How Population Aging Drives Labor Productivity: Evidence from China

Abstract

Population aging is a critical demographic trend in China, creating both challenges and opportunities for sustainable development. As aging alters the structure of the workforce and capital demand, understanding its effect on productivity is essential to managing demographic transitions in China. This study investigates the causal impact of population aging on labor productivity, with a focus on the mediating role of the capital–labor ratio and heterogeneities across industries, skill levels, and regions. Using data from Chinese listed firms between 2011 and 2018, this paper employs industry- and year-fixed effects regression models to control for unobservable heterogeneity and conducts a formal causal mediation analysis. The analysis reveals that population aging significantly enhances labor productivity. Specifically, a one-percentage-point increase in the old-age dependency ratio is associated with a 1.47% increase in firm-level labor productivity. The capital–labor ratio emerges as a critical mechanism, mediating the relationship between aging and productivity by incentivizing firms to increase capital intensity in response to labor shortages. Approximately 72.4% of the total effect is mediated through changes in capital intensity. The findings highlight notable heterogeneities. Labor-intensive firms and low-skilled worker segments experience stronger productivity gains from aging compared with their capital-intensive and high-skilled counterparts. At the regional level, the productivity effects are most pronounced in first- and second-tier cities, while third-tier cities show negligible impacts, reflecting resource and structural constraints. This study underscores the dual role of population aging as a challenge and an opportunity. Policy recommendations include (1) expanding targeted fiscal support for capital investment and automation in aging-intensive industries; (2) promoting vocational training programs tailored to older workers and digital skills development; and (3) strengthening infrastructure and institutional capacity in third-tier cities to better absorb productivity spillovers from demographic adjustment. By addressing these demographic and productivity linkages, the study contributes to achieving Sustainable Development Goals 8 (Decent Work and Economic Growth), 9 (Industry, Innovation, and Infrastructure), and 10 (Reduced Inequalities), by promoting inclusive productivity growth, enhancing industrial adaptation to demographic change, and reducing regional and skill-based disparities.These findings offer valuable insights for policymakers and businesses navigating the complexities of aging economies.

1. Introduction

Population aging is central to achieving key United Nations Sustainable Development Goals (SDGs), such as SDG 8 (Decent Work and Economic Growth), SDG 9 (Industry, Innovation, and Infrastructure), and SDG 10 (Reduced Inequalities) (data are sourced from the Sustainable Development Goals platform (https://sdgs.un.org/goals, accessed on 31 March 2025). As the share of elderly individuals rises, population aging increasingly shapes labor market dynamics, industrial competitiveness, and income distribution—thereby influencing the realization of these SDGs. Specifically, it affects the availability of productive labor (SDG 8), firms’ demand for technological upgrading (SDG 9), and intergenerational equity (SDG 10). Population aging represents one of the most significant demographic trends in the 21st century, particularly in China, where the rapid decline in fertility rates and increased life expectancy have led to profound societal and economic transformations. China’s population is aging at an accelerated pace, having already reached an upper-middle level globally. Between 1953 and 2021, China’s population aged 65 and above increased from 26.32 million to 200 million, or from 4.4 percent to 14.2 percent. Historically, the degree of aging increased by 0.15, 0.18 and 0.46 percentage points per year, respectively, from 1990 to 2000, from 2000 to 2010 and from 2010 to 2020, indicating a significant acceleration of aging (data are sourced from the National Bureau of Statistics of China (http://www.stats.gov.cn, accessed on 22 November 2024). This demographic shift presents both risks and strategic opportunities: while a shrinking workforce may dampen output potential [1,2,3], firms can respond by adopting automation [4,5,6,7], investing in capital, and optimizing their production technologies [6]. This paper investigates whether population aging causally improves firm-level labor productivity in China and to what extent this relationship is mediated by capital deepening. Grounded in the neoclassical production framework, we theorize that firms facing reduced labor availability will adjust input ratios by raising capital intensity, thereby enhancing productivity.

To empirically identify this relationship, we employ firm-level panel data and use fixed-effects models to address unobserved time-invariant heterogeneity. We further adopt mediation models to assess the role of capital–labor ratio as a transmission channel, and conduct robustness checks using dynamic panel methods to strengthen the causal interpretation.

Labor productivity, a cornerstone of economic efficiency, directly influences competitiveness, innovation, and sustainable development [8,9,10]. Recent research underscores the critical influence of demographic changes on productivity dynamics. Firstly, population aging leads to a shortage of young workers, and firms will replace them with more machinery. Population aging reduces the working-age population, leading to labor shortages [11,12,13], particularly in sectors reliant on manual and repetitive tasks. Ref. [4] finds that population aging drives the increased adoption of robots and other automation technologies, as the decline in middle-aged workers engaged in manual production tasks necessitates automation, and aging populations correlate with higher adoption rates of robots and automation technologies globally. Fortunately, automation technologies often improve labor productivity by substituting labor with capital [14]. Prior research also emphasizes that aging or health-vulnerable populations tend to exhibit reduced resilience in the face of external risks, including environmental and institutional shocks [15]. This underscores the need to consider human capital fragility when analyzing the labor productivity implications of demographic aging.

Further, the effect of population aging on the improvement of labor productivity varies across different countries and regions [3,4,5,6,16,17,18]. Cross-country studies show that institutional quality, human capital levels, and technological absorptive capacity mediate this relationship [3,4,5,16,17]. Within China, similar heterogeneity is observed: while developed coastal provinces benefit from aging-induced automation and capital deepening, rural and inland regions often experience productivity stagnation or decline [6,18,19,20].

Additionally, China’s vast size and uneven distribution of population and resources create major differences across regions, leading to significant regional and industrial variations in labor productivity [6,7,20,21]. Thus, when exploring the relationship between population aging and labor productivity, it is crucial to consider regional and industrial variability. Ref. [18] finds population aging has a significant positive impact on economic growth, which promotes economic growth in more developed regions as well as in rural areas [19]. However, there are few studies on how China’s population aging affects corporate labor productivity. This paper addresses this research gap by empirically testing a structured causal pathway, where capital–labor ratio serves as a theoretically grounded mediator linking aging to productivity outcomes. This study investigated the impact of population aging on corporate labor productivity using fixed-effects models and mediation models for econometric regressions, with a specific focus on the mediating role of the capital–labor ratio. The rationale for using capital–labor ratio lies in its central role in neoclassical and endogenous growth models, where firms re-optimize input factors in response to demographic shocks. Additionally, heterogeneous effects of population aging on corporate labor productivity are examined in greater detail.

As a result, our work contributes in the following three ways to this increasing knowledge: First, this study employs firm-level data from Chinese listed companies and fixed-effect and mediation econometric models to determine the effect of population aging on corporate labor productivity. Second, we also find out the effects of aging vary across regions, industries, and skill levels, underscoring the heterogeneous nature of its economic implications. Finally, we investigate the significant positive impact on labor productivity is primarily mediated through increases in the capital–labor ratio.

The structure of this paper is as follows: Section 2 provides a review of the relevant literature on labor productivity and the capital–labor ratio, followed by the development of the research hypotheses. Section 3 outlines the data, empirical methodology, and variable definitions. Section 4 presents the empirical findings and their implications. Section 5 provides a detailed analysis of robustness checks and performs the mechanism analysis. Finally, Section 6 summarizes the key findings and offers policy recommendations.

2. Literature Review

2.1. Labor Productivity and Population Aging

Labor productivity, a key indicator of economic efficiency, has been a central focus in the fields of economics and management. Labor productivity is typically defined as the output per unit of labor input, measured by metrics such as GDP per capita, output per hour worked, or sectoral labor productivity [17,22].

The foundational theory establishes how firms decide investment under capital cost constraints [23] and highlights the combined role of capital and labor services in determining productivity [8], while some theories explain how physical decline among older workers reduces productivity [24], especially in physically demanding sectors. The endogenous growth theory emphasizes the productivity effects of capital accumulation and technological progress [25].

The points on population aging and labor productivity reveal a complex and sometimes contradictory set of findings. Scholars diverge not only in their conclusions but also in the mechanisms, empirical contexts, and causal assumptions underpinning their analyses. On one side, a substantial body of work emphasizes the negative impacts of aging on productivity through declining labor supply, deteriorating physical capacity, and shrinking innovation potential. Aging reduces per capita labor input and depresses long-run growth unless offset by policy intervention [1]. Similarly, aging is defined as a driver of secular stagnation [2], where diminished savings and investment depress productivity. At the micro level, physiological decline among older workers—particularly in physically intensive sectors—can reduce effective labor input [24,26], while deteriorating health further constrains labor transitions [11].

Conversely, other scholars highlight adaptive responses that may counterbalance aging’s negative effects. Aging-induced labor scarcity can incentivize automation and capital deepening, thereby enhancing productivity in capital-intensive sectors [4,5]. This aligns with firm-level evidence from China, where labor protection reforms and pension agency restructuring have spurred technological upgrading and increased capital–labor ratios [27,28]. Further, population aging is positively correlated with productivity in capital-intensive industries through innovation [6], although rigid labor market institutions may limit the effect. Importantly, studies diverge on sectoral and institutional conditions. In rural and informal economies, where automation is limited and physical labor dominates, population aging tends to reduce productivity [19,29]. In contrast, urban or tech-intensive sectors are more likely to benefit from capital–labor substitution [7,30]. Cross-country comparisons also reveal structural gaps: while advanced economies such as Japan or Germany have leveraged robotics to maintain productivity amidst aging, emerging economies like China still face institutional barriers [20,31].

2.2. Capital–Labor Substitution and Technological Channels

The capital–labor ratio is defined as the total capital stock divided by the total labor input in terms of hours or the number of employees, which plays a critical role in representing labor productivity [8,22,32].

In response to aging-induced labor constraints, firms increasingly shift toward capital-intensive production modes, thereby raising the capital–labor ratio [4,27]. However, the productivity-enhancing effects of such capital deepening are significantly magnified when combined with advanced technological capabilities—such as automation, ICT infrastructure, or innovation-driven upgrades [5,6,10,30].

