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Urban poverty: Measurement theory and evidence from American cities

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• Published: 03 August 2021
• Volume 19 , pages 599–642, ( 2021 )

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• Francesco Andreoli   ORCID: orcid.org/0000-0002-0751-5520 1 , 2 ,
• Mauro Mussini   ORCID: orcid.org/0000-0003-0770-8450 3 ,
• Vincenzo Prete   ORCID: orcid.org/0000-0003-3990-0105 1 &
• Claudio Zoli   ORCID: orcid.org/0000-0003-3786-4198 1  

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We characterize axiomatically a new index of urban poverty that i) captures aspects of the incidence and distribution of poverty across neighborhoods of a city, ii) is related to the Gini index and iii) is consistent with empirical evidence that living in a high poverty neighborhood is detrimental for many dimensions of residents’ well-being. Widely adopted measures of urban poverty, such as the concentrated poverty index, may violate some of the desirable properties we outline. Furthermore, we show that changes of urban poverty within the same city are additively decomposable into the contribution of demographic, convergence, re-ranking and spatial effects. We collect new evidence of heterogeneous patterns and trends of urban poverty across American metro areas over the last 35 years.

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Acknowledgments

We are grateful to conference participants at RES 2018 meeting (Sussex), LAGV 2018 (Aix en Provence) and ECINEQ 2019 (Paris) and to two anonymous reviewers for valuable comments. The usual disclaimer applies. Replication code for this article is accessible from the authors’ web-pages. This article forms part of the research project The Measurement of Ordinal and Multidimensional Inequalities (grant ANR-16-CE41-0005-01) of the French National Agency for Research and the NORFACE project IMCHILD: The impact of childhood circumstances on individual outcomes over the life-course (grant INTER/NORFACE/16/11333934/IMCHILD) of the Luxembourg National Research Fund (FNR), whose financial support is gratefully acknowledged.

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Francesco Andreoli, Vincenzo Prete & Claudio Zoli

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Appendix A: Proofs

1.1 a.1 proof of theorem 1.

We will prove the theorem making use of a sequence of lemmas that will highlight the role of the different axioms in the derivation of the final result.

Let \(\mathcal {A} \in {\Omega }\) , ζ ∈ [0, 1), and z ≥ 1, U P (.; ζ ) satisfies AGG and INV-S if and only if there exist a continuous function \(A:[0,1]^{2}\rightarrow \mathbb {R}_{+}\) and a function \(h:[0,1]\rightarrow \mathbb {R}\) continuous in (0,1) with h (0) = 0 such that:

with \(\bar {N}_{0}:=0\) .

The proof combines the effect of AGG with INV-S by deriving a functional restriction on the class of weighting functions \(w_{i} \left (\frac {N_{1}}{N},\ldots ,\frac {N_{i}}{N},\ldots ,\frac {N_{n}}{N}\right )\) that appear in the definition of AGG. We leave to the reader to verify that the index in Eq.  4 satisfies AGG and INV-S, here we focus on the proof of the (only if) part of the statement in the lemma.

First recall that, given AGG, we can write

where \(A:[0,1]^{2}\rightarrow \mathbb {R}_{+}\) and \(w_{i}: {\Delta }_{n}\rightarrow \mathbb {R}\) satisfy the conditions specified in AGG.

Let z ≥ 1, we apply INV-S. Note that because of the definition of INV-S, the scaling component \(A\left (\frac {P}{N}, \frac {\bar {P}_{z}}{\bar {N}_{z}}\right )\) of Eq.  5 is not affected by splitting operations. Thus INV-S only affects the component \({\sum }_{i=1}^{z} \frac {N_{i}}{N} \cdot \left (\frac {P_{i}}{N_{i}} - \zeta \right ) \cdot {w_{i}} \left (\frac {N_{1}}{N}, \ldots , \frac {N_{i}}{N}, \ldots , \frac {N_{n}}{N}\right )\) .

We construct the proof in two steps. We first derive the restrictions on the function w 1 (.) and then in a recursive manner we derive also the restrictions on all the other functions w i (.) for i = 2, 3,…, n .

We first note that the function w i (.) does not depend on ζ , and then we set ζ such that for a given \(\mathcal {A} \in {\Omega }\) we have that n = z . Note that for any \(\mathcal {A} \in {\Omega }\) there exist values of ζ such that n = z , for instance this is the case if we let ζ = 0.

Step 1. Suppose that n = z = 2, and assume that \(\frac {P_{1}}{N_{1}} >\zeta \) , while \(\frac {P_{2}}{N_{2}}=\zeta \) . Apply repeatedly the splitting operations over the neighborhood indexed by i = 2. Because of the invariance requirement in INV-S and the specification in Eq.  5 , if we denote by \(\hat {n}_{i}:=\frac {N_{i}}{{N}}\) we obtain that \(\hat {n}_{1} \left (\frac {P_{1}}{N_{1}} - \zeta \right ) \cdot w_{1} (\hat {n}_{1}, 1-\hat {n}_{1}) = \hat {n}_{1} \left (\frac {P_{1}}{N_{1}} - \zeta \right ) \cdot w_{1} (\hat {n}_{1}, \hat {n}_{2}, \hat {n}_{3}, \ldots , \hat {n}_{z})\) with \(\hat {n}_{2} + \hat {n}_{3} + {\ldots } + \hat {n}_{z} = 1-\hat {n}_{1}\) , this result holds for all z = n ≥ 2. Recalling that \(\frac {P_{1}}{N_{1}} - \zeta >0\) , we then obtain

with \(\hat {n}_{2} + \hat {n}_{3} +\ldots +\hat {n}_{z}=1-\hat {n}_{1}\) , for all z = n ≥ 2 and \(\hat {n}_{1}\in (0,1)\) . We can thus define the function \(h:[0,1]\rightarrow \mathbb {R}\) such that \(h(\hat {n}):=\hat {n} w_{1} (\hat {n}, 1-\hat {n})\) . It then follows that by definition

for all z = n ≥ 2 and \(\hat {n}_{1}\in (0,1)\) . Given that by AGG \(\hat {n}_{1} w_{1}(\hat {n}_{1},1-\hat {n}_{1})\) is continuous for \(\hat {n}_{1}\in (0,1)\) then h (.) is continuous on (0,1).

Step 2. Let z = n = 1, and assume to split into two neighborhoods the neighborhood 1 where \(\frac {P_{1}}{N_{1}}-\zeta >0\) , then one obtains two neighborhoods of relative sizes \(\hat {n}_{1}\) and \(1-\hat {n}_{1}\) . INV-S then implies that \(w_{1}(1) = \hat {n} w_{1} (\hat {n},1-\hat {n}) + (1- \hat {n}) w_{2} (\hat {n},1-\hat {n})\) . Let h (1) := w 1 (1), then one obtains for z = n = 2, \((1-\hat {n}) w_{2}(\hat {n},1-\hat {n})=w_{1}(1)-\hat {n} w_{1} (\hat {n},1-\hat {n})\) , that is \((1-\hat {n}) w_{2} (\hat {n},1-\hat {n}) = h(1)-h(\hat {n})\) , in other words \((1-\hat {n}) w_{2}(\hat {n},1-\hat {n})=h(\hat {n}+(1-\hat {n})) - h(\hat {n})\) . This gives the definition of w 2 (.) for z = n = 2.

The argument could be further generalized. Let z = n = 2, assume that \(\frac {P_{1}}{N_{1}}>\zeta \) , while \(\frac {P_{2}}{N_{2}}=\zeta \) . Then split neighborhood 1 of relative size \(\hat {n}\) into two neighborhoods of relative sizes respectively \(\hat {n}_{1}\) and \(\hat {n}_{2}\) such that \(\hat {n}_{1} + \hat {n}_{2}=\hat {n}\) , and, either leave neighborhood 2 unaffected, or split it into many others. According to INV-S it follows that \(\hat {n} \left (\frac {P_{1}}{N_{1}} - \zeta \right ) \cdot w_{1} (\hat {n},1-\hat {n})=\hat {n}_{1} \left (\frac {P_{1}}{N_{1}} - \zeta \right ) w_{1}(\hat {n}_{1},\hat {n}_{2},\hat {n}_{3},\ldots ,\hat {n}_{z^{\prime }}) + \hat {n}_{2} \left (\frac {P_{1}}{N_{1}} - \zeta \right ) w_{2}(\hat {n}_{1},\hat {n}_{2},\hat {n}_{3},\ldots , \hat {n}_{z^{\prime }})\) where \(z^{\prime } = n\geq 3\) and \(\hat {n}_{3}+\ldots + \hat {n}_{z^{\prime }} = 1-\hat {n}=1-\hat {n}_{1}-\hat {n}_{2}\) .

That is, \((\hat {n}_{1}+\hat {n}_{2}) \cdot w_{1} (\hat {n}_{1} + \hat {n}_{2}, 1-\hat {n}_{1}-\hat {n}_{2})=\hat {n}_{1}w_{1}(\hat {n}_{1},\hat {n}_{2},\hat {n}_{3},\ldots ,\hat {n}_{z^{\prime }}) + \hat {n}_{2} w_{2}(\hat {n}_{1},\hat {n}_{2},\hat {n}_{3},\ldots ,\hat {n}_{z^{\prime }})\) . Recalling that \(\hat {n}_{1} w_{1} (\hat {n}_{1},\hat {n}_{2},\hat {n}_{3},\ldots ,\hat {n}_{z}) = h(\hat {n}_{1})\) for all z = n ≥ 2 and \(\hat {n}_{1}\in (0,1)\) , one obtains

for all \(z^{\prime } = n\geq 2\) and \(\hat {n}_{1} + \hat {n}_{2}\in (0,1],\hat {n}_{1},\hat {n}_{2}\in (0,1)\) .

By replicating the same logic and splitting into three neighborhoods the first one, then one can derive the definition of w 3 (.) from

for all \(z^{\prime } = n\geq 3\) and \(\hat {n}_{1}+\hat {n}_{2}+\hat {n}_{3}\in (0,1],\hat {n}_{1},\hat {n}_{2},\hat {n}_{3}\in (0,1)\) .

We can then obtain in general that \(\frac {N_{i}}{\bar {N}_{z}} \cdot w_{i} \left (\frac {N_{1}}{\bar {N}_{z}},\ldots , \frac {N_{i}}{\bar {N}_{z}},\ldots , \frac {N_{z}}{\bar {N}_{z}}\right ) =h \left (\frac {\bar {N}_{i}}{\bar {N}_{z}}\right ) - h\left (\frac {\bar {N}_{i-1}}{\bar {N}_{z}}\right )\) for i = 1, 2,…, z and z = n where \(\frac {\bar {N}_{0}}{\bar {N}_{z}}:=0\) and h (0) := 0. If z = n then we have that \(\bar {N}_{z}=N\) , leading to

for i = 1, 2,…, n where \(\frac {\bar {N}_{0}}{N}:=0\) and h (0) := 0.

As pointed out the function w i (.) does not depend on ζ , therefore even if it is derived under the assumption that ζ is such that z = n , the specification also holds for any ζ ∈ [0, 1), and therefore for any z ≤ n , provided that z ≥ 1 as required in the definition of AGG. □

Let \(\mathcal {A}\in {\Omega }\) , ζ ∈ [0, 1), and z ≥ 1, U P (.; ζ ) satisfies AGG, INV-S, INV-T if and only if there exist a continuous functions \(A:[0,1]^{2}\rightarrow \mathbb {R}_{+}\) and \(\beta _{0},\gamma _{0}\in \mathbb {R}\) such that:

We take the result from Lemma 1 and investigate the implications on the specification of U P (.; ζ ) generated by further imposing INV-T. We leave to the reader to check that the obtained specification of U P (.; ζ ) satisfies all axioms, here we focus on the “only if” part of the lemma.

For z = 1, INV-T does not hold. Note that when z = 1 the specification of U P (.; ζ ) in the lemma is consistent with the one derived in Lemma 1 where h (1) = β 0 if z = n = 1. While the specification in the lemma for h (.) that is valid also when z = 1 < n , will be obtained in the next general part of the proof.

We set z ≥ 2 and consider the transfers involved in the definition of INV-T. Note that with z = 2, the axiom is satisfied by construction given that it involves two transfers of population taking place in opposite directions and therefore their effects cancel out leading to the initial configuration \(\mathcal {A}\) .

Without loss of generality we assume that there are z ≥ 2 neighborhoods with highly concentrated poverty with \(\frac {P_{i}}{N_{i}} \geq \zeta \) and such that their population size is equal, that is N i = N 0 for i = 1, 2,…, z . It follows that their relative population size within this set of neighborhoods is \(\frac {N_{i}}{\bar {N}_{z}} = \frac {1}{z}\) , with \(\frac {\bar {N}_{i}}{\bar {N}_{z}} = \frac {i}{z}\) .

