Milewski_et_al_englisch.indd Monitoring of German Fertility: Estimation of Monthly and Yearly Total Fertility Rates on the Basis of Preliminary Monthly Data Gabriele Doblhammer, Nadja Milewski, Frederik Peters Abstract: This paper introduces a set of methods for estimating fertility indicators in the absence of recent and short-term birth statistics. For Germany, we propose a set of straightforward methods that allow for the computation of monthly and yearly total fertility rates (mTFR) on the basis of preliminary monthly data, including a confi dence interval. The method for estimating most current fertility rates can be applied when no information on the age structure and the number of women ex- posed to childbearing is available. The methods introduced in this study are useful for calculating monthly birth indicators, with minimal requirements for data quality and statistical effort. In addition, we suggest an approach for projecting the yearly TFR based on preliminary monthly information up to June. Keywords: Demographic monitoring · Germany · monthly total fertility rate · confi dence interval · TFR 1 Introduction Despite the increasing interest – from both population researchers and the pub- lic – in short-term trends and variations in fertility patterns in Germany, no up-to- date birth statistics are currently available. There are two main reasons for the lack of recent and short-term demographic data. First, information on birth numbers is made available to scientists with a time lag. Second, the possibilities for estimating demographic measures based on monthly data have, up to this point, barely been explored. The goal of this paper is to propose a new approach for rapidly estimating short- term developments in fertility rates in Germany. The demographic monitoring of recent developments is especially interesting in contexts in which, for example, a new policy has been introduced, or a sudden social upheaval has occurred. The focus of this paper is, however, on the technical aspects of the proposed strategy for demographic monitoring. We leave out any theoretical, historical, political, and Comparative Population Studies – Zeitschrift für Bevölkerungswissenschaft Vol. 35, 2 (2010): 245-278 © Federal Institute for Population Research 2010 URL: www.comparativepopulationstudies.de DOI: 10.4232/10.CPoS-2010-07en URN: urn:nbn:de:bib-cpos-2010-07en4 • Gabriele Doblhammer, Nadja Milewski, Frederik Peters246 sociological framework that relates to fertility. Instead, we seek to provide a detailed demonstration of our technical approach. We provide methodological tools that will enable us to calculate monthly fertility rates, and to estimate up-to-date indicators of fertility behaviour based on aggregate monthly statistics. Our claims and our research were inspired by the latest state-of-the-art approach for calculating monthly fertility rates, which was introduced in a study by Sobotka et al. (2005). Unfortunately, it is not possible to apply the methods and indicators used in the study for Austria to the German case, because the calculations require high- quality data, such as parity-specifi c information, which is not available for Germany (or for many other countries). Therefore, we propose the construction of a monthly rate that serves as a basis for a relatively prompt estimation of the total fertility rate (TFR). The paper is structured as follows. We start by describing the peculiarities and limitations of fertility data in Germany. Next, we review the literature on four ap- proaches that have been brought up in recent years in order to solve similar data problems. After providing an overview of the different data sources in Germany that contain information on birth numbers (section 3), we introduce our method for calculating a monthly TFR, along with the confi dence intervals in section 4. The forth section deals also with the estimation of the yearly TFR on the basis of monthly data, as well as the projection of the yearly TFR after data for the fi rst six months have become available. The fi fth section presents an evaluation of our method. We conclude with a discussion and some refl ections. 2 Background 2.1 Motivation For the analysis of seasonal patterns of births (e.g., Lam/Miron 1991; Doblhammer et al. 2000), as well as for studies in the growing fi eld of life-course research, data that is monthly, rather than yearly, is required. The effects on fertility of an eco- nomic crisis, welfare state reforms, or legislative changes can only be observed and studied properly when recent and detailed information is available. Information on fertility behaviour that is solid and internationally comparable is, however, pub- lished with a time lag in a yearly cycle. In Germany, the total fertility rate (TFR) for a given year is generally calculated und published in late summer of the following year. More detailed demographic data, such as the age of the women at childbirth and regional distributions, are not made available until even later dates. A further limitation of the German birth statistics is the lack of information on intra-year dynamics. For scientifi c or public use, no monthly data on the number of births per age of the mothers are published, mainly due to privacy restrictions. As a consequence, researchers with an interest in short-term variations in birth numbers are faced with a lack of recent and disag- gregated data. Monitoring of German Fertility • 247 As is the case for most other countries that maintain national statistics, the monthly summarized total number of births is the only short-term indicator that is currently available for Germany (Sobotka et al. 2005). This raw number of births is published by the Federal Statistical Offi ce with a time lag of about three months. Both members of the media and policy makers tend to cite this raw number exten- sively. However, like any other crude number in demographic research, this fi gure has several serious shortcomings that are mostly neglected by the public: because no standardization is done, interpretations and comparisons over time and by coun- try are very limited. Without information on the number of potential mothers ex- posed to childbearing, and the age structure of women who gave birth during a particular month, the number of births is almost useless for research purposes. Short-term trends and changes in births behaviour – i.e., intra-year dynamics – can- not be detected on the basis of the birth numbers currently available. We seek to address these problems by providing a standardized monthly rate that can be continuously updated, and that is made available with little or no delay to researchers, as well as to the public. We call it the “Monitor of births”. One of the key challenges in creating this monitor is to fi nd a balance between demographic precision, which calls for a complex set of methods, and a high degree of acces- sibility. In addition, we strive to take into account the specifi c German context, ob- serving fertility differentials between the eastern and the western federal states by calculating separate rates for the two regions. The challenge that we have been facing in doing so is two-fold: fi rst, we need to obtain adequate data; and, second, we need to solve the methodical problem of calculating a rate standardized for the unknown age of the mothers at childbearing, and for the unknown population at risk in a given month. 2.2 Previous research Monthly fertility rates Before describing our approach, we will review previous projects that have made similar attempts to estimate short-term trends in fertility rates. For several decades of the previous century, fertility rates were calculated exclusively on the basis of yearly data, even though monthly birth numbers were also published (Calot/Na- dot 1977). These two demographic sources were linked for the fi rst time in 1977 in France by Calot and Nadot (1977). Although they used monthly birth data, their stat- ed goal was the estimation of the expected number of births for the current year. The fi rst method for the observation of monthly fertility rates was introduced four years later (Calot 1981)1. In contrast to the ideas Calot and Nadot developed in 1977, the new method used only one data source on monthly births, and was simul- 1 This paper, later termed “the Calot method”, was translated and published in German in the same year by Höhn (1981). • Gabriele Doblhammer, Nadja Milewski, Frederik Peters248 taneously applied to France, Germany, and England and Wales (Calot 1981). Due to the lack of age-specifi c information on births and the number of women exposed to childbearing, Calot made a detailed investigation of the relationship between the yearly total number of births and the total fertility rate. He separated the two meas- ures in order to calculate the mean size of the