In aging economies, the substitution of capital for labor is a common response to shifts in labor market dynamics. When labor supply decreases due to demographic changes, such as population aging, or when labor costs rise, firms increasingly rely on capital investment to maintain or enhance efficiency [6,31,33]. This mechanism, often referred to as capital deepening, reflects firms’ adaptive strategies to mitigate demographic pressures. However, the effectiveness of this substitution is not uniform and depends critically on the sectoral context and technological absorptive capacity.

While some studies suggest a positive association between higher capital–labor ratios and firm productivity, this relationship is often correlational and conditional upon technology readiness. For example, the productivity effects of capital substitution are mediated by firm-level technological capabilities [11]. In particular, the presence of advanced technologies such as machine learning, robotics, and industrial IOT enhances the efficiency of capital-intensive operations, amplifying productivity gains in firms capable of integrating such innovations.

Nevertheless, this substitution effect is not universally observed. The rate and scope of technology adoption vary widely across regions and industries, leading to substantial heterogeneity in outcomes. Studies [12,21,22] highlight that disparities in access to and utilization of technology contribute to uneven productivity gains. For instance, while firms in high-tech or urban clusters may benefit from demographic-induced automation, labor-intensive or rural sectors often lack the digital infrastructure to implement capital substitution effectively [12,19,20]. This divergence underscores the importance of policy frameworks [33], innovation ecosystems [10], and firm-level capabilities in shaping the productivity implications of aging [30].

In the Chinese context, the diffusion and impact of capital–labor substitution technologies remain highly uneven across both regions and sectors. Empirical studies consistently show that eastern coastal provinces—such as Jiangsu, Zhejiang, and Guangdong—have experienced more pronounced productivity gains through automation and digital transformation, largely due to superior infrastructure, higher human capital accumulation, and supportive industrial policies [6,7,18]. In contrast, firms in central and western regions often encounter significant institutional constraints, such as limited access to financing, digital infrastructure deficits, and lower-skilled labor pools, which collectively hinder the effectiveness of capital deepening strategies [5,19,20]. Even when investment in machinery occurs, the lack of complementary capabilities may result in low returns to capital.

Sectoral variation further complicates the picture. While capital-intensive manufacturing firms—particularly those integrated into global value chains—benefit from digital upgrading, traditional labor-intensive industries and informal sectors remain largely untouched by technological spillovers [12,16]. This is particularly concerning given that a considerable proportion of China’s older workforce remains employed in informal or agricultural settings, where capital substitution is either infeasible or economically inefficient [19,20]. These patterns are especially salient in western and rural regions, where structural barriers further inhibit the adoption of labor-saving technologies.

These disparities cast doubt on the assumption of a uniform productivity gain from capital–labor substitution. Instead, they suggest that regional development gaps, industrial structures, and labor market segmentation must be explicitly accounted for in empirical modeling [21,30]. Ignoring these structural features risks overstating the benefits of capital deepening and mischaracterizing the real effects of demographic change.

2.3. Hypotheses

Population aging, as a significant demographic shift, exerts profound and multifaceted impacts on labor markets and economic structures [1,3,11,16,29,34]. Its effects are not only direct, through changes in the composition and behavior of the workforce, but also indirect, mediated by firms’ strategic responses to demographic challenges. Existing literature highlights two key pathways: first, the direct enhancement of labor productivity through accumulated experience and knowledge of workers [35,36,37], and second, the role of the capital–labor ratio as a critical mechanism enabling firms to adapt to labor shortages [4,6,27]. These mechanisms can be theoretically grounded in the neoclassical production framework, where output is a function of capital and labor inputs, and firms respond to demographic shocks by optimizing factor intensities [8,23,25,32]. Building on these insights, the following hypotheses are proposed to explore the relationship between population aging and labor productivity in greater depth.

Hypothesis 1.

Population aging has a positive impact on labor productivity.

Population aging drives significant structural changes in labor markets, primarily through a reduction in the working-age population [1,3,29,34]. This decline in labor supply incentivizes firms to adopt productivity-enhancing technologies and improve operational efficiency [4,5,6,7,18]. Additionally, older workers, with their accumulated experience and knowledge, contribute positively to productivity in industries where expertise and decision-making are critical [12,36,37,38]. Formally, this can be modeled by assuming a CES production function where a decline in labor quantity increases the marginal return to capital, inducing firms to reallocate toward capital-intensive processes [23,25,32]. Such behavioral adjustments can offset the negative scale effects of labor shrinkage, resulting in net productivity gains.

Hypothesis 2.

The positive impact of population aging on labor productivity is primarily achieved through an increase in the capital–labor ratio.

The capital–labor ratio of a firm is affected by changes in the two major production factors of capital and labor. We argue that population aging incentivizes firms to adopt advanced production technologies and automation, which increases the capital–labor ratio and, in turn, enhances labor productivity [5,6,7,18]. This hypothesis is grounded in the classical mechanism of capital–labor substitution under demographic constraints: as labor becomes relatively scarce and costly, its shadow price increases, prompting firms to reallocate toward capital-intensive production methods [4,25,32]. This mediating mechanism can be formally modeled using a CES production function, where declining labor input increases the marginal productivity of capital. To test this channel empirically, a mediation analysis using firm-level panel data can be applied, assessing whether the effect of population aging on labor productivity is transmitted through changes in the capital–labor ratio [11].

3. Materials and Methods

3.1. Data Sources

This study is conducted using a sample of Chinese listed companies from 2011 to 2018, a period characterized by significant demographic transitions and structural economic changes in China.We focus on this period because the data quality and consistency are well established, and the sample already provides sufficient variation and robustness to support the study’s main conclusions. The choice of listed companies is appropriate for this analysis as population aging, treated as an exogenous variable, allows for a clearer assessment of its effects on firm-level dynamics.

Firm-level data are sourced from the CSMAR and WIND databases (firm-level data are sourced from the CSMAR database (https://data.csmar.com, accessed on 22 November 2024) and WIND database (https://www.wind.com.cn, accessed on 22 November 2024).), while demographic statistics, including measures of population aging such as the proportion of the elderly population to the working-age population (Old_depth), are obtained from the National Bureau of Statistics of China (region-level data are sourced from the National Bureau of Statistics of China (http://www.stats.gov.cn, accessed on 22 November 2024).

These regional-level demographic indicators are merged with firm-level data based on the location of corporate headquarters, facilitating the analysis of the spillover effects of aging on firm operations.

To ensure the accuracy and robustness of the analysis, continuous variables are winsorized at the top and bottom 1% percentiles to mitigate the influence of outliers, which could skew regression results and lead to biased estimates. Firms in the financial sector are excluded due to their distinct regulatory and operational frameworks, which differ substantially from non-financial industries. Companies listed on the risk warning board during any sample year are excluded to avoid potential biases arising from financial instability. Delisted firms are removed to ensure data continuity and to focus on active market participants. Observations with missing key variables, such as labor productivity, demographic measures, or financial indicators, are excluded to maintain data integrity.

After applying these exclusions and refinements, the final dataset comprises 3076 listed companies, resulting in 18,775 firm-year observations. This dataset provides a comprehensive and representative sample for analyzing the relationship between population aging and labor productivity. The firm-year structure enables a robust panel data analysis, accounting for both cross-sectional and temporal variations.

3.2. Econometric Model

To explore the mechanism through which population aging affects firm-level labor productivity, we adopt a causal mediation analysis framework. Specifically, we test whether the firm’s capital–labor ratio, proxied by $cl{r}_{it}$, mediates the relationship between aging and productivity.

We estimate the following set of fixed-effects panel regression models:

$${\mathrm{Y}}_{it}={\alpha }_0+{\alpha }_1{old\_depth}_{pt}+{\alpha }_2{X}_{it}+{\mu }_i+{\lambda }_t+{ϵ}_{it}$$

(1)

$${\mathrm{clr}}_{it}={\beta }_0+{\beta }_1{old\_depth}_{pt}+{\beta }_2{X}_{it}+{\mu }_i+{\lambda }_t+{\nu }_{it}$$

(2)

$${\mathrm{Y}}_{it}={\gamma }_0+{\gamma }_1{\mathrm{Aging}}_{pt}+{\gamma }_2{old\_depth}_{pt}+{\gamma }_3{X}_{it}+{\mu }_i+{\lambda }_t+{\eta }_{it}$$

(3)

In the mediation framework, the dependent variable $Y_{it}$ denotes the labor productivity of firm i in year t, measured by the firm’s operating revenue per employee [17,22]. This indicator captures the efficiency of labor input in generating output and is widely used in productivity analyses at the firm level. The key explanatory variable ${old\_depth}_{pt}$ reflects the depth of population aging in province p during year t. It is defined as the old-age dependency ratio, i.e., the proportion of individuals aged 65 and above relative to the working-age population (15–64 years old). This variable captures demographic pressure at the regional level and is matched to firm-level data based on geographic location. The mediating variable $cl{r}_{it}$, proxied by the firm-level capital–labor ratio. Specifically, it is calculated as the ratio of fixed assets to the number of employees, capturing the extent of capital deepening at the firm level. This variable represents the firm’s strategic response to demographic changes via technology and capital investment. The control vector $X_{pt}$ includes a comprehensive set of firm-specific covariates that may influence both productivity and capital intensity. Specifically, we control for return on assets (roa) to capture firm profitability, leverage ratio (lev) to account for financial risk, firm size (size) measured by total assets, and capital intensity (ppe) proxied by net fixed assets. We also include cash holdings (cash) as an indicator of liquidity and Tobin’s Q (tq) to reflect a firm’s investment opportunities and market expectations. Macroeconomic and regional characteristics are controlled for by including provincial GDP growth (gdp) and average regional wages (avgwage), ensuring that local labor market conditions and economic development are accounted for. Year fixed effects ($u_t$) and industry fixed effects (${\sigma }_j$) are included to absorb time-varying macroeconomic shocks and unobserved sectoral heterogeneity. Firm-level robust standard errors clustered over time are used to mitigate issues related to heteroskedasticity and autocorrelation.

