Introduction

Child poverty is an issue attracted lasting and increasing attention worldwide, and alleviating child poverty is an urgent task across the world. The report issued by UNICEF showed that at least 333 million children worldwide, accounting for about one-sixth of the total global child population, were living in poverty in 2022 (Daylan et al. 2023). Even in some developed countries, child poverty rates are rising sharply. Denmark has the lowest child poverty rate, with 9.9% of children living in poverty. In Finland and Slovenia, approximately 1 in 10 children live in poverty. In contrast, in countries such as Bulgaria, Colombia, Italy, Mexico, Romania, Spain, Turkey, and the United States, over a quarter of children live in poverty. This highlights the urgent need for effective measure to address child poverty. Poverty exerts negative effect on children’s well-being immediately, and indirectly impact individuals’ life-long results by impairing children’s development, among which cognitive ability is one of the most important dimensions.

A substantial body of literature has accumulated in academia on the impact of poverty on children’s cognitive ability (Duncan, Morris and Rodrigues 2011; Mayer 1997; Xu 2023). However, the majority of existing studies related to child poverty define “poverty” from economic perspective, categorizing children as the poor while the income of household where they live below a specified threshold. It confounds child poverty and adult poverty, due to the fact that children may not directly benefit from household income since some children are deliberately neglected by their guardians, leading to underestimate the incidence of child poverty and the impact of poverty on children’s cognitive ability. For instance, when identifying child poverty solely through income measure, rural and urban areas show comparable poverty rates. However, multidimensional assessment reveals significantly higher poverty prevalence among rural children—demonstrating income-based approaches’ failure to accurately capture severity and dimensionality of child deprivation (Qi and Wu 2019). Therefore, based on Sen’s multidimensional poverty theory, we established an indicator system to identify children in poverty, aiming to recognize potential cases of child poverty and accurately examine its impact on children’s cognitive ability.

Currently, many countries around the world highly prioritize the development of children’s cognitive ability. For instance, in the “Framework for 21st Century Learning”, the United States identifies creativity and critical thinking as essential core competencies for children to succeed in an increasingly dynamic world; The European Union’s 2005 publication, “Key Competences for Lifelong Learning: A European Reference Framework”, outlines eight core competences that individuals are expected to develop during schooling process, emphasizing that critical thinking, creativity, and problem-solving form the foundation of these competences. These skills—critical thinking, creativity, and problem-solving—all belong to cognitive ability.

Cognitive ability refers to the human brain’s capacity to process, store, and retrieve information, reflecting an individual’s “intrinsic ability”. Compared to indicators such as academic performance or level of education, which also reflect personal brain functional capability, cognitive ability provides a more precise representation of an individual’s human capital. In recent years, cognitive ability has garnered significant attention from scholars in both economics and education fields. From the macro perspective, Simulation showed that each one standard deviation increased in children’s cognitive ability boosted nation’s economic growth about 2% when these children enter the labor market (Hanushek and Woessman 2023). From the micro perspective, enhancing individual cognitive ability can significantly improve workers’ skill and partially explain income disparities among individuals (Blackburn and Neumark 1993; Griliches 1977; Griliches and Mason 1972; Hauser and Huang 1996; Heckman 2006; Spence 1973). This is particularly relevant in highly information-driven societies, where increasing complexity in job requirements raises demands for individuals’ ability to process and handle information. As a result, individuals with lower cognitive ability are at a competitive disadvantage in the labor market, and the role of cognitive ability in determining income disparities is becoming increasingly pronounced.

We primarily examine the impact of relative deprivation on children’s cognitive ability in China context. As the largest developing country, although China achieved full poverty alleviation in 2020, there are still numerous children experiencing relative deprivation. For example, with the acceleration of urbanization, China has seen a significant increase in the number of left-behind and migrant children. Although these children are not economically impoverished, they may still experience relative deprivation. The conclusions drawn from our study can guide other developing countries in understanding and supporting children facing relative deprivation.

This paper contributes to this field of study in three aspects: First, drawing on Sen’s capability approach and guided by the framework of the United Nations Convention on the Rights of the Child, we construct multidimensional deprivation indicators to more precisely identify children in China who are relatively deprived. By doing so, we reduce measurement error in our key explanatory variable and thereby partially mitigate the endogeneity arising from such errors.

Second, by taking advantage of the tracking characteristics of the China Family Panel Studies (CFPS), we examine the changes in cognitive ability of adolescents who were trapped in multidimensional deprivation in their early years. This provides a long-term perspective on the impact of multidimensional deprivation on children’s cognitive ability.

Third, we explore strategies from a family parenting perspective to mitigate the impact of multidimensional deprivation on children’s cognitive ability. This approach is crucial for enhancing the quality of family caregiving and improving parental educational practices.

The paper is organized as follows: the second section illustrates theoretical foundation and reviews existing literature; the third section describes the data and methods used in this paper; the fourth section reports results of the empirical research, answering the research questions: incidence of Deprivation in Each Dimension, impact of multidimensional deprivation on children’s cognitive ability and strategies for improving cognitive ability of multidimensionally deprived children; and finally, the concluding section briefly summarizes the research and discusses the policy implications.

