How Do House Prices and Financial Expenditure Affect Birth Rate? New Evidence from the Dynamic Threshold Panel Model

Abstract

Owing to low birth rate, the demographic dividend in China is disappearing. It is thus of great significance to study the regional differences and influencing factors of the birth rate, further proposing political advices on how to raise birth rate. In this study, 31 administrative units in China were chosen as the regional targets, and the nonlinear effects of house prices and financial expenditure on birth rate were extensively investigated by using a dynamic panel threshold model. A dynamic panel threshold model with disposable income as threshold variable, house price as independent variable, financial expenditure that concluding education funds and social security as variables influenced by threshold variable was established, which can effectively handle regional heterogeneity and endogeneity problems. The results show that the effect of financial expenditure on birth rate is complex, exhibiting a “S” shape for education funds and an inverted “U” shape for social security. Previous controversial conclusions on the impact of financial expenditure on birth rate in the literature can thereby be reasonably explained. It shows that birth rate is influenced by the lagged birth rate and house prices have negative effects on birth rate. The rationality of the present results has been verified by using consumption and input-output economic theories. Based on the empirical investigation, specific suggestions have been proposed in order to acquire sustainable development of population.

1. Introduction

Falling birth rate threatens sustainable population development and human well-being all over the world [1,2,3], and China’s birth rate has fallen for consecutive years since 2017. The number of newborns registered in 2020 (10.03 million) reduced nearly 15% compared with that in 2019 (11.79 million). However, over the past two decades, the proportion of China’s elderly population has been rising. In 2020, population aged over 65 reached 190.59 million, accounting for 13.75% of the total. The UN’s criterion for aged population is that the proportion of people over 65 exceeds 7%. Due to the aging population and decreasing demographic dividend, the low birth rate in China is an urgent problem to be solved. The phenomenon of continuous decline in birth rate has become a hot topic in academic research.

The birth rate curve in China has six inflection points, for 34.03‰ in 1957, 18.13‰ in 1961, 43.6‰ in 1963, 17.82‰ in 1979, and 7.52‰ in 2021. The key factors for these timing points can be attributed to the national famine suffered in 1960 and family planning introduced in 1979 [4]. The family planning policy in China can effectively control the excessive growth of the birth rate. However, the downward trend is hard to change. Many countries in the worldwide face the same problem, so scholars researched on birth control in the 1970s and birth promotion in the 21st century. In the 1970s, Davis [5] and Kirk [6] studied population control policies in the United States, Oechsli and Kirk [7] studied the reasons for the rapid population growth in the Latin America and the Caribbean, and Mauldin et al. [8] searched for conditions of fertility decline in developing countries. As early as 1978, Tsui and Bogue [9] concerned about the problem of global population decline. Nomura et al. [10] explored the reasons for Japan’s population decline in view of the policies. Many scholars have focused on the impact of contraception and abortion on declining birth rate [11,12,13,14,15,16]. Kearney and Levine [17] believed that the recession causes the low birth rate, but Pison [18] holds an opposite view. However, there is little in the literature that provides persuasive empirical evidence based on actual conditions in China while incorporating the house prices, the financial expenditure, and the birth rate into a unified analytical framework.

The structure of this article is organized as follows. Section 1 is the introduction. Section 2 provides brief literature review. Section 3 describes data source, current situation and important methods used in this paper. Section 4 introduces the empirical logic structure, the empirical models and results. Section 5 provides conclusions and related policy implications.

2. Literate Review

The earliest research on birth rate was reported by Lotka [19] in 1907. A large number of researches have been reported on birth rate, however most of which focused on the medical factors and childbearing policy [20,21,22,23,24]. A few studies on birth rate were performed in the view of economics [25,26,27,28]. On the basis of abundant statistic data, empirical research is regarded as an effective way to verify economic theories and provide a baseline in the development of parameters in simulation modeling studies. According to house prices, Guo et al. [29] established a linear model of time series and found that a short-time increase of house prices leads to a decline in birth rate. Later, a similar conclusion was proposed by William et al. [30] with the development of instrumental models. Mulder and Wagner [31] studied the relationship between family formation and first-time home ownership by using the data from west Germany and the Nether-Lands. By using a dynamic panel model, Dettling and Kearney [32] found that house prices have obvious negative influence on fertility behavior. According to income, Grogger and Bronars [33] investigated the relationship between welfare payments and fertility behavior by twins’ data. Jennifer et al. [34] examined community-level factors on the decline of the birth rate by using ordinary least squares regression, and found that birth rate declines more in urban than rural areas. According to education founds and social security, Pecchenino and Pollard [35] found that high quality education system and lower social security agree with the growth of economic and welfare. Martha et al. [36] reviewed the state policy and teen childbearing situation, and found that some cross-sectional analyses about the relationship between expanded or improved public education policies and lower birth rate are tentative owing to the limited number of rigorous studies or the older data.

