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Social Choice and Welfare

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26.06.2018 | Original Paper

Intertemporal pro-poorness

verfasst von: Florent Bresson, Jean-Yves Duclos, Flaviana Palmisano

Erschienen in: Social Choice and Welfare | Ausgabe 1/2019

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Abstract

A long-lasting scientific and policy debate queries the impact of growth on distribution. A specific branch of the micro-oriented literature, known as ‘pro-poor growth’, seeks in particular to understand the impact of growth on poverty. Much of that literature supposes that the distributional impact should be measured in an anonymous fashion. The income dynamics and mobility impacts of growth are thus ignored. The paper extends this framework in two important manners. First, the paper uses an ‘intertemporal pro-poorness’ formulation that accounts separately for anonymous and mobility growth impacts. Second, the paper’s treatment of mobility encompasses both the benefit of “mobility as equalizer” and the variability cost of poverty transiency. Several decompositions are proposed to measure the importance of each of these impacts of growth on the pro-poorness of distributional changes. The framework is applied to panel data on 23 European countries drawn from the ‘European Union Statistics on Income and Living Conditions’ survey.

Vorheriger Artikel Are estimates of intergenerational mobility biased by non-response? Evidence from the Netherlands

Nächster Artikel How incentives matter? An illustration from the targeted subsidies reform in Iran

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See for instance the indices proposed by Kakwani and Pernia (2000) and Kakwani and Son (2003).

See on this Fields (2010).

This is consistent with the approach used in Chakravarty et al. (1985) and Fields (2010), although the benchmark in Chakravarty et al. (1985) is based on relative immobility, i.e. the share of each individual in total income is assumed to remain stable across time.

This property is called normalization in Hoy and Zheng (2011), requiring that if an individual gets every period the same income level, then his lifetime poverty can be represented by snapshot poverty.

As mentioned by an anonymous referee, a possible issue related to our choice of the counterfactual distribution is that the initial period could be ‘abnormal’ compared to the following periods, hence resulting in large values of the \({ IPP }\), in particular if T is relatively large. A possible fix could be to test the sensitivity of the results by considering a contiguous year as the reference year, or averaging individual incomes for the first years of the growth spell.

Recent contributions, like Dutta et al. (2013), Zheng (2012) or Jäntti et al. (2014), have investigated the role of affluence in intertemporal poverty measurement. The core idea is that, up to some threshold, affluence at a certain date could compensate for past or future deprivation. In this paper’s perspective, this could be done by assuming \(g_{it}\in [a,1]\) with \(a\le 0\) and possibly introducing slight changes in the definition of the indices introduced in this section such as to avoid odd consequences (e.g., having \(p_\beta >0\) for non poor person or excessively mitigating affluence effects).

Having weights that sum to one is not necessary to obtain a consistent poverty pre-order. However, slackening this constraint would not make it possible to interpret \(\pi _{\beta i}\) as an individual EDE gap.

See on this Hoy and Zheng (2011), Calvo and Dercon (2009), and Bresson and Duclos (2015).

A generalization with other definitions of the poverty domain using a counting approach à la Alkire and Foster (2011) can be performed by censoring the vector \(\varvec{g}_{(i)}\) when the (weighted) number of deprivations is less than a given threshold \(\in ]1,T]\).

Using for instance Chakravarty’s (1983b) aggregation formula, we obtain the alternative intertemporal poverty index \(P'_{\beta ,\delta }\):

\(P'_{\beta ,\delta } := \frac{1}{n}\sum \limits _{i=1}^{n}1-\left( 1-\pi _{\beta i} \right) ^{\delta },\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad (7)\)

with \(\delta \in ]0,1]\). The corresponding EDE gap \(\Pi '_{\delta ,\beta }\) is then:

\(\Pi '_{\beta ,\delta } := 1 - \left( 1-\frac{1}{n}\sum \limits _{i=1}^{n}1-\left( 1-\pi _{\beta i} \right) ^{\delta }\right) ^{\frac{1}{\delta }}.\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad (8)\)

This can be more easily seen if we express \(\Pi _{\alpha ,a }\left( \varvec{G}\right) \) as:

\(\Pi _{\alpha }\left( \varvec{G}\right) = \left( \sum \limits _{t=1}^{T} \omega _t \frac{1}{n} \sum \limits _{i=1}^{n}g_{i,t}^\alpha \right) ^{\frac{1}{\alpha }} = \left( \sum \limits _{t=1}^{T} \omega _t P_\alpha (\varvec{g}_t)\right) ^{\frac{1}{\alpha }}. \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad (10)\)

See Dutta et al. (2003) and Decanq and Lugo (2012).

The case \(\alpha <\beta \) is illustrated on Fig. 9 in the Appendix. With the chosen values for the two individual profiles, for the periodic weights and \(\beta \), it can be noticed that the sign of IPP does not depend on the value of \(\alpha \). The magnitude of the index however increases with \(\alpha \).

See the Appendix for a generalization to larger values of T.

In the case of example (1) in the introduction, given the distribution of poverty gaps in the initial period and final period \(\varvec{g}_1 = (0.43, 0.14, 0, 0)\) and \(\varvec{g}_2 = (0, 0, 0.43, 0.14)\), \(\varvec{g}_1^{I}\) is given by \(\left( g_{3,2}, g_{4,2},g_{1,2}, g_{2,2}\right) \times \frac{P_1(\varvec{g}_1)}{P_1(\varvec{g}_2)}=(0.43, 0.14, 0, 0) \times \frac{0.285}{0.285}\).

See Ruiz-Castillo (2004) for a similar decomposition of the CDW (the Chakravarty et al. 1985) ethical index of mobility.

This decomposition is path-dependent. The value of the components would be different with different ‘paths’ for the decomposition. For instance, one might have wanted to capture first the growth effect, then the reranking effect and finally the inequality one (see, e.g. Fortin et al. 2011). An alternative procedure would be to apply a Shapley–Shorrocks decomposition, consisting of computing the Shapley-value of each effect across all possible paths of the decomposition (see Shorrocks 2013).

The modified OECD scale makes the first adult count as a full consumption unit; each additional person aged 14 or more corresponds to 0.5 consumption unit, and each person aged 13 or less contributes to 0.3 consumption unit.

For completeness, in Table 1 we also consider the case of \(\beta =2\) and \(\beta =\infty \)

These results are generally robust to moderate changes in the value \(\alpha \), although the use of larger values for the inequality aversion parameter results in some growth spells being regarded as anti-poor. This is for instance the case for Denmark (\(\alpha \ge 2.1\)), Bulgaria (\(\alpha \ge 4.4\)), Sweden (\(\alpha \ge 4.7\)), the Czech Republic (\(\alpha \ge 5.4\)), Finland (\(\alpha \ge 6.4\)), Spain (\(\alpha \ge 9.3\)), and Italy (\(\alpha \ge 21.8\)).

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Titel: Intertemporal pro-poorness
verfasst von: Florent Bresson
Jean-Yves Duclos
Flaviana Palmisano
Publikationsdatum: 26.06.2018
Verlag: Springer Berlin Heidelberg
Erschienen in: Social Choice and Welfare / Ausgabe 1/2019
Print ISSN: 0176-1714
Elektronische ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-018-1140-6

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