Parental Time Restrictions and the Cost of Children: Insights from a Survey among Mothers

Transcription

1 October 2018 Parental Tme Restrctons and the Cost of Chldren: Insghts from a Survey among Mothers Melane Borah, Andreas Knabe, Kevn Pahlke

2 Impressum: CESfo Workng Papers ISSN (electronc verson) Publsher and dstrbutor: Munch Socety for the Promoton of Economc Research CESfo GmbH The nternatonal platform of Ludwgs Maxmlans Unversty s Center for Economc Studes and the fo Insttute Poschngerstr. 5, Munch, Germany Telephone +49 (0) , Telefax +49 (0) , emal offce@cesfo.de Edtors: Clemens Fuest, Olver Falck, Jasmn Gröschl group.org/wp An electronc verson of the paper may be downloaded from the SSRN webste: from the RePEc webste: from the CESfo webste: group.org/wp

3 CESfo Workng Paper No Category 3: Socal Protecton Parental Tme Restrctons and the Cost of Chldren: Insghts from a Survey among Mothers Abstract In ths paper, we provde estmates of the subjectvely perceved cost of chldren dependng on the extent of parental tme restrctons. Buldng on a study by Koulovatanos et al. (2009) that ntroduces a novel way of usng subjectve ncome evaluaton data for such estmatons, we conduct a refned verson of the underlyng survey, focusng on young women wth chldren n Germany. Our study confrms that the monetary cost of chldren s substantal and ncreases wth parental nonmarket tme restrctons. The loss n the materal lvng standard assocated wth supplyng tme to the labor market s szeable for famles wth chldren. JEL-Codes: I320, J130, J220. Keywords: chld cost, equvalence scales, full-tme employment, subjectve ncome evaluatons. Melane Borah Otto-von-Guercke Unversty Magdeburg / Germany Melane.Borah@ovgu.de Andreas Knabe Otto-von-Guercke Unversty Magdeburg / Germany andreas.knabe@ovgu.de Kevn Pahlke Otto-von-Guercke Unversty Magdeburg / Germany pahlke.kevn@ovgu.de

4 1. Introducton At gven levels of total commodtes consumpton, the standard of lvng of households vares wth ther sze and structure. In general, larger households need more commodtes than smaller households to provde ther members the same standard of lvng. Due to economes of scale n consumpton, a household s consumpton needs are generally not proportonal to the number of ts members. Moreover, the consumpton requrements of certan household members may be systematcally lower or hgher than those of an average sngle person. Chldren, for nstance, provde such a case. For physologcal reasons (e.g. lower calore ntake), ther needs may be consderably lower than those of an addtonal adult. Equvalence scales are an mportant tool capturng such dfferences n needs and economes of scale n household consumpton. They quantfy the percentage ncrease n household ncome or expendture necessary to leave a household s standard of lvng unchanged as addtonal members jon t. Frequently, equvalence scales are restrcted to consderng money ncomes or expendtures. Whle ths s helpful n many applcatons, t neglects that materal consumpton requrements, n prncple, can be satsfed (although not fully nterchangeably) n two dfferent ways by purchasng marketed goods and servces usng money ncome and by producng them at home usng tme. Household producton as a substtute for market commodtes appears to be especally relevant when one s tryng to assess the cost of chldren. Household producton can presumably satsfy a relatvely large fracton of chldren s consumpton needs at the expense of parental tme (e.g., n supervsory chldcare, food preparaton, tutorng or lesure actvtes). Naturally, ths wll be more dffcult for households whose adult members work a sgnfcant number of hours n the market and hence have less tme avalable for household producton. Tmerestrcted parents wll have to cover more of ther chldren s needs usng marketed goods and servces (e.g., by affordng formal chldcare servces, ready-made meals, prvate tutors, or entertanment technologes), whch ncreases pressure on ther money ncome. Followng ths logc, the monetary cost of chldren, and thus ther weght n the ncome equvalence scale, may prove senstve to the extent of parental tme restrctons. There s a large body of lterature on the monetary cost of chldren and ther weght n ncome equvalence scales. Emprcal approaches to ther estmaton ether employ ndrect accounts of economc well-beng va observed household consumpton demand and expendture patterns or rely on drect measures of well-beng usng subjectve survey data (for - 1 -

5 a revew, see van Praag and Warnaar, 1997). Demand-based approaches suffer from ther strong dependence on the underlyng model s assumptons and problems related to the dentfcaton of utlty functons that are comparable across households (for a crtque, see Pollak and Wales, 1979). Subjectve approaches crcumvent these problems and may thus provde an alternatve approach to estmatng the cost of chldren. Of course, these approaches also rely on a set of assumptons. Most mportantly, they assume that ndvduals correctly assess ther own households welfare or standard of lvng when assgnng verbal labels to actual or hypothetcal levels of ncome or when assgnng ncome requrements to actual or hypothetcal levels of welfare (see e.g. Coulter et al., 1992, and van Praag and van der Sar, 1988). Whle one mght be fundamentally skeptcal about the nterpersonal comparablty and meanngfulness of subjectve evaluatons (see Bertrand and Mullanathan, 2001), varous studes have shown that people answer subjectve evaluaton questons on ncome and well-beng n a meanngful and consstent way (for a revew, see Frey and Stutzer, 2002, pp ). Studes that have appled the subjectve method to estmate equvalence scales have generally obtaned results at the lower end of the ranges known from common expert scales (e.g. the OECD scale) or those obtaned by demand-based studes. Due to data lmtatons, most emprcal studes on the cost of chldren that use the subjectve approach do not nclude parents tme nput nto rasng ther chldren and may thus underestmate chldren s relatve consumpton needs. An excepton s a study by Koulovatanos, Schröder and Schmdt (2009), henceforth abbrevated KSS, who apply the subjectve approach to estmate the monetary cost of chldren dependng on ther parents employment status as a proxy for ther tme avalablty. They ntroduce a novel survey nstrument that lets respondents evaluate the ncome requrements of hypothetcal households that dffer n ther demographc structure as well as ther nonmarket tme endowment as expressed by parents employment states. Dfferences n respondents ncome statements across household types provde drect evdence of the ncome ncrements needed to keep the household s standard of lvng constant when addtonal members jon the household or when more tme s devoted to labor market work. Ther analyss, for whch the authors collected data through onlne surveys n Belgum and Germany, suggests that that there s a szable tradeoff between money and tme, n general. Furthermore, ther results ndcate that households wth chldren requre even slghtly larger ncome compensatons n return for a restrctve reducton n adults nonmarket tme than chldless households