As reviewed above, the influence of various factors such as house price, income, education funds and social security on birth rate has been extensively investigated, however with limitations as following. Most of the current investigations focus on single or two factors, while the interactive effects among these factors cannot be ignored. Especially, birth rate can be affected by the value of itself in the previous year. In addition, the regional divergence of birth rate in China is obvious. Up to now, the influence of various factors on birth rate was investigated by using a linear model or merely statistical studies. However, financial expenditure does not directly affect the birth rate, which involves a complicated process. It behaves a substantial nonlinear effect on birth rate. Few studies on nonlinear panel model in China have been reported, which is more suitable and reasonable to exhibit the complex relationship between birth rate and its impression factors. A dynamic nonlinear modeling based on statistical data on birth rate is of great importance.

In this study, the complicated relationship between birth rate and various factors, including dependent and independent variables, different regions in China, has been investigated. Prior to modeling, the variables were chosen and fixed based on linear panel model and nonlinear fitting by using Gauss function. Subsequently, a dynamic panel threshold model was established with disposable income as threshold variable, house price as independent variable, financial expenditures concluding education funds and social security as variables influenced by threshold variable.

3. Materials and Methods

3.1. Data Source and Current Situation Analysis

3.1.1. Birth Rate (BR)

Birth rate, denoted by BR, refers to the number of births in a place as a percentage of the average population over a year. Figure 1 shows the birth rate trends of 31 administrative units in China from 2008 to 2019. As can be seen in Figure 1, birth rates in adjacent years in the same area are similar, which indicates that the BR is influenced by the data in the previous period. So, it is reasonable to regard the lag term of BR as a dependent variable. According to the BR data in 2019, the highest BR is 14.6‰, while the lowest one is 5.73‰, which indicates that the gap between regions is very large. In addition, the birth rate line in 2008 is above that in 2009, indicating that the trend of birth rate in China is downward.

Figure 2 presents a map drawn by using ArcGis10.7 software to visually distinguish the regional differences and dynamic changes of the birth rate in 2008 and 2019 by means of five-fifths method [37]. The birth rate is ranked for 5 levels in the sequence from lowest to highest. To save space, only the data in 2019 and 2008 are shown. As can be seen, the regional difference of the birth rate in 2019 is very obvious. The birth rate in northeastern region is located in the first level, and northern region in the second level. The birth rate in eastern region is polarized with Shanghai and Jiangsu in the first and second level, while the others in the third level or above. The birth rate in northwestern region is above the third level, except Xinjiang in the second level. The birth rates in central, southern and southwest regions are in the third level or above. Compared with the data in 2008, the birth rates in all regions in 2019 decrease with a certain extent except Hubei, which exhibits a slight increase. A sharp reduce can be observed in Xinjiang. The reason for the region difference will be discussed in the following text.

3.1.2. Disposable Income (DI)

Disposable income is calculated by the per-capita value of wage income, operating income, property income and transfer income, which reflects the income of local residents. Data resources of several years differ in the caliber of the statistics, survey scope or survey method. The National Bureau of Statistics has been carried out according to the urban-rural integration household income and living conditions survey since 2013, the data of which were adopted in the present study. Disposable income is represented by DI.

Similar as Figure 2 and Figure 3 shows the five-fifths map of China’s disposable income in 2019 and 2008. As can be seen, until 2019, most regions remain in the lowest level, only a few regions are in the high level. The advanced positions of China’s economy, including Beijing, Tianjin and several coastal cities, are in the third level or above. The rest regions are in the first level, except Inner Mongolia and Chongqing, both of which are in the second level. Inner Mongolia, a sparsely populated region, raises cattle and sheep and is the home of two major dairy companies in China. Its economy grows rapidly in recent years because the consumption of milk, beef and mutton has soared in China. Chongqing is the only municipality directly under the central and western regions, with many tourist attractions. Chongqing Pilot Free Trade Zone was established by the State Council of China in 2017, which gives favorable conditions for economic development.

3.1.3. House Price (HP)

Comparing to the prices of villa, high-grade apartment, office building and commercial business housing, residential commercial housing is closer to the fertility behavior of Chinese families. House price was calculated by the average sales price of residential commercial housing and is represented by HP.

