Poverty Duration in Denmark Mohammad Azhar Hussain - SFI

sfi.dk

Poverty Duration in Denmark Mohammad Azhar Hussain - SFI

Poverty Duration in Denmark

Mohammad Azhar Hussain

Welfare Distribution

Working Paper 28:2002

Working Paper

Socialforskningsinstituttet

The Danish National Institute of Social Research


Poverty Duration in Denmark

by

Mohammad Azhar Hussain *

Abstract: The total number of years in poverty over an 11-year period is simulated for Danes

entering poverty between 1981-1987. The basis for simulations is exit rates from poverty and reentry

rates in to poverty, which are estimated in the paper. To measure the sensitivity of applying

a single spell or a multiple spell approach both approaches are implemented and compared to

the actual distribution of total years spent in poverty. The sensitivity of results with respect to

left-censored spells is also investigated. Unobserved heterogeneity is accounted for by a discrete

distribution with two support points. It is found that the multiple spells approach clearly

outperforms the single spell approach. Ignoring unobserved heterogeneity or including left

censored poverty spells does not imply much less precise estimates of the distribution of years in

poverty or average poverty duration.

JEL code: C14, C23, C25, I32, J64

Key words: Poverty, duration, low inc ome, multiple spells, exit rate, re-entry rate, simulation,

unobserved heterogeneity, right censoring, left censoring

Acknowledgements: I am grateful to Nina Smith and Tor Eriksson for very useful comments and suggestions. All

remaining errors are mine.

?? Department of Economics, The Aarhus School of Business, DK-8210 Aarhus V, Denmark, and CIM, CLS

??

and SFI. E-mail: mh@sfi.dk

1


1. Introduction

Earlier research on poverty has mainly focused on the short-term incidence of poverty, e.g. the

fraction of people under the poverty threshold. With the emergence of panel data, researchers are

now concentrating more on the dynamics of poverty and the duration of poverty. This is

important because static poverty can be very misleading, when the burden of poverty on

individuals is analysed. The group of poor could be very mobile, so that a person is only poor for

a short while and then leaves poverty for a long time, implying that poverty is a transitory

phenomenon. Alternatively, poverty could be long-term, with low escape probability, which

means that the poor individuals stay in poverty for a long time: This is a bigger problem. An

uneven distribution of poverty, with only a small fraction of individuals being affected and the

greater part unaffected, implies that the major part of society never experiences poverty, which

can threaten cohesion and political support for people with low incomes. Further, repeated

poverty spells are usually not counted for, implying that poverty over a given time period could

be longer than a single spell approach would show. The aim of this paper is to model the duration

of poverty spells for individuals in Denmark from 1981 to 1997, by applying a multivariate

model to quantify the factors that influence the duration of poverty.

The paper is an extension of previous Danish research on poverty in different ways. First,

multiple spells are taken into account and thereby a more accurate measure of total time being

poor is possible. This is done by estimation of exit and re-entry rates, and then using these rates

to estimate the distribution of years in poverty. Second, a multivariate approach is followed, so

that the effect of different demographic and labour market variables can be estimated.

The next Section is a review of previous research on poverty persistence. Section three presents

the econometric model. The fourth Section deals with data and issues of poverty thresholds,

while Section five presents results from estimation and simulations. The last Section concludes.

2. Earlier research

There is some variation in the modelling of poverty durations. Early studies used non-parametric

methods, e.g. calculated the number of years in poverty in a given time span, see Duncan (1983),

and Duncan and Rodgers (1991). This approach ignores that a person ending (starting) a poverty

2


spell, maybe is only in the beginning (ending) of a long spell of poverty, although only one or

two years are observed. Long poverty spells are thus underestimated, because some of the short

term poor are left- or right-censored. Right-censored cases are easily handled, while a proper

modelling of left-censored spells is less frequent. Moffitt and Rendall (1995) model left-censored

spells, but only by including variables, whose values are known back in time (age and calendar

year).

Bane and Ellwood (1986) take the right-censored cases into account and use a spell-based

approach to estimate mean spell durations for different kinds of spell beginning events. However,

their study is mainly concerned with single spells, which is far from sufficient when analysing

poverty duration. Stevens (1994) updates Bane and Ellwood by including an additional six years

of the PSID. A probit model is applied to estimate exit rates from poverty, controlling for year

and business cycle effects. The model allows for duration dependence in the hazard rate. The

analysis is extended further by focusing on multiple spells and concludes that this is important,

because persons ending a long poverty spell are more likely to re-enter poverty.

Devicienti (2000) uses a log-log model and defines a discrete time hazard rate h ij

for person i to

leave poverty (and non-poverty) in time interval j as

'

hij ( Xij

) ? 1?

exp[ ? exp( Xij? ? ? ( d))]

(1)

where X is a set of explanatory variables, ? is the set of parameters to be estimated, and ? is a

functional form specifying how the hazard rate changes with duration (d) of poverty. To avoid

constraints on ? , a fully flexible specification is used by introducing interval (year) specific

dummies for the baseline hazard. Apart from the hazard specification and omitted modelling of

unobserved heterogeneity, his study is very much like Stevens (1999).

Stevens (1999) uses a multivariate approach when estimating the poverty duration, taking

multiple poverty and non-poverty spells into account. The multivariate approach increases the

understanding of the factors influencing poverty duration. A discrete time hazard framework

accounts for multiple spells, and the framework is used to derive estimates of total time being

poor. The treatment of poverty duration is advanced since issues concerning multiple spells, leftand

right-censoring and heterogeneity are all addressed as described below. Stevens approach is

also used in this paper.

3


Focusing on the duration of poverty means that other important poverty issues are not addressed

in such detail. This is true for the severity of poverty, traditionally measured by the distance from

the poverty line to the income level of an individual, and inequality among the poor. An index

simultaneously taking several dimensions, but duration, into account is the index in Sen (1976).

However, severity in another sense may be included. Combining the traditional way of measuring

severity and duration is proposed in Nicholson (1979) as

p = sev*dur

where p is a poverty measure (burden), sev is severity and dur is duration of a poverty spell.

When the number of poor years is simply counted, then sev is implicitly assumed to equal 1, so

persons are counted equally poor whether they are just below the poverty line or have an income

equal to half the poverty line. If instead sev is properly included, then a person with income equal

to ¼ of the poverty line for one year (dur=1) will effectively be counted as having 4 years in

poverty, whereas a person having income equal to the poverty line will be counted as having 1

year of poverty. However, the approach is not followed here, because the focus is on the duration

of poverty and not its intensity.

Danish contributions to the poverty duration literature are mainly contained in Pedersen and

Smith (1998). Poverty exit probabilities are estimated and durations are derived from them. Their

study thus follows the single spell approach and the re-entry into poverty is therefore not taken

into account. Othe r Danish studies are primarily concerned with the cross-sectional calculation of

poverty rates, see e.g. Ministry of Economic Affairs (1993).

3. Econometric model

Define e s

as the exit probability from poverty after s years of poverty and r s

as the re-entry

probability from non-poverty after s years of non-poverty. The probability of experiencing a

completed poverty spell T with duration d is then:

d

? ?

P T ? d ? f d ? ?? ? 1

) ( ) (1 ? e s

)? ed

s?

1

( (2)

?

