截止到2018年，中国已经成为世界上老年人口最多的国家，并且根据OECD统计数据库的预测，在今后很长的一段时间内，中国人口老龄化的趋势还会不断加深，到2060年中国65岁以上老年人口会达到3.93亿，占总人口的比例将达到30.52%，届时全球将有四分之一的老年人口生活在中国。这意味着我国依靠人口数量与结构优势所推动的传统经济增长模式已难以继续，寻求新的经济增长动力，加快人力资本积累，将人口的数量和结构优势转变为人口质量的优势是我国现阶段实现经济发展方式转变和持续发展的有效途径。然而，人口老龄化的不断加剧，会增加社会和家庭的养老负担，这可能对保持人力资本投资水平持续稳定的增长产生不利影响。由此可见，在人口老龄化不可逆转的情况下，认识人口老龄化与人力资本投资二者之间的关系对于深入了解经济增长的潜能、保持经济可持续发展具有重要的现实意义。

现有研究多从宏观视角分析人口老龄化对国家及地区人力资本投资的影响，但事实上，居民家庭人力资本投资也是影响人力资本积累的重要因素。因此，本研究由人口老龄化与家庭人力资本投资的动态演化关系切入，结合我国现实情境，从家庭养老视角剖析了现阶段人口老龄化可能挤出家庭人力资本投资的微观机制，并评估了我国现行的社会养老保险制度是否可以在其中发挥缓解作用。具体而言，研究内容包括以下四部分：第一，在一般均衡视角下，构建包含人口年龄结构、家庭人力资本积累和养老模式的世代交叠模型，刻画人口老龄化影响家庭人力资本投资的理论机制；第二，在理论分析的基础上，利用省级面板数据，采用非线性方法实证检验人口老龄化对家庭人力资本投资的阶段性影响；第三，结合当前中国人口老龄化不断加剧的现实背景，基于微观家庭追踪调查数据实证分析了家庭养老负担对人力资本投资的挤出效应及其作用路径；第四，考虑到社会养老对家庭养老的补充作用，实证检验我国现行的社会养老保险制度是否可以缓解家庭养老负担对人力资本投资的不利影响。

通过理论分析和实证检验，本文得到的主要结论包括：

第一，理论分析发现，人口老龄化对家庭人力资本投资的影响具有阶段性差异；而基于家庭养老视角来看，养老负担的增加会减少家庭人力资本投资水平；我国现行的社会养老保险制度可以缓解家庭养老负担，从而对家庭人力资本投资产生促进作用。具体而言，基准模型的分析结果表明，人口出生率的降低会增加家庭人力资本投资，而寿命延长会对家庭人力资本投资产生不利影响，这意味着我国人口老龄化对家庭人力资本投资的影响可能表现出阶段性差异。进一步地，在基准模型中引入家庭养老机制，结合我国现实经济参数的校准分析发现，养老负担会挤出家庭人力资本投资，原因在于养老负担增加了家庭的经济与时间成本，从而对人力资本投资产生不利影响。然而，在基准模型中引入社会和家庭相结合的养老模式，利用数值分析的结果显示，我国现行的社会养老保险制度促进了家庭人力资本投资，一定程度上缓解了家庭养老负担所带来的负向效应。

第二，基于宏观数据的实证检验表明，人口老龄化与家庭人力资本投资之间呈现明显的倒“U”型关系，现阶段中国人口老龄化水平已经跨越拐点，对家庭人力资本投资产生不利影响。具体而言，利用我国1998-2018年省级面板数据分析发现，在不考虑人口老龄化对家庭人力资本投资的非线性影响时，人口老龄化会显著降低家庭人力资本投资水平；在加入了非线性关系的考察后，人口老龄化与家庭人力资本投资之间存在显著的倒“U”型关系，并且与最高家庭人力资本投资水平相对应的人口老龄化拐点值在8.82%-9.28%之间，出现于2011年左右。另外，异质性分析结果发现，人口老龄化对农村和西部地区家庭人力资本投资的负向影响更为显著；分时段的结果显示，现阶段我国人口老龄化对家庭人力资本投资的影响已跨越拐点，人口老龄化的持续加剧会不断挤出家庭人力资本投资。