6 KSS s survey desgn allows obtanng ncome evaluatons for arbtrary household types. It does so even f survey respondents do not belong to any such household. Ths doubtlessly has the advantage that one can obtan data on relatve ncome requrements of a large number of household types even f the number of respondents s small. One mght wonder, however, whether relable answers can be obtaned when respondents have only lmted knowledge of the needs of households unlke ther own, e.g. when askng young chldless sngles about the needs of marred couples wth chldren (Bradbury 1989). Ths s especally true for KSS German sample, where 85.4 percent of the respondents do not have chldren and 57.9 percent of the respondents do not have a partner ether. In fact, the majorty of respondents n the German sample are male students that lack the experence of parenthood, market work and the costs assocated wth these two. The Belgan sample used by KSS s more balanced n terms of gender and employment, but the majorty of respondents s chldless as well. To address ths ssue, we conduct an onlne survey among mothers n Germany askng them to evaluate ther own nstead of hypothetcal households ncome requrements. Even though ths does not gve us a representatve sample of the entre populaton, our convenence sample of mothers allows us to collect ncome evaluatons from ndvduals who typcally face the cost of chldren on a daly bass (see Pahl, 2008). By focusng on a purposefully selected convenence sample, our paper allows us to examne the robustness of KSS s fndngs wth respect to modfcatons n sample selecton. Another purpose of our paper s to check the robustness of KSS s fndngs wth respect to modfcatons n survey technques. KSS ask respondents to assess ncome requrements of hypothetcal households that dffer n ther number of chldren (and are presented n ascendng order) and n the number of full-tme employed adults (ordered such that households become ever more tme-restrcted). Agan, the advantage of ths s the large number of household types whose ncome requrements can be evaluated by a lmted number of respondents. However, one could be afrad that ths way of presentng the set of hypothetcal households may nduce a knd of focusng lluson or framng effect (Kahneman et al. 2006). Respondents mght be mplctly nduced to thnk that, as the number of chldren or tme-restrctons ncrease, ncome requrements of these households should ncrease as well. In ths case, they mght end up assgnng too hgh values to the dmensons emphaszed n the survey,.e. chldren and market work. In our paper, we reduce the scope of unntended focusng by askng each respondent a sngle ncome evaluaton queston about one type of household (hs or her own)

7 Whle t s clear that equvalence scales are supposed to represent the ncome dfferentals between households that put them on the same level of welfare or well-beng, t s less clear what exactly s meant by welfare or well-beng. Nelson (1993) ponts out that theoretcal contrbutons, as well as many recent emprcal applcatons, focus on a choce-theoretc concept of subjectve utlty as a measure of welfare, whle polcy applcatons typcally defne welfare n terms of a household s materal standard of lvng. She argues that, for polcy-related uses of household equvalence scales, the crtcal queston s what level of consumpton of goods and servces people are able to afford, not what level of overall happness they may happen to attan. (Nelson, 1993, p. 473) Ths concerns polcy areas such as the measurement of poverty or the determnaton of welfare benefts for famles wth chldren. In our paper, we follow ths polcy-orented perspectve and analyze ncome dfferentals that keep the materal standard of lvng constant. Our research queston thus dffers from that of KSS who nqured about the standard of lvng n general, whch s presumably closer to total utlty than to the pure materal standard of lvng. Whle KSS s results are thus nformatve about the value of tme and tme-restrctedness for famly well-beng n general, our results are supposed to dentfy the monetary value of materal needs assocated wth addtonal household members and labor market work, where the latter may reflect expendtures drectly related to employment or the need to substtute household producton by market commodtes. These methodcal consderatons allow us to extend the study by KSS and substantate ther fndngs. Our results mply magntudes and patterns of the cost of chldren smlar to those found by KSS. For example, the frst chld of a couple n whch one partner works fulltme whle the other partner s not employed has 55 percent of the fnancal needs of a sngle, nonworkng adult. The compensaton needed for devotng tme to the labor market found n our study appears to be farly large f there are chldren n the household. Ths suggests that the materal cost of labor s manly caused by a reducton n the tme avalable for chld-related household producton actvtes and chldcare, n partcular. Moreover, we show that subjectve ncome evaluatons are senstve to the level of the respondent s actual household ncome. We llustrate how to correct for ths preference drft. Our paper s structured as follows. We frst revew the related lterature and dscuss the paper by Koulovatanos et al. (2009) n detal. Secton 3 provdes a detaled account of the data we use, ncludng a descrpton of the survey desgn, data collecton procedure, and sample characterstcs. Secton 4 s devoted to the emprcal analyss of the survey data. It presents descrptve statstcs, the econometrc model, and results. Secton 5 concludes

