‘Immortality’ may have been the ignorant fantasy of the ancient emperors while ‘Longevity’ is the common wish for the common people. In recent decades, the innovations and breakthroughs in the medical field have sharply reduced the death rate of various diseases, while the promotion of living standard has improved people’s health level, jointly resulting in people living much longer. A series of social and economic problems resulting from ageing, such as the insufficient labour force supply and the increased government financial burdens, will further restrict the sustainable development of the economy [1]; therefore, the problem of population ageing has always been the focus for the economists. Since the opening-up and reform of China, both the living standard and health condition of the people in our country have been obviously promoted, and the average life span has increased from 67.8 years old in 1982 to 74.83 years old in 2010, and the population age structure of our country has also changed from the restrictions of the family policy. In 2015, the population aged >65 years in China reached 144,340,000, making China the county with the most elderly people in the world with and a population proportion (the proportion of population aged >65 years) of 10.50% [2]. It’s international thought that when a country or region has a population of the elderly aged >60 years, taking up 10% of the total population or a population of the people aged >65 years reaching 7% of the total population, it’s entering the category of an ageing society; this means that the whole world has entered the category of an ageing society. This indicates that our country has become an ageing society.

In accordance with the development economics theories, high investment is the effective path for the economically backward areas to realise the economic growth, while high saving rate is the safeguard for high investment. Therefore, the saving rate will definitely affect the economic development, especially that of the economically backward areas. Therefore, the problem of ageing will have an impact on the economic growth through its transmission mechanism, that is, the saving rate. According to the life-cycle theory [3], the rational man will save money in his middle age and consume at his old age; therefore, when the proportion of the elderly in a region increases, the saving rate at the local place will decline. However, when adopting the transnational data to do an empirical study on the impact of population ageing on the saving rate, the research conclusions vary to a certain extent: there always is a big gap between the empirical conclusion of the research with the high-income country as the data sample and that of the study with the low-income country as the data sample. Whether such a difference in empirical conclusions result from the economic development level? In fact, the huge differences in the cultures of different countries have a very prominent impact on the saving rate; for example, East Asian regions advocate the Confucian Culture, and people will prefer the higher saving rate. Therefore, adopting the transnational data to carry out the empirical test will bear the risk of missing a variable, and the difference in empirical conclusions may have resulted from the culture diversity. To verify the impact of income, the effect of cultural factors shall be excluded first. There is a certain degree of cultural difference in the regions of our country. It has been shown by the data from 2015 that the proportion of the elderly in Eastern regions, the Middle regions and the Western regions is 10.59%, 10.46% and 10.28%, respectively, demonstrating that the population ageing gap in our country is not big and the cultural diversity between the regions in our country is much smaller than that of other countries. Therefore, the influence of the differences in the data of our country on the economic development could well solve the problem of cultural heterogeneity. Besides, implementing the research by targeting the nonlinear impact of ageing is good for the relevant departments to formulate related policies and measures according to circumstances, bearing a significant practical and guiding significance for the development of all regions of China.

According to the existing theories, the population ageing could affect the saving rate through the consumer population, the life expectancy and other precautionary motives.

According to the life-cycle theory [4, 5], a man’s lifetime could be divided into three stages: youth stage, middle-age stage and old-age stage. At the youth stage, the consumer has a low income, which is expected to increase in the future. Therefore, at such a stage, the consumption of the consumer is larger than the saving, i.e. a negative saving is carried out. At the middle-age stage, the consumer has the highest income level; however, the consumer not only needs to pay the debts owed at the youth stage but also has to save for the consumption needed during the coming old-age stage. Therefore, at such a stage, the propensity to consume is not high, while the propensity to save will increase. At the old-age stage, the consumer will conduct the consumption with the deposits from the middle age and bear no will to save for the future; therefore, the consumption tendency at the moment will be strong [6–8]. According to the precautionary saving hypothesis [9], we can make a similar conclusion: due to the fact that the elderly will consume according to their previous deposits, the uncertainty of his income barely exists, i.e. the elderly absolutely could predict his income. Due to the elderly being at the last life stage, he/she doesn’t need to consider more for the uncertainty in the future, and tend to conduct higher consumption.

According to the aforesaid analysis, it’s discovered that, due to the fact that the elders consume with the deposits from the middle age and don’t need to consider about the consumption in the future, when the ageing population in a region increase, the proportion of consumers with higher consumption tendency will increase, and so the propensity to consume in that local area will increase while the propensity to save will decline. Thus, we see that, for a region, the overall national saving rate will be affected by the local age proportion of the elderly. When the proportion of the elderly increases, the overall national saving rate will decline, i.e. the population ageing has a negative effect on the overall local national saving rate [10–12], and such a negative effect commonly is called as the ‘Burden Effect’ of ageing [13]. However, the empirical study on whether the ‘burden effect’ of ageing does exist bears a certain degree of controversy: when the samples chosen by the empirical study are different, especially when the chosen regions are different, the empirical conclusions will vary; when the empirical sample is the region of a comparatively backward economic development, the empirical research result commonly will support the existence of the ‘burden effect’ [14–16]; when the study sample is the region with a developed economy, the empirical research result commonly will query the existence of the ‘burden effect’ [17–19].

