Stephanie von Hinke Kessler Scholder, George Davey Smith, Debbie A. Lawlor, Carol Propper, Frank Windmeijer

Transcription

1 Stephane von Hnke Kessler Scholder, George Davey Smth, Debbe A. Lawlor, Carol Propper, Frank Wndmejer Chld heght, health and human captal: evdence usng genetc markers Dscusson paper 2010/13 September 2010

2 Chld Heght, Health and Human Captal: Evdence usng Genetc Markers Stephane von Hnke Kessler Scholder 1 George Davey Smth 2 Debbe A. Lawlor 2 Carol Propper 3 Frank Wndmejer 4 20 September 2010 Heght has long been recognsed as assocated wth better outcomes: the queston s whether ths assocaton s causal. We use chldren s genetc varants as nstrumental varables (IV) to deal wth possble unobserved confounders and examne the effect of chld and adolescent heght on a wde range of outcomes: academc performance, IQ, self-esteem, symptoms related to depresson and behavoural problems, ncludng hyperactvty, emotonal, conduct and peer problems. OLS fndngs show that taller chldren have hgher IQ scores, perform better n school tests, and are less lkely to have emotonal or peer problems. The IV results dffer. They show that taller chldren have better cogntve performance but, n contrast to the OLS, ndcate that taller chldren are more lkely to have behavoural problems. The magntude of these IV estmates s large. For example, the effect of one standard devaton ncrease n heght on IQ s comparable to the IQ dfference for chldren born approxmately 6 months apart wthn the same school year, whle the ncrease n hyperactvty s comparable to the raw dfference n hyperactvty between boys and grls. Key words: JEL: Chld and Adolescent Heght; Human Captal; Mental Health; Behavoural Outcomes; Instrumental Varables; Mendelan Randomzaton; Genetc Varants; ALSPAC I1, J24 Acknowledgements: We thank John Cawley, George Lecke, Sarah Smth, and Ncholas Tmpson for helpful suggestons. We are extremely grateful to all the famles who took part n ths study, the mdwves for ther help n recrutng them, and the whole ALSPAC team, whch ncludes ntervewers, computer and laboratory techncans, clercal workers, research scentsts, volunteers, managers, receptonsts and nurses. Fundng: The UK Medcal Research Councl (MRC), the Wellcome Trust and the Unversty of Brstol provde core support for ALSPAC. GDS and DAL work n a centre that receves fundng from the UK MRC (G ) and Unversty of Brstol. Fundng from three grants supportng the specfc work presented here s gratefully acknowledged: two from the UK Economc and Socal Research Councl (RES and PTA ) and one from the UK MRC (G ). No fundng body nfluenced data collecton, analyss or ts nterpretaton. Ths publcaton s the work of the authors, who wll serve as guarantors for the contents of ths paper. 1 Imperal College Busness School, Imperal College London; CMPO, Unversty of Brstol 2 MRC Centre for Causal Analyses n Translatonal Epdemology (CATE), School of Socal and Communty Medcne, Unversty of Brstol 3 CMPO and Department of Economcs, Unversty of Brstol; Imperal College Busness School, Imperal College London; CEPR 4 CMPO and Department of Economcs, Unversty of Brstol; Centre for Mcrodata, Methods and Practce 1

3 1. Introducton The assocaton between heght and wealth has been noted n the academc lterature for many decades. As early as the 17 th Century, Guarnon one of the founders of preventve medcne ponted to the dfference n growth rates between the rch n towns and the poor n the countrysde (Tanner, 1982). More recent studes fnd heght to be postvely related to educaton (Magnusson, Rasmussen and Gyllensten, 2006) and ncome (Persco, Postlewate and Slverman, 2004). The advantages assocated wth greater heght have also been reported for chldren. For example, Case and Paxson (2008) fnd that taller chldren perform better n school tests compared to shorter chldren and suggest that the relatonshp between chldhood heght and ncome and educaton n adulthood s due to heght beng assocated wth greater ntellgence. One problem n estmatng the relatonshp between heght and outcomes s that the relatonshp may not be causal. Heght s nfluenced by a wde range of envronmental factors experenced n chldhood whch may be the determnants of the outcomes, rather than heght per se, for example, unobserved famly wealth or dfferences n chldren s nutrton. To the extent that these unobserved dfferences are famly specfc, one approach s to dentfy the causal mpact from twn or sblng dfferences n heght and outcomes. Case and Paxson (2010) use ths approach, explotng dfferences between sblngs. They conclude that taller chldren perform better n school, progress faster through school and consder themselves more scholastcally competent than ther shorter sblngs. However, accountng for fxed unobserved famly effects usng twn (or sblng) dfferences does not necessarly elmnate the nconsstency of the conventonal cross-sectonal estmator and can even aggravate t (Grlches, 1979; Bound and Solon, 1999). The ntuton s that takng twn or sblng dfferences flters out some, but not all, endogenous varaton but also flters out exogenous varaton. If the endogenous varaton comprses as large a proporton of the remanng wthn-sblng varaton as t does of the between-sblng varaton, the parameters usng wthn-sblng estmaton are as vulnerable to endogenety bas as that found n between-sblng estmaton. The nconsstency of the wthn-sblng estmator s less than the between-sblng estmator only f the endogenous varaton comprses a smaller share of the wthn-sblng varaton n heght than t does of the between-sblng varaton (Bound and Solon, 1999). There s no reason to be confdent that ths s the case. Ths paper therefore takes a dfferent approach to estmate the causal effect of chld heght on chldren s cogntve and non-cogntve outcomes. We explot dfferences n chldren s genetc make- 2