female population of reproductive ages. To calculate an estimated monthly TFR of the most recent year, the TFR and the population numbers from the most recent year of observation were used, ad- justed for seasonal variations and the different lengths of months and the distribu- tion of weekdays per month (Calot 1981). To evaluate the accuracy of his method, Calot analyzed separately any possible errors due to changes in the female popu- lation and age-specifi c fertility rates. The analysis showed that the deviation per calendar year from 1971 to 1983 was no more than two percent. These errors were mainly attributed to migration and changes in the mean age at birth (Calot 1981). This method can be referred to as the “historic approach”, because it is not ap- plied today, even though comprehensive plans to establish an international monitor- ing system of monthly fertility rates did exist2 (Höhn 1981). We can only speculate as to why Calot’s method failed to become widely accepted: First, the fundamental basis of the method – i.e., the relationship between the summary measures TFR and total number of births, expressed as a mean generational size – may have been too unconventional to fi nd a place in the practices of the federal statistical calculation system. Second, Calot calculated the error of his estimated mean generational size, but failed to evaluate the preliminary birth counts against the later published fi nal numbers. A further problem is related to the inclusion of weekday coeffi cients to control for the different numbers of weekdays and weekend days in each month.3 Even though a bias is caused by such heterogeneity, in many countries the neces- sary information on daily records is not available, and the avoided error is so small that providing an additional data source and calculation method would be far out of proportion to the benefi ts of doing so. Today, there are two approaches that are being used to calculate and publish monthly fertility rates, which we refer to here as “recent approaches”. The fi rst method was developed and applied by the Offi ce for National Statistics in England and Wales (ONS 2009), with the goal of calculating monthly fertility rates for past years, but not for the present year. Accordingly, no estimation of births or use of preliminary data is performed, but a correction for seasonal fl uctuations is made. Seasonal fl uctuations are eliminated through the application of the X-11 algorithm method. The denominator for each monthly rate is calculated by linear interpolation between two known mid-year populations (ONS 2009). 2 In addition to England and Wales, France, Germany, Hungary, the Netherlands, Switzerland, Spain, and Portugal planned to implement the “Calot method” (Höhn 1981). 3 On Sunday and Saturday the number of births is up to 20 % lower than during the week (Höhn 1981). Monitoring of German Fertility • 249 The second, more recently developed approach is the “Fertility Monitoring Sys- tem” of the Vienna Institute of Demography (VID). This approach, which is the only method for calculating monthly TFR on the basis of preliminary and the most recent data, has been described by Sobotka et al. (2005); here termed as “Sobotka ap- proach”. These authors have developed an innovative and complex method that dif- fers fundamentally from its predecessors. They calculate total fertility rates for each birth order separately. In combination with an exposure-specifi c female population denominator, a period average parity (PAP), based on parity progression ratios, is then calculated. Hence, in addition to being standardized for age and parity, the resulting number is not affected by tempo effects. The similarity of this method to previous approaches lies in the adaptation of seasonal and calendar factors. Fur- thermore, they have resolved the problem of instable endings in smoothed time series through the use of auto-regressive, integrated moving-average models (ARI- MA), in combination with the Box-Jenkins method (Sobotka 2005). While Sobotka et al. have succeeded in creating a high-quality system of fertility monitoring for Austria, demographers who want to use the Sobotka approach to create a birth monitoring system in other countries face a serious problem: for this approach to work, disaggregated individual data is needed. Complete data on birth order, the date of the previous birth, and the yearly age- and order-specifi c distribu- tion of women exposed to a birth of a certain order, as well as on daily births, are very rarely available. Thus, the application of the Austrian method to other coun- tries is seldom possible, and Calot’s (1981) original idea of constructing an indicator which allows international comparisons is, even today, not fully realized. To sum up, we can report that historic and recent approaches have been devel- oped to observe and estimate monthly reproductive behaviour. Of the approaches that use preliminary data, only the method developed by Sobotka et al. is in use today. Most attempts have failed to provide an easy-to-understand and easy-to-cal- culate indicator. Based on the lessons of the failure of the Calot method, these two fundamental characteristics should be demanded from an indicator, which could persist for more than just a couple of years. Yearly fertility rates Up to the present, no method for estimating a yearly TFR based on preliminary monthly data has been developed. So far, there have only been attempts at calculat- ing the yearly number of births, as mentioned above (Calot/Nadot 1977). Calot and Nadot proposed a procedure for estimating in advance the number of births that will be observed throughout the current year. In order to make this kind of short-term forecast, two data sources on monthly births are used. The fi rst source contains a provisional number of births, based on manual counts of birth certifi - cates, and published with a delay of at least three months. The second data source is even more up-to-date: it consists of a selected number of births in certain French towns that were released one month after they occurred. In order to estimate the total number of yearly births, a linear extrapolation technique based on the ratio of both sources and a seasonal variation factor was applied (Calot/Nadot 1977). • Gabriele Doblhammer, Nadja Milewski, Frederik Peters250 According to the evaluations of the authors themselves, the mean quadratic er- ror of this extrapolation depends on the distance of the month to the forecast and the amount of provisional data available in the respective year. Because this error is normally distributed, a 95 % confi dence interval could be computed (Calot/Nadot 1977). Even though their approach seemed to work quite well, the authors did not im- plement it in a regular report. In addition, no effort to calculate a rate instead of the number of births was made. 3 Data For Germany, four different types of birth data exist (see Tab. 1); three of them con- tain information about the month of birth. These datasets differ in terms of regional classifi cation, time reference, and time lag of release; and each set of data has its specifi c limitations. First, the most recent source, labeled N1 (we use the names of the datasets as given by the statistical offi ces), contains the number of births pro- vided by the Federal Statistical Offi ce about three months after the submission of the number of births from the local offi ces of vital statistics (Standesämter) to the statistical offi ces of the federal states (Länder). It is important to note that the date of this information does not necessarily match the date of birth. Most signifi cantly, births that occur at the end of December often are not registered by the offi ce of vital statistics until January of the following year. Second, after the births were reported by the offi ces of vital statistics to the sta- tistical offi ce of the federal states, these Länder offi ces add the place of residence of the parents to the statistics and check the data for plausibility. The result of this procedure is aggregated in the preliminary statistics N10, which also contains the variable “Federal state”. While it contains a considerable amount of information, a major problem with this dataset is that all implausible cases are initially excluded, and are not entered into the statistics until a much later date, following clarifi ca- tion of each case. Thus, notable numbers of births are systematically missing every month. It is important to note that the cases that are excluded from N10 because of implausibility are not added to N10 at any time in the future, but are, rather, included in the fi nal dataset N30. Third, the N30 statistics by the Federal Statistical Offi ce provides aggregated birth numbers upon request, and also contains information on the ages of the moth- ers