4.3.1 Household Digital Financial Inclusion Index
To design the micro digital financial inclusion indicator system, it is necessary to fully consider the macroscopic reality of China’s economic development and financial exclusion as well as the financial characteristics of Chinese households at the micro level. Based on the main macro financial inclusion index systems and drawing on the practices of Yin et al. (2019) and Sarma (2008, 2016), we used the Euclidean distance method to design the digital financial inclusion index of households. The advantage of this approach is that it is easy to calculate the index, and it does not impose different weights on each dimension.
The first step is to design the index system. Based on the data from the China Household Financial Survey, we selected seven indicators from the three levels of digitalization, usability, and coverage, as shown in the table below.
Table 1
Composite sub-dimension indicators of digital financial inclusion
Dimension | Variable name | Definition |
Digitalization | E-payment | Have you ever used electronic payment? 1 = Yes; 0 = No |
Internet finance | Have you ever had an Internet financial account? 1 = Yes; 0 = No |
Usability | Insurance | Have you ever purchased commercial insurance or social insurance services? 1 = Yes; 0 = No |
Loan | Have you ever had a loan from a bank? 1 = Yes;0 = No |
Credit card | Have you ever had a credit card? 1 = Yes; 0 = No |
Deposit | The number of deposit cards or current passbooks |
Coverage | Distance | Distance from home to the nearest bank. (This index is treated logarithmically) |
The second step is to standardize digital financial inclusion indicators. To solve the dimension problem of the data index, we used deviation standardization to deal with the original index data. The index of the \({d_i}\) is computed by the following formula:
\({d_i}=\frac{{{A_i} - {m_i}}}{{{M_i} - {m_i}}}\) (2)
where \({A_i}\) is the true value of the dimension, \({M_i}\) is the maximum value, and \({m_i}\) is the minimum value. The purpose of the above formula is to standardize in order to ensure that the value interval of each indicator is [0,1]; through standardization, each indicator can meet the unit independence and boundedness. The higher the value of \({d_i}\), the higher the level achieved by this indicator.
The third step is to synthesize a digital financial inclusion index. Referring to the practice of Yin et al. (2019) and Sarma (2008, 2016), and the equal weight assumption and the average Euclidean distance method to sum up sub-indexes, the financial inclusion index is constructed:
\(IF{I_{i1}}={{\sqrt {\sum\nolimits_{{i=1}}^{n} {d_{i}^{2}} } } \mathord{\left/ {\vphantom {{\sqrt {\sum\nolimits_{{i=1}}^{n} {d_{i}^{2}} } } {\sqrt n }}} \right. \kern-0pt} {\sqrt n }}\) (3)
\(IF{I_{i2}}={{1{\text{-}}\sqrt {\sum\nolimits_{{i=1}}^{n} {d_{i}^{2}} } } \mathord{\left/ {\vphantom {{1{\text{-}}\sqrt {\sum\nolimits_{{i=1}}^{n} {d_{i}^{2}} } } {\sqrt n }}} \right. \kern-0pt} {\sqrt n }}\) (4)
$$IF{I_i}=\frac{{IF{I_{i1}}+IF{I_{i2}}}}{2}$$
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$$IFI=\frac{{IF{I_1}+IF{I_2}+IF{I_3}}}{3}$$
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where\(IF{I_{i1}}\),\(IF{I_{i2}}\), and\(IF{I_i}\) represent the distance from the actual point to the worst point, the reverse distance to the best point, and the average distance of each indicator under the \({d_i}\) dimension, respectively. \(IFI\) is the final household digital financial inclusion index obtained by summing up the average three sub-dimension indexes.
4.3.2 The risk of returning to poverty
According to the World Bank, poverty vulnerability is defined as the possibility of becoming poor or poorer in the future (World Bank, 2001). There are three quantitative dimensions of vulnerability: Vulnerability as Expected Poverty (VEP), Vulnerability as Uninsured Exposure to Risk (VER), and Vulnerability as Low Expected Utility (VEU). Correspondingly, there are three different methods of measuring these vulnerability dimensions (Chaudhuri and Suryahadi, 2002; Gaiha and Ima, 2004; Gaiha and Katsushi, 2008), which respectively use risk sensitivity, gaps in welfare effects, and the probability of falling into poverty to express poverty vulnerability. A higher sensitivity to risk corresponds to a larger gap in welfare effects and a greater probability of falling into poverty corresponds to a higher level of vulnerability.