Equation (1) estimates the total effect of aging on productivity. Equation (2) tests whether aging significantly increases the capital–labor ratio. Equation (3) evaluates whether the inclusion of old_depth attenuates the effect of aging, providing evidence of a mediation mechanism. A reduction in the magnitude of ${\gamma }_1$ compared with ${\alpha }_1$, along with a statistically significant ${\gamma }_2$, supports the hypothesis that aging indirectly improves productivity through capital deepening.

Endogeneity may arise in this study due to several potential sources, including omitted variable bias, simultaneity, and reverse causality. To address these concerns, we adopt a multipronged identification strategy. First, we include firm fixed effects to absorb time-invariant unobserved heterogeneity across firms, and year fixed effects to account for macroeconomic shocks common to all firms in a given year. Second, we lag the key explanatory variable $Old\_depth$ in alternative specifications to mitigate contemporaneous feedback effects. Third, we conduct multiple robustness checks. Fourth, we employ a system GMM estimator, using lagged dependent variables as instruments to address potential endogeneity arising from reverse causality and omitted variable bias.

We also test the stationarity of key variables given the panel structure of our data. As our panel is unbalanced and includes missing periods, we apply the Fisher-type unit root test based on the Phillips–Perron approach, which accommodates unbalanced panels. For labprod, the test rejects the null hypothesis of a unit root at the 1% level across all statistics (Inverse chi-squared, Inverse normal, Inverse logit, and modified chi-squared), as shown in

Table 1. Fisher-Type Unit Root Test for labprod (Phillips–Perron).

Test Statistic	Value	p-Value
Inverse chi-squared (P)	9935.76	0.0000
Inverse normal (Z)	−1.9972	0.0229
Inverse logit t (L*)	−17.9883	0.0000
Modified inv. chi-squared (Pm)	47.4158	0.0000

Note: Null hypothesis is that all panels contain unit roots. L* denotes the inverse logit of the t-statistic.

. This provides strong evidence that labor productivity is stationary over time, validating the use of fixed-effects estimation in the main regressions.

3.3. Variable Selection

3.3.1. Core Explanatory Variables

The dependent variable, $Labor\_Productivit{y}_{i,t}$, measures the labor productivity of firm i in year t. Following the methodology of [39], it is calculated as the natural logarithm of the firm’s per capita operating revenue. This approach provides a consistent and robust measure of labor productivity, capturing variations in firms’ operational efficiency across years and regions.

The primary explanatory variable, $Old\_dept{h}_{i,p,t}$, represents the old-age dependency ratio in province p, where firm i is located in year t. The old-age dependency ratio, defined as the proportion of elderly individuals (aged 65 and above) to the working-age population (aged 15–64), serves as a key indicator of population aging. By linking provincial demographic trends to firm-level productivity, $Old\_dept{h}_{i,p,t}$ captures the external pressures of aging on corporate performance.

3.3.2. Mediating Variable

The mediating variable, $cl{r}_{i,t}$, represents the capital–labor ratio of firm i in year t. $cl{r}_{i,t}$ is constructed to reflect the per capita capital holdings within firms [40]. It is calculated as net fixed assets over the number of employees. As a critical mechanism linking population aging to labor productivity, the capital–labor ratio highlights firms’ strategic adjustments in response to demographic shifts, such as increased investment in capital to compensate for labor shortages.

3.3.3. Other Control Variables

To ensure robustness and mitigate potential omitted variable bias, this study incorporates a comprehensive set of control variables, capturing both firm-level characteristics and regional macroeconomic conditions. The return on assets ($roa$) is calculated as the ratio of pre-tax profits to total assets at year-end, reflecting the profitability of the firm. The leverage ratio ($lev$) is defined as the ratio of total liabilities to total assets at year-end, capturing the firm’s financial structure. Fixed asset intensity ($ppe$) is measured as the net value of fixed assets divided by total assets at year-end, indicating the degree of capital intensity. The cash ratio ($cash$) is calculated as the ratio of total cash to current liabilities at year-end, providing an indication of liquidity. Firm size ($size$) is measured as the natural logarithm of total assets at year-end, representing the scale of the firm. The book-to-market ratio ($bm$) is calculated as the ratio of the firm’s total market capitalization to net assets at year-end, reflecting the valuation of the firm. Tobin’s Q ($tobinq$) is defined as the ratio of market value to the difference between total assets and the net value of intangible assets and goodwill, serving as a proxy for growth opportunities. The independent director ratio ($indratio$) is calculated as the proportion of independent directors on the board, indicating governance quality. Finally, ownership concentration ($top1$) is measured as the proportion of shares held by the largest shareholder relative to total shares outstanding, capturing the degree of control exerted by major shareholders. To account for regional macroeconomic conditions, additional controls include the GDP growth rate ($gdp$) of the city where the firm is registered and the local wage level ($avgwage$), measured as the natural logarithm of the average wage of employees in the firm’s province.

4. Empirical Results

4.1. Descriptive Statistics

The results of the descriptive statistics concerning the main variables in this paper are shown in

Table 2. Descriptive statistics.

Variables	Sample Size	Mean	Standard Deviation	Minimum	Maximum
labprod	18,769	13.72	0.868	11.95	16.41
old_depth	19,180	14.20	3.319	8.600	21.10
size	18,775	22.10	1.281	19.89	26.09
clr	18,775	12.49	1.129	9.354	15.58
lev	18,775	0.416	0.209	0.0497	0.886
ppe	18,775	0.217	0.162	0.00226	0.702
cash	18,775	0.959	1.639	0.0285	10.78
bm	18,775	4.166	3.604	0.810	22.72
roa	18,775	4.632	5.581	−16.15	21.41
tq	18,040	2.074	1.342	0.865	8.765
indratio	18,392	0.374	0.0532	0.333	0.571
top1	18,392	35.48	14.70	9.443	74.29
avgwage	18,392	11.09	0.330	10.45	11.89
gdp	18,702	9.959	4.613	−4.890	23.96

. The dependent variable, labor productivity ($labprod$), has a mean value of 13.72 and moderate variability, indicating differences in firm-level productivity. The core explanatory variable, the old-age dependency ratio ($old\_depth$), averages 14.20, with significant regional variation, reflecting the uneven impact of population aging across provinces. The capital–labor ratio ($clr$) has a mean of 12.49, aligning with the study’s focus on the role of capital intensity in mediating the effects of aging on labor productivity. Other firm-level variables, such as firm size ($size$), leverage ($lev$), and return on assets ($roa$), show reasonable variability, providing a robust context for analyzing productivity dynamics. Regional controls, including average wages ($avgwage$) and GDP growth ($gdp$), exhibit substantial differences, capturing the economic diversity of the sampled regions. These statistics highlight the relevance of the dataset for examining the relationship between population aging, capital intensity, and labor productivity. The observed variation across key variables supports the empirical analysis of aging’s impact on corporate outcomes.

Variance inflation factors (VIFs) are all below the commonly accepted threshold of 5, with a mean VIF of 1.37, indicating no serious multicollinearity concerns among the explanatory variables. We also conduct standard regression diagnostics to evaluate model assumptions. Figure 1 shows the distribution of regression residuals. The histogram and kernel density plot suggest that residuals are approximately normally distributed. Figure 2 includes the residual-vs-fitted plot and Q-Q plot, which further indicate no strong deviations from homoscedasticity or normality. These diagnostics support the reliability of our fixed-effects estimation results.

4.2. The Effect of Population Aging on Labor Productivity

The regression analysis demonstrates a significant positive relationship between population aging (measured by $\mathtt{old}\_\mathtt{depth}$) and labor productivity ($\mathtt{labprod}$). The results support Hypothesis 1 that population aging enhances labor productivity. To improve interpretability, we complement the regression results with a marginal effects plot (Figure 3), which visualizes the predicted values of labor productivity across a range of values for the old-age dependency ratio. The figure confirms that the relationship is consistently positive and increases with aging intensity, reinforcing the idea that demographic pressure may incentivize productivity-enhancing firm responses.

This finding is consistent across all three model specifications, and the statistical significance of the $\mathtt{old}\_\mathtt{depth}$ coefficient strengthens as more control variables are introduced. Specifically, in Model (1), the coefficient of $\mathtt{old}\_\mathtt{depth}$ is positive and statistically significant at the $p<0.10$ level. In Models (2) and (3), the significance improves to $p<0.01$, highlighting a robust relationship between population aging and labor productivity. This result aligns with the hypothesis that aging populations drive structural changes in labor markets, such as increased reliance on automation and other productivity-enhancing adjustments [2,4]. The inclusion of control variables in Model (3) provides further insights into the factors influencing labor productivity. Building upon this specification, Model (4) additionally incorporates city fixed effects to control for unobserved, time-invariant heterogeneity across cities. These fixed effects account for structural differences in local economic environments, such as infrastructure quality, policy implementation efficiency, and urban agglomeration advantages, that may simultaneously influence demographic structure and firm performance.

The estimated coefficients on old_depth range from 0.0083 to 0.0147 across the four model specifications in

Table 3. Regression Results: Impact of Population Aging on Labor Productivity.

