Dynamic Feedbacks Among Physical Activity, Health Capital, and Household Financial Resilience: A Systems Analysis Using China Family Panel Studies

Abstract

Physical inactivity and household financial fragility are often studied separately, yet households may respond to health and financial shocks through interrelated behavioral, health, and financial processes. This study examines whether physical activity, health capital, and household financial resilience are dynamically associated in China. Using five waves of the China Family Panel Studies, we construct a household-wave panel and multidimensional indices of health capital and financial resilience. We apply lagged household fixed-effects models, dynamic mediation analysis, and panel vector autoregression with impulse response functions and forecast error variance decomposition. The results indicate that physical activity is positively associated with subsequent health capital, health capital positively predicts subsequent household financial resilience, and financial resilience has a smaller but statistically significant association with later physical activity. The mediation results are consistent with health capital serving as a partial transmission channel between physical activity and financial resilience. The PVAR results show persistent cross-variable responses, suggesting modest dynamic interdependence among the three components rather than definitive causal evidence of a strong self-reinforcing system. Heterogeneity analyses suggest that these associations are more pronounced among low-income, older-head, and chronic-risk households. These findings extend health-capital and household finance research by showing that health behavior and financial resilience can be examined as jointly evolving household-level processes. The results suggest that integrated approaches to physical activity promotion and household financial protection may be worth further policy experimentation and evaluation, especially for vulnerable households.

1. Introduction

Physical inactivity has become an important public health and household welfare issue. A large body of evidence shows that insufficient physical activity increases the risks of chronic disease, premature mortality, and health-care costs [1,2,3]. These health consequences may also affect households beyond the health domain. When poor health reduces work capacity, increases medical expenditure, or weakens saving capacity, it can undermine the household’s ability to withstand economic shocks. Therefore, physical activity may be relevant not only to individual health but also to household financial resilience. The health-capital framework provides a useful foundation for understanding this relationship. In Grossman’s model, health is a durable capital stock that can be accumulated through time and resource investment [4]. Physical activity can therefore be viewed as a non-medical investment in health capital. At the household level, stronger health capital may reduce medical expenditure pressure, stabilize labor supply, and improve the capacity to maintain financial buffers. Financial resilience, in turn, refers to a household’s ability to absorb, adapt to, and recover from financial shocks [5,6,7]. This suggests that physical activity, health capital, and financial resilience may be closely connected.

Recent studies have begun to examine the connection between physical exercise and household financial outcomes. Huang et al. [8] provide CFPS-based evidence that physical activity is associated with lower household financial vulnerability and further discuss health and social networks as potential channels. He et al. [9] examine a different financial outcome, showing that physical exercise is related to household risky asset allocation through health and future confidence. These studies are important because they establish that physical activity may be relevant to household financial behavior and financial vulnerability. However, their primary empirical focus remains one-directional: physical activity is treated mainly as an antecedent of household financial outcomes. They do not explicitly model physical activity, health capital, and household financial resilience as jointly evolving system components, nor do they examine whether financial resilience may feed back into subsequent health behavior.

Building on this emerging literature, the present study does not claim to be the first to link physical activity with household finance. Instead, its incremental contribution is to examine this relationship from a dynamic systems perspective. We shift the financial outcome from financial vulnerability or risky asset allocation to multidimensional household financial resilience, conceptualized as a household’s capacity to absorb, adapt to, and recover from financial shocks. We also distinguish health capital from physical activity and treat it as an intermediate household state variable through which health behavior may be connected to later financial resilience. Empirically, we combine lagged household fixed-effects models, dynamic mediation analysis, and panel vector autoregression (PVAR). The PVAR framework is used not as definitive causal proof of a feedback loop, but as a tool for assessing whether the longitudinal associations among physical activity, health capital, and household financial resilience are consistent with dynamic interdependence among household system components [10,11,12].

Accordingly, this study makes three more specific contributions. First, it extends recent research on physical activity and household finance by moving beyond one-directional financial-outcome models and examining whether health behavior, health capital, and household financial resilience are dynamically interrelated. Second, it shifts the financial construct from static financial vulnerability to multidimensional household financial resilience, capturing income–expenditure margin, liquidity buffer, debt burden, medical expenditure burden, and risk-management capacity. Third, it provides feedback-consistent evidence from PVAR impulse responses and forecast error variance decomposition, while interpreting this evidence cautiously as dynamic association rather than strong causal confirmation. In this way, the study offers a systems-oriented extension of the emerging literature on physical activity and household finance.

2. Literature Review and Hypothesis

2.1. A Systems Perspective on Physical Activity, Health Capital, and Household Financial Resilience

Households are not merely passive units exposed to health and financial shocks. Rather, they can be understood as adaptive socio-economic systems in which health behavior, health capital, labor capacity, consumption, saving, debt management, and risk-coping resources jointly evolve over time. A systems perspective is particularly appropriate for this study because the relationship among physical activity, health capital, and household financial resilience is unlikely to be strictly one-directional. Physical activity may accumulate health capital; health capital may strengthen household financial resilience by stabilizing income and reducing health-related expenditure shocks; and stronger financial resilience may, in turn, enable households to sustain health-promoting behaviors. This recursive structure suggests that the three components may form a dynamic feedback system rather than a set of isolated associations. The theoretical foundation of this study is rooted in the health-capital model. Grossman conceptualizes health as a durable capital stock that produces healthy time and can be accumulated through individual investments [4]. In this framework, health is not only a consumption good that directly increases utility but also an investment good that affects productivity, time allocation, and future economic opportunities. Subsequent health-economic research further emphasizes the reciprocal relationship between health and economic status. Smith argues that health and economic resources are jointly determined, with health influencing income and wealth while economic resources shape the ability to maintain health [13]. This dual relationship is essential for understanding why physical activity, health capital, and household financial resilience should be modeled as interdependent components.

The notion of financial resilience also fits naturally within a systems framework. Financial resilience refers to the capacity of individuals or households to absorb, adapt to, and recover from adverse financial shocks. It is broader than the absence of financial distress because it captures liquidity buffers, resource access, financial capability, risk management, and adaptive capacity [5,7,14]. Related studies on financial vulnerability and financial fragility show that households may face financial distress when income shocks, medical expenditure shocks, debt burden, or insufficient liquidity undermine their ability to maintain consumption and meet unexpected expenses [6,15,16,17]. Therefore, household financial resilience can be viewed as a dynamic state variable that reflects how well households maintain financial stability under uncertainty.

A systems perspective also requires attention to feedback, delay, and mutual endogeneity. Complex social and health systems often generate outcomes through reinforcing or balancing feedback loops rather than through simple linear causation [18]. In empirical terms, this implies that physical activity, health capital, and household financial resilience should not be treated only as exogenous predictor, mediator, and outcome, respectively. Instead, each may influence the future trajectory of the others. This logic is consistent with dynamic panel and panel vector autoregression approaches, which are designed to analyze interdependent variables over time [10,11]. Building on this view, this study develops a dynamic framework in which physical activity, health capital, and household financial resilience are mutually connected state variables within the household system.

2.2. Physical Activity and Health Capital

Physical activity can be understood as a behavioral investment in health capital. Unlike medical expenditure, which often responds to illness after health has deteriorated, physical activity is a preventive and maintenance-oriented form of health investment. Regular physical activity can improve cardiovascular function, metabolic health, musculoskeletal capacity, weight management, and psychological well-being, thereby slowing the depreciation of health capital and improving the stock of healthy time. The existing medical and public health literature provides strong evidence that physical activity is associated with lower risks of chronic disease, premature mortality, and mental health problems [1,19,20,21].

The health benefits of physical activity are relevant to the concept of health capital for three reasons. First, physical activity contributes to physiological functioning. Evidence from large-scale epidemiological and meta-analytic studies indicates that physical inactivity is associated with major non-communicable diseases, whereas higher levels of non-occupational physical activity are associated with lower risks of cardiovascular disease, cancer, and all-cause mortality [1,20]. Second, physical activity supports mental health. An overview of systematic reviews shows that physical activity interventions are effective in improving symptoms of depression, anxiety, and psychological distress in adult populations [21]. Third, physical activity has economic significance because inactivity imposes substantial health-care and productivity costs on society [2,22]. These findings suggest that physical activity should be interpreted not simply as leisure consumption but as a long-term investment that preserves functional ability and reduces future health risks.

Recent global evidence further highlights the importance of physical activity as a public health and economic issue. Strain et al. document persistent and rising levels of insufficient physical activity among adults worldwide from 2000 to 2022 [3]. This trend is important for household-level research because insufficient physical activity may accelerate health-capital depreciation, increase disease risk, and expose households to greater medical and income-related shocks. In the household context, the decision to participate in physical activity may therefore influence not only individual health but also the longer-term stability of household economic life. Based on the health-capital framework, physical activity is expected to improve subsequent health capital through both physical and psychological channels. Because the benefits of physical activity accumulate over time, the relationship should be examined dynamically rather than only contemporaneously. Accordingly, this study proposes the following hypothesis:

Hypothesis 1 (H1).

Physical activity positively predicts subsequent health capital.

