The Body Mass Index (BMI) provides a biased assessment of individual weight condition when there are substantial frame and muscle size deviations from the average for a given height. A method for overcoming this problem is presented. It allows an unbiased assessment of the individual level and degree of overweight and of the prevalence and intensity of overweight within the population.Body Mass Index, overweight

Levy, Amnon

English

Research Papers in Economics

 
 
 
 
 
 
 
 
 
Measuring Overweight: A Note 
 
 
 
 
 
 
Amnon Levy 
 
 
 
 
 
 
 
 
 
 
WP 03-11 
 
August 2003 
University of Wollongong 
Economics Working Paper Series 
2003 
 
http://www.uow.edu.au/commerce/econ/wplist.html    
Measuring Overweight: A Note 
 
 
 
Amnon Levy 
University of Wollongong 
 
 
 
 
 
Abstract: The Body Mass Index (BMI) provides a biased assessment of individual 
weight condition when there are substantial frame and muscle size deviations from the 
average for a given height. A method for overcoming this problem is presented. It 
allows an unbiased assessment of the individual level and degree of overweight and of 
the prevalence and intensity of overweight within the population. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Corresponding Author: Amnon Levy, Economics Discipline, School of Economics 
and Information Systems, University of Wollongong, Wollongong, NSW 2522, 
Australia. E -mail: amnon_levy@uow.edu.au, Tel: 61-2-42213658, Fax: 61-2-
42213725.  1
1. Introduction 
The rates of overweight and obesity have been rising world-wide. In many 
countries these problems are now replacing smoking as the main public health issue. 
According to the National Heart, Lung, and Blood Institute (1998), the prevalence of 
overweight and obesity in the adult population of the United States has increased from 
46 per cent in 1980 to 55 per cent in 1994. Finkelstein, Fiebelkorn and Wang (2003) 
have argued that the annual medical spending attributable to overweight and obesity is 
9.1 per cent of all US national health expenditures. Furthermore, the morbidity and 
mortality associated with overweight and obesity generate a loss of output and well-
being.  
Some of the attempts to explain the spread of overweight and obesity are 
focused on technological developments that have made the production of food easier 
and cheaper (Cutler, Glaeser and Shapiro, 2003) and household and market work 
easier or more sedentary (Philipson and Posner, 1999; Lakdawalla and Philipson, 
2002). Some other attempts emphasise the role of behavioural factors – addiction, rate 
of time preference and social norms, in particular. Following Becker and Murphy 
(1988) one may argue that if food items are addictive, consumers’ expectations for 
long-run decline in the prices of these items might have led to a large increase in the 
consumption of food. Considering inter-temporally rational, non-addictive eating with 
trade-off between satisfaction from eating and risk to life posed by overweight, or 
underweight, Levy (2002) has proposed that the rationally optimal stationary weight 
exceeds the physiologically optimal weight and that the rationally optimal stationary 
level of overweight rises with the elasticity of utility from food and the individual rate 
of time preference. Hence, a rise in rate of time preference, ceteris paribus, may help 
explaining the rise in the prevalence and intensity of overweight and obesity (see also   2
Komlos, Smith and Bogin, 2002). Levy (2002) has also argued that the existence of 
social-cultural norms of appearance moderates the individual rational stationary level 
of overweight. 
The international standard measure used by the medical profession for 
assessing weight condition and the prevalence of overweight and obesity is the Body 
Mass Index. This index is computed with externally measurable individual features 
and is equal to the ratio of i-th adult individual weight ( i W , in kilograms) to his, or 
her, height ( i H , in metres) squared 
2
i
i
i
H
W
BMI = .                 (1) 
Yet equally tall people may have different physiologically desirable weights due to: 1. 
differences in skeleton width, and 2. differences in muscularity. Hence, the 
assessment whether the individual weight is physiologically (or medically) proper lets 
the BMI be within an interval. A ccording to the World Health Organization’s 
definitions, BMI between 25  2 /m kg  and 29.9 2 /m kg  is overweight, and greater than, 
or equal to, 30  2 /m kg  is obese.  
However, it is possible, on the one hand, that the BMI values of lean people 
with considerably large frame (wide skeleton) and muscles are beyond the normal 
interval’s upper-bound and hence these people are reported as overweight. This 
possibility has been strengthened by the lowering of the upper-bound of the normal 
weight range from 27.3 2 /m kg  for women and 27.8 2 /m kg  for men to a unisex value 
of 25 2 /m kg during the 1990s  – a period that saw a tremendous increase in gym 
membership and attendance and in gym instruments at homes. It is also possible, on 
the other hand, that the BMI values of fat people with very small frame (narrow   3
skeleton) and muscles are within the World Health Organization’s range of normal 
weight. Consequently, the aggregation of the individual results might lead to a biased 
assessment of the prevalence of overweight and obesity within the population.  
Furthermore, the use of the BMI and ranges does not reveal the individual’s 
level and degree of overweight, or underweight, and, subsequently, does not enable an 
accurate assessment of the intensity of overweight and obesity within the population. 
The objective of this note is to construct an external weight measure that 
explicitly takes into account differences in frame and muscularity within a framework 
where the frame-width mean within a group of people with equal height as well as the 
individual physiologically desirable weight are not observable. Section 2 outlines a 
height-frame-muscle (HFM) approach for externally assessing weight condition. The 
HFM approach generates a reduced form of the individual weight equation whose 
parameters can be estimated by regression analysis with cross individual observations. 
The estimates of these parameters can be used to compute the HFM degree, 
prevalence and intensity of overweight presented in section 3. 
 