	(1)	(2)	(3)	(4)	(5)	(6)
	labprod	labprod	labprod	labprod	labprod	labprod
	Fixed-Effects Models				GMM Models
old_depth	0.0083 *	0.0107 ***	0.0144 ***	0.0147 ***	0.0114 ***	0.0068 *
	(0.0045)	(0.0041)	(0.0038)	(0.0038)	(0.0034)	(0.0041)
roa			0.0133 ***	0.0132 ***	0.0109 ***	0.0108 ***
			(0.0019)	(0.0019)	(0.0012)	(0.0015)
lev			0.6229 ***	0.6241 ***	0.5484 ***	0.4419 ***
			(0.0831)	(0.0831)	(0.0582)	(0.0941)
ppe			−0.5281 ***	−0.5293 ***	−0.3778 ***	−0.3293 ***
			(0.0888)	(0.0899)	(0.0508)	(0.0778)
cash			0.0003	0.0006	0.0036	0.0016
			(0.0063)	(0.0063)	(0.0043)	(0.0045)
size			0.1761 ***	0.1763 ***	0.0834 ***	0.0575 ***
			(0.0131)	(0.0131)	(0.0091)	(0.0169)
bm			−0.0163 ***	−0.0161 ***	−0.0161 ***	−0.0127 ***
			(0.0032)	(0.0032)	(0.0025)	(0.0035)
tq			−0.0032	−0.0033	−0.0045	−0.0037
			(0.0040)	(0.0040)	(0.0028)	(0.0030)
indratio			0.1058	0.1068	0.0181	0.0167
			(0.2016)	(0.2014)	(0.1118)	(0.0908)
top1			0.0008	0.0008	0.0004	−0.0000
			(0.0008)	(0.0008)	(0.0005)	(0.0004)
avgwage			0.4012 ***	0.4195 ***	0.1943 ***	0.1354 ***
			(0.0547)	(0.0610)	(0.0345)	(0.0401)
gdp			−0.0093 ***	−0.0092 ***	−0.0018	0.0007
			(0.0022)	(0.0022)	(0.0013)	(0.0013)
L.Labprod					0.5355 ***	0.3892 **
					(0.0348)	(0.1836)
L2.Labprod						0.2650 **
						(0.1113)
Constant	13.6019 ***	13.5675 ***	5.0712 ***	4.8563 ***	2.1259 ***	1.8487 ***
	(0.0665)	(0.0597)	(0.6539)	(0.7153)	(0.3863)	(0.4547)
Year-FE	Yes	Yes	Yes	Yes	Yes	Yes
Industry-FE	No	Yes	Yes	Yes	Yes	Yes
City-FE	No	No	No	Yes	No	No
R-squared	0.0103	0.2041	0.3436	0.3438
Observations	18,769	18,768	17,964	17,964	14,996	12,035

Note: Robust standard errors are shown in parentheses. *, **, and *** denote $p<0.10$, $p<0.05$, and $p<0.01$, respectively.

, and are consistently statistically significant at the 1% or 10% level. Interpreted in log-linear terms, these estimates suggest that a one-unit increase in the old-age dependency ratio is associated with approximately a 0.83% to 1.47% increase in firm-level labor productivity. To assess practical relevance, consider a more realistic demographic shift: if the old-age dependency ratio rises by 1 percentage point (such as from 14% to 15%), the corresponding increase in labor productivity would range from 0.83% to 1.47%. (According to the United Nations classification, societies with an old-age dependency ratio above 14% belong to moderately aging societies. The sample mean of old-age dependency in the data used in this paper is 14.2%). While these effect sizes may appear modest, they are economically meaningful given the large and persistent demographic transition in China, where the dependency ratio has increased by over 6 percentage points in the past decade alone. Moreover, labor productivity is a slow-moving macroeconomic variable; thus, even marginal improvements at the firm level, driven by demographic pressures, represent significant adaptive responses such as capital deepening, automation, or labor reallocation. These findings underscore that population aging is not merely a demographic burden but also an economic signal that firms respond to through measurable improvements in productive efficiency.

Profitability (roa) and firm size (size) both exhibit significant positive impacts on labor productivity, suggesting that higher profitability and larger firm size enhance operational efficiency. The significant positive coefficient implies that higher leverage(lev) may improve productivity by optimizing resource allocation and increasing investment efficiency [23]. The negative coefficient of ppe suggests that an excessive reliance on capital-intensive investment may not always translate into productivity gains, potentially due to resource misallocation [41]. The positive coefficient of avgwage indicates that higher wage levels, reflecting either improved worker skills or industry-specific productivity gains, contribute to labor productivity. The negative relationship between GDP growth and productivity suggests that lower growth rates may reflect structural economic adjustments, prompting firms to utilize resources more efficiently [42].

The coefficients on control variables such as cash and indratio are statistically insignificant across all model specifications. This lack of significance may reflect several factors. For cash, the non-significant relationship suggests that short-term liquidity does not directly affect labor productivity in a systematic way, especially in the context of population aging, where capital reallocation and long-term investment decisions may be more relevant. Similarly, indratio, which captures industry concentration, may not exhibit significant variation across firms within the same sector or may influence productivity through indirect channels not captured in the current specification. It is also possible that the effects of these variables are mediated or offset by other included controls, such as size, bm, and roa, reducing their standalone explanatory power in a multivariate setting.

To address potential endogeneity concerns—particularly the possibility that unobserved firm characteristics or reverse causality may bias the estimated relationship between population aging and labor productivity—we employ a two-step system GMM estimator in columns (5) and (6) of Table 3. Compared with the fixed-effects models in columns (1)–(4), the GMM results remain robust in magnitude and statistical significance. The coefficient of old_depth remains positive and significant, although slightly smaller in size, suggesting that the positive effect of demographic aging on labor productivity is not entirely driven by omitted variables or simultaneity. The consistency across specifications reinforces the causal interpretation of the baseline relationship and supports the credibility of our findings.

In addition to the direct estimation of population aging’s impact on labor productivity, we anticipate that the underlying mechanism may operate through changes in firms’ input structure—particularly through capital deepening in response to labor supply constraints. As the working-age population shrinks, firms may be incentivized to substitute labor with capital, thereby increasing the capital–labor ratio, which in turn enhances productivity. Although Table 3 focuses on the direct relationship, this potential mechanism warrants further exploration. We formally investigate this in the next section through a mediation analysis, where the capital–labor ratio is introduced as a key transmission channel linking demographic aging to productivity gains.

5. Results—Robust Test

5.1. Robustness Test: Changing the Dependent Variable

To ensure the robustness of the baseline results, this study employs an alternative measure of labor productivity ($\mathtt{labprod}\_\mathtt{adjust}$), defined as the natural logarithm of a firm’s operating revenue minus non-operating income, divided by the number of employees. By excluding non-operating income, this adjusted measure better reflects changes in firms’ productivity attributable to regular production and operational efficiency. The regression results using $\mathtt{labprod}\_\mathtt{adjust}$ as the dependent variable are presented in

Table 4. Robustness Test Results: Changing the Dependent Variable.

	(1)	(2)	(3)
	labprod_adjust	labprod_adjust	labprod_adjust
old_depth	0.0087 *	0.0112 ***	0.0147 ***
	(0.0045)	(0.0041)	(0.0038)
roa			0.0139 ***
			(0.0019)
lev			0.6249 ***
			(0.0837)
ppe			−0.5240 ***
			(0.0896)
cash			−0.0013
			(0.0065)
size			0.1776 ***
			(0.0131)
bm			−0.0165 ***
			(0.0032)
tq			−0.0034
			(0.0040)
indratio			0.0986
			(0.2029)
top1			0.0008
			(0.0008)
gdp			−0.0096 ***
			(0.0022)
avgwage			0.3983 ***
			(0.0551)
Constant	13.5799 ***	13.5454 ***	5.0515 ***
	(0.0670)	(0.0601)	(0.6585)
Year-FE	Yes	Yes	Yes
Industry-FE	No	Yes	Yes
Observations	18,755	18,754	17,952
R-squared	0.0116	0.2063	0.3453

Note: Robust standard errors are shown in parentheses. * and *** denote $p<0.10$ and $p<0.01$, respectively.

.

Across all three model specifications, the coefficient for $\mathtt{old}\_\mathtt{depth}$ remains positive and statistically significant. Specifically, in Model (1), the coefficient is significant at the $p<0.10$ level, while in Models (2) and (3), the significance improves to $p<0.01$, with the coefficients increasing in magnitude from 0.0112 to 0.0147. Specifically, a 1% increase in the old-age dependency ratio significantly increases the adjusted labor productivity of firms by 1.47%. The $R^2$ values increase significantly from Model (1) (0.0116) to Model (3) (0.3453), indicating that the inclusion of firm-level controls and fixed effects substantially improves the explanatory power of the model. This highlights the importance of firm-specific and industry-level characteristics in explaining labor productivity variations.

These results confirm that population aging, proxied by the old-age dependency ratio, consistently enhances firm-level labor productivity, even when using a refined productivity measure.

5.2. Robustness Test: Changing the Independent Variable

To further validate the relationship between population aging and labor productivity, the primary explanatory variable $\mathtt{old}\_\mathtt{depth}$ is replaced with $\mathtt{old}\_\mathtt{ratio}$, defined as the proportion of the elderly population (aged 65 and above) to the total population. This alternative measure provides a broader perspective on population aging, allowing for a more comprehensive assessment of its impact. The regression results, presented in

Table 5. Robustness Test Results: Changing the Independent Variable.

	(1)	(2)	(3)
	labprod	labprod	labprod
old_ratio	0.0254 ***	0.0257 ***	0.0218 ***
	(0.0067)	(0.0060)	(0.0056)
roa			0.0133 ***
			(0.0019)
lev			0.6241 ***
			(0.0830)
ppe			−0.5269 ***
			(0.0888)
cash			0.0006
			(0.0063)
size			0.1761 ***
			(0.0131)
bm			−0.0163 ***
			(0.0032)
tq			−0.0032
indratio			0.1092
			(0.2016)
top1			0.0008
			(0.0008)
gdp			−0.0088 ***
			(0.0021)
avgwage			0.3768 ***
			(0.0542)
Constant	13.4520 ***	13.4486 ***	5.3091 ***
	(0.0724)	(0.0650)	(0.6429)
Year-FE	Yes	Yes	Yes
Industry-FE	Yes	Yes	Yes
Observations	18,769	18,768	17,964
R-squared	0.0129	0.2063	0.3438

Note: Robust standard errors are shown in parentheses. *** denotes $p<0.01$.

, confirm the robustness of the findings across this alternative specification.