Literature Review

Multidimensional Deprivations

“Multidimensional deprivation” is an updated version of “deprivation”, and “deprivation” is evolved from the idea of “poverty”. The concept of “poverty” has transformed from absolute poverty to relative deprivation last century. For instance, Rowntree (1997) defined absolute poverty as a household’s total income being insufficient to afford the minimal necessities required to maintain basic physical functioning. The World Bank, for example, set absolute poverty line as the consumption below $1 per person per day in 1980sFootnote 1. adjusted by purchasing power parity in 1985. However, “no matter how well an economic system operates, some people can be typically on the verge of vulnerability and can actually succumb to great deprivation as a result of material changes that adversely affect their lives” (Sen 1999), and thus the concept of “relative deprivation” was introduced. Relative deprivation occurs when individuals or households’ resources are below a community’s particular level, under which they would exclude from normal ways of living and social activities, even though their basic material needs are satisfied (Sen 1976).

Relative deprivation is typically benchmarked by mean or median income of a community or a specific referenced group (Townsend 1979). For instance, according to the World Bank, individuals whose income is below one-third of the mean income are relatively deprived population, while the European Union’s sets the cut-off point at 50% of the mean income. Obviously, relatively deprived individuals includes both of those whose income fall below the absolute poverty line and those who hover on the edge of absolute poverty.

Understandings on poverty was deepened as scholars proposed that an individual’s fitting into the society decently without being excluded by others should also be considered as an important criterion as well, since income alone is insufficient to capture an individual or household’s well-being. As quoted by Sen: “It would be absurd to call someone poor just because he had the means to buy only one Cadillac a day when others in that community could buy two of these cars each day” (Sen 1998). Sen further expanded the construct of “relative deprivation”, asserting that poverty is caused by inequalities of individuals’ capability to live a life they have reason to value, and thus should be measured by an individual’s feasible capability to get materials required for their basic livelihood (Sen 1981). In other words, deprivation should not only be reflected to the economic dimension such as low income, but also should be expanded to multiple dimensions like political deprivation, cultural deprivation, institutional deprivation, etc. Sen’s theory laid the foundation for developing indicators to conceptualize multidimensional deprivation.

Early multidimensional deprivation metrics relied on the union identification rule, which fails to meet the deprivation-focus axiom. In response, Atkinson (2003) introduced the counting approach, integrating it with union and intersection identification into a unified deprivation-identification framework. This method gained widespread adoption (Gordon and Nandy 2012). Building on the counting approach, Alkire and Foster (in “Counting and Multidimensional Poverty Measurement”) introduced the AF methodology. The method defines multidimensional deprivation by first setting deprivation thresholds for each dimension, and then establishing a deprivation threshold for all dimensions. Its advantage lies in its ability to enhance the accuracy of multidimensional deprivation measurement through processes of deprivation identification, aggregation, and decomposition. This method is considered a mature approach for identifying multidimensional deprivation.

With respect to identifying children deprivation, most of previous studies relied on family income as the main indicator to separate the deprived children from the remaining others (Blau 1999; Dickerson and Popli 2016; Duncan et al. 2011; Duyme et al. 1999; Nicole et al. 2015; Taylor 2004; Weiss et al. 2003; Beck et al. 2004). As demonstrated above, children born in economically well-off households but worse-off in education, health, survival and development, protection, and nutrition may be excluded by traditional measure of “child poverty”. In other words, some children who are severely deprived in non-economic dimensions but not poor by family income standard may be omitted and neglected (Tegoum and Hevi 2016), and thus incidence of child poverty is underestimated due to measurement errors of “child deprivation”. From perspective of econometrics, measurement error of key explanatory variable is associated with endogeneity issue, leading to potential biased estimates. This paper aligns with Sen’s perspective by measuring children’s relative deprivation across multiple dimensions and then examines the impact of multidimensional deprivation on children’s cognitive ability.

Some existing studies had measured children’s multidimensional deprivation based on Sen’s capability deprivation theory. For example, Leu and Chen (2016), using data from Taiwan, measured children’s multidimensional deprivation and found that children in Taiwan face severe social exclusion and power deprivation. The three most severe dimensions identified were living environment, recreation, and education. Similarly, UNICEF developed eight indicators related to child well-being—food, sanitation facilities, safe drinking water, health, shelter, education, access to information, and service availability—and established deprivation thresholds for each indicator to measure children’s multidimensional deprivation. Biggeri and Ferrone (2021) assessed the multidimensional deprivation status of children in 25 countries worldwide from the perspectives of nutrition, education, health, and information. Gao et al. (2022) identified children’s multidimensional deprivation through seven dimensions including water, sanitation, housing, and education, and explored the impact of rural subsistence allowances on children’s multidimensional deprivation.

Children multidimensional deprivation on cognitive ability

Cognitive ability plays a crucial role in shaping children’s academic achievement, and as a result, most studies consider academic achievement as a proxy for cognitive ability. For the sake of discussion, this section includes research on the impact of poverty on children’s academic performance. In the education production function, factors influencing students’ outcomes include individual student characteristics, family characteristics, and school characteristics. Based on a large-scale survey of 4000 schools and 640000 students in the United States, Coleman et al. (1966) used a multiple linear regression model to find that family factors, rather than school factors, had a significant impact on students’ academic performance. This is known as “Coleman Report”. Its publication drew widespread attention in academia to the influence of students’ family social and economic status, sparking a series of studies focused on the relationship between families social and economic status and children development.

Using children’s family income to identify child deprivation and explore the impact of deprivation on children’s cognitive ability is a part of those series of studies. However, research focusing on the impact of children’s deprivation on their cognitive ability do not reach consensus on their findings so far.

