Huong Trinh Thi

Michel Simioni

Christine Thomasagnan

Decomposition of Changes in the Consumption of Macronutrients in Vietnam Between 2004 and 2014

Keywords: Nutrition transition, macronutrient consumption, decomposition methods in economics, copula, Vietnam

Vietnam is undergoing a nutritional transition like many middle-income countries. This transition is characterized by an increase in per capita total calorie intake resulting from an increase in the consumption of fat and protein while the carbohydrate consumption decreases. This paper proposes to highlight the sociodemographic drivers of this transition over the period 2004-2014, using Vietnam Household Living Standard Survey data. We implement a method of decomposition of between-year dierences in economic outcomes recently proposed in the literature. This method decomposes the between-year change in various indicators related to the outcome distribution (mean, median, quantiles. . . ) into the eect due to between-year change in the conditional distribution of the outcome given sociodemographic characteristics, or structure eect, and the eect due to the dierences in sociodemographic characteristics across years, or composition eect. In turn, this last eect is decomposed into direct contributions of each sociodemographic characteristics and eects of their interactions. The composition eect, always positive, generally outweighs the structure eect when considering the between-year changes in distributions of per capita calorie intake or calorie intake coming from protein or fat. The eects of changes in the composition of the Vietnamese population thus overcome the eects of changes in preferences of the same population. This nding is reversed in the case of carbohydrates. Food expenditure and household size appear to be the main contributors to the composition eect. The positive eects of these two variables explain well most of the between-year shifts observed in the calorie intake distributions. Urbanization and level of education contribute negatively to the composition eect, with the noticeable exception of fat where the eect of urbanization is positive. But these two variables eects are negligible compared to those of food expenditure and household size.

Introduction

Since the launch of economic reforms in 1986, Vietnam has recorded impressive achievements in growth performance and has gone from one of the world's poorest nations to a lower middle-income country. Vietnamese GDP has grown from 383.381 in 1986 to 1834.652 IFPRI (2017) shows that dietary diversity in South-East Asia and China has considerably increased from 2005 to 2015. The share of cereal demand (in terms of quantity) has decreased by 12% while the share of meat and sh demand and those of dairy and eggs have increased by 8% and 30% respectively, the share of fruits and vegetables staying steady.

As [START_REF] Popkin | Nutritional patterns and transitions[END_REF][START_REF] Popkin | The nutrition transition in low-income countries: an emerging crisis[END_REF] pointed out rst, improvements in per-capita incomes are generally accompanied by a major shift in dietary patterns. Total energy intake increases and diet moves from a relatively monotonous and starchy diet with low fat and high ber intakes, to a more varied diet with more fruits and vegetables. Furthermore, intakes in meat, fat and sugar increase while high ber intakes decline. [START_REF] Popkin | Nutritional patterns and transitions[END_REF][START_REF] Popkin | The nutrition transition in low-income countries: an emerging crisis[END_REF] coined the expression nutrition transition to describe these changes. He also emphasized that two other processes of change occur simultaneously with the nutrition transition [START_REF] Popkin | The shift in stages of the nutrition transition in the developing world diers from past experience![END_REF].

The rst process, or epidemiologic transition, is characterized by a transition from a situation where infectious diseases related to chronic malnutrition, periodic starvation, and poor environmental sanitation prevail, to a situation now characterized by the prevalence of chronic and degenerative diseases related to urban-industrial lifestyles. The second process, or demographic transition, involves a major shift in age-specic mortality patterns and a consequent increase in life expectancy. These three concomitant transitions occur more rapidly in lower-and middle-income countries than they have in western countries [START_REF] Popkin | The shift in stages of the nutrition transition in the developing world diers from past experience![END_REF].

Many studies have been devoted to the evolution of food consumption in both developed and developing countries. Some of them aim to document how the evolution of the socioeconomic status of country's inhabitants has inuenced their diets (see [START_REF] Thang | Patterns of food consumption in Vietnam: eects on socioeconomic groups during an era of economic growth[END_REF]Burggraf et al., 2015, among others).

Recently, [START_REF] Mayen | Socioeconomic determinants of dietary patterns in low-and middle-income countries: a systematic review[END_REF] reviewed 33 studies on this issue. These studies show that (1) high socioeconomic status or living in urban areas is associated with higher intakes of calories, protein, total fat, cholesterol, polyunsaturated, saturated, and mono-unsaturated fatty acids, iron, and vitamins A and C and with lower intakes of carbohydrates and ber, and (2) high socioeconomic status is also associated with higher fruit and/or vegetable consumption, diet quality, and diversity. The improvement of the socio-economic status of populations 1 Poverty is measured using poverty headcount at 1.90 US dollars a day (2011 Purchasing Power Parity).

Comment citer ce document : Trinh, H. T., Simioni, M., Thomas-Agnan, C. (2018). Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and 2014. Economics and Human Biology, 31, 259-275.

, DOI : 10.1016/j.ehb.2018.09.002

Page 3 of 35

A c c e p t e d M a n u s c r i p t thus seems to lead to a better feeding of human beings. But the other side of the coin is the link between improved diets and noncommunicable diseases as emphasized by [START_REF] Popkin | Global nutrition dynamics: the world is shifting rapidly toward a diet linked with noncommunicable diseases[END_REF] and [START_REF] Riera-Crichton | Macronutrients and obesity: revisiting the calories in, calories out framework[END_REF]. Thus, both policy makers and citizens are concerned by these concomitant evolutions and the ght against their consequences in terms of nutrition and health. All this requires rst of all knowledge of the drivers of these evolutions.

However, most studies mentioned above have important limitations. Some limitations are purely technical. The issue of potential interactions among factors that may explain observed changes in the diet is not addressed. For instance, it is thus conceivable that, in some countries, increasing urbanization of the population is concomitant with the increase in incomes of the same population. Moreover, these studies do not take into account that the link between socio-demographic variables can have changed over the period under study. For instance, the relationship between income and location in an urban area may have become stronger over time. Nevertheless, the major limitation of most studies cited above is that they do not take into account the fact that, in addition to changes in the composition of the population, observed changes in dietary patterns may also be related to changes in consumer behavior [START_REF] Popkin | The shift in stages of the nutrition transition in the developing world diers from past experience![END_REF]. For the same level of education or income, a consumer would buy dierent amounts of food items at dierent points of time. Consumer habits may evolve over time (for example, a more pronounced addiction for sweet foods or a growing consumption of dairy products based on the belief that they are good for health, in countries not-used to produce cow's milk) and this can lead to changes in dietary patterns. Thus, the analysis of the drivers of nutritional transition in a given country must consider two potential sources of observed trends: one related to shifts in the composition of the population in that country, and the other to changes in consumer behavior, or behavioral shifts.

Decomposition methods in economics make it possible to evaluate the two aforementioned eects (see [START_REF] Fortin | Decomposition methods in economics[END_REF], for an extensive survey). Hereinafter, we use the method recently proposed by [START_REF] Rothe | Decomposing the composition eect: the role of covariates in determining between-group dierences in economic outcomes[END_REF] which, in addition, addresses the two technical problems mentioned above. We apply it to the analysis of the drivers of nutrition transition in Vietnam over the 2004-2014 period.

Indeed, thanks to data from Vietnamese Households Living Standard Survey, or VHLSS, we can calculate total energy intakes of Vietnamese households (in Kcal). We convert these intakes into adult equivalent, or per capita, calorie intakes, thus allowing comparison between households. Finally, per capita calorie intakes are decomposed into per capita calorie intakes coming from the three macronutrients: proteins, fat and carbohydrates. VHLSS also contains detailed information on the socio-demographic characteristics of Vietnamese households.

Each wave of this survey is, moreover, representative of the Vietnamese popu- recently proposed by [START_REF] Rothe | Decomposing the composition eect: the role of covariates in determining between-group dierences in economic outcomes[END_REF], we use in this paper. Section 4 gives a description of VHLSS data and details per capita calorie intake computation.

Results are presented and commented in section 5. Section 6 draws concluding remarks.

Nutrition transition in Vietnam

Recently, [START_REF] Nguyen | Non-communicable diseases, food and nutrition in Vietnam from 1975 to 2015: The burden and national response[END_REF] provide a survey of the literature dealing with the issues of non-communicable diseases, food and nutrition security in Vietnam. They point out that a large part of this literature is gray literature, i.e. reports, presentations . . . They report only 13 published papers including [START_REF] Dien | Food consumption patterns in the economic transition in Vietnam[END_REF] and [START_REF] Thang | Patterns of food consumption in Vietnam: eects on socioeconomic groups during an era of economic growth[END_REF] who deal with patterns of food consumption at the end of the twentieth century in Vietnam. The detailed analysis of these 13 papers as well as 10 signicant reports provides insight into the three transitions discussed in the introduction (epidemiological, demographic, and nutritional). Figure 1, we extracted from [START_REF] Nguyen | Non-communicable diseases, food and nutrition in Vietnam from 1975 to 2015: The burden and national response[END_REF], outlines changes in dietary patterns experienced by Vietnam during the last thirty years. This gure shows an increase in the consumption of meat, sh, eggs, milk and dairy products, and fruits and vegetable, and thus an increase in the consumption of fat and protein between 1981 and 2010. More detailed data covering the period 2004-2014 are presented in [START_REF] Trinh | Relations between socio-economic factors and nutritional diet in Vietnam from 2004 to 2014: New insights using compositional data analysis[END_REF]. This paper reveals an increase in the median value of per capita total energy intake, and

shows that the share obtained from fat in total calorie intake has increased by 37.5% (resp. 23%) for Vietnamese rural households (resp. urban households), at the expense of calories obtained from carbohydrates, calories obtained from proteins staying quite stable. See Figure 2 [START_REF] Ha | Nationwide shifts in the double burden of overweight and underweight in Vietnamese adults in 2000 and 2005: two national nutrition surveys[END_REF] show that the nationwide prevalence of overweight (body mass index ≥ 25kg/m 2 ) and obesity (body mass index ≥ 30kg/m 2 ) was 6.6% and 0.4% respectively in 2005, almost twice the rates of 2000 (3.5% and 0.2%).