The coefficient for $\mathtt{old}\_\mathtt{ratio}$ is consistently positive and statistically significant at the $p<0.01$ level across all three models, indicating a positive relationship between the proportion of the elderly population and labor productivity. These results verify the relationship between population aging and labor productivity when changing the independent variable.

5.3. Robustness Test: Placebo Tests

Two methods were used to perform the placebo test. Firstly, we conduct a permutation test on the explanatory variable and the dependent variable separately. Columns (1) and (2) of

Table 6. Robustness Test Results: Placebo Tests

	labprod	labprod_adjust	labprod	labprod_adjust	labprod_p	labprod_adjust_p
	(1)	(2)	(3)	(4)	(5)	(6)
old_depth_p	0.0000	−0.0000
	(0.0015)	(0.0015)
old_depth_f			0.0014	0.0016
			(0.0020)	(0.0020)
old_depth					−0.0013	−0.0015
					(0.0023)	(0.0023)
roa	0.0134 ***	0.0140 ***	0.0135 ***	0.0140 ***	0.0001	0.0003
	(0.0019)	(0.0019)	(0.0019)	(0.0019)	(0.0015)	(0.0015)
lev	0.6209 ***	0.6228 ***	0.6210 ***	0.6229 ***	−0.0164	−0.0121
	(0.0834)	(0.0840)	(0.0833)	(0.0840)	(0.0529)	(0.0534)
ppe	−0.5200 ***	−0.5150 ***	−0.5211 ***	−0.5169 ***	0.0327	0.0316
	(0.0893)	(0.0901)	(0.0893)	(0.0900)	(0.0492)	(0.0497)
cash	−0.0005	−0.0022	−0.0006	−0.0022	0.0002	−0.0002
	(0.0063)	(0.0064)	(0.0063)	(0.0064)	(0.0048)	(0.0048)
size	0.1759 ***	0.1774 ***	0.1756 ***	0.1771 ***	0.0059	0.0053
	(0.0131)	(0.0132)	(0.0131)	(0.0132)	(0.0077)	(0.0077)
bm	−0.0168 ***	−0.0169 ***	−0.0167 ***	−0.0168 ***	0.0042 *	0.0040 *
	(0.0032)	(0.0032)	(0.0032)	(0.0033)	(0.0023)	(0.0023)
tq	−0.0029	−0.0031	−0.0030	−0.0031	−0.0046	−0.0045
	(0.0040)	(0.0040)	(0.0040)	(0.0040)	(0.0049)	(0.0049)
indratio	0.0700	0.0615	0.0735	0.0655	−0.0125	−0.0101
	(0.2021)	(0.2034)	(0.2022)	(0.2034)	(0.1243)	(0.1254)
top1	0.0008	0.0008	0.0008	0.0008	−0.0001	−0.0002
	(0.0008)	(0.0009)	(0.0008)	(0.0009)	(0.0005)	(0.0005)
gdp	−0.0093 ***	−0.0095 ***	−0.0094 ***	−0.0097 ***	−0.0026	−0.0028
	(0.0022)	(0.0022)	(0.0021)	(0.0022)	(0.0018)	(0.0018)
avgwage	0.3861 ***	0.3828 ***	0.4060 ***	0.4048 ***	0.0117	0.0090
	(0.0544)	(0.0548)	(0.0622)	(0.0627)	(0.0270)	(0.0273)
Constant	5.4623 ***	5.4536 ***	5.2230 ***	5.1875 ***	13.5036 ***	13.5341 ***
	(0.6424)	(0.6474)	(0.7419)	(0.7471)	(0.3371)	(0.3402)
Year FE	Yes	Yes	Yes	Yes	Yes	Yes
Industry FE	Yes	Yes	Yes	Yes	Yes	Yes
Observations	17,964	17,952	17,964	17,952	17,964	17,579
$R^2$	0.3414	0.3417	0.3414	0.3431	0.0016	0.0016

Note: Robust standard errors are shown in parentheses. * and *** denote $p<0.10$ and $p<0.01$, respectively.

permute the core explanatory variable (old-age dependency ratio). The regression results indicate that the explanatory variable after random permutation has no significant impact on labor productivity. Columns (5) and (6) permute the dependent variables (labprod and labprod_adjust). The regression results indicate that the old-age dependency ratio has no significant effect on the dependent variables after random permutation. The permutation test enhances the robustness of regression results. Secondly, the placebo test is added by replacing the old dependency ratio with the child-age dependency ratio in some areas to construct a false explanatory variable. Columns (3) and (4) replace the old-age dependency ratio (top 75%) above 11% with the child-age dependency ratio to construct a false explanatory variable. The insignificant regression results enhance the robustness of the baseline regression.

5.4. Robustness Test: Delayed Effects of Aging

To evaluate the delayed effect of aging, this paper replaces the explanatory variable in the fixed-effects model with a lagged old-age dependency ratio. Columns (1) and (2) of

Table 7. Robustness Test Results: Lagged Model.

	(1)	(2)
	labprod	labprod_adjust
L.old_depth	0.0126 ***	0.0128 ***
	(0.0041)	(0.0041)
L.roa	0.0137 ***	0.0144 ***
	(0.0022)	(0.0022)
L.lev	0.6336 ***	0.6390 ***
	(0.0878)	(0.0885)
L.ppe	−0.5100 ***	−0.5037 ***
	(0.0924)	(0.0931)
L.cash	−0.0088	−0.0105
	(0.0064)	(0.0066)
L.size	0.1928 ***	0.1928 ***
	(0.0137)	(0.0138)
L.bm	−0.0070 **	−0.0077 **
	(0.0032)	(0.0032)
L.tq	−0.0017	−0.0020
	(0.0041)	(0.0041)
L.indratio	0.0181	−0.0240
	(0.2130)	(0.2143)
L.top1	0.0006	0.0006
	(0.0009)	(0.0009)
L.gdp	−0.0097 ***	−0.0098 ***
	(0.0023)	(0.0024)
L.avgwage	0.3834 ***	0.3831 ***
	(0.0564)	(0.0568)
Constant	5.0024 ***	4.9880 ***
	(0.6731)	(0.6775)
Year FE	Yes	Yes
Industry FE	Yes	Yes
Observations	14953	14942
$R^2$	0.3609	0.3621

Note: Robust standard errors are shown in parentheses. ** and *** denote $p<0.05$ and $p<0.01$, respectively.

indicate that the lagged old-age dependency ratio has a significant positive impact on labor productivity, and the coefficient is similar to the benchmark regression results. Specifically, a 1% increase in the lagged old-age dependency ratio significantly increases the labor productivity of firms by 1.26%. The regression results in Table 7 indicate that aging has a delayed effect on labor productivity, as it takes some time for firms to optimize their factor structure to cope with the impact of population aging.

5.5. Robustness Test: Capital-Intensive vs. Labor-Intensive Firms

Population aging reduces labor supply, increasing the labor cost of firms [43]. Besides, the increase in the age of workers will reduce labor productivity, especially for manual workers [24,26]. According to microeconomic principles, a change in the price of one factor of production will cause a change in the demand for another factor, known as the substitution effect between factors of production. In order to save employment costs, labor-intensive firms that rely more on labor input are more incentivized to replace labor with capital and actively transition from labor-intensive production methods to capital-intensive production methods, thereby improving labor productivity. To examine the heterogeneity of firms in the impact of population aging on labor productivity, firms are classified into capital-intensive and labor-intensive groups. To examine the heterogeneity of firms in the impact of population aging on labor productivity, firms are classified into capital-intensive and labor-intensive groups (capital intensity = total assets/operating revenue; labor intensity = the number of employees/operating revenue). The separate regressions are run for each group using both $\mathtt{labprod}$ and $\mathtt{labprod}\_\mathtt{adjust}$ as dependent variables.

Table 8. Robustness Test Results: Capital-Intensive vs. Labor-Intensive Samples.

	(1)	(2)	(3)	(4)
	labprod	labprod	labprod_adjust	labprod_adjust
	Capital-Intensive	Labour-Intensive	Capital-Intensive	Labour-Intensive
old_depth	−0.0004	0.0067 ***	−0.0001	0.0069 ***
	(0.0043)	(0.0025)	(0.0043)	(0.0025)
roa	−0.0007	0.0080 ***	−0.0006	0.0087 ***
	(0.0022)	(0.0013)	(0.0022)	(0.0013)
lev	0.2763 ***	0.1298 **	0.2748 ***	0.1289 **
	(0.0927)	(0.0550)	(0.0932)	(0.0560)
ppe	−0.4339 ***	−0.0872	−0.4347 ***	−0.0764
	(0.0965)	(0.0584)	(0.0971)	(0.0585)
cash	−0.0077	−0.0027	−0.0085	−0.0044
	(0.0070)	(0.0042)	(0.0071)	(0.0043)
size	0.0764 ***	0.0420 ***	0.0772 ***	0.0432 ***
	(0.0148)	(0.0099)	(0.0148)	(0.0101)
bm	0.0009	−0.0113 ***	0.0005	−0.0114 ***
	(0.0041)	(0.0022)	(0.0042)	(0.0022)
tq	−0.0041	0.0013	−0.0042	0.0012
	(0.0047)	(0.0030)	(0.0047)	(0.0030)
indratio	0.1208	−0.0183	0.1196	−0.0332
	(0.2289)	(0.1338)	(0.2296)	(0.1349)
top1	0.0011	0.0007	0.0011	0.0007
	(0.0009)	(0.0006)	(0.0009)	(0.0006)
gdp	−0.0075 ***	−0.0013	−0.0078 ***	−0.0013
	(0.0023)	(0.0015)	(0.0024)	(0.0015)
avgwage	0.2112 ***	0.1046 ***	0.2092 ***	0.0976 **
	(0.0566)	(0.0384)	(0.0569)	(0.0388)
Constant	10.2847 ***	10.8831 ***	10.2781 ***	10.9104 ***
	(0.6746)	(0.4920)	(0.6772)	(0.4980)
Year-FE	Yes	Yes	Yes	Yes
Industry-FE	Yes	Yes	Yes	Yes
Observations	8936	8980	8935	8969
R-squared	0.2612	0.1618	0.2620	0.1715
Fisher’s permutation test	−0.007 **		−0.007 **
	(p = 0.016)		(p = 0.028)