Some researchers found that deprivation exerted significantly negative effect on children’s cognitive development (Duncan, Morris and Rodrigues 2011; Beck, Eric and Kathleen 2004). However, other researchers have found that deprivation has little or no effect on child development (Mayer 1997; Scarr and Weinberg 1978; Xu 2023). Inconsistent conclusions generated by existing literature is partially due to the fact that previous studies employed different methods to measure deprivation, and some research samples have selection bias. For example, Duncan et al. (2011) found that for low-income families, every additional $1,000 in income would increase children’s academic achievement by 0.05–0.06 standard deviations, but the student sample in this study all came from single-parent families. Scarr & Weinberg (1978) used samples of adopted and biological children and found that family background factors had no effect on children’s cognitive ability. However, the study’s sample only covered affluent families.

Based on existing research, there is still a lack of studies that identify children relative deprivation from multidimensional perspectives and examine its impact on children’s cognitive ability, particularly evidence from developing countries.

Strategies for improving cognitive ability of multidimensionally deprived children

Previous research has made considerable efforts to explore pathways for mitigating the negative impacts of multidimensional deprivation on children. These studies primarily adopt a public service perspective to evaluate the effectiveness of developmental policies for impoverished children implemented by various countries and organizations. For instance, Stampini et al. (2018) found that conditional cash transfer programs can enhance the human capital of school-aged children in low-income households; Xu et al. (2019) conducted a meta-analysis of 17 intervention studies and revealed that China’s school meal programs significantly improved the health of children in impoverished rural areas.

Few studies have explored strategies to improve the development of relatively disadvantaged children from the micro-level perspective of the family. In reality, among the numerous factors influencing children development, the family holds significant importance and value in fostering children’s growth. Children not only inherit parental genes that shape their innate ability and skill endowments (Heckman and Mosso 2014; Houmark et al. 2024), but their post-natal development is also effectively molded by the home-caregiving environment provided by parents, which shapes their behavioral competencies (Bisin and Verdier 2023; Chowdhury et al. 2022; Francesconi and Heckman 2016; Wang et al. 2024).

Research by Coleman et al. (1966) on educational equality across ethnic groups in the United States revealed that student development is more strongly influenced by family and peer factors. Studies have found that family factors can explain 40%–60% of the total variance in human capital development (Björklund and Salvanes 2011; Chowdhury et al. 2022). Subsequently, Heckman and others established a skill formation function, integrating family investments, family environment, and children’s human capital into a unified analytical framework (Heckman and Mosso 2014). The scope of family investment gradually expanded to encompass investments of time and effort (Del Boca et al. 2017; Francesconi and Heckman 2016; Guryan et al. 2008). As research has further developed, parenting styles have increasingly emerged as a frontier topic in promoting children’s human capital development and are recognized as a key indicator of parenting quality.

Therefore, this study seeks to explore family parenting factors that promote cognitive development in relatively disadvantaged children from the micro-environment of the family, focusing on three dimensions: parenting beliefs, human capital investment, and parenting styles.

Marginal contribution of the current research

In comparison to existing literature, this paper contributes this field of study by lending methodological lessons to future studies focusing on this topic in the following aspects: First, based on theory proposed by Amartya Sen, we measure child poverty or relative deprivation in a multidimensional approach, which minimize measurement errors of child deprivation and more accurately targets relatively deprived children.

Second, exploiting the longitudinal nature of the China Family Panel Studies (CFPS) data, this study examines the medium-to-long-term impacts of multidimensional deprivation on children’s cognitive ability. The findings provide further empirical evidence to support early-stage interventions for children experiencing multidimensional deprivation.

Third, leveraging large-scale survey data from China, we investigate potential pathways to mitigate the impact of multidimensional deprivation on children’s cognitive ability through the lens of family parenting practices, thereby further enriching intervention strategies for improving outcomes among children experiencing multidimensional deprivation.

Methodological Issues

Sample

Data used in this study to test the hypothesis derives from China Family Panel Studies (hereafter referred to as “CFPS”), which was designed and collected by Institute of Social Science Survey (ISSS) at Peking University. The CFPS primary relied on structured questionnaires for data collection, with the NSRC ensuring strict adherence to ethical protocols by neither conducting human subject experiments nor utilizing human tissue samples throughout the survey process.

CFPS is a nationally representative sample to build the educational landscape in China. NSRC initially launched the CFPS baseline survey in 2010 and has conducted biennial follow-ups across 162 counties in 25 Chinese provinces, targeting individuals of all age groups within household units. Employing a multi-stage stratified probability sampling design, CFPS achieves nationally representative coverage of approximately 95% of China’s population, with baseline samples comprising 14,960 households and 42,590 individuals. The current research utilizes six waves of longitudinal data spanning 2010–2020 for analyses. The complete sampling procedure is detailed in Fig. 1.

Fig. 1: CFPS Sampling Design.
Fig. 1: CFPS Sampling Design.
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PSU means Primary Sampling Unit.

This study processes CFPS through two key procedures: First, child data from each survey year are merged with household databases, therefore, we integrate separate sheet of children, parents, and household information one, enabling comprehensive multidimensional identification of child deprivation status. Six waves of merged datasets are pooled into a repeated cross-sectional dataset at child level then. Second, leveraging the longitudinal design of CFPS, we construct a child-level panel data to simultaneously capture multidimensional deprivation status in early childhood and medium-to-long-term cognitive outcome, enabling examination of the potential cumulative effects of deprivation on individual’s cognitive development trajectories.

Measure

Key explanatory variable: multidimensional deprivation

We follow the framework of the United Nations Convention on the Rights of the Child to construct the dimensions of child relative deprivation. Confined to data availability of CFPS, this study ultimately includes 12 indicators which can be divided into 5 dimensions to measure child multidimensional deprivation. These five dimensions mainly involve education, health, survival and development, protection, nutrition. It is noted that we present the specific dimensions of multidimensional deprivation as well as the deprivation rates of each indicator in the first part of the empirical results.

