Though a lot of models have been set forth and applied in electricity demand prediction, due to the detailed data acquisition limitations of households especially in terms of their fertility planning, some methods, such as time-series algorithms (Chou and Tran, 2018), artificial neural networks (Kim and Cho, 2019), or others needing large-sample (Somu et al., 2021), don’t suit the study. For this reason, this article employs an approach that firstly deconstructing the study issue into two sub-issues (i.e., household population prediction and the electricity demand); then constructing their respective corresponding models; at last building a integrated model system to prediction the electricity demand of residential household under the influence of fertility policy. The main logic is shown in Figure 1.

As Figure 1 demonstrates, the cohort-component projection model (CCPM), the grey forecasting algorithm (GF), and the interactive ritual chain (IRC) method are used in the population prediction; on the other hand, the double logit model (DL) based on the China Family Panel Studies (CFPS) database is adopted for forecasting the residential electricity demand and to obtain the logarithmic linear relationship between electricity consumption ( ln ⁡ q ) and other household-related variables ( ln ⁡ X i ), where α 0 and α i are coefficients; and the integrated model which is named by the linear regression prediction (LSP) method is used to obtain the residential electricity prediction results.

The UTCP and the TCP might well affect the age structure of households and household electricity demand by influencing the fertility intention and behavior of women of childbearing age (reflected by the fertility rate). To explore the relationship between fertility policy and residential electricity demand, we take the release time (year) of the UTCP and the TCP as two time points, hence forming the three time phases: before the UTCP, after the UTCP, and between the two policies.

Phase Ⅰ: 2010–2015, the period before the UTCP. The National Bureau of Statistics (NBS) released annual TFR and age-specific fertility data of women of childbearing age during this period.

Phase Ⅱ: 2016–2021, the first 6 years of the implementation of the UTCP. The NBS has not released fertility data since 2015.

Phase Ⅲ: After 2022, the period after the TCP.

The CCPM and other simplified variations remain in common use because of their simplicity and low data requirements (Wilson, 2016; Li and Wang, 2021). In this section, the CCPM is adopted to predict the household population. In prediction, assume that the population system is closed-loop with no migration during the prediction cycle. The relevant variables are defined as shown in Table 1.

The CCPM is shown below: M x , t + 1 , k = p x , t , k m ⋅ M x − 1 , t , k , ∀ x , k ≥ 1 , (1) F x , t + 1 , k = p x , t , k f ⋅ F x − 1 , t , k , ∀ x , k ≥ 1 , (2) T F R t , k = ∑ x = 15 49 b x , t , k , (3) B t , k = ∑ x = 15 49 b x , t , k F x , t , k , B t , m , k = s r t , k 100 + s r t , k B t , k , B t , f , k = B t , k − B t , m , k , (4) M 0 , t + 1 , k = p 0 , t , k m ⋅ B t , m , k , (5) F 0 , t + 1 , k = p 0 , t , k f ⋅ B t , f , k , (6) MOD R t , k = M x ≥ 65 , t , k + F x ≥ 65 , t , k M 15 ≤ x ≤ 64 , t , k + F 15 ≤ x ≤ 64 , t , k × 100 % , (7) where Eqs. 1, 2 predict the male population and the female population in year t + 1 in phase k , respectively; Eq. 3 predicts the TFR in year t + 1 in phase k ; Eq. 4 predicts the total number of newborns, male newborns, and female newborns in year t in phase k ; Eqs. 5, 6 represent the number of male newborns and female newborns in year t growing up in year t + 1 , respectively; and Eq. 7 predicts the MODR in year t in phase k .

In this paper, the residential electricity consumption is used as the dependent variable, average electricity price, annual household income, average annual temperature and household-level old-age dependency ratio (HODR) are used as household attribute variables, and then a double logit model for the three phases is constructed, as shown in Eq. 8. ln q i t k = α 0 k + α 1 k ln p r i c e i t k + α 2 k ln t a r i i t k + α 3 k ln t e m p i t k + α 4 k ln H O D R i t k + ε i t k , (8) where q i t k , p r i c e i t k , t a r i i t k , t e m p i t k and H O D R i t k are the electricity demand, the average electricity price, the annual income, the average annual temperature and the HODR of household i in year t in phase k ; X = { l n p r i c e i t k , ln t a r i i t k , ln t e m p i t k , ln H O D R i t k } is the set of independent variables, including the logarithmic values of p r i c e i t k , t a r i i t k , t e m p i t k and H O D R i t k , ε i t k is an error term in line with a normal distribution.

To encourage childbirth further, some administrative regions of China, like Zhejiang province and Guangdong province introduced a “multi-population” tiered electricity pricing (TEP) system in 2021. For instance, to the family owning more than seven family members, if they consume 750 kWh a month, a subsidy of 30 RMB will be given under that policy. The other provinces such as Hunan and Yunnan also introduced maternity allowance and subsidy policies in 2022. However, seeing from the outcomes so far, with the development of China’s economic level and the improvement in residents’ living standards, but the effects of these measures are limited. Thus, we can rewrite Eq. 8 as follows: ln q i t k = α 0 + α 1 ln p r i c e i t + α 2 ln t a r i i t + α 3 ln t e m p i t + α 4 k ln H O D R i t k + ε i t k . (9)

Furthermore, we can obtain: q k = e α 0 p r i c e α 1 t a r i α 2 t e m p α 3 H O D R α 4 k . (10)

The population-related data in this paper are obtained from World Population Prospects 2022, the 2015–2021 China Population and Employment Statistics Yearbooks and the 2015 National 1% Population Sample Survey. Specifically, the life expectancy of men and women for 2022–2050 is obtained from World Population Prospects 2022; the age-specific sex ratio is obtained from the Yearbooks 2015–2021; the fertility rate of women of childbearing age by age group, the population by age and sex, and the MODR are obtained from the 2015 National 1% Population Sample Survey.