The risk of returning to poverty refers to the probability that the living standard of a family or individual who has been out of poverty will fall below the poverty line in the future because of the risk hitting, such as diseases, economic fluctuation, natural disasters and so on. Because the two definitions are similar, we considered the measurement of poverty vulnerability in existing studies as a measure of the risk of returning to poverty. We applied the VEP method to estimate the probability of a household’s loss of future welfare resulting from exposure to risk as a measure of poverty vulnerability. The VEP method has two main advantages. First, it can be adapted and used with cross-sectional data, which is necessary given the difficulty in obtaining multi-year data from micro-surveys conducted in rural areas. Second, the likelihood of falling into poverty measured using the VEP method can be objectively compared. The key objective of the VEP method is to predict the probability of falling into poverty during a certain future period using historical data on incomes or consumption and based on the normal distribution form of a given welfare level (Moore, 2001; Ward, 2016). The following equation was used to calculate the VEP:
$$~~{V_{h,t}}=Pr({Y_{h,t+1}} \leqslant G)$$
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The above formula expresses the probability of household returning to poverty during period , indicating the probability that the income level\({Y_{h,t+1}}\) of household during period \(t+1\) is lower than the poverty line,.
Assuming that the level of household income follows a lognormal distribution, income levels \({Y_{h,t}}\)are expressed as follows:
\(\ln {Y_{h,t}}={\beta _1}\cdot power+{\beta _2}{X_h}+{e_k}\) (8)
where \({X_h}\) is a collection of family feature vectors. It is worth noting that existing research generally includes family demographic and endowment characteristics such as the age, gender, health, and education of the head of the household. In addition, we took into account the family’s endogenous power index of poverty alleviation in the model. The endogenous power of poverty alleviation is the fulfilment of basic needs, including income and rights, use one’s own knowledge or skills to actively link social resources, and convert resources into potential action trends that can sustain poverty alleviation and development (Fu et al., 2020; Liu et al., 2020). If a family’s internal motivation for poverty alleviation is insufficient, even with extensive external aid, once support is no longer received, the family will often fall into poverty again because of internal reasons such as lack of willingness to develop independently or initiative and enthusiasm for poverty alleviation. Drawing on existing research, we select indicators based on four aspects, namely the health level (\(health\)), education level (\(edu\)), subjective well-being (\(wellbeing\)), and attitude of trust towards strangers (\(trust\)) of the head of household. Using the equal-weight assumption and the method of adding the total sub-indices of the average Euclidean distance method to construct the endogenous driving force of household poverty alleviation (\(power\)), it is calculated as follows:
$$power={{1{\text{-}}\sqrt {{{(1 - edu)}^2}+{{(1 - health)}^2}+{{(1 - wellbeing)}^2}+{{(1 - trust)}^2}} } \mathord{\left/ {\vphantom {{1{\text{-}}\sqrt {{{(1 - edu)}^2}+{{(1 - health)}^2}+{{(1 - wellbeing)}^2}+{{(1 - trust)}^2}} } {\sqrt 4 }}} \right. \kern-0pt} {\sqrt 4 }}$$
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In addition, we controlled other household features including the political status of the household head, household registration, age, gender, health, education, household size, annual household expenditure, and the values of the household’s durable goods and financial assets. \(\beta\) is the parameter to be estimated, and \({e_k}\) is the random error.
We assumed that fluctuations in household income could be replaced by the regression residual squared, that is, by future income variance. According to the heteroscedasticity of the cross-sectional data, this variance was determined by the characteristics of the sampled households:
\(\sigma _{{e,h}}^{2}=\lambda {X^{\prime}_h}\) (10)
We applied the three-stage feasible generalized least squares method to estimate the expectations of incomes and income variance among the sampled households:
$$E\left[ {\ln {Y_{h,t}}|{{X^{\prime}}_h}} \right]={X^{\prime}_h}\beta$$
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\(Var\left[ {\ln {Y_{h,t}}|{{X^{\prime}}_h}} \right]={X^{\prime}_h}\lambda\) (12)
Ultimately, the following formula was obtained:
\({V_{h,t}}=\Pr ({Y_{h,t+1}} \leqslant G)=\phi [(\ln G - {X^{\prime}_h}\hat {\beta })/\sqrt {{{X^{\prime}}_h}\hat {\lambda }} ]\) (13)
where \({V_{h,t}}\) denotes the probability that household will return to poverty in period , \(\Pr (\cdot )\) denotes the probability value, and \(\varphi [\cdot ]\) is the positive distribution function. \({X^{\prime}_h}\) represents the set of all family feature vectors of the family, including endogenous dynamics. In this paper, the poverty vulnerability of the family is classified according to whether it is greater than the average poverty vulnerability of the sample in order to assess whether a poverty-stricken family is vulnerable. That is, a family is considered vulnerable if the probability of returning to poverty in the future is greater than or equal to the mean poverty vulnerability. Furthermore, we treated the probability as a zero-one dummy variable, which indicates whether poverty-stricken families are at risk of returning to poverty. We applied the World Bank’s poverty line standard of US$1.9/day as the poverty line, and converted it at the exchange rate of 6.7519 yuan per US dollar (using the 12-month average in 2017). Accordingly, we calculated 4618.29 yuan per annum as the global poverty line.