The standard life-cycle hypothesis has ignored the ‘Precautionary Motive’ of the middle-age people. Starting from the case of the elderly, the elderly’s propensity to consume is relatively high, and the ageing will result in the increase of consumption tendency and the decline of saving rate in local areas. However, when an ageing phenomenon arises in a region, the middle-age people will adjust their consumption and saving behaviours as well [20]. As a result, when considering the impact of ageing on the overall national saving rate, the behaviours of the middle-age consumers should be taken into consideration as well. Under this deterministic condition, the traditional life-cycle hypothesis holds that the saving tendency of the consumer will only change along with his age stage, or in other words, the consumption tendencies of the consumers at different stage in the life cycle are exogenic. Obviously, such a hypothesis is unreasonable. For the consumers in a region, when the ageing phenomenon arises in a local area, the local citizens’ lifetime will constantly increase, and so the consumers would naturally expect a longer lifetime [21, 22]. According to the persistent income hypothesis, if the citizen expects a longer lifetime, that is, a longer life stage after retiring, at a time when the income level is extremely low or almost close to zero, the middle-age consumers will naturally choose to save to achieve a sufficient power of consumption in the longer old-age stage in order to more reasonably distribute the saving and consumption in the longer life cycle. In case the consumer expects a longer lifetime, the uncertainty of future will be higher for the consumer, and the expected income will decline, i.e. the future will be pointing in a relatively more untoward condition. In order to maintain the consumption level, according to the precautionary saving hypothesis, the consumer will reduce his consumption and increase his deposits in middle age. Therefore, when an ageing phenomenon arises in a region, the middle-age people will change their consumption behaviours, increase their deposits and reduce their consumption [23]. In consequence, the ageing has a certain degree of positive effect on the local saving rate, and such an effect will be called as ‘Lifetime Effect’ of the ageing of the population [24]. The empirical study targeting the ‘lifetime effect’ of the ageing of the population is in dispute. Although the empirical studies adopting transnational data and individual region data have all demonstrated that lifetime effect does exist significantly, the empirical researches in the developing countries and the developed countries have borne a certain degree of differences.

Besides preparing for future consumption, ageing will also affect other ‘precautionary saving motives’ of the people; for example, ageing will also result in changes to the family consuming behaviour decision. A single consumer could make his investment and consumption decisions from angles like the preference between the current consumption, the future consumption, and the asset allocation according to the maximum utility level at different lifetime stages. However, for the family unit, the situation will be more complicated. The family behaviour decision will consider not only the personal utility but also the family member characteristics, especially the characters of the age structure. The families with different age structures will result in different decisions in investment and consumption. In case of more nonaged members in the family, the consumption for the youth will be more, so the family’s propensity to consume will be higher; because of more consumption, this family tends to choose the currency asset on the aspect of asset allocation. In case that there are more older members in the family, this family will have to pay for their consumption, so the burden of this family will be bigger. The medical cost for the elderly will be higher, so this family’s precautionary deposits will increase. What’s more, in the asset allocation of this family, the investment with risks (such as stock et al.) will decrease, the corresponding investment with no risk (such as insurance and bond) will increase. The changes in the decisions in family behaviour precisely are made up by the personal behaviour decisions. In other words, every family member will make the behaviour decision according to the family feature. Out of precautionary motives, for the families with more elder members and less nonaged members, the members of this family (such as the children of the elderlies) will increase their saving rate; on the contrary, for the families with less elderly members and more nonaged members, the members of this family (such as the children of the elderlies) will reduce their saving rate.

When the ageing phenomenon emerges in a region, the proportion of the old-age people in this region will increase, meanwhile that of the nonage people will decrease. As a result, the family age structure of this region will change, i.e. the proportion of nonaged people will be low while the families with higher proportion of aged population will be more and more. Therefore, considered from the precautionary motive, for families with a lower proportion of nonaged members and the families with a higher proportion of aged members, the family members (except the elderlies) will increase their saving rates, and as a result, the overall national saving rate in this region will rise accordingly.

The existing empirical researches mostly centre on finding whether the ‘burden effect’ and the ‘lifetime effect’ predicted by the life-cycle theory and the precautionary saving hypothesis significantly exist. However, in the case that the empirical studies make use of a different sample data, especially when there is a huge difference in the economic developments of the adopted data samples, both the ageing population’s ‘burden effect’ and ‘lifetime effect’ will be dramatically different. Why does such a difference emerge in the empirical research?

By studying the analysis of the current theories and the comparisons between the previous empirical researches, the empirical results adopting regions at the same or similar phase of economic development will always be very similar. Regardless of whether it’s the ‘burden effect’ of ageing or the ‘lifetime effect’ of ageing, the empirical results have demonstrated that the directions and significance of these effects are basically consistent. However, if the empirical analysis is conducted by using the data samples at different development stages, the results will be different. From such an observation, it can be predicted that in the regions with different economic development stages, the impacts of population ageing on the saving rate will be different. Nevertheless, the existing literature have all focused on the impact testing and ignored the existence of such a difference. In fact, the ‘burden effect’ and the ‘lifetime effect’ of ageing and other precautionary motives have varied according to the difference in economic development stage. To verify such a difference, this thesis will adopt the threshold model to conduct an empirical study on it on the basis of theoretical analysis.