2. The HFM Approach 
The proposed HFM approach is based on the assumption that the unobserved 
physiologically desirable weight ( o W ) may vary across people with equal height in 
accordance with the deviation of their frame and muscle size from the means in their 
height group: 
)] ( [ )] ( [ 2 1
2
i m i i f i i i
o H M H F H W m b m b a - + - + =       (2) 
for  N i ,..., 3 , 2 , 1 =  adult individuals of the same gender. Here, a  is a scalar denoting 
the medically optimal BMI value for a person with average frame and muscle size in   4
his, or her, height group;  i F  is the frame size
1 of an adult individual i;  ) ( i f H m  is the 
unobserved mean of the frame width within the group of people who are as tall as 
person i;  1 b  is an unknown positive scalar indicating the effect of deviation from this 
mean on the individual’s physiologically desirable weight;  i M  is the muscle size of 
an adult individual i;  ) ( i m H m  is the unobserved mean of the muscle size within the 
group of people who are as tall as person i; and  2 b  is an unknown positive scalar 
denoting the effect of muscularity on the individual’s physiologically desirable 
weight. The unobserved means of the frame width and the muscle size within the 
group of people who are as tall as person i are assumed to be proportional to height 
i s i f H H g m = ) (                 (3) 
i m i m H H g m = ) (                 (4) 
where  f g  and  m g  are unknown positive scalars. 
The deviation of the individual actual weight from his, or her, physiologically 
optimal weight is assumed to be given by a linear function of a vector,  i X , of 
observed deviations of the individual physical characteristics from the population 
average (age, chronic illness, disability, ethnicity, race, occupation, marital status, 
location, climate, etc.) and of a vector of latent deviations of some other individual 
characteristics from the average (e.g., rate of time preference, consumption 
preferences and mental disposition) constituting a zero-mean random disturbance  i e  
 
i i i
o
i X W W e d + = -                 (5) 
                                                 
1 For instance, the Metropolitan Life Insurance Company has used the distance between the two 
prominent bones on either side of the elbow for assessing individuals’ frame size (see 
http://www.metlife.com/Lifeadvice/Tools/Heightnweight/Docs/frametable.html). Elbow-width or 
wrist-width are highly correlated with bone and muscle mass.   5
where  d  is the vector of the unknown coefficients indicating the effects of the 
observed deviations of personal characteristics. 
The structural equations (2), (3), (4) and (5) lead to the following expression 
of the deviation of the individual actual weight from the medically optimal weight for 
a person of his, or her, height with average frame width and muscle size: 
 
i i i i i m f i i X M S H H W e d b b g b g b a + + + + + - = - 2 1 2 1
2 ) ( .    (6) 
 