Using the Asian body mass index cut-o of 23kg/m 2 the overweight prevalence was 16.3% in 2005 and 11.7% in 2000. According to the World Health Organization, the percentage of overweight people in the total population of Vietnam is 21% in 2014, the percentage of obese people being 4%. Moreover, the same study points out that the underweight prevalence (body mass index < 18.5kg/m 2 ) of 20.9% in 2005 is lower than the rate of 25.0% in 2000. This rate has decreased by half in ten years and is currently 11%. Finally, [START_REF] Ha | Nationwide shifts in the double burden of overweight and underweight in Vietnamese adults in 2000 and 2005: two national nutrition surveys[END_REF] also analyze the possible sources of this evolution. They note urban residents were more likely to be overweight and less likely to be underweight compared to rural residents in both years. The shifts from underweight to overweight were clearer among the higher levels of food expenditure.

Methodology

We propose to use decomposition methods for assessing the determinants of change in macronutrients consumption in Vietnam using the 2004 and 2014 waves of VHLSS. Decomposition methods were rst introduced in order to quantify the contributions of labor, capital, and unexplained factors (productivity) to economic growth [START_REF] Solow | Technical change and the agrregate production function[END_REF]. They have been extensively used in labor economics, following the seminal papers of [START_REF] Oaxaca | Male-female wage dierentials in urban labor markets[END_REF] and [START_REF] Blinder | Wage discrimination: reduced form and structural estimates[END_REF].

The Oaxaca and Blinder decomposition method is still used in many elds in economics (see Nie et al., 2018, for instance). This method has been rened in several methodological papers and extended to the cases of distributional parameters besides the mean over the last four decades. [START_REF] Fortin | Decomposition methods in economics[END_REF] provide a comprehensive overview of these developments. Applications to Vietnam include [START_REF] Nguyen | A quantile regression decomposition of urbanrural inequality in Vietnam[END_REF] on urban-rural income inequality, [START_REF] Sakellariou | The Vietnam reforms, change in wage inequality and the role of the minimum wage[END_REF]

∆ ν Y = ν(F t Y ) -ν(F s Y ) (1)
where ν(.) measures a feature of the considered distribution: mean, median, quantile. . . The question decomposition methods address is thus: how is the between-group dierence ∆ ν Y between the joint distributions in the two groups F t X and F s X , related to a vector of covariates (denoted by X)

F s|t Y (y) = x F s Y |X (y, x)dF t X (x) (2)
The between-group dierence ∆ ν Y can then be written as

∆ ν Y = ν F t Y -ν F s|t Y ≡∆ ν S + ν F s|t Y -ν (F s Y ) ≡∆ ν X (3)
Let us consider the rst term in equation (3). The same covariate distribution is used when calculating the two terms in ∆ ν S , i.e. F t X . These two terms only dier by the conditional distribution of the outcome given the covariates used in their computation, i.e. F t Y |X and F s Y |X . ∆ ν S captures the between-group dierence in the relationship between the outcome and covariates. ∆ ν S is called the structure eect. Consider now the second term in equation (3).The dierence between the two terms of ∆ ν X comes from the marginal covariate distribution used in their computation, i.e. F t X and F s X . Indeed, the same conditional distribution F s Y |X is used in their computation. ∆ ν X is thus dened as the composition eect.

The Oaxaca-Blinder decomposition method focuses on between-group dierence in mean and is only valid when the data are generated by a linear model.

Therefore, [START_REF] Barsky | Accounting for the blackwhite wealth gap: A nonparametric approach[END_REF] ∆ ν Y into structure and composition eects. But once again, the implementation of the decomposition method is based on a linearity assumption and it is not possible to decompose the composition eect.

The semiparametric reweighting method introduced by DiNardo et al. (1996) can be used to overcome the limitations of the methods discussed so far. The idea of this method is to reweight individual observations depending on whether they are over-or underrepresented when computing the counterfactual distribution. A weighted kernel density routine is used when estimating the counterfactual density of the outcome (see Leibbrandt et al., 2010, for an application). This decomposition method is attractive because it makes no parametric assumptions about the conditional distribution of the outcome given the covariates. Nevertheless, this method is path dependent as it does not allow a non-sequential decomposition of the composition eect into the individual covariate eects in the same way they can be decomposed using the conventional Oaxaca-Blinder method.

The Recentered Inuence Function, or RIF, regression decomposition method is in line with the Oaxaca-Blinder method, proposing decomposition of the structure and composition eects which is not path-dependent and generalizing it to any distributional feature, not only the mean [START_REF] Firpo | Decomposing wage distributions using recentered inuence function regressions[END_REF][START_REF] Firpo | Decomposing Wage Distributions Using Recentered Inuence Function Regressions[END_REF]. In a rst stage, the RIF method proposes the decomposition of the distributional statistics of interest into the structure and composition eect using a reweighting approach. The idea of this rst stage is very similar to DiNardo et al.

( 1996) and comes from theoretical results on the identication of distributional statistics besides the mean. In a second stage, the structure and composition eects are decomposed into the contribution of each covariate, using a linear regression-based method. However, unlike the Oaxaca-Blinder method where the dependent variable in the regression is the outcome of interest, the RIF method uses the recentered inuence function for the distributional statistics of interest as the dependent variable, following [START_REF] Firpo | Unconditional quantile regressions[END_REF] work on unconditional quantile regressions. As emphasized by [START_REF] Firpo | Decomposing Wage Distributions Using Recentered Inuence Function Regressions[END_REF], using a linear specication has the advantage of providing a much simpler interpretation of the decomposition, as in Oaxaca-Blinder decomposition. But, they also underline that the linear regression-based procedure only provides a rst-order approximation to the composition eect. So, there is an approximation error.

This error can be obtained as a by-product of the decomposition of the composition eect and used as a specication test of the regression-based procedure.

Comment citer ce document : If its size is small, it may be thought that the approach of [START_REF] Firpo | Decomposing wage distributions using recentered inuence function regressions[END_REF][START_REF] Firpo | Decomposing Wage Distributions Using Recentered Inuence Function Regressions[END_REF] provides an accurate enough approximation for the problem at hand. No solution is proposed when the approximation error is large. So, for example, should we incorporate interactions between variables? To our knowledge, no response is given in the literature on the RIF method. And although it has been applied in many elds (see [START_REF] Etile | Education policies and health inequalities: Evidence from changes in the distribution of Body Mass Index in France, 1981-2003[END_REF], for instance), few empirical works provide a discussion about the magnitude of the approximation error.

In this paper, we use the copula-based decomposition procedure recently proposed by [START_REF] Rothe | Decomposing the composition eect: the role of covariates in determining between-group dierences in economic outcomes[END_REF]. This method also allows decomposition involving any distributional feature, not only the mean. But, unlike most of the methods mentioned above, this method (1) does not rely on any linearity assumption,

(2) is not path-dependent, and (3) introduces into this decomposition the eect of the interaction between covariates. Specically, this decomposition method expands classical methods by adding to the usual decomposition of the composition eect into the direct contribution of each covariate due to between-group dierences in their respective marginal distributions, several two way and higher order interaction eects due to the interplay between two or more covariates, and a dependence eect, accounting for the between-group dierence in the dependence pattern among the covariates. The copula-based decomposition procedure therefore provides a detailed analysis of one of the two sides of the decomposition, the composition eect, but it says nothing about the structure eect. The issue of deriving a decomposition of the structure eect, that is, dividing between-group dierences in the structural functions that link the covariates and the outcome variable, into components that can be attributed to individual covariates, still is an open issue.

To get a better understanding of the goals of the decomposition method

Comment citer ce document : Trinh, H. T., Simioni, M., Thomas-Agnan, C. ( 2018). Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and2014. Economics andHuman Biology, 31, 259-275

Sociodemographic variables

Y educc

Highest educational level of the head of households (year):

= 0

No schooling = 5

primary level

= 9

Secondary school level

= 12

High school level

= 16

College degree

= 18

Master degree

= 21

Ph.D level

South

Region:

= 1

if Household is located in the South of Vietnam = 0 otherwise to calculate the per capita calorie intake (namely P CCI), per capita volume of calories obtained from protein (namely V P ), per capita volume of calories obtained from fat (namely V F ), and per capita volume of calories obtained from carbohydrate (namely V C) for each household. These per capita measures are obtained by dividing the corresponding energy intakes by household specic equivalence scale.