第三，基于微观数据的实证检验显示，养老负担对家庭人力资本投资的挤出效应是通过增加家庭的经济和时间成本发挥作用的。具体而言，采用2010-2018年中国家庭追踪调查（CFPS）数据检验表明，家庭养老负担增加，会显著地降低家庭人力资本投资水平。进一步分析发现，养老负担越重的家庭，进行人力资本投资的概率和规模越低。采用中介效应模型的机制分析显示，养老负担会通过增加家庭医疗支出（经济成本）和减少成年子女劳动供给时间（时间成本）两个渠道对家庭人力资本投资产生挤出效应。此外，基于家庭特征的异质性分析发现，在农村、中低收入水平、子女处于中小学阶段、拥有高龄老年人、受传统文化影响较深的家庭中，养老负担对其人力资本投资的挤出效应更加明显。

第四，考虑到社会养老保险相对于家庭养老的长期性和稳定性优势，实证检验证实了我国现行社会养老保险制度对家庭人力资本投资具有促进作用，缓解了家庭养老负担的不利影响。具体而言，结合微观调查数据的实证检验结果显示，家庭参与社会养老保险会显著地提高其人力资本投资水平。进一步地，通过分组检验以及引入交叉项的实证分析发现，社会养老保险制度对于家庭养老负担影响人力资本投资具有积极的调节效应，即社会养老保险制度可以缓解家庭内部的养老负担对其人力资本投资的挤出效应。需要指出的是，通过异质性分析发现，由于我国存在不同形式的社会养老保险制度，社会养老保险的上述调节效应存在城乡和区域差异。

本文的创新点有以下三个方面：一是从研究视角上，将人口结构与人力资本投资纳入到统一的理论框架下，试图从微观视角解释人口老龄化对人力资本积累的影响，一定程度上拓展了现有理论分析；二是在实证策略上，通过宏观与微观相结合的方式，检验了人口老龄化与家庭人力资本投资之间的动态变化关系，并为其提供了一个可能的作用路径；三是在机制探讨上，不仅从经济成本和时间成本两个层面证实了养老负担对家庭人力资本投资的挤出效应，还发现社会养老保险可以缓解这种挤出效应，从而为我国社会养老保险制度的完善提供了一定程度的政策启示。

Population aging has entered a rapid development stage in China. By 2018, China has become the country with the largest elderly population in the world. According to the forecast of OECD statistical database, the trend of population aging in China will continue to deepen for a long time in the future. By 2060, the number of elderly people over 65 will reach 393 million, accounting for 30.52% of the total population. At that time, a quarter of the world's elderly people will live in China. This means that China's traditional economic growth model driven by the advantages of population and structure is difficult to continue. Therefore, it is an effective way for China to realize the transformation of economic development mode and sustainable development at the present stage to seek new economic growth power, accelerate the accumulation of human capital, and transform the advantages of population quantity and structure into the advantages of population quality. However, the increasing aging of population will increase the pension burden of society and families, which may have a negative impact on maintaining the sustained and stable growth of human capital investment. Therefore, under the irreversible situation of population aging, it is of great practical significance to understand the relationship between population aging and human capital investment for further understanding the potential of economic growth and maintaining sustainable economic development.

Most of the existing studies analyze the impact of population aging on national and regional human capital investment from a macro perspective, but in fact, the human capital investment of households is also an important factor affecting the accumulation of human capital. Therefore, this study starts from the dynamic evolution relationship between population aging and family human capital investment, combined with the actual situation in China, analyzes the micro mechanism of population aging crowding out family human capital investment from the perspective of family pension, and evaluates whether China's current social pension insurance system can play a role in alleviating it. Specifically, the research contents include the following four parts: Firstly, from the perspective of general equilibrium, this paper constructs an overlapping generation model including population age structure, family human capital accumulation and pension mode to describe the theoretical mechanism of the impact of population aging on family human capital investment; Second, on the basis of theoretical analysis, combined with provincial panel data, we use nonlinear method to empirically test the phased impact of population aging on family human capital investment; Thirdly, considering the increasing aging of population in China, this paper empirically analyzes the crowding out effect of family pension burden on human capital investment and its path based on micro family tracking survey data; Fourth, considering the substitution of social pension for family pension, this paper empirically tests whether the current social pension insurance system can alleviate the adverse impact of pension burden on family human capital investment.