4 up as nstrumental varables (IV) for ther heght. 1 At concepton, genes are randomly allocated from parents to offsprng. Whlst ths random allocaton s at a famly tro level, at a populaton level t has been demonstrated that genetc varants are largely unrelated to the many socoeconomc and behavoural characterstcs that are closely lnked wth each other and that confound conventonal observatonal studes (Bhatt et al., 2005; Davey Smth et al., 2008; Kvmäk et al., 2008; Lawlor et al., 2008). Furthermore, snce genetc varaton s determned at concepton, t cannot be affected by later outcomes. Hence, n addton to dealng wth reverse causalty and fxed characterstcs that affect both heght and the outcome, Mendelan randomzaton can also deal wth tme-varyng characterstcs that affect heght and outcomes. Therefore, under certan assumptons that we dscuss below, genetc varants wll allow us to solate the causal effect of chld heght on the outcome of nterest. Ths paper s the frst to explot genetc varants for heght n an attempt to estmate the causal effect of heght on cogntve and non-cogntve outcomes for chldren. We begn therefore by outlnng the condtons needed to use genetc varants as nstruments. To examne and test the valdty of the IV approach n our context, we show frst that the genetc varants are uncorrelated wth a large set of famly background varables whch may confound the relatonshp between heght and outcomes. We then run a falsfcaton check n whch we nvestgate the effect of heght on body weght. As weght and heght are causally related, we should fnd strong postve effects n both the OLS and IV models. Any substantally dfferent or negatve effects n the IV estmates would cast doubt on the IV specfcaton and/or the nstruments used. Fndng no sgnfcant dfferences between the OLS and IV, we then use the genetc varants as nstruments to examne the relatonshp between heght and an extensve set of cogntve, mental health and behavoural outcomes. In so dong, we add to the range of outcomes examned n the prevous lterature. In addton to chldren s academc attanment, scholastc competence and self-worth studed by Case and Paxson (2010), we nvestgate the effects of heght on IQ, symptoms of depresson and behavoural problems, ncludng hyperactvty, emotonal, conduct and peer problems. We use data from a cohort of UK chldren currently n ther late teens (the ALSPAC survey, descrbed below). The OLS results show that taller chldren perform better n school tests, have hgher IQ, and are less lkely to have emotonal and peer problems, though these relatonshps dffer slghtly by gender. Tall grls have hgher depresson scores, but we fnd no evdence of dfferences n self-esteem for chldren of dfferent heghts. The IV results suggest there s a causal relatonshp between heght 1 Ths approach s also known as Mendelan randomzaton, see e.g. Davey Smth and Ebrahm (2003). It s closely related to Randomsed Controlled Trals, where the allocaton of treatment s randomsed over all elgble ndvduals, as there s an equal probablty that ether parental allele s transmtted to offsprng (Davey Smth and Ebrahm, 2003). For a bref overvew of genetcs and some of the terms used here, see Appendx A. 3

5 and IQ, though ths s not reflected n test scores. However, n contrast to Case and Paxson (2010), we fnd no evdence that heght explans varaton n scholastc self-esteem, global self-worth or depresson. Further, we fnd evdence that heght confers dsadvantage rather than advantage as t ncreases hyperactve behavour, emotonal and peer problems. The next secton begns by examnng the possble mechansms through whch heght may be related to the outcomes of nterest. In secton three we set out our methodology and secton four descrbes the data. The results are presented n secton fve; secton sx concludes. 2. Mechansms We examne a large set of outcomes: academc attanment, IQ, self-esteem, depresson symptoms, and behavoural problems. There are two ways n whch heght may be related to these outcomes. Frst, beng tall could cause dfferences n the outcome of nterest. We defne causal however, not necessarly as heght per se affectng the outcome, but as heght trggerng socal reactons that n turn affect the outcome. Hence, we hypothesze the effect of heght to run va dfferent pathways, whch we dscuss below. We represent ths causal effect n a Drected Acyclc Graph (DAG) n Fgure 1, where chld heght H affects the outcome C va varous pathways P rather than t affectng drectly (whch would be ndcated by the dashed drected edge). 2 Second, nstead of there beng a causal relatonshp, the assocaton between heght and the outcome of nterest may be drven by other unobserved factors that affect both. In Fgure 1, ths s shown by the unobservables affect both H and C. 3 C e that Several pathways through whch heght can causally affect outcomes are dscussed n the lterature, ncludng taller people enjoyng socal domnance (Hensley, 1993) and havng hgher self-esteem (Judge and Cable, 2004). The (socologcal and psychologcal) lterature posts several theores as to why (physcal) characterstcs may affect behavour or achevement. Frst, the possesson of certan characterstcs (lke beng tall) can trgger expectatons from others (lke peers or teachers). These expectatons may nfluence ther behavour towards the possessor, whch n turn affects the possessor s behavour, often confrmng the expectatons. Ths self-fulfllng prophecy s also referred to as the expectancy effect (see for example Darley and Fazo, 1980). For example, some evdence 2 In the DAG, each node represents a varable, wth square nodes beng observed and crcular nodes beng unobserved. 3 In theory, poor outcomes could lead chldren to change ther eatng patterns, whch may affect ther growth resultng n reverse causaton. We argue however, that ths s very unlkely and consder ths to be less of an ssue than (for example) n the case of body weght. However, even f there s reverse causaton, our dentfcaton strategy would deal wth ths. 4

