themselves consisting of a variety of sub-communities. Haredi Jews are distinguished by high levels of geographic concentration in New York and surrounding suburbs. Compared to other US Jews they are distinguished by youthful profile, early marriage, universal in-marriage, high birthrates, limited educational attainment, and higher rates of poverty. Modern Orthodox Jews 3% of Jewish adults. Compared to Haredim, they are far more highly educated and less sectarian. At the same time, they are more socially cohesive and religiously observant than non-Orthodox American Jews.

Conservative Jews 18% of Jewish adults, and are situated between the Orthodox and other (Reform and no-denomination) Jews in terms of residential concentration, in-group marriage and friendship, and ritual observance. They are the oldest denominational category.

Reform Jews 37% of Jewish adults and are distinguished from the others by their liberal politics, high rates of intermarriage, and relatively low rates of observance No-denomination and 26% of Jewish adults. They score the lowest of all denominational categories on all indices of Jewish minor denominations engagement.

S1 Table. Denomination description.

Denominational Group Age Range Jewish No Denom Reform or Conservative Orthodox 18-19 68,000 76,000 19,000 [29,000 - 106,000] [46,000- 106,000] [9,000- 28,000] 20-29 410,000 410,000 103,000 [325,000 - 503,000] [307,000 - 514,000] [86,000- 121,000] 30-39 318,000 279,000 122,000 [233,000 - 402,000] [207,000 - 350,000] [60,000 - 184,000] 40-49 249,000 379,000 83,000 [165,000 - 333,000] [311,000 - 447,000] [64,000 - 103,000] 50-59 280,000 654,000 91,000 [239,000 - 320,000] [588,000- 720,000] [67,000 - 115,000] 60-69 307,000 575,000 50,000 [262,000 - 353,000] [514,000 - 636,000] [29,000 - 72,000] 70-79 124,000 273,000 24,000 [102,000 - 145,000] [249,000 - 298,000] [18,000- 31,000] 80-89 83,000 175,000 16,000 [66,000 - 100,000] [153,000 - 198,000] [9,000 - 22,000] 90-97 5,000 32,000 1,000 [2,000 - 8,000] [24,000– 40,000] [0 - 3,000]

S2 Table. Initial population age structure by denomination for ages 18+ with 95% confidence intervals.

Denomination Marriage Jewish Children Jewish Children Raised Non-Jewish Raised Non- Status Age 0- 9 Age 10-17 Age 0-9 Jewish Age 10-17 Married Jewish spouse 42,000 23,000 16,000 0 95% CI [32,000 - 52,000] [17,247 - 29,607] [0-41,541] [0-0] Married non- Jewish no Jewish spouse 101,000 49,000 104,000 64,000 denom 95% CI [53,000 - 150,000] [34,000 - 64,000] [62,000-146,000] [16,000-112,000] NOT married 31,000 22,000 17,000 11,000 95% CI [10,000 - 52,000] [13,000 - 31,000] [6,000-29,000] [3,000-20,000] Total 174,000 94,000 137,000 75,000 Married Jewish spouse 153,000 153,000 0 95% CI [126,000 - 181,000] [134,000 - 173,000] - [0-0] Married non- Reform or Jewish spouse 130,000 76,000 36,000 30,000 Conservative 95% CI [100,000 - 161,000] [58,000 - 95,000] [29,000-42,000] [28,000-30,000] NOT married 25,000 45,000 13,000 10,000 95% CI [10,000 - 40,000] [28,000 - 62,000] [9,000-18,000] [4,000-16,000] Total 308,000 284,000 49,000 40,000 Married Jewish 219,000 96,000 spouse [191,000 - 248,000] [80,000 - 112,000] 95% CI - - Orthodox NOT married 13,000 20,000 95% CI [9,000 - 17,000] [11,000 - 28,000] - - Total 232,000 116,000 - -

S3 Table. Number of children in each household environment and children raised non-Jewish in households with a Jewish adult. How Raised