When using the five-fifths method as that in Figure 2, only Beijing and Shanghai are in the fifth level in 2019 and all the rest regions are in the first level owing to the huge gap of HP in different regions. To improve the analyzability of the map, the HP data of the 31 regions in 2019 were sorted from lowest to highest, and then every continuous 6 regions were put into a level. For the fifth level, 7 regions were included. By using this categorization method, a map of China’s house prices in 2019 and 2008 is presented in Figure 4. As can be seen, house prices in most regions experienced a sharp inflation. House prices of 25 regions are in the first level in 2008, while only 6 regions in the first level in 2019. Due to the high house price bases, the rest 6 regions in 2008 are located in second and above levels with Beijing in the fifth level, Shanghai in the fourth level, Zhejiang and Guangdong in the third level, Tianjin and Hainan in the second level.

3.1.4. Educational Funds (EF)

In this work, educational funds were measured by the education expenditure per capita. The education investment from government in China is mainly expended on nine-year compulsory education. As a result, we only consider the number of students in junior middle school and primary school as total number. The per capita education funds is represented by EF.

Similar as Figure 2 and Figure 5 shows the five-fifths map of China’s educational funds per capita in 2019 and 2008. As can be seen, education funds have obvious improvement in most regions, however there are still large disparities in 2019 from region to region. Beijing and coastal regions including Shanghai, Jiangsu, Zhejiang and Guangdong in the fourth or fifth level, while 14 regions, including three northeastern provinces, remain in the first level.

3.1.5. Social Security (SS)

In order to measure social security more accurately, social security was measured by local government expenditure per capita on social security and employment, referring to Li and Bian [38]. The social security per capita is represented by SS.

Similar as Figure 2 and Figure 5 shows the five-fifths map of China’s social security expenditures in 2019 and 2008. As can be seen from Figure 5, social security has improved obviously in most areas, especially in the Midwest and Northeast. 30 regions are located in the first level in 2008, except Shanghai in the second level, while 18 regions are located in the second level or above in 2019. Interestingly, contrary to the economic level, the level of social securities in central and western regions and three northeastern provinces is higher than that of the southeastern regions and coastal cities in 2019. This is mainly due to the Chinese government’s policy of guaranteeing basic medical care. The rural cooperative medical insurance was gradually implemented in 2010 and the State Council unified medical insurance benefits for urban and rural residents in 2016. So the social security of backward areas with low individual contributions is accordingly higher than that of developed areas (Figure 6).

3.1.6. Explanation of Variables

This study took 31 administrative units in China as the research object, and the time frame is from 2008 to 2019. The reasons for choosing such a time span are as follows. On the one hand, the data are available between 2008 and 2019, and on the other hand, China’s family planning policy is very strict before this period, which could eliminate the influence of economic factors on the birth rate. The original data came from the official website of the National Bureau of Statistics. Due to the long time span, in order to eliminate the interference of price factors, all indicators related to money have been deflated with 2008 as the base period. In order to avoid the influence of statistical caliber varies, some data have been converted. Considering that the levels of educational funds and social security in the same region are different, financial expenditure is divided into two independent parts, education funds and social security. In addition, a small amount of missing data was repaired by picking points from a smooth curve with the preceding and following years.

The source and basic characteristics of the original data mainly used in this paper are shown in

Table 1. Description of variables.

Variables	Meaning	Definition	Average	Maximum	Minimum	Unit
BR	Birth rate	See Section 3.1.1	11.35	14.6	5.73	‰
DI	Disposable income	See Section 3.1.2	17,298	53,198	5276	CNY
HP	House price	See Section 3.1.3	5786	30,175	2359	CNY
EF	Education funds	See Section 3.1.4	813	3081	31	CNY
SS	Social security	See Section 3.1.5	1220	4884	267	CNY

.

In particular, China has relaxed fertility policies twice from 2008 to 2019. In 2013, couples were allowed to have two children if they were an only child themselves, and in 2016 all couples were allowed to have two children. Considering the time of pregnancy, 2014 and 2017 are the execution dates of the policy. However, there was no significant increase in the birth rate in those two years, seeing Figure 1. In addition, when we took fertility policy as a dummy variable, with the value of 1 in 2014 and 2017 and 0 in other years, it was tested as an irrelevant variable. So, lenient policies are considered to have no obvious promoting effect on birth rate, and thus are not listed in the following model.

In order to keep the dimensional consistency, data were normalized with a maximum value of 100 before importing into model. Specific method is shown in Equation (1).

$$a=100\times x/x^g$$

(1)

where $a$ represents the score value of a single indicator, $x^g$ indicates the maximum value of its category of data, $x$ represents a single point data. The processed data are distinguished by subscripts 100. Taking the DI for example, Beijing’s DI is 44,069 in 2016 and the largest value is 53,178 in Shanghai in 2019. According to Equation (1), the DI₁₀₀ of Beijing in 2016 can be calculated to be 82.87. This method was also utilized to calculate BR₁₀₀, EF₁₀₀ and SS₁₀₀.