Moreover, we consider first the case where ζ ∈ [0, 1) is such that for a given \(\mathcal {A}\in {\Omega }\) we have z = n ≥ 2.

Consider the effect of the combined transfers of population in INV-T, and apply them to the specification derived in Lemma 1. Note that these transfers take place among neighborhoods in {1, 2,…, z } and do not affect the components \(A\left (\frac {P}{N}, \frac {\bar {P}_{z}}{\bar {N}_{z}}\right )\) and \(\left [h\left (\frac {\bar {N}_{i}}{N}\right ) - h \left (\frac {\bar {N}_{i-1}}{N}\right )\right ]\) but only the distributions of \(\left (\frac {P_{i}}{N_{i}} - \zeta \right )\) . The application of the transfers in INV-T leads to the following condition

for ε > 0, satisfying the conditions specified in INV-T for all i , j ∈{1, 2,…, z − 1} with z = n ≥ 2.

It then follows that \(\left [h\left (\frac {j+1}{z}\right ) - h\left (\frac {j}{z}\right )\right ] - \left [h\left (\frac {j}{z}\right ) - h\left (\frac {j-1}{z}\right )\right ] = \left [h\left (\frac {i+1}{z}\right ) - h\left (\frac {i}{z}\right )\right ] - \left [h\left (\frac {i}{z}\right ) - h\left (\frac {i-1}{z}\right )\right ]\) for all i , j ∈{1, 2,…, z − 1}, and for all z = n ≥ 2. Thus, we have that \(\left [h\left (\frac {i+1}{z}\right ) - h\left (\frac {i}{z}\right )\right ] - \left [h\left (\frac {i}{z}\right ) - h\left (\frac {i-1}{z}\right )\right ]\) does not depend on i but eventually only on 1/ z . In general, there exists a function g (1/ z ) such that

for all i ∈{1, 2,…, z − 1}, all z = n ≥ 2.

To simplify the exposition, denote \(\frac {1}{z}=\sigma \) and let f ( i ) := h ( i σ ) for a fixed σ . We then have

Let d ( i ) := f ( i ) − f ( i − 1) for i ∈{1, 2,…, z − 1} with by construction f (0) = h (0) = 0. Thus, d (1) + d (2) + … + d ( i ) = f ( i ) − f (0) = f ( i ). We then have

for i ∈{1, 2,…, z − 1}, that leads to d ( j ) = d (1) + ( j − 1) g ( σ ) for i ∈{1, 2,…, z } and all z = n ≥ 2.

Thus, \(f(i)={\sum }_{j=1}^{i}d(j) = {\sum }_{j=1}^{i}d(1) +(j-1)g (\sigma )\) , with f (1) = d (1). It follows that

for i ∈{1, 2,…, z }, z = n ≥ 2. Recalling that f ( i ) := h ( i / z ) we have

for i ∈{1, 2,…, z }, z = n ≥ 2. Given that i and z can take any pair of natural number values such that i ≤ z = n , and that h (0) = 0 by construction, then the above formula is a functional equation that allows to specify the value of the function h (.) for all rational numbers in [0, 1].

Let i = z , we then obtain

note that the value of h (1) is constant and therefore independent from z , rearranging it then follows that for any z = n ≥ 2 it holds that

Recalling the derivation of \(h\left (\frac {i}{z}\right )\) and inserting \(h\left (\frac {1}{z}\right )\) one obtains

for i ∈{1, 2,…, z }, z = n ≥ 2.

Note that \(\frac {i}{z}\) are unaffected if both i and z = n are replicated r times for r ∈{1, 2, 3, 4,…}, we then obtain \(h\left (\frac {i}{z} \right ) = h\left (\frac {ri}{rz}\right ) = h(1) \frac {ri}{rz} - \frac {ri(rz-ri)}{2}g \left (\frac {1}{rz}\right ) =h(1) \frac {i}{z}-r^{2} \frac {i(z-i)}{2}g \left (\frac {1}{rz}\right )\) for all r . As a result it should hold that

for all r , z ∈{2, 3, 4,…} with z = n , thus, \(g\left (\frac {1}{rz}\right ) = \frac {1}{r^{2}}g \left (\frac {1}{z}\right )\) . By switching z with r one obtains \(g\left (\frac {1}{rz}\right ) = \frac {1}{z^{2}}g \left (\frac {1}{ r}\right )\) . As a result \(\frac {1}{r^{2}}g \left (\frac {1}{z}\right ) = \frac {1}{z^{2}}g \left (\frac {1}{r}\right )\) for all r , z ∈{2, 3, 4,…}, that is, \(z^{2}g \left (\frac {1}{z}\right ) =r^{2}g \left (\frac {1}{r}\right )\) for all r , z . Thus, there exists a constant \(\gamma _{0}\in \mathbb {R}\) such that \(z^{2}g\left (\frac {1}{z}\right ) =-\gamma _{0}\) , leading to \(g\left (\frac {1}{z}\right ) =-\frac {\gamma _{0}}{z^{2}}\) for all z ∈{2, 3, 4,…}. By substituting into the definition of \(h\left (\frac {i}{z}\right )\) and letting \(h(1) =\beta _{0}\in \mathbb {R}\) it follows that \(h\left (\frac {i}{z}\right ) =\beta _{0}\frac {i}{z}+\frac {\gamma _{0}}{2} \frac {i}{z} \frac {(z-i)}{z}\) . Note that we have derived the specification of h (.) under the assumption that z = n ≥ 2, then replacing z with n we obtain

Recall that \(\frac {i}{n}\) by construction could be any rational number in (0, 1], with h (0) = 0 already set in Lemma 1. Given that the set of rational numbers is dense in (0, 1] and that h (.) is continuous in that interval the result could be extended to all real numbers in [0, 1], with h (0) = 0. Recalling that \(\frac {\bar {N}_{i}}{N} =\frac {i}{n}\) we can then write more generally

Consider the weighting function \(\left [ h\left (\frac {\bar {N}_{i}}{N}\right ) - h\left (\frac {\bar {N}_{i-1}}{N}\right )\right ]\) from Lemma 1, it can then be specified as:

By substituting into the specification of \(UP(\mathcal {A};\zeta )\) in Lemma 1, one obtains the results presented in this lemma.

Recall that we have derived the result under the assumption that for ζ ∈ [0, 1) we have z = n ≥ 2 and note that the function h (.) does not depend on ζ . In order to extend the result to all cases where n ≥ z ≥ 2 it needs to be checked that the obtained functional form for h (.) allows to satisfy INV-T also when z < n . Note that, as in Eq.  7 , the application of the transfers in INV-T when n > z ≥ 2 requires that the following condition

has to be satisfied for all i , j ∈{1, 2,…, z − 1}, for n > z ≥ 2, for ε > 0. That is, after substituting for the derived specification of \(h\left (\frac {\bar {N}_{i}}{N}\right ) - h\left (\frac {\bar {N}_{i-1}}{N}\right )\) , it should be verified that

Note that \(\left [h\!\left (\frac {\bar {N}_{i}}{N}\right ) - h\!\left (\frac {\bar {N}_{i-1}}{N}\right )\right ] - \left [h\left (\frac {\bar {N}_{i+1}}{N}\right ) - h\!\left (\frac {\bar {N}_{i}}{N}\right ) \right ]\) equals \(\beta _{0} \frac {N_{i}}{N} + \frac {\gamma _{0}}{2} \frac {N_{i}}{N} \!\left (\frac {(N-\bar {N}_{i})-\bar {N}_{i-1}}{N}\right )\! -\) \(\beta _{0} \frac {N_{i+1}}{N} - \frac {\gamma _{0}}{2} \frac {N_{i+1}}{N} \left (\frac {(N-\bar {N}_{i+1})-\bar {N}_{i}}{N}\right )\) , and recall that according to INV-T N i = N j = N i + 1 = N j + 1 it then follows that

This is similarly the case if we consider the neighborhood with index j . As a result INV-T holds also for n > z ≥ 2.

To complete the exposition we consider the case where n > z = 1. In this case INV-T cannot be applied, however we have already derived the required specifications for function h (.) from the previous steps of the proof. □

Let \(\mathcal {A}\in {\Omega }\) , ζ ∈ [0, 1), U P (.; ζ ) satisfies AGG, INV-S, INV-T, INV-PL, MON, TRAN and NOR if and only if there exist β , γ ≥ 0 such that:

with \(\bar {N}_{0}:=0\) , if z ≥ 1, otherwise \(UP(\mathcal {A};\zeta )=0\) .

We consider the result from Lemma 2 and investigate the implications on the specification of U P (.; ζ ) generated by further imposing INV-PL, MON, TRAN and NOR. We leave to the reader to check that the obtained specification of U P (.; ζ ) satisfies all axioms, here we focus on the “only if” part of the lemma. Recall that, if z ≥ 1, then according to Lemma 2 it is possible to write

We first consider INV-PL(i). By applying the scale component λ > 0 one obtains that from \(\mathcal {A}\) to \(\mathcal {A}^{\prime }\) the values \(\left (\frac {P}{N}, \frac {\bar {P}_{z}}{\bar {N}_{z}}, \frac {P_{i}}{N_{i}}, \zeta \right )\) are scaled to \(\left (\lambda \frac {P}{N}, \lambda \frac {\bar {P}_{z}}{\bar {N}_{z}}, \lambda \frac {P_{i}}{N_{i}}, \lambda \zeta \right ) \) , it then follows that \(UP(\mathcal {A};\zeta )=UP(\mathcal {A}^{\prime }; \lambda \zeta )\) if and only if \(A\left (\frac {P}{N}, \frac {\bar {P}_{z}}{\bar {N}_{z}}\right ) = \lambda A\left (\lambda \frac {P}{N}, \lambda \frac {\bar {P}_{z}}{\bar {N}_{z}}\right ) \geq 0\) .

We take into account two cases, first when ζ = 0 and then when ζ ∈ (0, 1).

Case 1: ζ = 0. In this case holds only INV-PL(i). If ζ = 0 then \(\frac {P}{N}=\frac {\bar {P}_{z}}{\bar {N}_{z}}\) . By applying INV-PL(i) it then follows that \(A \left (\frac {P}{N}, \frac {P}{N}\right ) = \lambda A\left (\lambda \frac {P}{N}, \lambda \frac {P}{N}\right )\) for λ > 0. Let \(\lambda \frac {P}{N}=1\) , we obtain \(A \left (\frac {P}{N}, \frac {P}{N}\right ) = \frac {A(1,1)}{\frac {P}{N}}\) , letting A (1, 1) := K ≥ 0, then \(A\left (\frac {P}{N}, \frac {P}{N}\right ) = \frac {K}{\frac {P}{N}}\) .

Case 2: ζ ∈ (0, 1]. In this case \(\frac {P}{N} \leq \zeta \leq \frac {\bar {P}_{z}}{\bar {N}_{z}} \leq 1\) . INV-PL(i) holds if and only if \(A\left (\frac {P}{N}, \frac {\bar {P}_{z}}{\bar {N}_{z}}\right ) = \lambda A\left (\lambda \frac {P}{N}, \lambda \frac {\bar {P}_{z}}{\bar {N}_{z}}\right ) \geq 0\) for λ > 0. Moreover, according to INV-PL(ii) one obtains \(A\left (\frac {P}{N}, \frac {\bar {P}_{z}}{\bar {N}_{z}}\right ) = A\left (\frac {P}{N}, \frac {\bar {P}_{z}}{\bar {N}_{z}} + \theta \right )\) where \(\frac {P}{N}<\zeta \leq \frac {\bar {P}_{z}}{\bar {N}_{z}}\) . By INV-PL(ii) it follows that there exists a continuous function H (.) such that \(A\left (\frac {P}{N}, \frac {\bar {P}_{z}}{\bar {N}_{z}}\right ) := H\left (\frac {P}{N}\right )\) whenever \(\frac {P}{N} < \zeta \leq \frac {\bar {P}_{z}}{\bar {N}_{z}}\) . Note that \(\frac {P}{N} = \frac {\bar {P}_{z}}{\bar {N}_{z}} \frac {\bar {N}_{z}}{N} + \left (1-\frac {\bar {N}_{z}}{N}\right ) \zeta ^{\prime }\) for \(\zeta ^{\prime } < \zeta \) , where \(\zeta ^{\prime }\) denotes the average poverty incidence of the neighborhood with incidence below ζ . By letting \(\bar {N}_{z} \rightarrow 0\) and \({\zeta }^{\prime } \rightarrow {\zeta }\) one obtains the case where \(\frac {P}{N} \rightarrow \zeta \) . We then have that \(A\left (\frac {P}{N}, \frac {\bar {P}_{z}}{\bar {N}_{z}}\right ) = H\left (\frac {P}{N}\right )\) for \(\frac {P}{N} < \frac {\bar {P}_{z}}{\bar {N}_{z}}\) . Thus, by INV-PL(i) we have \(\lambda A \left (\lambda \frac {P}{N}, \lambda \frac {\bar {P}_{z}}{\bar {N}_{z}}\right ) = \lambda H \left (\lambda \frac {P}{N} \right ) = H\left (\frac {P}{N}\right ) = A\left (\frac {P}{N}, \frac {\bar {P}_{z}}{\bar {N}_{z}}\right )\) for \(\frac {P}{N}<\frac {\bar {P}_{z}}{\bar {N}_{z}}\) and for λ > 0 such that \(\lambda \frac {\bar {P}_{z}}{\bar {N}_{z}}\leq 1\) . Suppose that there exists \(\bar {c}\) such that \(\lambda \frac {P}{N}=\bar {c}\) , then \(\lambda H\left (\lambda \frac {P}{N} \right ) = H\left (\frac {P}{N}\right )\) implies that \(\frac {\bar {c}H \left (\bar {c}\right )}{\frac {P}{N}} = H\left (\frac {P}{N}\right )\) . By letting \(\bar {c} H (\bar {c}) := K\geq 0\) one obtains that \(A\left (\frac {P}{N}, \frac {\bar {P}_{z}}{\bar {N}_{z}}\right ) = H\left (\frac {P}{N}\right ) = \frac {K}{\frac {P}{N}}\) for \(\frac {P}{N} < \frac {\bar {P}_{z}}{\bar {N}_{z}}\) .