2.3. Health Capital and Household Financial Resilience

Health capital is a central channel through which individual behavior may affect household financial outcomes. A household with higher health capital is more likely to maintain stable labor supply, reduce health-related expenditure shocks, and preserve financial buffers. Conversely, poor health can reduce earnings, increase medical spending, limit credit access, and force households to draw down savings or accumulate debt. Thus, health capital is not merely a health outcome; it is also a productive asset that shapes the household’s capacity to withstand financial pressure. The economic literature has long emphasized the two-way relationship between health and economic status. Smith argues that good health and economic resources reinforce one another, while health deterioration can contribute to weaker income and wealth accumulation [13]. Medical expenditure is also an important motive for household saving, particularly when households face uncertainty about future health shocks [23]. Evidence from hospital admissions further shows that acute health shocks can generate substantial economic consequences, including reduced earnings, higher out-of-pocket medical spending, unpaid medical bills, bankruptcy risk, and changes in credit access [24]. These studies indicate that health shocks may weaken household financial resilience through both income and expenditure channels.

The literature on financial vulnerability provides additional support for this argument. Household financial vulnerability is often measured by whether households have sufficient liquidity, solvency, or income–expenditure margins to handle unexpected shocks [15,16]. More recent studies explicitly incorporate income and medical expenditure shocks into the measurement of household financial vulnerability, emphasizing that health-related expenses are a major source of household financial distress [6]. Under COVID-19 and other macroeconomic shocks, households with reduced income and limited financial buffers were particularly vulnerable to financial instability [17]. These studies imply that health capital can strengthen financial resilience by reducing the probability and severity of health-related financial shocks. Health capital may improve household financial resilience through three mechanisms. First, healthier household members are more likely to maintain employment, work intensity, and stable income. Second, better health may reduce the need for costly medical treatment and prevent medical expenditure from crowding out savings and other essential consumption. Third, health capital may improve household planning capacity by reducing uncertainty and allowing households to allocate resources toward savings, insurance, and long-term investments. In this sense, health capital is a bridge between individual health behavior and household financial resilience.

Therefore, this study proposes the following:

Hypothesis 2 (H2).

Health capital positively predicts subsequent household financial resilience.

The preceding discussion also suggests an indirect pathway from physical activity to household financial resilience. Physical activity is expected to improve health capital, and stronger health capital is expected to enhance financial resilience. Recent CFPS-based evidence indicates that physical activity can reduce household financial vulnerability and that health is one of the channels linking physical activity to household financial stability [8]. However, existing studies mainly examine a one-directional relationship between physical activity and financial vulnerability. They do not fully investigate whether health capital serves as a dynamic state variable through which physical activity gradually improves household financial resilience. Accordingly, this study further proposes the following:

Hypothesis 3 (H3).

Physical activity enhances subsequent household financial resilience through the accumulation of health capital.

2.4. Financial Resilience and Feedback to Physical Activity

While physical activity and health capital may improve financial resilience, the reverse pathway is also theoretically important. Household financial resilience may shape future physical activity by relaxing resource constraints, reducing stress, and increasing the household’s capacity to invest in health-promoting behaviors. In this sense, financial resilience should not be regarded only as an outcome of health behavior; it may also be a driver of subsequent health investment.

This reverse pathway also means that the proposed feedback pattern does not necessarily begin with physical activity. For some households, financial resilience may be the condition that makes health investment possible in the first place. Households with adequate income, liquidity, time flexibility, and psychological security may be better able to allocate resources to regular physical activity, preventive care, and healthier lifestyles. Conversely, households below a minimum resource threshold may find it difficult to maintain physical activity even when they recognize its health benefits. In this sense, financial resilience may function as an enabling condition for health behavior rather than merely as an outcome of prior health capital. This possibility is especially relevant for low-income or financially constrained households, for whom immediate consumption needs and unstable work arrangements may crowd out preventive health investment.

Financial resilience provides households with the material and psychological resources needed to sustain physical activity. Households with stronger liquidity buffers, lower debt pressure, better insurance coverage, and greater financial capability are more likely to have the time and resources necessary for regular exercise, preventive health care, and healthy lifestyles. In contrast, financially vulnerable households may prioritize immediate survival needs, reduce leisure and health-related expenditures, and postpone preventive health investments. The financial resilience literature emphasizes that liquid assets, financial literacy, and risk-management capacity allow households to withstand shocks and recover from disturbances [5,7,14]. These capacities may also support continued investment in health behavior.

This feedback pathway is especially relevant in the Chinese household context. Recent evidence shows that physical exercise can influence household financial decisions, including risky asset allocation, partly through improved health and future confidence [9]. Another CFPS-based study finds that physical activity reduces household financial vulnerability through health and social networks [8]. These studies suggest that health behavior and household finance are connected, but they mainly emphasize how physical activity affects financial outcomes. The present study extends this literature by proposing that stronger financial resilience may feed back into subsequent physical activity, creating a reciprocal relationship between health behavior and household financial conditions. The feedback from financial resilience to physical activity can operate through three channels. First, financial resources can reduce the direct cost constraints associated with exercise, including transportation, sports equipment, fitness facilities, and health-related consumption. Second, financial resilience may reduce time pressure by allowing households to avoid excessive labor supply or unstable work arrangements that crowd out physical activity. Third, financial resilience may improve future expectations and psychological security, making households more willing to invest in long-term health rather than focus solely on short-term financial survival. Accordingly, this study proposes the following:

Hypothesis 4 (H4).

Household financial resilience positively predicts subsequent physical activity.

2.5. Dynamic Feedback Loop and Research Hypotheses

The above hypotheses imply a possible dynamic feedback pattern among physical activity, health capital, and household financial resilience. For expositional purposes, this pattern can be summarized as follows:

$$\begin{array}{cc}\hfill \mathrm{Physical}{\mathrm{Activity}}_t& \to \mathrm{Health}{\mathrm{Capital}}_{t+1}\hfill \\ & \to \mathrm{Household}\mathrm{Financial}{\mathrm{Resilience}}_{t+2}\hfill \\ & \to \mathrm{Physical}{\mathrm{Activity}}_{t+3}.\hfill \end{array}$$

This representation should be interpreted as a theoretical organizing framework rather than as a deterministic causal sequence. In this framework, physical activity may contribute to the accumulation of health capital; health capital may be associated with stronger household financial resilience by stabilizing income and reducing medical expenditure pressure; and stronger financial resilience may enable households to sustain future physical activity and health investment. Over time, these lagged associations may create a mutually reinforcing tendency, although the strength of such reinforcement is an empirical question. Figure 1 illustrates the theoretical framework of this dynamic feedback pattern. The arrows denote hypothesized lagged associations rather than definitive causal directions.

The arrows should therefore not be read as implying that physical activity is always the initial cause of the system. In practice, the process may also be initiated by household financial resilience when sufficient resources, time, and security enable investment in physical activity and health maintenance. This bidirectional interpretation is consistent with the view that health and economic resources can mutually shape one another over time.

The same logic also implies the possibility of an adverse feedback pattern. Low physical activity may be followed by faster health-capital depreciation; weakened health capital may be associated with greater medical expenditure pressure and reduced labor income; and declining financial resilience may further restrict the household resources available for physical activity and preventive health investment. Such a negative pattern may be particularly relevant for low-income households, households with older heads, or households exposed to chronic disease and medical expenditure shocks.

This dynamic systems view distinguishes the present study from prior research in two ways. First, prior studies on physical activity and household finance have largely focused on one-directional associations, such as the relationship between physical activity and household financial vulnerability or risky asset allocation [8,9]. Second, financial vulnerability studies have often treated financial distress as a relatively static outcome, although recent work increasingly emphasizes liquidity dynamics, income shocks, and recovery capacity [6,7,17]. By contrast, this study treats physical activity, health capital, and household financial resilience as potentially interrelated components in a dynamic household system.

Empirically, this framework requires a modeling strategy that can accommodate lagged associations and mutual dependence among variables. Panel vector autoregression is useful for this purpose because it allows each system component to respond to its own history and to the past values of other components [10,11]. Therefore, the central theoretical expectation of this study is not that the empirical models can prove a strong self-reinforcing causal system, but that the longitudinal patterns will be consistent with dynamic interdependence among the three household-level components.

Accordingly, this study proposes the final hypothesis:

Hypothesis 5 (H5).

The longitudinal associations among physical activity, health capital, and household financial resilience are consistent with a dynamic feedback pattern.

3. Data and Methods

3.1. Data Source and Sample Construction

This study uses data from the China Family Panel Studies (CFPS), a nationally representative longitudinal survey conducted by the Institute of Social Science Survey of Peking University. The CFPS collects repeated information on individuals, households, and communities, and is designed to support longitudinal research on social, economic, demographic, and health-related processes in China [25,26]. The household is used as the unit of analysis because household financial resilience is determined by family-level income, consumption, assets, debt, medical expenditure, insurance coverage, and access to risk-coping resources.

The empirical sample is constructed from the 2014, 2016, 2018, 2020, and 2022 CFPS waves. The adult questionnaire is linked with the family economic questionnaire by household and survey wave. The physical activity and health-capital variables are measured using information from the household head, while the financial-resilience variables are measured at the household level. This design links the health behavior and health status of the household head to the financial capacity of the household, which is consistent with the theoretical framework of a household-level dynamic system.