6 suggests that taller people are perceved as more attractve (Macntyre and West, 1991). Attractveness can n turn nfluence the behavour and assessment of teachers (Clfford and Walster, 1973) or potental employers (Dpboye et al., 1975), causng taller chldren to behave and perform dfferently. Second, short chldren are beleved to have negatve socal experences, ncludng bullyng, less socal acceptance, and fewer frends (Sandberg and Voss, 2002; Voss and Mullgan, 2000), 4 though t s worth notng that tallness n grls has also been shown to have smlar negatve psychologcal effects (Pyett et al., 2005; Bnder et al., 1997). Havng problematc socal relatonshps can n turn affect selfesteem, socal adjustment, behavour, and scholastc performance (Morson and Masten, 1991; Parker and Asher, 1987; Wentzel, 2009). Related to ths s the queston of whether parents compensate or renforce chldren s endowments. The former may mean that parents spend relatvely more tme wth a small compared to a tall chld, to compensate for the potental negatve experences related to short stature. As the chld develops through chldhood, ths addtonal attenton and support can n turn ncrease ther cogntve sklls, or reduce ther behavoural problems. 5 Another strand of the lterature suggests that ndvduals (peers, parents, teachers as well as medcal personnel) treat chldren at a sze-approprate rather than age-approprate level: tall chldren are generally perceved to be (and treated as) older, whereas smaller chldren are treated as younger (Jones and Bayley, 1950; Rotnem et al., 1977; Underwood, 1991; Sandberg et al., 2004). Adults n turn may have dfferent expectatons dependng on chldren s heghts (Skuse et al., 1994), whch can subsequently affect chldren s behavour. Chldren who look young accordng to ther peers are perceved to be less (physcally and verbally) aggressve and more emotonal and passve (Sandberg et al., 2004). In addton, the lterature has found taller chldren to have more behavoural problems, such as aggresson or volent behavour. Rane et al. (1998) fnd that heght n 3-year-old chldren s assocated wth ncreased aggressveness at age 11, and Farrngton (1989) fnd that heght at age 8-10 years s assocated wth volence at age years. They argue that ther early lfe may have taught them that t s an effectve strategy n wnnng socal conflcts, renforcng ths behavour. In 4 In fact, the treatment of short chldren wth growth hormone s, n part, based on the belef that beng taller wll mprove short chldren s peer relatonshps (Sandberg et al., 2004; Sandberg and Voss, 2002). However, the evdence showng that short chldren have more negatve experences s ambguous: a revew by Sandberg and Voss (2002) for example, concludes that the psychologcal adaptaton of shorter-than-average ndvduals s largely ndstngushable from others, whether n chldhood, adolescence or adulthood. Others however, argue that short people may smply be dscrmnated aganst (Magnusson, Rasmussen and Gyllensten, 2006; West, 1991). Persco, Postlewate and Slverman (2004) nstead suggest that taller adolescents are more lkely to partcpate n socal actvtes that develop human captal. Hamermesh and Bddle (1994) also argue that (labour market) dscrmnaton does not arse from correlatons wth heght. Instead, they clam t s manly based on the employee s looks ( beauty ). 5 The evdence on whether parents compensate or renforce chldren s endowments s mxed, see e.g. Grlches (1979) and Behrman et al. (1994). 5

7 contrast, smaller and physcally weaker chldren lack the physcal capacty to execute ths behavour (Rane et al., 1998). As opposed to a causal effect, there may be other factors (represented by the unobservables e n Fgure 1) that relate to both heght and the outcome of nterest and that drve the assocatons. One set of canddates s the pre- and postnatal envronment. Regardng the latter, the fastest growth n chldren occurs up to age 2. There s evdence of lnks between early (post-natal) nutrton and chld heght, and between nutrton and cogntve and socal development. 6 But although early nutrton s a possble canddate, several studes have shown that even under condtons of severe malnutrton (prenatal, such as foetuses subjected to war-tme famne and postnatal, such as starvaton n the early years of lfe) complete equalty n heght wth sblngs or peers s attaned before puberty (Tanner, 1978). In terms of the pre-natal det, there s evdence that nutrton n utero plays an mportant role n chld development. But nutrments whch help development (such as the omega 3 fatty acds n fsh and seafood consumpton) may also hurt development. For example, fsh and seafood are the prmary source of (non-occupatonal) mercury exposure (Oken and Bellnger, 2008) and several studes have shown prenatal methylmercury exposure to be assocated wth decreased IQ and test scores (Axelrad et al, 2007; Cohen et al., 2005). Lkewse, some studes fnd that maternal alcohol consumpton and smokng durng pregnancy negatvely affect brth weght and chld growth (Mlls et al., 1984; Glman, Gardener and Buka, 2008). Lower brth weghts n turn are assocated wth poorer cogntve performance (Rchards et al., 2002; Ercson and Kallen, 1998) and behavoural development (Elgen et al., 2002), though the lterature suggests that ths relatonshp s drven by famly background characterstcs rather than a specfc ntrauterne effect (Yang et al., 2008). 7 Ths dscusson suggests that the use of both OLS and mother fxed effects to estmate a causal effect can result n bas that can go n ether drecton. If parents compensate for ther chld s endowment by spendng more tme wth shorter chldren, ths would ncrease short chldren s performance relatve to taller chldren, and hence ncludng mother fxed effects would lead to the estmates beng a lower bound. Smlarly, f a well-balanced det or the famly s soco-economc poston postvely affects heght, but also leads to fewer behavoural problems, the OLS s lkely to under-estmate the true effect of heght on behavoural problems. If, however, ths same det leads to better educatonal outcomes, OLS s lkely to over-estmate the true effect on educaton. However, f certan detary components lead to decreased cogntve functonng, the OLS may under-estmate the true effect on 6 For example, ron-defcency n nfants and chldren s assocated wth poorer cogntve, motor and soco-emotonal functon (see e.g. Lozoff et al., 2006). In addton, some studes report that ron supplementaton postvely affects heght (Angeles et al., 1993). 7 There s mxed evdence on the effects of maternal smokng and alcohol consumpton durng pregnancy on chld outcomes, wth some argung t lowers outcomes and others fndng no effect (see for example Olds et al., 1994; Glman, Gardener and Buka 2008; Kafour et al., 2009; Davey Smth, 2008; Nlsson, 2008; Russell, 1991). 6