8 2. Related Lterature The determnaton of equvalence scales or the cost of addtonal household members tradtonally nvolves an ndrect account of dfferent households relatve welfare levels. One approach lets experts assess relatve needs. A well-known example s the (modfed) OECD scale (OECD, 2005). A second approach uses objectve expendture data to estmate equvalence scales emprcally. Recently, both types of scales have been extended to consder (parts of) the tme cost of addtonal household members. Based on a revew of emprcal evdence regardng dfferences n expendture and tme use patterns of households, Folbre et al. (2017) propose an expert-type equvalence scale n extended ncomes (the sum of monetary ncome and household producton). The authors argue that economes of scale n adultequvalent consumpton and the needs of a chld relatve to an addtonal adult are greater n the consumpton of household producton than n the consumpton of marketed goods and servces. The equvalence parameters they suggest formalze these hypotheses but lack a precse emprcal foundaton. Apps and Rees (2002), Bradbury (2008) and Gardes and Starzec (2017) nvestgate the full consumpton needs of addtonal household members (ncludng domestc producton and lesure) by combnng nformaton on tme-use wth objectve ncome and expendture data, respectvely. Apps and Rees (2002) establsh that the monetary cost of chldren s sgnfcantly hgher n households facng greater tme restrctons from full-tme employment. Chldren s full cost, however, s vrtually dentcal across these households and s consderably larger n relaton to an addtonal adult than the monetary cost. Bradbury (2008) and Gardes and Starzec (2017) confrm the latter result. Ths corresponds to varous other studes that nvestgate the tme cost of chldren alone and fnd these to be substantal (see e.g. Gustafsson and Kjuln, 1994, Bttman and Goodn, 2000, and Ekert-Jaffé and Grossbard, 2015). As must be noted for all studes based on an ndrect account of households welfare, the cted results rely on a number of strong assumptons. To avod these, an ncreasng body of the lterature on equvalence scales centers around a thrd approach that uses subjectve evaluatons of well-beng and ncome. In a revew of the related methods, Bradbury (1989) dstngushes four types of subjectve data that can be used to approxmate households cost or welfare functons drectly n order to construct the assocated equvalence scales. The frst type s the evaluaton of one s own lvng standard, where respondents are asked to evaluate the level of welfare or satsfacton they experence at ther current household ncome or, more generally, ther current fnancal stuaton. The second type s the evaluaton of a hypothetcal lvng - 5 -

9 standard, where ndvduals have to assess the level of well-beng experenced at gven ncomes by dfferent hypothetcally structured households. The thrd type represents evaluatons of respondents own ncome. Here, people are confronted wth a descrpton of a certan level of welfare and are asked to ndcate the ncome they would need to enjoy that same standard of lvng n ther current household stuaton. In contrast to ths, the fourth type of subjectve evaluatons concerns hypothetcal ncomes, whch capture a respondent s evaluaton of ncome levels that a range of hypothetcal households would requre to reach a pre-specfed level of welfare. Many studes estmate equvalence scales by analyzng ncome dfferences across households of dfferent sze and structure condtonal on ther self-reported level of wellbeng, and dfferentate between adults and chldren based on own lvng standards responses. Usng German panel data, Schwarze (2003), van Praag and Ferrer--Carbonell (2004) and Bewen and Juhasz (2017) show that the equvalence weght of chldren s lower than the weght of addtonal adults (whch also appear relatvely low compared to expert scales, e.g. the OECD scale). Most studes based on data from other countres confrm ths result. Notable exceptons are Rojas (2007) and Bollnger et al. (2012). Van Praag and Ferrer--Carbonell (2004) also employ a specfcaton that accounts for the number of workng adults. Ths allows them to draw conclusons about the equvalence scale dependng on the household s endowment wth parental nonmarket tme. They fnd that monetary needs are greater n famles wth two workng adults as compared to famles wth one workng and one nonworkng adult. A number of earler studes analyze own ncome responses and also fnd rather low equvalence weghts for adults and chldren. By lettng the same respondent evaluate a number of dfferent welfare levels, several studes construct welfare functons of ncome and estmate equvalence scales on ther bass (see e.g. van Praag, 1971, Kapteyn and van Praag, 1976, van Praag and van der Sar, 1988). Other studes focus on a sngle own ncome response, where respondent have to report how much ncome they would need to make ends meet (Goedhart et al., 1977). Among others, van den Bosch et al. (1993) and Garner and de Vos (1995) have used ths so-called mnmum ncome queston n the determnaton of equvalence scales. Smlar to the latter approach, our survey reles on one sngle own ncome response for a gven welfare level specfed n terms of the reference household s ncome. Our study bulds on analyses by Koulovatanos et al. (2005, 2009), who use hypothetcal ncome evaluatons. Frst, Koulovatanos et al. (2005) desgn a questonnare to collect hypothetcal ncome responses, wth the am of testng the ncome dependence of equvalence - 6 -