4 Table 2 gives various summary statistics on P CCI, V C, V P , and V F . These statistics will be discussed below.

The previous calculations of calorie intake may suer from measurement errors. Indeed, recall food expenditure data, such as collected in VHLSS, is believed to suer from considerable measurement error. Diary records should be preferred because they are believed to be more accurate when dealing with calorie intake measurement. But a clear evidence of the superiority of the latter relative to the recall data does not seem to emerge from the literature. For instance, a recent study using a unique data set that collects recall and diary data from the same households show evidence that, while recall data exhibits substantial measurement errors, diary measures are themselves imperfect [START_REF] Brzozowski | A comparison of recall and diary food expenditure data[END_REF]. Moreover, as emphasized by [START_REF] Magrini | Vulnerability from trade in Vietnam[END_REF] which use VHLSS data to assess household vulnerability from trade, it is generally agreed that VHLSS data can be considered to be of high quality and provide legitimate nationally representative household data based on stratied random samples. But, even if the VHLSS survey meets all the criteria dening a "good" living standard survey [START_REF] Deaton | Designing Household Survey Questionnaires for Developing Countries: Lessons from Ten Years of LSMS Experience[END_REF][START_REF] Browning | The measurement of household consumption expenditures[END_REF] The calculation procedure presented above allows more to compute calorie availability than calorie intake [START_REF] Bouis | Are estimates of calorie-income elasticities too high? A recalibration of the plausible range[END_REF]. Indeed, VHLSS data do not include losses and waste from food preservation and preparation. Calorie intakes are thus overestimated. Unlike United States for which these losses have been evaluated for each food item [START_REF] Muth | Consumer-level food loss estimates and their use in the ERS loss-adjusted food availablity data[END_REF], reliable data on food losses

Changes in per capita calorie intake distributions

Figure 4 reports the weighted kernel estimates 5 of the densities of per capita calorie intake for the two years. There is a shift to the right for the density from 2004 to 2014, indicating an increase in per capita calorie intake over the period, not only on average but also for all quantiles such as those reported in Table 2.

Figure 4 also reports the weighted kernel estimates of the densities of per capita calorie intakes of carbohydrates, fat, and proteins, for the two years.

Signicant changes appear when comparing the estimated densities for fat and proteins, while the estimated densities for carbohydrates appear to be very similar. There is a signicant shift to the right for the estimated densities for fat and protein in 2014. Meanwhile, the estimated density for carbohydrates in 2014 has the same mode as in 2004, but becomes atter. This visual observation is conrmed by the evolution of average values, standard deviations, and quantiles at 10, 50 and 90% as reported in over the considered period. Per capita calorie intake from carbohydrates remained stable on average, while this stability hides a contrasted picture with an increase for some households and a decrease for others. A c c e p t e d M a n u s c r i p t

Decomposition results

Signicant changes in distributions of per capita intake (total or macronutrients) between 2004 and 2014, have just been noted. What are the main drivers of these changes? To answer this question, we implement the decomposition method proposed in [START_REF] Rothe | Decomposing the composition eect: the role of covariates in determining between-group dierences in economic outcomes[END_REF]. This implementation is based on the preliminary estimation of marginal distributions of covariates, dependence parameters in copulae and conditional distributions of per capita calorie intake given covariates. These results, which are not central compared to those of decomposition, are summarized in Appendix C.

Tables 5,6, 7, and 8 present the results of our decomposition of per capita total calorie intake and calorie intake coming from the three macronutrients, for two measures of location: mean and median, and for the two quantiles at 10% and 90%. Row by row, we report estimates of total change, i.e. ∆ ν Y , usual structure and composition eects, i.e. ∆ ν S and ∆ ν X . Then the composition eect is in turn decomposed into the dependence eect, i.e. ∆ ν D , and marginal distribution eect, i.e. β ν (1). Finally, this last eect is decomposed into the direct contribution for each of the six covariates, i.e. the β ν (e k ), and the twoway interaction eects, i.e. the ∆ ν Int . Each estimated value in a decomposition is accompanied by the estimated value of its standard error. Theses standards errors are computed using using nonparametric bootstrap with 300 replications as proposed by [START_REF] Rothe | Decomposing the composition eect: the role of covariates in determining between-group dierences in economic outcomes[END_REF]. 6

Figure 5 explains how tables 5, 6, 7, and 8 should be read. This gure considers the decomposition of the between-year dierence in mean, in per capita calorie intake presented in table 5. Bold estimated values are signicantly dierent from zero.

Overall quality of decompositions. Knowledge of the estimated values of total dierence and the associated standard errors rst allow to have an indication as to whether the chosen modeling of decomposition using parametric restrictions on copulas and conditional distributions, provides a reasonable t. Indeed, these estimated values of total dierence can be compared with the dierences that can be directly calculated from the descriptive statistics given in Table 2.

It should be noted that, in all cases, the dierence computed from the descriptive statistics belongs to the 95% condence interval that can be constructed from the estimated value of total dierence and its estimated standard error.

Moreover, the estimated values of total dierence for quantiles capture well the observed shifts in empirical quantiles of calorie intake distributions. The chosen model thus provides a reasonable t to the data.

6 [START_REF] Rothe | Decomposing the composition eect: the role of covariates in determining between-group dierences in economic outcomes[END_REF] shows the asymptotic convergence of the estimator of each element in a decomposition to a mean zero normal distribution. But, as the asymptotic variance of these estimators takes a fairly complicated form, a practical way to estimate this variance is standard nonparametric bootstrap in which the estimates are recomputed a large number of times on bootstrapped samples { Y t i , X t i } n t i=1 drawn with replacement from the original data {Y t i , X t i } n t i=1 . The bootstrap variance estimator then coincides with the empirical variance of the bootstrapped estimates.

Comment citer ce document : Trinh, H. T., Simioni, M., Thomas-Agnan, C. ( 2018 Per capita total energy intake. Let us now look more closely at each of the tables. Table 5 presents the estimated values of the various elements in the decomposition of dierences in mean, median and quantiles at 10% and 90%

between the two years for per capita calorie intake. The decomposition of total dierence in structure eect and composition eect reveals two eects that play in opposite directions. A strong positive composition eect then appears while the structure eect is negative and quite stable among quantiles. The composition eect is only counterbalanced by the structural eect in the case of the quantile at 10%. Moreover, the composition eect increases with the quantile.

In other words, the between-year change in the conditional distributions of per capita calorie intake given the sociodemographic characteristics, or in the relationship between per capita calorie intake and these covariates, caused a signicant decrease in per capita calorie intake on average as well as on the three considered quantiles. Meanwhile, the change in the composition of the sample of households between the two years led to a signicant increase in per capita calorie intake. This increase was larger than the decrease due to changes in the relationship between per capita calorie intake and sociodemographic variables, except for the 10% quantile where the two compensate.

The dependence eect that captures the contribution of between-year dierences in the covariates' copula functions plays no role in the decomposition of composition eect. The dependence eect is never signicantly dierent from zero. The composition eect is almost always equal to the marginal eect resulting from dierences in the marginal covariate distributions across the two years.

Consider now the decomposition of the marginal eect into direct eects of each covariate and "two-way" interactions eects. This decomposition shows the importance of the contribution of food expenditures and household size to total marginal distribution eect, i.e., here, the composition eect. These contributions are indeed positive, large, and signicantly dierent from zero. It should be noted that these contributions increase according to the considered quantile order. Food expenditures and household size play a more and more important role in the increase of per capita calorie intake when moving from the 10% quantile to the 90% quantile. The eects of these two variables are barely oset by the negative and signicantly dierent from zero eects of urbanization and years of education of the head of the household. Moreover, almost all "twoway" interaction eects are negligible.

Macronutrients. Similar comments can be made regarding decompositions for consumption in terms of calories from fat and protein (see Tables 6 and7)

Thus, the estimated values of the total dierence for the dierent quantiles household size. The estimated values of the impacts of these two covariates on changes in consumed calories from fat and protein increase when moving from the 10% quantile to the 90% quantile. Now, the number of years of education of the head of household still impacts negatively on changes, the eects being sometimes not signicantly dierent from zero. The eect of urbanization is negligible in the case of proteins, whereas it becomes positive in the case of fat.

Nevertheless, although signicantly dierent from zero for most of the considered statistics, the eect of urbanization is negligible when compared to those of food expenditure or household size.

The results obtained in the case of carbohydrates are more contrasted than the previous ones (see Table 8). Here again, the estimated values of the total dierence trace well what is observed for the empirical distributions of calories consumed from carbohydrates, whether in terms of location or spread statistics.

Thus, total dierences for mean and median are not signicantly dierent from zero at the 10% and 5% threshold respectively, while total dierences for 10% and 90% quantiles are signicantly dierent from zero, the rst being negative while the second is positive. The results capture well the attening of the distribution between 2004 and 2014. But now, the structure eect compensates the composition eect in the cases of the mean and median, or even exceeds it for the 10% quantile when decomposing total dierence. As for the decomposition of the composition eect, it gives rise to similar comments to those made above for per capita calorie intake: negligible dependence eect, and strong positive contributions of food expenditures and household size compensated in part by negative contributions of urbanization and level of education of head of household.

Conclusion and discussions

The aim of this paper is to document the evolution of Vietnamese household consumption in terms of total calorie intake and consumption of macronutrients over the period 2004-2014. The availability of VHLSS surveys makes it possible to have detailed data on these consumptions. The descriptive analysis of the data reveals an increase in per capita calorie intake over the period not only on average but also at all the quantiles of the corresponding distribution. The same evolution is observed for the consumption of proteins and that of fat. The distribution of carbohydrate consumption, on the other hand, attens, showing an increase in low and high consumption between the two years while staying stable on average.