in one-year age groups, as well as on the mothers’ places of residence, and on the revised implausible cases. These numbers are not published until another year has passed, and, unfortunately, they appear without any information on a monthly or regional basis. In order to distinguish this source from the fourth dataset, we call it N30a, where “a” indicates aggregated data. Fourth, the disaggregated data from N30 become available with a time lag of about one year at the Federal Research Data Center (Forschungsdatenzentrum at the Federal Statistical Offi ce or the Statistical Offi ces of the Federal States), but this data can only be accessed by making an offi cial request. We call this scientifi c-use Monitoring of German Fertility • 251 fi le N30suf. These data contain monthly information, together with the age of the mother, as well as a regional breakdown to the district level for all individual cases. Figure 1 shows the deviations of each preliminary data source (N1 and N10) from the fi nal offi cial result N30suf for the total number of children born in 2007. The lower degree of accuracy of the later published statistics N10 is an unexpected fi nd- ing. While N1 differs no more than 10 % from N30suf within a given month, over the long term, N10 varies about -/+25 %, especially in January and December. The cause of this paradoxical phenomenon is a cumulative effect of the inclusion of those cases that were initially considered implausible, and were only later included in N30suf. Because of this shortcoming, we decided to use the less accurate source N10 for the comparison between eastern and western Germany only. For the calcula- tion of the rate for all of Germany, the data quality of N1 is superior until N30suf is fi nally published. Due to the systematic under- and over-coverage of the prelimi- nary monthly birth statistics, a weighting factor for January and December must be added, at least for the data contained in N10. Since the time lag of the publication of the offi cial statistics is also important, Table 2 shows the dates and types of the announcements of the Federal Statistical Offi ce in the year 2009. The offi cial German TFR for 2009 was published in Septem- ber 2009. At this time, the number of births in N10 and N1 for 2009 was updated for March (N10) and June (N1), as well. The fi nal result N30 for 2008 did not become available at the Federal Research Data Center until December 2009; by this time, the preliminary data had already been updated to July 2009 and September 2009. Tab. 1: Types of monthly birth data in Germany Data source Type of data Regional depth Age of the mother at birth Time reference Time lag of release by Federal Statistical Office Other characteristics N1 Aggregated number of births Total Germany No Month > 3 months Date of registration at the Office of Vital Statistics N10 Aggregated number of births Federal State No Month > 6 months Place of residence, date of birth, excluding implausible cases N30a Aggregated number of births District Yes Year > 9 months Place of residence, date of birth including implausible cases N30suf Individual level District Yes Month > 12 months Place of residence, date of birth, including implausible cases Source: Statistical Offi ces in Germany • Gabriele Doblhammer, Nadja Milewski, Frederik Peters252 In addition to information about births, data on the population at risk is needed in order to calculate demographic rates. We approximate the female population at risk by the mid-year population to be in the age range 15 to 45. Since accurate data for women that are monthly and age-specifi c are not available, we use the offi - cial annual fi gures on the numbers of people residing in Germany, which implies the assumption of equally distributed censoring events (death and migration) during a calendar year. Like the yearly TFR, the mid-year population numbers are published by the Fed- eral Statistical Offi ce with a lag of at least 10 months after the end of a given calen- dar year. A simple up-to-date estimation for calendar year t could be obtained by using the population at risk from the previous year: Fig. 1: Deviation between the absolute monthly number of births in the N1 and N10 statistics and the offi cial result N30suf, Germany, 2007 (%) -30 -20 -10 0 10 20 30 Ja nu ar y Fe br ua ry Ma rch Ap ril Ma y Ju ne Ju ly Au gu st Se pte mb er Oc tob er No ve mb er De ce mb er Deviation between andN1 N30suf Deviation between andN10 N30suf Deviation in Percent Month Source: Federal Statistical Offi ce Germany f ]45,15[P )1t(P)t(P f ]44,14[ f ]45,15[ (1) Monitoring of German Fertility • 253 Accordingly, a small bias may be caused by migration and the number of deaths that occur during the preceding year. As will be seen later in our results section, this does not constitute a major problem for Germany as a whole, but introduces a bias for East Germany. 4 Methods We develop one approach for calculating monthly fertility rates on the basis of the preliminary data N1 and N10, and label them “preliminary mTFR”. Then we estimate a preliminary yearly TFR that is based on N1, and which is available well before the offi cial announcement. We also calculate the fi nal TFR on a monthly and a yearly basis once all the fi nal data of a year have become available, and label this the “fi nal mTFR (monthly)” and the “fi nal TFR (yearly)”. We test the signifi cance of the difference in the fi nal mTFRs of the current and previous years by assuming that the number of births follows a Poisson distribu- tion. Finally, we project the yearly total fertility rate as soon as the preliminary data have become available for the fi rst half of the current year (January to June); this fi gure is labelled the “projected yearly TFR”. 4.1 Estimating monthly total fertility rates Estimation of the fi nal mTFR The fi nal mTFR can be computed accurately on the basis of the fi nal data N30suf. Since the births included in this data, here referred as , are classifi ed by months and the age x of the mother, and the population at risk is known (as derived Tab. 2: Dates of announcements by the Federal Statistical Offi ce regarding birth data (years 2008 and 2009) Month Type of Announcement September 2009 Official TFR for Germany in 2008 (N30a) September 2009 Number of births by Federal Länder in March 2009 (N10) September 2009 Number of births in June 2009 (N1) December 2009 Final result for the year 2008 (N30suf) becomes available at the Federal Research Data Center December 2009 Number of births by Federal Länder in July 2009 (N10) December 2009 Number of births for Germany in September 2009 (N1) Source: Federal Statistical Offi ce Germany suf30N xB • Gabriele Doblhammer, Nadja Milewski, Frederik Peters254 from equation 1), a fi nal mTFR (m,t) for month m and calendar year t can be obtained by (2): Note that we introduce here the calendar adjustment factor caf (m,t), which standardizes each month m to 1/12 of each calendar year t. The factor caf (m,t) is calculated by dividing the number of days of a particular month n(m) by the number of days of the given year n(t). The term is then multiplied by 12 in order to construct an easy-to-interpret indicator as follows: As a result, the mTFR (m,t) for month m and calendar year t expresses the av- erage number of children a woman would have if the conditions of the particular month m were constant throughout the whole year t. Estimation of the preliminary mTFR For computing most recent fertility rates, based on the statistics N1 and N10 (which are available well before N30suf), an additional intermediary step is necessary, since only the total number of births, without any information on the age of the mothers at birth, are available here. We assume that the age-specifi c birth rates of a given year r x (t) are the same as in the preceding year.4 Subsequently, the monthly number of births per age can be obtained by multi- plying the number of women of the previous year by the recent birth rate r x (t). )t,m(caf )t(P )t,m(B )t,m(mTFR 45x 15x f x suf30N x (2) )m(n )t(n 12 )m(n 12/)t(n )t,m(caf (3) 4 Originally, we had in this case used the approach that the expected relative number of births per age and month is the same as the relative number of births per age in the preceding year. In the evaluation of our results, we compared both approaches and found that they produced almost equal results; deviations occurred only on the third decimal (Peters/Milewski/Doblham- mer 2009). )1t(P )1t(B )t(r f x suf30N x x (4) )1t(P f ]1x[ )1t(P)t(r)t(B f ]1x[x const x (5) Monitoring of German Fertility • 255 The resulting number represents the births per age that would have been observed if the age-specifi c fertility rates had been identical to year (t-1). Accord- ingly, we can now answer the following question: “How many births would have been observed in the respective age if