Evaluación de los aprendizajes

A formally equivalent problem arises when adding on Laspeyeres or Paasche cost of living indices from adjacent periods.

The procedure can of course be generalised to cases where the end date of the earlier period and the initial date of the later period differ, or to comparing differences in poverty dynamics between regions or countries. Note that the procedure is independent from the relative lengths length of the period under consideration.

Each o f the terms in (2.9) has an interpretation. AS^ refers to differences in changes o f

the p o pu lation structure between the periods 7tand \f/, while AL^ captures differences

in the am ount o f subgroup poverty change, which may, e.g., reflect income growth or increased transfer payments. and AL^ therefore compare directly the structural and level changes in both subperiods.

ARS^ captures that an identical amount of structural change AQ^ may affect poverty change differently in different periods, because the subgroups have different (average) poverty levels. This is best illustrated with an example. Suppose that in y/, unemployment is (on average) associated with a high poverty risk. Movements out of unemployment during y/ will therefore be highly effective in reducing poverty. In k,

however, unemployment is associated with a moderate poverty risk only. Hence, movements out of unemployment will not reduce aggregate poverty all that much. Similarly, ALS^ captures the impact of different subgroup sizes on the achievable poverty reduction. Say that in ^ m a n y people are unemployed, while in ;ronly few are. Raising the incomes of the unemployed by a certain amount, for example by increasing unemployment benefits, will therefore reduce poverty significantly during y/, while it will have a small effect only during tü. Thus, A/?5^ and ALS^ reflect that developments which reduce poverty are the less effective in doing so the less poverty there is in the first place. As can he verified easily, AS^ + ARS^ = AS^ and AL^ + ARL^ = AL^

M ultinom ial Decom positions

So far, the subgroups for the decompositions have not yet been specified. In the simplest case, the /ds represent just one characteristic, say employment status (employed/unemployed). Then (2.8c) has a straightforward interpretation: some part of poverty change can be attributed to an increase (or decrease) in unemployment, while the other part relates to changes of poverty within both the employed and the unemployed subgroups.

52

It can be shown that if (and only if) the initial date of K coincides with the end date of y/, then

= A/?5^ .

The subgroups can, however, also be constructed from a larger number of characteristics {cx,p...,(p)\ say employment status, age, gender, household composition, etc.. A specific subgroup may then comprise, for example, all unemployed women aged 20-40 living in households with two adults and one child. In this case, S measures the poverty impact of changes in the population structure in a much wider sense (and L the effect o f changes in subgroup poverty). The downside of such a multi-way decomposition, however, is that the various sources of poverty change can not be identified separately.

Various options can be thought of on how to deal with this issue. Shorrocks (1999), e.g., suggests to assign each decomposition characteristic a weight of ( 1/^), such that the effect of changes in unemployment on poverty, for example, is calculated as the single­ characteristic effect of unemployment changes over the number of characteristics that are employed in the decomposition. I believe that, in this context, a more informative option is available, which is to work out explicitly how the different structural/level effects interact. For the sake o f the exposition, take only two characteristics a = l,...,A

and Say a is employment status (employed/non employed) and P is health

(healthy/ill). Decomposing separately with respect to each characteristic gives the structural effects

(2.10)

^ car ~^jPa^Qcar

^ d ,

S

,

a=l ^=1

while decomposing jointly results in

A B

a p tT A u A a a p ' - ^ ^ a p t r a = l 0=1

and Qapt ^ 6 subgroup poverty/the population share of individuals that have the specific characteristics or (say unemployed) and p (say ill). By direct calculation

(2.12)

a=\ p=\

II

(note that = ^ A g ^ ). Thus, the joint share effect S^p is the mean of the one- M

characteristic share effects and Sp plus a cross term

(2.13) A B AG a = l p - \ a p ry V y aPtT •

For illustration, consider the case where a and p denote the same characteristic. Then

Pap = Pa - Pp’ hence = 0 and 6"^^ = = Sp,^. In all other cases,

however, CS^p^^ will deviate from 0, and it will be positive if, from t to t+T, reinforcing

poverty risks grow and compensating poverty risks shrink. In the above example, unemployment and illness are reinforcing if it is worse (i.e. associated with higher poverty) to be both unemployed andill than to be eitherunemployed or ill.

In the case of R, rather than only two, interactive characteristics with S^^,Sp^^,...,S^^ one-characteristic structural effects, (2.12) becomes

A B F

(2-1^) ^ap...<ptr = 2 X • • • S ^ap..4^Qap...<ptr a=\ P=\ é=\

1 ^ A B F f 1 /?

= ; ^ 2 ‘^rrr + 2 2 - 2 P a p . . 4 - ^ ^ P r

r=a a=] p=\ ^ = 1 \ ^ r=a J ap...<lKT

In similar fashion, the joint level effect may be decomposed into

A B F (2.15) Pap...^r -

2 2 2

= ~fL^nT + ZS-Z

Qaf..4

Thus, the joint level effect is the mean of all one-characteristic level effects plus a cross term CL^p^^ that will typically be positive if multiple po verty risks becom e more

reinforcing from t i o t+ T (in the above example: it is relatively worse to be unemployed

andill in r+ rth a n it was in t).It can be shown that CL^p^^ = -C S ^ p ^ ^ .

Changes of the Population Structure in East and W est Germany after Unification

Tables 2.3a and 2.3b report the development of some population characteristics in East and W est Germany during the periods under consideration. The simple population average is reported as well as a statistic where the observations are weighed with the Watts Poverty index.^^ Comparing table 2.3a with 2.3b shows that poverty is associated with more children, less education (the differential is about 1 year in West Germany, but smaller in the East), more frequent unemployment, and lower employment intensity within the household.

West Germany’s population structure changed little over time. The number of adults per household shrank somewhat between 1985 and 1995, while the number of young children (i.e. children younger than 6 years) rose a bit between 1990 and 1995. Somewhat larger fluctuations are observed for unemployment, where the poverty weighed average displays more variation than at the simple population mean.

In contrast, large changes of the population structure occurred in East Germany. For the entire population, the number of young children per household shrank from 0.36 in 1990 to 0.16 in 1995, pointing to a drastic reduction in f e r t i l i t y . Wh e n the observations are weighed with the Watts poverty index, however, this pattern is far less pronounced, which indicates that young children concentrated more and more in poor households. It is also noteworthy that in 1995, the poverty-weighed share of East Germans living in single parent households was similar to the West German statistic, while in 1990 it had been much lower.

East Germany’s average household employment intensity fell by more than 20 percent between 1990 and 1995, although even in 1995 it remained higher than in the West. Poor East Germans were also disproportionately affected by the surge in unemployment following unification.

Weighting observations with the headcount ratio would give the mean characteristics of the poor. This, however, would give all poor equal weight independent of the intensity of their poverty, and would thus be inconsistent with the standard axioms of poverty measurement (see chapter 1).

Table 2.3: Population Characteristics in Germany, 1985 - 1995