The residential electricity consumption data used in this paper include household microdata and climate data, where household microdata are obtained from the CFPS for 2014, 2016 and 2018, and climate data are obtained from the statistical yearbooks of the provinces and municipalities for 2015, 2017 and 2019. The CFPS can provide the monthly electricity charges, annual income, household size, and household structure of residential households. In addition, we also collate the data about households that already have young children aged 0–14 from 15 provinces and municipalities, including Beijing, Tianjin, Shanghai, Gansu and Liaoning. The distribution of samples is shown in Figure 2, from which we can see that Gansu province has the largest sample size, accounting for 30.4%, and Beijing has the smallest proportion, accounting for 0.4%. The variables are described in Table 2.

Given that the monthly electricity charges are provided in the CFPS database, the annual electricity consumption and the average electricity price should be calculated from Eqs. 11, 12, respectively. Let us define the monthly electricity charge of household i in year t as e i t and the average electricity price of residential household i in year t as p r i c e i t . Taking Hunan province as an example, a three-stage tiered electricity tariff system is currently implemented in Hunan, the thresholds of electricity consumption are γ 1 = 200 k W h and γ 2 = 350 k W h , and the tiered electricity tariffs are 0.588 RMB/kWh, 0.638 RMB/kWh and 0.888 RMB/kWh. q i t = { e i t 0.588 , e i t ≤ 0.588 γ 1 , γ 1 + e i t − 0.588 γ 1 0.638 , 0.588 γ 1 < e i t ≤ 0.638 γ 2 , γ 2 + e i t − 0.588 γ 1 − 0.638 ( γ 2 − γ 1 ) 0.888 , e i t > 0.638 γ 2 , (11) p r i c e i t = f e e i t q i t , (12)

According to Qi and Liu (2020), the HODR can be further obtained as shown in Eq. 13. H O D R = o s 65 f s − c s − o s 65 × 100 % , (13) where o s 65 represents the number of elderly persons aged 65+ in the household and c s represents the number of children aged 0–14 in the same household.

According to the CCPM in Section 2.3, it is obvious that several important parameters should be obtained before solving the CCPM, including the forecast cycle, TFR, life expectancy, and sex ratio.

(1) Forecast cycle. Since 2015, the NBS has not released fertility data again. Therefore, we set 2016 as the beginning year of the forecast cycle and make 20-year predictions from 2016 to 2035.

Phase Ⅰ: Based on the TFR data released by the NBS from 2010 to 2015, the TFRs from 2016 to 2035 can be predicted through the GF algorithm.

Phase Ⅱ: Based on the TFR data estimated by Prof. Qiao for 2016–2020, the TFRs from 2021 to 2035 can be predicted through the GF algorithm.

Phase Ⅲ: Assuming that the TCP has a positive effect on fertility rate, this paper assumes the TFRs of no less than 1.3 from 2022 to 2035.

(3) Life expectancy. Based on the data in the World Population Prospects 2022, the life expectancy for men and women in 2022–2035 are obtained by the linear interpolation method.

The 3,999 residential electricity consumption samples from the CFPS database in 2014, 2016, and 2018 are modeled as a double logit model according to Eq. 8 and subjected to least squares (OLS) linear regression, and the results are shown in Table 3. In Table 3, column (I) shows the regression results of average electricity price and HODR with annual household electricity consumption, and column (II) shows the regression results of average electricity price, HODR, annual income, and average temperature with annual household electricity consumption.

The main results are as follows:

(1) Residents are very sensitive to changes in electricity prices. When electricity prices rise, residents will consume less electricity. Columns (I) and (II) report that the average electricity price is statistically significant at the 1% level, with values of −0.156 and −0.140 respectively. This conclusion is in line with the law of the market (quantity discount); that is, the more electricity is consumed, the lower the price.

Based on the IRC theory, we regard that the MODR is the overall performance of the HODR, and the HODR is the radiative distribution of the MODR. So this paper tends to explore the statistical relationship between MODR and HODR. Through calculating the HODR in 3,999 samples, we have obtained some results: the skewness value of 2.66, the mean value μ of 16.03% and a standard deviation σ of 31.62%. Comparing μ with the average MODR of 15.2% for 2014, 2016 and 2018 (data from the China Population and Employment Statistics Yearbook 2020), the error is calculated as 5.46%. It is, therefore, further demonstrated that the HODR obeys a positive skewed distribution with the MODR as the mean. For further analysis, we assume that the HODR obeys a normal distribution with the MODR as the mean, i.e., H O D R ∼ N ( M O D R , σ 2 ) .

Based on the results in Section 4.3, the electricity demand for the five selected households in 2022–2035 are obtained according to Eq. 10, as shown in Table 7.

According to Table 7, the following findings could be gained.

(1) The annual household electricity demand decreases year by year. By comparing the annual electricity consumption in 2035 and 2022, it is found that the annual electricity demand of household ^#1 decreases the most, with decreases of 2.23% (Column BTC) and 2.02% (Column ATC). The annual electricity consumption of household ^#5 has the smallest decline, with declines of 0.82% (Column BTC) and 0.73% (Column ATC).

Based on the above analysis, it can be concluded that for households without the pressure of supporting the elderly, the fertility policies may encourage their electricity consumption to some extent, but over time the electricity demand will gradually diminish. For households with great pressure to support elderly individuals, the fertility policies have a very limited promotion effect and little impact on their electricity demand. The results show that the space for further energy savings is very large for households with less pressure of supporting the eldly.