the TFR had been the same as in the previous year, and no changes in the age distribution had occurred?” In order to calculate the number of births per age which fi t to the observed total number in the statistics N1 or N10, a weighting procedure has to be adopted: For computing the age-specifi c births for eastern and western Germany, BN10(m,t), instead of BN1(m,t), is used in equation 6. According to equation 2, the preliminary monthly total fertility rate for Germany, labelled mTFR, is calculated by summing up the age-specifi c birth rates over ages 15 to 45: In the same manner, the total fertility rates for eastern and western Germany are computed as: Since the number of births in N10 for western Germany is systematically un- derestimated in January by about 25 % (20 % for eastern Germany), and is sys- tematically overestimated in December by approximately 25 % (20 % for eastern Germany) (see Fig. 1), a weighting factor for these months is specifi ed. This factor is termed error e, and is 0.25 for western Germany and 0.2 for eastern Germany. )t,m(B )t(B )t(B )t,m(B 1N 45x 15x const x const x1N x (6) )t,m(caf )1t(P )t,m(B )t,m(mTFR 45x 15x f ]1x[ 1N x (7) )t,m(caf )1t(P )t,m(B )t,m(mTFR 45x 15x f ]1x[ 10N x (8) )m(n )e1()t(n )t(cafDecember (9) )t(B constx )m(n )e1()t(n )t(cafJanuary • Gabriele Doblhammer, Nadja Milewski, Frederik Peters256 Estimation of the preliminary yearly TFR In addition to allowing us to observe monthly fertility behaviour, our approach for monitoring births in Germany meets the demand for an up-to-date yearly TFR. Nor- mally, this indicator is offi cially published by the Federal Statistical Offi ce for the previous year around August5 of the following year, while the preliminary number of total births in a calendar year N1 is already available in early spring of the follow- ing year. Due to this time lag, we decided to estimate a yearly TFR that is based on N1, and which can be made available before the offi cial announcement. Again, the major problem that we had to solve was the missing information on the age structure of the mothers. As for monthly fertility, only the total number of births is available for the previous year, and the population at risk is unknown. As was done for the computation of the monthly TFR, we assume that neither mor- tality nor migration occurred among the women in reproductive ages during the pre- vious year. The population at risk can then be computed according to equation (1). In order to obtain age-specifi c fertility rates without having any information on the age-at-birth distribution, we use the respective distribution of the previous year. As was done in estimating preliminary monthly age-specifi c births counts, r x (t) of equation 4 is used for estimating yearly data, performed in equation 10. As (t) represents the number of births that would be expected if fertility rates had been the same as in the preceding year; equation 11 weights this number by the actually observed preliminary number of births. Finally, the preliminary yearly TFR for Germany can be computed analogically to our monthly procedure: 5 The offi cial TFR for 2007 was published on August 20, 2008; www.destatis.de/jetspeed/portal/ cms/Sites/destatis/Internet/DE/Presse/pm/2008/08/PD08_ _298_ _12641,templateId=renderPri nt.psml [Access: 07/14/2009]. The offi cial TFR for 2008 was published on September 3rd 2009: www.destatis.de/jetspeed/portal/cms/Sites/destatis/Internet/DE/Presse/pm/2009/09/PD09_ _ 327_ _12641,templateId=renderPrint.psml )1t(P)t(r)t(B f ]1x[x const x (10) const xB )t(B )t(B )t(B )t(B 1N 45x 15x const x const x1N x (11) 45x 15x f ]1x[ 1N x1N )1t(P )t(B )t(TFR (12) Monitoring of German Fertility • 257 The quality of this preliminary yearly TFR depends, fi rst, on the degree of mis- match between the preliminary and the fi nal total number of births; and, second, on the amount of variation in age-specifi c distributions of births. Generally, these limitations should not seriously distort the estimated TFR, because the preliminary number of births N1 usually has few missing cases, and fertility behaviour concern- ing age may not change dramatically from one year to another. Signifi cance test of the difference in the TFR of the current month compared to the same month of the previous year One of the most characteristic features of monthly fertility rate measurement is its seasonal pattern (c.f. Flaskämper 1962: 258f.; Doblhammer et al. 2000)6. Therefore, signifi cant trends in fertility cannot be detected by comparing monthly TFRs during one year. In addition, we have to control for calendar-month variation by compar- ing fertility rates of a particular month to the fertility rates in the same month of the previous year: Deviation(m,t) = mTFR (m,t) – mTFR(m,t–1) Another important issue that arises when observing monthly time series involves the distinction between random and systematic variations. Due to the high degree of uncertainty of preliminary data, we will not compute any form of test statistics for monthly calculated fertility rates on the basis of N1 and N10. Thus, we will only test differences on the basis of N30suf. Note that this approach works for monthly, as well as for yearly data. A fi rst approximation involves treating births occurring in a certain month by a fi xed number of women of a specifi c age as rare events,7 and therefore as the re- alization of a Poisson distribution. Accordingly, the estimated age-specifi c variance of births is: By treating births at each age as stochastically independent from one another, the variance for the TFR can be computed by summing up the age-specifi c vari- ances from ages 15 to 45:8 (13) 6 We decided to avoid eliminating seasonal fl uctuations by a certain algorithm since the prelimi- nary data used as input do not include stable seasonal patterns. 7 Rare events are characterized by the probability of occurrence converging to zero, while, at the same time, the number of trials converges to infi nity. 8 The sum of Poisson-distributed random variables follows a Poisson distribution whose param- eter is the sum of the component parameters. 2f ]1x[ suf30N xsuf30N x )P( B )ASBR(Var (14) • Gabriele Doblhammer, Nadja Milewski, Frederik Peters258 Given a suffi ciently large number of births we can approximate the Poisson dis- tribution by the Normal distribution and we compute the confi dence interval of the TFR by the following formula: We follow Payton et al. (2003), who demonstrate that non-overlapping confi dence intervals corresponding to an -error of 17 % (z 0.83 =1.0) are suffi cient to approxi- mate a signifi cance test based on an -error of 0.05 (Payton et al. 2003: 5). Projection of the yearly TFR based on the fi rst six months of the current year In addition to the estimation of a preliminary yearly TFR, our goal is the projection of the fi nal yearly TFR on the basis of the births that occurred in the fi rst half of the current year. For example, to estimate a TFR in 2007, we calculated the proportion of the cumulated preliminary mTFR up to June from the later observed fi nal TFRN30a, as published by the Federal Statistical Offi ce, separately for the period 2001-2006, according to equation 17. The geometric mean of these six proportions is almost exactly 50 %, as seen in Table 5, and serves as a weighting factor for the projection of the yearly TFR, demonstrated in equation 18. 5 Evaluation of the estimates of the preliminary monthly and yearly TFRs For the evaluation of our approach, we use the year 2007 (additional material for the years 2001 to 2006 is displayed in the Appendix). We start by evaluating the estimates of the monthly TFRs for Germany (Tab. 3A). Then we review our prelimi- nary monthly estimates for eastern and western Germany (Tab. 3B-C). Finally, we )TFR(VarzTFRUpperLimit/LowerLimit suf30N83.0 suf30N (16) a30N 1N Junm Janm TFR )t,m(mTFR )t(p (17) p Junm Janm 1N )t,m(mTFR)6t,...,1t(p)t(RTF (18) 45x 15x 2f ]1x[ suf30N xsuf30N )P( B )TFR(Var (15) Monitoring of German Fertility • 259 evaluate our estimates of the preliminary yearly TFR (Tab. 4A-C) and show our early projection of the TFR of the current year on the basis of six-month data (Tab. 5). 