3.2. Dynamic Panel Threshold Model

Many studies have contributed to the development of the model, and the following studies have played a milestone role. Early in 1999, Hansen [39] firstly proposed a non-dynamic threshold regression method, which allows the existence of nonlinear relationship between variables. Later, based on the non-dynamic threshold model, Seo and Shin [40] developed a first-differenced generalized dynamic threshold method in 2016, which can tolerate and endogenous in both regression and threshold effect. Most recently, Seo et al. [41] developed a program implanting the dynamic threshold model in Stata software, which makes the treatment of large and complex data, especially the short time span panel data more flexible. The general dynamic panel model can be expressed in Equation (2).

y_it = (1, x_it) β₁ 1 {q_it ≤ C} + (1, x_it) β₂ 1 {q_it > C} + α_i + δ_it, i = 1,..., n; t = 1,..., T

(2)

where y_it is a dependent variable, x_it is the k1 × 1 vector of time-varying. In addition, both y_it and x_it may include the lagged dependent variable. 1 {.} is an indicator function, and q_it is the threshold variable. C is the threshold parameter, and β₁ and β₂ are slope parameters associated with different regimes. α_i is random disturbance term. δ_it is the error term, which can be expressed as Equation (3).

δ_it = u_i + v_it

(3)

where u_i is an unobserved individual fixed effect and v_it is a an unobserved time fixed effect. In particular, this model allowing endogeneity in both the regressor x_it and the threshold variable q_it.

4. Empirical Results

4.1. Estimation Results of the Basic Model

There is no need to choose a complex model if a simple one will solve the problem. Referring to Lisa and Melissa [12], we set a simple multiple linear function showing in Equation (4). To maintain dimensional consistency, all data were treated by Equation (1).

BR_100(it) = β₁ + β₂DI_100(it) + β₃HP_100(it) + β₄EF_100(it) + β₅SS_100(it)

(4)

where i and t represent administrative units and years, respectively (i = 1, 2,..., 31; t = 2008, 2009,..., 2019), β_x (x = 1, 2,..., 5) are coefficients fitted by linear function.

Conceded inelastic coefficients and heteroscedasticity maybe exist by using Equation (4), and thus we handled data by natural logarithm. Finally, Equation (4) can be improved into Equation (5).

lnBR_100(it) = β₁ + β₂lnDI_100(it) + β₃lnHP_100(it) + β₄lnEF_100(it) + β₅lnSS_100(it)

(5)

The description of variables is shown in

Table 2. The statistical description of variables.

Variable	Obs	Mean	Std. Dev	Min	Max
lnBR100(it)	372	4.12	0.26	3.40	4.61
lnDI100(it)	372	3.34	0.45	2.29	4.61
lnHP100(it)	372	2.76	0.51	1.81	4.61
lnEF100(it)	372	2.96	0.90	0.01	4.61
lnSS100(it)	372	3.06	0.56	1.70	4.61

. 100 in Equations (4) and (5) means that data were normalized with Equation (1). As can be seen, the maximum values of variables are the same. The reason is that the data have been pre-processed by using Equations (1) and (5), and the maximum value is 4.61 (ln100). In addition, EF varies the most from region to region, followed by SS. These two indicators reflect the imbalance of fiscal expenditure.

Compared with individual-fixed-effects model, two-way-fixed-effects model, random-effects model, and the time-fixed-effects least square model were selected to estimate Equation (5). The estimation results are shown in Figure 7, the red dots represent the coefficients of the variables.

It is clear that HP has a negative effect on BR, while DI, EF and SS have a positive effect approximately. However, the value of p > t is large, indicating that many small probability events that are not included in the estimation results. The critical reason may be attributed to the fact that the sample size is not large enough. However, this problem is hard to solve due to the lack of data. In addition, sigma_u failure to undergo the test either. We can draw a conclusion that the linear panel model is defective to estimate the influence under the present sample. An approach that tolerates non-linear relationship need to be considered.

4.2. Slection of Threshold Variables

Based on the analysis of factor coefficient matrix, DI behaviors strong endogenous characterization. Endogenous variables will lead to biased estimation on the causal effect of measured variables in liner models. However, common sense and the previous researches showed that DI plays an important role in family fertility decisions. So, it is necessary to find a model that tolerates the endogeneity of DI. And coincidentally, Seo and Shin [23] proved that GMM estimator allows threshold variable endogenous, and thus it was treated as an endogenous variable in SYS-GMM dynamic threshold panel model.