4


where the first term is the probability of not exiting poverty up to time d-1. The probability of a

d- years non-poverty spell is defined analogously

d

? ?

g d ? ?? ? 1

) (1 ? r s

)? rd

s?

1

( (3)

?

The probability of observing a right-censored poverty spell is

d

?

P( T ? d ) ? 1?

P(

T ? d)

? 1?

F(

d ) ? (1 ? )

(4)

s?

1

e s

and the probability of observing a right-censored non-poverty spell is

d

?

P( T ? d)

? 1?

G(

d)

? (1 ? )

(5)

s?

1

r s

where F and G are the cumulative density functions for poverty and non-poverty durations. In the

spell based approach right-censored spells are thus easily incorporated.

The probability of transition in or out of poverty depends on personal characteristics X it

. Together

with duration terms this gives a model for poverty duration. But apart from observable

characteristics X it

there can be unobservable characteristics that create dependence among

individuals’ exit probabilities across time. For instance persons with a long poverty spell in the

past might be more likely to re-enter poverty or, persons with low exit rates might also have high

re-entry rates. Ignoring unobserved heterogeneity, can thus bias estimated parameters, e.g.

overstate the effect of explanatory variables on the hazard rate, see Lancaster (1990). Here,

unobserved heterogeneity among individuals is modelled as in Eberwein et al. (1997) and

Stevens (1999), whose specification allows correlation across individual spells in and out of

poverty, and at the same time allows the heterogeneity to enter both poverty spells as well as nonpoverty

spells through the intercept terms. Using a logistic specification, the exit and re-entry

rates are defined as

e

ijdt

p p p

exp( ?

ij

? ?

d

? ? X

it

)

? (6)

p

p

1?

exp( ? ? ? ? ? X )

ij

p

d

it

5


ijdt

n n n

exp( ?

ij

? ?

d

? ? X

it

)

? (7)

n

n

1?

exp( ? ? ? ? ? X )

ij

n

d

it

where

n

? and ? are individual specific effects of type j for person i during poverty spells (p)

p

ij

ij

n

p

n

and non-poverty spells (n), ? and ? are duration dummies for spell lengths d and ? and ?

are effects of background variables.

p

d

d

n

? and ? are chosen to have discrete distributions with two support points each (j=2), so that

p

ij

ij

there are two types of poverty spell,

p

? and p 1 ? 2

(i subscript suppressed), and two types of nonpoverty

spell,

n

? and n 1 ? . This gives four possible types of person: With probability

2

P 1

the person

is of type ( p n p n

p n

? ,

1 ? ), (

1 ? ,

1 ? ) has probability

2

P 2

, (? ,

2 ? ) has probability

1

P 3

and a person has

n

probability P 4

of being of type (? ,? ). Each individual is of either type with some probability,

p

2

2

so P 1

+ P 2

+ P 3

+ P 4

=1. With this specification heterogeneity implies having the combination of

high or low exit probability and high or low re-entry probability. Each individual is characterized

by a vector containing heterogeneity terms

likelihood of being of type l, l={1,2,3,4}, is

p n p n p n p n

? = [(? ,? ),( ? ,? ),(? ,? ),( ? ,? )]. The

l

1

1

1

2

2

1

2

2

ni

mi

?

??

?

?

Li( ?

i, l

) ? ? fis(

d,

?

i,

l

)

? gis(

d,

?

i,

l)

[1 ? Fi

( d,

?

i,

l

)] [1 ? Gi(

d,

?

i,

l

)]

? s?

1 ??

s?

1 ?

1?

?

(8)

where ?=1 if a person’s last spell ends in poverty, and ?=0, if it ends with non-poverty. n i

and m i

are numbers of poverty and non-poverty spells. Each individual has some probability of being of

either type, so individual i’s contribution to the likelihood function is

4

L ? PL

? )

(9)

i

?

l?

1

l

i( i,

l

Maximising the likelihood in (9) produces estimates for P, ? , ? and ?.

6


4. Data sources and definition of poverty

The data used in the analysis stem from administrative registers in Statistics Denmark. Further

documentation on the data may be found on www.cls.dk. It is a longitudinal ½ percent

representative unbalanced panel data set of the Danish population for the years 1976-1997. The

data set contains information on demographic, educational, income and labour market variables.

There is no standard way of proceeding with analysis of an equivalent income measure. Thus,

there is some variation in defining needs, which income or tax components to include, the unit of

calculation and the accounting period. In this study the income concept is equivalent annual

family income after transfers and taxes (EDI). Its calculated from EDI=DI/ES, where ES is the

equivalence scale and DI is family disposable income defined as the sum of total family gross

income minus total family taxes. Only individuals with positive EDI are included.

Gross income is the sum of labour earnings, asset flows, imputed value of owner-occupied

housing, private transfers and public transfers such as sickness benefits, unemployment insurance

benefits, pensions and social assistance. Asset flows include income from rent, interest and

dividends. Public non-taxable transfers such as housing benefits and individual supplementary

means-tested benefits for pensioners are not included. As these benefits are targeted at the bottom

of the income distribution (primarily first and second deciles for housing benefits, see Danish

Economic Council, 2001) this might overstate the percentage in poverty. Conversely the

consequence is also a downward biased poverty line, so the total effect of excluding these

benefits is not clear. Further, non-public transfers between separated parents of a child are not

included.

In this paper ES is the sum of discrete weights attached to each individual in a family, the socalled

new OECD equivalence scales. The first adult receives the weight 1, the second has a

weight of 0.7 and children weigh 0.5 each, see Pedersen and Smith (1998) for an application of

similar weights. Each individual in the family is “given” the same EDI, which leads to the

implicit assumption that resources are equally distributed among the family members. This

assumption can lead to biased poverty estimates for children, women or men, if different intrafamily

distribution systems are actually applied, see Findlay and Wright (1996).

Recent international comparisons of poverty and inequality discuss equivalence scale choice and

implications, see Förster (1995), Atkinson et al. (1995) and Buhmann et al. (1988), whose overall

conclusion is that the ranking of countries is generally maintained when altering the equivalence

7


scale. On German and American data, Burkhauser et al. (1996) do not find poverty and inequality

rates to be sensitive to the equivalence scale choices. The insensitivity no longer seems to hold

when the equivalence scales are income level dependent, see Aaberge and Melby (1998).

There is not much consensus about the appropriate poverty line and the implicit poverty lines in

the different countries differ. Gustafsson (1995) examines the quantitative poverty measurement

literature. In Denmark there is no officially defined absolute poverty line. The relative growth of

public individual transfers (e.g. pensions, unemployment benefit and means-tested transfers)

follows the relative growth in hourly labour wages. This implies that Denmark implicitly has a

relative poverty line, which does not only account for price increases but also for increases in

productivity. In contrast the official American poverty line is absolute, so that changes only occur

due to price changes and not due to productivity gains. In this study the 50% of median EDI is

applied. Other studies use the 40% cut-off to define severe poverty or the 60% cut-off to define

low income or other cut-offs are used as a sensitivity analysis tool. Using the 40% poverty line

will give lower poverty rate estimates, while the 60% poverty line will give higher poverty rates.