8 educatonal outcomes and IQ. Under the assumptons we dscuss n detal below, the use of the chld s genetc markers as nstrumental varables wll shed more lght on these ssues and wll allow us to estmate the causal effect of chld heght. 3. Methodology 3.1. The Chld Human Captal Producton Functon We examne the mpact of chld heght on three sets of outcomes: (1) cogntve sklls, (2) mental health, and (3) behavoural problems. 8 We dscuss the outcomes n more detal below. As both heght and outcomes dffer by gender, we allow for dfferental effects by nteractng heght wth gender n all analyses. We model the relatonshp between heght and outcomes n terms of a human captal producton functon: C f H, X, e, (1) where C, the outcome of nterest for chld, s a functon of chld heght ( H, measured contemporaneously) and a set of chld and famly background characterstcs ( unobserved confounders. We begn wth OLS usng a lnear verson of (1): X ). e represents any C 0 1H 2 X e. (2) The parameter of nterest, the relatonshp between chld heght and the outcome varable, s 1. The possble endogenety of heght s charactersed by the fact that the unobservable confounders e determne the outcome of nterest C, but also determne heght H, leadng to based OLS estmates. We use IV to deal wth ths, specfyng the chld s genetc varants heght. These varants are assocated wth Z as nstruments for H, and we assume that they are only assocated wth C ndrectly through ther assocaton wth H. In the absence of a constant treatment effect, we 8 Although avalable n our data, we do not examne physcal health, as the IV assumptons are more lkely to be problematc: genetc varants that affect heght may also affect physcal health. For example, ndvduals wth hgher levels of GDF5 on average have ncreased bone and cartlage growth. The latter n turn s protectve aganst osteoarthrts (Sanna et al., 2008). Smlarly, HMGA2 s assocated wth heght, but s also over-abundant n many types of cancerous tumours (Lgon et al., 2005; Weedon et al., 2007), suggestng that some varants of genes that encourage growth may also cause uncontrolled cell growth n tssues leadng to cancer (McEvoy and Vsscher, 2009). 7

9 dentfy the average causal response usng the standard lnear IV estmator n (2) wthn a potental outcomes framework, followng Angrst, Graddy and Imbens (2000). We brefly summarze ther assumptons here. Let C, H and Z denote random varables representng, respectvely, the outcome of nterest, chld heght and the genetc varant as IV. For smplcty, we dscuss the case of a bnary nstrument, though n the estmaton we use multple nstruments as s more common n Mendelan randomzaton experments. Let h z C, be the potental outcome for ndvdual that would be obtaned f heght, the treatment varable, was set to h and the nstrument set to z. Equvalently, let H z be the potental heght for ndvdual when the nstrument s set equal to z. We make the followng assumptons: Assumpton 1. (Independence and Excluson) Z C h, z, H z h, z h, 1 C h,0, C for all h. Independence mples that the nstrument s ndependent of the potental outcome and the potental heght, for all values of h and z. In other words, the nstrument s as good as randomly assgned. Ths s reflected by the mssng edge between Z and e n the DAG n Fgure 1. The mssng edge between Z and C reflects the condtonal ndependence assumpton mpled by the model for C, H and e: C Z H, e,.e. the entre effect of Z on C s medated through ts assocaton wth H. Excluson mples that the potental outcomes, at any heght h, are unchanged by the presence or absence of the genetc varant. Assumpton 2. (Nonzero effect of nstrument on heght) E H 1 H 0 0 Ths mples that expected potental heght s affected by the genetc varant and that therefore the coeffcent n the (frst stage) regresson of edge between G and H n Fgure 1. H on Z s non-zero. Assumpton 2 s reflected by the Assumpton 3. (Monotoncty) P H 1 H 0 1 8

10 Ths means that the potental heght for ndvdual wth the genetc varant s at least as hgh as the potental heght for the same ndvdual wthout the genetc varant. From the excluson restrcton, t follows that C h z C h,. Specfyng heterogeneous responses, the potental outcome for ndvdual can be wrtten as a general functon of h, say C h g h Omttng characterstcs. X for smplcty, the IV (or Wald) estmator n equaton (2) s then equal to where g ˆ IV q s the dervatve of h E C Z 1 E C Z 0 E H Z 1 E H Z 0 ' E g q H 0 q H 1 P P H 0 q H 1 H 0 q H 1 dq g w.r.t. h evaluated at q. Therefore, the IV estmator s a dq weghted average of the dervatve functon. As Angrst, Graddy and Imbens (2000) show, when the causal response functon s lnear g h h, then E H ˆ E H H IV, (3) H.e. the IV estmate s a weghted average of the random coeffcents proportonal to the heght change nduced by the genetc varant. 9, wth the weghts 3.2 The Genetc Varants We use a set of nne genetc varants (SNPs) that have all been robustly assocated wth heght: HMGA2 (rs ), ZBTB38 (rs ), GDF5 (rs ), LOC (rs ), EFEMP1 (rs ), SCMH1 (rs ), ADAMTSL3 (rs ), DYM (rs ) and C6orf106 9 Ths easly extends to the case of multple and mult-valued (rather than bnary) nstruments, as dscussed n Angrst and Pschke (2009) and Angrst, Graddy and Imbens (2000). For a more detaled dscusson of the use of genetc markers as nstrumental varables from an economc perspectve usng a smlar framework as the above, see von Hnke Kessler Scholder et al. (2010). Lawlor et al. (2008) ncludes a more general dscusson of the stuatons and (bologcal) processes that may nvaldate Mendelan randomzaton studes. 9