The main analytic file is an unbalanced household-wave panel. The sample construction follows four rules. First, households must have valid household identifiers and wave identifiers. Second, the household head must be aged 18 years or above. Third, observations with missing values for the three core system variables, namely physical activity, health capital, and household financial resilience, are excluded. Fourth, households are required to appear in at least two survey waves so that lagged dynamic relationships can be estimated. Nominal monetary variables are converted into real 2014 yuan using province-year consumer price indices, with 2014 as the base year, and winsorized at the 1st and 99th percentiles to reduce the influence of extreme values. Descriptive statistics are calculated using the CFPS household weights. The main regression models are estimated without survey weights because the empirical focus is within-household dynamic change rather than cross-sectional population description. Household fixed effects, wave fixed effects, and province-by-wave fixed effects are included to control for time-invariant household heterogeneity, common macro shocks, and province-specific time-varying conditions. Standard errors are clustered at the household level. Because the CFPS waves used in this study cover five biennial survey rounds, the panel provides repeated household observations but a relatively short time dimension. Therefore, the lagged estimates should be interpreted as short- to medium-run dynamic associations rather than strong evidence of long-run feedback mechanisms.

3.2. Variable Measurement

The empirical analysis contains three core system variables: physical activity, health capital, and household financial resilience. Physical activity is denoted by pa, health capital by hc, and household financial resilience by fri. All variables are coded so that higher values indicate more favorable conditions, except for raw negative components such as debt burden and medical expenditure burden, which are reverse-coded before index construction.

Table 1. Variable definitions.

Name	Role	Definition
core system variables
pa	physical activity	Binary indicator equal to one if the household head participates in physical exercise in the survey wave, and zero otherwise.
pafrq	activity frequency	Ordered measure of physical exercise frequency. This variable is used as an alternative measure of pa in robustness checks.
hc	health capital	Standardized health-capital index constructed from srh, noch, bmi, nodis, and mh. Higher values indicate stronger health capital.
fri	financial resilience	Standardized household financial-resilience index constructed from mgn, liq, debt, med, and risk. Higher values indicate stronger household financial resilience.
components of health capital
srh	self-rated health	Single-item self-rated health measure of the household head. The original scale ranges from 1 = excellent to 5 = poor and is reverse-coded so that higher values indicate better perceived health.
noch	no chronic disease	Indicator equal to one if the household head reports no physician-diagnosed chronic disease, and zero otherwise.
bmi	body mass status	Indicator equal to one if the household head’s body mass index falls within the normal adult range, and zero otherwise.
nodis	no discomfort	Indicator equal to one if the household head reports no recent physical discomfort or activity limitation, and zero otherwise.
mh	mental health	Wave-specific mental-health score constructed from the CFPS mental-health module. The 2014 wave uses six psychological-distress items, whereas the 2016–2022 waves use the common eight-item CES-D subset. Items are coded so that higher values indicate better mental health before aggregation and standardization.
components of household financial resilience
mgn	income margin	Income–expenditure margin, calculated as $(\mathtt{inc}-\mathtt{cons})/\mathtt{cons}$. Higher values indicate stronger current financial buffer.
liq	liquidity buffer	Ratio of liquid financial assets to annual household consumption, calculated as $\mathtt{fin}/\mathtt{cons}$. Higher values indicate stronger short-term liquidity.
debt	debt burden	Ratio of total household liabilities to annual household income, calculated as $\mathtt{loan}/\mathtt{inc}$. This component is reverse-coded when constructing fri.
med	medical burden	Ratio of out-of-pocket medical expenditure to annual household consumption, calculated as $\mathtt{oop}/\mathtt{cons}$. This component is reverse-coded when constructing fri.
risk	risk capacity	Average of three indicators: commercial insurance ownership, financial product holding, and absence of borrowing rejection. Higher values indicate stronger risk-management capacity.
individual-level controls
age	age	Age of the household head.
agesq	age squared	Squared age divided by 100.
male	gender	Indicator equal to one for male household heads, and zero otherwise.
marr	marital status	Indicator equal to one if the household head is married or cohabiting, and zero otherwise.
edu	education	Years of schooling of the household head.
emp	employment	Indicator equal to one if the household head is employed or self-employed, and zero otherwise.
smk	smoking	Indicator equal to one if the household head currently smokes, and zero otherwise.
drk	drinking	Indicator equal to one if the household head currently drinks alcohol, and zero otherwise.
household-level controls
hhsz	household size	Number of household members.
dep	dependency burden	Ratio of children and older adults to total household members.
home	home ownership	Indicator equal to one if the household owns residential property, and zero otherwise.
urb	urban residence	Indicator equal to one for urban households, and zero for rural households.
identifiers and fixed effects
hid	household id	Household identifier used to construct the panel and cluster standard errors.
wave	wave effect	Survey-wave fixed effects capturing common shocks across CFPS waves.
prov	province effect	Province identifier used to construct province-by-wave fixed effects.

Notes: The auxiliary monetary variables are inc for household income, cons for household consumption, fin for liquid financial assets, loan for household liabilities, and oop for out-of-pocket medical expenditure. Monetary variables are measured in real 2014 yuan. Continuous ratios are winsorized at the 1st and 99th percentiles.

summarizes the definitions of the core system variables, index components, control variables, and identifiers used in the empirical analysis.

3.3. Construction of the Health-Capital Index and Household Financial-Resilience Index

The construction of the health-capital index follows the health-capital perspective, in which health is treated as a durable stock that can affect future time allocation, productivity, and economic outcomes [4]. The index hc is constructed from five components: srh, noch, bmi, nodis, and mh. These components capture subjective health, chronic disease status, body mass status, recent physical functioning, and mental health. Each component is coded so that higher values indicate better health and is then standardized to have a mean of zero and a standard deviation of one.

Table 2. Measurement details for health-capital components.

Component	Item Source and Number of Items	Coding	Reliability and Validity Note
srh	Single-item self-rated health question: “How would you rate your health status?”	Original scale ranges from 1 = excellent to 5 = poor. The item is reverse-coded so that higher values indicate better perceived health.	Internal consistency reliability is not applicable because this is a single-item global health measure. The item captures the household head’s overall perceived health status.
noch	Single indicator of physician-diagnosed chronic disease status.	Coded as 1 if the household head reports no chronic disease and 0 otherwise.	This indicator captures the chronic disease dimension of health capital. Internal consistency reliability is not applicable to a binary disease-status indicator.
bmi	Body mass index calculated from reported height and weight.	Coded as 1 if the household head’s BMI falls within the normal adult range and 0 otherwise.	This indicator captures the body mass and physical-risk dimension of health capital. Internal consistency reliability is not applicable to this anthropometric indicator.
nodis	Single indicator of recent physical discomfort or activity limitation.	Coded as 1 if the household head reports no recent physical discomfort or activity limitation and 0 otherwise.	This indicator captures recent physical functioning. Internal consistency reliability is not applicable to a single functional-status indicator.
mh	Wave-specific mental-health items from the CFPS mental-health module. The 2014 wave contains six psychological-distress items, whereas the 2016–2022 waves use the common eight-item CES-D subset.	All items are coded so that higher values indicate better mental health before aggregation and wave standardization.	Cronbach’s $\alpha$ is 0.782 in 2014, 0.814 in 2016, 0.809 in 2018, 0.827 in 2020, and 0.811 in 2022, indicating acceptable-to-good internal consistency across waves.

Notes: CFPS denotes China Family Panel Studies; CES-D denotes Center for Epidemiologic Studies Depression Scale. The health-capital index is constructed as a survey-based multidimensional composite proxy rather than as a measurement-error-free latent construct.

reports the measurement details for the five health-capital components. These indicators are included because they capture complementary dimensions of the household head’s health stock: perceived overall health, chronic disease status, body mass status, recent physical functioning, and mental health. The components differ in measurement form. srh, noch, bmi, and nodis are single-item or binary health-status indicators, so internal consistency reliability is not applicable to these variables. By contrast, mh is a multi-item mental-health score, and its internal consistency is acceptable to good across survey waves. At the same time, the health-capital index should be interpreted as a survey-based multidimensional composite proxy rather than as a measurement-error-free latent construct. Because PCA aggregates observed survey indicators, the resulting index may inherit reporting error, scale differences, and wave-specific measurement variation from its components, in addition to uncertainty from the PCA aggregation itself. This measurement uncertainty is one reason why the empirical results are interpreted cautiously.

Principal component analysis is used to aggregate the standardized health components into a single index. PCA is appropriate because it extracts the dominant common variation from multiple correlated indicators and reduces the dimensionality of the health-capital construct [27]. The health-capital index is defined as

$$h{c}_{it}=w_{1}sr{h}_{it}^s+w_{2}noc{h}_{it}^s+w_{3}bm{i}_{it}^s+w_{4}nodi{s}_{it}^s+w_{5}m{h}_{it}^s,$$

(1)

where the superscript s denotes standardized variables and $w_1$ to $w_5$ are the loadings from the first principal component. The resulting index is standardized again so that its mean is zero and its standard deviation is one in the analytic sample. Higher values of hc represent stronger health capital.