After the decision of threshold variable, we needed to clarify variables which are affected by the threshold variable. We tried to match influencing factors and BR by various functions, such as Gaussian, Allometric, Beta, Bolezmann and Logistic. After comparison, we found that Gaussian function has the highest goodness-of-fit, and was thus chosen to search variables which are affected by the threshold.

Equations (6)–(8) were fitted expressions by Gaussian function with BR as dependent variable and EF₁₀₀, HP₁₀₀ and SS₁₀₀ as independent variables.

$$BR=13.53+(-74.22/(9.81\times \sqrt{\pi /2}))\times {{\displaystyle e}}^{-2\times {((0.15\times E{F}_{100}-9.05)/9.81)}^2}$$

(6)

$$BR=7.71+(2457.56/(8.36\times \sqrt{\pi /2}))\times {{\displaystyle e}}^{-2\times {((0.035\times H{P}_{100}+11.57)/8.36)}^2}$$

(7)

$$BR=7.99+(254.87/(47.42\times \sqrt{\pi /2}))\times {{\displaystyle e}}^{-2\times {((SS100-34.85)/47.42)}^2}$$

(8)

Figure 8 is drawn based on Equations (6)–(8), which presents the corresponding relationship between BR and independent variables EF₁₀₀, HP₁₀₀, SS₁₀₀. 100 in Equations (6)–(8) indicates that data have been normalized by using Equation (1).

As can be seen in Figure 8, the curve of BR-EF₁₀₀ is roughly u-shaped with a turning point at EF₁₀₀ = 60. This may be attributed to the following reasons. In the regions where EF is low, the family income is low too. The income of families is mainly spent on basic subsistence needs and the expenditure on education is relatively low. As the substitution relationship between quality and quantity of children is strong, the government’s increasing investment on education can not enhance families’ willingness to have children, and thus financial expenditure on education coupled with low fertility rate. When EF is high, family incomes are commonly high too. High-income families are willing and able to spend a large proportion of family expenses on children’s education. The cost of compulsory education mainly made up of household and government investments, so high education funds correspond to low household costs. So, families are willing to have more children, which results in high fertility rate. Based on the above analysis, EF can be identified as a variable affected by threshold variables.

The curve of BR-HP₁₀₀ is downward. Some cases can support for this phenomenon. In the 1950s, the number of abortions in the Soviet Union exceeded the number of births. The official Soviet Union conducted a questionnaire survey of more than 20 thousand couples, and found that more than half of urban women dared not to have children without residential house [42]. According to Zillow data, it was found that housing prices have a strong effect on birth rate. A 10 percent increase in housing prices equals a 1.5 percent decrease in birth rate. Similar to Soviet Union and United States, many families in China can’t afford to buy residential houses. According to China’s Bureau of Statistics, from 2001 to 2020, the CPI was increased by 58%, accompanied with the average of commodity housing prices by 373%. It is obvious that house price was rising much faster than inflation. In the view of individual regions, the increase rate of house price in Guangxi is slowest, by 244%, while that of Beijing by 997%. Considering the linear impact of HP₁₀₀ on BR, HP can be identified as an independent variable, which is not affected by the threshold variable.

The curve of BR-SS₁₀₀ is inverted U-shape with the critical point at SS₁₀₀ = 40. When there is no social security, people dare not to have children under economic pressure. As a result, the birth rate significantly rises along with the improvement of social security. However, with the continuous increase of social security, birth rate inverses to decrease, which may be attributed to the reason that people don’t need children to protect them from old age. So, appropriate social security corresponds to a high birth rate, either high or low social security is unfavorable for birth rate. Considering the non-linear impact of SS₁₀₀ on BR, SS can be identified as a variable affected by the threshold variable.

4.3. Dynamic Panel Threshold Model

Combined with the above analysis, we acquired the threshold panel model, with DI as the threshold variable, EF and SS as the independent variables affected by the threshold variable, HP as the independent variable not affected by the threshold variable. In addition, the analysis of birth rate in China indicates that the birth rate is also affected by the value of itself in the previous year. As a result, a dynamic panel threshold model was considered in the present work. Considering the nonlinear feature of SS and EF, a single threshold dynamic panel model was applied, which can be expressed in Equation (9). Threshold effect here refers to the phenomenon that when DI reaches a certain value, the influence of EF and SS on BR suddenly turns to another form. And dynamic effect here refers to the phenomenon that BR is affected by its own value of the previous year.

