Influencing factors and efficiency of funds in humanitarian supply chains: the case of Chinese rural minimum living security funds

Abstract

While humanitarian efforts are critical for assisting those affected by natural disasters, it is also essential for those affected by poverty, such as China’s rural poor. In this regard, China introduced the rural minimum living security system to provide humanitarian relief to its rural poor. The aim of this study is to explore the influencing factors and efficiency of humanitarian supply chains funds using rural minimum living security funds (RMLSF) as an example. Based on data from 31 provinces (autonomous regions and municipalities) in China from 2007 to 2016, this study employs the logarithmic mean Divisia index approach to decompose the RMLSF and investigates the contributions of seven factors on the change therein. This study also uses the three-stage data envelopment analysis method to assess the poverty reduction efficiency of RMLSF. The results show that the economic development level, the extent to which minimum living security funds are tilted toward rural areas, and the fiscal expenditure scale are the three main factors for the increase in RMLSF. Moreover, the technical efficiency in most provinces and the average technical efficiency in the eastern and central regions are underestimated due to external ambient factors, whereas the average technical efficiency in the western region is overestimated. These results provide a basis for increasing the scale and efficiency of RMLSF.

Appendix A

1.1 A.1. The first stage

In this stage, we will use the BCC model, which can separate the two causes of DMU technology inefficiency: the poor efficiency of production technology, and not being in the optimum scale. The calculated efficiency values include three parts: technical efficiency (TE), pure technical efficiency (PTE), and scale efficiency (SE). The relationship among them is given by $TE = PTE \times SE$.

The DEA model is generally divided into output-oriented, input-oriented, and non-oriented. This study focuses on minimizing the inputs of RMLSF without reducing outputs. Thus, it chooses the input-oriented BCC model for efficiency analysis.

1.2 A.2. The second stage

DMU’s efficiency value calculated at the first stage is affected by its internal management level as well as external environments and random errors (Fried et al. 2002). To remove the impacts of ambient factors and random errors, we will construct an SFA model for regression adjustment. In this model, the differences between the actual value and the target value of each input indicator (that is, the slack variable of each input indicator obtained at the first stage) are considered dependent variables, and the ambient variables (supposing the number is $p$) are considered independent variables. The model is constructed as below.

$$ s_{ij} = f^{i} \left( {z_{j} ;\beta^{i} } \right) + v_{ij} + u_{ij} $$

(A.1)

where $i$ and $j$ represent the input $i$ and the DMU $j$ ($i = 1,2, \ldots ,m$; $j = 1,2, \ldots ,n$), $s_{ij}$ indicates the slack variable of input $i$ of the DMU $j$, $z_{j}$ represents the vector composed of $p$ observable ambient variables of the DMU $j$, $z_{j} = \left( {z_{j1} ,z_{j2} , \ldots ,z_{jp} } \right)$, $\beta^{i}$ denotes the parameter vector to be estimated, and $f\left( \cdot \right)$ is a functional form to express the impact of ambient variables on input slack variable. Generally, $f\left( \cdot \right) = z_{j} \beta^{i}$. $v_{ij} + u_{ij}$ denotes a mixed error, where $v_{ij}$ demonstrates the stochastic disturbance term, $v_{ij} \sim\,N\left( {0,\sigma_{vj}^{2} } \right)$; $u_{ij}$ denotes the management inefficiency term, $u_{ij} \sim\,N^{ + } \left( {u^{j} ,\sigma_{uj}^{2} } \right)$; and $v_{ij}$ and $u_{ij}$ are independent of each other. $\gamma = \frac{{\sigma_{uj}^{2} }}{{\sigma_{uj}^{2} + \sigma_{vj}^{2} }}$ indicates the proportion of variance of management inefficiency to the total variance. If $\gamma \approx 1$, management inefficiency is the primary cause. If $\gamma \approx 0$, $u_{ij}$ can be removed from model (A.1). At this time, we can utilize ordinary least squares (OLS) directly to estimate model (A.1).Then, we use the ambient variable coefficients obtained to adjust the initial input indicators of each DMU; thus, all DMUs are in identical external environments and suffer the same random impact. The specific adjustments are as follows.

$$ \hat{x}_{ij} = x_{ij} + \left[ {\max_{j} \left\{ {z_{j} \hat{\beta }^{i} } \right\} - z_{j} \hat{\beta }^{i} } \right] + \left[ {\max_{j} \left\{ {\hat{v}_{ij} } \right\} - \hat{v}_{ij} } \right] $$

(A.2)

In the above equation, $x_{ij}$ and $\hat{x}_{ij}$ represent the actual value and adjusted value of input $i$ of DMU $j$, respectively, while the remaining terms have the same meaning as in Eq. (A.1). Moreover, “^” represents the estimated value, $\left[ {\max_{j} \left\{ {z_{j} \hat{\beta }^{i} } \right\} - z_{j} \hat{\beta }^{i} } \right]$ denotes the adjustment of ambient variables, and $\left[ {\max_{j} \left\{ {\hat{v}_{ij} } \right\} - \hat{v}_{ij} } \right]$ represents the adjustment of random error terms.

1.3 A.3. The third stage

The adjusted input $\hat{x}_{ij}$ computed in the second stage replaces the primitive input $x_{ij}$ as a new input indicator, and the output indicators remain unchanged. Then, we utilize the BCC model to compute DMUs’ efficiency values after excluding the impacts of ambient factors and random errors.