11 (rs ) (Weedon et al., 2007, 2008; Lettre et al., 2008; Gudbjartsson et al., 2008). 10 Ths pror knowledge, and the fact that these assocatons have been replcated n dfferent ndependent samples, justfy the use of these varants and ther complance wth Assumpton 2. In secton 5.2 we examne ths assumpton usng the standard statstcal tests. Note however, that although the relatonshps between the SNPs we use and heght are robust, ther phenotypc effects are small: 20 SNPs, whch nclude the nne that we use only explan up to 3% of the varaton n heght (Weedon et al. 2008). We therefore combne the dfferent SNPs nto a count of the number of tall alleles carred by each chld to get around the problem of low power (see secton 4.4 below for detals). Assumpton 1, ndependence and excluson, s not drectly testable. Based on the scence lterature however, we argue that the nstruments are vald and so that Assumpton 1 holds. We also examne ts valdty ndrectly. Volatons of ths Assumpton can take several forms. Frst, genetc confoundng may occur because of populaton stratfcaton, for example, due to ethncty. Ths would mply that there s a systematc relatonshp between the allele frequency and the outcome n dfferent ethnc groups, resultng n an assocaton between the two at the populaton level but wthout a causal effect, volatng Assumpton 1. Ths s unlkely to affect our sample, as our cohort s recruted from a specfc geographcally defned regon wth a predomnantly whte populaton, and n our analyss, we only examne chldren whose mothers descrbe themselves and the chld s father as whte. Second, f the varants have multple functons (known as pleotropy), Assumpton 1 could be volated f over and above the assocaton wth heght any addtonal functons drectly nfluence the outcome of nterest. Smlarly, f a varant s co-nherted wth another genetc varant (known as beng n lnkage dsequlbrum (LD)), volaton of Assumpton 1 depends on the effect of the conherted varant on the outcome of nterest. The current evdence suggests that some heght varants may ndeed be pleotropc or n LD wth other varants. For example, ndvduals wth hgher levels of GDF5 on average have both ncreased bone and cartlage growth (Sanna et al., 2008). However, there s currently no evdence that the varants used here also affect (or are n LD wth varants that affect) our outcomes of nterest For example, Weedon et al. (2007) dentfy a common varant of the HMGA2 gene, usng 4,921 ndvduals of European ancestry. To valdate the robustness of ths fndng, they genotyped an addtonal 29,098 ndvduals from fve further studes, ncludng 6,827 chldren from the age of 7. Ther fndngs show each copy of the heght-ncreasng allele to be assocated wth an ncrease n heght of 0.4 cm, wth no dfferences between males and females. Smlarly, Weedon et al. (2008) use data from a total of 30,147 ndvduals of European ancestry and dentfy 20 loc that robustly affect stature, ncludng all those used here. These have snce been confrmed n more ndependent samples (see e.g. Lettre et al., 2008; Gudbjartsson et al., 2008). 11 Some lterature suggests that part of the heght-ntellgence assocaton s drven by a genetc component (Sundet et al., 2005), though others fnd no evdence of ths genetc component n the heght-educaton assocaton (Slventonen et al., 2000). Smlarly, Magnusson et al. (2006), comparng frst and second born bologcal brothers n Sweden, fnd that the taller 10

12 Although (n common wth all IV approaches) we cannot test Assumpton 1 drectly, we can do so ndrectly. In secton 4.4 we examne the relatonshp between the genetc varants and a large set of chld and famly background characterstcs. We fnd no assocaton, suggestng that the genetc varants do not affect these potental confounders. However, even after examnng ths broad range of background varables, there may stll be other varables unobserved to the researcher. We therefore rely on the theory of random allocaton of genetc varants and on the more general emprcal evdence that shows that genetc varants are unlkely to be related to unmeasured confounders (see for example, Bhatt et al., 2005; Davey Smth et al., 2008; Kvmäk et al., 2008; Lawlor et al., 2008). Gven random allocaton of genetc varants and the fact that ndvduals do not know ther genotypes, we assume that an ndvdual who carres a tall allele s at least as tall as the same ndvdual, had she not carred the tall allele, thus satsfyng the monotoncty Assumpton Data We use data from a cohort of chldren born n the Avon area of England. Avon has approxmately 1 mllon nhabtants, ncludng 0.5 mllon n ts man cty, Brstol. Women elgble for enrolment n the populaton-based Avon Longtudnal Study of Parents and Chldren (ALSPAC) had an expected delvery date between 1 Aprl 1991 and 31 December Approxmately 85% of these mothers enrolled, leadng to about 14,000 pregnances. The Avon area s broadly representatve of the UK, though mothers were slghtly more affluent compared to the general populaton (Goldng et al., 2001). 13 Detaled nformaton on the chldren and ther famles has been collected from a varety of sources, brother s sgnfcantly more lkely to attend hgher educaton. However, the heght effect estmated between brothers s almost dentcal to that across all men, suggestng that the correlaton between heght and ntellgence s not drven solely by genetc or envronmental factors common to brothers. However, even f some genetc component affects both heght and the outcome of nterest, t does not necessarly mply that a specfc genetc varant causes ths through (for example) pleotropy or LD. It may be caused, for example, by nteractons between genes (from smple pars to complex networks), other varaton n DNA, such as Copy Number Varants (CNV, where whole sectons of DNA are duplcated or deleted), and so on. To date, about 50 genes and regons of the genome have been assocated wth human heght, explanng only 5% of ts total varaton. Hundreds, maybe thousands more effects are stll lost n the genome (McEvoy and Vsscher, 2009). Yang et al. (2010) show that the reason why most of these have not yet been detected, s because the ndvdual SNP effects are too small to pass the strngent sgnfcance tests. Hence, t s possble for one (or more) of the nne nstruments used here to be pleotropc or n LD wth a varant that drectly affects our outcome. Based on the best avalable evdence however, we assume ths s not the case and that assumpton 1 holds. 12 As ths reles on knowng each ndvdual s counterfactual ths remans an assumpton. The lterature only shows that at a group or populaton level those who possess the genetc varant are taller than those who do not. The monotoncty assumpton could, for example, be volated n the presence of gene-envronment nteractons. 13 See for a more detaled descrpton of the sample, ts enrolment, and response rates. 11