The characterization of the drivers of these evolutions is based on the use of a decomposition method recently proposed by [START_REF] Rothe | Decomposing the composition eect: the role of covariates in determining between-group dierences in economic outcomes[END_REF]. In addition to the classical decomposition of between-year changes in terms of structure and decomposition eects, this method allows to compute the direct contributions of various socio-demographic variables and the eects of their interactions in these between-year changes. Moreover, this method allows to identify the impact of between-year changes in the dependence structure among covariates.

Comment citer ce document : Trinh, H. T., Simioni, M., Thomas-Agnan, C. ( 2018 We implement [START_REF] Rothe | Decomposing the composition eect: the role of covariates in determining between-group dierences in economic outcomes[END_REF] method on VHLSS data to characterize the dierent eects on between-year mean, median, and 10% and 90% quantiles changes in per capita calorie intake and macronutrient consumptions in Vietnam. The main results we obtained can be summarized as follows (see also

Figures 6 and7 that summarize most of the results presented in Tables 5, 6, 7, and8): 1. Decompositions using parametric restrictions on copulas and conditional distributions provide a t. The estimated values of the between-year total dierences clearly reect the observed dierences, either on average or for the considered quantiles.

2. The structure and composition eects play in an opposite direction, whatever the considered decomposition. Structure eects, which come from between-year dierences in the relationship that links the covariates to the considered outcome, are always negative, while composition eects, which are due to dierences in the distributions of observable covariates across years, are always positive.

3. The composition eect often outweighs the structure eect when considering the between-year changes in distributions of per capita calorie intake or calorie intake coming from protein or fat. The eects of changes in the composition of the Vietnamese population thus overcome the eects of changes in preferences of the same population. This nding is particularly striking in the case of calorie intake from fat where structure eects are never distinguishable from zero. In the case of carbohydrates, this nding is reversed, with the exception of the 90% quantile.

4. Food expenditure and household size appear to be the main contributors to the composition eect, regardless of the considered decomposition. The positive eects of these two variables explain well most of the betweenyear shifts observed in the calorie intake distributions. Urbanization and level of education contribute negatively to the composition eect, with the noticeable exception of fat where the eect of urbanization is positive. In all cases, the eects of the latter two variables are negligible compared to those of food expenditure and household size.

5. Dependence eects and two-way interaction eects appear to be negligible or insignicant.

Food expenditure and household size appear as the main drivers of the composition eect, thus corroborating the results of many previous studies [START_REF] Mayen | Socioeconomic determinants of dietary patterns in low-and middle-income countries: a systematic review[END_REF]. While urbanization is often advocated as an important driver in dietary pattern changes [START_REF] Popkin | The shift in stages of the nutrition transition in the developing world diers from past experience![END_REF], its between-year changes do not seem to matter in explaining the composition eect in Vietnam.

As noted above, the structure eect captures between-year behavioral changes in the population under study. Specically, this eect captures between-year changes in consumer preferences and habits. Thus, for example, the impact of mass media or advertising can change consumer choices from traditional choices linked to the country's food culture towards choices more oriented to Western culture. For the same level of education or income, a consumer would then buy kable to see that between-year behavioral changes have practically no impact on the observed changes in fat and protein consumption, whereas they have an important eect in the case of carbohydrates. In the latter case, the structural eect may even oset the eect of between-year changes in the composition of the population, eect on which most published papers on the drivers of nutrition transition focus [START_REF] Mayen | Socioeconomic determinants of dietary patterns in low-and middle-income countries: a systematic review[END_REF]. Nevertheless, we are then faced with a limitation of the approach proposed by [START_REF] Rothe | Decomposing the composition eect: the role of covariates in determining between-group dierences in economic outcomes[END_REF] which does not make it possible to decompose the structure eect and to analyze its main drivers.

Comment citer ce document : Trinh, H. T., Simioni, M., Thomas-Agnan, C. ( 2018 Suppose, for ease of presentation, that we have observed two covariates for each individual in the sample of a given year: for example, food expenditures and location in either urban or rural areas. Of course, the presentation given below can be easily generalized to more than two covariates. We denote the vectors of the two covariates

∆ ν Y = ν F 2014 Y -ν F 2004|2014 Y + ν F 2004|2014 Y -ν F 2004 Y = ∆ ν S + ∆ ν X (A-3)
where ∆ ν S is a structure eect, solely due to dierences in the conditional distribution of the outcome given values of covariates between the two years, and ∆ ν X is a composition eect, solely due to dierences in the distribution of the covariates between the two years.

The dierent elements of the decomposition (A-3) can be easily estimated using nonparametric estimates of CDFs. One such strategy, focusing on densities instead of CDFs, is applied in [START_REF] Dinardo | Labor market institutions and the distributions of wage, 1973-1992: a semiparametric approach[END_REF] or [START_REF] Leibbrandt | Incomes in South Africa after the fall of Apartheid[END_REF]. But the application of such a strategy soon encounters the problem of the curse of dimensionality.

For a xed sample size, the precision of the nonparametric estimators deteriorates very rapidly when the number of covariates increases, even if these estimators are free from any specication error [START_REF] Silverman | Density estimation for statistics and data analysis[END_REF]. In addition, it is also interesting to break down the composition eect for the dierent covariates. This can be easily done using the [START_REF] Oaxaca | Male-female wage dierentials in urban labor markets[END_REF] and [START_REF] Blinder | Wage discrimination: reduced form and structural estimates[END_REF] approach when focusing on the between-year dierence of average outcomes. But the possibility of disentangling the impact of each of the covariates in the composition eect rests on the very restrictive assumption that the data are generated from a linear model. As pointed out by [START_REF] Rothe | Decomposing the composition eect: the role of covariates in determining between-group dierences in economic outcomes[END_REF], in the general case, it is dicult to express the composition eect as a sum of terms which depend on the marginal distribution of a single covariate only. Instead, an explicit decomposition of the composition eect in terms of the respective marginal covariate distributions typically contains interaction terms resulting from the interplay of two or more covariates, and also dependence terms resulting from between-year dierence in the dependence pattern among the covariates. [START_REF] Rothe | Decomposing the composition eect: the role of covariates in determining between-group dierences in economic outcomes[END_REF] proposes to use results from copula theory in order to disentangle the covariates' marginal distributions from the dependence structure among them. Indeed, the CDF of X t can always be written as F t X (x) = C t (F t X 1 (x1), F t X 2 (x2)) for t ∈ {2004, 2014}

(A-4) following Sklar's Theorem [START_REF] Sklar | Fonctions de répartition à n dimensions et leurs marges[END_REF]. C t (.) is a copula function, i.e., a bivariate CDF with standard uniformly distributed marginals, and F t X j (.) is the marginal distribution of the jth component of X t (Trivedi and Zimmer, 2007). The copula describes the joint distribution of individuals' ranks in the two components of X t . The copula accounts for the dependence between the covariates in a way that is separate from and independent of their marginal specications. This result holds for continuous covariates. When some of them are discrete, some identiability issues may arise, that can be solved by making parametric restrictions on the functional form of the copula.

In this context, the decomposition given by Eq. (A-3) can then be generalized as follows. Let k denote an element of the 2-dimensional product set {2004, 2014} 2 , i.e. k = (k1, k2) where k1 (resp. k2) is equal to either 2004 or 2014. We can dene the distribution of the outcome in a counterfactual setting where the conditional distribution is as in year t, the covariate distribution has the copula function of year s, and the marginal distribution of the lth covariate is equal to that in group k by where 0 = (2004,2004). Now we can write the composition eect ∆ ν X as

∆ ν X = ν F 2004|2014 Y -ν F 2004 Y = ν F 2004|2014,1 Y -ν F 2004|2004,0 Y = ν F 2004|2014,1 Y -ν F 2004|2004,1 Y + ν F 2004|2004,1 Y -ν F 2004|2004,0 Y = ∆ ν D + β ν (1) (A-7)
The rst term of the decomposition in Eq. (A-7), or In other words, β ν (e 1 ) and β ν (e 2 ) measure the respective direct contributions of the rst and second covariate. Let ∆ ν Int (1) ≡ β ν (1) -β ν (e 1 ) -β ν (e 2 ). ∆ ν Int (1) can then interpreted as a pure interaction eect.

∆ ν D = ν F 2004|2014,1 Y -ν F
To sum up, the composition eect can be written as ∆ ν X = β ν (e 1 ) + β ν (e 2 ) + ∆ ν Int (1) + ∆ ν D , (A-9)

i.e, as the sum of the respective contributions of each covariate, a term measuring the pure eect of their interaction, and a term measuring the contribution due to the between-year variation of the dependence between covariates. This decomposition can easily be generalized in the case of more than two covariates and focus either on individual eect of each of them and the pure eect of their interaction as shown above, or on the eect of groups of variables and of the interaction among these groups.

Comment citer ce document : H. T., Simioni, M., Thomas-Agnan, C. ( 2018 Conditional CDFs F t Y |X are modeled by a distributional regression model with a Gaussian link function. We do not report the results as they are not very helpful in the discussions that follow. Nevertheless, they are available from the authors.