The region at different economic development stages will bear different burden effects. According to the definition of burden effect, the elderly will consume depending on their saving in middle age. In such a stage, the elderly will choose the consumption portion and decide on the heritage proportion to be inherited by their children. The higher the elderly’s consumption proportion is, the less the leftover heritage will be, and vice versa. For residents of a higher income level, the savings in middle age are not only sufficient to support the elderly to consume at the old-age stage but also enough to be left for the offspring in a certain proportion; for residents of a lower income level, the savings are painstaking to conduct in middle age and could be only enough to afford the livelihood in old age with none to reserve for the children. Therefore, compared with the residents of higher income level, the residents of lower income level will have a higher propensity to consume. The income level of the residents in the economically-developed region is generally higher, while that of the residents in the economically backward region is lower. Therefore, compared with the economically backward region, the developed region has a smaller ‘burden effect’.

The regions at different economic development stages will have different ‘lifetime effects’. The developed region enjoys advanced medical conditions, while the economically backward region suffers outdated medical conditions, and as a result, the residents in the developed region will expect a life cycle longer than that of the residents in the economically-undeveloped region. What’s worse, the residents of a higher income level will be more optimistic than those of a lower income level, and their expected lifetime is longer than that of the residents of a lower income level. By integrating the aforesaid two effects, the residents in middle age in the developed region will have a stronger will to save for the consumption in old age. Therefore, compared with the economically backward region, the developed region has a bigger ‘lifetime effect’.

In the regions at different economic development stages, the saving rates caused by other precautionary motives will be different too. According to the Precautionary Saving Theory, the consumer will deposit the current income due to the uncertain future income, to prevent the decline of future income level. Zeldes believes that there is a best proportion between the careful saving and the best consumption. Obviously, the resident of a higher income level will have a higher saving rate. For the resident of a higher income level, the precautionary saving will be conducted with the sufficient income after fulfilling the consumption level. For the resident of a lower income level, it’s hard to have enough income to conduct the precautionary consumption [25]. Due to the different income levels of consumers, it’s found by the precautionary saving analysis that the saving proportions implemented for precautionary motives are different, and that the consumers of a higher income level will always tend to use a higher saving rate as a precautionary saving, while the consumers of a lower income level will tend to use a lower saving rate as a precautionary saving. Therefore, it’s predicted that in the regions at different economic development stages, the impacts of ageing on the national saving rate will vary accordingly. For the developed region, the local consumers have a higher wealth level, and the proportion of consumers with a higher wealth value will be higher. Therefore, the precautionary saving of this region will generally account for a bigger proportion of the wealth, so the ageing has a bigger positive effect on the national saving rate. For the relatively economically backward region, the local consumers have a lower wealth level, and the proportion of consumers with higher wealth value will be lower. Therefore, the precautionary saving of this region will generally account for a smaller proportion of the wealth, and so the ageing has a smaller positive impact on the national saving rate.

According to the aforesaid analysis, in case of difference in economic development, the ‘burden effect’, the ‘lifetime effect’ and the effects of ‘other precautionary motives’ caused by the ageing of the population on the national saving rate will vary; therefore, it ensures that in the regions at different economic development stages, the impacts of ageing on the national saving rate are different. To verify such a kind of difference, this thesis will adopt the Threshold Regression Model to conduct the parameter estimation, and to affirm the impact of differences of ageing on the saving rate in the regions of different economic development levels.

According to the theoretical analysis, the ageing of the population will have a certain degree of impact on the national saving rate. Therefore, this thesis has learned from the practice of Wang Wei and Ai Chunrong to set up the basic measurement regression model, with the detailed model design as follows:

Thereinto, _{1}_{2}_{i}_{it}

To verify the difference in the impacts of ageing on the saving rate in the regions at different economic development stages, this thesis has adopted the Threshold Regression Model [26] of Hansen, with per capita income to represent the economic development level as the threshold variable in the threshold model. Based on the basic model, the threshold regression model is set up as follows:

Thereinto, _{1}_{2}

The explained variable in this thesis is the national saving rate. Commonly, the national saving rate could be calculated from the proportion of national saving to the national disposable income, and the national saving equals to the national disposable income minus the national consumer spending. However, commonly in the statistical indicators of our country, the relevant indexes of rural residents and urban residents will be separated; therefore, this thesis will learn from its related researches [27, 28], and use the following formula to calculate the national saving rate: national saving rate = urban population proportion × urban saving rate + rural population proportion × rural saving rate; urban saving rate = (urban per capita disposable income − urban per capita consumption expenditure) ÷ urban per capita disposable income; rural saving rate = (rural per capita net income − rural per capita consumption expenditure) ÷ rural per capita net income. The threshold variable is the economic development level, so we adopt the per capita income level to measure and the 2000 price level to deduct. The regime-dependent variable in this thesis is the ageing degree, and we have adopted two ways to measure this index. According to the common standard, this thesis defines the population aged >65 years as the ageing population, and the proportion of population aged >65 years to the total population is adopted as the measure index for the ageing measurement. Besides, the old-age dependency ratio is another measure index to measure the ageing, and it takes the proportion index of population aged >65 years to be the explained variable as a robustness test for the first measurement method.