Thus, we have that both

for \(\frac {P}{N} < \frac {\bar {P}_{z}}{\bar {N}_{z}} \leq 1\) and for \(\frac {P}{N} = \frac {\bar {P}_{z}}{\bar {N}_{z}} \leq 1\) that identify all possible ranges of values of the arguments of A (.).

By applying the result to the specification in Lemma 2, and letting β := β 0 K and γ := γ 0 K /2 one obtains

We now investigate the effects of MON and TRAN. According to MON considering that \(UP(\mathcal {A}^{\prime }; \zeta ) = {\sum }_{i=1}^{z} \left (\frac {\nu P_{i}}{\nu P} - \zeta \frac {N_{i}}{\nu P} \right ) \cdot \left [\beta + \gamma \left (\frac {(N-\bar {N}_{i}) - \bar {N}_{i-1}}{N}\right )\right ]\) for ν > 1, it should hold \(UP(\mathcal {A}^{\prime }; \zeta ) - UP(\mathcal {A}; \zeta )\geq 0\) , this requires that

for all ν > 1, all ζ ∈ [0, 1), all \(\mathcal {A}\in {\Omega }\) . Rearranging the condition, it implies that

for all ν > 1, all ζ ∈ [0, 1), all \(\mathcal {A}\in {\Omega }\) .

This is the case if and only if \({\sum }_{i=1}^{z} \frac {N_{i}}{N} \cdot \left [\beta +\gamma \left (\frac {(N-\bar {N}_{i})-\bar {N}_{i-1}}{N}\right )\right ] \geq 0\) for all \(\mathcal {A}\in {\Omega }\) . This condition depends on the value of z ≥ 1, and in particular, because of the construction of the weighting function w i (.) that satisfies INV-S, the condition depends only on \(\frac {\bar {N}_{z}}{N}\) . In fact, in this case, because of INV-S, without loss of generality, one can consider distributions with two neighborhoods and z = 1. In this case \(N_{1} = \bar {N}_{1} = \bar {N}_{z}\) and recall that \(\bar {N}_{0}=0\) . After substituting, one obtains the condition

for all \(\frac {\bar {N}_{z}}{N}\in (0,1]\) . Letting \(\frac {\bar {N}_{z}}{N} =1\) , that is if z = n , it follows that a necessary condition for MON to hold is β ≥ 0. Moreover, letting \(\frac {\bar {N}_{z}}{N}\rightarrow 0\) , the additional derived necessary condition is β + γ ≥ 0, because otherwise, if γ < − β for sufficiently small values of \( \frac {\bar {N}_{z}}{N}\) is possible to violate the condition in Eq.  10 . Both necessary conditions β ≥ 0 and β + γ ≥ 0 turn out to be sufficient for Eq.  10 to hold for all \(\frac {\bar {N}_{z}}{N}\in (0,1]\) .

We consider now the restrictions required by axiom TRAN. First we consider the case where, because of the transfer, the poverty incidence in neighborhood j does not fall below ζ , that is \(P_{j}^{\mathcal {A}^{\prime }}/{N}_{j}^{\mathcal {A}^{\prime }}\geq \zeta \) .

Recall moreover, that according to TRAN the considered transfer does not affect the ranking of the neighborhoods. Consider Eq.  9 and note that according to TRAN, only P i and P j are modified by the transfer, it should then be verified that

for j > i , with j ≤ z , and ε > 0. Thus

with \(\bar {N}_{j} - \bar {N}_{i}>0\) and \(\bar {N}_{j-1} - \bar {N}_{i-1}>0\) , which implies

as a result should hold γ ≥ 0.

Note that the condition should hold for all i < j ≤ z with z ≤ 2 and therefore letting z = n , should hold for all i < j ≤ n .

We consider now the case where \({P}_{j}^{\mathcal {A}^{\prime }}/{N}_{j}^{\mathcal {A}^{\prime }}<\zeta \) , with j = z , by applying TRAN, it follows that

where \(0\leq \varepsilon ^{\prime } \leq \varepsilon \) with \(\varepsilon ^{\prime } = {\min \limits } \{\varepsilon ,P_{j}-\zeta N_{j} \}\) . The condition can then be simplified as

Recalling that \(\frac {(N - \bar {N}_{i}) - \bar {N}_{i-1}}{N} > \frac {(N-\bar {N}_{j}) - \bar {N}_{j-1}}{N}\) for j > i , that \(\varepsilon ^{\prime } \leq \varepsilon \) , and that β ≥ 0, then γ ≥ 0 is sufficient to verify that \(UP(\mathcal {A}^{\prime };\zeta ) \geq UP(\mathcal {A};\zeta )\) .

Thus, γ ≥ 0 is necessary and sufficient for TRAN to hold. By combining with the parametric restrictions derived by applying MON one obtains β ≥ 0, and γ ≥ 0.

All derivations illustrated so far consider the case where z ≥ 1. Note that for \(\mathcal {A}\in {\Omega }\) and given ζ ∈ (0, 1) it is possible to take into account also configurations where \(\frac {P_{i}}{N_{i}}<\zeta \) for all neighborhoods i . In this case the value of the index is derived by considering axiom NOR. For all these configurations the value of the index coincides with the infimum of the index taken over all the other possible configurations in \(\mathcal {A}\) where z ≥ 1. Consider the obtained derivation of UP for z ≥ 1, where

with β , γ ≥ 0, note that the first term in the summation \(\frac {P_{i} - \zeta N_{i}}{P}\geq 0\) is non-increasing in i , and that the term \(\frac {(N-\bar {N}_{i}) - \bar {N}_{i-1}}{N}\) is also non-increasing in i . It follows that, given that β , γ ≥ 0 also \(\beta +\gamma \left (\frac {(N-\bar {N}_{i}) - \bar {N}_{i-1}}{N}\right )\) is non-increasing in i . The summation in Eq.  11 is then minimized, for each z ≥ 1 if the terms \(\frac {P_{i} - \zeta N_{i}}{P}\) are equalized. Given that \(\frac {P_{i}-\zeta N_{i}}{P}\geq 0\) then the minimum for each z ≥ 1 is obtained for P i − ζ N i = 0 for all i ≤ z . It follows that in this case U P = 0.

Thus, by NOR the value of the index is 0 when \(\frac {P_{i}}{N_{i}}<\zeta \) for all i .

To complete the proof we rearrange the specification of U P (.; ζ ) in Eq.  11 . We can rewrite:

in fact \({\sum }_{i=1}^{z} N_{i} \left (\bar {N}_{z} - \bar {N}_{i} - \bar {N}_{i-1}\right ) = {\sum }_{i=1}^{z} N_{i} \bar {N}_{z} - {\sum }_{i=1}^{z} N_{i} (\bar {N}_{i} + \bar {N}_{i-1}) = (\bar {N}_{z})^{2} - {\sum }_{i=1}^{z} (\bar {N}_{i} - \bar {N}_{i-1}) (\bar {N}_{i} + \bar {N}_{i-1})\) where \({\sum }_{i=1}^{z} (\bar {N}_{i} - \bar {N}_{i-1}) (\bar {N}_{i} + \bar {N}_{i-1}) = {\sum }_{i=1}^{z} (\bar {N}_{i})^{2} - (\bar {N}_{i-1})^{2} = (\bar {N}_{z})^{2}\) . It then follows that the term \({\sum }_{i=1}^{z} \left (\frac {P_{i}-\zeta N_{i}}{P}\right ) \cdot \left (\frac {(\bar {N}_{z} - \bar {N}_{i}) - \bar {N}_{i-1}}{\bar {N}_{z}} \right )\) simplifies to \({\sum }_{i=1}^{z} \frac {P_{i}}{P} \cdot \left (\frac {(\bar {N}_{z} - \bar {N}_{i}) - \bar {N}_{i-1}}{\bar {N}_{z}}\right )\) . Thus, we obtain:

In order to complete the proof of the Theorem one has to link the result in Lemma 3 with the Gini index formula \(G(\mathcal {A};\zeta )\) . Next lemma provides this link.

Let \(\mathcal {A}\in {\Omega }\) , ζ ∈ [0, 1), and z ≥ 1, then

The Gini index G (.; ζ ) can be written as follows:

We now develop the first term appearing in squared brackets in Eq.  12 , denoted \(\max \limits \) in short-hand notation, to show that it can written as a function of the rank weights. First, let develop the double summations term as follows:

After subtracting \({\sum }_{i=1}^{z} \frac {N_{i}}{\bar {N}_{z}} \frac {P_{i}}{N_{i}}\) we obtain

As a result \(\bar {P}_{z}G(\mathcal {A};\zeta )={\sum }_{i=1}^{z} P_{i} \left (\frac {\bar {N}_{z} - \bar {N}_{i}}{\bar {N}_{z}} - \frac {\bar {N}_{i-1}}{\bar {N}_{z}}\right )\) , after dividing both sides by P we obtain the result in the lemma. □

By substituting from Lemma 4 into the specification of Lemma 3 in Eq.  8 for z ≥ 1, we obtain the specification of U P (.; ζ ) in the Theorem for z ≥ 1 :

To complete the proof we show that all axioms are independent , meaning that it is possible to derive alternative functional forms for U P (.; ζ ) by dropping one of the axioms and considering all the others.

Drop NOR: consider Eq. 3 for z ≥ 1 and set U P (.; ζ ) = k < 0 in all other cases.

Drop TRAN: consider Eq. 3 with γ = − 1 and β = 0 for z ≥ 1, and set \(UP(.;\zeta )=-\sup \{\frac {{\bar {N}_{z}}}{N}\frac {\bar {P}_{z}}{P}\cdot G(\mathcal {A};\zeta )+\frac {N{-\bar {N}_{z}}}{N}{\frac {\bar {P}_{z}-\zeta {\bar {N}_{z}}}{P}}:\mathcal {A}\in {\Omega } \) with z ≥ 1} in all other cases.

Drop MON: consider Eq. 3 with γ = 0 and β = − 1 for z ≥ 1, and set U P (.; ζ ) = − 1 in all other cases.

Drop INV-PL: consider Eq. 3 multiplied by P / N for z ≥ 1, and set U P (.; ζ ) = 0 in all other cases.

Drop INV-T: consider

with \({\bar {N}_{0}:=0}\) for z ≥ 1, and set U P (.; ζ ) = 0 in all other cases.

Drop INV-S: consider

for z ≥ 1, and set U P (.; ζ ) = 0 in all other cases.

Drop AGG: consider

for z ≥ 1, and set U P (.; ζ ) = 0 in all other cases. QED.

1.2 A.2 Proof of Corollary 4

Let \(p_{i}=\frac {P_{i}}{N_{i}}\) and \(s_{i}=\frac {N_{i}}{N}\) denote the poverty incidence and population share of neighborhood i , respectively.