Alkire-Foster (A-F) algorithm is adopted to get multidimensional deprivation index in our study. Steps for multidimensional deprivation index construct are presented as follows.

Step one, construct the matrix and vector for multidimensional deprivation. Assume that An,d represents a matrix containing n*d cells, and all elements of the matrix yij ∈ An,d, viz the specific value of dth indicator for nth individual (i = 1,2,3……n; j = 1, 2, 3……d). Row vector yi = (yi1, yi2, yi3……yid) projects all values of ith individual on each indicator, and column vector yj = (y1j, y2j, y3j……ynj) represents individual-specific attributes of jth indicator.

Step two, set the deprivation threshold z for each indicator and threshold k for dimension. Deprivation threshold z is used to determine whether an individual is below the cut-point or not with respect to a single indicator. If yij is no less than zj, then the individual under consideration is not deprived as to jth indicator under which situation yij is assigned a value1; on the contrary, if yij is below zj, then yij take the value 0.

Weight vector w reflects the importance of each indicator. The weight of jth indicator wj is above 0 but below 1, and summation of all wj should be 100%, viz, \({\sum }_{n}^{d}{w}_{j}\) = 1. Sum all weighted indicators wj for ith individual and then get the weighted deprivation coefficient ci, ci ∈ [0,1], ci = \({\sum }_{j=1}^{d}{w}_{j}{y}_{{ij}}\). Following the conventional practice adopted by mainstream researches, this study assigns equal weights to all indicators with each dimension. Weight of a specific indicator depends on number of indicators each dimension comprised of (Alkire and Foster 2011; Alkire and Seth 2015). Since we develop five dimensions to construct child multidimensional deprivation, weight of these five dimensions is set as 1/5 respectively, and weight of each indicator within a dimension varied with dimensional size. For example, Education dimension contains two indicators, so weight of each indicator is 1/10.

Deprivation threshold k is introduced to identify whether an individual is multidimensionally deprived or not. If ci ≥ k, then ith individual is being deprived multidimensionally. Otherwise, he or she may be deprived in some dimensions but not overall multidimensionally deprived by this study’s standard. Previous studies have mostly set the cutoff value k at 0.3. For example, Li & He (2024) constructed a six-dimensional framework and used k = 0.3 to identify the multidimensional deprivation status of women living in rural areas; Wang et al. (2022) also set the threshold at k = 0.3 to examine rural households’ multidimensional deprivation and its dynamic changes. Therefore, we follow this conventional practice to set the value of k at 0.3. Furthermore, we present the distribution of the multidimensional deprivation index, as shown in Fig. 2.

Fig. 2: Distribution of the Multidimensional Deprivation Index.
Fig. 2: Distribution of the Multidimensional Deprivation Index.
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The horizontal axis represents the multidimensional deprivation score, while the vertical axis represents the kernel density. The shaded area corresponds to the proportion of children identified as multidimensionally deprived when the cutoff value k is set at 0.3.

Outcome variable: cognitive ability

CFPS project team designed two sets of scales (A and B) to measure cognitive ability all individuals aged 10 and above. These two sets were used alternately during the surveys: scale A was administered in 2010, 2014 and 2018, while scale B was used in 2012, 2016, and 2020. Both scales measured individuals’ literacy and numeracy skills. The key difference lies in their focus: scale A emphasizes crystallized intelligence, which reflects knowledge and experience accumulated through learning, whereas scale B aims to assess fluid intelligence, referring to the ability such as memory, learning, reasoning, and problem-solving. Based on this distinction, to ensure comparability of cognitive ability scores across different survey years, we standardized the literacy and numeracy test scores separately by scale set and birth cohort. Then, we combined the standardized literacy and numeracy scores by averaging them, thus obtaining a composite measure of individuals’ cognitive ability level.

Moderating variables

The moderating variables in this study primarily focuses on familial environmental factors, with particular emphasis on parenting quality, including parental educational belief, parental investment in human capital, and parenting styles. Parental educational belief refers to parents’ perspectives on educating and raising their children, encompassing their attitudes towards child development, the malleability of children, and confidence in turning children into well-educated person. Drawing on previous literature, we measure this construct through family educational expectations (Buchmann, Grütter and Zuffianò 2022). Specifically, this variable is captured by the question: “What is the highest level of education you hope your child will complete?”

In terms of human capital investment, this study focuses solely on the financial aspect of human capital investment due to limited information revealed by the CFPS dataset. Respondents’ educational expenditures are utilized as a proxy of human capital investment. Noteworthy, CFPS datasets provide a comprehensive and detailed breakdown of educational spending, covering a wide range of cost categories such as tuition and fees, textbook costs, accommodation, transportation, meals, extracurricular training fees, and other related costs. In our study, extracurricular training fees are categorized as out-of-school human capital investment, while the remaining other expenses are classified as in-school educational investment, offering a clear distinction between supplementary and core educational spending. All the above education expenditure variables are transformed into their logarithmic forms.

With regard to parenting styles, we follow the approach of Doepke & Zilibotti (2017) by constructing two indices: the demandingness index and the responsiveness index, to measure different dimensions of parenting behavior. The demandingness index, derived from five key indicators, evaluates parental behavioral expectations and enforcement strategies, including academic performance expectations, homework supervision and checking, as well as TV watching time and content restrictions. Conversely, the responsiveness index, constructed from five items, measures parental warmth and emotional support, manifested through sacrifices for academic support, constructive discussions on, independent thinking encouragement, rationale explanations for requests, and enjoyment of parent-child conversations. Both indices are standardized within the CFPS dataset to ensure longitudinal comparability across survey waves.

