University of Wollongong Economics Working Paper Series 2003

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University f Wllngng Ecnmics Wrking Paper Series 003 http://www.uw.edu.

1 University f Wllngng Ecnmics Wrking Paper Series Measuring Overweight: A te Amnn Levy WP August 003

2 Measuring Overweight: A te Amnn Levy University f Wllngng Abstract: The Bdy Mass Index (BMI) prvides a biased assessment f individual weight cnditin when there are substantial frame and muscle size deviatins frm the average fr a given height. A methd fr vercming this prblem is presented. It allws an unbiased assessment f the individual level and degree f verweight and f the prevalence and intensity f verweight within the ppulatin. Crrespnding Authr: Amnn Levy, Ecnmics Discipline, Schl f Ecnmics and Infrmatin Systems, University f Wllngng, Wllngng, SW 5, Australia. amnn_levy@uw.edu.au, Tel: , Fax:

3 1. Intrductin The rates f verweight and besity have been rising wrld-wide. In many cuntries these prblems are nw replacing smking as the main public health issue. Accrding t the atinal Heart, Lung, and Bld Institute (1998), the prevalence f verweight and besity in the adult ppulatin f the United States has increased frm 46 per cent in 1980 t 55 per cent in Finkelstein, Fiebelkrn and Wang (003) have argued that the annual medical spending attributable t verweight and besity is 9.1 per cent f all US natinal health expenditures. Furthermre, the mrbidity and mrtality assciated with verweight and besity generate a lss f utput and wellbeing. Sme f the attempts t explain the spread f verweight and besity are fcused n technlgical develpments that have made the prductin f fd easier and cheaper (Cutler, Glaeser and Shapir, 003) and husehld and market wrk easier r mre sedentary (Philipsn and Psner, 1999; Lakdawalla and Philipsn, 00). Sme ther attempts emphasise the rle f behaviural factrs addictin, rate f time preference and scial nrms, in particular. Fllwing Becker and Murphy (1988) ne may argue that if fd items are addictive, cnsumers expectatins fr lng-run decline in the prices f these items might have led t a large increase in the cnsumptin f fd. Cnsidering inter-temprally ratinal, nn-addictive eating with trade-ff between satisfactin frm eating and risk t life psed by verweight, r underweight, Levy (00) has prpsed that the ratinally ptimal statinary weight exceeds the physilgically ptimal weight and that the ratinally ptimal statinary level f verweight rises with the elasticity f utility frm fd and the individual rate f time preference. Hence, a rise in rate f time preference, ceteris paribus, may help explaining the rise in the prevalence and intensity f verweight and besity (see als 1

4 Kmls, Smith and Bgin, 00). Levy (00) has als argued that the existence f scial-cultural nrms f appearance mderates the individual ratinal statinary level f verweight. The internatinal standard measure used by the medical prfessin fr assessing weight cnditin and the prevalence f verweight and besity is the Bdy Mass Index. This index is cmputed with externally measurable individual features and is equal t the rati f i-th adult individual weight ( W i, in kilgrams) t his, r her, height ( H i, in metres) squared W BMI i i =. (1) Hi Yet equally tall peple may have different physilgically desirable weights due t: 1. differences in skeletn width, and. differences in muscularity. Hence, the assessment whether the individual weight is physilgically (r medically) prper lets the BMI be within an interval. Accrding t the Wrld Health Organizatin s definitins, BMI between 5 kg / m and 9.9 kg / m is verweight, and greater than, r equal t, 30 kg / m is bese. Hwever, it is pssible, n the ne hand, that the BMI values f lean peple with cnsiderably large frame (wide skeletn) and muscles are beynd the nrmal interval s upper-bund and hence these peple are reprted as verweight. This pssibility has been strengthened by the lwering f the upper-bund f the nrmal weight range frm 7.3 kg / m fr wmen and 7.8 kg / m fr men t a unisex value f 5 kg / m during the 1990s a perid that saw a tremendus increase in gym membership and attendance and in gym instruments at hmes. It is als pssible, n the ther hand, that the BMI values f fat peple with very small frame (narrw

5 skeletn) and muscles are within the Wrld Health Organizatin s range f nrmal weight. Cnsequently, the aggregatin f the individual results might lead t a biased assessment f the prevalence f verweight and besity within the ppulatin. Furthermre, the use f the BMI and ranges des nt reveal the individual s level and degree f verweight, r underweight, and, subsequently, des nt enable an accurate assessment f the intensity f verweight and besity within the ppulatin. The bjective f this nte is t cnstruct an external weight measure that explicitly takes int accunt differences in frame and muscularity within a framewrk where the frame-width mean within a grup f peple with equal height as well as the individual physilgically desirable weight are nt bservable. Sectin utlines a height-frame-muscle (HFM) apprach fr externally assessing weight cnditin. The HFM apprach generates a reduced frm f the individual weight equatin whse parameters can be estimated by regressin analysis with crss individual bservatins. The estimates f these parameters can be used t cmpute the HFM degree, prevalence and intensity f verweight presented in sectin 3.. The HFM Apprach The prpsed HFM apprach is based n the assumptin that the unbserved physilgically desirable weight ( W ) may vary acrss peple with equal height in accrdance with the deviatin f their frame and muscle size frm the means in their height grup: W i = αhi + β1[ Fi µ f ( Hi )] + β [ M i µ m ( Hi )] () fr i = 1,,3,..., adult individuals f the same gender. Here, α is a scalar denting the medically ptimal BMI value fr a persn with average frame and muscle size in 3