Figure 1 :

 1 Figure 1: Trends in per capita daily consumption of foods (panel A) and macronutrients (panel B) (in grams)

  Figure 2: Trends in macronutrient shares between 2004 and 2014 in Vietnam

Figure

  Figure 3: Decomposition framework

2

  we will illustrate it by a simple example. Here, we analyze the dierence in calorie intake distributions for two years, 2004 and 2014. Our outcome is measured by per capita calorie intake. We are interested in two potential drivers of the dierence in per capita calorie intake distributions in 2004 and 2014: (1) evolution of Vietnamese households' food expenditures, and (2) urbanization. For instance, Vietnamese households increased their food spending between 2004 and 2014 and Vietnamese population is more urban in 2004 than in 2014. Moreover urban citizens tend to spend more on food (dependence between these two covariates) hence leading to an extra increase in overall food expenditures. We are interested by decomposing the dierence between per capital calorie intake averages in 2014 and 2004. The structure eect is the part of this dierence that can be explained by the between-year dierence in the conditional distributions of per capita calorie intake given food expenditures and location in an urban area. The composition eect is the part of the dierence that can be explained by the between-year dierences in observable characteristics (food expenditures and living in an urban area). The rst direct contribution is the part of the composition eect that can be attributed to the fact that Vietnamese households have higher food expenditures in 2014 compared to 2004. The second direct eect captures the part in the composition eect due to the fact that the Vietnamese population is more urban in 2014 than in 2004. The (only) interaction eect measures the additional contribution of the fact that the Vietnamese population at the same time spends more for food and is more urban in 2014. Finally, the dependence eect accounts for between-year dierences in association patterns among the two covariates, food expenditures and location in an urban area. In other words, the dependence eect captures the fact that the relative food expenditure of urban and rural households diers in the two years. Figure3summarizes the dierent stages of the copula-based decomposition method. The notations used for the dierent elements in the decomposition correspond to those used in appendices A and B where technical details about the copula-based decomposition method and its implementation are given.4. DataThis study relies on the Vietnam Household Living Standard Survey, or VHLSS. This survey is conducted by the General Statistics Oce of Vietnam, or GSO, with technical assistance of the World Bank, every two years since 2002. Each VHLSS survey contains modules related to household demographics, education, health, employment, income generating activities, including household businesses, and expenditures. The survey is conducted in all of the 64 Vietnamese provinces and data are collected from about 9000 households for each wave. The survey is nationally representative and covers rural and urban areas. 2 The reader is referred to Trinh Thi et al. (2018) for a detailed description of VHLSS. Comment citer ce document : Trinh, H. T., Simioni, M., Thomas-Agnan, C. (2018). Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and 2014. Economics and Human Biology, 31, 259-275. , DOI : 10.1016/j.ehb.2018.09.002 A c c e p t e d M a n u s c r i p t Below, we use the two waves of VHLSS conducted in 2004 and 2014 as our groups when implementing the copula-based decomposition method. We do not choose the 2002 wave as our reference group since food consumption was less detailed than in the subsequent waves: only 16 aggregate food items in 2002 instead of 56 in the following waves. Moreover, the demarcation of households is not the same in 2002 and in the following waves. In 2002, VHLSS considered all persons present in the household at the time of the survey as members of the household. Thereafter, household membership has been dened on the basis of physical presence: individuals must eat and live with other members for at least six out of the past twelve months, and contribute to collective income and expenses. Among other things, this means that family members who have moved away to work or school (e.g., migrants) are not considered anymore as household members.

  , we can-Comment citer ce document : Trinh, H. T., Simioni, M., Thomas-Agnan, C. (2018). Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and 2014. Economics and Human Biology, 31, 259-275. , DOI : 10.1016/j.ehb.2018.09.002 Page 12 of 35 A c c e p t e d M a n u s c r i p t

  and waste are not yet available for Vietnam, and dierences in consumption habits between the two countries prevent us from applying the estimated loss coecients for the US to Vietnamese data. As in[START_REF] Muth | Consumer-level food loss estimates and their use in the ERS loss-adjusted food availablity data[END_REF], we assume that there is a systematic bias to overestimation when transforming consumption data into nutrition data. This bias is assumed to be the same regardless of the considered household. Due to lack of data allowing a thorough treatment of this assumption, we maintain it in this paper.Comment citer ce document : Trinh, H. T., Simioni, M., Thomas-Agnan, C. (2018). Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and 2014. Economics and Human Biology, 31, 259-275., DOI : 10.1016/j.ehb.2018.09

Figure 4 :

 4 Figure 4: Density of per capita calorie intake

  ). Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and 2014. Economics and Human Biology, 31, 259-275., DOI : 10.1016/j.ehb.2018.09

  standard errors are computed using 300 replications. Comment citer ce document : Trinh, H. T., Simioni, M., Thomas-Agnan, C. (2018). Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and 2014. Economics and Human Biology, 31, 259-275. , DOI : 10.1016/j.ehb.2018.09.002 A c c e p t e d M a n u s c r i p t

  standard errors are computed using 300 replications. Comment citer ce document : Trinh, H. T., Simioni, M., Thomas-Agnan, C. (2018). Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and 2014. Economics and Human Biology, 31, 259-275., DOI : 10.1016/j.ehb.2018.09

  closely trace the observed uniform changes in these distributions towards higher consumption of the two macronutrients. Again, the main source of change comes from the composition eect that the structural eect only partially compensates for. It should be noted that the structural eect is never signicantly dierent from zero in the case of fat. The dependence eect is negligible, and the main contributors to the composition eect are still food expenditures and Comment citer ce document : Trinh, H. T., Simioni, M., Thomas-Agnan, C. (2018). Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and 2014. Economics and Human Biology, 31, 259-275., DOI : 10.1016/j.ehb.2018.09

  ). Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and 2014. Economics and Human Biology, 31, 259-275., DOI : 10.1016/j.ehb.2018.09

  food items at dierent points of time, faced to a dierent mass media or advertising exposure. The preceding analysis shows the importance of taking this eect into account when studying nutrition transition in a country such as Vietnam, a country with a strong food culture. It is thus remar-

  Figure 6: Total dierences, composition and structure eects

  Figure 7: Direct contributions to the composition

)

  their joint CDFs by F 2004 X and F 2014 X , respectively. The decomposition method aims at understanding how the observed dierence between the distribution feature ν(F 2014 Y 2004 with the distribution of covariates in year 2014, Y |X (y, x) denotes the conditional distribution of outcome given values of the covariates in year 2004. In our example, we can interpret F 2004|2014 Y (y) as the distribution of per day and per capita carbohydrates consumption after a counterfactual experiment in which the joint distribution of the two covariates is changed from year Comment citer ce document : Trinh, H. T., Simioni, M., Thomas-Agnan, C. (2018). Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and 2014. Economics and Human Biology, 31, 259-275., DOI : 10.1016/j.ehb.2018.092014, but the conditional distribution of per day and per capita carbohydrates consumption given these characteristics remains that of 2004. One can then decompose the observed between-year dierence ∆ ν Y into

F

  t|s,k Y = F t Y |X (y, x)dF s,k X (x) (A-5)Comment citer ce document : Trinh, H. T., Simioni, M., Thomas-Agnan, C. (2018). Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and 2014. Economics and Human Biology, 31, 259-275., DOI : 10.1016/j.ehb.2018.09= C s (F k 1 X 1 (x1), F k 2 X 2 (x2)).

  (2014, 2014). In other words, the computation of the counterfactual distribution F 2004|2014 Y uses the conditional distribution of the outcome given the covariates in year 2004, the dependence structure of year 2014 , and the marginal distributions of the covariates in year 2014. Similarly, we can get F 2004

  of the between-year dierence of the covariates' copula functions. ∆ ν D is thus a dependence eect. The second term, or β ν (1) = ν F contribution of between-year dierences in the marginal covariate distributions.Let now e 1 =(2014, 2004) and e 2 = (2004, 2014). β ν (1) can in turn be decomposed as β ν (1) = β ν (1) -β ν (e 1 ) -β ν (e 2 ) + β ν (e 1 ) + β ν (e 2 )

  ). Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and 2014. Economics and Human Biology, 31, 259-275., DOI : 10.1016/j.ehb.2018.09

  US 2010 dollars in 2017. Poverty 1 was reduced from 35.5% of the population in 1998 to only 2.6% in 2014. Life expectancy has increased from 69.30 years in 1986 up to 76.05 in 2016. Meanwhile, Vietnam has also experienced a nutrition transition like many other middle-income countries in South East Asia. Recently,

  show that, if the linear model is misspecied,

	this method leads to misleading classication into structure or composition ef-
	fects. Moreover, focusing only on the mean introduces a limitation when ad-
	dressing more general changes in the outcome distribution and it can be more
	M interesting to look at what happens at dierent quantiles of this distribution. Machado and Mata (2005) and Melly (2005) extended decomposition methods to between-group dierence in quantiles. But they kept the linear structure for quantile regression and their methodologies cannot be used to separate the com-position eects into the contribution of each covariate. Recently, Chernozhukov et al. (2013) put more theoretical foundations into the construction of the coun-a n u s c r i p t terfactual distribution needed when decomposing the between group dierence
	A c c e p t e d
	Comment citer ce document : Trinh, H. T., Simioni, M., Thomas-Agnan, C. (2018). Decomposition of changes in the consumption	Page 7 of 35
	of macronutrients in Vietnam between 2004 and 2014. Economics and Human Biology, 31, 259-275.
	, DOI : 10.1016/j.ehb.2018.09.002

  Trinh, H. T., Simioni, M., Thomas-Agnan, C. (2018). Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and 2014. Economics and Human Biology, 31, 259-275.