Note: Robust standard errors are shown in parentheses.** and *** denote $p<0.05$ and $p<0.01$, respectively. This paper used [44] bootstrap intergroup coefficient difference (Bdiff) test method to test whether the difference between the group coefficients of group regression is significant.

shows the coefficient for $\mathtt{old}\_\mathtt{depth}$ is negative but statistically insignificant in both the $\mathtt{labprod}$ (Model 1) and $\mathtt{labprod}\_\mathtt{adjust}$ (Model 3) regressions, which suggests that for capital-intensive firms, population aging does not significantly impact labor productivity. In contrast, for labor-intensive firms, the coefficient for $\mathtt{old}\_\mathtt{depth}$ is positive and highly significant ($p<0.01$) in both the $\mathtt{labprod}$ (Model 2) and $\mathtt{labprod}\_\mathtt{adjust}$ (Model 4) regressions, indicating that as population aging intensifies, labor-intensive firms experience significant productivity gains.Specifically, a 1% increase in the old-age dependency ratio significantly increases the labor productivity of labor-intensive firms by 0.67%. Table 8 shows that population aging has a more direct impact on labor-intensive firms; therefore, under the pressure brought by population aging, labor-intensive firms can invest more capital and then improve labor productivity. For capital-intensive firms, due to less reliance on the input of labor factors, the impact of population aging shocks on them is small, and there is no incentive for capital deepening.

5.6. Robustness Test: Distinguishing Skilled Workers

Compared with the high-skilled labor market, population aging is more likely to impact the low-skilled labor market, resulting in a shortage of low-skilled workers, such as the shortage of migrant workers in China [7]. For firms with a higher proportion of low-skilled workers, the shortage of young workers in the labor market will increase the employment cost. Besides, the increase in the proportion of elderly workers will push up medical and welfare expenditures, causing the relative price of labor factors to rise [45]. Therefore, firms with a higher proportion of low-skilled workers are more willing to replace labor with capital, thus improving labor productivity. To examine the heterogeneous effects of population aging on labor productivity across different worker skill levels, firms are categorized into groups based on the proportion of high-skilled workers (high-skilled worker proportion is defined as the ratio of employees with a bachelor’s degree or higher to the total number of employees). Firms with a higher proportion of such employees are classified as employing high-skilled workers, while others are categorized as employing low-skilled workers.

Table 9. Robustness Test: Distinguishing Skilled Workers.

	(1)	(2)	(3)	(4)
	labprod	labprod	labprod_adjust	labprod_adjust
	Low-Skilled	High-Skilled	Low-Skilled	High-Skilled
old_depth	0.0084 **	−0.0024	0.0211 ***	0.0059
	(0.0038)	(0.0046)	(0.0048)	(0.0051)
clr	0.5992 ***	0.3466 ***
	(0.0181)	(0.0224)
roa	0.0150 ***	0.0263 ***	0.0101 ***	0.0199 ***
	(0.0020)	(0.0025)	(0.0025)	(0.0028)
lev	0.6653 ***	0.9917 ***	0.4691 ***	0.8335 ***
	(0.0882)	(0.1041)	(0.1105)	(0.1138)
ppe	−2.5796 ***	−2.1275 ***	−0.2649 **	−0.4482 ***
	(0.1131)	(0.1658)	(0.1130)	(0.1343)
cash	−0.0050	−0.0146 **	0.0181	−0.0140 *
	(0.0094)	(0.0063)	(0.0112)	(0.0075)
size	0.0610 ***	0.0583 ***	0.2023 ***	0.1211 ***
	(0.0153)	(0.0155)	(0.0192)	(0.0166)
bm	−0.0086 **	−0.0222 ***	−0.0114 **	−0.0259 ***
	(0.0041)	(0.0039)	(0.0045)	(0.0044)
tq	−0.0049	−0.0001	−0.0068	−0.0018
	(0.0042)	(0.0050)	(0.0054)	(0.0054)
indratio	−0.0801	−0.0746	0.2336	−0.1112
	(0.1994)	(0.2432)	(0.2566)	(0.2636)
top1	0.0038 ***	0.0002	0.0018	0.0002
	(0.0009)	(0.0010)	(0.0011)	(0.0011)
gdp	−0.0031	−0.0059 **	−0.0086 ***	−0.0113 ***
	(0.0022)	(0.0028)	(0.0029)	(0.0030)
avgwage	0.2624 ***	0.2891 ***	0.3508 ***	0.3459 ***
	(0.0675)	(0.0577)	(0.0885)	(0.0629)
Constant	1.9727 **	5.1322 ***	4.7100 ***	7.1744 ***
	(0.8139)	(0.7049)	(1.0768)	(0.7564)
Year-FE	Yes	Yes	Yes	Yes
Industry-FE	Yes	Yes	Yes	Yes
Observations	8886	9030	8881	9023
R-squared	0.5122	0.5198	0.2441	0.4414
Fisher’s	0.011 ***		0.105 ***
permutation test	(p = 0.000)		(p = 0.000)

Note: Robust standard errors are shown in parentheses. *, **, and *** denote $p<0.10$, $p<0.05$, and $p<0.01$, respectively.

presents the regression results for these two subsamples using labprod and labprod_adjust as dependent variables.

As for the low-skilled workers group, the coefficient of $\mathtt{old}\_\mathtt{depth}$ is positive and statistically significant in both $\mathtt{labprod}$ (Model 1, $p<0.05$) and $\mathtt{labprod}\_\mathtt{adjust}$ (Model 3, $p<0.01$) regressions. Specifically, the coefficients are 0.0084 in Model 1 and 0.0211 in Model 3, indicating that population aging has a strong positive effect on the productivity of firms with a higher proportion of low-skilled workers. Specifically, a 1% increase in the old-age dependency ratio significantly increases the labor productivity of firms with a higher proportion of low-skilled workers by 0.84%. This suggests that population aging compels firms with low-skilled labor to enhance labor productivity.

For firms with a higher proportion of high-skilled workers, the coefficient for $\mathtt{old}\_\mathtt{depth}$ is statistically insignificant in both $\mathtt{labprod}$ (Model 2) and $\mathtt{labprod}\_\mathtt{adjust}$ (Model 4). The coefficients are −0.0024 in Model 2 and 0.0059 in Model 4, suggesting that population aging has a negligible direct impact on the productivity of high-skilled workers, which implies that firms with a high proportion of skilled employees are less affected by aging-related labor market dynamics, potentially due to their reliance on advanced skills and knowledge rather than manual labor. Compared with firms with a higher proportion of low-skilled workers, firms with a higher proportion of skilled workers usually do not rely on physical labor for production, making the impact of aging on labor productivity relatively limited, thus having no incentive to further substitute capital for labor.

5.7. Robustness Test: City-Level Heterogeneity in Population Aging Effects

The differences in industrial structure and talent structure among different types of cities have led to differences in the cost of technological upgrading for firms in response to the impact of aging. Generally speaking, big cities are dominated by financial and high-tech industries and are more able to attract young and creative talent. The aging population is forcing companies to accelerate technological substitution, and young and creative talent structures are more likely to lead and adapt to technological changes [46], offsetting the negative impact of aging. However, small cities are mainly dominated by traditional manufacturing, making it difficult to attract young and creative talents. The cost of technological upgrading is high, and it is difficult to achieve capital substitution under the impact of an aging population. To examine the heterogeneous effects of population aging (old_depth) on labor productivity (labprod) across different city tiers, as defined by the “City Business Attractiveness Ranking” published by Yicai’s New First-Tier Cities Research Institute. Cities are classified into first-tier (including new first-tier cities), second-tier, and third-tier cities.

To examine the heterogeneous effects of population aging ($\mathtt{old}\_\mathtt{depth}$) on labor productivity ($\mathtt{labprod}$) across different city tiers, as defined by the “City Business Attractiveness Ranking” published by Yicai’s New First-Tier Cities Research Institute. Cities are classified into first-tier (including new first-tier cities), second-tier, and third-tier cities. To account for unobserved city-specific factors, city fixed effects are included in all regressions.

Table 10. Robustness Test: City-Level Heterogeneity in Population Aging Effects.

	(1)	(2)	(3)	(4)
	All Samples	First-Tier	Second-Tier	Third-Tier
old_depth	0.0147 ***	0.0159 ***	0.0236 ***	0.0006
	(0.0038)	(0.0049)	(0.0086)	(0.0080)
roa	0.0132 ***	0.0106 ***	0.0139 ***	0.0152 ***
	(0.0019)	(0.0028)	(0.0037)	(0.0035)
lev	0.6241 ***	0.6904 ***	0.6759 ***	0.4733 ***
	(0.0831)	(0.1194)	(0.1699)	(0.1542)
ppe	−0.5293 ***	−0.7178 ***	−0.6539 ***	−0.1751
	(0.0899)	(0.1397)	(0.1808)	(0.1514)
cash	0.0006	0.0006	0.0009	0.0064
	(0.0063)	(0.0086)	(0.0131)	(0.0129)
size	0.1763 ***	0.1584 ***	0.1969 ***	0.2013 ***
	(0.0131)	(0.0183)	(0.0279)	(0.0259)
bm	−0.0161 ***	−0.0128 ***	−0.0223 ***	−0.0166 ***
	(0.0032)	(0.0046)	(0.0063)	(0.0061)
tq	−0.0033	−0.0044	0.0020	−0.0076
	(0.0040)	(0.0055)	(0.0076)	(0.0077)
indratio	0.1068	0.0521	0.3305	0.0167
	(0.2014)	(0.2888)	(0.3847)	(0.3756)
top1	0.0008	0.0010	0.0016	0.0002
	(0.0008)	(0.0012)	(0.0017)	(0.0016)
gdp	−0.0092 ***	−0.0222 ***	−0.0057	−0.0050
	(0.0022)	(0.0041)	(0.0041)	(0.0032)
avgwage	0.4195 ***	0.3626 ***	0.0519	0.6828 ***
	(0.0610)	(0.0681)	(0.2074)	(0.2149)
Constant	4.8563 ***	6.0447 ***	8.2039 ***	1.5716
	(0.7153)	(0.8101)	(2.4197)	(2.4362)
Year-FE	Yes	Yes	Yes	Yes
Industry-FE	Yes	Yes	Yes	Yes
City-FE	Yes	Yes	Yes	Yes
Observations	17,964	8966	4398	4599
R-squared	0.3438	0.3986	0.3360	0.2402

Note: Robust standard errors are shown in parentheses.*** denotes $p<0.01$. The sampling frequency of bootstrap-based Fisher’s permutation test is set to 500 times. The p-value of Fisher’s permutation test (first-tier vs third-tier cities, second-tier vs third-tier cities, and first-tier vs second-tier cities) passed the significance test, which indicates a significant difference in the samples.

presents the results for the full sample and each city tier.