Household financial resilience is conceptualized as the ability of a household to absorb, adapt to, and recover from financial shocks. This definition follows the multidimensional view of financial resilience, which emphasizes liquidity, financial resources, risk-coping capacity, and recovery ability rather than a single indicator of financial distress [5,7]. The index fri contains five components: income margin, liquidity buffer, debt burden, medical expenditure burden, and risk-management capacity. Including medical expenditure burden is important because medical shocks are a major source of household financial vulnerability [6].

The five components are defined as follows:

$$mg{n}_{it}={\displaystyle \frac{in{c}_{it}-con{s}_{it}}{con{s}_{it}}},$$

(2)

$$li{q}_{it}={\displaystyle \frac{fi{n}_{it}}{con{s}_{it}}},$$

(3)

$$deb{t}_{it}={\displaystyle \frac{loa{n}_{it}}{in{c}_{it}}},$$

(4)

$$me{d}_{it}={\displaystyle \frac{oo{p}_{it}}{con{s}_{it}}}.$$

(5)

The component risk is calculated as the average of three binary indicators: commercial insurance ownership, financial product holding, and absence of borrowing rejection. Before PCA, mgn, liq, and risk are coded as positive components, while debt and med are reverse-coded. The financial-resilience index is then constructed as

$$fr{i}_{it}=v_{1}mg{n}_{it}^s+v_{2}li{q}_{it}^s-v_{3}deb{t}_{it}^s-v_{4}me{d}_{it}^s+v_{5}ris{k}_{it}^s,$$

(6)

where $v_1$ to $v_5$ are the loadings from the first principal component. The final index is standardized to have a mean of zero and a standard deviation of one. Higher values of fri indicate stronger household financial resilience.

Table 3. Principal component analysis diagnostics and component loadings.

Index and Component Indicator	Loading	Eigenvalue	Variance Explained	KMO	Bartlett’s Test
Health-capital index (hc)		1.846	36.92%	0.739	$p<0.001$
Self-rated health (srh)	0.704
Mental health (mh)	0.681
No physical discomfort (nodis)	0.632
No chronic disease (noch)	0.553
Body mass status (bmi)	0.427
Financial-resilience index (fri)		1.723	34.46%	0.704	$p<0.001$
Income margin (mgn)	0.646
Liquidity buffer (liq)	0.621
Medical burden, reversed (med)	0.585
Risk capacity (risk)	0.584
Debt burden, reversed (debt)	0.487

Notes: PCA denotes principal component analysis; KMO denotes Kaiser–Meyer–Olkin sampling adequacy statistic. All component variables were standardized before PCA. Negative financial indicators, namely med and debt, were reverse-coded so that higher values indicate more favorable economic conditions. Reported loadings are standard component loadings scaled by the square root of the corresponding eigenvalue, calculated as $\mathrm{loading}=\mathrm{eigenvector}\times \sqrt{\lambda }$. The signs of the first principal components were oriented so that higher index values indicate stronger health capital or stronger household financial resilience.

reports the first-component loadings, eigenvalues, percentage of variance explained, KMO statistics, and Bartlett’s tests for the health-capital and financial-resilience indices. All component variables were standardized before PCA, and the signs of the first principal components were oriented so that higher values indicate stronger health capital or stronger household financial resilience. The PCA diagnostics indicate acceptable sampling adequacy for both indices, with KMO values of 0.739 for the health-capital index and 0.704 for the financial-resilience index. The first principal component explains 36.92% of the variance in the health-capital components and 34.46% of the variance in the financial-resilience components. These results suggest that the selected components contain sufficient common variation for constructing composite indices, although the resulting indices should still be interpreted as survey-based multidimensional composite proxies rather than measurement-error-free latent constructs.

3.4. Baseline Dynamic Panel Models

The baseline empirical analysis estimates lagged household fixed-effects models. These models examine whether changes in one component of the household system predict subsequent changes in another component. This lagged structure is consistent with the theoretical argument that physical activity, health capital, and household financial resilience evolve over time rather than only contemporaneously.

To test whether physical activity predicts subsequent health capital, the following model is estimated:

$$h{c}_{i,t+1}={\alpha }_1+{\beta }_{1}p{a}_{it}+{\mathbf{z}}_{it}^{\prime }{\gamma }_1+{\mu }_i+{\tau }_t+{\rho }_{pt}+{\epsilon }_{i,t+1},$$

(7)

where i denotes household, t denotes survey wave, and p denotes province. The vector ${\mathbf{z}}_{it}$ contains the control variables age, agesq, male, marr, edu, emp, smk, drk, hhsz, dep, home, and urb. The term ${\mu }_i$ denotes household fixed effects, ${\tau }_t$ denotes wave fixed effects, and ${\rho }_{pt}$ denotes province-by-wave fixed effects. A positive and statistically significant ${\beta }_1$ supports Hypothesis 1.

To test whether health capital predicts subsequent household financial resilience, the following model is estimated:

$$fr{i}_{i,t+1}={\alpha }_2+{\beta }_{2}h{c}_{it}+{\mathbf{z}}_{it}^{\prime }{\gamma }_2+{\mu }_i+{\tau }_t+{\rho }_{pt}+{\epsilon }_{i,t+1}.$$

(8)

A positive and statistically significant ${\beta }_2$ supports Hypothesis 2.

To test whether household financial resilience feeds back into subsequent physical activity, the following model is estimated:

$$p{a}_{i,t+1}={\alpha }_3+{\beta }_{3}fr{i}_{it}+{\mathbf{z}}_{it}^{\prime }{\gamma }_3+{\mu }_i+{\tau }_t+{\rho }_{pt}+{\epsilon }_{i,t+1}.$$

(9)

Because pa is binary, this specification is estimated as a household fixed-effects linear probability model. This choice preserves comparability with the linear dynamic panel and PVAR models. A positive and statistically significant ${\beta }_3$ supports Hypothesis 4.

The dynamic mediation pathway is examined by estimating two linked lagged models:

$$h{c}_{i,t+1}={\alpha }_4+{\theta }_{1}p{a}_{it}+{\mathbf{z}}_{it}^{\prime }{\gamma }_4+{\mu }_i+{\tau }_t+{\rho }_{pt}+{\epsilon }_{i,t+1},$$

(10)

$$fr{i}_{i,t+2}={\alpha }_5+{\theta }_{2}h{c}_{i,t+1}+{\theta }_{3}p{a}_{it}+{\mathbf{z}}_{it}^{\prime }{\gamma }_5+{\mu }_i+{\tau }_t+{\rho }_{pt}+{\epsilon }_{i,t+2}.$$

(11)

The indirect effect of physical activity on household financial resilience through health capital is calculated as ${\theta }_1\times {\theta }_2$. The confidence interval for the indirect effect is obtained using 1000 household-level bootstrap replications. A positive indirect effect supports Hypothesis 3.

3.5. Panel Vector Autoregression and Dynamic Feedback Analysis

The core empirical model is a panel vector autoregression. This model treats physical activity, health capital, and household financial resilience as jointly endogenous system variables. PVAR is appropriate for this study because it allows each component of the system to depend on its own history and on the past values of the other components [10,11,12]. This approach directly matches the theoretical argument that health behavior, health capital, and household financial resilience form a dynamic feedback system.

Let

$${\mathbf{y}}_{it}=\left[\begin{array}{c}p{a}_{it}\\ h{c}_{it}\\ fr{i}_{it}\end{array}\right].$$

The baseline PVAR model is specified as

$${\mathbf{y}}_{it}={\mathbf{a}}_1{\mathbf{y}}_{i,t-1}+\mathbf{b}{\mathbf{z}}_{i,t-1}+{\mu }_i+{\tau }_t+{\mathbf{e}}_{it},$$

(12)

where ${\mathbf{a}}_1$ is the dynamic coefficient matrix, $\mathbf{b}$ is the coefficient matrix for lagged controls, ${\mu }_i$ denotes household fixed effects, ${\tau }_t$ denotes wave fixed effects, and ${\mathbf{e}}_{it}$ is the vector of innovations. The baseline model uses one lag for both substantive and statistical reasons. Substantively, the CFPS is conducted every two years, so a first-order lag captures a two-year interval over which physical activity, health capital, and household financial resilience can plausibly adjust. Statistically, the analytic panel contains five survey waves, and higher-order lags would substantially reduce the number of usable observations and weaken the internal-instrument structure in the GMM-based PVAR estimation. We therefore treat the first-order lag as the preferred specification and assess this choice using lag-order selection criteria and lag-2 sensitivity checks.

The PVAR model is estimated using generalized method of moments. Household fixed effects are removed using forward orthogonal deviations, and lagged endogenous variables are used as internal instruments. The stability condition of the PVAR system is assessed before interpreting the dynamic results. The system is considered stable when all eigenvalues lie inside the unit circle. After estimating the PVAR model, impulse response functions are used to examine how a shock to one component affects the future trajectories of the other components. The baseline orthogonalized impulse response uses the ordering pa, hc, and fri, which follows the theoretical sequence from health behavior to health capital and then to household financial resilience. The responses are traced over four future survey intervals. Confidence intervals are calculated using 1000 Monte Carlo replications.

Forecast error variance decomposition is also used to quantify the contribution of each system component to future variation in the other components. If shocks to pa explain future variation in hc, shocks to hc explain future variation in fri, and shocks to fri explain future variation in pa, we interpret this pattern as evidence consistent with dynamic interdependence among the three variables. Because the panel is relatively short and the measures are subject to survey and index-construction uncertainty, this analysis is not treated as definitive proof of a self-reinforcing causal system. Instead, it is used to assess whether the observed longitudinal dynamics are compatible with the feedback-system interpretation in Hypothesis 5.