	M a n u s c r i p t
	A c c e p t e d
	, DOI : 10.1016/j.ehb.2018.09.002

Table 1

 1

	9). Carbohydrate intakes is obtained by subtracting the protein and fat intakes
	(in Kcal) to total calorie intake (in Kcal). Finally, we compute adult-equivalent
	calorie intakes to make household comparable. We use the household equiva-
	lence scale calculation procedure recently proposed by Aguiar and Hurst (2013),
	3 Only average annual food consumption was recorded in 2004 while monthly average food
	consumption was surveyed in 2014.

summarizes the sociodemographic variables we use as covariates when implementing the copula-based decomposition method. Detailed summary statistics on these variables are given in Table

2

. These statistics show several interesting developments. First, total food expenditures of Vietnamese households increased over the considered period. Second, the population of these same households is more urbanized in 2014 than in 2004. Third, the average household size has decreased slightly, with about 65% of these households having four or fewer members in 2014 compared to about 55% ten years earlier.

Fourth, heads of households are, on average, more educated in 2014 than in 2004. Furthermore, the proportion of heads with more than 12 schooling years (high school level) increased signicantly from 2004 to 2014. Finally, the proportions of households with heads belonging to the Kinh ethnicity or living in South Vietnam remained stable.

4.2. Macronutrient intakes

Average annual or monthly food expenditures and quantities about 56 food items are collected for each household surveyed in the two considered VHLSS waves.

3 Conversion factors of grams into calories coming from the food compo- sition table constructed by the Vietnam National Institute of Nutrition in 2013 are used to compute macronutrient consumption amounts (see Table

3

). For each household, we compute the total calorie intake (in Kcal), and the protein and fat intakes (in grams) per day. Then, we convert for each household the quantity in grams of protein (resp. fat) into Kcal by multiplying by 4 (resp.

Comment citer ce document : Trinh, H. T., Simioni, M., Thomas-Agnan, C. (

2018

). Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and 2014. Economics and Human Biology, 31, 259-275.

, DOI : 10.1016/j.ehb.2018.09.002

Table 1 :

 1 Description of sociodemographic variables

	Variable	Values	Description
	lExp		Food expenditures per year in US$ (in logarithms) (ination adjusted)
	Hsize		Number of household members
	U rban		Location of the household:
		= 1	if household is located in Urban area
		= 0	if household is located in rural area
	Ethnic		Ethnicity of head of household
		= 1	if Kinh Ethnicity
		= 0	if minority

Table 2 :

 2 Descriptive statistics by VHLSS wave

		Mean	Standard		Quantile
			deviation Wave = 2004 10%	50%	90%
	P CCI	3359.746	1015.451	2259.852	3195.859	4609.399
	V C	2415.078	756.170	1565.208	2318.522	3343.795
	V P	457.920	156.403	294.643	428.629	653.904
	V F	486.748	239.576	247.206	433.159	792.876
	lExp	6.135	0.547	5.461	6.125	6.844
	U rban	0.235
	Hsize	4.355	1.636	2	4	6
	Ethnic	0.893
	Y educc	6.222	4.712	0	5	12
	South	0.345	Wave = 2014
	P CCI	3764.194	1421.362	2313.206	3488.157	5528.041
	V C	2493.419	1032.906	1445.146	2297.777	3764.969
	V P	548.367	219.059	320.181	501.073	830.010
	V F	722.409	343.119	367.404	647.299	1174.950
	lExp	6.638	0.611	5.843	6.667	7.399
	U rban	0.311
	Hsize	3.808	1.526	2	4	6
	Ethnic	0.869
	Y educc	7.097	5.047	0	9	12
	South	0.339	Dierences 2014 -2004
	P CCI	404.448	405.911	53.354	292.298	918.642
	V C	78.341	276.736	-120.062	-20.745	421.174
	V P	90.447	62.656	25.338	72.444	176.106
	V F	235.661	103.543	120.198	214.140	382.074
	lExp	0.503	0.064	0.382	0.542	0.555
	U rban	0.076
	Hsize	0.447	0.110	0	0	0
	Ethnic	-0.024
	Y educc	0.895	0.335	0	4	0
	South	0.006

not avoid all possible sources of measurement errors. Indeed, following

[START_REF] Nakata | Asking retrospective questions in household surveys: evidence from vietnam[END_REF]

, measurement errors can be expected to be related to household size. Consequently, caution should be exercised in interpreting a signicant effect of this last variable in the change in caloric intake between 2004 and 2014.

Table 3 :

 3 Conversion table

	Food Item	Energy	Protein	Fat
		(Kcal)	(gram)	(gram)
	Plain rice	344.5	8.5	1.55
	Sticky rice	347	8.3	1.6
	Maize	354	8.3	4
	Cassava	146	0.8	0.2
	Potato of various kinds	106	1.4	0.15
	Wheat grains, bread, wheat powder	313.7	10.2	1.1
	Fresh rice noodle, dried rice noodle	143	3.2	0.2
	Vermicelli	110	1.7	0
	Pork	26016.5	21.5
	Beef	142.5	20.3	7.15
	Bualo meat	122	22.8	3.3
	Chicken meat	199	20.3	13.1
	Duck and other poultry meat	275	18.5	22.4
	Other types of meat	-	-	-
	Processed meat	-	-	-
	Fresh shrimp, sh	83	17.75	1.2
	Dried and processed shrimps, sh	361	49.16	14.6
	Other aquatic products and seafoods	-	-	-
	Eggs of chicken, ducks, Muscovy ducks, geese	103.74	8.34	7.74
	Tofu	95	10.9	5.4
	Peanuts, sesame	570.5	23.8	45.5
	Beans of various kinds	73	5	0
	Fresh peas of various kinds	596	0.4
	Morning glory vegetables	25	3	0
	Kohlrabi	36	2.8	0
	Cabbage	29	1.8	0.1
	Tomato	20	0.6	0.2
	Other vegetables	-	-	-
	Orange	37	0.9	0
	Banana	81.5	1.2	0.2
	Mango	69	0.6	0.3
	Other fruits	-	-	-
	Lard, cooking oil	863.5	0	99.8
	Fish sauce	60	12.55	0
	Salt	0	0	0
	MSG	0	0	0
	Glutamate	0	0	0
	Sugars, molasses	390	0.55	0
	Confectionery	412.2	8.9	10.7
	Condensed milk, milk powder	395.7	23.4	11.9
	Ice cream, yoghurt	-	-	-
	Fresh milk	61	3.9	4.4
	Alcohol of various kinds	47	4	0
	Beer of various kinds	11	0.5	0
	Bottled, canned, boxed beverages	47	0.5	0
	Instant coee	353	12	0.5
	Coee powder	0	0	0
	Instant tea powder	0	0	0
	Other dried tea	0	0	0
	Cigarettes, waterpipe tobacco	0	0	0
	Betel leaves, areca nuts, lime, betel pieces	0	0	0
	Outdoor meals and drinks	-	-	-
	Other foods and drinks	-	-	-
	Note: Amount per 100 grams of food ; protein contains 4 calories per gram and fat
	contains 9 calories per gram

Table 2 .

 2 All these values increase signicantly for fat and proteins. Average and median values stay quite stable between 2004 and 2014 for carbohydrates while standard deviation increases, 10% quantile decreases, and 90% quantile increases. In other words, per capita calorie intakes from fat and proteins in Vietnamese households have increased 5 All observations are weighted by their respective VHLSS sample weights.

	Page 15 of 35

Comment citer ce document : Trinh, H. T., Simioni, M., Thomas-Agnan, C. (2018). Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and 2014. Economics and Human Biology, 31, 259-275. , DOI : 10.1016/j.ehb.2018.09.002 Two-way interaction eects: -1.73 + 23.58 + . . . + 0.04 Direct eects: 532.86 -11.06 + . . . + 0.99

Table 4 :

 4 Results of Kolmogorov-Smirnov test of equality of the CDFs in 2004 and 2014

	Variable	KS-statistics	p-value
	PCCI	0.14	< 0.0001
	Protein	0.20	< 0.0001
	fat	0.34	< 0.0001
	Carbohydrate	0.06	< 0.0001
	Kernel estimates of per capita calorie intake densities and summary statistics
	show the observed changes in energy intake and macronutrients consumption
	over the 2004-2014 period. Kolmogorov-Smirnov nonparametric test (Conover,
	1971) can be implemented to conrm if these changes are signicant or not.
	Results are presented in Table 4. The null hypothesis of equality of the CDFs in
	2004 and 2014 is clearly rejected whatever the considered variable. We can now
	analyze which covariates have contributed signicantly to these changes over
	time.

Comment citer ce document : Trinh, H. T., Simioni, M., Thomas-Agnan, C. (2018). Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and 2014. Economics and Human Biology, 31, 259-275.