13 ncludng self-completed questonnares, data extracton from medcal and educatonal records, ndepth ntervews, and clncal assessments and so our data set contans a large range of chld health and development, famly background, famly nputs and school measures. A total of 12,620 chldren survved past the age of 1 and returned at least one questonnare. Of these, 642 were excluded because ether ther mother or father s of non-whte ethnc orgn, leavng 11,978 potental partcpants. Our sample selecton process s as follows. Frst, we select those chldren for whom we observe all nne genotypes, leavng us wth approxmately 7,100 chldren. Second, we drop chldren for whom we do not observe ther heght. Chldren were nvted to attend specally desgned clncs, where ther anthropometrc measures were recorded. As not all chldren attended these clncs, our sample szes reduce to between 4,594 (age 8) and 3,867 (age 13). Fnally, we restrct the sample to those chldren for whom we observe the outcome of nterest, leadng to a fnal sample sze of around 3,900 at age 8 and 3,300 at age 13. We deal wth mssng values on other covarates by usng multvarate mputaton (Royston, 2004) Outcome Measures We examne three sets of outcomes. Frst, we observe two measures of cogntve functon. These are the chld s score on the natonally set Key Stage 3 (KS3) exam (taken by all 14-year-olds educated n the state sector) and the chld s IQ, measured as age Both measures are objectve and comparable across all chldren. Increasng scores ndcate better performance. It s mportant to note that IQ does not only measure nnate ablty. Instead, our measure of IQ (WISC-III) s an ndex of general ntellectual functonng, whch s shaped by both nherted and acqured attrbutes, ncludng any famly and envronmental nfluences. For example, there s evdence of dfferences n IQ between chldren of dfferent qualty home envronments and soco-economc poston (see e.g. Molfese et al. (1997) and references theren), so suggestng that the measure of IQ s not nnate but rather reflects a large set of famly and envronmental nfluences that also affect chldren s development. Second, we examne three measures of mental health or self-esteem: depresson symptoms, scholastc competence and global self-worth. The latter two are measured at age 8, usng the Harter s Self Percepton Profle for Chldren (Harter, 1985), wth ncreasng scores ndcatng hgher self-esteem. The depresson score s self-reported by the teenager at age 13 usng the Moods and Feelngs Questonnare (Angold et al., 1995). Increasng scores ndcate more depresson symptoms. 14 The KS3 scores are averaged over three subjects (Englsh, maths and scence) and obtaned from the Natonal Pupl Database, a census of all pupls n England wthn the state school system (ths ncludes 93% of Englsh chldren), whch s matched nto ALSPAC. IQ s measured usng the Wechsler Intellgence Scale for Chldren (WISC-III; Wechsler et al., 1992) and s admnstered by the ALSPAC psychology team. 12

14 Thrd, we examne the chld s behavoural problems, as measured by the mother s report on the Strength and Dffcultes Questonnare (SDQ; Goodman, 1997) admnstered at age 13. SDQ has four sub-scores, whch we examne separately (as s common n the lterature). These are hyperactvty, emotonal problems, conduct problems and peer problems. Increasng scores ndcate ncreasng problems. For comparablty, all outcomes are standardsed on the full sample of chldren for whom data s avalable, wth mean 100, standard devaton Measures of Chld Heght and the Genetc Varants We examne the effect of contemporaneous heght on each outcome. Heght s adjusted for the exact age n month at whch t s measured and standardsed to have mean 100, standard devaton 10. All measurements are taken by traned nurses. We nstrument heght wth a set of SNPs that have been consstently shown to relate to stature. These are: HMGA2, ZBTB38, GDF5, LOC387103, EFEMP1, SCMH1, ADAMTSL3, DYM and C6orf We combne these nto a count of the number of tall alleles carred by each chld (see secton 4.4 for more detals) Controls We observe a rch set of chld and famly background characterstcs that we nclude as covarates. We control for the chld s brth weght and for the number of older and younger sblngs under 18 n the household. As the outcomes of nterest may vary wth wthn-year-age, we also account for the chld s age (n months) at the tme the outcome s measured. We control for the famly s socoeconomc poston wth varous measures: log equvalsed famly ncome and ts square, four bnary varables for mother s and father s educatonal level, the mother s parents educatonal level, an ndcator for whether the chld s rased by the natural father, varables ndcatng the famly s socal class, and parents employment status when the chld s 21 months. As a further measure, we nclude a measure of small (local) area deprvaton, as measured at the chld s brth. 16 In addton to these generally observed controls, our data allow us to also account for several further 15 All genotypng was performed by KBoscence ( SNPs were genotyped usng the KASPar chemstry, whch s a compettve allele-specfc PCR SNP genotypng system usng FRET quencher cassette olgos ( 16 Famly ncome s an average of two observatons (when the chld s aged 3 and 4) and s n 1995 prces. The educatonal ndcators are: less than ordnary (O) level, O-level only, advanced (A) level that permts hgher educatonal study, and havng a unversty degree. We use the standard UK classfcaton of socal class based on occupaton (professonal (I), manageral and techncal (II), non-manual sklled (IIInm), manual sklled (IIIm), sem-sklled (IV) and unsklled (V)). The Index of Multple Deprvaton (IMD) s based on sx deprvaton domans, ncludng health deprvaton and dsablty; employment; ncome; educaton, sklls and tranng; housng; and geographcal barrers to servces. Increasng IMD scores ndcate greater deprvaton. The IMD measure relates to areas contanng around 8000 persons. 13