3.6. Robustness Checks and Heterogeneity Analysis

Several robustness checks are conducted. First, the binary physical activity variable pa is replaced with pafrq, the ordered measure of physical activity frequency. Second, the health-capital index and the financial-resilience index are reconstructed using equal-weighted and entropy-weighted methods. The alternative health-capital indices are denoted by hceq and hcen, and the alternative financial-resilience indices are denoted by frieq and frien. Third, household financial vulnerability is constructed as a reverse outcome, denoted by fv, where higher values indicate weaker household financial conditions. Fourth, the models are re-estimated using a balanced panel. Fifth, households with changes in household headship are excluded to ensure that the measured health behavior and health capital refer to the same decision-maker over time. Sixth, the 2020 and 2022 waves are excluded to assess the influence of pandemic-period shocks. Seventh, the PVAR impulse responses are recalculated using alternative variable orderings and generalized impulse responses. Dynamic panel robustness checks are also performed. Specifically, the baseline lagged models are re-estimated using difference GMM and system GMM, following the dynamic panel-data literature [28,29]. These models are used to assess whether the results are robust to lagged dependent variables, internal instrumentation, and dynamic persistence. Heterogeneity analysis is conducted across four dimensions. First, households are divided into urban and rural groups using urb. Second, households are divided into low-income and high-income groups according to the wave-specific median of household income. Third, households are divided by the age of the household head, with older-head households defined as those with age equal to 60 or above. Fourth, households are divided by baseline chronic disease status using noch. The same dynamic panel and PVAR models are estimated within each subgroup. These analyses show whether the feedback loop among pa, hc, and fri is stronger among households with greater economic or health vulnerability.

4. Results

4.1. Descriptive Statistics and Preliminary Evidence

Before presenting the empirical results, it is useful to clarify the estimation samples used across the analyses.

Table 4. Estimation samples across empirical analyses.

Analysis	Temporal Requirement	Obs.	Households	Main Reason for Sample Change
Descriptive statistics	Valid current-wave core variables	49,162	–	Uses all household-wave observations available for the main analytic sample.
Baseline lagged FE models	Valid variables at t and $t+1$	38,427	10,215	Requires one-wave-ahead outcomes; the last wave cannot serve as a baseline wave.
Dynamic mediation models	Valid variables at t, $t+1$, and $t+2$	28,145	8932	Requires a longer three-wave structure for the two-step lagged pathway.
PVAR model	Complete lagged endogenous variables and valid internal instruments	26,854	8112	Requires lagged system variables and usable observations after forward orthogonal deviations and GMM instrumentation.

Notes: FE denotes fixed effects; PVAR denotes panel vector autoregression; GMM denotes generalized method of moments. The descriptive statistics are reported at the household-wave level, and the corresponding number of households is not separately reported in the descriptive table.

summarizes why the number of observations differs across tables. The descriptive statistics use all household-wave observations with valid current-wave core variables. The baseline lagged fixed-effects models require valid observations for the predictor at wave t and the outcome at wave $t+1$, which mechanically excludes the last survey wave as a baseline wave and removes observations without valid adjacent-wave information. The dynamic mediation models require a longer three-wave structure involving t, $t+1$, and $t+2$, so the effective sample is smaller. The PVAR model further requires complete lagged endogenous variables and valid internal instruments after forward orthogonal deviations. Therefore, the decline in observations from the descriptive statistics to the lagged, mediation, and PVAR analyses reflects the increasing temporal requirements of the dynamic models rather than an additional substantive sample restriction.

Table 5. Descriptive statistics.

Var	Obs	Mean	Sd	p25	p50	p75
pa	49,162	0.342	0.474	0.000	0.000	1.000
pafrq	49,162	1.831	2.584	0.000	0.000	3.000
hc	49,162	0.003	0.988	−0.635	0.114	0.742
fri	49,162	−0.011	0.992	−0.584	−0.078	0.517
mgn	49,162	0.354	1.218	−0.127	0.203	0.681
liq	49,162	0.841	1.652	0.053	0.315	0.942
debt	49,162	0.412	0.935	0.000	0.000	0.356
med	49,162	0.095	0.183	0.008	0.034	0.105
risk	49,162	0.427	0.286	0.333	0.333	0.667
age	49,162	51.34	13.82	41.00	51.00	62.00
edu	49,162	8.243	4.156	6.000	9.000	12.000
emp	49,162	0.678	0.467	0.000	1.000	1.000
hhsz	49,162	3.521	1.643	2.000	3.000	5.000
dep	49,162	0.315	0.284	0.000	0.250	0.500

Notes: pa denotes physical activity, hc denotes health capital, and fri denotes household financial resilience. Monetary variables are measured in real 2014 yuan and winsorized at the 1st and 99th percentiles. The variables hc and fri are standardized indices.

reports the descriptive statistics for the main analytic sample, which contains 49,162 household-wave observations. The mean of pa is 0.342, indicating that 34.2% of household heads participated in physical activity. The frequency variable pafrq has a median of zero, suggesting that regular exercise is unevenly distributed across households. The standardized indices show reasonable distributions. The mean and standard deviation are 0.003 and 0.988 for hc, and −0.011 and 0.992 for fri, respectively. Among the components of financial resilience, mgn has a positive mean of 0.354, while liq, debt, and med display right-skewed distributions, indicating substantial heterogeneity in liquidity, debt exposure, and medical expenditure burden across households. The average household head is 51.34 years old, with 8.243 years of schooling, and 67.8% are employed or self-employed.

Table 6. Pairwise correlations among core system variables.

	pa	hc	fri
pa	1.000
hc	0.217	1.000
fri	0.134	0.283	1.000

Notes: All correlations are calculated at the household-wave level. All reported coefficients are statistically significant at the 1% level.

presents the pairwise correlations among the three core system variables. The correlations between pa and hc, between hc and fri, and between pa and fri are 0.217, 0.283, and 0.134, respectively.

4.2. Baseline Dynamic Panel Results

Table 7. Baseline dynamic panel estimates.

	Dependent Variable
	hct+1	frit+1	pat+1
pat	0.084 ***
	(0.021)
hct		0.115 ***
		(0.018)
frit			0.032 ***
			(0.009)
controls	Yes	Yes	Yes
hh fe	Yes	Yes	Yes
prov×wave fe	Yes	Yes	Yes
obs	38,427	38,427	38,427
households	10,215	10,215	10,215
$R^2$	0.142	0.187	0.093

Notes: Household-clustered standard errors are reported in parentheses. The controls include age, agesq, male, marr, edu, emp, smk, drk, hhsz, dep, home, and urb. *** $p<0.01$.

reports the baseline lagged household fixed-effects estimates. Column (1) shows that pa positively predicts hc in the following wave. The coefficient is 0.084 and statistically significant at the 1% level, indicating that physical activity is associated with a 0.084 standard-deviation increase in subsequent health capital. This result supports Hypothesis 1. Column (2) shows that hc positively predicts subsequent fri. The coefficient is 0.115 and statistically significant at the 1% level, suggesting that stronger health capital is associated with greater household financial resilience in the next wave. This finding supports Hypothesis 2. Column (3) further shows that fri positively predicts subsequent pa. The coefficient is 0.032 and statistically significant at the 1% level, implying that a one-standard-deviation increase in household financial resilience is associated with a 3.2 percentage-point increase in the probability of physical activity participation in the following wave. This result supports Hypothesis 4. The baseline results provide initial dynamic evidence for the proposed feedback structure: physical activity predicts later health capital, health capital predicts later financial resilience, and financial resilience feeds back into later physical activity.

Table 8. Practical interpretation of main dynamic estimates.

Path or Estimate	Estimate	Meaningful Unit	Practical Interpretation
Baseline FE: pat$\to$ hct+1	0.084	SD of hc	Physical activity participation is associated with a 0.084-standard-deviation higher subsequent health-capital index.
Baseline FE: hct$\to$ frit+1	0.115	SD of fri	A one-standard-deviation higher health-capital index predicts a 0.115-standard-deviation higher subsequent financial-resilience index.
Baseline FE: frit$\to$ pat+1	0.032	Percentage points	A one-standard-deviation higher financial-resilience index predicts a 3.2 percentage-point higher probability of subsequent physical activity participation, about 9.4% of the sample mean of pa.
Dynamic mediation: indirect path through hc	0.009	SD of fri	The indirect association is small in absolute magnitude and accounts for approximately 19.1% of the modeled total association in the mediation specification.
PVAR: pat−1$\to$ hct	0.063	SD of hc	The PVAR cross-lagged association from physical activity to health capital is positive but modest.
PVAR: hct−1$\to$ frit	0.088	SD of fri	The PVAR cross-lagged association from health capital to financial resilience is positive and larger than the feedback path from financial resilience to physical activity.
PVAR: frit−1$\to$ pat	0.024	Percentage points	The feedback path corresponds to a 2.4 percentage-point higher probability of physical activity participation and is the smallest of the three core cross-lagged paths.