5.1 Monthly fertility rates Germany Table 3A presents the results for the preliminary and the fi nal mTFR. The second column, fi nal mTFR, contains the fi nal rate for the respective month, together with the confi dence intervals (in columns 3 and 4, UL: Upper Limit, LL: Lower Limit), as calculated on the basis of N30suf. Column 5 contains our preliminary mTFR, cal- culated on the basis of N1. Column 6 shows the absolute deviation of our estimate from the fi nal mTFR. The calculations for total Germany are based on the earliest available statistics (N1). When using N1, the biggest absolute deviation appears in December (-0.15), with comparatively large deviations also seen in September and October 2007. The deviations are somewhat smaller in the preceding years (see Tab. A1a in the Ap- pendix), and appear more frequently in January and April. Figure 2A displays the average percentage deviation and the span of the percentage deviations for the years 2001 to 2007. Western Germany and eastern Germany Table 3B shows the values of the mTFR for western Germany, while Table 3C dis- plays the corresponding values for eastern Germany. The calculations for western and eastern Germany are based on a different data source (i.e., N10) than the estimations for Germany (N1). It should be noted that, whereas Berlin is included in the German mTFR, it is excluded from the western and eastern mTFR; here we follow the common practice of the statistical offi ces. In addition, N10 excludes implausible cases. Therefore, the German estimates cannot be compared to the eastern-western results. (Example: We calculate a preliminary German mTFR of 1.39 for January 2007, but the rate for western Germany is 1.31, and the rate for eastern Germany 1.26. This indicates that a proportion of the births are missing in the regional mTFR.) Nevertheless, the deviation of our preliminary western German mTFR from the fi nal result based on N30suf (Tab. 3B, Tab. A1b in the Appendix) is, on average, small. The maximum absolute deviation in 2007 is 0.13 in October. Figure 2B shows the average percentage deviation and the span of percentage deviations for western Germany in the years 2001 to 2007. Whereas our estimates for western Germany show positive and negative deviations from the fi nal mTFR, the trend is different for eastern Germany (Tab. 3C and A1c in the Appendix): Here, we underestimate the preliminary mTFR by about roughly three percent, or, in absolute values, between -0.15 to -0.12. We assume that this systematic underestimation is related to our as- sumptions that there is no out-migration from eastern Germany, and that we can use the population structure of the previous year as an approximation of the current • Gabriele Doblhammer, Nadja Milewski, Frederik Peters260 Tab. 3: Estimations of mTFR in 2007 – confi dence intervals and absolute errors A) Germany Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N1) from final mTFR January 1.35 1.35 1.34 1.39 0.04 February 1.33 1.34 1.32 1.34 0.01 March 1.32 1.33 1.31 1.31 -0.01 April 1.25 1.25 1.24 1.25 0.00 May 1.33 1.33 1.32 1.34 0.01 June 1.40 1.41 1.39 1.39 -0.01 July 1.46 1.46 1.45 1.48 0.02 August 1.47 1.48 1.46 1.51 0.03 September 1.51 1.52 1.50 1.40 -0.11 October 1.40 1.41 1.39 1.53 0.13 November 1.32 1.33 1.31 1.36 0.04 December 1.29 1.30 1.29 1.14 -0.15 Source: Calculations based on N1 and N30 suf. B) Western Germany Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N10) from final mTFR January 1.37 1.38 1.36 1.31 -0.06 February 1.34 1.35 1.33 1.32 -0.02 March 1.33 1.34 1.32 1.32 -0.01 April 1.25 1.26 1.24 1.26 0.01 May 1.33 1.34 1.32 1.34 0.01 June 1.40 1.41 1.39 1.38 -0.02 July 1.45 1.46 1.44 1.46 0.01 August 1.48 1.49 1.47 1.50 0.03 September 1.50 1.51 1.49 1.40 -0.11 October 1.40 1.41 1.39 1.53 0.13 November 1.33 1.34 1.32 1.37 0.04 December 1.30 1.31 1.29 1.24 -0.06 Note: January weighted by 0.75, December weighted by 1.25. Source: Calculations based on N10 and N30suf. C) Eastern Germany Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N10) from final mTFR January 1.31 1.33 1.29 1.26 -0.05 February 1.30 1.32 1.28 1.25 -0.04 March 1.30 1.32 1.28 1.27 -0.03 April 1.24 1.26 1.22 1.19 -0.05 May 1.34 1.36 1.32 1.33 -0.01 June 1.44 1.46 1.42 1.37 -0.07 July 1.51 1.53 1.49 1.51 0.00 August 1.49 1.52 1.47 1.48 -0.01 September 1.55 1.57 1.53 1.39 -0.15 October 1.39 1.41 1.37 1.44 0.05 November 1.30 1.32 1.28 1.35 0.04 December 1.25 1.27 1.23 1.18 -0.08 Note: January weighted by 0.8, December weighted by 1.2. Source: Calculations based on N10 and N30suf. Monitoring of German Fertility • 261 Fig. 2: Average percentage deviation (solid line) and span of deviations of the preliminary mTFR from the fi nal mTFR – years 2001 to 2007 -20 -10 0 10 20 Ja nu ar y Fe br ua ry Ma rch Ap ril Ma y Ju ne Ju ly Au gu st Se pte mb er Oc tob er No ve mb er De ce mb er Deviation in Percent Month -20 -10 0 10 20 Ja nu ar y Fe br ua ry Ma rch Ap ril Ma y Ju ne Ju ly Au gu st Se pte mb er Oc tob er No ve mb er De ce mb er Deviation in Percent Month A) Germany B) Western Germany • Gabriele Doblhammer, Nadja Milewski, Frederik Peters262 year’s risk population. In addition, a real increase in birth numbers may have oc- cured in the second half of the year, which would be underestimated by our mTFR. 5.2 Yearly fertility rates Estimation After the preliminary data of all months have been published, we estimate the pre- liminary yearly TFR. Table 4 shows the fi nal TFR (calculated on the basis of N30suf; column 2) and its confi dence intervals (columns 3 and 4), our estimation on the basis of N1 and N10, respectively, and its deviation from the fi nal TFR (columns 5 and 6). For all of Germany (Tab. 4A), our estimates of the preliminary yearly TFR deviate from the fi nal fi gures on average by +/0.01, while the maximum deviation is 0.03. The average deviation for western Germany (Table 4B) is zero, while for eastern Germany, it is -0.03 (Tab. 4C). Source: Calculations based on N1, N10 and N30suf. -20 -10 0 10 20 Ja nu ar y Fe br ua ry Ma rch Ap ril Ma y Ju ne Ju ly Au gu st Se pte mb er Oc tob er No ve mb er De ce mb er Deviation in Percent Month C) Eastern Germany Monitoring of German Fertility • 263 Tab. 4: Estimations of yearly TFR – confi dence intervals and absolute errors for the years 2001 to 2007 A) Germany Final TFR Confidence intervall Preliminary TFR Deviation preliminary TFR Year (N30suf) UL LL (N1) from final TFR 2001 1.35 1.35 1.34 1.35 0.00 2002 1.34 1.35 1.33 1.37 0.03 2003 1.34 1.35 1.33 1.37 0.03 2004 1.36 1.36 1.35 1.38 0.02 2005 1.34 1.35 1.33 1.35 0.01 2006 1.33 1.34 1.32 1.34 0.01 2007 1.37 1.38 1.36 1.37 0.00 Average deviation 0.01 Source: Calculations based on N1 and N30suf. B) Western Germany Final TFR Confidence intervall Preliminary TFR Deviation preliminary TFR Year (N30suf) UL LL (N10) from final TFR 2001 1.38 1.39 1.37 1.38 0.00 2002 1.37 1.38 1.36 1.38 0.01 2003 1.36 1.37 1.35 1.36 0.00 2004 1.37 1.38 1.36 1.38 0.00 2005 1.35 1.36 1.34 1.35 0.00 2006 1.34 1.35 1.33 1.34 0.00 2007 1.37 1.38 1.36 1.37 -0.01 Average deviation 0.00 Source: Calculations based on N10 and N30suf. C) Eastern Germany Final TFR Confidence intervall Preliminary TFR Deviation preliminary TFR Year (N30suf) UL LL (N10) from final TFR 2001 1.23 1.25 1.21 1.20 -0.03 2002 1.24 1.26 1.22 1.21 -0.02 2003 1.26 1.28 1.24 1.24 -0.02 2004 1.31 1.33 1.29 1.29 -0.02 2005 1.30 1.32 1.28 1.27 -0.02 2006 1.30 1.32 1.28 1.28 -0.02 2007 1.37 1.39 1.35 1.34 -0.03 Average deviation -0.03 Source: Calculations based on N10 and N30suf. • Gabriele Doblhammer, Nadja Milewski, Frederik Peters264 Projection of the yearly TFR based on monthly rates We use our approach presented above to project the yearly TFR of the current year after the preliminary data for the months January to June have become available. We demonstrate the calculations using the years 2007 and 2008 as examples. The projection procedure consists of three steps. Based on the retrospectively gathered preliminary data N1, we fi rst estimate cumulated monthly fertility rates for the years 2001 to 2006. Second, we calculate the proportion of the estimated cumulated TFR on the fi nal yearly TFR based on the N30suf, which is published at a later date. Third, we use June as a cut-off point for the projection, because over the period 2001 to 2006, an average of 50 % of the yearly TFR of the respective year was reached at the end of June. Table 5 shows this procedure for the projection of the TFR for the year 2007, based on the previous fi ve years 2001 to 2006, and the projection of the TFR for 2008, based on the years 2002 to 2007. We could test this method only for the years 2007 and 2008, since the method of data collection in N1 was changed in 2001. Therefore, data on the years before 2001 are not comparable with data after this year. For the year 2007, the projected yearly TFR is 1.34, which is an underestimation of 0.03 of the fi nal TFR, and which, on the basis of N30suf, turned out to be 1.37. The Tab. 5: Projection of the yearly German TFR, 2007 (based on years 2001 to 2006) and 2008 (based on years 2002 to 2007) Year Preliminary mTFR Final TFR Proportion of mTFR January-June Reference Period January-June (N1) (N30suf) from final TFR in % 2001 0.676 1.346 50.3 2002 0.678 1.339 50.7 2003 0.674 1.338 50.4 2004 0.674 1.357 49.7 2005 0.667 1.338 49.9 2006 0.659 1.329 49.5 2007 0.668 1.368 48.8 2008 0.685 1.376 49.6 Geom. Mean 2001-06 50.1 Geom. Mean 2002-07 49.8 Projection TFR 2007 1.335 Deviation from final TFR -0.034 Projection TFR 2008 1.375 Deviation from final TFR -0.001 Source: Calculations based on N1 and N30suf. Monitoring of German Fertility • 265 reason for this underestimation is that from the middle of 2007 onwards, monthly birth rates are signifi cantly higher than those in the previous year. When we apply this simple technique to the 2008 data, our projection based on the births from January to June results in a yearly TFR of 1.38, which coincides with the fi nal TFR at the end of 2008 (1.38). 