10 scales. In a subsequent study, the authors adjust the survey nstrument to evaluate the cost of chldren dependng on the employment status of ther parents (Koulovatanos et al., 2009). Because our paper s very closely related to t, we present the survey desgn and results of ths orgnal study n detal, pontng out ts strengths and potental weaknesses. Koulovatanos et al. (2009) nvestgate whether and by how much the monetary cost of chldren dffers dependng on a household s nonmarket tme endowment. To characterze tme endowments, the authors classfy households by the number of full-tme employed adults wthn one- and two-adult households. They assume that households experence a restrctve reducton of nonmarket tme when all adult members are full-tme employed. A couple consstng of one full-tme employed and one nonworkng partner s sad to face a nonrestrctve reducton of ts tme endowment, whereas a nonworkng sngle or two nonworkng partners are subject to no tme reducton at all. These tme-endowment constellatons, together wth dfferng numbers of chldren, defne hypothetcal household types whose ncome requrements are evaluated n the survey. Respondents ndcate the net household ncome they thnk dfferent household types need to enjoy the same standard of lvng as a sngle, chldless, nonworkng adult wth a prespecfed net monthly reference ncome. More specfcally, the authors ask respondents to fll n 4 5 matrces whose rows represent the number of chldren (from zero to three) and columns dstngush the number of adults (one or two) and ther possble work status combnatons (nonworkng and/or workng full tme). The questonnare specfes a reference ncome for one of these constellatons (nonworkng sngle wthout chldren), such that respondents have to fll n the remanng 19 cells. Ths s repeated for three dfferent reference ncomes, such that one obtans 57 observatons per respondent. Ths survey desgn has the advantage that t collects nformaton for a broad range of household types. Ths allows KSS to estmate equvalence scale parameters even though the number of partcpants to ther onlne survey n Belgum and Germany s relatvely small (149 and 164, respectvely) and partcpants manly come from a small number of household types. Analyzng responses from both countres separately, KSS fnd equvalence scale parameters that are wthn the range set by other equvalence scales, but are relatvely large compared to those found by earler studes usng the subjectve approach. Equvalence weghts tend to fall wth reference ncome, whch suggests that there are more economes of scale when lvng standards are hgher. Most mportantly, the results ndcate that the monetary cost of chldren s sgnfcantly hgher n fully tme-restrcted than n other households, whereas a nonrestrctve reducton n nonmarket household tme does not affect the ncome requrements - 7 -

11 assocated wth a chld. The results mply that the tradeoff between money and tme s sgnfcantly hgher n households wth chldren when all adults are workng full-tme. At the same tme, the results suggest that there s a strong tradeoff between money and tme even f there are no chldren n the household. The dsutlty of labor appears to be substantal. Snce KSS ask about the ncome necessary to hold the general standard of lvng constant, the greater monetary needs of workng adults may stem from three dfferent sources. Frst, there may be expendtures drectly related to beng employed (costs of commutng, work equpment etc.). Second, labor market work decreases the tme avalable for household producton actvtes, whch can be substtuted for by the purchase of market goods and servces (e.g. eatng out nstead of cookng at home or affordng external chldcare). Thrd, ndvduals may seek monetary compensaton for ther loss n lesure, whch would allow them to substtute lesure by materal consumpton. Whle the frst two knds of compensatons are supposed to hold the household s materal standard of lvng constant, the thrd one s meant to ncrease the materal standard of lvng to compensate for the loss of lesure tme such that total utlty remans unchanged. As we argued n the ntroducton, welfare economsts mght be nterested n the effect on total utlty, whereas socal polcymakers are typcally nterested n the materal standard of lvng (Nelson, 1993). In our survey, we focus on the latter and specfcally ask about the ncome necessary to secure equal materal lvng standards across household types. 3. Data 3.1 The Questonnare We analyze responses to an onlne questonnare that we created usng the software package SoSc. We provde an Englsh verson of the entre (orgnally German) questonnare n the appendx. The maxmum number of questons a respondent had to answer was 17. The majorty of questons concerned the soco-economc characterstcs of the respondent, hs/her chldren and, f applcable, hs/her partner. Supplemented by a sngle ncome evaluaton queston, the generated dataset provdes a sutable bass for the analyss of addtonal household members fnancal needs. Among the nqured personal characterstcs are the respondent s natonalty, regon of resdence (German federal state), gender, age, hghest educatonal degree and employment status. Gender nformaton s used to restrct the sample to women, whle the other varables - 8 -

12 serve as covarates n our emprcal analyss. Of specal mportance s the employment status, whch subsumes f the respondent s currently workng, the knd of employment or nonemployment, as well as weekly hours of work, f applcable. Furthermore, we asked ndvduals to state f they were sngles or n a relatonshp wth a partner lvng ether n the same or n a separate household. We also requested them to ndcate f there were any other adult household members except for them, ther partners or, possbly, ther chldren. To construct a measure of the tme restrctedness of the respondent s household, we had to assess the partner s employment status, f present. Ths nvolved the exact same questons as those concernng the respondent s own employment. In order to nvestgate the dfferental monetary needs of chldren gven the dfferences n ther parents non-market tme endowment, we also asked respondents to state the number and age of chldren lvng n ther households. In the second-last queston of the survey, we enqured respondents to specfy ther households actual net monthly ncome. In an attempt to receve measures as accurate as possble, we provded a detaled lst of ncome components that they should nclude n the respectve answer. Fnally, we assess our dependent varable va the followng queston regardng own ncome requrements: How much ncome do you thnk you would need n your current famly stuaton to enjoy the same materal standard of lvng as a sngle adult, who s unemployed, has no chldren and receves socal securty benefts amountng to 822 euros? 822 euros was the average amount of monthly welfare benefts to households provded by the German welfare system (Arbetslosengeld II) n 2012 (Bundesagentur für Arbet, 2013). Although t s more than 60 percent hgher than the lowest reference ncome used by KSS 1, t reflects a relatvely low standard of lvng n Germany. To remnd respondents of the dmensons along whch they dffer from the reference household, we presented a table to them, contrastng ther own to the hypothetcal household s characterstcs. It summarzed the respondents earler statements regardng ther household s number of adults, ther employment, and the number of chldren n comparson to the detals mentoned n the above queston. Table 1 represents an llustratve example. 1 We set all our results n relaton to estmates by KSS that rely on the assumpton of a reference ncome of 500 euros