Notes: FE denotes fixed effects; PVAR denotes panel vector autoregression; SD denotes standard deviation. The sample mean of pa is 0.342. Percentage-point interpretations apply to models in which pa is the dependent variable.

translates the main estimates into meaningful units. Because hc and fri are standardized indices, coefficients involving these outcomes can be interpreted in standard-deviation units. Because pa is a binary indicator estimated using a fixed-effects linear probability model, coefficients in the pa equation can be interpreted as percentage-point changes in the probability of physical activity participation. The main estimates are statistically detectable but modest in magnitude. For example, the baseline financial-resilience-to-physical-activity estimate of 0.032 corresponds to a 3.2 percentage-point increase in the probability of subsequent physical activity, which is about 9.4% of the sample mean participation rate of 34.2%.

4.3. Dynamic Mediation Through Health Capital

Because CFPS is biennial, $t+2$ corresponds to two survey-wave intervals after the baseline wave.

Table 9. Dynamic mediation results.

	hct+1	frit+2
pat	0.081 ***	0.038 **
	(0.022)	(0.016)
hct+1		0.107 ***
		(0.019)
controls	Yes	Yes
hh fe	Yes	Yes
prov×wave fe	Yes	Yes
obs	28,145	28,145
households	8932	8932
$R^2$	0.145	0.191
indirect effect	0.009
bootstrap 95% ci	[0.004, 0.015]

Notes: Household-clustered standard errors are reported in parentheses. The indirect effect is calculated as the product of the coefficient of pa_t in the first-stage model and the coefficient of hc_t+1 in the second-stage model. The confidence interval is based on 1000 household-level bootstrap replications. ** $p<0.05$, and *** $p<0.01$.

reports the dynamic mediation results. Column (1) shows that ${\mathtt{pa}}_t$ positively predicts ${\mathtt{hc}}_{t+1}$. The coefficient is 0.081 and statistically significant at the 1% level, indicating that physical activity is associated with a subsequent increase in health capital. Column (2) further shows that ${\mathtt{hc}}_{t+1}$ positively predicts ${\mathtt{fri}}_{t+2}$. The coefficient is 0.107 and statistically significant at the 1% level. Meanwhile, the coefficient of ${\mathtt{pa}}_t$ remains positive and significant, suggesting that health capital partially mediates the relationship between physical activity and household financial resilience. The estimated indirect effect is 0.009, with a bootstrap 95% confidence interval of [0.004, 0.015]. Since the confidence interval excludes zero, the mediation pathway through health capital is statistically significant. These results support Hypothesis 3 and indicate that physical activity enhances household financial resilience partly through the accumulation of health capital.

In practical terms, the estimated indirect association is small in absolute magnitude. The indirect effect of 0.009 indicates that the pathway through health capital corresponds to a 0.009-standard-deviation increase in household financial resilience. Relative to the modeled total association in this mediation specification, the indirect pathway accounts for approximately 19.1%, calculated as $0.009/(0.009+0.038)$. This result suggests that health capital is a statistically detectable but partial transmission channel rather than the sole pathway linking physical activity and household financial resilience.

4.4. Panel Vector Autoregression Results

Table 10. Panel vector autoregression estimates.

	Dependent Variable
	pat	hct	frit
pat−1	0.312 ***	0.063 ***	0.031 **
	(0.028)	(0.017)	(0.013)
hct−1	0.018 **	0.458 ***	0.088 ***
	(0.008)	(0.025)	(0.021)
frit−1	0.024 ***	0.027 **	0.384 ***
	(0.007)	(0.012)	(0.031)
controls	Yes	Yes	Yes
fod	Yes	Yes	Yes
wave fe	Yes	Yes	Yes
obs	26,854	26,854	26,854
households	8112	8112	8112
largest eig	0.472

Notes: Household fixed effects are removed using forward orthogonal deviations. Standard errors clustered at the household level are reported in parentheses. The model treats pa, hc, and fri as jointly endogenous variables. ** $p<0.05$, and *** $p<0.01$.

reports the PVAR estimates. The own-lag coefficients are positive and statistically significant for all three system variables, indicating persistence in physical activity, health capital, and household financial resilience. Specifically, the coefficients of ${\mathtt{pa}}_{t-1}$, ${\mathtt{hc}}_{t-1}$, and ${\mathtt{fri}}_{t-1}$ in their own equations are 0.312, 0.458, and 0.384, respectively. The cross-lagged coefficients are consistent with dynamic interdependence among the three variables. The coefficient of ${\mathtt{pa}}_{t-1}$ in the ${\mathtt{hc}}_t$ equation is 0.063 and statistically significant at the 1% level, indicating that physical activity is positively associated with subsequent health capital. The coefficient of ${\mathtt{hc}}_{t-1}$ in the ${\mathtt{fri}}_t$ equation is 0.088 and statistically significant at the 1% level, suggesting that health capital positively predicts subsequent household financial resilience. The coefficient of ${\mathtt{fri}}_{t-1}$ in the ${\mathtt{pa}}_t$ equation is 0.024 and statistically significant at the 1% level, suggesting a smaller but detectable feedback-consistent association from financial resilience to later physical activity. The estimated system satisfies the stability condition, with the largest eigenvalue modulus equal to 0.472. Since this value is below one, the PVAR system is stable and suitable for impulse response and variance decomposition analyses. Overall, the PVAR results are consistent with Hypothesis 5, but they should be interpreted as evidence of modest dynamic interdependence rather than definitive causal confirmation of a strong self-reinforcing system.

It is also important to compare the relative magnitudes of the three cross-lagged paths. The coefficient for the financial-resilience-to-physical-activity path is 0.024, which is smaller than the physical-activity-to-health-capital path of 0.063 and the health-capital-to-financial-resilience path of 0.088. This pattern suggests that the feedback from financial resilience to later physical activity is present but modest. Therefore, the PVAR evidence is better interpreted as supporting a weak or moderate feedback-consistent association rather than a strong self-reinforcing loop.

Figure 2 presents the impulse response functions from the PVAR model. Panel A shows that a positive shock to physical activity is followed by a positive response in health capital, with the response peaking in the first survey interval and gradually declining thereafter. Panel B shows that a positive shock to health capital is followed by a positive response in household financial resilience, with the strongest response appearing in the second survey interval. This delayed response is consistent with the view that health capital may be related to financial resilience through reduced health-related pressure and more stable household resources. Panel C provides evidence consistent with a feedback channel from household financial resilience to physical activity. A positive shock to financial resilience is followed by a positive response in subsequent physical activity, although the response is smaller and weakens over longer horizons. Panel D further shows a positive response of financial resilience to a physical activity shock, with the effect reaching its peak in the second survey interval. Overall, the impulse response results are consistent with the proposed dynamic feedback pattern among $\mathtt{pa}$, $\mathtt{hc}$, and $\mathtt{fri}$, while also showing that the estimated responses are modest and strongest in the short-to-medium run.

4.5. Variance-Decomposition Evidence

Table 11. Forecast error variance decomposition.

Response	Horizon	pa Shock	hc Shock	fri Shock
pa	1	100.00	0.00	0.00
	2	97.24	1.15	1.61
	3	94.51	2.38	3.11
	4	92.18	3.42	4.40
hc	1	4.52	95.48	0.00
	2	6.81	91.04	2.15
	3	8.16	87.52	4.32
	4	9.37	84.62	6.01
fri	1	1.23	5.84	92.93
	2	2.15	8.42	89.43
	3	3.46	11.27	85.27
	4	4.87	13.56	81.57

Notes: The recursive ordering is pa, hc, and fri.

reports the forecast error variance decomposition from the PVAR model. The results show that each system variable is mainly explained by its own shocks in the short run, but the contribution of cross-variable shocks increases over longer horizons. For physical activity, own shocks explain 100.00% of the variation at horizon 1 and 92.18% at horizon 4. The contribution of fri shocks rises to 4.40% by horizon 4, providing additional evidence for the feedback channel from household financial resilience to physical activity. For health capital, pa shocks explain 4.52% of the variation at horizon 1 and 9.37% at horizon 4. This pattern indicates that physical activity is an important source of future changes in health capital. For household financial resilience, hc shocks explain 13.56% of the variation at horizon 4, which is the largest cross-variable contribution in the system.

The variance decomposition results are consistent with the impulse response analysis. Although own shocks dominate short-run variation, the rising contribution of cross-variable shocks suggests dynamic interdependence among $\mathtt{pa}$, $\mathtt{hc}$, and $\mathtt{fri}$. At the same time, the cross-variable shares remain moderate, which further supports a cautious interpretation of the feedback loop.