6 Discussion We have developed an approach for estimating the monthly TFR in the current year based on preliminary data that does not include the age of the mother at birth. Since this crucial information is only available for the previous year, we impute the age of the mother at birth in the current year by applying the age-specifi c birth rate to the data of the current year. Timely information on the monthly TFR is of no help if the quality of the prelimi- nary data is poor. This paper presents an overview of the various sources used for the calculation of the monthly fertility rates. Calculating these rates can be challeng- ing because the different sources are available at different points in time, they refer to different regional units, and certain cases are excluded from certain sources. The data source that becomes available fi rst is N1. Here, the main problem is that the births are not correctly distributed to the month. N10, the data source that becomes available next, is supposed to provide more precise data, since it also includes in- formation about whether the birth took place in eastern or in western Germany. However, we fi nd that the estimations that are based on N10 are the least accurate, because the cases that are unclear are not included in these statistics. In addition, the case of Berlin is diffi cult to handle. In line with the practices of the statistical of- fi ces in Germany, we excluded Berlin from the estimations that are based on the N10 source. This leads to deviations of up to 10 % from the fi nal TFR in N30suf, which is, of course, most often an underestimation. Therefore, the results for eastern and western Germany based on N10 have to be interpreted with caution. If the goal is to have timely results for all of Germany, N1 is the most accurate data source. If, on the other hand, the goal is to make a regional comparison, N10 can serve as a starting point. However, researchers using N10 should be aware that there will be a six-month delay before this data becomes available, and that a certain degree of underestimation of the fertility rates may be expected to occur. Different opinions exist concerning the statistical treatment of the seasonal fl uc- tuations in fertility. The Sobotka approach eliminates them which has the advantage that the level of fertility can be compared within a year. Changes in fertility patterns can thus be judged from one month to the other. Our approach keeps the seasonal fl uctuations which has the advantage that users of the monitor are becoming aware of the large systematic fl uctuations that occur over the course of a year. Another reason for keeping the seasonal fl uctuations is the limited type of data that we are using. We have to approximate the age structure of the mothers, as well as the pop- ulation at risk. We do not want to modify the data any further and thus decided to estimate the fertility rates that fi t the aggregate number of births. Not adjusting for • Gabriele Doblhammer, Nadja Milewski, Frederik Peters266 seasonality, however, has the disadvantage that the TFR of a specifi c month cannot be used as a predictor of the yearly TFR and that changes in fertility behaviour can only be evaluated in comparison to the same month of the previous year. Our procedure systematically underestimates eastern German fertility. We trace this back to the assumption that the population of the previous year is an adequate estimation of the mid-term population of the current year. In fact, we know that this is not the case and that out-migration plays a large role in changing the underlying population structure in the eastern federal states. Future improvements of our pro- cedure should thus explore to what extent out-migration can be incorporated into the estimates. Despite the problems that arise from the data sources, we believe that our ap- proach provides adequate monthly fertility rates. Nevertheless, we acknowledge that our method still has some shortcomings. For detailed research in the future, parity-specifi c data is necessary. Since this information is as yet missing from the German birth statistics, other sources have to be taken into account. A promising source could be the German perinatal statistics, which contains detailed informa- tion about the biological birth order (Kreyenfeld et al. 2010). Without implementa- tion of parity-specifi c information, important demographic measures, such as the mean age at fi rst birth or particular tempo standardizations, which are addressed in the Bongaarts-Feeney approach (2005), and parity-progression ratios as calculated in Sobotka et al. 2005, cannot be calculated. Another shortcoming of our approach is that we assume the age distribution of births to be constant between the previous and the current year. This assumption is particularly problematic in eastern Germany, since the age distribution in that part of the country may be affected by high out-migration fl ows. A solution could be to implement a factor drawn from the previous years. Since migration behaviour is, however, the least predictable demographic force, an introduction of a migration adjustment seems problematic in itself. We are aware of the fact that the age-specif- ic distribution of births varies permanently, with a relatively constant rate of change in several age groups. An easy solution could be the implementation of a sort of drift; i.e., to assume that the particular age-specifi c rates increase, while others de- crease. In our opinion, a detailed time-series analysis would be necessary to attain that goal. One advantage of using such a procedure would be that it would allow us to model many different assumptions and scenarios regarding variations in the age distribution of births. A disadvantage of using time-series analysis is that we would need a suffi ciently long time series, which would not be possible currently because adequate birth data have only been available since 2000. Our approach of projecting the yearly TFR of the current year based on prelimi- nary monthly data up to June results in an estimate of high validity. The projection procedure works when there are no systematic differences between the birth rates in the fi rst and second halves of the calendar year. If a substantial change occurs – which may, for example, be caused by social upheavals or considerable changes in family policies – early conclusions regarding yearly rates will prove incorrect, as was the case in the year 2007. By contrast, if we want to investigate the short- term effects on birth behaviour of certain events, such as the introduction of family Monitoring of German Fertility • 267 policies, we can use the monthly total fertility rates produced by our approach. For example, our approach was used to measure the impact on fertility rates of the new parental-leave benefi t, which went into effect in Germany in January 2007. Since the new childcare benefi t was not announced until in mid-2006, we expected that the ef- fects of the new law would not become visible in the offi cial birth statistics until the second half of 2007. In fact, we found signifi cantly increased monthly fertility rates compared to the previous year from autumn 2007 onwards. This systematic change in fertility rates led to the underestimation in the projection of the fi nal yearly TFR. The number of births in Germany and the trends in fertility rates have been of great interest to the general public, and they feature prominently in the political discussion. Given the interest in this topic, it is surprising that offi cial data on births are published with a considerable time lag, and that preliminary data lack important information for the calculation of fertility statistics. The result is that systematic changes in fertility, caused by new policies or societal changes, can only be de- tected with a considerable time lag. The monitoring procedure presented in this paper overcomes most of the data limitations of the preliminary data, and provides timely and adequate information on fertility trends in Germany. Our approach can detect systematic changes in fertility trends, such as in the second half of 2007, and it can project the fi nal total fertility rate with a high degree of accuracy, after data have become available for the fi rst six months. The monitoring procedure is implemented on the webpage www.rostockerzentrum.de/ and