As income distributions are rightly skewed the median is less than the mean, so poverty lines and

poverty rates based on the median are lower than when based on the mean. For applications of

poverty lines other than the one employed here, see e.g. Bishop et al (1999), Hauser and Fabig

(1999), and Gallie and Paugam (2000).

8


Table 1. Table 1. Poverty lines, 1981-1997, Danish Kroner

1981 27,717

1982 31,514

1983 33,219

1984 35,306

1985 37,645

1986 39,480

1987 42,500

1988 45,000

1989 47,000

1990 49,412

1991 49,500

1992 50,588

1993 51,176

1994 54,545

1995 57,000

1996 59,706

1997 62,045

Absolute growth 1981-1997 34,328

- Annual growth 2,146

Percentage Growth 1981-1997, % 123.8

- Annual growth, % 5.2

Using 50% of median, the poverty line was 27,700 DKK in 1981 and 62,000 DKK in 1997, see

Table 1. The poverty line’s annual growth rate is 5.2% (2,146 DKK).

Individuals with equivalent income below the poverty line in a given year are classified as poor,

while individuals with equivalent income above the poverty line are classified as non-poor.

Denmark is one of the Scandinavian welfare states, implying relatively high social transfers over

long periods. “Poor” may therefore be a misleading characterization of Danes with low incomes

because these low-income people will probably all have access to basic human needs (food,

clothing and shelter). Instead, these people are relatively poor, meaning that they are not able to

maintain the standard of living that the main part of Danes are able to maintain. Nevertheless, the

term “poor” is used in the following, because the literature often uses this term to characterize

people at the bottom of the income distribution.

9


The unit of analysis is the individual, although the household is the unit of calculation. The

household consists of one or two adults and children less than 18 years of age living with an

adult. For Denmark, it has not been possible to pool the income of cohabiting partners, because

income only exists for both partners if they are married. Children over 18-years of age living with

an adult are treated as singles. This will tend to overstate the estimated proportion living under

the poverty threshold.

The aggregate unemployment rate used in the estimations is not from the CLS database, but

instead it is the official annual figure from Statistics Denmark. The rate is defined as the

registered unemployed divided by the work force, which consists of the registered unemployed

and people in employment.

Data are present since 1980, but to avoid modelling left-censored spells, only people starting a

poverty spell in a year after 1980, are included, see Stevens (1999) and Devicienti (2000). So in

the first year of the 12-year period, the individual is non-poor and in the second year the

individual is poor. Therefore 11 years is the maximum number of years in poverty. Using this

method could have allowed a maximum of 17 years (1981-1997), but this would reduce the

number of observations, because fewer individuals are present for longer periods. The chosen 12

years is thus a compromise between sample size and the size of the observation window.

The subpopulation analysed in this paper consists of all persons aged 18-74 years who were

present in 12 consecutive years between 1980 and 1997. Data is thus a balanced panel containing

6,072 person-years or 552 persons. Individuals who do not have a complete 12-year sequence are

excluded from the analysis. To each poverty or non-poverty spell a vector of constant or time

varying demographic and labour market variables is attached. Some variables are included as

dummies and others in continuous form.

Although the lower age limit is 18 years, there are probably not many students included in the

sample, since only initially non-poor and then poor individuals are included. As students often

have low incomes, they will not meet the first criterion.

In order not to complicate estimations further, the initial conditions problem is not addressed in

this paper, although it is present, because of the conditions that the individual is non-poor in the

first year and poor in the second year of the 12-year period, see Heckman (1981).

10


Sample statistics are presented in Table A1 in the Appendix.

5. Estimation results

5.1. Aggregate exit and re-entry probabilities (only duration terms included)

Simple aggregate measures of exit and re-entry rates are obtained by only controlling for the

duration of poverty and non-poverty. Using the logit framework by maximizing the likelihood in

(9), but only with the presence of duration dummies

p

? and

n

d

? , so

d

e ijdt

p

exp( ?

d

)

? and

1?

exp( ? )

p

d

r ijdt

n

exp( ?

d

)

?

n

1?

exp( ? )

d

gives the estimates in Table 2. The exit and re-entry rates are calculated from the estimated

parameters by transforming back the logit estimates.

Table 2. Exit and re-entry parameter estimates and hazard rates of poverty and nonpoverty

spells. ML-estimation of (9), but only with duration dummies included

Duration (d), years

Estimate

(? )

p

d

Exit

St.error

(Estimate)

Rate

(e d )

Estimate

(? )

n

d

Re-entry

St.error

(Estimate)

1 -0.0121 0.0649 0.4970 -1.5699 0.0928 0.1722

2 -0.3271 0.0949 0.4189 -2.1773 0.1276 0.1018

3 -0.7062 0.1323 0.3304 -2.6613 0.1660 0.0653

4 -0.7234 0.1651 0.3266 -2.8111 0.1868 0.0567

5 -0.4326 0.2009 0.3935 -3.7425 0.1941 0.0231

6 -0.8728 0.2615 0.2947 -3.3103 0.2505 0.0352

7 -1.4685 0.3036 0.1872 -3.7508 0.3154 0.0230

8 -1.2766 0.4286 0.2181 -3.2340 0.2268 0.0379

9 -1.8778 0.6960 0.1326 -3.8421 0.3614 0.0210

10 -2.2970 0.9461 0.0914

Log likelihood -2,324.3

Rate

(r d )

11


All parameters, but one (poverty duration after 1 year), are highly significant. The logit estimates

implies that the probability of exiting poverty after one year of poverty is 49.7%, but after two

years of poverty the exit chance is reduced to 41.9%, and after 10 years of poverty there is a

much lower chance of escape (9.1%). The probability of re-entry into poverty from non-poverty

is 17.2% after one year in non-poverty, but only 2.1% after 9 years out of poverty. Thus escaping

poverty becomes more difficult the longer is the poverty spell and re-entering poverty is more

likely the shorter is the non-poverty spell. The cause of this negative duration dependence or state

dependence could be loss of motivation, loss of self-confidence or changing attitudes and

behaviour over time in response to being in the poor state and perhaps receiving social benefit.

This could make it more difficult to escape poverty if the poor for instance reduce job search

efforts. However, the calculations do not include any explanatory variables, which means that the

observed negative duration dependence could be caused by different characteristics among the

individuals, which is not modelled in Table 2.

Pedersen and Smith (1998) find 1-year exit rates for Denmark in the interval 75 to 90%, which is

much higher than reported here. This difference in hazard rates could be caused by Pedersen and

Smith’s data, which are an unbalanced sample containing a mixture of recent entrants and longterm

poor, while the figures in Table 2 are based on a more homogeneous population, with

hazard rates calculated for persons with the same duration of poverty or non-poverty. Pedersen

and Smith’s estimate of average poverty duration is also much smaller (1.25 years), as compared

to 3.3 years in Table 3. In contrast, their exit rates are close to the ones in Table 2.

The declining hazard of exiting poverty or non-poverty is usually observed in duration analysis,

see e.g. Hill et al. (1998) concerning American individuals in young adulthood, Stevens (1999)

and Devicienti (2000). On American data Stevens (1999) estimates a poverty exit chance of 53%

after one year, 22% after 5 years, but only 11% after 10 years, while Devicienti (2000) with UK

data has an exit rate of 41% after 1 year and 6% after 5 years. At the same time re-entry rates into

poverty are lower in Denmark (17% after 1 year, and 2% after 5 years), while they are very

similar in the UK (27% after 1 year, and 7% after 5 years) and the USA (27% after 1 year, and

8% after 5 years). Comparing the exit and re-entry rates implies a higher UK poverty persistence

than in Denmark and the USA, and the average number of years in poverty can be expected to be

the highest in the UK and the lowest in Denmark.