Control variables

This study primarily focuses on the following individual and household characteristics to select control variables, such as the children’s gender, ethnicity, whether children reside in an urban area, birth year, birth weight, and gestational age. Additionally, parental characteristics such as maternal or fraternal years of schooling are also included. Table 1 presents the differences in individual and household characteristics between multidimensionally deprived children and non-deprived children.

Table 1 Descriptive Statistics.
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Identification strategy

We use pooled cross-sectional data from the 2010–2020 waves of the CFPS to test the impact of multidimensional deprivation on children’s cognitive ability. To examine the short-term effects, the model is specified as follows:

$${{cog}}_{{ia}}={\beta }_{0}+{\beta }_{1}{{pov}}_{{ia}}+\varphi {X}_{{ia}}+{\varphi }_{j}+{\sigma }_{s}+{\delta }_{b}+{\varepsilon }_{i}$$
(1)

In the above model, \({{cog}}_{{ia}}\) represents cognitive ability level of child i at age a, and \({{pov}}_{{ia}}\) denotes the multidimensional deprivation status of child i at the same age. \({X}_{{ia}}\) is a vector including a set of control variables that may affect children’s cognitive ability. \({\varphi }_{j}\) represents province fixed effect, which account for common regional factors that may influence all children’s cognitive development. \({\sigma }_{s}\) denotes survey year fixed effect, included to eliminate potential common trend generated by survey time. \({\delta }_{b}\) captures birth cohort fixed effect, which control for variations associated with children’s birth cohorts. \({\varepsilon }_{i}\) is the random error term. Given that children in the same province may share similar growth environments, we cluster standard errors at the provincial level to allow for intra-province correlation in the error terms.

Then, we further introduce the interaction term between multidimensional deprivation and family parenting quality in model 1 to examine mitigation strategies for the impact of multidimensional deprivation on children’s cognitive development, with other model settings remaining unchanged.

To further examine whether multidimensional deprivation has a cumulative effect on children’s cognitive development, we investigate the impact of deprivation experienced during early childhood (ages 2–6) on cognitive outcomes during later childhood and adolescence (ages 7–15). The model is specified as follows:

$${{cog}}_{i}^{7-15}={\beta }_{0}+{\beta }_{1}^{2-6}{{pov}}_{i}^{2-6}+\varphi {X}_{i}^{2-6}+{\alpha }_{j}+{\sigma }_{s}+{\delta }_{b}+{\varepsilon }_{i}$$
(2)

In the above model, \({{cog}}_{i}^{7-15}\) denotes the cognitive ability of child i during the ages of 7–15, and \({{pov}}_{i}^{2-6}\) represents the multidimensional deprivation status during early childhood (ages 2–6). Given that a child’s deprivation status may vary across different years within this age range, we construct a measure based on the proportion of years in which the child experienced multidimensional deprivation between ages 2 and 6, using information collected across multiple CFPS waves. This proportion is calculated as shown in Equation (4):

$${{pov}}_{i}^{2-6}=\frac{1}{{N}_{i}^{2-6}}* \mathop{\sum }\limits_{a=2}^{6}{{pov}}_{{ia}}$$
(3)

In the above equation, \({N}_{i}^{2-6}\) represents the number of survey rounds in which child i was observed between the ages of 2 and 6, and \({{pov}}_{{ia}}\) indicates the multidimensional deprivation status of child i at age a. For example, if a child appears in the data twice during this period (at ages 2 and 4, so \({N}_{i}^{2-6}\) = 2) and he or she experiences multidimensional deprivation only at age 2, then \({{pov}}_{i}^{2-6}\) would take the value of 1/2.

Empirical Results

Incidence of deprivation in each dimension

As shown in Table 2, in addition to deprivation in terms of family income, children also experience varying aspects of deprivation across other dimensions. In fact, incidence of deprivation in certain indicators—such as father absence—are even higher than that of income deprivation. This demonstrates that the measurement of children’s multidimensional deprivation cannot be limited to economic dimension only; it must also include dimensions such as education, health, protection, and nutrition. These findings underscore methodological advantage of identifying children’s multidimensional deprivation framed by The United Nations Convention on the Rights of the Child. Compared to the single variable of household income, this approach provides a more comprehensive understanding of children’s well-being.

Table 2 Multidimensional Deprivation Dimensions/Indicators/Deprivation Threshold for Children.
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Multidimensional deprivation and child cognitive development

Table 3 presents the main results of the relationship of between multidimensional deprivation and children’s cognitive ability. In Column (1), we do not include any control variables and find a significant negative correlation between multidimensional deprivation and children’s cognitive ability. In Column (2), after adding individual and household control variables, the coefficient decreases in magnitude but remains statistically significant at the 1% level. In Column (3), we further control for a set of fixed effects, and the coefficient continues to decline. Specifically, the cognitive ability of children experiencing multidimensional deprivation is 0.098 standard deviations lower than that of non-deprived children.

Table 3 Impact of Multidimensional Deprivation on Children’s Cognitive ability Development.
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Unlike adults, who possess independent behavioral capacities, children are often in a passive state of acceptance when facing the impact of deprivation due to their physiological vulnerability and environmental dependency. Moreover, childhood is a critical period for the development of cognitive ability, which makes the negative effects of multidimensional deprivation on children’s cognitive ability potentially more severe than those on adults. Considering that the development of cognitive ability is essential for individual survival and constitutes a key component of children’s human capital, focusing on multidimensional deprived children and providing measure to enhance their cognitive development could promote high-quality population growth globally. This effort holds significant practical value for mitigating the loss of human capital among children in multidimensional deprivation and advancing high-quality economic growth in various countries.

