Empirical model
We applied the methodology of Liu et al. [20] to estimate the relationship between household nutritional outcomes and migration:
$$\begin{aligned}{Y_{it}} &= {\beta _0} + {\beta _1}Migratio{n_{it}} \cr&\quad+ {\beta _2}H{H_{it}} + {\beta _3}Provinc{e_{jt}} \cr&\quad+ {\beta _4}Yea{r_t} + {\mu _i} + {\varepsilon _{it}}\end{aligned}$$
(1)
Where:
\({Y_{it}}\) represents the nutritional consumption of household \(i\) in year \(t\), including energy, macronutrients, micronutrients, and other food categories. Specifically,, \({Y_{it}}\) includes proxy variables for food security, such as energy intake, macronutrients (protein, fat, carbohydrate), micronutrients (vitamins and minerals), and food expenditures by group. These variables are measured in standard units (kcal, grams, mg) per capita per day. Total consumption is segmented by various sources, including purchases, home production, and gifts.
\(Migratio{n_{it}}\) is a vector of variables indicating whether a household has short-term or long-term migrants. The coefficients for long-term and short-term migration variables are estimated in two separate equations since only 60 households have both short-term and long-term migrants.
\(H{H_{it}}\) is a vector of household characteristics, including the household’s total years of education, gender-disaggregated years of schooling for household members, per capita household income, housing durability, agricultural land area, rice paddy area, and the age distribution across four groups (0–16, 7–14, 15–24, and 25–29). Health indicators such as the number of household members with severe illnesses, the frequency of severe illness, and the number of days affected are also included in the model. Household characteristics also encompass the attributes of the household head (gender, age, and marital status).
\(Provinc{e_{jt}} \)is a vector of province-level characteristics, including land area, unemployment rate, population, real GRDP, real growth rate, real GRDP per capita, and labor force size. \(Yea{r_t}\) represents time fixed effects, \({\mu _i}\) represents household fixed effects, and \({\varepsilon _{it}}\) is the error term.
Estimating strategy
Previous studies often use the logarithm of per capita nutritional consumption as the dependent variable in Eq. (1) and estimate the coefficients of interest using the OLS method [12, 38]. However, Silva and Tenreyro [39] have pointed out that this approach may be inappropriate for two reasons. First, some nutritional outcomes may be zero, making the logarithm of zero undefined. Second, taking the logarithm of the dependent variable may cause the error term to correlate with the independent variables, resulting in inconsistent estimated coefficients [39]. The authors suggest using the Poisson pseudo-maximum-likelihood (PPML) estimator as an alternative.
Consequently, we implemented two versions of Eq. (1) to estimate the coefficients. In the first version, Eq. (1) was estimated using panel fixed-effects linear models. In the second version, we employed panel fixed-effects Poisson models. The dependent variables were measured in levels in both versions.
We employ both fixed-effects linear and Poisson models for several methodological reasons. The fixed-effects linear model is selected for its ability to handle panel data and control for unobserved household-level heterogeneity. The Poisson model is additionally applied to address the issue of zero values in the dependent variables and potential correlations between the error term and independent variables, as highlighted by Silva and Tenreyro [39].
Major sources of endogeneity in this study include omitted variable bias, time-invariant heterogeneity, and reverse causality, for example, when poor nutritional status may prompt migration decisions. [20] investigated the impact of adult children’s migration on the nutritional status of elderly parents in rural China using a panel fixed-effects approach with data from the China Health and Nutrition Survey (CHNS). Specifically, [20] applied household fixed-effects regression to control for time-invariant unobserved household characteristics, along with comprehensive control variables including demographic factors, socioeconomic status, health conditions, and community characteristics. This approach effectively addresses selection bias and omitted variable concerns by relying on within-household variation over time to estimate the causal effects of migration on nutrition outcomes.
We adopted the methodological framework of Liu et al. [20] to minimize endogeneity in our analysis. First, we incorporated extensive control variables at both the household and provincial levels that may influence both migration and nutritional status. These variables, which have been identified in previous research as important determinants of migration and nutrition [12, 20, 40], help reduce the influence of time-varying unobservable factors. Second, we used both unit and time fixed effects to account for time-invariant unobservable factors [20, 41].
While the fixed-effects approach does not fully eliminate endogeneity stemming from time-varying unobserved factors—such as changes in food preferences, local economic shocks, or seasonal variations in food availability—our analysis incorporates comprehensive controls for observable household characteristics (including education, income, demographics, health, and land assets) and provincial factors (such as GRDP, unemployment rate, population, and labor force size). These measures help to mitigate potential bias from observable influences.