According to the previous research, the thesis also has controlled the following variables:

Economic growth rate. As predicted by the Permanent Income Hypothesis, in case that the economic growth rate could be stable permanently, the saving rate will be stable, i.e. the economic growth rate change will result in the saving rate fluctuation. Therefore, the thesis has controlled this variable and adopted the per capita GDP growth rate to measure this index;

Government expenditure scale. According to the common theories, the social security expenditure in the government expenditure scale has a big impact on the saving rate. However, the statistical calibre of the official social security statistical data in China had experienced a drastic change in 2007. In order to maintain the data consistency, the thesis has learned from the practices of relevant research [6], adopting the government expenditure scale as the proxy variable in social security expenditure and the proportion of government expenditure to the local GDP to measure the index;

The proportion of secondary industry. The proportion of secondary industry could measure the industrialisation degree of a region, which will affect people’s living and consumption habits, as well as the saving rate. This thesis has used the proportion of secondary industry to measure this index;

Birth rate. As analysed in the preamble, birth rate has an effect on the proportions of young and middle-aged populations in the economy. The young population has a high consumption tendency; therefore, the birth rate has a negative impact on the saving rate. This thesis has used the number of newborns in 1000 people to measure this index;

Child dependency ratio. For the middle-aged people, the expenditure for children is a major expenditure; therefore, the more the children raised, the higher the consumption, and the lower the saving rate. This thesis has adopted the proportion of population aged <14 years to the labouring population to be measured;

Urbanisation level. Same as industrialisation, urbanisation also has changed people’s living and consumption ways. This thesis has used the proportion of urban permanent resident population to the total population to measure the urbanisation level;

Urban-rural income gap. According to the Relative Income Theory, others’ consumption will affect one’s consumption decision, and the income gap will widen such an effect. This thesis has used the ratio of urban per capita disposable income to rural per capita net income to measure the urban-rural income gap;

Inflation rate. Inflation rate will stimulate people to choose the current consumption as much as possible, affecting the saving rate. This thesis has adopted the growth rate of consumer price index (CPI) to measure this index;

Per capita life expectancy. The longer the life expectancy is, the more the savings conducted in middle age will be. However, the longevity means there are more old-aged people, whose consumption tendency will be high. In order to offset the effect of life expectancy, this thesis has controlled it. At present, the statistics of per capita life expectancy in all provinces will only be conducted in the years of national population census; therefore, death rate has been adopted by some scholars to be the controlled variable of per capita life expectancy.

Besides, some scholars also have adopted the regression way to estimate the approximate value [29] of the per capita life expectancies of all provinces. For a long term, the death rate in our country bears small changes, while the per capita life expectancy keeps increasing constantly. Therefore, it’s not appropriate to use death rate to measure the life expectancy change. Therefore, this thesis has adopted the regression estimation method, to estimate the per capita life expectancy of every province;

Per capita education degree. Education degree will affect the consumption view, resulting in an impact on the saving rate. This thesis has learned from the relevant research [30, 31] by using the average schooling year of population over 6 years old to measure the per capita education degree. In other words, it’s to set primary school as 6 years, middle school as 9 years, high school and technical secondary school as 12 years and junior college and above as 16 years. The definitions and calculation methods of all variables are shown in Table 1.

Variable, definition and calculation method

Variable | Symbol | Calculation method |
---|---|---|

National saving rate | save | Urban population proportion × urban saving rate + Rural population proportion × rural saving rate |

Proportion of population aged >65 years | old1 | Population aged >65 years/total population |

Old-aged dependency ratio | old2 | Population aged >65 years/labouring population |

Per capita income | inc | Per capita income by using 2000 CPI to deflate |

Per capita GDP growth rate | gro | (actual per capita GDP-the actual per capita GDP last year)/the actual per capita GDP last year |

Government expenditure scale | gov | Government expenditure/GDP |

Birth rate | birth | newborn number/total population |

Proportion of secondary industry’s output value | seo | The secondary industry’s output value/GDP |

Children dependency ratio | chi | Population aged<14 years/labouring population |

Urbanisation level | urb | Urban resident population/total population |

Urban-rural income gap | gap | Urban per capita disposable income/rural per capita net income |

Inflation rate | cpi | Use consumer price index |

Life expectancy | lif | Please refer to Hu Ying (2010) and Yang Jijun (2013) |

Per capita education degree | edu | The average schooling year of population aged >6 years |

CPI, consumer price index

On the aspect of choosing the cross section sample, this thesis has chosen the 31 provincial administrative units in mainland China as the studied cross-section samples. In the subsample research, the 31 provinces and cities have been divided into three subsamples as East, Middle and West in accordance with the State Council’s delineating way in the east part, the Middle part and the West part. On the aspect of choosing a time span, due to the urban indexes only be tracing back to 2004 at the earliest, the time span is taken from 2004. The statistical departments at all levels in our country have stopped publishing the rural per capital net income index since 2014 but put out the rural per capita disposable income, it’s definite to bear differences and hard to integrate; therefore, the research span in the empirical part of this thesis is stopped in 2013, i.e. the study time span of this thesis is from 2004 to 2013. As a result, the research samples of this thesis are the panel data samples of the 31 cross sections during the 10-year time span from 2004 to 2013.