For all samples (Column 1), the coefficient for $\mathtt{old}\_\mathtt{depth}$ is positive and statistically significant ($p<0.01$), suggesting that population aging has an overall positive impact on labor productivity across all city tiers, reflecting the broader structural adjustments and technological advancements triggered by demographic shifts in urban economies.

For first-tier cities (Column 2), the coefficient for $\mathtt{old}\_\mathtt{depth}$ remains positive and significant ($p<0.01$) and is slightly larger than that for the full sample, indicating that first-tier cities, with their advanced economic infrastructure and access to resources, benefit more from aging-related productivity enhancements. These cities are likely to leverage better technology adoption, skilled labor, and institutional frameworks to mitigate the challenges of an aging workforce. Further, the coefficient for $\mathtt{old}\_\mathtt{depth}$ for first-tier cities (Column 2) is even larger and remains highly significant ($p<0.01$), which suggests that second-tier cities may experience the most pronounced productivity gains from population aging.Specifically, a 1% increase in the old-age dependency ratio significantly increases the labor productivity of firms in first-tier cities by 1.59% and increases the labor productivity of firms in second-tier cities by 2.36%. As transitional economies, these cities are increasingly adopting automation and other efficiency-enhancing technologies to address labor shortages, resulting in substantial productivity improvements.

In contrast, for the third-tier cities (Column 4), the coefficient for $\mathtt{old}\_\mathtt{depth}$ is statistically insignificant, indicating no measurable effect of aging on labor productivity in third-tier cities. This result may reflect the limited economic diversification, inadequate resources, and slower adoption of advanced technologies in these cities. The constrained ability to invest in education, infrastructure, and industrial upgrades hampers their capacity to transform demographic challenges into productivity gains. Compared with first-tier and second-tier cities, third-tier cities are dominated by traditional manufacturing and are difficult to attract young and creative talents. Under the impact of aging, the talent structure of these cities increases the cost of technological upgrading and makes it easier to form a low-end lock-in.

The findings reveal substantial heterogeneity in the impact of population aging on labor productivity across city tiers. These insights underscore the importance of tailored policy interventions that consider the unique economic and demographic dynamics of each city tier.

5.8. Mediating Effect of Capital–Labor Ratio

5.8.1. Mediating Econometric Model

The relationship between population aging and labor productivity is deeply rooted in the structural changes brought about by demographic shifts. A declining labor force, driven by aging populations, results in an increase in the capital available per unit of labor, thereby enhancing firm-level productivity. To formally assess the significance of the mediation mechanism, we apply the Sobel test and bootstrapping methods. The Sobel test confirms that the indirect effect of population aging on labor productivity through capital deepening (old_depth) is statistically significant at the 1% level. In addition, we conduct bootstrapping with 1000 replications, which yields similar significance levels and confidence intervals, reinforcing the robustness of the mediating effect.

5.8.2. Results: Mediating Effect of Capital–Labor Ratio

Table 11. The Mediating Effect of the Capital–Labor Ratio (CLR).

	(1)	(2)	(3)
	clr	labprod	labprod_adjust
old_depth	0.0221 ***	0.0040	0.0044
	(0.0042)	(0.0033)	(0.0033)
clr		0.4698 ***	0.4674 ***
		(0.0163)	(0.0165)
roa	−0.0155 ***	0.0206 ***	0.0211 ***
	(0.0021)	(0.0017)	(0.0017)
lev	−0.4554 ***	0.8351 ***	0.8350 ***
	(0.0878)	(0.0723)	(0.0733)
ppe	4.0936 ***	−2.4511 ***	−2.4364 ***
	(0.0936)	(0.0974)	(0.0985)
cash	0.0229 ***	−0.0107 **	−0.0122 **
	(0.0070)	(0.0053)	(0.0054)
size	0.2261 ***	0.0700 ***	0.0721 ***
	(0.0134)	(0.0116)	(0.0118)
bm	−0.0046	−0.0141 ***	−0.0142 ***
	(0.0033)	(0.0028)	(0.0029)
tq	−0.0018	−0.0023	−0.0024
	(0.0041)	(0.0035)	(0.0035)
indratio	0.3330	−0.0489	−0.0550
	(0.2160)	(0.1748)	(0.1768)
top1	−0.0017 *	0.0016 **	0.0016 **
	(0.0009)	(0.0007)	(0.0007)
avgwage	0.2141 ***	0.2998 ***	0.2970 ***
	(0.0549)	(0.0467)	(0.0472)
gdp	−0.0105 ***	−0.0043 **	−0.0046 **
	(0.0023)	(0.0019)	(0.0019)
Constant	4.2271 ***	3.0921 ***	3.0849 ***
	(0.6605)	(0.5592)	(0.5655)
Year-FE	Yes	Yes	Yes
Industry-FE	Yes	Yes	Yes
Observations	17,970	17,964	17,952
R-squared	0.5694	0.5038	0.5010

Note: Robust standard errors are shown in parentheses. *, **, and *** denote $p<0.10$, $p<0.05$, and $p<0.01$, respectively.

presents the analysis of the mediating role of the capital–labor ratio ($clr$) in the relationship between population aging ($old\_depth$) and labor productivity ($labprod$ and $labprod\_adjust$). The findings provide robust evidence that the capital–labor ratio serves as a significant channel through which aging impacts productivity.

Model (1) demonstrates that $old\_depth$ has a positive and statistically significant effect on $clr$ ($0.0221,p<0.01$). This indicates that population aging leads to an increase in the capital–labor ratio. The result aligns with the hypothesis that firms respond to labor shortages caused by aging populations by increasing capital investments relative to labor inputs, thereby raising capital intensity. The inclusion of clr in models (2) and (3) significantly reduces the explanatory power of $old\_depth$, providing strong evidence for its mediating role. In Models (2) and (3), the inclusion of $clr$ as a mediating variable substantially alters the relationship between $old\_depth$ and labor productivity: The direct effect of $old\_depth$ on both $labprod$ and $labprod\_adjust$ becomes statistically insignificant ($p>0.10$), indicating that the impact of aging on productivity is fully mediated by the capital–labor ratio. $clr$ itself exhibits a strong positive and significant effect on both $labprod$ ($p<0.01$) and $labprod\_adjust$ ($0.4674,p<0.01$). This confirms that a higher capital–labor ratio enhances labor productivity, acting as the primary mechanism through which aging influences productivity outcomes.

These results confirm the centrality of the capital–labor ratio as a mediating variable in Hypothesis 2. Population aging prompts firms to increase capital investment relative to labor, mitigating the adverse effects of labor shortages. The increased capital–labor ratio directly improves labor productivity, emphasizing the importance of structural adjustments in aging economies.

As shown in Table 11, we find strong empirical evidence supporting a full mediation mechanism through the capital–labor ratio. In Column (1), the coefficient on old_depth is positive and statistically significant at the 1% level when regressed on clr, indicating that population aging leads to greater capital deepening at the firm level. In Column (2), the direct effect of old_depth on labor productivity is statistically insignificant. However, when clr is included in Column (3), its coefficient is large and highly significant, while the coefficient on old_depth remains statistically insignificant. This pattern implies that the influence of population aging on firm productivity is entirely transmitted through changes in capital intensity. These results are consistent with a full mediation relationship, wherein population aging induces capital–labor substitution, and it is this structural shift in input composition—rather than demographic changes per se—that enhances productivity. The dominance of the indirect path via clr, coupled with the absence of a statistically significant direct effect, confirms the full mediating role of capital deepening in the demographic–productivity nexus.

This finding underscores the need for policies that encourage capital investment and technological advancements to support productivity in aging societies. Investments in automation, infrastructure, and workforce development can help sustain productivity growth amid demographic transitions.

We also conduct a formal Sobel–Goodman mediation analysis to examine whether the capital–labor ratio mediates the impact of population aging (measured by the old-age dependency ratio) on labor productivity.

Table 12. Sobel–Goodman Mediation Test Results: Capital–Labor Ratio as Mediator.

Effect Type	Coefficient	Std. Error	p-Value
Indirect effect (a × b)	0.0104	0.00092	<0.001
Direct effect (c’)	0.0040	0.00161	0.014
Total effect (c)	0.0144	0.00185	<0.001
Sobel z-statistic	11.28		<0.001
Proportion mediated	72.39%
Indirect/Direct ratio	2.62
Total/Direct ratio	3.62

Note: The table reports the results of the Sobel–Goodman mediation test, where the capital–labor ratio mediates the effect of population aging (old_depth) on labor productivity (labprod). The indirect effect is statistically significant at the 1% level. The direct effect remains significant at the 5% level, indicating partial mediation.

shows a statistically significant indirect effect of 0.0104 (Sobel z = 11.28, p < 0.001), indicating that a substantial portion of the effect of aging operates through increased capital deepening. The direct effect remains statistically significant at 0.0040 (p = 0.014), and the total effect is 0.0144. These estimates imply that approximately 72.39% of the total effect is mediated through the capital–labor ratio, and the indirect effect is over 2.6 times larger than the direct effect. This provides strong evidence for partial mediation and supports our theoretical argument that population aging enhances productivity primarily via capital–labor substitution.