Let \(\mathbf {p} = \left (p_{1},\ldots ,p_{n}\right )^{T}\) be the n × 1 vector of neighborhood poverty rates sorted in decreasing order and \(\mathbf {s} = \left (s_{1}, \ldots , s_{n}\right )^{T}\) be the n × 1 vector of the corresponding population shares. A urban poverty configuration is fully identified by the pair ( s , p ), and is used interchangeably. Let 1 n being the n × 1 vector with each element equal to 1, P is the n × n skew-symmetric matrix:

where \(\bar {p}\) is the overall poverty rate in the city. The elements of P are the n 2 relative pairwise differences between the neighborhood poverty incidences as ordered in p . Let \(\mathbf {S}=\mathit {diag}\left \{\mathbf {s}\right \}\) be the n × n diagonal matrix with diagonal elements equal to the population shares in s , and G be a n × n G -matrix (a skew-symmetric matrix whose diagonal elements are equal to 0, with upper diagonal elements equal to − 1 and lower diagonal elements equal to 1) (Silber 1989 ). The Gini index of urban poverty is expressed in matrix form:

where the matrix \(\tilde {\mathbf {G}}=\mathbf {S}\mathbf {G}\mathbf {S}\) is the weighting G -matrix, a generalization of the G -matrix introduced by Mussini and Grossi ( 2015 ) to add weights in the calculation of the Gini index. The change in urban poverty from t to \(t^{\prime }\) is measured by the difference between the Gini index in \(t^{\prime }\) and the Gini index in t :

Equation  18 can be broken down into three components by applying the matrix approach used in Mussini and Grossi ( 2015 ) and in Mussini ( 2017 ). The three components separate the contributions of changes in neighborhood population shares, ranking of neighborhoods and disparities between neighborhood poverty rates. Let \(\mathbf {s}_{t|t^{\prime }}\) stand for the n × 1 vector of the t population shares arranged by the decreasing order of the corresponding \(t^{\prime }\) poverty rates. Let \(\lambda = \bar {p}_{t^{\prime }}/\bar {p}_{t^{\prime }|t}\) be the ratio of the actual \(t^{\prime }\) overall poverty rate to the fictitious \(t^{\prime }\) overall poverty rate which is the weighted average of \(t^{\prime }\) poverty rates where the weights are the corresponding population shares in t . After defining \(\mathbf {S}_{t|t^{\prime }} = \mathit {diag} \left \{\mathbf {s}_{t|t^{\prime }}\right \}\) , the Gini index of \(t^{\prime }\) neighborhood poverty rates calculated by using the t neighborhood population shares is

where \(\tilde {\mathbf {G}}_{t|t^{\prime }} = \mathbf {S}_{t|t^{\prime }}\mathbf {G}\mathbf {S}_{t|t^{\prime }}\) is the weighting G -matrix obtained by using the neighborhood population shares in t instead of those in \(t^{\prime }\) . In Eq.  22 , the multiplication of \({\mathbf {P}}_{t^{\prime }}^{T}\) by λ ensures that the pairwise differences between the \(t^{\prime }\) neighborhood poverty incidences are divided by \(\bar {p}_{t^{\prime }|t}\) instead of \(\bar {p}_{t^{\prime }}\) . By adding and subtracting \(G\left (\mathbf {s}_{t|t^{\prime }},\mathbf {p}_{t^{\prime }}\right )\) in Eq.  21 , the contribution to Δ U P due to changes in neighborhood population shares can be separated from that attributable to changes in disparities between neighborhood poverty rates:

where \(\mathbf {W} = \tilde {\mathbf {G}}_{t^{\prime }} - \lambda \tilde {\mathbf {G}}_{t|t^{\prime }}\) . Component W measures the effect of changes in neighborhood population shares. A positive value of W indicates that the weights assigned to more unequal pairs of neighborhoods are larger in \(t^{\prime }\) than in t , increasing urban poverty from t to \(t^{\prime }\) . A negative value of W indicates that the weights assigned to more unequal pairs of neighborhoods are smaller in \(t^{\prime }\) than in t , reducing urban poverty.

The difference enclosed within square brackets on the right-hand side of Eq.  23 can be additively split into two components: one component measuring the re-ranking of neighborhoods, a second component measuring the change in disparities between neighborhood poverty rates. Let \(\mathbf {p}_{t^{\prime }|t}\) be the n × 1 vector of \(t^{\prime }\) neighborhood poverty rates sorted in decreasing order of the respective t neighborhood poverty rates, and B be the n × n permutation matrix re-arranging the elements of \(\mathbf {p}_{t^{\prime }}\) to obtain \(\mathbf {p}_{t^{\prime }|t}\) , that is \(\mathbf {p}_{t^{\prime }|t} = \mathbf {B}\mathbf {p}_{t^{\prime }}\) . Matrix \(\mathbf {P}_{t^{\prime }|t} = \left (1/\bar {p}_{t^{\prime }|t}\right ) \left (\mathbf {1}_{n}\mathbf {p}^{T}_{t^{\prime }|t}-\mathbf {p}_{t^{\prime }|t}\mathbf {1}^{T}_{n}\right )\) contains the n 2 relative pairwise differences between the neighborhood poverty rates as arranged in \(\mathbf {p}_{t^{\prime }|t}\) . The concentration index of the \(t^{\prime }\) neighborhood poverty rates sorted by the t neighborhood poverty rates, calculated by using the t population shares, is defined as follows:

By using permutation matrix B , the concentration index \(C\left (\mathbf {s}_{t},\mathbf {p}_{t^{\prime }|t}\right )\) can be re-written as a function of \(\mathbf {P}_{t^{\prime }}\) instead of \(\mathbf {P}_{t^{\prime }|t}\) . Since \(\mathbf {P}_{t^{\prime }|t}=\mathbf {B}\lambda \mathbf {P}_{t^{\prime }}\mathbf {B}^{T}\) , the concentration index \(C\left (\mathbf {s}_{t}, \mathbf {p}_{t^{\prime }|t}\right )\) expressed as a function of \(\mathbf {P}_{t^{\prime }}\) becomes

By adding \(C\left (\mathbf {s}_{t},\mathbf {p}_{t^{\prime }|t}\right )\) as expressed in Eq.  24 and subtracting it as expressed in Eq.  25 to the difference enclosed within square brackets on the right-hand side of Eq.  23 , we obtain

where \(\mathbf {R}=\tilde {\mathbf {G}}_{t|t^{\prime }}-\mathbf {B}^{T}\tilde {\mathbf {G}}_{t}\mathbf {B}\) and \(\mathbf {D}=\mathbf {P}_{t^{\prime }|t}-\mathbf {P}_{t}\) . Component R measures the effect of re-ranking of neighborhoods from t to \(t^{\prime }\) and its contribution to the change in urban poverty is always non-negative. The nonzero elements of R indicate the pairs of neighborhoods which have re-ranked from t to \(t^{\prime }\) .

Component D measures the effect of disproportionate changes in neighborhood poverty rates. The generic ( i , j )-th element of D compares the relative difference between the t poverty rates of the neighborhoods in positions j and i in p t with the relative difference between the \(t^{\prime }\) poverty rates of the same two neighborhoods in \(\mathbf {p}_{t^{\prime }|t}\) . A positive (negative) value of D indicates that relative disparities in neighborhood poverty rates have increased (decreased) from t to \(t^{\prime }\) , increasing (reducing) urban poverty. If all neighborhood poverty rates have changed in the same proportion from t to \(t^{\prime }\) , then D = 0.

Given Eqs.  23 and  26 , a three-term decomposition of Δ U P is obtained:

Since component D would not reveal changes in neighborhood poverty rates if all neighborhood poverty rates changed in the same proportion, this component is split into two further terms: one measuring the change in the city poverty rate, the second measuring the changes in disparities between neighborhood poverty rates by assuming that the city poverty rate remains the same from t to \(t^{\prime }\) . Let c stand for the change in the city poverty rate by assuming that neighborhood population shares are unchanged from t to \(t^{\prime }\) :

Let \({\mathbf {p}}_{t^{\prime }|t}^{c} = \mathbf {p}_{t} + c\mathbf {p}_{t}\) be the vector of neighborhood poverty rates we would observe in \(t^{\prime }\) if every neighborhood poverty rate changed by proportion c . This implies that \({\bar {p}}_{t^{\prime }|t}^{c} = \bar {p}_{t^{\prime }|t}\) . Vector \(\mathbf {p}_{t^{\prime }|t}\) can be expressed as

where the elements of vector \({\mathbf {p}}_{t^{\prime }|t}^{\delta }\) are the element-by-element differences between vectors \(\mathbf {p}_{t^{\prime }|t}\) and \({\mathbf {p}}_{t^{\prime }|t}^{c}\) . Since \({\mathbf {p}}_{t^{\prime }|t}^{c}=\mathbf {p}_{t}+c\mathbf {p}_{t}\) , \(\mathbf {p}_{t^{\prime }|t}\) can be re-written as

where the elements of \(\mathbf {p}^{e}_{t^{\prime }|t}\) account for disproportionate changes in neighborhood poverty rates from t to \(t^{\prime }\) , as \(\mathbf {p}^{e}_{t^{\prime }|t}\) would equal p t if there were no disproportionate changes in neighborhood poverty rates. Given equations above, matrix \(\mathbf {P}_{t^{\prime }|t}\) can be written as

Since matrix D in Eq.  27 is obtained by subtracting P t from \(\mathbf {P}_{t^{\prime }|t}\) , D can be re-written as

By replacing D in Eq.  27 with its expression in Eq.  31 , the decomposition of the change in urban poverty becomes

1.3 A.3 Proof of Corollary 5

Building on the Rey and Smith ( 2013 ) spatial decomposition of the Gini index and the spatial decomposition of the change in inequality in Mussini ( 2020 ), Δ U P , W , R and E can be broken down into spatial components. Let N t be the n × n spatial weights matrix having its ( i , j )-th entry equal to 1 if and only if the ( i , j )-th element of P t is the relative difference between the poverty rates of two neighborhoods that are spatially close, otherwise the ( i , j )-th element of N t is 0. Using the Hadamard product, Footnote 1 the relative pairwise differences between the poverty rates of neighborhoods that are spatially close can be selected from P t :

For each pair of neighborhoods, the relative difference between their \(t^{\prime }\) poverty rates in \(\mathbf {P}^{e}_{t^{\prime }|t}\) has the same position as the relative difference between their t poverty rates in P t . Thus, N t also selects the relative pairwise differences between neighbors from \(\mathbf {P}^{e}_{t^{\prime }|t}\) :

Since \(\mathbf {E} = \mathbf {P}^{e}_{t^{\prime }|t}-\mathbf {P}_{t}\) , the Hadamard product between N t and E is a matrix with nonzero elements equal to the elements of E pertaining to neighborhoods that are spatially close:

Let \(\mathbf {N}_{t^{\prime }}\) be the n × n spatial weights matrix having its ( i , j )-th entry equal to 1 if and only if the ( i , j )-th element of \(\mathbf {P}_{t^{\prime }}\) is the relative difference between the poverty rates of two neighborhoods that are spatially close, otherwise the ( i , j )-th element of \(\mathbf {N}_{t^{\prime }}\) is 0. The Hadamard product of \(\mathbf {N}_{t^{\prime }}\) and \(\mathbf {P}_{t^{\prime }}\) is the matrix

The nonzero elements of \(\mathbf {P}_{N,t^{\prime }}\) are the relative pairwise differences between the \(t^{\prime }\) poverty rates of neighborhoods that are in spatial proximity.

The decomposition of the change in the neighborhood component of urban poverty is obtained by replacing \(\mathbf {P}_{t^{\prime }}\) and E in Eq.  32 with \(\mathbf {P}_{N,t^{\prime }}\) and E N , respectively:

Let J n be the matrix with diagonal elements equal to 0 and extra-diagonal elements equal to 1, the matrix with nonzero elements equal to the relative pairwise differences between the \(t^{\prime }\) poverty rates of neighborhoods that are not in spatial proximity is

The matrix selecting the elements of E pertaining to the pairs of neighborhoods that are not spatially close is

The decomposition of the change in the non-neighborhood component of urban poverty is obtained by replacing \(\mathbf {P}_{t^{\prime }}\) and E in Eq.  32 with \(\mathbf {P}_{nN,t^{\prime }}\) and E n N , respectively:

Given Eqs.  40 and  37 , the spatial decomposition of the change in urban poverty is

Appendix B: Additional results

Urban poverty calculated by using balanced longitudinal data and raw data on census tracts in American MSAs, from 1980 to 2014

Urban poverty and poverty incidence in the city, from 1980 to 2014

Urban poverty estimates based on poverty thresholds at 75%, 100% and 200% of the official poverty line, years 1980 and 2014

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Andreoli, F., Mussini, M., Prete, V. et al. Urban poverty: Measurement theory and evidence from American cities. J Econ Inequal 19 , 599–642 (2021). https://doi.org/10.1007/s10888-020-09475-2

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• Published: 30 May 2024

Escaping poverty: changing characteristics of China’s rural poverty reduction policy and future trends

• Yunhui Wang   ORCID: orcid.org/0000-0001-8824-6109 1   na1 ,
• Yihua Chen   ORCID: orcid.org/0000-0001-9089-4172 2 , 3   na1 &
• Zhiying Li   ORCID: orcid.org/0000-0002-2219-5473 4  

Humanities and Social Sciences Communications volume  11 , Article number:  694 ( 2024 ) Cite this article

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• Development studies
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Eliminating poverty is a shared aspiration of people worldwide. This article analyzes 762 rural poverty-related texts promulgated and implemented by the Chinese Government since 1984 using content analysis based on a three-dimensional framework encompassing the time of policy issuance, policy goals, and types of policy instruments. The study outlines the overall landscape and evolutionary context of the policy system. The results show that, during absolute poverty governance, China’s rural poverty governance can be broadly divided into three stages: regional development-oriented poverty alleviation, comprehensive poverty alleviation, and targeted poverty alleviation. Based on the production-oriented welfare model, economic development became the primary goal of poverty alleviation policies, while insufficient attention was given to service support and capacity-building goals. The alleviation of poverty mainly relied on the propulsive force generated by supply-side policy instruments led by the Government and the external driving force generated by environmental policy instruments, with a significant deficiency in the propulsive force produced by demand-side policy instruments. Entering the phase of relative poverty governance, optimizing poverty governance policy instruments requires breaking free from path dependence, following the evolutionary pattern of poverty governance. It involves ensuring that policy instruments support economic development while emphasizing addressing service support and capacity-building goals. It is crucial to increase the frequency of using demand-side policy instruments, stimulate their pulling force on poverty alleviation, and achieve a trend of evolutionary innovation and the collaborative governance of policy instruments.