Through theoretical analysis and empirical test, the main conclusions are as follows

At first, theoretical analysis shows that there is a nonlinear relationship between population aging and family human capital investment. From the perspective of family pension, the increase of pension burden will reduce the level of family human capital investment. Additionlly, China's current social endowment insurance system can alleviate the adverse impact of family pension burden to a certain extent. Specifically, the results of the benchmark model show that the impact of China's aging population on family human capital investment may show stage differences. Furthermore, by introducing the family pension mechanism into the benchmark model and combining with the calibration analysis of China's real economic parameters, it is found that the pension burden will crowd out the family's human capital investment, because the pension burden increases the family's economic and time costs, which has a negative impact on the human capital investment. The results of numerical analysis show that the current social endowment insurance system in China promotes the investment of family human capital and alleviates the negative effect of family pension burden to a certain extent.

Secondly, the empirical test based on macro data shows that there is a non-linear effect of population aging on family human capital investment. Specifically, using the provincial panel data from 1998 to 2018, it is found that the increase of the proportion of the elderly population will significantly reduce the level of family human capital investment without considering the nonlinear impact of population aging on family human capital investment; However, after adding the nonlinear relationship, there is a significant inverted "U" relationship between population aging and family human capital investment, and the inflection point of aging relative to the highest level of family human capital investment is between 8.82% and 9.28%, which appears in 2011. The results show that the impact of population aging on family human capital investment has crossed the inflection point, and the increasing population aging will continue to squeeze out family human capital investment.

Thirdly, the empirical test based on micro data shows that the crowding out effect of pension burden on family human capital investment plays a role by increasing family economic and time cost. Based on the data of Chines Family Pannel Studies (CFPS) from 2010 to 2018, the empirical test shows that the increase of family pension burden (elderly care, elderly health impact) will significantly reduce the level of family human capital investment. Specifically, the heavier the burden of pension, the lower the probability and scale of human capital investment. Furthermore, the mediating effect model is used to test the mechanism. It is found that the burden of providing for the aged has a negative effect on the level of family human capital investment through two channels: economic cost (increasing family medical expenditure) and time cost (reducing labor supply time for adult children). Furthermore, based on the heterogeneity of family characteristics, the empirical test finds that the crowding out effect of pension burden on human capital investment is more obvious in rural areas, low-income families, children in primary and secondary schools, families with elderly people and deeply influenced by traditional culture.

Fourth, considering the long-term and stable advantages of social endowment insurance compared with family endowment insurance, the empirical test confirms that the current social endowment insurance system in China has a promoting effect on family human capital investment and alleviates the adverse impact of family endowment burden. The empirical test results show that family participation in social endowment insurance can significantly improve the level of human capital investment. The increase in the amount of pension for the elderly will have a more obvious effect on the promotion of family human capital investment. In addition, by matching the provincial panel data with the micro family data, through the grouping test and the introduction of cross item empirical method, it is found that the social pension insurance system has a positive regulatory effect on the impact of family pension burden on human capital investment, that is, the social pension insurance system can alleviate the adverse impact of family pension burden on human capital investment.

The innovation of this paper includes the following three aspects: Firstly, from the research perspective, it brings the population structure and human capital investment into a unified theoretical framework, trying to explain the impact of population aging on human capital accumulation from the micro perspective, expanding the existing theoretical analysis to a certain extent; Secondly, in the empirical strategy, it tests the dynamic relationship between population aging and family human capital through the combination of macro and micro, and provides a possible path for it; Thirdly, on the mechanism, it not only confirms the crowding out effect of pension burden on family human capital investment from two aspects of economic cost and time cost, but also finds that social pension insurance can alleviate this crowding out effect, which provides a certain degree of policy enlightenment for the improvement of China's social pension insurance system.