is updated monthly as soon as the latest data are published by Federal Statistical Offi ce Germany (see Fig. A1 in the Appendix). The authors are especially grateful to Johannes Klotz of Statistics Austria for advice on the project “Monitor of births”, especially regarding the calculation of a TFR con- fi dence interval. Comments and suggestions from the members of the Max Planck Institute for Demographic Research, Rostock, the Rostock Center for the Study of Demographic Change, and two anonymous reviewers are gratefully acknowledged. The publication on the webpage has been realized by Juliane Steinberg. We thank Miriam Hils for valuable language editing of the paper. References Bongaarts, John; Feeney, Griffi th, 2005: The Quantum and Tempo of Life Cycle Events. Population Council, Working Paper 207. New York: Population Council Calot, Gérard, 1981: L’observation de la fécondité à court et moyen terme. In: Population 36,1: 9-40 Calot, Gérard; Nadot, Robert, 1977: Combien y aura-t-il de naissances dans l’année? In: Population 32 (numero special): 185-229 Doblhammer, Gabriele; Rodgers, Joseph C.; Rau, Roland, 2000: Seasonality of birth in Nineteenth and Twentieth Century Austria. In: Social Biology 47,3: 201-217 • Gabriele Doblhammer, Nadja Milewski, Frederik Peters268 Flaskämper, Paul, 1962: Bevölkerungsstatistik. Mit einleitenden Ausführungen über den Gegenstand der Besonderen Sozialwissenschaftlichen Statistik überhaupt. Hamburg: Richard Meiner Höhn, Charlotte, 1981: Die CALOT-Methode zur aktuellen Beurteilung von Geburtenni- veau und -trend. In: Zeitschrift für Bevölkerungswissenschaft 7,2: 231-254 Kreyenfeld, Michaela; Scholz, Rembrandt; Peters, Frederik, Wlosnewski, Ines, 2010: Order-Specifi c Fertility Rates for Germany: Estimates from Perinatal Statistics for the Period 2001-2008. In: Comparative Population Studies 35,2: 207-224 [DOI: 10.4232/10. CPoS-2010-06en] Lam, David A.; Miron, Jeffrey A., 1991: Seasonality of births in human populations. In: Social Biology 38: 51-78 Offi ce for National Statistics, 2009: Review of the National Statistician on births and patterns of family building in England and Wales, 2008 [http://www.statistics.gov.uk/ downloads/theme_population/FM1-37/FM1-37.pdf] Payton, Mark E.; Greenstone, Matthew; Schenker, Nathaniel, 2003: Overlapping confi - dence intervals or standard error intervals: What do they mean in terms of statistical signifi cance? In: Journal of Insect Science 34,3: 34 Peters, Frederik; Milewski, Nadja; Doblhammer, Gabriele, 2009: The “Geburtenmoni- tor” – Estimating Births Rates in Germany on the Basis of Monthly Data. Discussion Paper No. 27 of the Rostock Center for the Study of Demographic Change. Rostock: RZ [http://www.rostockerzentrum.de/publikationen/rz_diskussionpapier_27.pdf] Sobotka, Tomas et al., 2005: Monthly Estimates of the Quantum of Fertility: Towards a Fertility Monitoring System in Austria. In: Lutz, Wolfgang; Feichtinger, Gustav (Eds.): Vienna Yearbook of Population Research 2005. Vienna: Verlag der Österreichischen Akademie der Wissenschaften: 109-141 [DOI: 10.1553/populationyearbook2005s109] A German translation of this authorised original article by Federal Institute for Population Research is available under the title “Monitor der Entwicklung der Geburtenhäufi gkeit in Deutschland: Schät- zung von monatlichen und jährlichen zusammengefassten Geburtenziffern auf der Grundlage vor- läufi ger monatlicher Daten”, DOI 10.4232/10.CPoS-2010-07de or URN urn:nbn:de:bib-cpos-2010- 07de0, at http://www.comparativepopulationstudies.de. Dr. Nadja Milewski ( ), Prof. Dr. Gabriele Doblhammer, M. Sc. Frederik Peters. Rostock Center for the Study of Demographic Change, Konrad-Zuse-Str. 1, 18057 Rostock. E-Mail: nadja.milewski@uni-rostock.de, doblhammer@rostockerzentrum.de, peters@ rostockerzentrum.de Monitoring of German Fertility • 269 Appendix Example for the estimation of the preliminary mTFR in 2007 Basic information given: Number of births age 20 in 2006 (N30suf): 14,256 Total number of birth in 2006 (N30suf): 672,722 Number of births January 2007 (N1): 58,875 Population of age 19 in 2006: 475,857 Population of age 20 in 2006: 472,189 Estimation for 2007: 1st step: calculation of r 20,2007 according to equation (4) In 2007 the age-specifi c birth rate for age 20 is 0.030. 2nd step: calculation of according to equation (5) If the age-specifi c birth rate at age 20 had been the same as in 2006, 14,276 children would have been born in 2007. 3rd step: calculation of according to equation (6): In January 2007, 1,268 births are estimated to have occurred at age 20. 030.0 472189 14256 )2006(P )2006(B )2007(r f 20 30N 20 20 )2007(B const20 14276475857030.0 )2006(P)2007(r)2007(B f ]19[20 const 20 )2007,January(B 1N20 126814276 662407 58857 )2007(B )2007(B )2007,January(B )2007,January(B const2045x 15x const x 1N 1N 20 • Gabriele Doblhammer, Nadja Milewski, Frederik Peters270 4th step: calculation of mASBR January (2007) according to equation (7) and (9): In January 2007 for every woman at age 20, 0.0314 children are estimated. Summed up over ages 15 to 45, the monthly total fertility rate is computed, which represents the number of children a woman would have had if the conditions in January had been constant throughout the whole year 2007. Online-Publication of the “Monitor of births” at the Rostock Centre for Demographic Change The “Monitor of births” is updated monthly for total Germany, the regional levels of Germany, eastern Germany and western Germany. In addition, a virtual press kit is published as soon as the new estimation of the yearly TFR is calculated, see www. rostockerzentrum.de/. Figure A1 is an example from the website, which is published in German. The solid line represents fi nal data based on N30suf. Preliminary data (N1 and N10) are presented as dashed line. Below the line chart, bars indicate the respective differences between a given month and the same month of the previous year. Here, the arrows show signifi cant differences at a confi dence level of 95 %, which is performed only for fi nal data. Lastly, the two boxes in the upper section of the chart contain the most recent fi nal and preliminary monthly TFR. 0314.0 31 365 475857 1268 )2007,January(caf )2006(P )January(B )2007(mASBR f ]19[ 1N 20 January Monitoring of German Fertility • 271 Fig. A1: Monthly TFR for Germany, July 2004 to June 2009, as published on the website (in German only) Note: The dashed line indicates estimated age structures and a w eighting f actor f or January and December Signif icant increase compared to the respective month in the previous year (95%) Signif icant decrease compared to the respective month in the previous year (95%) Figure: Rostock Center f or the Study of Demographic Change / w w w .zdw a.de Source: Statistical off ices of the f ederal states, Federal Statistical Of f ice Monthly total fertility rate for Germany January 2005 to December 2009 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 January 05 July 05 January 06 July 06 January 07 July 07 January 08 July 08 January 09 July 09 M o n th ly t o ta l f er ti lit y ra te -15% 0% 15% 30% 45% C h an g e co m p ared to th e sam e m o n th in th e resp ective year December 2007: 1.29 December 2009: 1.27 • Gabriele Doblhammer, Nadja Milewski, Frederik Peters272 Tab. A1a: Estimations of mTFR in 2001 to 2006, Germany – confi dence intervals and absolute errors 2001 Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N1) from final mTFR January 1.38 1.39 1.37 1.41 0.03 February 1.33 1.33 1.32 1.35 0.02 March 1.32 1.32 1.31 1.33 0.02 April 1.31 1.32 1.30 1.27 -0.04 May 1.36 1.37 1.35 1.43 0.07 June 1.37 1.38 1.36 1.33 -0.04 July 1.43 1.44 1.42 1.45 0.02 August 1.42 1.42 1.41 1.46 0.05 September 1.41 1.41 1.40 1.33 -0.07 October 1.32 1.33 1.31 1.44 0.12 November 1.28 1.28 1.27 1.31 0.04 December 1.24 1.25 1.23 1.09 -0.15 2002 Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N1) from final mTFR January 1.34 1.34 1.33 1.49 0.15 February 1.35 1.36 1.35 1.38 0.03 March 1.33 1.34 1.32 1.26 -0.07 April 1.31 1.32 1.30 1.42 0.11 May 1.29 1.30 1.28 1.30 0.01 June 1.34 1.35 1.33 1.30 -0.04 July 1.43 1.43 1.42 1.51 0.08 August 1.39 1.40 1.39 1.40 0.01 September 1.44 1.45 1.43 1.44 0.00 October 1.34 1.35 1.33 1.44 0.10 November 1.25 1.26 1.25 1.26 0.01 December 1.26 1.27 1.25 1.19 -0.06 2003 Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N1) from final mTFR January 1.32 1.32 1.31 1.45 0.13 February 1.32 1.33 1.31 1.35 0.03 March 1.28 1.29 1.27 1.28 0.01 April 1.31 1.32 1.30 1.33 0.02 May 1.32 1.33 1.31 1.28 -0.04 June 1.36 1.37 1.36 1.39 0.02 July 1.47 1.48 1.46 1.54 0.07 August 1.40 1.41 1.39 1.35 -0.04 September 1.47 1.47 1.46 1.51 0.05 October 1.32 1.32 1.31 1.41 0.10 November 1.24 1.25 1.23 1.22 -0.03 December 1.25 1.25 1.24 1.27 0.02 Monitoring of German Fertility • 273 2004 Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N1) from