lnBR_100(it)= β₁+ β₂lnHP_100(it)+ β₃lnEF_100(it)·I(q_it ≤ w) + β₄lnEF_100(it)·I(q_it > w) + β₅× lnSS_100(it)·I(q_it ≤ w) + β₆× lnSS_100(it)·I(q_it ≤ w) + β₇lnBR_100(it−1) + α_i + δ_it

(9)

If DI in the model has two certain values, the influence of EF and SS on BR suddenly turns to another form, which is called double threshold dynamic panel model and is shown in Equation (10).

lnBR_100(it)= β₁+ β₂lnHP_100(it)+ β₃lnEF_100(it)·I(q_it ≤ u₁) + β₄lnEF_100(it)·I(u₁< q_it ≤ u₂) + β₅lnEF_100(it)·I(u₂< q_it) + β₆× lnSS_100(it)·I(q_it ≤ u₁) + β₇× lnSS_100(it)·I(u₁< q_it ≤ u₂) + β₈× lnBR_100(it−1) (u₂ < q_it) + α_i + δ_it

(10)

In Equations (9) and (10), q_it is a threshold variable, and means lnDI_100(it). w, u₁ and u₂ are critical thresholds, I is indicator function, BR_t−1 is the lag term of BR, and α_i is random disturbance term. δ_it is the error term, which can be expressed as Equation (11).

δ_it = u_i + v_it

(11)

where u_i is an unobserved individual fixed effect and v_it is an unobserved time fixed effect. 100 in Equations (9)–(11) means that data have been normalized by using Equation (1).

In order to avoid spurious regression, correlation tests on variables are carried out. The statistic test values are less than 5% critical values in both ADF and LLC tests, and p-values in LLC test are nearly 0, seeing

Table 3. Unit root test and stationarity test.

Variables	ADF Test		LLC Test p-Value	IPS
	Test Statistic	5% Critical Value		Test Statistic	5% Critical Value
BR	−6.830	−2.876	0.002	−3.821	−2.385
DI	−9.696	−2.875	0.000	−2.508	−2.383
HP	−3.450	−2.875	0.000	−4.654	−2.382
EF	−11.375	−2.570	0.000	−4.408	−1.740
SS	−8.944	−2.570	0.002	−3.275	−2.480

. Therefore, data passed the unit root test and stationarity test. In addition, according to p-values in Wald test, all the dynamic threshold models have significant threshold effects at 5% significant value.

The correlation test results of the single and double threshold dynamic panel models are shown in

Table 4. Correlation test results of the single and double threshold panel models.

Type (SYS-GMM)	RSS	MSE	Fstat	Prob	Sigma_u	Sigma_e
single threshold	1.547	0.004	6.820	0.650	0.124	0.068
double threshold	1.464	0.004	20.350	0.013	0.125	0.066

, which prove that the double one is more suitable. Consequently, the double threshold dynamic panel model was utilized in the present work. According to the F test and their p-values in Table 4, the double threshold dynamic model rejects the original hypothesis of no threshold effect at the confidence level of 5%. Meanwhile, BR_t−1 and HP exhibit significant linear effects, while EF and SS exhibit significant threshold effects on BR at the significant level of 5%.

Double threshold dynamic panel results are shown in Figure 9. u₁ and u₂ are threshold values, u₁ = 3.84, u₂ = 3.97. The red dots represent the coefficients of the variables. As can be seen from Figure 9, BR_t−1 has a promoting effect on BR. Similar to basic panel model and Gaussian function fitting, HP has a restraining effect on BR. EF has a positive effect on BR, and the effect is strongest between 3.84 < q_it < 3.97. SS has both positive and negative effects on BR, and the effect is strongly positive at q_it ≤ 3.84, weak positive between 3.84 < q_it < 3.97, and negative at q_it > 3.97.

On the basis of 31 provincial administrative units panel data among 2008–2019, birth rate indicators, such as disposable income, house prices, education funds and social security, have been established. The relationship between independent variables and dependent variables from multiple perspectives has been investigated. Firstly, basic linear models were used to find the influence of independent variables roughly, and found that HP has a negative effect on BR, while EF and SS have a positive effect on BR. However, the linear models are unable to deal with non-linearity and endogeneity. Consequently, Gaussian function was used to test non-linear variables, which regarded DI as threshold variable, while EF and SS as variables affected by DI. And then unit root test, stationarity test and Wald test were performed to confirm the validity of the model. Finally, we established a dynamic threshold panel model in order to solve nonlinear and endogenic problems. Compared with single threshold dynamic panel model, double threshold dynamic panel model was more suitable and thus chosen in the present work.