One Jewish One Jewish 2 Jewish Denomination Parent Two Jewish One Jewish Parent Reform 2 Jewish Parents 2 Jewish As an Adult Non- Parent Non- parent or Parents Reform or Parents Ages 30-49 Jewish Jewish* Non-Denom* Conservative non-Denom Conservative Orthodox Non Jewish 78% 78% 54% 34% 18% 6% 0% 95% CI [0.71,0.85] [.711,.851] [0.44,0.63] [0.11,0.27] [0.26,0.53] [0.04,0.08] [0.02,0.07] No Denomination 17% 17% 40% 16% 60% 21% 20% 95% CI [0.10,0.23] [0.10,0.23] [0.28,0.47] [.486,.677] [0.04,0.26] [0.15,0.24] [0.05,0.48] Reform or Conservative 5% 5% 6% 50% 18% 63% 16% 95% CI [0.03,0.09] [0.03,0.09] [0.04,0.16] [0.14,0.26] [0.33,0.62] [0.61,0.73] [0.09,0.25] Orthodox 0% 0% 0% 0% 4% 10% 64% 95% CI 0 0 [0.00,0.10] [0.03,0.07] [0.01,0.22] [0.04,0.18] [0.44,0.78] Total 100% 100% 100% 100% 100% 100% 100%

S4 Table. Denomination determination of the 30-49 year old as a function of environment they were raised in as children.

How many children Pct Children Effective Jewish Denomination Marriage group ever had Jewish Children Jewish spouse 2.47 0.78 1.91 95% CI 2.12-2.82 0.45-1 No Non-Jewish Denomination spouse 2.30 0.44 1.02 95% CI 0.73-3.83 0.24-0.6 NOT married 0.85 0.96 0.82 95% CI 0.1-1.59 0.89-1.0 Jewish spouse 2.09 1.00 2.09 95% CI 1.99-2.19 0.97-0.99 Reform or Non-Jewish Conservative spouse 1.99 0.85 1.70 95% CI 1.7-2.29 0.76-0.91 NOT married 1.12 0.92 1.03 95% CI 0.83-1.41 0.85-0.99 Jewish spouse 5.64 1.00 5.64 Orthodox 95% CI 5.27-6.01 1.0 5.64 NOT married 0.80 1.00 0.80 95% CI 0.0-1.61 1.0 0.80

S5 Table. Completed fertility by marital status ages 40-49. Married Jewish Married non- Gender and Age Population spouse Jewish spouse Not married 7% 47% 45% All (30-39) No Denom [5% - 12%] [34% - 61%] [33% - 58%] Reform or 20% 38% 42% All (30-39) Conservative [14% - 27%] [28% - 50%] [30% - 56%] 88% 12% All (30-39) Orthodox [71% - 96%] 0% [4% - 29%] 14% 42% 44% All (40-49) No Denom [8% - 23%] [28% - 58%] [27% - 63%] Reform or 33% 31% 36% All (40-49) Conservative [27% - 39%] [24% - 39%] [28% - 45%] 72% 28% All (40-49) Orthodox [58% - 83%] 0% [17% - 42%] 6% 58% 36% Female (30-39) No Denom [3% - 13%] [74% - 40%] [53% - 22%] Reform or 12% 44% 43% Female (30-39) Conservative [7% - 21%] [62% - 28%] [63% - 26%] 82% % 18% Female (30-39) Orthodox [54% - 95%] [% - %] [46% - 5%] 9% 34% 57% Male (30-39) No Denom [5% - 14%] [21% - 50%] [42% - 72%] Reform or 31% 29% 40% Male (30-39) Conservative [23% - 41%] [20% - 39%] [29% - 53%] 91% 9% Male (30-39) Orthodox [71% - 98%] 0% [2% - 29%] 10% 34% 55% Female (40-49) No Denom [5% - 21%] [15% - 60%] [28% - 80%] Reform or 27% 35% 38% Female (40-49) Conservative [20% - 35%] [25% - 47%] [26% - 50%]

81% 19% Female (40-49) Orthodox [60% - 92%] 0% [8% - 40%] 18% 51% 31% Male (40-49) No Denom [9% - 31%] [37% - 65%] [18% - 48%] Reform or 40% 26% 34% Male (40-49) Conservative [31% - 49%] [19% - 36%] [24% - 46%] 64% 36% Male (40-49) Orthodox [45% - 80%] 0% [20% - 55%]

S6 Table. Marital status rates with 95% confidence intervals by age denomination and gender.