The exit rates in Table 2 can be used to estimate the number of years spent in poverty during an

11-year period, if a person enters poverty in the first year of the period, in the following way

12


(single spell approach). After 1 year of poverty 49.7% leave poverty, so 49.7% of the sample

have a poverty of 1 year out of 11 years, under the assumption that they do not re-enter poverty in

the 11-year period. In the beginning of year 2, 50.3% of the original sample is left (1 minus exit

rate at year 1), and after two years of poverty 41.9% will escape poverty, thus

0.419x0.503=21.1% have two years of poverty. Continuing in this way, the fraction of people

who are poor for d years with the single spell approach is

d

? 1

d

(1 ? e s

s?

1

e ) , d={1,2,3, … }

where e s

is the exit probability after s years of poverty. The distribution according to duration in

the multiple spell approach is more complicated and is explained in Paragraph 5.2. Briefly, it is

worth noting, that re-entry is assumed possible in the multiple spells approach, which is in

contrast to the single spell approach, where only one spell for each individual is assumed.

Table 3. Distribution of years poor out of the next 11 years, if initially poor, %

Duration, years Single spell approach Multiple spells approach Actual

1 49.7 28.3 27.9

2 21.1 19.6 22.8

3 9.7 13.9 11.8

4 6.4 10.2 12.5

5 5.2 8.6 8.0

6 2.4 6.0 4.7

7 1.1 4.2 2.7

8 1.0 3.0 4.0

9 0.5 2.0 2.2

10 0.3 1.4 1.6

11 2.8 2.8 1.8

100 100 100

Average duration, years 2.4 3.5 3.3

Note: For single and multiple spells, 11 years duration actually represents durations of 11 years or more.

Using only the exit rates and not taking into account that people leaving poverty also sometimes

re-enter poverty, gives the figures in column 2 in Table 3. Compared to the actual distribution,

the single spell approach has approximately double the fraction of poor in one year. Generally,

13


lower chances of higher poverty durations implies that average duration for people entering

poverty is 2.4 years, compared to the actual 3.3 years. The single spell approach thus

underestimates the total time spent under the poverty line because it ignores that some individuals

experience multiple spells of poverty. Column 3 takes re-entry into account, giving a poverty

distribution that is much closer to the actual distribution of people entering poverty. One year of

poverty is almost the same as in the actual distribution and the same is true for the average

duration, which is estimated to be 3.5 years.

There has been some debate about whether poverty is a static phenomenon or whether there is

mobility in the income distribution, so that the same individuals are not always poor. Although

Table 3 does not answer this question, it is nevertheless clear that only about ¼ of individuals

entering poverty do not re-enter poverty in the next 10 years, implying ¾ will experience more

than a year in poverty. There is thus some tendency that poverty hits people who have been hit by

poverty in the past.

Applying the single spell approach clearly illustrates that the poverty distribution will be much

less precise and the average poverty duration will be unde restimated. This is true for Denmark as

well for the USA and the UK, see Table 4. For the three countries the preciseness of the two

approaches are measured by the mean of squared differences between the actual and the

estimated distribution of years in poverty. In all three countries the multiple spells approach is

much more accurate than the single spell approach. Mean square error for the distribution of

years in poverty is between 50 and 213 for the single spell approach and less than 18 for the

multiple spells approach.

14


Table 4. Comparison of single spell and multiple spells approaches to actual poverty

measures (distribution of years poor, average duration) in Denmark, the USA and the UK

USA

(10 years)

Stevens (1999)

UK

(6 years)

Devicienti (2000)

Denmark

(11 years)

Table 2

Mean square error 1)

Single spell approach 65.7 212.9 50.1

Multiple spells approach 17.8 11.4 2.4

Average duration, years

Actual 4.0 3.1 3.3

Single spell approach 2.7 2.2 2.4

Multiple spells approach 4.4 3.0 3.5

nc

1 c c 2

C

1) ? ( X

i

? Ai

) , where X i is the fraction with i years of poverty in a n c years period (10, 6 or 11) in country c (USA, UK or

nc

i?

1

Denmark). X is type of approach (Single spell or Multiple spells) and A is the actual distribution.

The average poverty duration is underestimated in all countries, when using the single spell

approach, whereas the multiple spells approach more accurately estimates the average duration.

Poverty duration for people entering poverty over a specified period is greater in the UK (51% or

3.1 years out of maximum 6 years) than in the US (40%) and Denmark (30%). Krause (1998)

examines poverty issues for Germany and presents the distribution of years in poverty for 1984-

1994. From his figures the average poverty duration is calculated to be 3.4 years or 31% of

maximum 11 years, which is close to the neighbouring Denmark. The higher average poverty in

the UK is perhaps surprising, because the European countries are usually expected to have a

better social safety net than in the USA. A reason for the ranking could be that the USA results

are based on an absolute poverty line, which is about 40% of median income, cf. Burkhauser et

al. (1995), while a relative poverty line defined as 50% of contemporaneous median equivalent

income is used for Denmark and 50% of mean equivalent income is used for the UK and

Germany. But the higher average for the UK very well reflects the international ranking of the

exit and re-entry rates mentioned earlier.

In Table 2, the duration term is included in a dummy form, e.g. a fully flexible specification

without imposing any structure on how the hazard rates depend on elapsed time since the start of

15


a spell. Estimation was also tried with including the duration in continuous form (d) together with

a cubic term (d 2 ) and an intercept (? ), implying exit and re-entry rates defined as (see also (1) for

a parametric representation of duration dependence):

e

ijdt

p p 2

exp( ?

p

? ?

1

d

p

? ?

2

dp

)

? and

p p 2

1?

exp( ? ? ? d ? ? d )

p

1

p

2

p

r

ijdt

n n 2

exp( ?

n

? ?

1

dn

? ?

2

dn

)

?

n n 2

1?

exp( ? ? ? d ? ? d )

n

1

n

2

n

p

These regressions show significant negative duration dependence ( ? =-0.2657,

1

p

p

n

n

n

SE[ ? ]=0.0816, ? =0.9205, SE[ ? ]=0.9704, and ? =-0.7112, SE[ ? ]=0.1085, ? =4.6937,

SE[

p

1

2

2

n

? ]=1.2577), with the best fit for the re-entry rates (predicted re-entry rates close to actual

2

re-entry rates). Making the same simulations as in Table 3 shows the same average duration (3.5

years), but the distribution of years in poverty is slightly different with greater weights to longer

durations.

1

1

2

5.2. Estimation with unobserved heterogeneity

In order to explain poverty duration more fully, the determinants of poverty (non-poverty) spell

beginnings and poverty (non-poverty) spell endings are found by introducing further variables in

the estimation. Apart from duration variables and heterogeneity terms, the following are included

(sample statistics are presented in Appendix):

- Gender: Male (reference), female

- Age: under 30 years (reference), 30-39 years, 40-49 years, 50-59 years and 60+ years

- Indicator for being single: Single, couple (reference)

- Number of children

- Education: Number of years of schooling

- Hours of work per year: Divided by 100

- Aggregate unemployment rate: Percent of workforce unemployed

As all duration dummies are included, normalization for the heterogeneity terms is required, so

that only two heterogeneity parameters are estimated. Here

Maximizing the likelihood in (9) gives the parameter estimates in Table 5.

