Household food consumption, individual caloric intake and obesity in France

Abstract

Using 2 years of home scanned data on household food purchases in France, we show how to infer the profile of average individual caloric intakes according to gender, age, and body mass index of household members. We also infer the individual consumption of macronutrients as carbohydrates, lipids or proteins. We then provide a descriptive analysis of eating in France over a long period of consumption that we compare to nutritional recommendations given by the French National Health and Nutrition Program. The results suggest that French people eat too much fats and proteins and not enough carbohydrates with respect to recommendations. They also show that obese or overweight individuals consume more calories at all ages and their consumption of fat is 20 % higher than normal individuals, meaning that public policies should aim at reducing fat consumption. We also find that the obesity of teenage boys cannot be explained by different food consumption as their dietary intake profiles are similar to other teenagers. Promoting physical activity for boys rather than public policies reducing food consumption could be more efficient.

Appendix

1.1 Imputation methodology

To overcome the problem of missing data in one of the categories without bar code, we implement a procedure of imputation at the household level.

As said above, let $y_{it}^{k}$ be the household consumption for category $k=1,2,3$ and let us define $S_{it}^{k}\in \{0,1\}$ equal to 1 only if $y_{it}^{k}$ is observed. With a large set of demographic variables $W_{it}$, we define $\omega _{it}^{k}=y_{it}^{k}-E\left( y_{it}^{k}|W_{it}\right)$. The conditional independence assumption (1) implies the mean independence of $y_{it}^{k}$ given $W_{it}$ with the observation of $y_{it}^{k}:$

$$\begin{aligned} E\left( y_{it}^{k}|W_{it},S_{it}^{k}=1\right) =E\left( y_{it}^{k}|W_{it},S_{it}^{k}=0\right) \end{aligned}$$

However, taking into account household heterogeneity by conditioning on as many variables as possible will lead to a more difficult non-parametric identification of the conditional means $E\left( y_{it}^{k}|W_{it},S_{it}^{k}=1\right)$ due to the lack of sufficient observations given the large dimension of $W_{it}$.

But, one can also use the fact that (1) implies (Rosenbaum and Rubin 1983)

$$\begin{aligned} \omega _{it}^{k}\perp S_{it}^{k}|P\left( S_{it}^{k}=1|W_{it}\right) \end{aligned}$$

and thus

$$\begin{aligned} E\left( y_{it}^{k}|P\left( S_{it}^{k}=1|W_{it}\right) ,S_{it}^{k}=1\right) =E\left( y_{it}^{k}|P\left( S_{it}^{k}=1|W_{it}\right) ,S_{it}^{k}=0\right) \end{aligned}$$

where $P\left( S_{it}^{k}=1|W_{it}\right)$ is the propensity score of observing category $k$. One advantage of such an implication is that we can then condition on a unidimensional variable, the propensity score, and thus solve the dimensionality problem of conditioning on a large set of variables.

Moreover, we can apply this to any conditional mean for intervals of the propensity score, conditional on some $W_{it}^{\prime }$, because we have

$$\begin{aligned}&E\left( y_{it}^{k}|W_{it}^{\prime },S_{it}^{k}=0,p\le P\left( S_{it}^{k}=1|W_{it}\right) \le p^{\prime }\right) \\&\quad =\int _{p}^{p^{\prime }}E\left( y_{it}^{k}|W_{it}^{\prime },S_{it}^{k}=0,P\left( S_{it}^{k}=1|W_{it}\right) \right) dF_{P\left( W_{it}\right) |W^{\prime },S_{it}^{k}=0} \\&\quad =\int _{p}^{p^{\prime }}E\left( y_{it}^{k}|W_{it}^{\prime },S_{it}^{k}=1,P\left( S_{it}^{k}=1|W_{it}\right) \right) dF_{P\left( W_{it}\right) |W^{\prime },S_{it}^{k}=0} \end{aligned}$$

where $F_{P(W)|W^{\prime },S_{it}^{k}=0}$ denotes the conditional cumulative distribution function of the propensity score given $W^{\prime }$ and $S_{it}^{k}=0$.

We thus first estimate the propensity score $P\left( S_{it}^{k}=1|W_{it}\right)$ and then impute the unobserved category $k$ households consumption with propensity score $p$ with the average observed household consumption of category $k$ food products with the same propensity score.

The regressions allowing us to estimate the propensity score matching for observation of the “fruits and vegetables” or “meat and fish” categories are not presented for brevity, but were done using a probit model.

1.2 Other Tables and Graphs