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Problem statement.

The aspiration to eliminate poverty has been a longstanding societal ideal since ancient times. It represents an intrinsic right for people across the globe in their pursuit of a fulfilling life. The elimination of hunger and poverty, central targets outlined in the 2030 Agenda for Sustainable Development, also stands as a cornerstone in the development agendas of numerous nations worldwide. Rowntree’s ( 1902 ) early definition of poverty in 1902 classified it as primary and secondary poverty. He argued that a family is in poverty when its total income fails to meet the essential survival needs of its members. This concept is considered the foundation of research into absolute poverty. Essentially, absolute poverty is a physiological concept that explores the link between nutrition and survival (Lister, 2021 ). As economic and social development advances, Peter Townsend contends that absolute poverty overlooks the social and cultural aspects of ‘human need,’ both ‘need’ and ‘poverty’ are products of social construction. “Both ‘need’ and ‘poverty’ are social constructs.” Townsend ( 1979 ) introduced the concept of relative poverty, which signifies exclusion from typical social lifestyles and activities. However, Sen ( 1982 ) proposed in “Poverty and Famine” that the core of poverty lies in the lack of viability rather than mere low income. Alongside research, countries generally categorize poverty into absolute and relative forms. Research shows that most of the world’s impoverished population resides in rural areas (Poverty and Initiative, 2018 ). The capacity of rural people to elevate themselves from poverty holds profound implications for their daily sustenance and global food security. The United Nations and countries worldwide are working to eradicate rural poverty by promoting inclusive growth and sustainable livelihoods.

As an agricultural powerhouse with a massive rural populace, China’s countryside constituted over 80% of its total population in the nascent years following the establishment of the People’s Republic. The rapid economic growth brought about by the reform and opening-up has also exacerbated the development gap between urban and rural areas. The natural and economic factors that have long impeded rural development have become more pronounced, with the hollowing out of the countryside, the aging of the population, the abandonment of infrastructure, environmental degradation, and persistent poverty drawing the Government’s attention. In 1978, 250 million rural residents living under the poverty threshold of 100 RMB annual per capita income represented a 30.7% rural poverty rate Footnote 1 (see Fig. 1 ). Alleviating rural poverty thus emerged as an urgent priority fettering China’s socioeconomic advancement. Since the 1980s, the Chinese Government has embarked on large-scale anti-poverty initiatives in the countryside, promulgating numerous policies that achieved remarkable success in eradicating absolute poverty. From 1985 to 2000, the rural absolute impoverished population rapidly declined from 125 million to 32.09 million, with poverty rates plummeting dramatically from 14.8% to 3.5%. Upon entering the 21st century, both the quantity and incidence of rural absolute poverty persisted in substantial decreases. In 2015, the Central Government further proposed targeted poverty alleviation targets. By 2020, China had accomplished its poverty alleviation targets, eliminating destitution under extant standards.

The rural poor population and poverty incidence rate for 1985–2000 were calculated using the 1978 poverty standard per capita net income of 100 yuan; the rural poor population and poverty incidence rate for 2000–2020 were calculated using the 2010 poverty standard per capita net income of 2300 yuan—data from China Statistical Yearbook.

Governance refers to the process by which a variety of governmental and non-governmental institutions and actors work together to establish conditions for social order and collective action (Stoker, 2012 ). It involves diverse approaches employed by individuals and institutions, both public and private, to manage public affairs. This ongoing process entails cooperative actions, including the implementation of formal institutional arrangements and the agreement on informal arrangements that align with their interests (The Commission on Global Governance, 1995 ). Kooiman and Jentoft ( 2009 ) introduced three essential elements of governance: imagery, instruments, and action. Imagery refers to the rationale behind governance, encompassing vision, judgment, beliefs, and goals, typically grounded in systematic values or knowledge systems. Instruments involve the selection and application of governance methods, serving as intermediaries that connect imagery to action. Action, in turn, represents the practical implementation of these “instruments”. Poverty governance in China constitutes a collaborative effort among the government, market, and society, with a focus on people’s interests, aimed at achieving common prosperity. It encompasses both economic and social dimensions, with the goal of reducing poverty, protecting the rights of the impoverished, and enhancing social equity. In this fight against poverty, which is the largest and most robust in the history of human poverty alleviation, China has taken many original and unique major governance initiatives and accumulated a series of replicable and generalizable experiences in poverty alleviation. However, eliminating absolute poverty does not mean there is no poverty in China, and China is still far from achieving high-quality and high-standard poverty alleviation (Zhou et al., 2020 ). Poverty presents dynamic, multifaceted challenges, including policy-dependent severe behaviors (Wan et al., 2021 ) and the objectivity that relative poverty cannot be entirely eradicated (Hagenaars, 2014 ). With China’s elimination of absolute poverty, the Government’s poverty alleviation focus has shifted from abolishing destitution to alleviating relative hardship (Shen and Li, 2022 ). Given the evolving forms and aims of poverty governance, the period of relative poverty alleviation necessitates continued efforts to prevent regression and enact efficacious policies to mitigate dependence. There is an urgent need to clarify questions about optimal relative poverty governance policies and how they differ from periods of absolute poverty governance. However, current literature exhibits limited systematic investigation into the textual content of absolute rural poverty policies. This study offers an original contribution by analyzing policy texts to reveal changes in China’s poverty reduction policy from the absolute to relative poverty governance periods.

This paper examines the Chinese Government’s rural poverty alleviation policies over time, utilizing content analysis to address two key questions: First, what characterized the Government’s poverty governance model during absolute poverty governance, and what was the operational logic? Second, in the relative poverty governance period, how is pro-poor policy logically related to absolute poverty governance, and what policies should the Government adopt? Answering these questions scientifically can delineate dynamic changes in China’s rural absolute poverty policy instruments, analyze the utility and limitations of existing pro-poor instruments, and inform suggestions to optimize relevant policies moving forward. The research aims to contribute Chinese experiences and insights to the broader cause of international poverty alleviation. Examining the evolution of poverty governance models and policy instruments across periods of absolute and relative poverty has implications for developing effective, context-specific poverty reduction strategies tailored to contemporary implementation environments.

Literature review

Research of the typology of policy instruments.

Policy instruments, sometimes called government or governance instruments, represent the government’s strategies and actions to attain policy targets (Hughes, 2017 ). No universal standard exists for categorizing policy instruments, leading researchers to classify them based on distinct characteristics and targets. Dahl and Lindblom ( 1953 ) have proposed a classification of instruments into regulatory and non-regulatory categories based on their authority attributes; Owen E. Hughes categorizes policy instruments into four distinct groups: government supply, production, subsidies, and regulation, based on the Government’s functions (Hughes, 2017 ); Rothwell and Zegveld categorize policy instruments into three groups: supply, environmental, and demand, considering their intended purposes Howlett and Remash distinguish among voluntary, hybrid, and coercive instruments based on the level of coercion (Howlett et al., 1995 ).

Based on typological analyses and investigations of policy instruments, some scholars have also directed their attention to the factors that influence the choice and utilization of policy instruments to better achieve policy targets in intricate public policy decision-making and implementation contexts. Several studies have emphasized the “fit” of policy instruments, whereby the selection of these instruments is associated with policy targets, the development of state capacity, civil society (Howlett et al., 1995 ), temporal characteristics, field-specific attributes, instrument attributes, and policy strength, all of which impact the effectiveness of policy instrument configurations (Zhang et al., 2022 ). This concept captures the degree of alignment between the selection of policy instruments and specific conditions. In line with this notion, research has conducted empirical analyses of the selection and allocation of policy instruments in specific domains, such as China’s research and development of new energy vehicles (Shao et al., 2021 ), low-carbon city pilot programs (Hong et al., 2021 ), and government attention to the power sector (Cheng and Yang, 2023 ).

Chinese scholars emphasize the role of the Government as a policy solution provider and prefer the “supply-demand-environment” policy instrument classification framework proposed by Rothwell and Zegveld (Rothwell and Zegveld, 1984 ) when conducting policy instrument research and apply it to environmental governance (Liao, 2018 ), energy policy (Li et al., 2023 ; Yang et al., 2021 ), and photovoltaic poverty alleviation (Zhang et al., 2018 ), among other policy area studies.

The selection of policy instruments in poverty alleviation research

In several developing countries, the implementation of measures such as increased financial support, infrastructure development, and enhanced educational levels plays a crucial role in elevating the income of impoverished individuals and stimulating economic growth in disadvantaged regions (Arsani et al., 2020 ; Cross and Neumark, 2021 ; Deepika and Sigi, 2014 ; Mugo and Kilonzo, 2017 ; Page and Pande, 2018 ). This pattern extends to China as well. With the growing focus on policy instrument research, the policy instrument perspective has become increasingly prominent in examining various policy domains (Peters, 2020 ). Nonetheless, the literature concerning inductive analysis utilizing policy instrument typology, grounded in the attributes and characteristics of poverty alleviation, remains exceedingly scarce. Although a substantial portion of research related to poverty alleviation centers on specific policy measures, it remains pertinent.

Promoting industrial development is a paramount strategy in pursuing poverty eradication. As elucidated by Mariara and Kiriti ( 2020 ), the advancement of the industrial sector can bring about more substantial benefits for impoverished communities by facilitating the organization and active participation of rural populations within the industrial framework. It enhances production efficiency and reshapes production dynamics, ultimately culminating in economic development-driven poverty alleviation. Furthermore, Economic development can also be attained through strategic infrastructure development. Zhou et al. ( 2023 ) found that transport infrastructure can significantly enhance economic development, especially public investment in poor areas, and therefore, infrastructure development should be a priority policy option.

Poverty alleviation through education represents an enduring mechanism for sustained poverty reduction. Song ( 2012 ) explored the influence of primary education on China’s labor market, discovering that universal access to primary education yielded a significant reduction in poverty within China, with urban areas particularly benefiting from this effect. Liu et al. ( 2023 ) found that compulsory education more effectively addresses rural poverty than upper-secondary education. The Government should prioritize implementing compulsory education as a long-term policy instrument in rural areas, recognizing its potency in poverty alleviation.

The empowerment of underprivileged individuals can be aptly realized through talent development and expanding employment opportunities. Guo and Wang ( 2021 ) found that rural labor transfer augments the per capita livelihood capital of the remaining population and facilitates the escape from vulnerability and the attainment of stable employment among the impoverished. The significance of government service support for impoverished segments of society should not be underestimated. Yang and Cao ( 2022 ) revealed that augmenting the provision of fundamental public services in rural areas constitutes a crucial strategy for alleviating rural poverty, significantly reducing the incidence of such poverty. Furthermore, Jiang et al. ( 2020 ) uncovered that engaging farmers in underdeveloped and impoverished regions of China in savings and commercial insurance can effectively diminish poverty vulnerability. Deng ( 2019 ) also found that savings and commercial insurance can reduce health expenditures where catastrophic or poverty-inducing levels occur.