When comparing the results with estimates from other countries internationally, we find that it is lower than the results obtained in those studies (Dickerson and Popli 2016). The main reason for this difference is that the impact of multidimensional deprivation on children’s cognitive ability is not linear. Specifically, as children grow, the negative effect of multidimensional deprivation on cognitive ability tends to diminish. Moreover, we conduct a future income projection based on this underestimation. Previous studies have found that for each one standard deviation increase in students’ cognitive ability, their future income will rise by 10%-15% (Murnane et al. 2000; Lazear 2003; Mulligan 1999). Using the lower bound of 10% and based on China’s per capita income and bank interest rates, we estimate that the income loss for children experiencing one year of multidimensional deprivation is 5121.28 USD. The specific calculation method is as follows: Per capita income in China in 2023 is 39220 yuan per person, and the fixed deposit interest rate at the Bank of China is 2.25%. Assuming an individual enters the labor market at the age of 22 after graduating from university and works until age of 60, with a total working span of 38 yearsFootnote 2. Finally, based on an exchange rate of 1 RMB = 0.1372 USD, we calculate the amount to be 5121.28 USD.

We further compared this finding with the effects of government-led educational interventions documented in prior studies, revealing that well-designed policy interventions can effectively compensate for the negative impact of multidimensional deprivation on children’s cognitive ability. For example, Duncan & Magnuson (2013) synthesized 84 educational programs, finding they improved participants’ cognitive ability by 0.35 standard deviations on average upon completion. Bianchi et al. (2022) demonstrated that “Modern Distance Education Program in Rural China” significantly enhanced students’ cognitive ability by 0.20 standard deviations.

Multidimensional deprivation may negatively impact children’s cognitive ability through two primary mechanisms. First, the stress model indicates that compared to non-deprived children, multidimensionally deprived children often reside in poorer housing environments where they are more exposed to polluted air, traffic, or industrial waste areas (Clark et al. 2014). These adverse conditions can induce physiological and emotional stress, thereby impairing cognitive development (Anderson 2018; Evans 2004). Simultaneously, families facing multidimensional deprivation often experience significant life pressures, resulting in insufficient parental time and financial investment in children, which further hinders cognitive growth (Orth 2018). Second, the culture of poverty model suggests that socio-environmental norms critically influence child development (Chetty et al. 2016). Since multidimensionally deprived children live in marginalized environments, they may adopt inappropriate behaviors or values to adapt (Akfirat et al. 2016; Cordasco 1967), leading to poorer self-control, reduced delayed gratification capacity, and heightened feelings of helplessness and inferiority—all of which detrimentally affect cognitive development (Sharkey and Elwert 2011).

Further, we examine how deprivation in each specific dimension affects children’s cognitive ability, and the results are displayed in the Fig. 3. It is evident that deprivation in the education and survival dimensions exerts a significant negative impact on children’s cognition, whereas deprivation in other dimensions has a comparatively minor effect.

Fig. 3
Fig. 3
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Effects of Dimensional Deprivations on Children’s Cognitive Ability.

The primary reasons are as follows: on the one hand, school education is systematic: beyond teaching basic literacy and numeracy, it also emphasizes training in logical thinking and hands-on skills, all of which effectively enhance children’s cognitive ability (Husén and Tuijnman 1991). A large body of empirical research shows that every stage of education can markedly foster students’ cognitive development (Bietenbeck et al. 2019; Dean and Jayachandran 2020; Xiao et al. 2017), which is why most countries attach great importance to education’s role within the national system. On the other hand, the survival dimension represents the most fundamental level of material well-being. When deprivation occurs in this dimension, children may suffer considerable psychological stress stemming from feelings of inferiority and social exclusion, while their parents’ attention often shifts to meeting basic material needs, neglecting home-based education. Consequently, children receive insufficient linguistic and cognitive stimulation, impeding the formation and accumulation of cognitive ability. Deprivation in the survival dimension closely mirrors findings from traditional studies that identify children’s deprivation purely through the economic dimension, once again corroborating detrimental effect of economic deprivation on children’s cognitive ability.

It should be noted that non-significant effects of other deprivation dimensions on children’s cognitive ability may be due to two factors: First, the number of children deprived in any single dimension is too small, resulting in insufficient statistical power; Second, this model focuses on immediate impacts, whereas adverse effects of these deprivations might require a longer time window to manifest.

Robustness check

To test the robustness of estimated effect of multidimensional deprivation on children’s cognitive ability, we implement several robustness checks. First, Multidimensional deprivation may not be randomly distributed among children with different characteristics. For instance, children from families with more years of parental education are more likely to live in better household conditions, and their parents may also be more knowledgeable about how to create a healthy environment for their children’s growth, thereby reducing the likelihood of these children falling into multidimensional deprivation. Similarly, birth weight and gestational age are directly related to a child’s current health status and are also significantly associated with family background. Since these factors can affect the probability of children experiencing multidimensional deprivation, we conduct matching based on child and family characteristics that may influence the likelihood of falling into multidimensional deprivation. Employing both kernel matching and radius matching, we then ran weighted regressions on the successfully matched samples. The estimates are reported in columns (1) and (2) of Table 4. As shown, the coefficients remain significantly negative under both matching techniques, confirming that our baseline results are robust.