4.6. Robustness Assessment

Table 12. Robustness checks.

	freq	hceq	hcen	frieq	frien	bal	no20	gmm
pa→hc	0.028 ***	0.079 ***	0.088 ***	0.083 ***	0.085 ***	0.094 ***	0.076 ***	0.105 ***
	(0.007)	(0.022)	(0.020)	(0.021)	(0.021)	(0.028)	(0.025)	(0.031)
hc→fri	0.113 ***	0.108 ***	0.121 ***	0.102 ***	0.126 ***	0.132 ***	0.098 ***	0.148 ***
	(0.019)	(0.017)	(0.021)	(0.019)	(0.020)	(0.025)	(0.022)	(0.029)
fri→pa	0.095 ***	0.031 ***	0.033 ***	0.028 ***	0.036 ***	0.041 ***	0.026 **	0.047 ***
	(0.024)	(0.009)	(0.009)	(0.008)	(0.010)	(0.014)	(0.011)	(0.015)
controls	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
hh fe	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
prov×wave fe	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes
obs	38,427	38,427	38,427	38,427	38,427	14,520	18,934	28,145

Notes: freq uses pafrq; hceq and hcen use alternative health-capital indices; frieq and frien use alternative financial-resilience indices; bal uses the balanced panel; no20 excludes pandemic-period waves; and gmm uses dynamic panel GMM. Household-clustered standard errors are reported in parentheses. ** $p<0.05$, and *** $p<0.01$.

reports the robustness checks. The first column replaces the binary physical activity indicator with pafrq. The coefficient remains positive and significant, showing that more frequent physical activity also predicts higher subsequent health capital. In this column, the feedback estimate should be interpreted as the effect of fri on subsequent activity frequency rather than on the binary participation indicator. Columns (2) and (3) reconstruct the health-capital index using alternative weighting methods, while Columns (4) and (5) reconstruct the financial-resilience index. The three core relationships remain positive and statistically significant across these specifications. Column (6) uses a balanced panel, and Column (7) excludes pandemic-period waves. The results remain consistent with the baseline estimates. Column (8) further reports dynamic panel GMM estimates, which also support the positive links among pa, hc, and fri. Overall, these robustness checks confirm that the main findings are not driven by a specific measure, sample structure, or estimation strategy.

Because the health-capital and household financial-resilience indices are compared across survey waves, we also assessed the cross-wave stability of the PCA-based composite structures. Strict CFA-style measurement invariance tests are designed primarily for reflective latent constructs and are not directly applicable to these PCA-based multidimensional composite indices. We therefore examined the reasonableness of the cross-time comparability assumption by estimating PCA structures separately within each survey wave and comparing them with the pooled PCA structure used in the main analysis.

Table 13. Cross-wave stability of PCA-based composite indices.

Component or Diagnostic	Pooled	2014	2016	2018	2020	2022
Panel A. Health-capital index (hc)
srh loading	0.704	0.695	0.711	0.701	0.688	0.706
noch loading	0.553	0.535	0.558	0.547	0.561	0.551
bmi loading	0.427	0.440	0.421	0.432	0.409	0.426
nodis loading	0.632	0.620	0.635	0.627	0.645	0.631
mh loading	0.681	0.682	0.679	0.681	0.708	0.684
Eigenvalue	1.846	1.812	1.858	1.834	1.872	1.849
Variance explained (%)	36.92	36.24	37.16	36.68	37.44	36.98
KMO statistic	0.739	0.744	0.731	0.741	0.728	0.735
Correlation with pooled index	–	0.994	0.996	0.995	0.991	0.997
Panel B. Household financial-resilience index (fri)
mgn loading	0.646	0.635	0.652	0.642	0.661	0.643
liq loading	0.621	0.612	0.626	0.618	0.634	0.619
debt loading, reversed	0.487	0.495	0.481	0.491	0.468	0.490
med loading, reversed	0.585	0.573	0.589	0.581	0.602	0.583
risk loading	0.584	0.586	0.588	0.583	0.581	0.585
Eigenvalue	1.723	1.694	1.741	1.712	1.758	1.719
Variance explained (%)	34.46	33.88	34.82	34.24	35.16	34.38
KMO statistic	0.704	0.709	0.701	0.711	0.693	0.706
Correlation with pooled index	–	0.992	0.996	0.994	0.988	0.995

Notes: PCA denotes principal component analysis; KMO denotes Kaiser–Meyer–Olkin sampling adequacy statistic. The pooled column reports the PCA diagnostics used for the main index construction. The wave-specific columns report the same diagnostics when PCA is estimated separately within each survey wave. The correlation with pooled index is calculated within each wave between the main pooled-weight index and the corresponding wave-specific PCA index. For wave-specific PCA, components were standardized within each wave before PCA. For pooled PCA, components were standardized in the pooled analytic sample before PCA. Negative financial indicators, namely debt and med, were reverse-coded so that higher values indicate more favorable financial conditions. The signs of the first principal components were oriented so that higher values indicate stronger health capital or stronger household financial resilience.

reports wave-specific PCA loadings, eigenvalues, variance explained, KMO statistics, and correlations between the pooled-weight index and the corresponding wave-specific PCA index. The component loadings remain positive and similar in magnitude across waves after orienting the first principal component so that higher values indicate more favorable conditions. The correlations between the pooled and wave-specific indices are very high, ranging from 0.991 to 0.997 for hc and from 0.988 to 0.996 for fri. These results support the reasonableness of comparing the composite indices over time, although the indices should still be interpreted as survey-based composite proxies rather than fully invariant reflective latent constructs.

We further assessed the lag-order choice for the PVAR model.

Table 14. Lag-order selection for the PVAR model.

Lag Order	MBIC	MAIC	MQIC	Hansen J p-Value	Stability
1	−41.28	−11.77	−24.52	0.114	Stable
2	−22.15	−5.16	−12.08	0.231	Stable

Notes: MBIC, MAIC, and MQIC denote moment and model selection criteria for GMM-based panel VAR models. Smaller values indicate a preferred specification. Stability indicates that all eigenvalues lie inside the unit circle.

reports moment and model selection criteria for one-lag and two-lag PVAR specifications. The MBIC, MAIC, and MQIC criteria all favor the first-order lag specification. Both lag specifications satisfy the stability condition, and the Hansen test does not indicate evidence against the overidentifying restrictions. We also estimated a lag-2 sensitivity check, as reported in

Table 15. Lag-2 sensitivity check for core PVAR paths.

Path	Lag 1 Baseline	Lag 2 Check
pa→hc	0.063 ***	0.041
hc→fri	0.088 ***	0.053 *
fri→pa	0.024 ***	0.012

Notes: The lag-2 check corresponds to a four-year interval because CFPS waves are biennial. * $p<0.10$, *** $p<0.01$.

. Because the CFPS is biennial, the second-order lag corresponds to a four-year interval and substantially reduces the effective time dimension of the panel. The lag-2 results retain the same positive signs as the baseline model, but the magnitudes are smaller and the estimates are less precise. This pattern supports the use of the first-order lag as the preferred specification while reinforcing the cautious interpretation of the long-run feedback dynamics.

4.7. Heterogeneity Patterns

Table 16. Heterogeneity analysis.

Subgroup	pa→hc	hc→fri	fri→pa
urban	0.091 ***	0.102 ***	0.038 ***
	(0.023)	(0.019)	(0.011)
rural	0.075 ***	0.131 ***	0.024 **
	(0.025)	(0.024)	(0.012)
low inc	0.078 ***	0.142 ***	0.037 ***
	(0.024)	(0.026)	(0.012)
high inc	0.088 ***	0.095 ***	0.026 **
	(0.021)	(0.017)	(0.010)
age $<60$	0.072 ***	0.096 ***	0.028 **
	(0.022)	(0.018)	(0.011)
age $\ge 60$	0.095 ***	0.138 ***	0.036 ***
	(0.027)	(0.025)	(0.013)
chronic risk	0.092 ***	0.145 ***	0.041 ***
	(0.026)	(0.028)	(0.014)
low risk	0.075 ***	0.091 ***	0.025 **
	(0.020)	(0.016)	(0.010)

Notes: Household-clustered standard errors are reported in parentheses. Low- and high-income groups are defined by the wave-specific median of household income. Older-head households are defined as those with household heads aged 60 or above. Chronic-risk households are those whose household heads report at least one chronic disease at baseline. All models include the same controls and fixed effects as the baseline specification. ** $p<0.05$, and *** $p<0.01$.

reports the heterogeneity analysis. The three core relationships remain positive and statistically significant across all subgroups, indicating that the dynamic links among physical activity, health capital, and household financial resilience are not driven by a single type of household. The urban–rural results show that the $\mathtt{pa}\to \mathtt{hc}$ and $\mathtt{fri}\to \mathtt{pa}$ coefficients are larger among urban households, while the $\mathtt{hc}\to \mathtt{fri}$ coefficient is larger among rural households. This pattern suggests that urban households may benefit more from access to physical activity resources, whereas health capital plays a stronger financial-protective role in rural households. The income, age, and health risk results further show that the feedback structure is more pronounced among more vulnerable households. The $\mathtt{hc}\to \mathtt{fri}$ coefficient is larger among low-income households, older-head households, and chronic-risk households. In particular, the coefficient reaches 0.145 for chronic-risk households, indicating that health capital is especially important for financial resilience when households face greater health vulnerability. Overall, the heterogeneity results suggest that the proposed dynamic feedback system is stronger among households with higher health or economic risks.