? and

n

? are normalised to zero.

p

1

1

16


The heterogeneity term for poverty spells,

p

? , is highly significant, whereas the heterogeneity

2

n

term for non-poverty spells, ? , shows less significance. About 29%

2

(P 4

) of the population has

favourable unobserved characteristics, implying a much higher exit rate from poverty (logit of

0.9592) and a much lower re-entry rate into poverty (logit of –2.4322). 32% of the population has

very unfavourable unobserved characteristics, so they have low exit rates and high re-entry rates.

39% of the population has high exit rates, but also low re-entry rates, and almost none (0.01%)

has low exit rates and high re-entry rates. The consequences of poverty persistence for the two

middle heterogeneity cases are thus not clear when only looking at estimated parameters alone.

This is one reason for simulating distributions of years in poverty, which is the topic of the next

paragraph.

For Whites in the United States, Stevens (1999) has the same signs for the heterogeneity terms,

but with higher magnitudes and lower standard errors. In her estimations 96% of individuals are

characterized by high exit rates and low re-entry rates and 4% have low exit rates and high reentry

rates. There are almost none in the intermediate two cases. Devicienti (2000) does not

model heterogeneity.

Negative duration dependence in the re-entry rates is still present when controlling for other

variables. Except after 1 year and after 5 years of poverty, all exit rates are insignificant. This is

not surprising, because economic and demographic variables are now controlled for, implying

that the observed negative duration dependence in Table 2 is partly due to heterogeneity among

individuals: Those with higher hazards tend to leave poverty before those with low hazards,

leaving a group increasingly made up of low hazard people. Since we can only estimate the

hazard rate at time t for those who still have a chance of leaving poverty, the estimated hazard

will be more like the lower hazard as time passes. At the aggregate level this will show up as

duration dependence although it may simply be a reflection of different groups having different

(constant) hazard rates.

The fewer significant duration parameters compared to Stevens (1999), suggests that state

dependence for poverty spells is a greater problem in the USA than in Denmark.

17


Table 5. Exit and re-entry rate parameter estimates, with heterogeneity. ML-estimates

from (9)

Exit

Re-entry

Estimate St.error Estimate St.error

Woman -0.1616 0.1029 -0.2761 0.1238

Age: 30-39 years 0.0193 0.1319 -0.2581 0.1338

40-49 years 0.2500 0.1434 -1.0391 0.1537

50-59 years -0.2540 0.1763 -1.3844 0.1539

60+ years -0.0247 0.1807 -2.0255 0.1778

Indicator for being single -0.6235 0.1123 0.3434 0.1427

No of children -0.3508 0.0602 0.4832 0.0798

Education, years, incl. sch. 0.0545 0.0209 -0.1230 0.0225

Annual hours employed/100 0.0674 0.0107 -0.0653 0.0101

Aggregate unemployment rate, % -0.1217 0.0304 0.0604 0.0284

Duration: 1 0.3704 0.1786 -0.0016 0.1211

Heterogeneity

2 0.2182 0.1630 -0.3645 0.1789

3 -0.0549 0.1610 -0.7401 0.1871

4 -0.0081 0.1096 -0.7937 0.1740

5 0.3748 0.1676 -1.6013 0.2879

6 0.0843 0.2364 -1.0961 0.2530

7 -0.3694 0.3878 -1.4740 0.1600

8 0.0370 0.4011 -0.8609 0.2154

9 -0.6031 0.4716 -1.4257 0.1821

10 -0.8959 0.6007

p

? 0

1

p

? 0.9592 0.2341

2

n

? 0

1

n

?

2

Person type probability P 1 (

P 2 (

P 3 (

P 4 (

? ,

n

p

1

1

? ,

n

p

1

p

2

-2.4322 1.4412

? ) 0.3248 (estimate) 0.0714 (St.err.)

? ) 0.3850 (estimate) 0.0709 (St.err.)

2

? ,

n

? ) 0.0001 (estimate) 0.0000 (St.err.)

1

? ,

n

p

2

? ) 0.2901 (estimate) 0.1246 (St.err.)

2

Log likelihood -2,142.1

18


Simulation of years in poverty

Although the signs of estimated coefficients are interpretable, the magnitude is less so. In this

paragraph the coefficients in Table 5 are therefore used to calculate the distribution of years in

poverty by applying the methodology described in the following.

Define ḙ as the estimated exit rate from poverty after

d

d years of poverty and define rˆ d

as the

estimated re-entry rate into poverty after d years of non-poverty. The following fraction of the

population, who starts a poverty spell, will have 1 year of poverty out of the next 11 years:

P ( d

? 1) ?

9

1 ? (1 ? rˆ

s

)

s?

1


In the same manner the fraction with poverty in the whole period is calculated as:

P ( d

? 11) ?

10

?

s?

1

(1 ?

ˆ )

e s

Duration between 2 and 10 years of poverty is more difficult to illustrate (six years of poverty is

possible in 252 different ways), but the technique is similar: First, calculate the probability of all

sequences that lead to d years of poverty. Second, sum the probabilities that each lead to d years

of poverty. The data include 11 years, but the first year is with certainty a year in poverty. The

total number of different sequences is thus 1,024 (=2 11-1 ). This simulation approach is different

from Stevens (1999), who simulates the distribution of years in poverty by using estimated

coefficients and random draws from the logistic distribution on observable characteristics for

10,000 individuals beginning a poverty spell. Applying the simulation methodology in the

present paper on Stevens (1999) American exit and re-entry rates actually better replicates the

true American distribution of years in poverty, since the mean square error is reduced from 17.8

to 10.8 and average duration is reduced from 4.4 to 4.2 years, which is closer to the actual figure

of 4 years for the USA, see Table 4.

19


Table 6. Distribution of years poor, %

Duration

Average

1 2 3 4 5 6 7 8 9 10 11 Total (Years)

Representative caseExit rate 0.56 0.53 0.46 0.47 0.56 0.49 0.39 0.54 0.39 0.32

Re-entry rate 0.17 0.13 0.09 0.09 0.04 0.07 0.05 0.04 0.02

Distribution 30.0 19.2 14.2 11.2 8.9 6.2 4.3 2.9 1.7 0.9 0.7 100 3.2

-Only exit rate 56.2 23.0 9.6 5.3 3.3 1.3 0.5 0.4 0.1 0.1 0.2 100 1.9

Heterogeneity Low e, high r 14.2 13.3 12.7 12.3 12.3 10.3 8.7 6.9 4.6 2.6 2.0 100 4.6

Low e, low r 22.4 20.9 18.8 15.0 10.7 6.6 3.4 1.5 0.5 0.1 0.0 100 3.2

High e, low r 36.5 21.4 12.3 9.0 7.9 4.3 2.4 2.4 1.1 0.7 2.0 100 2.9

High e, high r 57.8 23.4 9.7 4.8 2.6 1.0 0.4 0.2 0.1 0.0 0.0 100 1.8

Notes: Simulations are based on the average of explanatory variables, see Table A1 in appendix, and estimated parameters in Table 5. The entries in row

4 represent the distribution of year in poverty, when a single spell approach is used.