The variable descriptive statistics

Variable | Symbol | Unit | Sample size | Mean | Standard deviation | Min. value | Max value |
---|---|---|---|---|---|---|---|

National saving rate | save | % | 310 | 25.09 | 6.61 | 3.94 | 45.80 |

Proportion of population over 65 years old | old1 | % | 310 | 8.95 | 1.77 | 4.82 | 15.40 |

Old-aged dependency ratio | old2 | % | 310 | 12.27 | 2.41 | 6.71 | 20.31 |

Per capita income | inc | Yuan/person | 310 | 11137.01 | 60.10 | 3614.01 | 40492.66 |

Per capita GDP growth rate | gro | % | 310 | 10.31 | 2.18 | 3.59 | 18.93 |

Government scale | gov | % | 310 | 22.10 | 16.74 | 7.92 | 129.10 |

Birth rate | birth | ‰ | 310 | 11.38 | 2.75 | 5.36 | 17.94 |

Proportion of the secondary industry’s output value | seo | % | 310 | 47.66 | 8.16 | 22.30 | 61.50 |

Children dependency ratio | chi | % | 310 | 24.30 | 7.150 | 9.64 | 44.65 |

Urbanization level | urb | % | 310 | 48.74 | 14.17 | 22.67 | 89.60 |

Urban-rural income gap | gap | — | 310 | 3.03 | 0.60 | 1.76 | 4.93 |

Inflation rate | cpi | % | 310 | 103.20 | 2.051 | 97.65 | 110.10 |

Life expectancy | lif | Year old | 310 | 72.62 | 1.914 | 66.39 | 77.43 |

Per capita education degree | edu | Year/person | 310 | 8.67 | 5.86 | 1.12 | 39.56 |

Regarding the data source, the urban per capita disposable income, rural per capita net income, GDP, total population, population aged >65 years, old-aged dependency ratio, children dependency ratio, CPI, death rate and population education years in the regions that have been adopted in this thesis have all come from

Since the thesis has adopted the panel data threshold model, the estimation method of Hansen will be used for reference. First, the deviation form will be used to offset the individual effect in the panel data, then the data of deviation form will be utilised to conduct the parameter estimation.

Substitute _{0}: _{1} = _{2} could be used to verify the existence of the threshold effect. Hansen also has set up the LR statistic (_{1}):

The null hypothesis shall be verified. Although _{1} doesn’t conform to the strict ^{2} distribution, its distribution pattern depends on sample moments. Hansen has found that the first-order asymptotic distribution can be gained by the Bootstrap Method, on which P value has been set is incrementally effective. On the basis of verifying the existence of threshold effect, whether the estimated threshold value is equal to the real threshold value, i.e. _{2}):

The corresponding confidence interval also has been constructed:

Table 3 has presented the threshold value’s parameter estimation output and relevant verification results. It’s shown that the setup of single threshold model under the significance level of 1% has passed, while those of double threshold model and triple threshold model doesn’t. Therefore, the thesis has chosen the single threshold model.

Threshold value’s parameter estimation and relevant verification results

Parameter estimation output | Threshold effect verification | Threshold value confidence interval (95%) | ||||
---|---|---|---|---|---|---|

Model setup | Threshold value estimation output ( | _{1} | BP time | Empirical | Upper critical value | Lower critical value |