The coefficient of house price is negative and significant, similar to the result reported by Pan and Yang [43]. For education funds, Omori [44] discovered that public investment in education enhances birth rate, which agrees with the positive coefficients in education funds in Figure 9. For social security, Song et al. [45] found that the government policy does not significantly affect birth rate. According to the present modeling, it is obvious that the impact of social security on birth rate is erratic, the coefficient of which can be varied from negative to positive.

According to Figure 9, the coefficient of lnBR_100(it−1) is 0.578, indicating a positive effect of birth rate in the previous year. This can be explained by a theory of consumption economy. Due to the high cost of childcare, it is reasonable to regard fertility behavior as consumption. Hence, the fertility behavior in the previous year is similar to consumption habit. Meanwhile, the negative coefficient of HP can be also explained by the theory of consumption economy. Under the influence of the income effect, people can only reduce the fertility behavior in response to rising house prices. In addition, with the increase of DI, the corresponding curves of BR-EF and BR-SS are S-shaped and inverted U-shaped separately. Both shapes have a highest point, indicating a maximum value of BR. This can be explained by input-output theory in economics. Education funds and social security funds can be regarded as inputs to fertility. The maximum value of BR corresponds to the optimal scale of production.

As can be seen in Figure 9, the double threshold values of DI are located at lnDI_100(it) = 3.84 and lnDI_100(it) = 3.97. According to Equation (1), the actual values of DI at the threshold values can be calculated to be 24,471 and 28,195, respectively. Based on the DI values in 2019, 31 administrative units were divided into three categories, A, B and C, as shown in

Table 5. Area classification according to DI at 2019.

Categories	Disposable Income Range	Financial Expenditure		Regional List
		EF	SS
A	DI ≤ 24,471	Weak positive	Strong positive	Hebei; Shanxi; Inner Mongolia; Liaoning; Jilin; Heilongjiang; Anhui; Jiangxi; Shandong; Henan; Hubei; Hunan; Guangxi; Hainan; Chongqing; Sichuan; Guizhou; Yunnan; Xizang; Shaanxi; Gansu; Qinghai; Ningxia; Xinjiang
B	24,471 < DI ≤ 28,195	Strong positive	Weak positive	Fujian
C	DI > 28,195	Moderate positive	Negative	Beijing; Tianjin; Shanghai; Jiangsu; Zhejiang; Guangdong

.

As can be seen in Table 5, category A covers 25 administrative units and is characterized by low DI. In these areas, SS has a strong and EF has a weak positive effect on BR. While category B only includes Fujian, a province that characterized by higher household income but lower education level. In addition, category C includes 6 administrative units, which are characterized by high DI. In these regions, EF has middle positive effect and SS has negative effect on birth rate.

5. Discussion

According to the empirical results, birth rate is strongly influenced by the value of itself in the previous year, so the trends of birth rate are hard to be reversed. Interestingly, if the trend of low-birth is reversed, the reversion effect can be maintained for a long time. Chinese government has made some efforts to encourage birth, but the trend of declining birth rate has not been reversed. Hence, it is urgent to offer some creative policies, e.g., increasing young people’s desire for marriage and childbearing through the internet, raising the social status of childcare work, and helping married women to balance family and work.

High house price is one of the main inhibiting factors on birth rate, so the control of house prices will improve the low birth rate situation in all regions. Specific strategies are as follows. Firstly, the increment of real estate loans should be strictly controlled. According to the previous experiences [46], reducing bank loan funds has an immediate effect on house price. Secondly, introducing purchase restriction policies can efficiently control the house price. Referring to Changsha, government established several macro-control policies and achieved good inhibit effect on house price, such as purchasing restrictions on eligibility and quantity, increasing the minimum ratio of down payment and so on. The increment of average sale prices of residential commercial houses in Changsha is the slowest among the 19 first-tier cities from 2008 to 2019. Thirdly, the management of economically affordable houses should be improved. This type of houses is mainly distributed to low and middle income families, but often occupied by ineligible families, which significantly weakens the fertility desire of eligible families without housing. Finally, the vacant housing resources should be fully used. According to the report of Gan [47], the housing vacancy ratios in first-tier, second-tier and third-tier cities are 16.8%, 22.2% and 21.8%, respectively.