The primary approach to poverty alleviation is intricately linked to the formulation and execution of public policies. Government-led initiatives constitute a crucial facet of China’s poverty governance, highlighting the pivotal role of policy instrument selection and allocation. Scholarly investigations have delved into using policy instruments in poverty alleviation, enriching our comprehension of related policies. Nonetheless, research combining policy instruments to scrutinize pro-poor policy evolution remains limited (Zhang et al., 2018 ), with a dearth of comprehensive examinations that draw on policy instrument theory to elucidate pro-poor policy change and optimization recommendations. Consequently, this study commences when the Chinese Government launched large-scale poverty alleviation efforts, focusing on central policy documents closely associated with poverty alleviation between 1984 and 2022. It employs content analysis to conduct text mining of standardized policy documents, dissecting the semantic information conveyed by specific word frequencies and frequencies within the policy texts across various phases. When coupled with coding results, these findings facilitate the categorization and quantitative analysis of policy instruments for poverty alleviation, enabling a comprehensive discussion on their application in poverty governance.

Analytical framework and research methods

Policy text selection.

The sample for this study is primarily obtained from the Peking University-Chinese Laws and Regulations Database. Focus on policy samples regarding poverty alleviation and reduction from 1984 to 2022. First, utilizing the keywords “poverty, poverty reduction, poverty alleviation, help, and special hardship,” examining central laws and regulations, and conducting a full-text search for the timeframe up to November 2, 2022, is necessary. To ensure the comprehensiveness of the policy texts, this study supplemented the selected policies by using the policy repositories on the official websites of the State Council, the State Council’s Bureau of Rural Revitalization, and various government agencies.

Furthermore, this study follows specific policy selection criteria to ensure the representativeness of the selected policy document: first, the government-issued policy texts are heavily linked to poverty alleviation and reduction efforts. To accurately reflect the national Government’s attitudes and actions towards poverty alleviation, the literature must directly outline their measures. The literature’s scope should encompass policy documents from different areas of social development; second, the selected texts mainly include notices, announcements, opinions and methods, decisions, and other policy documents from the central Government and its supervised ministries and commissions. Finally, the study selected 762 policy texts that met its needs.

Policy analysis framework

Policy instruments are one of the most important ways to study and analyze public policies. As the primary means and effective way of government management, policy instruments have an essential impact on the implementation effect of public policies. China’s poverty alleviation policies have been regularly adjusted in response to changing goal circumstances, making the timing of policy implementations a crucial element in tracking the evolution and forecasting future trends of poverty alleviation in the country. The policy target is the core element of public policy, an essential criterion for measuring the degree of response to public problems, and it also determines the means chosen to achieve the target. Hence, this paper examines the trends in China’s anti-poverty policy from three perspectives: policy initiation time, policy targets, and policy instruments.

Time dimension. This paper analyzes the characteristics and influencing factors of China’s poverty alleviation policies in different periods by examining the quantitative trends and evolution of policies over time. Starting from the period of the Chinese Government’s large-scale poverty alleviation efforts, we will examine the development of these policies in a historical context.

Policy goal dimension. In order to sort out China’s anti-poverty policies in a more detailed way, China’s anti-poverty policy targets will be divided into specific categories based on the value of the targets. For a long time, China’s rural poor groups generally have had poor economic conditions, lack of ability, and insufficient support and assistance groups. Given this, this paper divides anti-poverty policy targets into three major categories: economic development category, capacity-building category, and service support category. The economic development category is to improve the infrastructure construction and economic development level of poor areas to drive the poor groups out of poverty and become rich. The service support category provides various services and policy support for developing poor groups, such as employment skills training, policy promotion and interpretation, and information and counseling services for poor groups. Capacity building focuses on the self-development awareness of poor groups and the cultivation and enhancement of their capacities to make up for the shortcomings of development and strengthen the endogenous motivation for poverty alleviation and enrichment.

Policy instruments dimension. Each classification of policy instruments has specific application scenarios, and their combination and comprehensive use aims to maximize effectiveness and synergistic value. However, the policy instrument model Roy Rothwell and Walter Zegveld developed is more comprehensive and operational from a comparative standpoint (Dylander, 1980 ). The analytical framework presents a downgraded view of the complex policy system, focusing on the instruments and measures for operationalizing policy instruments. It highlights the dual effectiveness of intra-dimensional aggregation and inter-dimensional differentiation to aid in identifying each policy instrument’s content and boundaries, thus simplifying the presentation of specific operations. Due to the superiority of this policy model, it has been widely used in policy research in many fields, such as economic development (Eisinger, 1988 ), environmental pollution prevention (Qin and Youhai, 2020 ), and public health care (Yue et al., 2020 ). Concurrently, within the realm of rural poverty governance in China, the backing furnished by both central and local governments for poverty alleviation development, the cultivation of a propitious economic, social, and legal milieu through high-level strategic planning to steer and oversee the trajectory of development in the sphere of poverty alleviation, alongside the emphasis placed on the regulatory functions of central and local governments in shaping poverty alleviation policies in line with market and societal demands to address the genuine requirements of impoverished segments of society, all underscore the pivotal role of government macroeconomic control.

These strategies primarily hinge on the implementation paths meticulously devised by policymakers to attain their designated policy targets. They exhibit a substantial congruence with the internal logic and external utility of supply-side, environment-side, and demand-side policy instruments. Consequently, this approach serves as a valuable analytical instrument within this paper.

Supply-side instruments refer to the Government’s role as a provider, taking the necessary measures to ensure the basic livelihood security of people experiencing poverty and to improve the quality of life and development motivation of people experiencing poverty, specifically including financial inputs, information services, talent training, and infrastructure construction. Demand-side instruments measures refer to the Government’s efforts to stimulate consumption in poverty-stricken areas by promoting poverty alleviation markets, expanding poverty alleviation channels, and promoting poverty alleviation industries, including government purchase, service outsourcing, market shaping, and collaborative exchanges. Environment-side instruments refer to the strong guarantee provided by the Government to create a favorable external environment for poverty alleviation, strengthen the elements of poverty alleviation, and stimulate the endogenous impetus, specifically target planning, regulatory control, tax incentives, and guiding publicity. Examining the policy instruments’ specific measures makes it possible to understand the differentiation of the anti-poverty governance approach, the existing problems, and the direction of future improvement.

The deployment of these three policy instruments within poverty alleviation reinforces one another, as depicted in Fig. 2 . When viewed through the lens of poverty reduction as a mechanism for propelling economic and social development in impoverished regions, the evolution and advancement of poverty alleviation stem from the interaction and synergy among pushing, pulling, and external forces. In this dynamic, the three policy instruments act as a direct impetus, a direct attractor, and an indirect influencer, respectively, jointly propelling the progression and development of poverty alleviation efforts. These three forces are not static but evolve over different stages of the developmental process, each concentrating on distinct policy targets and modes of poverty management. This study’s central inquiry examines the focal points and attributes of supply-side, demand-side, and environment-side policy instruments throughout China’s rural anti-poverty endeavors.

Schematic illustration of the impact of policy instruments on pro-poor development.

Research methodology

This study employs content analysis to categorize and distill policy texts regarding rural poverty governance in China. Content analysis is a scientific research method that objectively describes observable phenomena and can handle massive amounts of data over extended periods (Riffe et al., 2019 ). Based on specific statistical principles, content analysis can be employed for any type of text, such as policy documents, sounds, images, and videos (Drisko and Maschi, 2016 ). To conduct content analysis, the following vital steps must be followed: defining the study purposes, identifying the unit or sample to be analyzed, determining the categories to be analyzed, identifying and coding the coding elements, testing for reliability, and analyzing and interpreting the results. Policy documents contain explicit content with multiple dimensions and valuable information. The central Government of China holds absolute authority and leadership. Its policies are highly targeted, allowing effective regulation and management of economic and social development and safeguarding people’s well-being. Therefore, we applied the content analysis method to thoroughly analyze 762 anti-poverty policy texts. Through this analysis, we examined the development of China’s anti-poverty policies from three dimensions: policy initiation time, policy targets, and policy instruments.

With the help of NVivo12 software, this paper classified 762 pro-poor policy texts into quantifiable textual analysis units according to the three-level coding principle of “policy text period—type of policy instruments—specific policy content.” According to the type of instruments and the temporal order of the policy, the analysis unit of this paper is coded, and each code is categorized according to the feature words corresponding to the nodes to analyze the use of different policy instruments in terms of the frequency of use of policy instruments. Where “A, B, C” in the code represents the policy instruments type, “1, 2, 3” represents the policy period, and “a, b, c, d” represents the specific policy content. For instance, the document “A-1-d” includes details about the supply-side policy instrument in the “Notice on the National Poverty Alleviation Program of 1987,” released in 1994. The specific policy instruments reference point is “With the support of the state, develop and utilize local resources, develop raw material production, and rely on scientific and technological progress to provide production impetus for the masses to escape from poverty.” Then, following the policy instruments framework, each textual analysis unit is analyzed, and finally, each textual analysis unit is categorized into the corresponding policy instruments (see Table 1 ).

Another coder examined the policy text’s credibility to ensure the study’s validity and reliability. Both parties agreed on disputed issues to establish coding guidelines. The author then recoded for robustness in reverse policy text order, resulting in a final Kappa coefficient of 0.875 (>0.81), indicating high reliability and validity (Richard, 1977 ).

Policy text analysis

Time dimension analysis.

This paper delineates the various stages of policy evolution through a quantitative analysis of 762 policy documents and a comprehensive interpretation of the keywords within these texts. Furthermore, it offers a specific examination of the characteristics of anti-poverty policy evolution at different junctures. It sheds light on the trajectory of the Chinese Government’s efforts in poverty alleviation.

As Fig. 3 illustrates, from 1984 to 2022, there has been a discernible upward trend in introducing anti-poverty policies in rural China, with an exceptionally remarkable surge in recent years. Notably, the number of anti-poverty policies exhibited three peaks in 2000, 2013, and 2018, and the disparity in the number of policies before and after these peaks is quite substantial.

The trends in the distribution of the introduction time of anti-poverty policies in China.

In consideration of the actual context of rural poverty governance and the pivotal time points highlighted in the previous analysis, this paper categorizes the evolution of China’s anti-poverty policy into the following four distinct stages:

The first stage (1984–2000) is characterized as the “Regional Development-Side Poverty Alleviation” phase. During this period, the Chinese Government embarked on large-scale, organized, and meticulously planned rural poverty alleviation and development initiatives in impoverished rural areas. This approach to poverty alleviation was underpinned by a regional development strategy, marking the Government’s proactive involvement in addressing poverty. For instance, in 1986, the Central Government convened the inaugural national conference on poverty alleviation, setting forth the ambitious goal of achieving “Eighty-seven Years of Poverty Alleviation and Attack,” aiming to resolve the fundamental subsistence challenges of 80 million impoverished rural residents by 1990. In 1994, the Central Government issued the first national poverty alleviation and development program, the “National Plan for Poverty Alleviation in 1987.” This program emphasized the importance of focusing on impoverished counties that required assistance. It introduced the concentration of resources and the mobilization of social efforts to ensure the effective implementation of poverty alleviation programs. 109 relevant documents were introduced during this stage, all aimed at achieving the fundamental resolution of subsistence issues for impoverished rural households by 2000.

The second stage (2001–2012) is the “Comprehensive Poverty Alleviation” phase. During this stage, poverty alleviation efforts moved in a more diversified and sustainable direction. The focus of poverty alleviation policies shifted from poor districts to poor villages, and the approach to poverty alleviation transitioned from a “blood transfusion” approach to a “blood-creation” approach, gradually forming a government-led poverty alleviation model with the active participation of many parties. The goal is to empower poor individuals to escape from poverty through the development of industries and skills training. Key measures include implementing industrialized poverty alleviation policies, supporting and nurturing leading enterprises, and enhancing the agricultural industry’s added value to enable people experiencing poverty to improve their economic situation. Key policy documents during this stage included: In 2001, the Central Government issued the “Outline of Poverty Alleviation and Development in Rural China (2001–2010),” which provided a comprehensive framework for poverty alleviation and development in the new era. In 2007, the State Council issued the “Circular on the Establishment of a Rural Minimum Livelihood Security System throughout the country,” effectively addressing the challenges faced by impoverished individuals in rural areas. In particular, the number of complementary policies increased significantly with the establishment of the Rural Subsistence Security System in 2007, providing security for poor rural families.”. During this period, the number of pro-poor policies reached 224.