final mTFR January 1.36 1.36 1.35 1.38 0.02 February 1.33 1.34 1.32 1.34 0.00 March 1.29 1.29 1.28 1.38 0.10 April 1.31 1.31 1.30 1.33 0.03 May 1.28 1.29 1.28 1.18 -0.10 June 1.41 1.42 1.40 1.48 0.07 July 1.48 1.49 1.47 1.46 -0.02 August 1.46 1.46 1.45 1.51 0.05 September 1.47 1.48 1.46 1.51 0.04 October 1.32 1.33 1.32 1.30 -0.02 November 1.28 1.29 1.27 1.36 0.08 December 1.29 1.30 1.28 1.32 0.03 2005 Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N1) from final mTFR January 1.32 1.32 1.31 1.27 -0.05 February 1.35 1.36 1.34 1.35 0.00 March 1.31 1.32 1.30 1.31 -0.01 April 1.32 1.33 1.31 1.33 0.01 May 1.31 1.31 1.30 1.32 0.02 June 1.38 1.39 1.37 1.43 0.05 July 1.41 1.42 1.40 1.34 -0.07 August 1.41 1.42 1.41 1.49 0.08 September 1.44 1.45 1.43 1.43 -0.01 October 1.30 1.30 1.29 1.30 0.00 November 1.25 1.26 1.24 1.33 0.07 December 1.26 1.26 1.25 1.26 0.01 2006 Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N1) from final mTFR January 1.29 1.29 1.28 1.30 0.01 February 1.32 1.33 1.31 1.32 0.00 March 1.29 1.30 1.29 1.33 0.04 April 1.25 1.26 1.25 1.16 -0.09 May 1.35 1.36 1.35 1.41 0.05 June 1.36 1.37 1.35 1.38 0.03 July 1.42 1.43 1.41 1.36 -0.06 August 1.41 1.42 1.40 1.49 0.08 September 1.45 1.46 1.44 1.41 -0.04 October 1.34 1.35 1.33 1.38 0.04 November 1.26 1.27 1.25 1.34 0.08 December 1.21 1.21 1.20 1.16 -0.05 Source: Calculations based on N1 and N30suf. • Gabriele Doblhammer, Nadja Milewski, Frederik Peters274 Tab. A1b: Estimations of mTFR in 2001 to 2006, western Germany – confi dence intervals and absolute errors 2001 Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N10) from final mTFR January 1.42 1.43 1.41 1.39 -0.03 February 1.36 1.37 1.35 1.34 -0.02 March 1.35 1.35 1.34 1.35 0.00 April 1.34 1.35 1.33 1.30 -0.04 May 1.40 1.41 1.39 1.47 0.07 June 1.41 1.41 1.40 1.37 -0.04 July 1.46 1.47 1.45 1.48 0.01 August 1.45 1.46 1.44 1.49 0.04 September 1.44 1.45 1.43 1.37 -0.07 October 1.35 1.36 1.34 1.46 0.11 November 1.31 1.32 1.30 1.33 0.02 December 1.27 1.28 1.26 1.21 -0.06 2002 Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N10) from final mTFR January 1.36 1.37 1.36 1.35 -0.02 February 1.39 1.40 1.38 1.38 -0.01 March 1.37 1.37 1.36 1.29 -0.08 April 1.34 1.35 1.34 1.44 0.10 May 1.32 1.32 1.31 1.32 0.00 June 1.37 1.38 1.36 1.33 -0.04 July 1.45 1.46 1.44 1.53 0.08 August 1.42 1.43 1.41 1.41 -0.01 September 1.47 1.48 1.46 1.45 -0.02 October 1.37 1.38 1.36 1.49 0.12 November 1.28 1.29 1.27 1.28 0.01 December 1.29 1.30 1.28 1.25 -0.04 2003 Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N10) from final mTFR January 1.35 1.36 1.34 1.31 -0.04 February 1.35 1.36 1.34 1.35 0.00 March 1.30 1.31 1.29 1.28 -0.02 April 1.34 1.35 1.33 1.36 0.02 May 1.35 1.36 1.34 1.31 -0.04 June 1.39 1.40 1.38 1.40 0.01 July 1.49 1.50 1.48 1.57 0.08 August 1.42 1.43 1.41 1.38 -0.04 September 1.48 1.49 1.47 1.52 0.04 October 1.34 1.34 1.33 1.43 0.10 November 1.27 1.27 1.26 1.22 -0.04 December 1.27 1.28 1.26 1.25 -0.01 Monitoring of German Fertility • 275 2004 Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N10) from final mTFR January 1.38 1.39 1.37 1.32 -0.06 February 1.35 1.36 1.34 1.30 -0.05 March 1.30 1.31 1.29 1.40 0.10 April 1.32 1.32 1.31 1.33 0.01 May 1.30 1.31 1.30 1.20 -0.11 June 1.43 1.43 1.42 1.51 0.09 July 1.49 1.50 1.48 1.47 -0.02 August 1.47 1.48 1.46 1.52 0.04 September 1.49 1.49 1.48 1.53 0.05 October 1.34 1.35 1.33 1.32 -0.03 November 1.30 1.31 1.29 1.36 0.06 December 1.31 1.32 1.30 1.25 -0.05 2005 Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N10) from final mTFR January 1.34 1.35 1.33 1.25 -0.08 February 1.37 1.38 1.36 1.33 -0.03 March 1.33 1.34 1.32 1.35 0.02 April 1.34 1.35 1.33 1.35 0.01 May 1.32 1.33 1.32 1.33 0.01 June 1.40 1.40 1.39 1.44 0.04 July 1.42 1.43 1.41 1.34 -0.08 August 1.43 1.43 1.42 1.50 0.08 September 1.45 1.46 1.45 1.46 0.01 October 1.31 1.32 1.30 1.32 0.01 November 1.26 1.27 1.25 1.32 0.06 December 1.27 1.28 1.26 1.22 -0.06 2006 Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N10) from final mTFR January 1.30 1.31 1.29 1.23 -0.07 February 1.34 1.35 1.33 1.30 -0.04 March 1.31 1.31 1.30 1.37 0.06 April 1.26 1.27 1.25 1.18 -0.08 May 1.36 1.37 1.35 1.41 0.05 June 1.37 1.38 1.36 1.39 0.02 July 1.43 1.43 1.42 1.37 -0.05 August 1.41 1.42 1.40 1.50 0.08 September 1.46 1.46 1.45 1.40 -0.06 October 1.35 1.36 1.34 1.40 0.05 November 1.27 1.28 1.26 1.33 0.06 December 1.21 1.22 1.21 1.16 -0.05 Note: January weighted by 0.75, December weighted by 1.25. Source: Calculations based on N10 and N30suf. • Gabriele Doblhammer, Nadja Milewski, Frederik Peters276 Tab. A1c: Estimations of mTFR in 2001 to 2006, eastern Germany – confi dence intervals and absolute errors 2001 Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N10) from final mTFR January 1.24 1.26 1.22 1.27 0.03 February 1.21 1.23 1.19 1.17 -0.04 March 1.21 1.23 1.19 1.16 -0.05 April 1.20 1.22 1.18 1.13 -0.07 May 1.25 1.27 1.23 1.27 0.02 June 1.24 1.26 1.22 1.16 -0.07 July 1.35 1.37 1.33 1.33 -0.02 August 1.30 1.32 1.28 1.27 -0.04 September 1.29 1.31 1.27 1.20 -0.09 October 1.20 1.22 1.18 1.22 0.02 November 1.16 1.18 1.14 1.17 0.00 December 1.11 1.13 1.10 1.03 -0.08 2002 Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N10) from final mTFR January 1.22 1.24 1.20 1.23 0.02 February 1.22 1.24 1.20 1.20 -0.02 March 1.21 1.23 1.19 1.11 -0.10 April 1.21 1.22 1.19 1.26 0.06 May 1.20 1.22 1.19 1.18 -0.03 June 1.24 1.25 1.22 1.14 -0.10 July 1.35 1.37 1.33 1.37 0.02 August 1.31 1.33 1.29 1.26 -0.05 September 1.34 1.36 1.32 1.32 -0.02 October 1.24 1.25 1.22 1.25 0.02 November 1.17 1.18 1.15 1.16 0.00 December 1.15 1.16 1.13 1.08 -0.06 2003 Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N10) from final mTFR January 1.18 1.20 1.16 1.20 0.01 February 1.20 1.22 1.18 1.18 -0.02 March 1.19 1.21 1.18 1.15 -0.04 April 1.23 1.24 1.21 1.22 0.00 May 1.23 1.25 1.22 1.15 -0.09 June 1.30 1.32 1.28 1.28 -0.01 July 1.42 1.44 1.40 1.46 0.03 August 1.35 1.37 1.33 1.25 -0.11 September 1.44 1.46 1.42 1.48 0.03 October 1.26 1.28 1.24 1.26 0.00 November 1.16 1.18 1.14 1.13 -0.03 December 1.18 1.20 1.16 1.14 -0.04 Monitoring of German Fertility • 277 2004 Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N10) from final mTFR January 1.29 1.31 1.27 1.24 -0.05 February 1.27 1.28 1.25 1.21 -0.05 March 1.25 1.27 1.23 1.30 0.06 April 1.28 1.30 1.26 1.24 -0.03 May 1.22 1.24 1.21 1.11 -0.12 June 1.37 1.39 1.35 1.44 0.07 July 1.47 1.50 1.45 1.41 -0.07 August 1.43 1.45 1.41 1.46 0.03 September 1.43 1.45 1.41 1.42 -0.01 October 1.26 1.28 1.24 1.20 -0.06 November 1.21 1.23 1.19 1.27 0.06 December 1.24 1.26 1.22 1.16 -0.08 2005 Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N10) from final mTFR January 1.24 1.26 1.22 1.18 -0.07 February 1.30 1.32 1.28 1.28 -0.02 March 1.24 1.26 1.22 1.25 0.00 April 1.28 1.29 1.26 1.23 -0.04 May 1.25 1.27 1.23 1.26 0.01 June 1.36 1.38 1.34 1.33 -0.03 July 1.40 1.42 1.38 1.30 -0.10 August 1.38 1.41 1.36 1.43 0.05 September 1.40 1.42 1.38 1.39 -0.01 October 1.25 1.27 1.23 1.15 -0.09 November 1.24 1.26 1.22 1.33 0.08 December 1.20 1.22 1.18 1.15 -0.05 2006 Final mTFR Confidence intervall Preliminary mTFR Deviation preliminary mTFR Month (N30suf) UL LL (N10) from final mTFR January 1.21 1.23 1.19 1.19 -0.02 February 1.26 1.28 1.24 1.23 -0.02 March 1.26 1.28 1.24 1.24 -0.02 April 1.23 1.25 1.21 1.13 -0.10 May 1.33 1.35 1.31 1.35 0.02 June 1.34 1.36 1.32 1.33 0.00 July 1.43 1.45 1.41 1.35 -0.08 August 1.42 1.44 1.40 1.44 0.02 September 1.44 1.46 1.42 1.38 -0.06 October 1.30 1.32 1.28 1.24 -0.06 November 1.23 1.25 1.21 1.35 0.12 December 1.17 1.19 1.15 1.11 -0.06 Note: January weighted by 0.8, December weighted by 1.2. Source: Calculations based on N10 and N30suf. Published by / Herausgegeben von Prof. Dr. Norbert F. Schneider Layout and print: Federal Institute for Population Research, Wiesbaden (Germany) Managing Editor / Redaktion Frank Swiaczny Copy Editor / Schlußredaktion Dr. Evelyn Grünheid Scientifi c Advisory Board / Wissenschaftlicher Beirat Jürgen Dorbritz (Wiesbaden) Paul Gans (Mannheim) Johannes Huinink (Bremen) Dirk J. van de Kaa (Den Haag) Marc Luy (Wien) Notburga Ott (Bochum) Peter Preisendörfer (Mainz) Comparative Population Studies – Zeitschrift für Bevölkerungswissenschaft www.comparativepopulationstudies.de ISSN: 1869-8980 (Print) – 1869-8999 (Internet) Board of Reviewers / Gutachterbeirat Martin Abraham (Erlangen) Laura Bernardi (Lausanne) Hansjörg Bucher (Bonn) Claudia Diehl (Göttingen) Andreas Diekmann (Zürich) Gabriele Doblhammer-Reiter (Rostock) Henriette Engelhardt-Wölfl er (Bamberg) E.-Jürgen Flöthmann (Bielefeld) Alexia Fürnkranz-Prskawetz (Wien) Beat Fux (Zürich) Joshua Goldstein (Rostock) Karsten Hank (Mannheim) Sonja Haug (Regensburg) Franz-Josef Kemper (Berlin) Hans-Peter Kohler (Philadelphia) Michaela Kreyenfeld (Rostock) Aart C. 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