3.5 Instrumental variable approach
3.5.1 The instruments
There are several reasons to believe that body size is an endogenous regressor: labour market outcomes can itself affect body size, or unobserved factors such as individual time preferences may affect both body size and labour market outcomes. Furthermore, measurement errors in the BMI variable due to systematic misreporting of height or weight represent an additional source of bias.
To cope with this problem, an instrumental variable regression approach is applied. The set of instruments used in this paper includes variables that capture attitudes towards food, smoke and physical activity of the peers of the respondent, that is of people with whom the respondent may relate and compare himself. More specifically, the instruments are the percentages by
sex, age class and region of residence of the respondent, of non-smokers, of alcohol drinkers (individuals that drink more than half liter of beer or wine per day and individuals who are used to drink alcohol outside of meals), of people that consume no fruit or vegetables, of people that use to do some physical activity and the average number of hours daily spent watching TV.
The first requirement that an instrument has to fulfil to be valid, is that it is correlated with the endogenous measure of body size, conditional on the other variables that may affect occupational attainments. It is well known that the main risk factors for obesity are an incorrect nutrition (with an ex- cessive intake of high- fat, high-calorie foods and a limited consumption of high-fiber, low-calorie foods) and physical inactivity (NHLBI (1998) ). Smok- ing is another factor that affects individual’s weight. Although the direction of the relationship is still a matter of debate,37 the fact that smoke and eat-
ing habits are correlated (with smokers generally consuming less fruit and vegetables or less high fiber grains) it is widely accepted.38 While individual
preferences are ultimately driving these behaviours, environmental influences affect also individual attitudes to smoke, food intake and exercise becoming, in the end, another determinant of obesity (James (1995)). The selected instruments, therefore, are expected to be non-weak predictor of individual body size conditional on the other covariates, inasmuch as they provide a measure of obesity-affecting environmental influences. A simple way to test the strength of the instrument is to regress the endogenous variable on all the other covariates plus the instruments and to run than a F-test for the significance of the instruments coefficients. Staiger and Stock (1997) sug-
37While an extensive medical literature supports the idea that smoking facilitates weight
control (see U.S. Department for Health (1990) for a review of the medical studies), recent studies question the negative relationship between BMI and smoking (see Gruber and Frakes (2006)).
gested the rule of thumb that, in the case of a single endogenous regressor, instruments be deemed weak if the F-statistic is less than 10. With the only exception of the indicator for being clinically obese as a measure of body size, the F-statistic exceeds this minimum value both for men and women, sug- gesting that the selected instruments are significant predictors of the body size (Table 3.4).
Table 3.4: Validity of the instruments
Log(BMI) Weight Top quintile Clinically obese
Women Men Women Men Women Men Women Men
F-test 13.99 11.38 13.09 10.16 10.01 11.63 2.34 3.19
The second requirement of an instrument is that it is not correlated with the error term in the occupational attainment regression. If there are un- observed factors that affect both individual’s occupational attainment and some of the instruments, the IV estimation is then inconsistent. More specif- ically, given that the selected instruments are measures based on the area where the respondent is living, the correlation with the occupational attain- ment may arise if the choice of the location of residence is itself guided by the same factors (such as ability or time preferences) that determine also labour market outcomes. If that is the case, we would expect that people with lower time discount rates that may also have better labour market outcomes, move to regions where maybe it is easier to get fresh and healthy food or where it is easier to exercise. Although that is still a possibility, data on mobility within Italy show that the great majority of moving is within the region of previous residence.39 In other words, Italians do not move too much within
the country. They rather prefer to settle in the same region (and very often also in the same province) where they were born and where most of their
39In the year 2001, for example, out of the 1,133,006 changes of residence, more than
relatives are still living. Moving to other regions is mostly driven by job opportunities rather than by the desire of living healthier, so it is really un- likely that the choice of the location of residence is endogenous in the labour outcomes equation.