Table 4 Robustness Check.
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Second, to test whether our baseline results are affected by omitted variables, we follow Oster’s approach to conduct an omitted-variable test (Oster 2019). The idea hinges on the information conveyed by the model’s R²: if the coefficient on the key explanatory variable remains stable after adding new controls, the model is unlikely to suffer from omitted-variable bias. Specifically, the bias-adjusted coefficient β* depends on two parameters—δ and Rmax—where δ is the proportional selection parameter that measure the relative explanatory power of unobservable versus observable variables, and Rmax is the maximum goodness of fit the model would reach if it incorporated all unobserved factors. Following Oster’s recommendation, we set Rmax = 1.3 R and proceeded as follows to assess robustness: (1) set δ = 1 and raise the model’s R² to Rmax = 1.3 R, then check whether the resulting interval for β includes zero; if zero is excluded, the estimate passes the robustness test; (2) keep Rmax defined as 1.3 times current regression’s R², calculate value of δ that would drive β to zero, and if |δ | ≥ 1, the baseline estimate is deemed robust. The first test produced an interval of [-0.0980, -0.2508], and the second yielded a δ value of 1.92; both tests pass validation checks, indicating that the baseline regression results in this study are minimally affected by omitted-variable bias.

Third, k-value serves as the critical identification threshold for multidimensional deprivation. Although this study follows prior research in setting it at 0.3, this approach remains somewhat subjective. To mitigate potential bias from this subjectivity in our main regression results, we recalibrated k-value to 0.2 and 0.4 for re-identifying child relative deprivation and re-estimated Eq. (1). The outcomes are illustrated in column (3) and (4) of Table 4. As shown, regardless of how k is adjusted, the coefficients remain significantly negative, demonstrating robustness of our baseline results.

Fourth, although A-F method is a widely adopted approach for identifying individual poverty in the field, it may still face challenges related to equal weighting. To address this, we replace multidimensional deprivation identification method with the counting approach and identify children experiencing deprivation in three or more indicators as multidimensionally deprived. The results presented in column (5) of Table 4. It shows significantly negative coefficients. This demonstrates that our baseline result is not affected by the choice of poverty identification methodology.

Multidimensional deprivation and long-term cognitive development in children

Building on our earlier finding that multidimensional deprivation exerts a significant negative effect on children’s cognitive ability, we next ask whether this impact is cumulative: does experiencing deprivation before school age impose an even greater penalty on later cognitive development? Answering these questions deepens our understanding of the cognitive trajectories of deprived children and provides evidence for early identification and intervention. Accordingly, we use Eq. (2) to examine the long-term consequences of multidimensional deprivation, with the results reported in Table 5. Even without any controls, the coefficient is significantly negative; after sequentially adding a full set of controls, the coefficient shrinks but remains significantly negative, indicating that early-childhood deprivation markedly hampers cognitive development. Relative to the contemporaneous effect estimated earlier, this coefficient is nearly 1.7 times as large, indicating that an individual could face a income loss of around 8794 USD. The result confirming that the impact of deprivation is cumulative: falling into multidimensional deprivation before entering school has a more severe long-run effect on cognitive ability.

Table 5 Impact of Multidimensional Deprivation on Children’s Long-term Cognitive Development.
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This finding aligns with the existing literature. Life-course theory, centered on capability formation, argues that the timing of an event often shapes an individual’s developmental trajectory more profoundly than the event itself (Elder 1998). Early childhood, as the starting point of the life course, is a critical and sensitive period for human-capital formation, and its influence extends into the school years, subsequently affecting learning opportunities, academic achievement, and behavioral outcomes in adolescence (Heckman 2006). For example, in China, children at the age of 15 take the junior high school academic proficiency examination, which determines whether they can successfully enter an ordinary senior high school. According to the Chinese education system, only students whose exam scores rank in the top 50% are eligible to attend ordinary senior high schools. As a result, students in the bottom 50% are unable to access high-quality general education curricula, which may further have adverse effects on their cognitive development.

Therefore, it becomes evident that as children grow older, the long-term effects of multidimensional deprivation on cognitive ability may manifest in a pronounced gradient pattern. Put differently, the initial disadvantages in cognitive ability arising from multidimensional deprivation are likely to be progressively magnified by the reduced opportunities to access high-quality resources in later stages, thereby further widening the cognitive gap between deprived children and their peers.

From the perspective of psychological, Prior studies further show that early poverty accelerates cognitive decline (Oi and Haas 2019; Yang and Wang 2020). Cognitive neuroscience research demonstrates that multidimensional deprivation impacts children’s brain development from early childhood. Infants from impoverished households exhibit slower gray matter growth rates compared to those from resource-rich environments, ultimately impairing neuroregulatory capacities for behavioral and emotional control—including working memory and executive functions (Shonkoff et al. 2012). Moreover, some studies have pointed out that such effects are often irreversible; exposure to multidimensional deprivation during childhood can permanently alter the structure and function of bodily systems, such as the size of the hippocampus (Ben-Shlomo, Cooper, and Kuh 2016; Daviglus et al. 2010). Hence, particular attention should be given to children in early childhood.

Strategies for improving cognitive ability of multidimensionally deprived children

When children fall into multidimensional deprivation, what strategies can be adopted to effectively mitigate its negative impact on cognitive ability? We introduce interaction term to examine whether family parenting quality moderates relationship between multidimensional deprivation and children’s cognitive ability. As noted earlier, we measure parenting quality from three angles: parental educational attitudes, human-capital investment, and parenting styles. Specifically, parental educational attitudes are proxied by parents’ educational expectations; human-capital investment is captured by total educational spending per child, in-school expenditures, and out-of-school expenditures; and parenting styles is represented by the demandingness index and responsiveness index. The results are presented in Table 6.