15 measures of mother s health and behavour, whch may be correlated wth both chld heght and the outcome of nterest. We use two bnary varables whch measure whether the mother smoked or drank alcohol n the frst three months of pregnancy; an ordered ndcator for the ntensty of mother s breastfeedng (never, <1 month, 1-3 months and 3+ months); mother s age at brth (20-24, 25-29, 30-34, 35+); mother s locus of control, a psychologcal concept that descrbes whether ndvduals attrbute successes and falures to nternal or external causes (those wth an external locus of control attrbute success and falure to chance); two further measures of maternal mental health; and fnally several measures of parental nvolvement or nterest n the chld s development. 17 We also use these covarates n a test of Assumpton 1 above, examnng whether they dffer for the dfferent genotypes Descrptve Statstcs Table 1 presents mean heght (at age 8) for each of the SNPs, dstngushng between chldren who are homozygous for the heght-ncreasng allele, heterozygous and homozygous for the heght nonncreasng allele. These show that each of the ndvdual SNPs explan lttle of the varaton n chld heght. Ths would mply that the frst stage regressons have low explanatory power. For ths reason (and as Weedon et al. (2008) and Lettre et al. (2009)), we create a count of the total number of heght-ncreasng alleles carred by each chld and use ths as the nstrument for chld heght. Wth nne SNPs, ths varable has a possble range from 0 (homozygous for the non-heght-ncreasng allele at all varants) to 18 (homozygous for the heght-ncreasng allele at all varants). The left panel of Fgure 2 presents a hstogram of the number of tall alleles carred by each chld, showng a bellshaped dstrbuton. The lnear predcton of chld heght, obtaned from a regresson on the number of tall alleles, s presented by the straght lne. On average, each tall allele ncreases the chld s heght at age 8 by standard devatons (approxmately 0.25 cm). There s, however, a consderable amount of unexplaned varaton n heght (R 2 = 0.8%), as shown n the rght panel of Fgure 1, where the lnear predcton s presented by the same straght lne. Columns 1 and 2 n Table 2 present the descrptve statstcs (mean, standard devaton) of the varables used n the analyses. Ths shows an average heght at age 8 of cm and of cm at 17 Maternal mental health s measured by the Ednburgh Post-natal Depresson Score (EPDS) and Crown-Crsp Expermental Index (CCEI) at 18 weeks gestaton. EPDS ndcates the extent of post-natal depresson; CCEI captures a broader defnton of mental health, measurng general anxety, depresson and somatcsm. Hgher scores mean the mother s more affected. The mother s teachng score s constructed from questons that measure whether the mother s nvolved n teachng her chld (dependng on the chld s age) songs, the alphabet, beng polte, etc. We use an average score from three measures at ages 18, 30 and 42 months to capture longer-term nvolvement. Lkewse, a varable s ncluded ndcatng whether the mother reads/sngs to the chld, allows the chld to buld towers/other creatons etc, measured at age 24 months. Fnally, we also account for the extent to whch parents engage n actve (outdoor) actvtes wth ther chldren, such as gong to the park or playground and gong swmmng. 14

16 age 13. In the analyss, we use standardsed heghts. Columns 3 to 5 show the raw assocaton between ths measure, the covarates and the number of tall alleles, obtaned from a regresson of standardsed heght or each covarate on the number of heght-ncreasng alleles. The top two rows of these columns present the relatonshp between chld heght and the nstrument, showng a strong relatonshp for heght at both ages. On average, each tall allele s assocated wth a standard devaton ncrease n chld heght (note, as mentoned above, that heght s dstrbuted wth mean 100, standard devaton 10). The rest of columns (3) (5) show no clear patterns or (wth three exceptons) statstcally sgnfcant assocatons n the relatonshp between the contextual varables and the number of heght-ncreasng alleles. Usng a two-sded bnomal probablty test at the 5% level, a comparson of the observed versus expected number of sgnfcant correlatons suggests that the genetc varants show no greater assocaton wth the chld and famly background characterstcs than what would be expected by chance (p = 0.15), provdng support for Assumpton IV Falsfcaton Check Another way to examne the robustness of our IV approach and the valdty of our nstruments s by undertakng a falsfcaton check. If we examne the effect of heght on body weght, controllng for other covarates, we expect (a) to fnd strong postve effects n both OLS and IV, as the two are hghly (postvely) correlated partcularly n chldren who are stll growng (e.g. see any chldren s growth charts), and (b) for the two estmates to gve smlar coeffcents. There would be a slght downward bas of the OLS estmates n some case; for example, a healthy (unobserved) det mght postvely affect heght and negatvely affect weght. As shown by Tanner (1978) and dscussed above however, even wth severe (prenatal or postnatal) malnutrton, chldren attan smlar heghts as ther sblngs or peers. Hence, even f any bas exsts, we do not expect ths to be large. A substantally dfferent or null IV fndng would therefore cast doubt on our IV strategy. Table 3 shows strong postve estmates of body weght on heght at dfferent ages n both the OLS and IV. A one standard devaton ncrease n heght s assocated wth a standard devaton ncrease n weght n the OLS, and a standard devaton ncrease n weght n the IV. The pont estmates are smlar n both models, though the standard errors are much larger n the IV as expected. Usng the Durbn-Wu-Hausman test, we can statstcally dstngush the OLS from IV n 18 To shed more lght on whether the varants are lkely to be related to other background characterstcs, we also examne the relatonshp between the genetc varants and a wde set of further varables (64 addtonal parwse comparsons) that are not ncluded n our analyss (such as whether the chld had sleepng dffcultes, the chld s locus of control, whether the mother had a caesarean secton, mother s self-esteem, anxety, depresson, whether the famly owns ther own home, whether they have fnancal dffcultes, etc.). The fndngs (avalable from the authors upon request) also suggest the genetc varants are unrelated to these other varables (usng a two-sded bnomal probablty test, p = 0.77 at the 5% level; p = 0.83 at the 10% level). 15

17 only one case (11 year-old grls); the majorty of the IV estmates are ndstngushable from those estmated by OLS. Ths suggests that our nstruments perform well and that the IV approach correctly dentfes the causal effect of heght on body weght. Although ths does not guarantee that our IV approach also correctly dentfes the causal effect on the other outcomes of nterest, t does provde support for our argument that both the approach and the nstruments are vald to obtan causal estmates of the effects of stature. 5. Results 5.1. OLS Results We begn by examnng the OLS assocaton between heght, cogntve sklls and mental health. Columns (1) and (2) of Table 4 show a postve assocaton between heght, test scores and IQ that halves when controllng for the background characterstcs. However, the actual magntude of the assocaton s small: controllng for all covarates (the adjusted results), a one standard devaton ncrease n heght s assocated, for example, wth a standard devaton ncrease n grls IQ. Comparng ths to the effect of wthn-school-year age on IQ n our data, ths corresponds to a dfference n test scores between chldren born approxmately one month apart. Columns (3) to (5) examne the relatonshp between heght, the two measures of self-esteem and symptoms of depresson. Ths shows that heght s related to ncreases n self-esteem and depresson scores, though the estmates decrease and become ndstngushable from the null when controllng for the covarates (the postve assocaton wth depresson symptoms wthn grls s the one excepton). Table 5 presents both the unadjusted (raw) and adjusted (controllng for all covarates) assocatons between heght and behavoural problems. The latter shows that heght s unrelated to hyperactvty and conduct problems, but there s a negatve relatonshp wth emotonal problems. The effects are agan small: a one standard devaton ncrease n heght s assocated wth standard devatons decrease n emotonal problems. The results also show a small negatve assocaton between heght and peer problems for grls. 16