High exit rate from poverty (e) means that the person has heterogeneity of type 2, so the logit of exit is increased by 0.9592 (estimate from Table 5)

Low exit rate from poverty (e) means that the person has heterogeneity of type 1, so the logit of exit is unchanged (normalised to zero in Table 5)

High re-entry rate into poverty (r) means that the person has heterogeneity of type 1, so the logit of re -entry is unchanged (normalised to zero in Table 5)

Low re-entry rate into poverty (e) means that the person has heterogeneity of type 2, so the logit of re-entry is reduced by –2.4322 (estimate from Table

5)

As estimated parameters are not a result of linear regression, the parameters must be evaluated at

some values for the explanatory variables. The evaluation point here is the vector of averages for

the different explanatory variables using all person years (see Table A1 in the Appendix). This

representative case is a 34-year-old (starting year average) single woman with 11 years of

education incl. schooling and 1 child living at home. She works 648 hours a year in a labour

market with 9.8% unemployment. Except for age, all variables are held constant through out the

11-year period. The effect of explanatory variables is calculated by changing one variable at a

time in the representative case. The exit and re-entry rates are then used to calculate distribution

of years in poverty and average poverty during the next 11 years.

Starting with the representative case, 63% of persons with the above mentioned characteristics

who enter poverty, only stay there for one, two or three years out of the following 11, see Table

6. 33% have a duration lasting 4 to 8 years, while 3% are severely poor, implying that poverty

lasts at least 9 years out of 11. 0.7% are always poor. This distribution of years in poverty implies

an average of 3.2 years in poverty out of 11 years. The representative case much resembles the

average of the population, see column three in Table 3. The slight underestimation of average

poverty duration is primarily because the actual distribution has a heavier right tail than the

simulated distribution. The distribution depends on exit and re-entry rates, and compared to Table

20


2, it is clear that the actual distribution has lower exit rates than the simulated distribution and

generally higher re-entry rates than those calculated from Table 5.

The single spell approached has been used in row 4 of Table 6. Using only the exit rates from

poverty, more than half (56%) of the poor would only stay 1 year in poverty as opposed to less

than 1/3 in the multiple spells approach. The distribution of years in poverty implies that on

average a poverty spell lasts for 1.9 years.

The estimated heterogeneity has great implications for the years spent in poverty and therefore

average poverty duration. It is seen that the 32% with the least favourable unobservable

characteristics (low exit rate and high re-entry rate) have on average 4.6 years in poverty, as

opposed to 1.8 years for individuals with favourable unobservable characteristics (high exit rate

and low re-entry rate), see Table 6. Therefore, when the former group is hit by poverty, they stay

there 2½ times longer than the latter group. The intermediate groups (low exit rate, high re-entry

rate and high exit rate, low re-entry rate) have an average poverty duration similar to the

representative person.

The heterogeneity parameters are included in the simulations in the following way. For each

person type (e.g. men, 40-49-years old or 5.7% aggregate unemployment) four distributions of

years in poverty are calculated from the four sets of exit and re-entry probabilities. The final

single distribution for each person type, which is presented in the Tables, is then calculated as a

weighted average of the four different distributions, which reflects the four different

heterogeneity combinations. The weights are P ,

1 P ,

2

P and

3 P . For instance the representative

4

case in row 3 of Table 6 is the weighted average of the last four rows.

21


Table 7. Distribution of years poor, %

Duration

Average,

years

1 2 3 4 5 6 7 8 9 10 11 Total

Gender Men 28.8 18.6 14.4 11.8 9.4 6.6 4.5 2.9 1.7 0.8 0.5 100 3.3

Women 30.9 19.5 14.0 10.7 8.5 5.8 4.1 2.8 1.8 1.0 0.9 100 3.2

Age


etween single men and single women. Men and women have slightly different routes to this

almost common average, because women have relatively fewer in the middle of the distribution

and more in the upper and lower tail than men, see Figure 1. Women thus have a little higher

inequality in the distribution of poverty than men.

Figure 1. Distribution of years poor, %

Worst case

Best case

Unem.: 12.4%

Unem.: 5.7%

Unemp.: +1%-p.

Work: +500 h

Work: +100 h

Educ.: +5 year

Educ.: +1 year

3 children

2 children

1 child

No children

Single

Couple

60+ years

50-59 years

40-49 years

30-39 years

Under 30 years

Women

Men

0% 20% 40% 60% 80% 100%

1-3 years 4-8 years 9-11 years

Age has a negative impact on poverty duration (Table 7), which is mainly due to significant age

effects on the re-entry rates, while exit rates are unaffected by age. Individuals with a starting age

less than 40 years have an average poverty duration around 3.2-3.5 years, while older individual’s

23


durations are between 2.3-2.8 years. This negative age effect is also found in Stevens (1999). A

likely reason for this pattern is that the young have lower wages and higher unemployment rates.

The children and marital parameters in Table 5 are all highly significant and with predictable

signs. More children or living without a partner thus reduce the exit rate from poverty and

increase the re-entry rate from non-poverty. An extra child in the family increases poverty

duration by about 0.9-1.2 years on average and living alone increases poverty duration by 1.1

years, see Table 7. Owing to non-linearities in the estimation, the impact of children is increased

with the number of children. The presence of children could have adverse effects because they

usually do not earn income, but they are included as a consuming unit. All else equal, the

equivalence scales imply lower income for fami lies with children. Further, the caring and rearing

responsibilities of parents means that employed hours and career prospects could be reduced,

causing lower income.

Schooling and working time also has the expected signs and is highly significant. However, the

effect on average duration is not of great magnitude. 5 years’ extra education or 500 hours more

work annually thus reduce the average poverty duration by 0.6-0.8 years. Measured in years the

effect is not great, but it is a reduction of 20-25% compared to the representative person. In

Stevens (1999) higher or further education reduces average poverty duration by 17-20%. An

explanation for the positive effect of education is found in the human capital theory, which

predicts a positive relationship between human capital (number of years of schooling) and hourly

wage rates or the probability of having a job.

The only macroeconomic variable included, the aggregate unemployment rate, has significant

and predictable signs. A tight labour market thus increases the poverty exit rate, because

employment chances are better and people hit by poverty therefore have better prospects of

escaping it. Low unemployment chances likewise reduce the re-entry probability. Thus a 1 %-

point increase in the aggregate unemployment rate increases the average poverty duration from

3.2 to 3.4 years.

The most recent annual unemployment rate for Denmark is 5.7% in 2000 compared to a

maximum of 12.4% (in 1993) when the last recession had the most severe effect on the labour

market. Using these two unemployment rates (assuming 5.7% and then 12.4% unemployment in

all years, e.g. a non-gradual or sudden change is simulated) implies average poverty duration of

2.5 and 3.8 years, or a reduction of about 35%, when the economy moves from high to low

24


aggregate unemployment. Therefore, over the business cycle, the unemployment rate may indeed

have great effects on time spent in poverty.

