The Relationship Between EU Indicators of Persistent and Current Poverty

Abstract

The current poverty rate and the persistent poverty rate are both included in the European Union’s (EU's) portfolio of primary indicators of social inclusion. We show that there is a near-linear relationship between these two indicators across EU countries drawing on empirical analysis of EU-SILC and ECHP data. Using a prototypical model of poverty dynamics, we explain how the near-linear relationship arises and show how the model can be used to predict persistent poverty rates from current poverty information. In the light of the results, we discuss whether the EU's persistent poverty measure and the design of EU-SILC longitudinal data collection require modification.

Appendix: Derivation of Poverty Rate Expressions from the Prototypical and Mover–Stayer Models

1.1 The Prototypical Model

The derivation of the expression for the current poverty rate (Eq. 1) begins with the identity stating that the total number of poor people this year equals the total number of people poor last year plus the number of people entering poverty between the 2 years minus the number of people exiting poverty over the same period. The poverty entry rate is the number of persons entering poverty divided by the number of people who were non-poor last year; the poverty exit rate (one minus the poverty retention rate) is the number of persons leaving poverty divided by the number of persons who were poor last year. Equation (1) is derived by rewriting the identity in terms of the rates of current poverty, poverty entry, and poverty retention, imposing the steady-state and first-order Markov assumptions, and then rearranging the equation.

The derivation of the expression for the persistent poverty rate (Eq. 2) utilises the EU’s persistent poverty rate definition combined with the expression for the current poverty rate shown in Eq. (1). The probability of being persistently poor according to the EU definition is the probability of experiencing one of four possible 4-year sequences of poverty or non-poverty. For example, the probability of being poor for four consecutive years is the probability of being poor in year 1, P _c , multiplied by the probability of remaining poor in the following three years, i.e. P _c  × (R _c )³, where P _c is evaluated using Eq. (1). The probability of being non-poor in Year 1 and poor in Years 2, 3, and 4 is (1–P _c ) × E _c  × (R _c )², which is equal to P _c  × (1–R _c ) × (R _c )² in the steady-state case. The probabilities for the other two sequences can be derived similarly, and are each equal to P _c  × E _c  × R _c  × (1 − R _c ). The expression for S _c in Eq. (2) is the sum of the four probabilities. With a sufficiently large sample size, the probabilities correspond to population proportions (rates).

1.2 A Mover–Stayer Model

In our mover–stayer model, the poverty dynamics identity cited above has to be revised: the total number of poor people this year is equal to the number of people from the movers group who are poor plus the number of stayers (who are always poor). This total is equal to the number of stayers plus the number of movers from non-poverty to poverty minus the number of movers from poverty to non-poverty. The poverty retention rate for the population as a whole reflects the combination of the poverty retention rate among the movers who happened to be poor last year and the poverty retention rate among the stayers (100 %). Poverty entry rates refer to the number of poverty entries among movers who were non-poor. (Stayers are not at risk of entering poverty as they are never non-poor.) We could have also supposed the existence of a third class of people—those who are never poor—but this complicates the model without adding insights regarding persistent poverty.

The expression for the current poverty rate, $P_{c}^{*}$, is derived by rewriting the revised identity in terms of rates of current poverty, poverty entry, and poverty retention, imposing the steady-state and first-order Markov assumptions, and then rearranging the equation:

$$ P_{c}^{*} = P_{c} + W_{c} /(1 + D_{c} ) $$

(3)

where P _c , E _c , and R _c are as defined as in Eqs. (1) and (2), and now refer to rates for movers only. D _c is the ratio of the entry rate to the exit rate, E _c /(1 − R _c ) > 0, and W _c is the proportion of stayers in the population. We argue shortly that W _c is a small number and the second term in (3) must be smaller still since D _c  > 0.

The persistent poverty rate in the mover–stayer model, $S_{c}^{*}$, is equal to a weighted average of the persistent poverty rate among the movers and the persistent poverty rate among the stayers (100 %), where the weights are equal to proportions of movers and stayers in the population, respectively. Thus

$$ S_{c}^{*} = (1 -W_{c} )\theta_{c} P_{c} + W_{c} . $$

This expression can be re-written in terms of $P_{c}^{*}$ using Eq. (3):

$$ S_{c}^{*} = \theta_{c} P_{c}^{*} + \delta_{c} ,\quad {\text{where}}\quad \delta_{c} = W_{c} (1 - \theta_{c} ) $$

(4)

Allowing for heterogeneity in poverty dynamics in this way leads to prediction of a near-linear relationship as before, except that there is now a country-specific intercept term, δ _c , that was not present in Eq. (2). Since this intercept is positive, one would expect predictions of persistent poverty rates on the basis of Eq. (2) rather than Eq. (4) to produce under-estimates, other things being equal. The intuition is that reliance on current information does not take sufficient account of high poverty persistence propensities among some groups within a country. The empirical issue, and one we consider in the paper, is whether the degree of under-estimation is large or small. Our prior expectation is that the degree is small because W _c is likely to be quite small in all countries, and the other term, (1 − θ _c ), will not play a significant role if there is little cross-country variation in θ _c (the hypothesis discussed in the main text). Estimates of ‘permanent poverty’ rates are rare because there are few very long-running household panel surveys (Sect. 2). However there is some UK evidence that supports our claim. Drawing on British Household Panel Survey data, the Department for Work and Pensions (2010: Table 3.1) reports that the proportion of persons with an income placing them in the poorest fifth of the population in every year between 1991 and 2008 was 3 %, which suggests an upper bound to W _c of around 0.03. Greater chances of under-estimation may occur if one looks at subgroups such as elderly people more likely to contain individuals who are permanently poor. More generally, cross-national heterogeneity in W _c is another factor that potentially loosens the tightness of the near-linear relationship (Fig. 8).

Fig. 8

Predicted and observed current poverty rates (%), 2006 and 2005, old and new member states. Notes Authors’ calculations from EU-SILC longitudinal files. Predicted rates are derived using Eq. (1) in the main text. Year refers to income year. The estimates for 2007 are shown in the top panel of Fig. 5