18 5.2. IV results Table 6 presents the IV results for cogntve sklls and mental health. The estmates are obtaned from a pooled (by gender) frst stage regresson of heght (e.g. at age 8) on the number of heghtncreasng alleles carred by each chld. Our nstrument predcts heght well, wth a frst stage F- statstc between 34 and 42, satsfyng Assumpton To obtan gender-specfc second stage results, we regress the outcome on the predcted heght nteracted wth the chld s gender, bootstrappng the standard errors. Column 1, Table 6, shows the IV estmates for KS3. These are larger than the OLS but also have large standard errors. We cannot reject the null of no effect, nor can we reject the Durbn-Wu-Hausman (DWH) test, whch s a test of the hypothess that the IV estmates are the same as those n the OLS. Column 2 shows a postve effect of nstrumented heght on IQ for both boys and grls and the DWH test rejects the null of exogenous heght at the 10% level. The IV estmate s larger than the OLS, suggestng that the latter underestmates the true effect: a one standard devaton ncrease n nstrumented heght ncreases IQ by 0.3 standard devatons (we dscuss possble reasons for ths dfference below). The IV estmates suggest, n contrast to the OLS estmates, that heght s negatvely related to the mental health outcomes. Columns 3 to 5 of Table 6 show that for self-esteem, global self worth and depresson symptoms, the large standard errors mean we cannot reject the null of no effect. But all three sets of IV coeffcents relate ncreasng heght to worse outcomes. Table 7 presents the IV regresson results for behavoural problems. In contrast to the OLS results n Table 5, the IV estmates n Column 1 of Table 7 show heght to be a predctor of hyperactvty n grls, wth the DWH test rejectng the exogenety assumpton of heght. A one standard devaton ncrease n nstrumented heght ncreases the hyperactvty score by 0.34 standard devatons. The estmate for boys s also postve, though smaller and not statstcally dstngushable from the null. Smlarly, heght appears to be a postve predctor of boys emotonal and peer problems (columns 2 and 4) and the estmated effect, although not statstcally sgnfcant, s of a smlar magntude for grls emotonal problems. Column 3 shows there s no effect of heght on conduct problems for ether gender. 19 As a general test of gene-envronment nteractons, we explore whether our genetc varants are only expressed n specfc envronments, and therefore whether there s any drect evdence of volaton of the monotoncty assumpton. We estmate the frst stage regresson, nteractng the genetc varants wth ndcators for varous subgroups and test whether the nstrument coeffcent s the same across groups. We specfy the followng subgroups: gender, duraton of breastfeedng, socal class, mother s educatonal level, and quartles for brth weght, log ncome, the Index of Multple Deprvaton (IMD) and mother s teachng score. Wth one nteracton (breastfeedng for 11+ grls, but not for boys) showng p=0.057, and all other p-values between and 0.977, the results (avalable from the authors) show no more sgnfcant dfferences than what would be expected by chance, suggestng that gene-envronment nteractons do not play an mportant role for the genetc varants used here. 17

19 5.3 Non-lneartes As dscussed n secton 2, the exstng lterature has found both tallness and shortness to have negatve psychologcal effects n chldren. The estmates dscussed above only examne dfferences n the outcome of nterest at the mean, but the relatonshp between heght and the outcomes may dffer at dfferent ponts n the dstrbuton. We therefore nvestgate dfferent cut-ponts and examne the effects of beng below the 25 th and above the 75 th percentle of the age- and gender specfc heght dstrbuton. The results (avalable upon request) confrm our man fndngs. OLS estmates show that shorter chldren have lower IQ and do worse n school tests, and vce versa for taller chldren. The IV results also show that shorter chldren have lower IQ. But, as above, the IV estmates show no evdence of a relatonshp between heght and scholastc competence, self-worth or depresson. The IV effects of beng tall or short on the chld s behavoural problems also show smlar patterns to those above: relatvely short grls are less hyperactve and have fewer emotonal problems, and vce versa for tall grls. For boys, shortness decreases and tallness ncreases emotonal and peer problems. 6. Concluson and dscusson Ths paper s the frst to explot genetc varaton n heght to examne the causal effects of heght on human captal accumulaton. OLS results show that taller chldren perform better n terms of cogntve performance and are less lkely to have emotonal and peer problems (grls), though tall grls are more lkely to show symptoms of depresson. Usng genetc varaton n heght n an IV specfcaton, we attempt to deal wth the problems of endogenety. The IV fndngs are smlar to the OLS for cogntve performance; we fnd a postve effect of heght on IQ. However, we fnd a negatve relatonshp wth behavour. We show that the OLS results are downwardly based and that heght ncreases rather than decreases behavoural problems. Taller chldren are more hyperactve and are more lkely to have emotonal and peer problems. In many of our results, the IV estmates ndcate that OLS s based downwards. One possble explanaton for the dfference between IV and OLS could be a genetc one. For example, (one of) our SNPs could be pleotropc or n LD wth another varant that drectly affects IQ or cognton. But from the evdence dscussed n footnote 11 and from the fact that we use only nne SNPs out of possbly hundreds or thousands SNPs codng for heght, we make the assumpton that ths s not the case. More generally, the lterature does not gve any reason to expect volaton of the IV assumpton 18