13 Table 1: Summary Tool - Example Your own household Reference household Relatonshp status: n a partnershp sngle Employment status: both workng not workng Number of chldren: 3 chldren no chldren Income:??? 822 Below the table, respondents had to fll n the net ncome that they consdered equvalent to the reference ncome, n the sense of beng necessary to enjoy the same materal standard of lvng, gven the dfferences n ther households characterstcs (as ndcated by the??? cell). A response to ths queston completed the survey. 3.2 Data Collecton Bradbury (1989) argues that people are better able to evaluate ther own household s ncome requrements than those of a hypothetcal, dfferently composed household. When the research focus s on the cost of chldren, t thus seems desrable to ask parents about ther ncome evaluatons. Furthermore, t may be benefcal to enqure ndvduals that are concerned wth the household s chld-related expendtures prmarly. These are typcally mothers. 2 Therefore, we have made an effort to let as many mothers as possble answer our questonnare. We recruted a convenence sample of respondents va the socal networkng ste Facebook. A multtude of Facebook groups address parents specfcally and thus allow an easy dentfcaton of people n our target group. Therefore, we posted an appeal to partcpate n our survey to 116 groups and two large communtes 3 drectly related to parenthood or the exchange of chld-specfc goods and advce. Sometmes ths requred the approval by a group admnstrator whom we had to contact frst. Because we desgned our survey to study the fnancal needs of German households, we placed our call n German groups only. At the tme of survey, the number of members wthn the groups ranged from 59 to 10,786, whereas the communtes had as many as 277,339 and 182,248 subscrbers. Altogether, ths resulted n a 2 For emprcal evdence n support of ths vew, see Pahl (2008). 3 Groups are desgned for relatvely small numbers of people to communcate on subjects of common nterest and are ether publc or prvate, as chosen by the ntator. Communty pages, on the other hand, are offcal profles of publc fgures, busnesses and organzatons that are publcly avalable to all nternet users

14 total number of 736,922 potental partcpants, n theory. Of course, ths number s extremely optmstc because many members or subscrbers probably dd not access Facebook at all, or dd not receve notfcatons from the groups or communtes durng the survey perod. We conducted the survey n February A personal message explanng the purpose of our study and a lnk to the survey were posted to each group between February 5 and February 11, Facebook gave all group members the opton to comment on our entry. Ths opton was valuable to us for three reasons. Frstly, t allowed for the tmely nteracton wth potental respondents and the clearance of ther questons. Secondly, each comment led to a refreshment of the newsworthness of the entry, leadng t to appear at the top of the page repeatedly. Ths may have enhanced the vsblty of our request and thus may have ncreased the response rate. Thrdly, havng people recommend the survey to frends wth the help of a reference n the comment secton may have helped to acheve the same result. Seven to ten days after our entry s frst appearance, we posted a remnder also ndcatng the date at whch our survey would expre. The onlne survey tool was deactvated on February 28, 2017, thus endng the process of data collecton. We receved 1,062 responses, of whch 935 respondents completely answered the survey. 3.3 Sample Characterstcs Of the 935 completed questonnares, only 59 stemmed from male respondents. We dropped these responses because they dd not match our target group of mothers. Because of ambgutes n the ncome evaluaton of ndvduals that lve separately from ther partners, we also excluded 58 women who reported to have a partner not lvng wthn the same household. Wth the data collecton organzed accordng to the narrow defnton of our target group, the number of chldless ndvduals that had partcpated n our survey was very low. Not consderng them led to a loss of only nne observatons. There are no households wth other adult members (except for the partner) n our sample, because ndcaton of the same led to the mmedate termnaton of the survey. Hence, we have ensured that apartments shared by extended famles or unrelated adults do not affect our estmated equvalence scales. To approxmate the needs of dependent chldren, we exclude households from the analyss that consst of at least one chld above the age of 17. Ths concerns 16 observatons and leaves us wth nformaton about 793 mothers and ther households

15 Unfortunately, from some of these mothers we have receved mplausble responses to the ncome evaluaton queston. Although prevous answers clearly suggested that ther households conssted of more people than the reference household, they declared to requre less ncome than a chldless sngle to enjoy the same materal standard of lvng. Ths concerns 46 responses. We cannot be sure f these statements are the result of a msunderstandng, a normatve judgement about the adequacy of socal securty benefts n general, or the ncluson of nonpecunary welfare effects of addtonal household members. Whatever the reason, stated ncome requrements of less than 822 certanly do not correspond to our understandng of what ths varable should capture. Hence, we have decded to exclude the 46 crtcal observatons from our emprcal analyss. 4 Our fnal sample thus comprses 747 observatons. We provde sample statstcs for some of the enqured control varables n Table 2. A comparson of the sample characterstcs wth the ndvdual characterstcs of respondents n the German sample of KSS shows that our survey responses come more strongly from workng famles wth chldren. Whle the large majorty (more than 85 percent) of respondents n the sample of KSS reported to have no chldren, our sample allows us to analyze the ncome responses of people who actually face the cost of chldren n everyday lfe. Ths allows us to test whether the KSS results can be generalzed and apply also to famles wth chldren. Furthermore, our number of ndependent observatons s consderably larger than n the KSS study, whch consders 19 clearly nterrelated hypothetcal ncomes stated by each of the 164 respondents. Overall, we see that the vast majorty of our sample of mothers s German, lves wth a partner, and s between 20 and 40 years old. More than 89 percent of the respondents have ether one chld or two chldren. Many women n our sample have completed a vocatonal tranng. Despte motherhood, a large fracton of our sample s n employment. Yet, ths percentage s small n comparson to the employment share of the respondents partners. Dfferences also exst n the workng tme of mothers and ther partners. On average, mothers spend 29 hours per week n pad employment whle ther partner works about 42 hours per week. The mean net household ncome n our sample s about 2,661. Only a small fracton of households (<5%) reports to have an actual ncome below the reference level of A robustness test confrmed that retanng those 46 observatons n our sample results n only small changes n the estmated coeffcents. Our results reman qualtatvely unchanged