5. Discussion

5.1. Dynamic Feedback Among Physical Activity, Health Capital, and Financial Resilience

This study provides evidence consistent with dynamic connections among physical activity, health capital, and household financial resilience. The baseline dynamic panel models show that physical activity is positively associated with later health capital, health capital positively predicts later financial resilience, and financial resilience has a smaller but statistically significant association with later physical activity. The mediation analysis further suggests that health capital represents a partial transmission channel between physical activity and household financial resilience. These findings are consistent with recent evidence that physical activity is linked to household financial vulnerability and household financial decisions [8,9]. The PVAR results, impulse response functions, and variance decomposition suggest that these variables can be usefully examined as components of a household system rather than as isolated outcomes. A positive shock to physical activity is followed by a positive response in health capital; a health-capital shock is followed by a positive response in financial resilience; and a financial-resilience shock is followed by a smaller positive response in subsequent physical activity. This pattern is consistent with systems thinking, which emphasizes reciprocal relationships, time delays, and cumulative processes in social and health systems [18,30,31,32]. However, the magnitude of the feedback from financial resilience to physical activity is modest, and the results should be interpreted as feedback-consistent associations rather than definitive causal evidence.

The weaker magnitude of the financial-resilience-to-physical-activity path also has practical implications for interpreting the feedback system. The results suggest that financial resilience may help sustain later health behavior, but this channel appears to be more limited than the paths from physical activity to health capital and from health capital to financial resilience. This finding is consistent with the idea that a minimum level of financial security may be needed before households can convert financial resilience into regular health investment. Accordingly, the proposed feedback system should not be interpreted as a uniformly strong cycle that operates equally for all households. Rather, it is better understood as a conditional and resource-dependent pattern of dynamic association.

5.2. Level of Interpretation and Practical Meaning

The findings should be interpreted at the household-panel level. They do not imply that a particular family will necessarily improve its financial resilience by increasing physical activity, nor do they provide direct individual-level advice. The unit of analysis is the household-wave observation, and the estimates describe average lagged associations across households in the CFPS panel. At the same time, the results should not be interpreted as a purely macro-level relationship between health and finance. Rather, they capture household-level dynamic associations after accounting for household fixed effects, wave shocks, province-by-wave conditions, and observed covariates.

The positive association between health and finance is also partly intuitive. Wealthier households may live in more activity-supportive neighborhoods, have more discretionary time, and have better access to health care, preventive resources, and financial services. Household fixed effects help remove stable between-household differences of this kind, including time-invariant socioeconomic position, long-term preferences, and persistent neighborhood characteristics. Province-by-wave fixed effects further account for province-specific time-varying conditions. However, these controls cannot rule out all time-varying unobserved factors. Therefore, the contribution of this study is not to claim that the health–finance link is surprising in itself, but to provide a systems-oriented analysis of how physical activity, health capital, and household financial resilience move together over time within an observational household panel. The findings may inform hypotheses for future household-level interventions or policy evaluations, but they should not be interpreted as deterministic guidance for individual families.

5.3. Theoretical Contributions to Health Capital and Household Finance Research

The first contribution of this study is to extend the health-capital framework to the household financial domain. In Grossman’s model, health is a durable capital stock that affects productive time and future opportunities [4]. Our findings are consistent with this view by showing that physical activity is positively associated with subsequent health capital. They also extend prior research on the reciprocal relationship between health and economic status by showing that health capital is positively associated with household financial resilience [13,20,21,33]. The second contribution is to shift the household finance literature from a static vulnerability perspective toward a dynamic resilience perspective. Prior studies have shown that households face financial stress when they lack liquidity, insurance, or the capacity to absorb income and medical expenditure shocks [5,6,7,17]. This study adds cautious evidence that financial resilience may also be related to subsequent health behavior. This feedback-consistent association is aligned with research showing that financial literacy, risk management, and financial capability can improve resilience and help households respond to shocks [14,34,35].

5.4. Policy Implications for Household Health and Financial Resilience

The findings should not be read as direct evidence that any single policy intervention will necessarily increase household financial resilience. Rather, they suggest that physical activity promotion and household financial protection may be considered as potentially complementary areas for future policy design, experimentation, and evaluation. Regular physical activity is positively associated with later health capital, and health capital is positively associated with later household financial resilience. Therefore, programs that expand access to safe, affordable, and convenient opportunities for physical activity may have relevance not only for public health but also for broader household resilience, although such policy effects would need to be evaluated with appropriate experimental or quasi-experimental designs [2,3,22]. The heterogeneity results further suggest that integrated approaches may be especially relevant for vulnerable households, but the implications should remain cautious. For low-income households, low-cost community exercise opportunities could be considered together with basic financial counseling, emergency savings support, or liquidity-protection programs. For older-head households, age-friendly physical activity programs may be more useful when linked with chronic disease management and primary health-care services. For chronic-risk households, physical activity guidance may need to be combined with medical expenditure protection, insurance coverage, and follow-up care [36,37]. Built-environment evidence also suggests that walkable neighborhoods, transport access, and activity-supportive urban design can promote physical activity at the population level [38,39]. These policy directions should be interpreted as hypotheses for further evaluation rather than as direct prescriptions established by the present study.

These estimates are not intended to provide a formal cost–benefit analysis of physical activity promotion or household financial-protection policies, nor should they be read as direct individual-level prescriptions. Rather, they provide meaningful units for interpreting the observed household-level dynamic associations and for identifying hypotheses that may be evaluated in future policy or intervention studies.

Drawing on the heterogeneity results,

Table 17. Differentiated policy combinations suggested by heterogeneity results.

Target Group	Relevant Heterogeneity Pattern	Suggested Policy Combination	Implementation Focus
Low-income households	The health-capital-to-financial-resilience association is stronger among low-income households, suggesting that health capital may be especially financially protective when resources are limited.	Low-cost community physical activity opportunities combined with basic financial counseling, emergency savings support, liquidity-protection services, and medical-expense risk screening.	Community centers, public sports facilities, local social-assistance programs, and primary-care outreach.
Older-head households	The dynamic links are more pronounced among households with older heads, indicating that maintaining health capital may be particularly important for financial resilience in later life.	Age-friendly physical activity programs combined with primary health care, chronic disease management, fall-prevention services, and community-based social support.	Community health stations, senior centers, family-doctor services, and age-friendly neighborhood facilities.
Chronic-risk households	The health-capital-to-financial-resilience association is strongest among chronic-risk households, suggesting that health maintenance and financial protection are closely connected for households facing ongoing health risks.	Physical activity guidance or exercise prescriptions combined with chronic disease follow-up, medical expenditure protection, insurance coverage, and affordable preventive care.	Primary-care clinics, chronic disease registries, insurance programs, and coordinated follow-up services.

Notes: The policy combinations are derived from the heterogeneity patterns and should be interpreted as directions for future policy design and evaluation rather than as causal policy effects established by the present observational study.

presents differentiated policy combinations that could be considered in future policy design and evaluation. These combinations are framed as policy-design hypotheses rather than direct prescriptions, because the present study identifies observational household-level associations rather than experimentally identified policy effects. The purpose is to translate the heterogeneity patterns into more concrete and actionable combinations of physical activity promotion, health support, and household financial protection.

5.5. Limitations and Future Research

Several limitations should be acknowledged. First, this study uses observational longitudinal data. Although lagged models, household fixed effects, PVAR estimation, and robustness checks reduce several sources of bias, they cannot fully eliminate unobserved time-varying confounding or establish definitive causal effects. Second, the panel contains five CFPS waves. This short time dimension is common in biennial household panels but limits the strength of long-run dynamic inference, especially for models that rely on lagged relationships. Third, physical activity and health indicators are based on survey responses, which may involve reporting error and measurement uncertainty. Fourth, the health-capital and financial-resilience indices are composite measures constructed from multiple survey indicators. Although alternative index constructions are used in robustness checks, PCA-based indices may still carry measurement and construct-validity uncertainty. Fifth, the PVAR results depend on model specification, including lag length, variable ordering, and the use of internal instruments. For these reasons, the findings should be interpreted as evidence of modest dynamic associations that are consistent with a systems perspective, rather than as definitive causal evidence of a strong self-reinforcing household resilience system.

Future research could extend this study in three directions. First, studies could incorporate more detailed measures of exercise intensity, duration, and type, or combine survey data with wearable-device, medical record, or insurance-claim data. Second, future work could use quasi-experimental designs based on community sports facilities, health insurance reforms, or local public health interventions to strengthen causal interpretation. Third, further research could examine whether the feedback pattern differs across life-course stages, chronic disease profiles, or regional institutional environments. These extensions would help clarify when, for whom, and under what conditions physical activity and financial resilience become more strongly connected.

6. Conclusions

This study examined the dynamic relationships among physical activity, health capital, and household financial resilience using longitudinal data from the China Family Panel Studies. The results suggest that physical activity is positively associated with subsequent health capital, health capital positively predicts subsequent household financial resilience, and financial resilience has a smaller but statistically significant association with later physical activity. The dynamic mediation results are consistent with health capital serving as a partial transmission channel between physical activity and household financial resilience. The PVAR estimates, impulse response functions, and variance decomposition provide evidence consistent with modest dynamic interdependence among the three components. The main conclusion is that physical activity, health capital, and household financial resilience can be usefully examined as interconnected household-level processes rather than as isolated health or financial outcomes. From a systems perspective, physical activity promotion and household financial protection may be complementary areas for future research and policy evaluation, especially for households facing greater health and economic vulnerability. However, because the study is based on observational short-panel data and composite survey-based measures, the findings should be interpreted as dynamic associations rather than as definitive causal evidence or direct policy prescriptions.