The third stage (2013–2020) is characterized as the “Precise Poverty Alleviation” phase. In 2013, General Secretary Xi Jinping introduced the pivotal concept of precise poverty alleviation, which marked a transformative moment in China’s poverty alleviation efforts. This concept catalyzed the introduction of top-level designs and complementary poverty alleviation policies, resulting in minor fluctuations in the number of policies before and after 2013. The advent of precise poverty alleviation strategies brought about significant changes, elevating anti-poverty initiatives to a strategic level. For instance, In 2015, the central Government articulated the general requirements for poverty alleviation targets. In 2017, the introduction of the rural revitalization strategy elevated the “three rural areas” issue to a top priority for the entire party. In 2018, designated as the year of poverty alleviation, China implemented a series of targeted measures to combat corruption and formalism in poverty alleviation. In the same year, the Government issued the “Opinions on the Implementation of the Rural Revitalization Strategy” and the “Strategic Plan for Rural Revitalization (2018–2022)” aimed at rejuvenating the countryside and addressing deep poverty. It led to a significant increase in anti-poverty policies in rural areas in 2018, accelerating the implementation of policies in deeply impoverished regions. In 2019, “Two no worries and three guarantees” became a central focal point of poverty alleviation and development, with targets set to ensure that poor households would be lifted out of poverty by 2020 and address regional poverty comprehensively. Overall, policies during this phase experienced explosive growth, reaching 429. It is noteworthy that demand-side instruments began to proliferate during this stage.

The fourth and current phase (2021-) is the “Relative Poverty Governance” phase. In this stage, the approach to poverty governance transforms, focusing on consolidating absolute poverty governance’s effectiveness and addressing the issue of relative poverty. Given that this phase is still in its exploratory stage, this chapter will not delve into it extensively, and the governance outlook will be presented in the discussion section.

The preceding analysis outlines the progression of China’s policies to alleviate poverty and offers an interpretation of the Government’s initiatives within their contextual framework. The following section presents a categorization and evolutionary analysis of poverty alleviation policies by measuring high-frequency keywords extracted from Chinese rural poverty alleviation policy texts.

Based on an analysis of the stages of evolution of rural poverty alleviation policies in China, this study conducts a quantitative analysis of high-frequency keywords in China’s rural poverty alleviation policy texts to assess the development stages of these policies (see Table 2 ). The results show that terms such as “economy,” “finance,” and “funds” reflect the core principle of poverty alleviation, which revolves around bolstering economic growth in impoverished areas with the backing of government financial resources.

Combined with the time dimension, the terms “education,” “agriculture,” “training,” and “ethnic minorities” appear frequently between 1984 and 2000. It also reflects the Government’s focus on the crucial role of education in poverty alleviation, especially among ethnic minorities. High-frequency terms such as “development,” “impoverished villages,” “health,” and “pilot project” between 2001 and 2012 indicate that poverty alleviation efforts during this period focused on economic and social progress in impoverished rural areas, with a particular emphasis on the provision of essential public services and support mechanisms for disabled groups. 2013 During the period from 2013 to 2022, keywords such as “precision,” “file-listing card,” “plantation industry,” and “urban-rural integration” emphasize the transition to integrated urban-rural development. This stage emphasizes the development of the plantation industry to increase farmers’ income, thus driving people experiencing poverty to diversify their employment opportunities and increase their income through industrialization methods such as plantation. “Evaluation” also implies that local governments are beginning to pay attention to the effects of poverty alleviation and aim to strengthen monitoring.

In summary, it is evident that the emphasis on poverty alleviation endeavors has shifted over time, and this dynamic highlights the critical role of the various phases of poverty alleviation efforts in shaping the differences in the number and effectiveness of policies.

Policy targets dimension analysis

Policy targets represent the intended purposes and outcomes that policy implementation seeks to attain. The statistical analysis of 762 policy documents in this study reveals that China’s poverty alleviation policy targets can be broadly categorized into three primary groups: economic development, service support, and capacity building. As depicted in Fig. 4 , there are notable distinctions in the distribution characteristics of these three policy targets across different stages.

Nodal distribution of policy targets for rural poverty reduction in China.

First, policy nodes targeting the achievement of “economic development” targets were the most prevalent, constituting 76.07% of the total anti-poverty policy nodes. The number of policy nodes in the first, second, and third phases amounted to 186, 1,510, and 2,414, respectively, with the second and third phases experiencing significant expansion. This phenomenon can be primarily attributed to China’s poverty alleviation policies following a productivity approach (Holliday, 2000 ), which views wealth creation as a form of welfare and economic growth as a means of social security. In a context of absolute poverty, characterized by underdeveloped rural areas with weaker infrastructure than urban regions and an increasing urban-rural economic divide, the Government seeks to address poverty through the trickle-down effect of economic growth. Government pro-poor policies aimed at achieving the “economic development” goal include the construction of roads in impoverished areas, bolstering information infrastructure, supporting the agricultural industry, and implementing policies to aid and benefit the rural sector. Policies such as the “four exemptions and four subsidies” fall under this category, aiming to enhance the well-being of impoverished farmers through rural economic development, ultimately resulting in improved living conditions for these individuals.

Second, policy nodes aimed at achieving the “service support” goal constitute less than 20% of the total anti-poverty policy nodes. The number of policy nodes in the first, second, and third phases is 146, 375, and 514, respectively, indicating a consistent upward trend. China’s rural anti-poverty efforts encompass the ongoing enhancement of various support systems, with the Government introducing a series of policies to alleviate poverty in rural areas. Government-led poverty alleviation policies to attain the “service support” goal include establishing a minimum subsistence guarantee system for rural areas. The formulation of a policy regarding subsidies for individuals with disabilities. The deployment of first secretaries to assist in poverty alleviation efforts. The provision of care services for individuals with disabilities. Extending additional financial aid and tax incentives to households with established records. The promotion of volunteerism and the engagement of social organizations in anti-poverty initiatives. These initiatives collectively contribute to providing essential services and support to impoverished populations.

Third, policy nodes that aim to achieve the “capacity building” goal constitute less than 5% of the overall anti-poverty policy nodes. The number of policy nodes in the first, second, and third phases is 11, 46, and 201, respectively, displaying a modest upward trend. This phenomenon can be linked to China’s prevalent government-led nature of rural anti-poverty efforts. Especially in the initial stage, the Government adopted a “blood transfusion” approach to poverty alleviation, investing significant resources in impoverished villages to address basic subsistence needs while neglecting impoverished groups’ capacity building. As subsistence needs were addressed, in the second and third stages, the Government started paying more attention to enhancing the abilities of poor households to overcome poverty. Anti-poverty policies shifted towards a “blood-creation” approach; diversifying poverty alleviation methods aimed at stimulating the intrinsic motivation of impoverished groups. These methods encompassed training, management, education, and agricultural development. The goal was to boost the motivation of impoverished households to combat poverty actively. For example, initiatives like the industry-university-research model, promoting collaboration between universities and industries in sectors such as tourism and agriculture, have been employed to enhance the skills of impoverished households. Additionally, in the 2016 Circular of the State Council on the Issuance of the 13th Five-Year Poverty Alleviation Plan, the “Thousand Schools Action for Skills Poverty Alleviation” was introduced. This initiative aimed to provide impoverished individuals with the capacity and willingness to undergo vocational training, enabling them to secure employment opportunities.

Policy instruments dimension analysis

Policy instruments represent the means to attain policy targets or address societal issues. As illustrated in Fig. 5 , during the first stage, there is a substantial difference in the frequency of use of various policy instruments. Supply-side policy instruments are the most commonly used, accounting for 71.85%, followed by environmental-side policy instruments at 19.54%. Demand-side policy instruments are the least frequently employed, constituting only 8.61%. There are noteworthy shifts in utilizing these policy instruments in the second and third stages. The proportion of supply-side policy instruments exhibits a substantial decline, while the proportion of demand-side policy instruments shows a pronounced increase. The share of environmental-side policy instruments peaked during the second stage but continues to exhibit an upward trend.

Evolutionary trend of policy instrument nodes for rural poverty governance in China.

In this study, China’s rural poverty alleviation policy instruments have been counted, and their evolutionary trends and quantitative distribution are presented in Table 3 .

The results presented in Table 3 indicate 3235 nodes of supply-side policy instruments. Among these, the proportion of secondary nodes, in descending order, is as follows: infrastructure construction (39.41%), Financial inputs (31.66%), talent training (18.42%), and information services (10.51%). A Chinese proverb says, “To get rich, we must first build roads.” It is reflected in the frequent utilization of infrastructure construction and capital investment as supply-side policy instruments. The Government vigorously promotes the development of electricity, road networks, and other public facilities in impoverished areas through various agricultural funds and infrastructure guarantee funds. For instance, the 2018 Measures for the Management of Funds for Supporting Poverty Eradication in Poor Old Revolutionary Areas, supported by the Central Special Lottery Public Welfare Funds, highlights the backing for the construction of farmland, water conservancy facilities, and photovoltaic power stations, among other infrastructure in impoverished old revolutionary areas. This strategy aims to enhance the efficiency of fund utilization. However, excessive financial inputs may inadvertently encourage dependency among the impoverished population, making it challenging for them to become self-reliant and leading to increased reliance on welfare programs. It can hinder the development potential of people with low incomes. In contrast, talent training and information services have been used less frequently as supply-side policy instruments. It suggests that there is room for improvement in areas such as skills training, vocational education, and the provision of information services, particularly in regions with ethnic minorities and remote areas.

The results in Table 3 reveal 2471 nodes related to environment-side policy instruments. Among these, the secondary nodes, in descending order, are as follows: tax incentives (37.51%), target planning (36.02%), guiding publicity (19.87%), and regulatory control (6.60%). These specific measures appear clustered and polarized within environment-side policy instruments, focusing on strategic guidance for poverty alleviation through implementing tax incentives, transfer subsidies, establishing development plans, and updating work guidelines. Given poverty alleviation’s multifaceted and complex nature, which necessitates comprehensive institutional arrangements and strategic planning, goal planning is frequently employed within environment-side policy instruments. In China, intricate organizational relationships and networks exist, requiring constant coordination of targets and expectations among various actors. Typically, central targets provide guidance and planning, while local governments establish locally tailored targets based on their preferences and capacity for action. While advocacy guidance and regulatory control are less commonly used among environment-side policy instruments, it is crucial to emphasize advocacy and guidance in poverty alleviation efforts and to strengthen the rule of law and regulation within anti-poverty actions.

The results in Table 3 indicate 1202 nodes associated with demand-side policy instruments. Among these, the secondary nodes, in descending order, are as follows: market shaping (44.18%), collaborative exchanges (34.28%), services outsourcing (11.06%), and government purchase (10.48%). Demand-side policy instruments directly address the basic needs of impoverished households and provide them with more opportunities and resources. These instruments stimulate market demand and contribute to efforts to alleviate poverty. The rise of welfare pluralism has facilitated a shift from a model dominated by the “welfare state” to a “welfare society,” emphasizing the participation of multiple actors, including the market, NGOs, communities, and families, in meeting people’s welfare needs (Gilbert, 2000 ). China’s social security system has become more complex (Lu et al., 2013 ), aligning with this concept. The reform of China’s social security system also adheres to this idea, and demand-side policy instruments represent a critical step toward achieving this target. However, the frequency of using demand-side policy instruments is not exceptionally high, especially in the case of service outsourcing and government purchases, which remain at relatively low levels. This situation may hinder the transformation of the state’s role in addressing poverty-related issues.

In general, China’s anti-poverty initiatives have established a government-led policy implementation mechanism marked by a high degree of promotion. The execution of poverty alleviation policies primarily follows a top-down supply-side approach led by the Government, complemented by environmental support. This approach underscores that addressing rural poverty primarily relies on the impetus generated by government-led supply-side policy instruments and external support from environmental policy instruments. In contrast, the pull created by demand-side policy instruments is notably insufficient.

In summary, when it comes to policy targets, central-level poverty alleviation policies have primarily emphasized enhancing infrastructure construction and promoting economic development in impoverished regions. Conversely, policy targets related to service support and capacity building have not received sufficient attention from the Government. On the one hand, China’s predominant feature of poverty governance remains government-led. This governance model has evolved since 1984, with initiatives driven from the top-down by the central Government. Regional economic development delegates the task of poverty reduction to grassroots governments, connecting poverty governance with local economic development to create a “trickle-down effect.” The central Government utilizes incentives and assessment measures to motivate grassroots governments to achieve poverty reduction targets, granting them decision-making and deployment authority, along with inspection and evaluation powers. Ideally, this economic development-driven “trickle-down effect” should lead to income growth for people experiencing poverty.

On the other hand, the “polarization effect” of economic development has widened income inequality. At this stage, the marginal effect of relying solely on economic development for poverty reduction has diminished, making it increasingly challenging to achieve comprehensive poverty alleviation through economic development alone. As poverty alleviation governance continues to evolve, China’s approach to supporting people experiencing poverty has diversified, shifting from providing funds, materials, and food to raising the incomes of people experiencing poverty, enhancing the social security system, and bolstering human capital. The discussion above suggests that China should give more attention to policy targets related to service support and capacity building.