6 his, r her, height grup; F i is the frame size 1 f an adult individual i; µ f ( Hi ) is the unbserved mean f the frame width within the grup f peple wh are as tall as persn i; β 1 is an unknwn psitive scalar indicating the effect f deviatin frm this mean n the individual s physilgically desirable weight; M i is the muscle size f an adult individual i; µ m ( Hi ) is the unbserved mean f the muscle size within the grup f peple wh are as tall as persn i; and β is an unknwn psitive scalar denting the effect f muscularity n the individual s physilgically desirable weight. The unbserved means f the frame width and the muscle size within the grup f peple wh are as tall as persn i are assumed t be prprtinal t height µ f ( Hi ) = γ s Hi (3) µ m ( Hi ) = γ mhi (4) where γ f and γ m are unknwn psitive scalars. The deviatin f the individual actual weight frm his, r her, physilgically ptimal weight is assumed t be given by a linear functin f a vectr, X i, f bserved deviatins f the individual physical characteristics frm the ppulatin average (age, chrnic illness, disability, ethnicity, race, ccupatin, marital status, lcatin, climate, etc.) and f a vectr f latent deviatins f sme ther individual characteristics frm the average (e.g., rate f time preference, cnsumptin preferences and mental dispsitin) cnstituting a zer-mean randm disturbance ε i Wi W i = δ Xi + εi (5) 1 Fr instance, the Metrplitan Life Insurance Cmpany has used the distance between the tw prminent bnes n either side f the elbw fr assessing individuals frame size (see Elbw-width r wrist-width are highly crrelated with bne and muscle mass. 4

7 where δ is the vectr f the unknwn cefficients indicating the effects f the bserved deviatins f persnal characteristics. The structural equatins (), (3), (4) and (5) lead t the fllwing expressin f the deviatin f the individual actual weight frm the medically ptimal weight fr a persn f his, r her, height with average frame width and muscle size: Wi α Hi = ( β1γ f + β γ m ) Hi + β1si + βmi + δx i + εi. (6) 3. The HFM measures f the degree, prevalence and intensity f verweight The unknwn parameters f the reduced-frm equatin (6) can be estimated, fr adult males and adult females separately, with crss-sectin bservatins and nn-linear estimatin methd. Cnsistently with its afrementined interpretatin and the Wrld Health Organizatin s definitin, α can be set t be equal t the mid-value ( fr wmen and.8 fr men) f the nrmal BMI range ( fr wmen and fr men) in cnstructing the dependent variable. Subsequently, the individual cmputed physilgically desirable weight can be btained by substituting the estimated values f β 1, β, γ f and γ m int equatins (), (3) and (4). The deviatin f the individual actual weight frm his, r her, cmputed physilgically desirable weight ( Wˆ i ) is given by: ˆ W ˆ [ ˆ ] ˆ i Wi W i = Wi αhi β1 Fi γ f Hi β[ M i γˆ mhi ] (7) where βˆ βˆ 1,, γˆ f and γˆ m are the estimates f β 1, β, γ f and γ m, respectively and α is equal t fr wmen and.8 fr men. 5

8 If W i > 0, individual i is verweight. The individual degree f verweight and the aggregate measures f the prevalence and intensity f verweight in a ppulatin can be cmputed as fllws. Individual Overweight Degree (IOD): The individual verweight degree is given by IODi = Wi / Wˆ i. (8) Overweight Prevalence (OP): Let D i = 1 if W i > 0 and zer therwise, then the measure f the verweight prevalence in a ppulatin f adults can be expressed as OP = 1 D i i= 1 (9) and 0 OP 1. Overweight Intensity (OI): The prpsed OI measure takes int accunt bth the verweight prevalence and the individuals verweight degrees within the surveyed ppulatin: OI 1 1 W = i DiIODi = Di i= 1 i= 1 W i. (10) and 0 OI 1 if IOD i 1 fr every i with W i > 0. It can be expected that 0 OI 1 even when IOD > 1 fr sme individuals if there is a sufficiently large number f peple with IOD < 1. 6

9 References Becker, G., and K. Murphy, 1988, The Thery f Ratinal Addictin, Jurnal f Plitical Ecnmy 96, Cutler, D., E. Glaeser, J. Shapir, 003, Why Have Americans Becme Mre Obese? BER Wrking Paper Finkelstein, E., I.C. Fiebelkrn, and G. Wang, 003, atinal medical Spending Attributable t Overweight and Obesity: Hw Much and Wh s paying? Health Affairs W3, Kmls, J., P. Smith and B. Bgin, 00, the Rate f Time Preference and Obesity: Is there a Cnnectin? mime, University f Michigan-Dearbrn. Ladkawalla, D., and T. Philipsn, 00, The Grwth f Obesity and Technlgical Change: A Theretical and Empirical Examinatin, BER Wrking Paper Levy, A., 00, Ratinal Eating: Can it lead t Overweightness r Underweightness? Jurnal f Health Ecnmics 1, Philipsn, T., an R. Psner, 1999, The Lng-Run Grwth in Obesity as a Functin f Technlgical Change, BER Wrking Paper 743. atinal Heart, Lung, and Bld Institute, Clinical Guidelines n the Identificatin, Evaluatin, and Treatment f Overweight an Obesity in Adults, IH publicatin , September

Internal vs. external validity. External validity. This section is based on Stock and Watson s Chapter 9.

Sectin 7 Mdel Assessment This sectin is based n Stck and Watsn s Chapter 9. Internal vs. external validity Internal validity refers t whether the analysis is valid fr the ppulatin and sample being studied.