Single threshold model | 9001.69 | 65.83 | 3000 | 0.00 | 8988.26 | 9034.73 |

Double threshold model | 9001.69 | 9.84 | 3000 | 0.167 | 8975.58 | 9225.60 |

Triple threshold model | 6103.88 | 8.14 | 3000 | 0.323 | 5537.71 | 6106.25 |

The parameter estimation of the single threshold model has been conducted on the basis of this, and the detailed estimation outputs are shown in Table 4. It’s seen from the threshold model regression results in Table 4 that, the significant influence of the proportion of population aged >65 years is negative, in line with the conclusion of existing research [33]. Although the influences of the proportion of population aged >65 years on the saving rate are consistent, in case of different regions the impacts of the proportion of population aged >65 years on the saving rate will vary, verifying the prediction of the theoretical part of this thesis: in the regions of different economic development levels, the influences of the proportion of population aged >65 years on the saving rate will be different. In this regard, when the per capita income is bigger than the threshold value, the negative impact of the proportion of population aged >65 years hold on the saving rate will be smaller. When the per capita income is smaller than the threshold value, the negative impact of the proportion of population aged >65 years on the saving rate is bigger. This means that, in the region of lower income, the population ageing has a bigger negative impact on the national saving rate. In the region of higher income, the population ageing has a smaller negative influence on the national saving rate. Due to the fact that the population ageing problem will affect the economic growth through the transmission mechanism, that is, the saving rate, the region of lower income will receive an impact bigger than the region of higher income. There is a huge economic disparity existing between the regions in our country, in case the population ageing will result in the saving rate decline, the investment reduction and the regional economic growth. As a result, the population ageing definitely will result in the widened economic disparity, and the coordinated development of regional economies. Although such an impact influence is not big, it will further worsen the problem of unbalanced economic development and expanded regional development gap, causing the constant occurrence of such a difference. In case of not disturbing such an impact, the regional development gap will be bigger and bigger. Therefore, although such a difference looks small, it demands much attention from us.

Parameter estimation output of threshold model

(1) | (2) | |
---|---|---|

old1 (inc≤9001.69) | −1.021*** | −1.024*** |

(0.35) | (0.32) | |

old1 (inc>9001.69) | −0.909** | −0.922*** |

(0.35) | (0.28) | |

gro | 0.021 | 0.011 |

(0.13) | (0.33) | |

gov | 0.184*** | 0.192*** |

(0.05) | (0.03) | |

birth | −0.768** | −0.968** |

(0.31) | (0.41) | |

seo | 0.106* | 0.111* |

(0.06) | (0.08) | |

chi | −0.230** | −0.430** |

(0.10) | (0.18) | |

urb | 0.006 | 0.002 |

(0.05) | (0.07) | |

gap | 0.201 | 0.401 |

(1.30) | (2.30) | |

cpi | 0.153* | 0.183* |

(0.09) | (0.12) | |

lif | −0.649 | −0.749 |

(0.43) | (0.63) | |

edu | 0.992 | 0.734 |

(1.22) | (1.12) | |

con (constant term) | 69.141** | 59.031* |

(30.89) | (40.89) | |

Time fixed effect | No | Yes |

N | 310 | 310 |

^{2} | 0.282 | 0.291 |

Using the proportion of population aged >65 years to measure the population ageing, the thesis has conducted the parameter estimation of threshold model and found that, when the per capita income is in different threshold ranges, the impacts of population ageing on the saving rate will be different. To prove the robustness of conclusions, the thesis has used the old-aged dependency ratio as the index for measuring the population ageing; relevant estimations and verification on the threshold values have been carried out.

Table 5 has presented the parameter estimation outputs and relevant test results in using the old-aged dependency ratio. It’s shown that the relevant parameter estimation outputs and test results are similar to those in using the proportion of population aged >65 years. In the same significance level of 1%, the setup of single threshold model has passed the test while the setups of double threshold model and triple threshold model doesn’t. Therefore, the conclusions of single threshold model are robust, and the threshold estimation result of single model is consistent, demonstrating that the threshold value of per capita 9001.69 is robust.

Parameter estimation of threshold value and relevant inspection result

Parameter | Threshold | Threshold | ||||
---|---|---|---|---|---|---|

Model setup | Threshold estimation output | _{1} | BP time | Experience P value | Upper critical value | Lower critical value |

Single threshold model | 9001.69 | 65.83 | 3000 | 0.00 | 8988.26 | 9034.73 |

Double threshold model | 9001.69 | 9.84 | 3000 | 0.167 | 8988.26 | 9034.73 |

Triple threshold model | 6114.78 | 8.14 | 3000 | 0.323 | 5555.71 | 6116.25 |

Besides, the thesis also has made used of the old-aged dependency ratio to conduct the threshold model regression as the robustness regression result; as shown in Table 6. By comparing Table 6 and Table 5, it’s found that the coefficient symbols of model control variables are completely consistent, and the significance levels are extremely close, confirming that the estimation output of the model in this thesis is robust. When the per capita income in different intervals, he impacts of the old-aged dependency ratio on the saving rate: the old-aged dependency ratio, the same as the population aged >65 years, has a negative effect on the saving rate. What’s more, when per capita income is in different intervals, the impacts of old-aged dependency ratio on the saving rate will vary. In other words, when the per capita income is bigger than the threshold value, the negative impact of old-aged dependency ratio on the saving rate is smaller. When the per capita income is smaller than the threshold value, the old-aged dependency ratio has a bigger negative effect on the saving rate. Consistent with the previous conclusion, it has verified the robustness of the conclusion.