Data sources
This study utilizes data from the Vietnam Household Living Standards Survey (VHLSS) covering the period from 2016 to 2018, with data collected biennially. VHLSS is a nationally representative survey designed to assess household living standards across Vietnam, providing comprehensive information on both community and household characteristics. The survey employs a multi-stage stratified sampling method. In each survey cycle (year \(n + 2\)), 50% of the surveyed areas are retained from the previous cycle (year \(n\)), while the remaining 50% are newly selected. This rotating panel design enables both longitudinal analysis and the inclusion of new households, enhancing sample representativeness over time.
The survey uses a multi-topic household questionnaire, gathering extensive information on demographics, employment, income, health, education, and community characteristics. This study contains sections on food consumption (Section \(5a2\)) and migration status (Sections \(1a\) and \(1c\)). To quantify the nutritional composition of consumed food, we utilize the “Vietnam Food Composition Table” published by the National Institute of Nutrition [42]. This allows for a detailed analysis of household nutritional consumption patterns.
The study considers both short-term and long-term migration. Short-term migration is identified in Section \(1a\) of the VHLSS, recording individuals in the household for less than six months. Long-term migration is tracked by linking individual identification codes across survey waves, using the question “Did this household participate in the living standards survey in year \(n\)?” in Section \(1c\). For the regression analysis, labor migrants are defined as individuals aged 15 to 60 who migrate for employment, encompassing both short-term and long-term migrants.
Variable definitions
Dependent variables: nutrition
To estimate the consumption of 42 essential nutrients by Vietnamese households, we use the food composition table (data per 100 grams) in conjunction with the “Expenditures on Regular Food and Beverages” section of the VHLSS. However, the food expenditure data in the VHLSS presents methodological challenges due to inconsistent units of measurement across items. To address this issue, we classify food items into two separate groups: well-defined and poorly defined. Well-defined items include food measured in kilograms (kg), while poorly defined items include food with other units of measurement and food away from home.
For well-defined food items, we quantify the consumption of 42 essential nutrients by multiplying the weight in kilograms of each item by its corresponding nutrient content per kilogram, as outlined in the food composition table. This calculation provides the total quantity of each nutrient consumed from each well-defined food item over 30 days.
Poorly defined food items in this study include other meats, processed meats, seafood, vegetables, fruits, MSG, ice cream, instant coffee, food away from home, and miscellaneous foods. We use monetary values (thousand VND) for these items due to unavailable specific nutrient data or consumption quantities.
To account for these items, we use an approach that adjusts for changes in consumer prices over time. We use expenditure data from VHLSS in years \(n\) and \(n + 2\) for each food group and apply the Consumer Price Index (CPI) for year \(n + 1\) and \(n + 2\) to convert expenditure amounts back to the base year \(n\). This approach ensures monetary consistency across years, facilitating accurate comparisons and analysis. CPI categories from the General Statistics Office (GSO) include: Food and Foodstuff (applicable to other meats, processed meats, other seafood, other vegetables, other fruits, MSG, ice cream, and other foods), Beverages and Tobacco (for instant coffee), and Food Away from Home (for meals away from home).
Independent variables: migration
To analyze patterns of short-term migration, we utilize responses to the question, “What is the reason [name] has not lived in the household for more than six months?” from Sect. “Introduction” A of the VHLSS questionnaire. Short-term migration is defined as household members who have been absent from the household for over six months within the past 12 months but still retain their household membership status.
We recode these responses into a categorical variable (migration_shortterm), where \(0\) represents no migration, \(1\) represents migration for work purposes, and \(2 \) represents migration for non-work purposes. We then generate binary indicators for labor-related migration and non-labor-related migration. Next, we quantify migration at the household level by separately counting the number of individuals migrating for work (work_migration_count) and those migrating for non-work purposes (nonwork_migration_count).
For long-term migration, we applied a similar method based on responses to the question, “Why did [name] move out of the household?” from Sect. “Introduction”, including individual identifiers across survey rounds. Long-term migration is defined as household members who left the household and no longer hold membership status (present in the household in 2016 but not in 2018). We construct the variable migration_longterm using the same coding approach for short-term migration. Individuals who have passed away are excluded from the analysis to avoid biases. Counting long-term migrants within each household mirrors the approach used for short-term migration.