Unemployment effects reported here differ to those in Pedersen and Smith (1998), who also on

Danish data, conclude, that exit rates and re-entry rates are rather insensitive to macro economic

cyclical factors. The discrepancy may be due to the inhomogeneous data used in estimation of

hazard rates in Pedersen and Smith, see Paragraph 5.1.

High effects of unemployment over the business cycle suggest that although unemployment

benefits as well as other social benefits are comparatively high, the welfare state does not entirely

protect individuals from poverty in the case of rising aggregate unemployment.

Devicienti (2000) has a number of models in his study, but only for the model containing adults

does he get the same qualitative results regarding the aggregate (local) unemployment rate as in

this study.

To illustrate other possible analysis, a worst and a be st counterfactual is simulated. The best case

is a person with favourable observable as well as unobservable characteristics. It is a 40-year-old

man without children, but with the highest educational level (18 years) and working three times

longer than the average person in a labour market characterized by low aggregate unemployment

(7.9%). The opposite case is a young single mother (starting age 20 years) with three children,

low education (9 years), without work and living in a period with high unemployment (12.4 %).

The best case has an unobserved high exit rate and low re-entry rate, while the worst case has an

unobserved low exit rate and a high re-entry rate.

Individuals in the best case almost all only stay in poverty for one year. Only 5.7% stay another

year and less than ½% stay for 3 years. This implies average durations of 1.1 years. In the worst

case scenario more than half are always poor, once hit by poverty, while practically none of them

stay in poverty for less than 5 years. The average duration for this last group is 10.3 years out of a

maximum of 11 years of poverty.

The average poverty durations mentioned in this Paragraph are almost unaffected when leftcensored

spells included or when unobserved heterogeneity effects are not included, see the

results in Paragraphs A5.3 and A5.4 in the Appendix.

25


6. Conclusion

Poverty persistence has been modelled and estimated and the estimates have been used to

simulate distribution of years in poverty. This study confirms that the single spell approach is

quite inaccurate and clearly underestimates the total time spent in poverty, because the possibility

of re-entry is not taken into account. The multiple spells approach much more precisely replicates

the actual distributions of years poor.

Simulations show that estimated coefficients have some impact on the distribution of years poor

and thereby on the average total time spent in poverty over a given number of years. In particular,

education and working hours significantly increase exit rates from poverty and decrease re-entry

rates back into poverty, while the presence of children and living without a partner significantly

decrease exit rates and increase re-entry rates. Low unemployment in the economy is also

important in lowering the average duration of poverty. Gender is less important for the

determination of total time spent in poverty.

The hazard rate model with heterogeneity is significantly better than the model where unobserved

heterogeneity is ignored. However, the effects on the distribution of years poor are not

remarkable. The inclusion of left-censored cases like-wise does not greatly alter the results.

Although the duration of poverty is an important dimension of poverty, it is also important to

extend the analysis, to include other dimensions, e.g. the severity of poverty.

26


References

Aaberge, R., A. Björklund, M. Jäntti, P.J. Pedersen, N. Smith and T. Wennemo (1997):

”Unemployment Shocks and Income Distribution How Did the Nordic Countries Fare During

their Crises?” Discussion Papers 201, Statistics Norway

Aaberge, R. and I. Melby (1998): ” The Sensitivity of Income Inequality to Choice of

Equivalence Scales”, Review of Income and Wealth, vol. 44, no. 4

Bishop, J.A., J.P. Formby and B. Zheng (1999): “Distribution Sensitive Measures of Poverty in

the United States”, Review of Social Economy, vol. 57, no. 3

Bane, M.J. and D. Ellwood (1986): “Slipping Into and Out of Poverty: The Dynamics of Spells”,

Journal of Human Resources, vol. 21, no. 1

Buhmann, B. (1988): “Equivalence Scales, Well-Being, Inequality, and Poverty: Sensitivity

Estimates across Ten Countries Using the Luxembourg Income Study (LIS) Database”, Review

of Income and Wealth, vol. 34, no. 2

Burkhauser, R.V., B.A. Butrica and M.C. Daly (1995): “The Syracuse University PSID-GSOEP

Equivalent Data File: A Product of Cross-National Research”, All-University Gerontology

Center, Maxwell School of Citizenship and Public Affairs, Syracuse University

Burkhauser (1996), R.V., T.M. Smeeding, J. Merz: “Relative Inequality and Poverty in Germany

and the United States Using Alternative Equivalence Scales”, Review of Income and Wealth, vol.

42, no. 4

Coulter, F., F. Cowell and S. Jenkins (1992): “Equivalence scale relativities and the extent of

inequality and poverty”, The Economic Journal 102

Devicienti, F. (2000): “Poverty Persistence in Britain: A Multivariate Analysis Using the BHPS,

1991-1997”, Institute for Social and Economic Research, University of Essex

27


Duncan, G. (1983): “The Implications of Changing Family Composition for the Dynamic

Analysis of Family Economic Well-Being”, in “Panel Data on Incomes” by A.B. Atkinson,

London School of Economics

Duncan, G. and W. Rodgers (1991): “Has Children’s Poverty Become More Persistent?”

American Sociological Review, vol.56, no. 4

Eberwein, C, J. Ham and R. Lalonde (1997): “The Impact of Being Offered and Receiving

Classroom Training on the Employment Histories of Disadvantaged Women: Evidence from

Experimental Data”, Review of Economic ”, American Sociological Review, vol. 56, no. 4

Danish Economic Council (2001): “Dansk økonomi” (Danish Economy), Autumn 2001

Findlay, J. and R.E. Wright (1996): “Poverty and the Intra-household Distribution of Resources”,

Review of Income and Wealth, vol. 42, no. 3

Förster, M.F. (1994): “The Effects of Net Transfers on Low Incomes among Non-elderly

Families”, OECD-Economic-Studies, no. 22

Gallie, D. and S. Paugam (2000): “Welfare Regimes and the Experience of Unemployment in

Europe”, Oxford University Press, London, UK

Gustafsson, B. (1995): “Assessing Poverty: Some Reflections on the Literature”, Journal of

Population Economics, vol. 8, no. 4

Hauser, R. and H. Fabig (1999): “Labor Earnings and Household Income Mobility in Reunified

Germany: A Comparison of Eastern and Western States”. Review of Income and Wealth, vol. 45,

no. 3

Heckman, J.J. (1981): “The incidental parameters problem of initial conditions in estimating a

discrete time-discrete data stochastic process” in C.F. Manski and D. McFadden’s (eds.)

“Structural Analysis of Discrete Data with Econometric Applications, Cambridge, MIT Press

28


Hill, M., D. Hill and R. Walker (1998): “Intergenerational dynamics in the USA: poverty

processes in young adulthood”, in L. Leisering and R. Walker (eds.): “The Dynamics of Modern

Society – Poverty, policy and welfare”, The Policy Press, University of Bristol, UK

Krause, P. (1998): “Low income dynamics in Unified Germany” in L. Leisering and R. Walker

(eds.): “The Dynamics of Modern Society – Poverty, policy and welfare”, The Policy Press,

University of Bristol, UK

Lancaster, T. (1990): “The Econometric Analysis of Transition Data”, Cambridge University

Press, Cambridge

Meyer, M.D. (1990): “Unemployment Insurance and Unemployment Spells”, Econometrica, vol.