16 Table 2: Sample Characterstcs N % N % Total 747 Natonalty Own Employment German Yes Others No Partner Employment of the Partner (N=654) Yes Yes No No Chldren Own Workng Tme (N=463) One <= Two Three >= More than Three Age Mean: Partner s Workng Tme (N=617) < <= > >= Hghest Degree Net household ncome Mean: No degree < Secondary School Abtur Unversty Degree Vocatonal Tranng >= Others Emprcal Analyss 4.1 Descrptve Statstcs In the emprcal analyss of ths paper, the varable of prmary nterest s the rato of the ncome that respondents need to reach the pre-specfed materal standard of lvng and the reference ncome. Ths quotent represents the equvalence weght that the respondent assgns to her household n order to acheve the same level of well-beng as an unemployed sngle adult wth an ncome of 822. Followng KSS, we call ths varable the equvalent-ncome rato. Table 3 presents ts means and standard devatons for households dfferentated by the number

17 of adults and chldren as well as by the ncdence of full-tme employment (W), whch s defned as beng employed and workng for 35 hours per week or more. 5 The table also reports the number of observatons for each of these types, thus nformng about the dstrbuton of household characterstcs wthn our sample. Table 3: Mean Equvalent-Income Rato by Household Type Number of Chldren Sngle Couple N W NN WN WW *** (0.44) (0.46) (0.72) (1.11) (1.53) ** * ** *** ** (0.56) (0.28) (0.84) (1.18) (1.21) * (0.52) (0.69) (0.90) (1.53) (1.68) ** Note: Each cell conssts of the mean equvalent-ncome rato (n bold), the standard devaton (n parentheses) and the number of observatons. Stars between two cells ndcate that the dfference between ther means s statstcally sgnfcant wth * p < 0.1, ** p < 0.05, *** p < We observe the equvalent-ncome rato for sngle mothers and couples wth up to four chldren. Because there s only a small number of households havng four chldren, we do not nclude them n the presentaton of Table 3. Thus, we dstngush households accordng to the number of chldren n three rows. The sample statstcs n the frst two columns refer to sngle mothers wthout (N) and wth full-tme employment (W). From the number of observatons reported n the thrd lne of each cell, we know that full-tme employment among sngle mothers n our sample s qute rare, especally when there s more than one chld. The frst lne of each cell reports the mean equvalent-ncome rato generated from responses of women n the respectve households. Wth the reference household s ncome normalzed to one, we can mmedately derve the percentage ncrease n ncome needed for dfferent households to enjoy 5 We also conducted our analyses applyng dfferent defntons of beng tme-restrcted,.e. we consdered an adult as restrcted by workng when he/she reported to work more than 20 hours per week or smply a postve number of hours. A less strngent defnton of tme restrctons does not affect the estmated coeffcents for adults and chldren consderably but leads to lower or even nsgnfcant compensatons for chldren n tme-restrcted households. The results are avalable upon request

18 the same materal standard of lvng. From the top left cell, for nstance, we can conclude that non-workng sngle mothers wth one chld report that they need, on average, 69 percent more ncome than a non-workng sngle wthout chldren to enjoy the same materal standard of lvng. Sngle full-tme employed mothers requre an even greater monetary compensaton for the frst chld and ther tme restrcton or materal cost of labor. Women of ths knd ndcate a necessary ncome ncrease of 92 percent. The dfference between the ncome requrements of non-workng and workng sngle mothers wth one chld s not statstcally sgnfcant, though. The same s true for sngle mothers wth two or three chldren. Although workng mothers always ndcate greater mean equvalent-ncome ratos, the dfference s never statstcally sgnfcant, whch may be due to the relatvely small number of observatons n each cell. By comparng means vertcally, we can nvestgate the ncome ncrease needed for addtonal chldren. For mothers wthout full-tme employment, the cost of an addtonal second or thrd chld seems to be much lower than that of the frst chld. Whle the second chld s assocated wth an ncome ncrement of 27 percentage ponts, we only fnd a small and statstcally nsgnfcant ncome ncrement for a thrd chld (11 percentage ponts). For full-tme employed sngle mothers, there are not enough observatons to draw any relable concluson, unfortunately. For couples, we dstngush the degree of tme restrctedness by consderng three possble combnatons of adults employment states. Column NN refers to two adults who both are not full-tme employed. The combnaton WN represents what KSS call the tradtonal household, n whch one adult works full-tme whereas the other one does not. The last column studes fully tme-restrcted households, whose adult members both are n full-tme employment. The dstrbuton of the number of observatons clearly shows that the tradtonal household ndeed s the most common household arrangement n our sample. Agan, mean equvalent-ncome ratos provde frst evdence regardng the cost of addtonal household members under dfferent tme constrants. As suggested by these numbers, households wth an addtonal non-workng adult and a chld need 113 percent more ncome than the reference household. Subtractng from ths the requrement of the average non-workng sngle wth a chld yelds a 44 percentage pont ncome ncrement for the second non-workng adult. In the presence of at least one workng adult, these costs ncrease sgnfcantly. However, they do not depend on whether tme restrctons are partal or complete. Even though wth less statstcal sgnfcance, smlar fndngs appear also n households wth two or three chldren. Contrary to that, we fnd mxed evdence when comparng households that dffer n the number of chldren