Different financial policies in different income regions should be established and further applied in the promotion of birth rate. In category A, the government should increase the investments of education and social security. Firstly, the government should lower the minimum social security contribution base and give flexible contribution ratio in order to encourage poor areas and private enterprises to increase the proportion of insured people. Secondly, the fixed-age retirement can be flexibly changed to meet the needs of postponed retirement. Thus, the amount of government social security accounts gets growth and fiscal payment ability can be enhanced. Thirdly, the design and management of the medical insurance system should be improved. According to the audit announcement released by Chen [48], the violations of medical insurance fund reached 1.578 billion CNY. Administrative departments should establish policies to prevent under-paid in medical insurance premiums, misappropriation of medical insurance fund, repeated participation in basic medical insurance and repeated reimbursement of medical expenses, and illegal price increasing in medical institutions. Finally, according to the data provided by Ministry of Education of the People’s Republic of China, more and more college students are delaying their employment until they graduate from graduate school. In 2022, 4.57 million students took graduate entrance examination, which is 800 thousands more than that of previous year, and 350 thousands more than the number of college graduates in the same year. This situation is unfavourable to the participation ratio of social security, and can be changed by improving the social status of vocational school graduates, encouraging on-the-job postgraduate education and advocating employers to improve vocational skills rather than academic qualifications.

For the individual regions in category A, as can be seen from Figure 5 and Figure 6, EF of Sichuan, Hubei and Henan are in the third level, and those of the rest regions are in the second or first level. SS of Xizang and Chongqing are in the fifth level, Liaoning and Heilongjiang in the fourth level and the rest regions in the third level and below. The main contradiction in these regions is that it is difficult for the local governments to increase investment due to low income. Therefore, it is particularly important to seek the help from high-income regions and the central government. And the central government should allocate the limited financial fund according to the urgency of need. So, the investment distribution of education funds should be in areas except Sichuan, Hebei and Henan, and social security funds should be in areas except Xizang, Chongqing, Liaoning and Heilongjiang.

BR in category B regions is more sensitive to EF compared with A and C regions. For category B, the most effective way to increase birth rate is to ask government officials and local resident to pay more attention to education. Governments should avoid efficiency problems by shortening the time for declaration, delivery and using education funds. Meanwhile, local governments should expand the decision-making power of school itself, and reduce unreasonable restrictions on the direction of the use of education funds. In addition, finance, education and other departments should strengthen supervision over the use of funds, ensuring utility maximization.

As can be seen from Figure 4 and Figure 5, HP of category C is in the fifth level and the rest one, Jiangsu province, is in the fourth level. EF of 5 administrative units are in the fourth level and the rest one, Guangdong province, is in the fifth level. It is clear that the situation of DI, HP and EF in these 6 administrative units are similar. So, the methods to increase the birth rate in these regions are similar too. Considering the already high level of education spending and negative effect of social security, there is no need to make efforts on either. According to the extremely high housing price, the only and most effective way to improve birth rate is to control housing price.

Figure 2 shows that Xinjiang has the highest population decline level. The geographical and economic situation of Xinjiang and Xizang are similar. As can be seen in Figure 6, the SS of Xinjiang ranks the second level, and that of Xizang the fifth level. This is the biggest difference between these regions. According to Table 5, Xinjiang belongs to category A and SS has a strong positive effect on birth rate. Therefore, increasing social security is an effective way to increase the birth rate in Xinjiang.

Seeing Figure 2, it is clear that Hubei is the only region with a rising birth rate. Hubei and Hunan are adjacent to each other and have similar economic situations. As can be seen from Figure 5 and Figure 6, the EF increased by 2 levels and SS increased by 1 level in Hubei, while that of Hunan remained the same level from 2009 to 2019. As can be seen from Table 5, these two regions are located in category A, and both of EF and SS have a positive effect on birth rate. Therefore, combined with the development of EF and SS in the two regions, it is logical that the BR of Hubei rises while that of Hunan falls. Based on the above analysis, Hunan may achieve the goal of increasing birth rate by learning the successful experience of Hubei, that increasing EF and SS level.

Population growth of three northeastern provinces is negative, and these regions are also places with a good basis and more experience in family planning. The problem now is that local residents have difficulty in changing the concept from having fewer children to having more, and the trend of negative population growth is becoming more and more serious. As can be seen in Table 5, these regions are located in category A, where HP have a restraining effect and EF and SS have a positive effect on birth rate. In combination with Figure 3, only the HP of Liaoning is high and need to be controlled. And SS of these three regions rise rapidly, indicating no necessary to change its situation. However, EF in these regions is still at the first level in 2019, and thus increasing funding for education is the key to raise the birth rate.

Devoting to proposing the methods for increasing the birth rate, this study selected 31 administrative units to conduct a frame work. The most important discover is that China’s disposable income plays an intermediate role between birth rate and financial expenditure. Governments should consider the economic condition before making polices. Especially, as the value of disposable income change, thresholds may be crossed. Accordingly, the appropriateness of policies need to be reconsidered. Only in this way, may our society achieve sustainable population development and longtime well-being.