Parameter estimation output of threshold model

(3) | (4) | |
---|---|---|

old2 (inc≤9001.69) | −0.556** | −0.639** |

(0.244) | (0.292) | |

old2 (inc>9001.69) | −0.471** | −0.531** |

(0.244) | (0.274) | |

gro | 0.044 | 0.049 |

(0.13) | (0.14) | |

gov | 0.193*** | 0.231*** |

(0.05) | (0.06) | |

birth | −0.775** | −1.008** |

(0.31) | (0.40) | |

seo | 0.094 | 0.124 |

(0.06) | (0.16) | |

chi | −0.196* | −0.096 |

(0.11) | (0.15) | |

urb | 0.026 | 0.046 |

(0.05) | (0.11) | |

gap | 0.420 | 0.555 |

(1.30) | (1.20) | |

cpi | 0.161* | 0.191** |

(0.09) | (0.08) | |

lif | −0.889** | −0.989** |

(0.42) | (0.47) | |

edu | 1.021 | 0.834 |

(1.52) | (0.90) | |

con (constant term) | 71.241** | 68.141** |

(30.77) | (29.99) | |

Time fixed effect | No | Yes |

N | 310 | 310 |

^{2} | 0.292 | 0.311 |

According to the existing theories and empirical researches, the impacts of population ageing on the national saving rate are very complicated; the empirical results from different sample data will be sharply different. It’s found by comparison that, when there is a relatively huge economic gap between the sample regions, the difference in the empirical results will be huge. Therefore, in accordance with relevant theories, this thesis has divided the impacts of population ageing on national saving rate into the ‘Burden Effect’, the ‘Lifetime Effect’ and ‘Other Precautionary Motives’ for separately analysing them.

Among them, the ‘burden effect’ of population ageing has a negative impact on the national saving rate, while the ‘lifetime effect’ and ‘other precautionary motives’ have a positive effect on the national saving rate. It’s found by qualitative analysis that, compared with the economically backward region, the developed region has a smaller burden effect; compared with the economically backward region, the ‘lifetime effect’ and ‘other precautionary motives’ in the developed region have a bigger influence. It can be determined that, compared with the economically backward region, in the relatively developed region, the population ageing has a smaller negative influence on the national saving rate; compared with the economically backward region, in the relatively developed region, the population ageing has a bigger positive impact on the national saving rate. Therefore, it can be predicated that, when it’s in different regions at different economic development stages, the comprehensive impact of population ageing on national saving rate will be different.

To test the aforesaid theoretical conclusions, this thesis has conducted a threshold regression analysis with the panel data of 31 provinces from 2004 to 2013, to analyse on the threshold number, the threshold value estimation, the threshold value verification and the parameter estimation output of threshold model. The result has shown that, the single threshold model should be chosen, for the threshold effect of this model is significant. Although the population ageing has a negative impact on the saving rate, when the per capita income is in the interval of lower than the threshold value, the negative effect of population ageing on saving rate will be bigger; when the per capita income is in the interval of bigger than the threshold value, the negative impact of population ageing on the saving rate will be smaller.

According to Development Economics, the economic take-off of a region depends on the sufficient investment, which originates from savings that will undoubtedly affect the economic development to an extent. The economic growth of our country has always depended on the investment, so the savings plays an important role in the economic development of our country. Since 1990s, the implementation effects of our family planning policy have become more and more significant, and the population ageing seems to be an unavoidable problem. In the future, the population of old-aged people in our country definitely will increase sharply and affect the consumption and saving, as well as the economic development. According to the conclusions of this thesis, in different per capita income intervals, the impacts of population ageing on the national saving rate will vary to an extent: the impact will be bigger in the region of lower income while that in the region of higher income will be smaller. Obviously, the impact of ageing on the region of lower income will be bigger; for the region of lower income that is economically backward will face a bigger impact of ageing, widening the regional economic gap. Therefore, the regional coordination development of our country will face the extra challenges of ageing. Because of this, the thesis has proposed the following policy advice:

The old-age service industry development should be under guidance. Since the problem of population ageing is unavoidable, more preparations should be done for the future of ageing society. Guiding the development of old-age service industry not only can solve the consumption need problems of the elderly, but also will stimulate the consumption and make up the loss in economic growth caused by the decline in investments.

To deal with the negative effect of ageing, increasing the resident’s income is the most essential solution [29]. Increasing the resident income not only expands the domestic demand to stimulate the economic development but also offsets the negative impact of the decrease in saving rate, and to realise the consumption growth and saving increase.

Perfecting the family planning policy, insisting in the two-child policy and more positive population policies should be brought out. Definitely, the ageing of the population will be a barrier in the way of sustainable and healthy economic development of our country, perfecting the family planning policy and carrying out a more positive population policy will relieve the pressure of ageing beyond doubt.

Specific regional development plans and population policies should be implemented in the East-Central-West regions. For the regions with a huge economic development gap, the impacts of ageing on national saving rate will be different as well. The impact of ageing on the region of lower income will be bigger, widening the economic gap between regions. Therefore, when confronting with such a problem, the relevant departments will carry out the specific regional policies and populations measures, to deal with the impacts of ageing on regions and prevent ageing from affecting the economic development and regional coordinated development efforts.