Table 6 Parenting Quality and Cognitive Development of Multidimensionally Deprived Children.
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Column (1) of Table 6 shows that the interaction term is significantly positive, indicating that higher parental educational expectations can markedly enhance the cognitive ability of children facing multidimensional deprivation. Although such expectations generally rise with family socioeconomic status, some parents in deprived households understand that, lacking strong social networks, education is the only viable path for their children to change the family’s situation and achieve upward intergenerational mobility. Therefore, they raise educational expectations and actively support their children’s schooling, which in turn promotes the development of the children’s cognitive ability.

Column (2) of Table 6 shows that the interaction term is significantly positive, indicating that total individual education spending can mitigate the negative impact of multidimensional deprivation on children’s cognitive ability; Columns (3) and (4) report the results for in-school and out-of-school education expenditures, respectively, and both interaction coefficients are likewise significantly positive, demonstrating that, for children experiencing multidimensional deprivation, spending both inside and outside school improves their cognitive development. Existing research has established that human-capital investment plays a decisive role in children’s future outcomes and that its effects vary across developmental stages—generally, the earlier the investment, the more beneficial it is for the child. Our study confirms the applicability of this conclusion to children in multidimensional deprivation, highlighting that human-capital investment can still significantly enhance cognitive ability even under conditions of deprivation.

Columns (5) and (6) of Table 6 report the regressions using the demandingness index and the responsiveness index, respectively. These results show that, after controlling for other variables, higher levels of parental demandingness and responsiveness each attenuate the negative effect of multidimensional deprivation on children’s cognitive ability. Specifically, a higher demandingness index means that parents set clear behavioral norms for their children, helping them develop good study habits and thereby offsetting the hindering effect of deprivation on cognitive development. Meanwhile, a higher responsiveness index indicates that parents can promptly recognize and respond to their children’s needs; this emotional support not only helps solve practical problems in daily life and schoolwork but also provides ample linguistic and cognitive stimulation, further fostering children’s cognitive growth.

Conclusion

Based on Sen’s theory on poverty, this study utilizes A-F method to construct and compute multidimensional deprivation from five dimensions: education, health, survival and development, protection, and nutrition. Fixed effects model is to estimate the impact of multidimensional deprivation on children’s cognitive ability. Main results of this research are summarized as follows.

First, children experience varying degrees of deprivation across multiple dimensions. Thus, identifying child relative deprivation through a multidimensional framework—rather than relying solely on the single dimension of economic income—is methodologically justified. multidimensional deprivation negatively impacts children’s cognitive ability. Children multidimensionally deprived scored 0.098 standard deviations lower, which is robust to arrange of sensitivity tests. Based on the relationship between children’s cognitive ability and their future income, we estimate that this result will lead to an income loss of 5121.28 USD per individual.

Second, the impact of multidimensional deprivation on children’s cognitive ability demonstrates a cumulative nature, with preschool-age deprivation exerting more pronounced effects on future outcomes. Specifically, children experiencing multidimensional deprivation between ages 2 and 6 exhibit cognitive ability scores at ages 7–15 that are on average 0.171 standard deviations lower than their non-deprived peers.

Third, family parenting quality moderates the impact of multidimensional deprivation on children’s cognitive ability: parental educational attitudes, human-capital investment, and parenting styles all significantly enhance cognitive development. Higher educational aspirations, greater in-school and out-of-school human-capital spending, and more scientific, interaction-rich parenting practices effectively raise the cognitive ability of children in multidimensional deprivation, providing empirical evidence for the importance of improving parenting skills among these children’s families.

Children represent the future of a nation. Children living in a state of multidimensional deprivation not only face challenges to their physical and mental development but also contribute to future losses in the human capital necessary for national economic and social growth. Addressing the cognitive development of multidimensionally deprived children and enhancing their cognitive ability are critical tasks for child poverty alleviation efforts worldwide. Policy implication of this study for governments and educational organizations are drawn from main findings of this paper.

First, governments should establish a scientific indicator system for identifying children experiencing relative deprivation. Previous approaches relying solely on household income have significant limitations, as they often overlook children deprived in other dimensions, thereby hindering targeted interventions for child development. Moreover, governments should prioritize preschool children—our findings reveal that the impact of multidimensional deprivation on cognitive ability exhibits cumulative characteristics, with early childhood deprivation causing disproportionately greater harm to subsequent cognitive development. Therefore, region-specific initiatives targeting preschoolers must be implemented, focusing on supporting child development in relatively impoverished areas to ensure timely cognitive remediation for multidimensionally deprived children.

Second, family-education guidance services should be strengthened, with a particular focus on raising parenting literacy of parents in multidimensionally deprived households. Family is children’s first school and is critical to their development, and our study confirms that high-quality parenting markedly enhances the cognitive development of children facing multidimensional deprivation. Accordingly, governments and communities can institutionalize “parent classes”, delivering child-parenting knowledge and parent-child interaction demonstrations through home visits and online courses. For instance, the United States has established a key curriculum framework for family education and developed targeted parenting guidance programs tailored to diverse family needs. These initiatives encourage parents’ sustained involvement in child development through comprehensive family education plans. For especially disadvantaged families, local authorities can integrate charitable organizations and volunteer resources to offer one-to-one, companionship-styles assistance, thereby improving home environment in which multidimensionally deprived children grow up.