The nonlinear effects of ageing on national savings rate – An Empirical Study based on threshold model

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: 1 yit=μi+β1xit+β2′zit+εit \begin{align}y_{it} = \mu_{i} + \beta_{1}x_{it} + \beta^{\prime}_{2} z_{it} + \varepsilon_{it} \end{align}

Thereinto, i means cross section (province), t means time (year), y is the explained variable (here it means the national saving rate), x is the explanatory variable here as the index to measure the ageing, z is the column vector of k order composed of other control variables (here the control variable is assumed as k), β₁ is the solve-for parameter, β₂ is the column vector of k order composed of solve-for parameter, μ_i is the individual effect and ε_it is the random disturbance term.

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: 2 yit=μi+β1xitI(qit≤γ)+β2xitI(qit>γ)+β3zit+εit

Thereinto, I(•) is the indicative function; in case the proposition in the parentheses is true, it’s valued as 1, otherwise it’s 0. q is the economic development level, the threshold variable in the threshold regression model. x is the aging of the population, ‘the regime-dependent variable’ here. When q is different, the influence coefficients of population aging on the saving rate β₁ and β₂ will be different. Other symbols’ connotations are the same as those in Formula (1).

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;

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;

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.

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 China Statistical Yearbook; the proportion of output value of secondary industry and fiscal expenditure are from the data base of CEInet; urban resident number is from the statistical yearbooks of the provinces, Compilation of Statistical Data for Sixty Years of New China; and individual missing values have been supplemented through Difference Method.

Substitute γ∈{qi}n i = 1 into Formula (2), to calculate the corresponding residual sum of squares S(γ) of threshold γ, find the corresponding threshold value ,γ^ of the smallest S(γ), i.e. ,γ^=argminS(γ) , therefore, ,γ^ is the estimation value of threshold value, and calculate the corresponding ,β^1 and ,β^2 . The calculated threshold value doesn’t mean that the threshold effect does not exist. For the threshold regression model, the existence of the threshold effect shall be verified [32]. It’s advised by Hansen that, the proposition H₀: β₁ = β₂ could be used to verify the existence of the threshold effect. Hansen also has set up the LR statistic (LR₁): LR1=(S0−S(γ^))σ^2

The null hypothesis shall be verified. Although LR₁ doesn’t conform to the strict χ² 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. ,γ^=γ , shall be further verified. Hansen also has constructed LR statistic (LR₂): LR1=(S(γ)−S(γ^))σ^2

The corresponding confidence interval also has been constructed: C(α)=−2ln⁡(1−(1−α)1/2) , where, C(α) is the near critical value of accepting the null hypothesis ,γ^=γ=γ , and 1 – α is the confidence level.

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.

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.

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.

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.

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.