#### Threshold value’s parameter estimation and relevant verification results

Parameter estimation output | Threshold effect verification | Threshold value confidence interval (95%) | ||||
---|---|---|---|---|---|---|

Model setup | Threshold value estimation output ( |
_{1} |
BP time | Empirical |
Upper critical value | Lower critical value |

Single threshold model | 9001.69 | 65.83 | 3000 | 0.00 | 8988.26 | 9034.73 |

Double threshold model | 9001.69 |
9.84 | 3000 | 0.167 | 8975.58 |
9225.60 |

Triple threshold model | 6103.88 |
8.14 | 3000 | 0.323 | 5537.71 |
6106.25 |

#### Parameter estimation of threshold value and relevant inspection result

Parameter |
Threshold |
Threshold |
||||
---|---|---|---|---|---|---|

Model setup | Threshold estimation output | _{1} |
BP time | Experience P value | Upper critical value | Lower critical value |

Single threshold model | 9001.69 | 65.83 | 3000 | 0.00 | 8988.26 | 9034.73 |

Double threshold model | 9001.69 |
9.84 | 3000 | 0.167 | 8988.26 |
9034.73 |

Triple threshold model | 6114.78 |
8.14 | 3000 | 0.323 | 5555.71 |
6116.25 |

#### Variable, definition and calculation method

Variable | Symbol | Calculation method |
---|---|---|

National saving rate | save | Urban population proportion × urban saving rate + Rural population proportion × rural saving rate |

Proportion of population aged >65 years | old1 | Population aged >65 years/total population |

Old-aged dependency ratio | old2 | Population aged >65 years/labouring population |

Per capita income | inc | Per capita income by using 2000 CPI to deflate |

Per capita GDP growth rate | gro | (actual per capita GDP-the actual per capita GDP last year)/the actual per capita GDP last year |

Government expenditure scale | gov | Government expenditure/GDP |

Birth rate | birth | newborn number/total population |

Proportion of secondary industry’s output value | seo | The secondary industry’s output value/GDP |

Children dependency ratio | chi | Population aged<14 years/labouring population |

Urbanisation level | urb | Urban resident population/total population |

Urban-rural income gap | gap | Urban per capita disposable income/rural per capita net income |

Inflation rate | cpi | Use consumer price index |

Life expectancy | lif | Please refer to Hu Ying (2010) and Yang Jijun (2013) |

Per capita education degree | edu | The average schooling year of population aged >6 years |

#### The variable descriptive statistics

Variable | Symbol | Unit | Sample size | Mean | Standard deviation | Min. value | Max value |
---|---|---|---|---|---|---|---|

National saving rate | save | % | 310 | 25.09 | 6.61 | 3.94 | 45.80 |

Proportion of population over 65 years old | old1 | % | 310 | 8.95 | 1.77 | 4.82 | 15.40 |

Old-aged dependency ratio | old2 | % | 310 | 12.27 | 2.41 | 6.71 | 20.31 |

Per capita income | inc | Yuan/person | 310 | 11137.01 | 60.10 | 3614.01 | 40492.66 |

Per capita GDP growth rate | gro | % | 310 | 10.31 | 2.18 | 3.59 | 18.93 |

Government scale | gov | % | 310 | 22.10 | 16.74 | 7.92 | 129.10 |

Birth rate | birth | ‰ | 310 | 11.38 | 2.75 | 5.36 | 17.94 |

Proportion of the secondary industry’s output value | seo | % | 310 | 47.66 | 8.16 | 22.30 | 61.50 |

Children dependency ratio | chi | % | 310 | 24.30 | 7.150 | 9.64 | 44.65 |

Urbanization level | urb | % | 310 | 48.74 | 14.17 | 22.67 | 89.60 |

Urban-rural income gap | gap | — | 310 | 3.03 | 0.60 | 1.76 | 4.93 |

Inflation rate | cpi | % | 310 | 103.20 | 2.051 | 97.65 | 110.10 |

Life expectancy | lif | Year old | 310 | 72.62 | 1.914 | 66.39 | 77.43 |

Per capita education degree | edu | Year/person | 310 | 8.67 | 5.86 | 1.12 | 39.56 |

#### Parameter estimation output of threshold model

(3) | (4) | |
---|---|---|

old2 (inc≤9001.69) | −0.556** | −0.639** |

(0.244) | (0.292) | |

old2 (inc>9001.69) | −0.471** | −0.531** |

(0.244) | (0.274) | |

gro | 0.044 | 0.049 |

(0.13) | (0.14) | |

gov | 0.193*** | 0.231*** |

(0.05) | (0.06) | |

birth | −0.775** | −1.008** |

(0.31) | (0.40) | |

seo | 0.094 | 0.124 |

(0.06) | (0.16) | |

chi | −0.196* | −0.096 |

(0.11) | (0.15) | |

urb | 0.026 | 0.046 |

(0.05) | (0.11) | |

gap | 0.420 | 0.555 |

(1.30) | (1.20) | |

cpi | 0.161* | 0.191** |

(0.09) | (0.08) | |

lif | −0.889** | −0.989** |

(0.42) | (0.47) | |

edu | 1.021 | 0.834 |

(1.52) | (0.90) | |

con (constant term) | 71.241** | 68.141** |

(30.77) | (29.99) | |

Time fixed effect | No | Yes |

N | 310 | 310 |

^{2} |
0.292 | 0.311 |

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Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network