19 In movng from one chld to two chldren, we fnd sgnfcantly postve ncome ncrements needed for all types of households. Non-workng as well as fully employed households requre an addtonal 57 to 58 percent of reference ncome for the second chld, whereas tradtonal households need only half as much. On the other hand, ncome requrements appear not to rse wth a thrd chld to a non-workng couple, but to ncrease by more than 60 percentage ponts n the other two household types. From the descrptve statstcs and smple mean comparsons, t s thus very dffcult to draw unambguous conclusons regardng the cost of chldren n dfferently tme-constraned households. A multvarate regresson analyss wll prove more helpful n ths regard. 4.2 Econometrc Model Because one am of ths paper s to fnd out whether the results by Koulovatanos et al. (2009) are reproducble usng a dfferent sample and survey desgn, our emprcal analyss closely follows the regresson model of that study. KSS estmate an equvalence scale proposed by Cutler and Katz (1992). We do the same and regress the stated equvalent-ncome rato ( EIR ) on the accordngly defned household s equvalence weght along wth other personal and household characterstcs that mght affect responses to the hypothetcal ncome queston. Ths leads us to our Baselne Specfcaton: EIR n n X e (Baselne) ' ( A C) b The frst term on the rght-hand sde represents the equvalence scale, where n A s the number of adults n the household and n C s the number of chldren. s the weght that a chld receves n relaton to an addtonal adult and the parameter captures economes of scale n adult equvalents. X s a vector of personal and household characterstcs that may also have an mpact on the own ncome response. We nclude the respondent s age, her educaton as measured by the hghest degree attaned, a dummy for beng a German natonal as well as the state of resdence n all our regressons. To test whether actual household ncomes are related to own ncome responses, we furthermore consder the respondent s monthly net household ncome n parts of the analyss below. e s the error term. We obtan a model that s very smlar to KSS by extendng the defnton of the equvalence scale by the number of workng adults. Ths produces the followng Specfcaton 1:

20 EIR n n n X e (1) ' ( A C W) b n W reflects the number of workng adults n the household of respondent and the assocated coeffcent quantfes the compensaton for an adult s full-tme employment n terms of the cost of an addtonal non-workng adult. Specfcaton 2 provdes a more detaled account of the dfferental cost of chldren n relaton to the employment status of ther parents. It does so by nteractng the number of chldren wth dummes ndcatng the degree of the household s tme restrctveness: EIR n n n n D n D X e (2) ' ( A C W C WN C F) b D WN s equal to one f household s a tradtonal household and zero otherwse. DF refers to households that are fully tme-restrcted and s equal to one f ether a sngle or both adults n a couple are n full-tme employment. The assessment of a chld s relatve weght n those households must consder all the related coeffcents. Whle t equals n a household wth no full-tme employed adults, t s the sum of and n a tradtonal and the sum of and n a fully tme-constraned household. One queston we seek to answer s whether our results are robust to the functonal form that we mpose on the equvalence scale. By assumng a Cutler and Katz parametrzaton, our regresson model s clearly nonlnear. Therefore, we estmate equatons (Baselne) to (2) by nonlnear least squares. It s easy to transform these nto analogous lnear equatons f one s wllng to assgn fxed equvalence weghts to specfc household members, as n the commonly appled OECD-scale (see OECD, 2005). We do ths and estmate the lnear alternatves to the three prevous specfcatons: EIR n n X e (Baselne a) ' 1 ( A 1) C b EIR n n n X e (1a) ' 1 ( A 1) C W b EIR n n n n D n D X e (2a) ' 1 ( A 1) C W C WN C F b The advantage of estmatng the lnear alternatves to our baselne specfcatons s that they yeld the equvalence weght of addtonal household members mmedately. Thus, we can evaluate the relatve cost of a chld ndependent of the total number of famly members