Regarding policy instruments, it is evident that demand-side policy instruments are falling behind, potentially resulting in a skewed implementation of pro-poor policies. In the future, the Chinese Government should develop a more comprehensive set of demand-side policy instruments to provide additional impetus for poverty governance. Furthermore, flexible policy instruments such as government purchasing, collaborative exchanges, and guiding publicity are being underutilized. This underuse could lead to inadequate market, social, and public involvement in poverty alleviation. It also reflects that the Chinese Government’s approach to poverty alleviation governance has not entirely shifted from a coercive method to an endogenous drive. While government-led poverty alleviation effectively mobilizes resources and integrates efforts, it may not be conducive to establishing a long-term mechanism. It could result in dependence on poverty alleviation funds among those in need, creating a form of dependency that is more challenging to address. Nonetheless, it is worth noting that the Chinese Government has created a favorable policy environment, encouraged active participation from social organizations in poverty alleviation and development, and promoted endogenous motivation among impoverished groups. It is evident in the gradual increase in demand- and environment-side policy instruments.

Economic development often relies on state intervention when resources are scarce, resulting in a “government-led development” economic system (Oqubay and Lin, 2020 ). In China, where industrialization occurred relatively late, the Government played a crucial role in combating absolute poverty by implementing numerous supply-side policy instruments, leading to significant achievements. Regarding social policy expenditures, China’s government spending on social policies as a proportion of the Gross National Product (GNP) has approached the standards in developed countries. However, the continued growth of China’s social policy expenditures, particularly the high implementation of supply-side social policies designed to serve economic development, highlights the need to utilize policy instruments efficiently. It includes harnessing the pulling power of demand-side policy instruments and the driving force of environmental policy instruments to achieve sustainable development. In the phase of relative poverty governance, it is crucial to ensure that policy instruments, while still supporting economic development, are not solely used for redistribution but also focus on promoting equitable distribution. This emphasis should prioritize the targets of service support and capacity building, as neglecting them may hinder the resolution of relative poverty issues.

From absolute to relative poverty: an explanatory framework of “path dependency-institutional change”

Path dependence describes how past choices can have a lasting impact on the present and future, similar to the idea of “inertia” in physics, where once a particular path is chosen, it tends to be followed and maintained. David, an early proponent of the concept, was the first to apply it to the analysis of technological change. Arthur ( 1989 ) defined path dependence as the inability to deviate from a particular trajectory in a dynamic economic process. In other words, if different historical events and their developmental sequences cannot lead to the same market outcome with 100% certainty in a dynamic economic system, that system is path-dependent. Building on the ideas of David and Arthur, North integrated path dependence theory into the institutional analysis framework, giving rise to the path dependence theory of institutional change. Within established institutions and mechanisms, there are typically two possibilities for progressing (Pinch and Bijker, 1984 ). One is to maintain the existing system, even if it may be inefficient. The other is to create a new system. Path dependence and path creation are intertwined and complementary, and both play a role in driving the process of institutional change (Garud et al., 2010 ).

This paper highlights that the effectiveness of addressing absolute poverty is characterized by a “short-term, quick” approach (Wan et al., 2021 ) while addressing relative poverty requires establishing long-term mechanisms. Currently, China’s poverty alleviation efforts face several challenges, including a heavy reliance on rural support resources, significant multidimensional relative poverty in both urban and rural areas, and a lack of internal motivation in impoverished regions (Liu et al., 2017 ), which presents obstacles to effective poverty governance. In this new era of poverty governance, there is an urgent need for a strategic perspective, with the central Government taking a leading role in systemic coordination through top-level design to ensure the orderly progress of poverty governance. To better analyze poverty governance policy instruments, this study introduces North’s path dependence theory (North, 1990 ), treating poverty governance policy instruments as the evolution of institutional arrangements. It also considers other institutional factors and their impact on the poverty governance system, examining the evolution of poverty governance policy instruments through path dependence.

According to North’s theory, path dependence is primarily driven by the “limited rationality” of institutional actors and the high transaction costs of interest groups, influenced by political and economic constraints, as well as informal systems like culture (North, 1997 ). In poverty governance, when policy instruments such as “blood transfusion” and “development-side” approaches are frequently employed and deliver significant results, they become entrenched and even strengthened by vested interest groups. These policy instruments and the enduring influence of informal systems like the culture of poverty that aligns with absolute poverty gradually form multiple dependencies in the poverty governance process.

After eliminating absolute poverty, the Government seeks to consolidate the gains by maintaining the stability of existing policies and systems. It introduces institutional arrangements such as dynamic monitoring mechanisms and measures to prevent a return to poverty. It also strengthens the linkage between poverty eradication outcomes and rural revitalization. Simultaneously, as China enters the phase of relative poverty governance, the Government initiates innovations and expansions in the poverty governance system. It proposes creating a long-term mechanism for addressing relative poverty and modernizing the goal of achieving shared prosperity among all citizens. Through promoting and implementing government policies and systems, relative poverty governance gradually breaks through the closed environment and the lack of internal motivation characteristic of the original poverty governance. However, breaking the original multiple dependence paths takes time and involves a co-evolutionary process of new policies and the existing system. During this period, innovation and expansion of new policies coexist with stabilizing old policies, leading to path divergence. The system subjects consciously guide decision-making to challenge the old institutional arrangements. The Government continuously adjusts, optimizes, and constructs an ideal path for relative poverty governance. Its leading decision-making behavior drives the system’s transition from path divergence to path innovation, comprehensively replacing the old policy instruments for poverty governance and shaping the policy instruments for relative poverty governance.

Based on the above theoretical analysis, this paper constructed an analytical map of the evolution of the path of poverty governance (see Fig. 6 ).

Poverty governance pathway.

Conclusion and policy implications

In the context of poverty governance in China, the achievement of short-term poverty alleviation goals has been driven by a pressure-based system, characterized by centralized decision-making and strong administrative mobilization carried out by the central government. This has been facilitated through significant investments, major projects, and large-scale mobilization efforts. However, the predominant focus of poverty alleviation has been on income enhancement, with inadequate emphasis placed on fostering internal motivation and facilitating access to education to build aspirations for the impoverished. Consequently, there is an overreliance on supply-based policy instruments, leading to potential challenges in sustaining the effectiveness of this approach.

To achieve meaningful and sustainable poverty reduction, it is necessary to continuously optimize coordination among various stakeholders such as government, political cadres, and local enterprises. Looking at the development stages of poverty alleviation governance practices in rural China, the central government has consistently taken the lead in rural anti-poverty efforts at each stage. However, due to significant variations in the outcomes of nationwide policies among different regions, especially after entering the comprehensive poverty alleviation stage, the actions and preferences of political cadres have a more pronounced impact on local poverty outcomes (Deng, 2023 ; Liu and Liu, 2022 ). After transitioning to the precise poverty alleviation stage, the role of local enterprises has also been actively mobilized, participating in the national strategy of “industry-based poverty alleviation” to precisely assist impoverished rural areas, further harnessing the power of the market and society.

Moreover, it requires a precise synergy among multiple policy instruments based on both supply-based, demand-based, and environment-based approaches, aiming to foster comprehensive rural revitalization. This requires strategic allocation of resources and organizational coordination, centered upon a cohesive foundation, and dynamically integrated with the moral and cultural aspects. By doing so, it becomes possible to forge collective efforts in the governance of relative poverty. Ultimately, the collaborative model of poverty governance entails practical processes encompassing diverse resource allocation methods and balanced utilization of various policy instruments. Naturally, dynamic coordination among government, market, and societal actors, as well as the effective integration of supply-based, demand-based, and environment-based policy instruments, necessitate continuous exploration and innovative governance practices that are adaptable to local conditions, circumstances, and trends.

Policy implications

The poverty governance policy instrument facilitates the translation of national-level poverty governance policies into actionable directives implemented at the local government level. The strategic alignment of this policy instrument empowers local governments to establish a practical policy framework for impoverished areas. This framework helps bridge the gap between government supply and the needs of impoverished areas and households. It also promotes synchronization in the poverty governance policy system concerning supply and demand quality, quantity, and structure, ultimately facilitating poverty alleviation and prosperity. The interplay between government resource allocation and the needs of impoverished regions characterizes the process of implementing poverty alleviation policies. It involves the direct influence of government macro-control and the indirect impact of market forces on the poverty alleviation environment. Therefore, based on an overview of the evolution of policies in the period of absolute poverty governance and consideration of the path dependence theory, this study argues that the following points should be considered in the implementation of policies for the governance of relative poverty:

First, adhere to the evolutionary principles of poverty governance policies, emphasizing the sustainable development of poverty reduction and enhancing the relative poverty governance system. A comprehensive policy cycle comprises policy formulation, government-led policy implementation, evaluation, monitoring, and policy adjustment for optimization. Relative poverty governance is a lengthy and intricate endeavor. The Government should approach it from the policy cycle standpoint, formalize poverty governance in policy formulation, adhere to legal principles in relative poverty governance, enhance system precision, and boost resilience. Incorporating third-party evaluation entities and amplifying social oversight in assessing local government policy implementation will elevate public participation and voice, safeguarding people’s right to express their views. Reinforce the policy leadership in poverty governance, aligning it with the various stages of relative poverty governance. Adjust governance policies to harmonize with the evolving needs of each stage in relative poverty governance. Employ laws, regulations, and specific policies to effectively regulate and guide each stage.

Second, Strengthen the policy coherence and alignment in the governance of relative poverty. Relative poverty governance represents a holistic progression and advancement beyond absolute poverty eradication, focusing on establishing a sustainable mechanism for addressing relative poverty and comprehensively mitigating the multifaceted challenges of rural poverty. In the phase of absolute poverty governance, the utilization of policy instruments displayed fluctuations, imbalances, and path dependencies. Consequently, tailored adaptations are implemented during the relative poverty governance to utilize specific policy instruments across diverse dimensions to address deficiencies in rights, capabilities, and incentives. This strategy aims to achieve alignment with the policy targets of relative poverty governance.

Third, Enhance the coordinated management of policy instruments and refine the application system. In relative poverty governance, it is vital to focus on the effective deployment and integration of policy instruments that align with the specific attributes of relative poverty. Initially, optimization of supply-side policy instruments is essential. The Government should elevate the utilization of talent development, information services, and public services, thereby enhancing the quality of fundamental public services in rural regions. Additionally, actively promoting the digital industry and facilitating information resource exchange and vocational skills training for farmers are crucial measures. Second, intensifying the utilization of demand-side policy instruments is imperative. Expanding the Government’s procurement scope and leveraging the market’s potential is crucial. Cultivating a mechanism for the involvement of multiple stakeholders in poverty governance, enhancing collaboration among various actors, and attracting social organizations, businesses, and individuals to participate in service outsourcing, thereby compensating for governmental limitations, are essential steps. Finally, it is crucial to capitalize on the guiding potential of environment-side policy instruments. Enhancing related laws and regulations, fostering innovation in financial support, boosting tax incentives, strengthening capacity development, and nurturing farmers’ intrinsic motivation for poverty alleviation and prosperity through effective communication and guidance is vital. This approach aims to foster a conducive environment for poverty governance.

Data availability

The data that support the findings of this study are available from https://home.pkulaw.com . However, restrictions apply to the availability of these data, which were used under license for the current study and are not publicly available. Data are available from the authors upon reasonable request and with permission from the Beida Faber-China Laws and Regulations Database.

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Acknowledgements

Sincere thanks Dr. Jiang for his support of this article. This paper was supported by the Shanghai Social Science Innovation Research Base of “Research on Transitional Sociology with Chinese Characteristics”, China Scholarship Council (Grant No. 202206140110), National Philosophy and Social Sciences Research Fund of China: Research on the causes of the phenomenon of digital “incapacitation” of the elderly and coping strategies (Grant No.23BSH090) and Shanghai Municipal Education Commission: Research on Improving Social Policies to Address Relative Urban Poverty (Grant No.2021-01-07-00-08-E00129).

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School of Public Administration, Sichuan University, Chengdu, China

Yunhui Wang

School of Social Development, East China Normal University, Shanghai, 200041, China

Department of Global Development, College of Agriculture and Life Sciences, Cornell University, Ithaca, NY, 14850, USA

School of Public Administration And Policy, Shandong University of Finance and Economics, Jinan, China

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YW contributed mainly to text writing, data analysis, and revisions. YC contributed primarily to guidance, revisions, and communications. ZL prepared materials, collected data, and formally analyzed them. All the authors discussed the results.

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Wang, Y., Chen, Y. & Li, Z. Escaping poverty: changing characteristics of China’s rural poverty reduction policy and future trends. Humanit Soc Sci Commun 11 , 694 (2024). https://doi.org/10.1057/s41599-024-03204-0

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Received : 28 June 2023

Accepted : 16 May 2024

Published : 30 May 2024

DOI : https://doi.org/10.1057/s41599-024-03204-0

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