Table 13. Heterogeneous Mediation Effects by Industry Type.

	Capital Intensive		Labor Intensive
	clr	labprod	clr	labprod
old_depth	0.0138 **	−0.0037	0.0185 ***	0.0019
	(0.0058)	(0.0041)	(0.0045)	(0.0022)
roa	−0.0186 ***	0.0037 *	−0.0218 ***	0.0136 ***
	(0.0028)	(0.0021)	(0.0024)	(0.0012)
lev	−0.6661 ***	0.4343 ***	−0.6478 ***	0.2970 ***
	(0.1156)	(0.0904)	(0.0985)	(0.0509)
ppe	4.2392 ***	−1.4393 ***	4.1856 ***	−1.1677 ***
	(0.1220)	(0.1216)	(0.1152)	(0.0730)
cash	0.0142	−0.0111	0.0276 ***	−0.0098 ***
	(0.0108)	(0.0068)	(0.0073)	(0.0036)
size	0.1502 ***	0.0408 ***	0.1763 ***	−0.0035
	(0.0170)	(0.0141)	(0.0178)	(0.0093)
bm	0.0006	0.0007	−0.0011	−0.0110 ***
	(0.0054)	(0.0039)	(0.0035)	(0.0021)
tq	−0.0057	−0.0028	0.0054	−0.0001
	(0.0059)	(0.0044)	(0.0050)	(0.0028)
indratio	0.2261	0.0671	0.3891	−0.1188
	(0.2937)	(0.2192)	(0.2364)	(0.1131)
top1	−0.0007	0.0013	−0.0022 **	0.0012 ***
	(0.0012)	(0.0009)	(0.0010)	(0.0005)
avgwage	0.1670 **	0.1716 ***	−0.0389	0.1147 ***
	(0.0656)	(0.0539)	(0.0647)	(0.0325)
gdp	−0.0087 ***	−0.0055 **	−0.0071 ***	0.0006
	(0.0030)	(0.0022)	(0.0026)	(0.0014)
clr		0.2372 ***		0.2581 ***
		(0.0207)		(0.0121)
Constant	6.9247 ***	8.6424 ***	7.8760 ***	8.8500 ***
	(0.7926)	(0.6647)	(0.8329)	(0.4247)
Year-FE	Yes	Yes	Yes	Yes
Industry-FE	Yes	Yes	Yes	Yes
R-squared	0.618	0.329	0.582	0.314
Observations	8936	8936	8980	8980

Note: Robust standard errors are shown in parentheses. *, **, and *** denote $p<0.10$, $p<0.05$, and $p<0.01$, respectively.

reports the heterogeneous mediation effects of the capital–labor ratio across labor-intensive and capital-intensive industries. The results show that capital–labor substitution plays a stronger mediating role in labor-intensive industries, where aging significantly increases the capital–labor ratio, which in turn enhances productivity. In contrast, the mediation effect is weaker and statistically insignificant in non-labor-intensive sectors. These findings support the view that demographic pressure amplifies capital deepening, especially where labor is a key input.

Table 14. Mediation Effects by City Tier

	Tier 1 Cities		Tier 2 Cities		Tier 3 Cities
	clr	labprod	clr	labprod	clr	labprod
old_depth	0.0327 ***	0.0018	0.0270 ***	0.0093	−0.0054	0.0037
	(0.0059)	(0.0044)	(0.0083)	(0.0072)	(0.0078)	(0.0066)
clr		0.4303 ***		0.5280 ***		0.5662 ***
		(0.0221)		(0.0334)		(0.0285)
roa	−0.0188 ***	0.0187 ***	−0.0121 ***	0.0202 ***	−0.0121 ***	0.0221 ***
	(0.0032)	(0.0024)	(0.0040)	(0.0030)	(0.0033)	(0.0031)
lev	−0.4529 ***	0.8825 ***	−0.4940 ***	0.9347 ***	−0.4050 ***	0.7039 ***
	(0.1338)	(0.1070)	(0.1719)	(0.1388)	(0.1497)	(0.1305)
ppe	4.6521 ***	−2.7190 ***	4.0766 ***	−2.8070 ***	3.3162 ***	−2.0519 ***
	(0.1570)	(0.1467)	(0.1639)	(0.2066)	(0.1510)	(0.1567)
cash	0.0185 *	−0.0079	0.0246 *	−0.0120	0.0381 ***	−0.0152
	(0.0100)	(0.0073)	(0.0137)	(0.0097)	(0.0114)	(0.0108)
size	0.2023 ***	0.0715 ***	0.2418 ***	0.0693 ***	0.2570 ***	0.0556 **
	(0.0190)	(0.0164)	(0.0272)	(0.0258)	(0.0248)	(0.0222)
bm	−0.0030	−0.0115 ***	−0.0122 *	−0.0158 ***	−0.0016	−0.0157 ***
	(0.0048)	(0.0040)	(0.0064)	(0.0053)	(0.0063)	(0.0056)
tq	0.0054	−0.0067	−0.0118	0.0084	−0.0048	−0.0048
	(0.0060)	(0.0051)	(0.0078)	(0.0060)	(0.0072)	(0.0065)
indratio	0.2247	−0.0431	0.5372	0.0441	0.5629	−0.2994
	(0.3139)	(0.2517)	(0.4055)	(0.3311)	(0.3721)	(0.3157)
top1	−0.0014	0.0016	−0.0029 *	0.0031 **	−0.0028 *	0.0018
	(0.0013)	(0.0011)	(0.0017)	(0.0014)	(0.0015)	(0.0013)
avgwage	0.2564 ***	0.2512 ***	−0.1801	0.1479	0.4026 **	0.4548 ***
	(0.0707)	(0.0601)	(0.2118)	(0.1819)	(0.1942)	(0.1702)
gdp	−0.0181 ***	−0.0144 ***	−0.0068	−0.0021	−0.0082 ***	−0.0003
	(0.0044)	(0.0035)	(0.0047)	(0.0033)	(0.0031)	(0.0027)
Constant	4.0916 ***	4.2926 ***	8.1915 ***	3.8710 *	1.9927	0.4462
	(0.8652)	(0.7173)	(2.4514)	(2.1433)	(2.2296)	(1.9173)
Year-FE	Yes	Yes	Yes	Yes	Yes	Yes
Industry-FE	Yes	Yes	Yes	Yes	Yes	Yes
R-squared	0.582	0.536	0.608	0.514	0.527	0.459
Observations	8969	8966	4399	4398	4601	4599

Note: Robust standard errors are shown in parentheses. *, **, and *** denote $p<0.10$, $p<0.05$, and $p<0.01$, respectively.

reports the heterogeneous mediation effects of the capital–labor ratio across city tiers. The results show that the indirect effect of population aging through capital–labor substitution is most evident in first- and second-tier cities, where aging significantly increases the capital–labor ratio, which in turn enhances productivity. In contrast, the mediating channel is weaker in third-tier cities, where the effect of aging on the capital–labor ratio is statistically insignificant. This suggests that capital deepening as a response to demographic pressure is more prevalent in more developed urban areas.

6. Conclusions and Policy Implications

This paper investigates the causal relationship between population aging and labor productivity in China, using firm-level panel data and mediation analysis to reveal how demographic shifts reshape economic outcomes. The findings demonstrate that population aging, as measured by the old-age dependency ratio, significantly enhances labor productivity at the firm level. This positive effect is primarily mediated by an increase in the capital-labor ratio, suggesting that firms respond to labor shortages by deepening capital investments. Approximately 72.4% of the total effect is transmitted through this channel, while the remaining direct effect remains significant, underscoring partial mediation.

Further analyses reveal heterogeneities across firms and regions. Labor-intensive firms and those employing low-skilled workers experience stronger productivity gains, likely due to greater incentives for automation and structural adjustments. In contrast, capital-intensive and high-skilled labor environments show weaker or insignificant effects. Regionally, first- and second-tier cities benefit more from the productivity-enhancing effects of aging, while third-tier cities lag behind due to constraints in technological readiness, fiscal capacity, and human capital. These disparities highlight the importance of localized responses to demographic change.

In light of these findings, policymakers should adopt a multi-pronged approach. First, governments can promote capital investment and automation by offering tax incentives and subsidies, particularly in labor-intensive sectors where demographic pressures are most acute. Second, tailored workforce development programs—especially in third-tier cities—can help adapt labor supply to evolving technological demands. Third, infrastructure investments and targeted industrial policies are crucial to support lagging regions and reduce spatial inequalities. Fourth, innovation policies should prioritize technologies suited to aging societies, including healthcare innovations, elderly care systems, and labor-saving tools. Finally, policy interventions must consider tier-specific urban dynamics to maximize demographic dividends and mitigate structural gaps.

While this study identifies capital deepening as a key mechanism, future research should explore how technological innovation—especially artificial intelligence and advanced automation—interacts with demographic change to influence productivity. As firms increasingly integrate such technologies, the dynamics of aging and productivity may evolve in complex ways across sectors and regions. Additionally, the role of local governance, education systems, and institutional infrastructure in moderating these effects deserves closer attention. Labor market responses, such as workforce restructuring and targeted training strategies, also represent promising avenues for further investigation, particularly in understanding how firms optimize productivity under labor force aging.

In sum, this study provides robust empirical evidence on how population aging can drive firm-level productivity growth through capital accumulation and adaptive restructuring. It also underscores that this demographic transition does not inevitably hinder economic growth; instead, with the right policy mix, it can serve as a catalyst for upgrading industrial capabilities and reducing labor market inefficiencies. By addressing the structural, spatial, and institutional aspects of demographic change, this work contributes to advancing Sustainable Development Goals 8 (Decent Work and Economic Growth), 9 (Industry, Innovation, and Infrastructure), and 10 (Reduced Inequalities).