, DOI : 10.1016/j.ehb.2018.09.002

Table 5 :

 5 Estimated decomposition of per capita calorie intake

			Standard	error	(78.76)	(213.09)	(202.78)		(135.35)	(206.92)		(137.13)	(8.96)	(27.01)	(3.95)	(12.53)	(1.30)		(23.43)	(129.97)	(14.9)	(32.18)	(3.96)	(6.32)	(1.48)	(3.73)	(0.70)	(2.68)	(10.89)	(0.74)	(1.63)	(0.14)	(0.44)
		90%	Estimated	value	830.71	-328.38	1159.09		-7.97	1167.06		900.04	-9.49	246.08	-1.61	-26.18	1.11		3.38	34.87	2.36	-14.48	0.29	1.47	-0.39	-1.43	-0.64	0.73	-5.78	-0.22	-0.17	-0.10	-0.20
	Quantiles	50%	Estimated Standard	value error	279.48 (20.81)	-361.79 (39.69)	641.27 (36.71)		0.25 (23.26)	641.02 (33.65)		538.66 (33.05)	-9.56 (3.41)	112.77 (12.26)	0.34 (1.69)	-14.00 (5.72)	0.83 (1.30)		-9.83 (9.02)	30.04 (20.97)	2.36 (4.12)	-11.06 (11.26)	0.21 (1.28)	-6.45 (4.10)	-0.26 (0.54)	-2.37 (2.39)	-0.05 (0.31)	1.25 (1.37)	-14.84 (6.15)	0.63 (0.72)	0.29 (0.62)	-0.01 (0.14)	0.04 (0.38)
	Mean	10%	Estimated Standard Estimated Standard	value error value error	Total dierence ∆ ν Y 362.16 (28.90) 18.62 (26.38) ∆ ν Structure eect S -291.21 (52.53) -283.63 (49.12) ∆ ν Composition eect C 653.37 (44.47) 302.25 (46.16)	Composition eect :	Dependence eect ∆ ν D 0.91 (23.08) -30.6 (22.94) ∆ ν Marginal eect M 652.46 (39.97) 332.85 (42.83)	Direct contributions to composition eect :	lexp 532.86 (36.16) 250.05 (35.54)	Urban -11.06 (2.90) -11.55 (3.28)	Hsize 131.12 (8.94) 53.62 (8.46)	Ethnic 0.69 (1.53) 1.90 (1.33)	Yeduc -18.16 (7.08) -3.09 (6.21)	South 0.99 (1.06) 0.88 (0.96)	Two-way interaction eects:	lexp:Urban -1.73 (5.08) 7.41 (6.83)	lexp:Hsize 23.58 (10.38) 50.01 (24.08)	lexp:Ethnic 0.61 (2.70) 3.89 (3.58)	lexp:Yeduc -6.14 (6.01) -7.56 (10.87)	lexp:South 0.44 (0.70) 0.03 (0.80)	Urban:Hsize 0.14 (1.19) 2.62 (2.73)	Urban:Ethnic -0.45 (0.29) -0.54 (0.47)	Urban:Yeduc 0.41 (0.81) 0.17 (1.22)	Urban:South -0.20 (0.22) -0.01 (0.19)	Hsize:Ethnic 0.84 (0.48) 0.90 (1.09)	Hsize:Yeduc -2.38 (2.05) -1.76 (3.85)	Hsize:South -0.06 (0.15) -0.43 (0.46)	Ethnic:Yeduc -0.32 (0.40) -0.61 (0.50)	Ethnic:South 0.03 (0.05) 0.05 (0.09)	Yeduc:South 0.04 (0.07) -0.01 (0.14)	Note: Bootstrapped standard errors are computed using 300 replications.

Table 6 :

 6 Estimated decomposition of calorie intake from fat

			Standard	error	(28.06)	(55.00)	(55.94)		(46.76)	(54.53)		(36.63)	(2.11)	(7.29)	(1.17)	(2.79)	(0.93)		(7.07)	(32.16)	(3.51)	(7.42)	(0.69)	(1.90)	(0.31)	(0.86)	(0.21)	(0.76)	(2.71)	(0.46)	(0.47)	(0.10)	(0.29)
		90%	Estimated	value	364.92	-5.33	370.25		6.33	363.92		296.02	2.91	71.02	-0.65	-6.75	0.67		-3.23	25.03	1.85	2.70	-0.14	1.63	0.07	0.20	0.07	0.53	-0.88	0.01	-0.34	0.03	0.01
	Quantiles	50%	Estimated Standard	value error	200.73 (7.06)	-15.85 (10.51)	216.57 (9.58)		-0.67 (5.01)	217.24 (8.49)		173.74 (7.12)	2.39 (0.75)	44.33 (2.74)	0.14 (0.33)	0.75 (1.27)	0.30 (0.37)		-1.40 (1.24)	-1.56 (5.72)	-0.22 (0.75)	-2.07 (2.02)	0.13 (0.38)	-0.74 (0.67)	0.04 (0.11)	-0.32 (0.25)	-0.03 (0.06)	0.35 (0.27)	-0.83 (0.90)	0.01 (0.14)	-0.06 (0.11)	0.00 (0.02)	0.01 (0.06)
	Mean	10%	Estimated Standard Estimated Standard	value error value error	Total dierence ∆ ν Y 221.51 (8.68) 119.61 (6.13) ∆ ν Structure eect S -17.63 (13.93) -1.92 (6.8) ∆ ν Composition eect C 239.14 (12.39) 121.53 (8.13)	Composition eect :	Dependence eect ∆ ν D -0.77 (8.01) 2.34 (5.94) ∆ ν Marginal eect M 239.91 (11.11) 119.19 (5.95)	Direct contributions to composition eect :	lexp 178.97 (9.34) 80.78 (6.57)	Urban 2.51 (0.68) 0.77 (0.3)	Hsize 47.64 (2.68) 26.16 (2.55)	Ethnic 0.24 (0.44) -0.18 (0.21)	Yeduc -0.98 (0.92) -0.04 (1.19)	South 0.28 (0.34) 0.10 (0.15)	Two-way interaction eects:	lexp:Urban 0.31 (1.37) 2.62 (1.28)	lexp:Hsize 10.13 (3.30) 9.36 (5.19)	lexp:Ethnic 0.54 (0.91) 0.48 (0.47)	lexp:Yeduc -0.56 (1.26) 1.83 (2.46)	lexp:South 0.19 (0.23) 0.00 (0.16)	Urban:Hsize 0.54 (0.33) 0.62 (0.32)	Urban:Ethnic -0.02 (0.13) -0.01 (0.03)	Urban:Yeduc -0.05 (0.13) -0.01 (0.10)	Urban:South -0.04 (0.05) 0.00 (0.02)	Hsize:Ethnic 0.04 (0.16) 0.14 (0.16)	Hsize:Yeduc -0.33 (0.32) 0.77 (1.03)	Hsize:South 0.04 (0.05) 0.05 (0.06)	Ethnic:Yeduc -0.08 (0.10) -0.04 (0.06)	Ethnic:South 0.00 (0.02) 0.00 (0.01)	Yeduc:South 0.02 (0.02) 0.00 (0.03)	Note: Bootstrapped standard errors are computed using 300 replications.

Comment citer ce document : Trinh, H. T., Simioni, M., Thomas-Agnan, C. (2018). Decomposition of changes in the consumption of macronutrients in Vietnam between 2004 and 2014. Economics and Human Biology, 31, 259-275.

, DOI : 10.1016/j.ehb.2018.09.002

Table 7 :

 7 Estimated decomposition of calorie intake from protein

			Standard	error	(11.17)	(31.46)	(30.44)		(25.79)	(26.85)		(19.08)	(1.06)	(6.05)	(0.54)	(1.51)	(0.17)		(3.93)	(17.44)	(2.56)	(3.93)	(0.32)	(1.49)
		90%	Estimated	value	163.34	-41.46	204.8		-5.93	210.73		169.77	0.14	43.44	-0.37	-4.16	-0.08		4.36	-7.37	-1.60	-1.35	0.08	1.51
	Quantiles	50%	Estimated Standard	value error	70.93 (3.97)	-61.23 (7.35)	132.16 (7.18)		2.66 (4.74)	129.5 (6.73)		108.17 (5.54)	-0.91 (0.45)	23.34 (1.46)	-0.27 (0.26)	-2.44 (0.86)	-0.01 (0.04)		-2.89 (1.42)	6.84 (4.70)	-0.29 (0.60)	-1.76 (1.77)	0.21 (0.28)	0.25 (0.37)
			Standard	error	(4.37)	(7.05)	(7.06)		(4.98)	(6.78)		(5.10)	(0.32)	(1.63)	(0.15)	(0.94)	(0.03)		(0.99)	(4.47)	(0.53)	(1.97)	(0.10)	(0.28)
		10%	Estimated	value	23.76	-43.97	67.73		2.80	64.93		49.37	-0.82	15.33	-0.04	-0.29	0.00		1.28	0.80	-0.11	-1.41	0.06	-0.10
	Mean		Estimated Standard	value error	Total dierence ∆ ν Y 85.74 (4.54) ∆ ν Structure eect S -52.32 (9.08) ∆ ν Composition eect C 138.06 (8.09)	Composition eect :	Dependence eect ∆ ν D 2.94 (6.06) ∆ ν Marginal eect M 135.12 (7.13)	Direct contributions to composition eect :	(6.08) lexp 108.11	(0.40) -0.57 Urban	(1.43) 26.89 Hsize	(0.19) -0.21 Ethnic	(0.82) -1.84 Yeduc	(0.09) -0.06 South	Two-way interaction eects:	(0.98) -0.23 lexp:Urban	(2.10) 2.74 lexp:Hsize	(0.44) -0.56 lexp:Ethnic	(0.86) 0.14 lexp:Yeduc	(0.21) 0.14 lexp:South	(0.19) 0.28 Urban:Hsize	Urban:Ethnic

Table 8 :