3. The HFM measures of the degree, prevalence and intensity of overweight 
The unknown parameters of the reduced-form equation (6) can be estimated, for adult 
males and adult females separately, with cross-section observations and non-linear 
estimation method. Consistently with its aforementioned interpretation and the World 
Health Organization’s definition, a  can be set to be equal to the mid-value (22 for 
women and 22.8 for men) of the normal BMI range (19.1 – 24.9 for women and 20.7-
24.9 for men) in constructing the dependent variable. 
Subsequently, the individual computed physiologically desirable weight can 
be obtained by substituting the estimated values of  f g b b , , 2 1  and  m g  into equations 
(2), (3) and (4). The deviation of the individual actual weight from his, or her, 
computed physiologically desirable weight ( i
o W ˆ ) is given by: 
 
] ˆ [ ˆ ] ˆ [ ˆ ˆ
2 1
2
i m i i f i i i i
o
i i H M H F H W W W W g b g b a - - - - - = - ” D    (7) 
 
where  f g b b ˆ , ˆ , ˆ
2 1  and  m gˆ  are the estimates of  f g b b , , 2 1  and  m g , respectively and 
a  is equal to 22 for women and 22.8 for men.    6
If  0 > D i W , individual i is overweight. The individual degree of overweight 
and the aggregate measures of the prevalence and intensity of overweight in a 
population can be computed as follows. 
 
Individual Overweight Degree (IOD):  The individual overweight degree is given by 
i
o
i i W W IOD ˆ / D = .                 (8) 
 
Overweight Prevalence (OP): Let  1 = i D  if  0 > D i W  and zero otherwise, then the 
measure of the overweight prevalence in a population of  N  adults can be expressed 
as 
￿
=
=
N
i
i D
N
OP
1
1
                (9) 
and  1 0 £ £ OP . 
 
Overweight Intensity ( OI): The proposed  OI measure takes into account both the 
overweight prevalence and the individuals’ overweight degrees within the surveyed 
population: 
 
i
o
i
N
i
i i
N
i
i
W
W
D
N
IOD D
N
OI
D
= = ￿ ￿
= = 1 1
1 1
.          (10) 
 
and  1 0 £ £ OI  if  1 £ i IOD  for every  i with  0 > D i W . It can be expected that 
1 0 £ £ OI  even when  1 > IOD  for some individuals if there is a sufficiently large 
number of people with  1 < IOD . 
   7
 
References 
 
Becker, G., and K. Murphy, 1988, “The Theory of Rational Addiction”, Journal of 
Political Economy 96, 675-700. 
 
Cutler, D., E. Glaeser, J. Shapiro, 2003, “Why Have Americans Become More 
Obese?” NBER Working Paper 9446. 
 
Finkelstein, E., I.C. Fiebelkorn, and G. Wang, 2003, “National medical Spending 
Attributable to Overweight and Obesity: How Much and Who’s paying?” Health 
Affairs W3, 219-226. 
 
Komlos, J., P. Smith and B. Bogin, 2002, “the Rate of Time Preference and Obesity: 
Is there a Connection?” mimeo, University of Michigan-Dearborn. 
 
Ladkawalla, D., and T. Philipson, 2002, “The Growth of Obesity and Technological 
Change: A Theoretical and Empirical Examination, “NBER Working Paper 8946. 
 
Levy, A., 2002, “Rational Eating: Can it lead to Overweightness or 
Underweightness?” Journal of Health Economics 21, 887-99. 
 
Philipson, T., an R. Posner, 1999, “The Long-Run Growth in Obesity as a Function of 
Technological Change,” NBER Working Paper 7423. 
 
National Heart, Lung, and Blood Institute, Clinical Guidelines on the Identification, 
Evaluation, and Treatment of Overweight an Obesity in Adults, NIH publication 
98-4083, September 1998. 
 

Rational Eating: Can it lead to Overweightness or

The Long-Run Growth in Obesity as a Function of Technological Change,”

the Rate of Time Preference and Obesity: Is there a Connection?” mimeo,

The Theory of Rational Addiction”,

Measuring Overweight: A Note

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