21 A second ssue we want to address s the role that a respondent s actual ncome plays n determnng her ncome response and hence the equvalent-ncome rato assgned to her household. We would expect respondents to ndcate greater ncome requrements the hgher ther actual household ncomes and thus current consumpton habts are. To control for ths preference drft (van Praag, 1971, Kapteyn and van Praag, 1976), we nclude the rato of actual to reference ncome n supplementary regressons of all lnear and nonlnear specfcatons. As actual household ncome s postvely correlated wth the number of adults, of full-tme employed adults and of chldren (wth a correlaton coeffcent of 0.329, and 0.159, respectvely), omsson of ths varable wll lead to an overestmaton of the unadjusted equvalence parameters for (workng) adults and chldren. However, t wll be necessary to correct the estmated equvalence weghts when actual ncomes sgnfcantly affect ncome responses (Bradbury, 1989). Ths s because a respondent, whose actual ncome s hgher than that needed to attan the reference household s materal standard of lvng, would ndcate lower ncome requrements once she receved the ncome that she had prevously deemed necessary. To be able to make consstent comparsons of ncome responses across dfferently composed households, one therefore has to calculate the ncome requrement for a household whose actual ncome corresponds to ths ncome requrement.. Here, we use the same method as often appled n studes of the mnmum ncome queston or ncome functons (see e.g., van Praag and van der Sar, 1988). It mplctly mputes current household ncomes that would lead respondents to state these as ther requred ncomes. In the lnear verson of our Baselne Specfcaton, for nstance, the ncluson of the actual-ncome rato Y /822 as a regressor yelds the followng equaton: ' EIR 1 ( n 1) n Y / 822 X b e. A C Under the provson that current ncomes must be equal to requred ncomes, EIR ( Y / 822), we can express the equvalent ncome rato by 1 ' b e EIR ( na 1) nc X , where s the coeffcent on the actual-ncome rato, whch usually ranges between zero and one. To correct for the preference drft, we thus only need to multply the equvalence weght of the respectve famly member by the factor 1/(1 ). Ths also apples to the nonlnear

22 model, where we frst have to calculate the equvalence weghts from the estmated parameters before we can apply the correcton factor. 4.3 Regresson Results We now turn to the presentaton of the results obtaned from our novel dataset. As these are drectly comparable to the results by KSS, we frst focus on the parameter estmates obtaned from the non-lnear model. After that, we wll consder the lnear model assumng fxed equvalence weghts. The estmated coeffcents allow us to calculate equvalence weghts of specfc household members that are comparable across models and can be adjusted for a potental preference drft caused by own household ncome. Ths wll help us evaluate the senstvty of our fndngs wth respect to the chosen specfcaton as well as own ncome effects. Nonlnear Model The top panel of Table 4 summarzes the parameters obtaned from estmatng our three man specfcatons n the nonlnear framework (the (Baselne) and equatons (1) and (2)). The frst column of each specfcaton presents the coeffcents estmated when gnorng the respondent s actual ncome, whle we account for t n the second column. Except for the baselne specfcaton, whch was not consdered n the KSS study, the thrd column to each specfcaton lsts parameter estmates by KSS that are based on ther German subsample takng a reference ncome of 500 as gven. The estmated parameters are used to calculate the equvalence weght of addtonal household members. The bottom panel of Table 4 reports the weghts for a selecton of household members to llustrate the mplcatons of the estmated parameters. To allow a far comparson between adult and chld weghts, all of the numbers refer to a thrd person jonng the household. Consder frst the regressons that do not nclude the respondent s actual household ncome. In the baselne specfcaton, we estmate the most classcal form of the Cutler-Katz scale not accountng for tme restrctons of households. We fnd that the necessary ncome ncrease assocated wth a chld s about 56 percent of that of an addtonal adult (parameter ). The economes of scale parameter s found to be very close to one, mplyng relatvely low economes of scale n the number of adult equvalents. As a result, the equvalence weght of

23 an addtonal adult s 87 and that of a chld 49 percent, rrespectve of the employment status of the adults. Table 4: Estmated Coeffcents and Resultng Equvalence Weghts from the Nonlnear Model n C Baselne Spec. 1 Spec. 2 Own results Own results KSS Own results KSS wthout ncome wth ncome wthout ncome wth ncome wthout ncome wth ncome 0.56 *** 0.77 *** 0.74 *** 0.83 ** 0.64 *** 0.47 ** 0.50 * 0.57 *** (0.13) (0.25) (0.23) (0.33) (0.03) (0.23) (0.30) (0.03) n *** *** W.. (0.18) (0.20) (0.04) (0.25) (0.31) (0.05) n D (0.22) (0.28) (0.04) n D * ***..... (0.32) (0.42) (0.03) 0.92 *** 0.70 *** 0.83 *** 0.69 *** 0.93 *** 0.80 *** 0.67 *** 0.96 *** (0.08) (0.09) (0.09) (0.11) (0.02) (0.12) (0.14) (0.02) C WN C F y / *** *** ***.. (0.03). (0.03).. (0.03). N ,116 a ,116 a 2 R Equvalence Weghts non-workng adult 0.87 *** 0.73 *** 0.70 *** 0.68 *** *** 0.50 ** 0.89 jons workng adult wth a chld (0.12) (0.16) (0.16) (0.20). (0.19) (0.24). workng adult jons workng adult wth a chld frst chld jons one workng and one non-workng adult frst chld jons two workng adults 0.87 *** 0.73 *** 0.89 *** 0.73 *** *** 0.43 * 1.74 (0.12) (0.16) (0.13) (0.16). (0.20) (0.25) *** 0.55 *** 0.52 *** 0.56 *** *** 0.60 *** 0.50 (0.07) (0.10) (0.07) (0.11). (0.09) (0.13) *** 0.55 *** 0.51 *** 0.55 *** *** 0.83 *** 0.59 (0.07) (0.10) (0.07) (0.10). (0.15) (0.24). a Observatons stem from 164 respondents reportng 19 hypothetcal ncomes each. Note: The dependent varable s the ncome response dvded by the reference value of 822. Own regressons nclude educaton, age, natonalty and state dummes as addtonal control varables. Standard errors n parentheses. * p < 0.1, ** p < 0.05, *** p < 0.01 Specfcaton 1 ntroduces the number of full-tme employed adults nto the analyss. Ths specfcaton corresponds to the benchmark model of KSS, so we can easly compare our parameter estmates to thers. We fnd a relatve weght of chldren that s about ten percentage