 8 Estimated decomposition of calorie intake from carbohydrates

			Standard	error	(50.91)	(134.48)	(128.18)		(74.42)	(110.40)		(88.29)	(6.03)	(22.94)	(2.55)	(7.90)	(0.69)		(17.3)	(59.55)	(8.75)	(16.59)	(2.45)
		90%	Estimated	value	372.23	-300.78	673.01		18.43	654.58		528.18	-11.54	140.86	-0.50	-18.59	0.47		-14.17	14.15	3.43	0.29	1.08
	Quantiles	50%	Estimated Standard	value error	-27.88 (18.25)	-252.19 (24.66)	224.31 (22.52)		5.50 (10.70)	218.81 (19.74)		207.47 (19.2)	-13.01 (2.78)	43.53 (5.54)	0.93 (1.45)	-19.57 (4.18)	0.83 (0.94)		-0.93 (5.67)	-1.78 (10.89)	-0.38 (1.78)	-2.97 (7.21)	-0.25 (0.56)
			Standard	error	(21.14)	(30.56)	(29.32)		(15.75)	(24.67)		(20.79)	(3.88)	(6.60)	(1.95)	(6.62)	(1.00)		(5.57)	(8.55)	(2.70)	(8.78)	(0.76)
		10%	Estimated	value	-120.24	-238.99	118.75		-6.03	124.78		135.13	-16.17	19.53	1.29	-6.82	0.93		8.73	-7.25	4.82	-9.55	-0.52
	Mean		Estimated Standard	value error	Total dierence ∆ ν Y 45.36 (22.04)	Structure eect ∆ ν S -244.93 (36.73) ∆ ν Composition eect C 290.29 (32.66)	Composition eect :	Dependence eect ∆ ν D 0.68 (17.57) ∆ ν Marginal eect M 289.61 (29.3)	Direct contributions to composition eect :	(25.7) lexp 253.01	(2.34) -12.63 Urban	(5.07) 59.84 Hsize	(1.35) 0.60 Ethnic	(5.07) -15.53 Yeduc	(0.78) 0.75 South	Two-way interaction eects:	(4.04) -2.20 lexp:Urban	(6.80) 13.24 lexp:Hsize	(1.92) 0.83 lexp:Ethnic	(4.28) -6.16 lexp:Yeduc	(0.48) 0.08 lexp:South	Urban:Hsize

  Bootstrapped standard errors, based on 300 replications, are in parenthesis.

			Table A-1: Estimated copula parameters
		Urban	Hsize	Ethnic	Yeduc	South
		2004	2014	2004	2014	2004	2014	2004	2014	2004	2014
	lExp	0.502	0.410	0.542	0.582	-0.167	0.206	0.160	0.239	0.364	0.186
		(0.124)	(0.149)	(0.107)	(0.138)	(0.159)	(0.119)	(0.253)	(0.345)	(0.272)	(0.289)
	Urban			-0.034	0.007	-0.288	-0.624	0.113	0.278	0.377	0.349
				(0.269)	(0.204)	(0.084)	(0.093)	(0.092)	(0.097)	(0.066)	(0.077)
	Hsize					-0.544	-0.033	-0.009	-0.005	0.006	-0.081
						(0.245)	(0.199)	(0.118)	(0.129)	(0.129)	(0.108)
	Ethnic							-0.191	-0.131	-0.247	-0.384
								(0.077)	(0.086)	(0.289)	(0.360)
	Yeduc									-0.529	-0.320
										(0.127)	(0.122)
	Note:

The computation of household specic equivalence scales using[START_REF] Aguiar | Deconstructing life cycle expenditure[END_REF] is detailed[START_REF] Trinh Thi | Assessing the nonlinearity of the calorie-income relationship: an estimation strategy -With new insights on nutritional transition in Vietnam[END_REF].

Acknowledgements

The authors would like to thank the Editor of the review and two referees for their thoughtful comments and suggestions on the earlier draft of this paper.

Comments by participants at the

Vietnamese Economists Annual Meeting, Ho Chi Minh city, August 2017, 10th Asia Pacic Conference on Clinical Nutrition (APCCN 2017), Adelaide, November 2017, and International Center for Tropical Agriculture (CIAT) Regional Oce for Asia, November 2017, are fully acknowledged. We would like to thank Brian McCaig (Wilfrid Laurier University) and Binh T. Nguyen (Asian Development Bank, Philippines) for sharing with us data and program les. We are grateful to Thibault Laurent for technical assistance in R. This research was funded by the INRA-CIRAD Glo-FoodS meta-program (TAASE project), the Vietnam International Education Department Fellowships (911 Project), the CGIAR Program on Agriculture for Nutrition and Health (CRP-A4NH) through the Flagship Project on Food Systems for Healthy Diets, and the Graham Institute of Sustainability through the project Leveraging existing data and insights into the policy process to accelerate progress toward achieving sustainable diets in the Global South.

We consider the general case where the vector of the covariates has d elements, and we have two iid samples (Y t i , X t i )

of size nt from the distribution of (Y t , X t ) for t = 2004, 2014. The practical implementation of the decomposition procedure presented in Appendix A requires the estimation of various functions or parameters. Univariate CDFs.. Univariate CDFs are estimated nonparametrically using the classical empirical CDF, i.e.

where [START_REF] Foresi | The conditional distribution of excess returns: an empirical analysis[END_REF]. The distributional regression model assumes that

where Φ(.) is the standard normal CDF. The nite-dimensional parameter δ t (y) is estimated by the maximum likelihood estimate δ t (y) in a Probit model that relates the indicator variable I(Y t ≤ y) to the covariates X t .

Copula choice.. The last function necessary for the implementation of the decomposition procedure of [START_REF] Rothe | Decomposing the composition eect: the role of covariates in determining between-group dierences in economic outcomes[END_REF] is the copula function. Let us take a copula contained in a parametric class indexed by a k-dimensional parameter θ. A strategy for estimating the parameters characterizing the copula then consists in choosing the minimum distance estimator dened as (Weiÿ, 2011)

Dierent parametric copula functions can be used (Trivedi and Zimmer, 2007). But, here too, we must keep in mind when choosing this function to select a function that is suciently exible for generating all possible types of dependence. Moreover, we are confronted here with the fact that our variables are a mixture of continuous and discrete variables. To address these issues, we choose the Gaussian copula model

where Φ d Σ (.) denotes the CDF of a d-variate standard normal distribution with correlation matrix Σ, and Φ -1 (.) is the inverse function of the standard normal distribution function Φ(.). The parameters θ ≡ Σ determine the dependence pattern among the covariates.

The exibility and the analytical tractability of Gaussian copulas make them a handy tool in applications as emphasized by [START_REF] Jiryaie | Gaussian copula distributions for mixed data, with application in discrimination[END_REF]. First, This specication has a computational advantage, namely, that only the (a, b) element of Σ aects A c c e p t e d M a n u s c r i p t the pairwise dependence between the covariates X t a and X b b . So minimum distance estimation (A-12) can be performed for each pair of covariates, not by taking all the covariates together simultaneously.

Second, as noted above, the copula function describes the joint distribution of individuals' ranks in the various components of X t , and, here, the dependence between two components can be measured using a correlation coecient as we are working with Gaussian copula. Indeed, in the bivariate case, we get

where Φ 2 Σ a,b (.) denotes the CDF of the bivariate normal distribution with covariance matrix Σ a,b , and Φ -1 (FX a (Xai)) (resp.Φ -1 (FX b (X bi )) can be interpreted as the quantile of the univariate marginal distribution associated to the observation Xai (resp. X bi ).

Third, Gaussian copulas make it possible to have both continuous and discrete variables in the vector of covariates. We only have to assume that each discrete covariate X t j can be represented as X t j = tj( X t j ) for some continuously distributed latent variable X t j and a function tj(.) that is weakly increasing in its argument. For instance, if X t j is a binary, we could have X t j = I( X t j > cj) for some constant cj.

Details on the computation of the joint distribution of a vector of continuous and discrete variables using Gaussian copula can be found in [START_REF] Jiryaie | Gaussian copula distributions for mixed data, with application in discrimination[END_REF].

Counterfactual distributions.. After estimating the copula and the marginal distributions for each time period, we can construct the joint c.d.f. of the explanatory variables given by (A-6) in any counterfactual experiment where the copula is as in time s and the marginals as in time k1 and k2. Given this joint c.d.f, using equation (A-5) and the conditional c.d.f F t Y |X (y, x) at time t estimated by equation (A-11), we can construct an estimation of any counterfactual distribution of the outcome.

C. Preliminary results

To estimate the various elements of the decomposition of the composition eect, we proceed as described in Appendix B. Copulas are thereby modeled by a Gaussian copula and the joint CDF of each pair of covariates estimated using marginal empirical CDF estimators and copula estimators. Table A-1 reports the estimated values of the copula parameters from the 2004 and 2014 VHLSS waves. Estimated copula parameters show positive and signicant association between food expenditures and location in an urban area as well as food expenditures and household size. The rst association decreased between 2004 and 2014 while the second remained fairly stable.

The association between location in an urban area and ethnicity is negative and signicant whatever the considered waves, as expected, and increases over the period. The association between location in an urban area and years of education is positive but becomes signicant only in 2014. A stable positive and signicant association is also shown for location in an urban area and living in South Vietnam. We also notice a negative association between household size and ethnicity in 2004, which disappears completely in 2014. As recently pointed out by [START_REF] Benjamin | Growth with equity: income inequality in Vietnam, 2002-14[END_REF], the share of minorities in the rural population has risen over time, from below 15% in 2002 to over 18% in 2014. This is a consequence of a higher fertility among minorities, combined with rising urbanization among the Kinh. Finally, the association between the number of years of education and living in South Vietnam is negative and signicant but decreasing between 2004 and 2014.