58, no. 4

Ministry of Economic Affairs (1993): “Lovmodel” (Law Model), Denmark

Moffitt, R. and M. Rendall (1995): “Cohort Trends in the Lifetime Distribution of Family

Headship in the US, 1968-1985”, Demography, vol. 32, no. 4

Nicholson, J.L. (1979): “The assessment of poverty and the information we need” in HMSOs

“Social Security Research: the Definition and Measurement of Poverty”, London

Pedersen, P. and N. Smith (1998): ”Low Incomes in Denmark. 1980-1995”. Centre for Labour

Market and Social Research. Working Paper no. 19

Sen, A. (1976): “Poverty: An ordinal approach to measurement”, Econometrica, no. 44

Stevens, A.H. (1994): “The Dynamics of Poverty Spells: Updating Bane and Ellwood”,

American Economic Review, vol. 84, no. 2

Stevens, A.H. (1999): “Climbing Out of Poverty, Falling Back In”, The Journal of Human

Resources, XXXIV, no. 3

Stewart, M.B. and J.K. Swaffield (1999): “Low Pay Dynamics and Transition Probabilities”,

Economica, no. 66

29


Appendix

Table A1. Sample statistics over all person years, 1981-1997, 6,072 observations (average

etc. calculated over all years)

Mean St. error Minimum Maximum

Woman 0.544 0.498 0 1

Age 38.813 13.382 18 74

Single 0.601 0.490 0 1

Children 0.543 0.939 0 7

Education, years 11.437 2.574 9 18

Annual work hours/100 6.484 7.113 0 34.96

Aggregate unemployment rate, % 9.768 1.311 7.9 12.4

Fraction in different brackets

Age, years Under 25 0.144

26-45 0.569

46-54 0.125

55-64 0.106

65+ 0.056

Number of children None 0.678

01-feb 0.274

3+ 0.048

Education, years 9 0.348

10 0.121

11 0.011

12 0.327

14 0.075

16 0.061

18 0.056

Annual number of working hours None 0.413

1-500 0.134

501-1,000 0.117

1,001-2,000 0.332

2,000+ 0.005

30


A5.3. Estimation without unobserved heterogeneity

To detect any bias in estimates when not modelling unobserved heterogeneity estimation was

made without the heterogeneity terms in (9).

Table A8. Exit and re-entry rate parameter estimates, without

heterogeneity. ML-estimates from (9), excluding ? ’s

Exit

Re-entry

Estimate St.error Estimate St.error

Woman -0.1413 0.0951 -0.2903 0.1176

Age: 30-39 years 0.0341 0.1058 -0.2461 0.1288

40-49 years 0.2473 0.1310 -1.0360 0.1308

50-59 years -0.2155 0.1522 -1.3496 0.2143

60+ years 0.0240 0.1610 -1.9272 0.2650

Indicator for being single -0.5645 0.1091 0.2286 0.1365

No of children -0.3319 0.0548 0.4045 0.0668

Education, years, incl. schooling 0.0471 0.0215 -0.1338 0.0226

Annual hours employed/100 0.0601 0.0105 -0.0599 0.0094

Aggregate unemployment rate, % -0.1181 0.0346 0.0279 0.0299

Duration: 1 1.0093 0.3852 0.2243 0.2171

2 0.7720 0.3925 -0.2058 0.2307

3 0.4207 0.4010 -0.6160 0.2532

4 0.4042 0.4119 -0.7114 0.2679

5 0.6981 0.4132 -1.5673 0.3238

6 0.3530 0.4570 -1.1118 0.2964

7 -0.1501 0.5764 -1.5209 0.2609

8 0.2084 0.4663 -0.9774 0.3154

9 -0.4229 0.8230 -1.6121 0.2912

10 -0.7981 0.6146

Log likelihood -2,150.9

Compared to Table 5, the parameters in Table A8 generally have a lower ratio between estimates

and their standard errors. On a 5% significance level, the parameters of education and duration in

the exit regression, and the parameters of single, aggregate unemployment and duration 2 in the

re-entry regression are significant in Table 5, but not in Table A8.

31


Based on the two likelihoods in Table 5 and A8, there is a clear rejection of a model reduction

from the one with heterogeneity to the one without heterogeneity. The question is whether this

has any practical significance, for instance for the simulated durations. Because, looking at the

parameters, no major differences are revealed, except for the duration parameters. A simulation

based on the parameters in Table A8, gives the poverty distribution in Table A9.

Table A9. Distribution of years poor, % (without heterogeneity)

Duration

Average

1 2 3 4 5 6 7 8 9 10 11 Total (Years)

Representative case 27.3 20.4 15.6 12.0 9.2 6.3 4.1 2.6 1.4 0.7 0.6 100 3.2

Gender Men 25.2 20.0 16.1 12.8 9.9 6.8 4.3 2.6 1.3 0.6 0.5 100 3.3

Women 28.8 20.6 15.1 11.4 8.8 5.9 3.9 2.6 1.4 0.7 0.8 100 3.2

Age


Stevens (1999) also present estimates, where unobserved heterogeneity is ignored, but without

concluding about the differences. Inspecting the results shows that her estimated parameters are

also only little affected by the modelling of unobserved heterogeneity on American data.

A5.4. Estimation including left censored spells (without unobserved heterogeneity)

Until now a person was only included in the sample if the poverty spell started after the start of

the sample. This was to avoid left-censored spells that can bias estimated hazard rates. To see

how left-censored spells would affect the result, estimation is made with left-censored spells

included for the same time period, see Table A10.

Table A10. Poverty estimation with left censored spells (15,180 person years, 1,380 persons)

ML-estimation of (9), without heterogeneity Hazard rates Distribution, %

Exit Re-entry Exit Reentry

Estimate St.error Estimate St.error

Woman -0.080 0.062 -0.223 0.084

Age: 30-39 years -0.212 0.102 -0.289 0.125

40-49 years -0.182 0.107 -1.061 0.153

50-59 years -0.442 0.133 -1.338 0.198

60+ years -0.313 0.126 -1.900 0.200

Indicator for being single -0.551 0.080 0.294 0.103

No. of children -0.326 0.045 0.419 0.063

Education, years, incl. schooling 0.063 0.016 -0.124 0.020

Annual hours employed/100 0.076 0.007 -0.093 0.007

Actual Simu -

lated

Aggregate unemployment rate, % -0.136 0.024 -0.030 0.024

Duration: 1 0.757 0.247 0.711 0.202 0.544 0.194 24.7 26.6

2 0.581 0.252 0.333 0.211 0.500 0.142 18.8 21.0

3 0.468 0.262 -0.044 0.223 0.420 0.078 14.1 16.0

4 0.354 0.269 -0.534 0.245 0.392 0.049 10.5 11.6

5 0.142 0.277 -0.487 0.253 0.343 0.052 8.4 8.4

6 0.936 0.275 -0.704 0.277 0.536 0.042 9.1 6.6

7 -0.236 0.342 -0.874 0.306 0.263 0.036 3.0 4.1

8 -1.044 0.469 -0.483 0.292 0.138 0.052 3.0 2.5

9 -0.436 0.431 -1.129 0.370 0.227 0.028 2.8 1.4

10 -0.498 0.481 0.216 2.0 0.8

11 3.8 0.9

Total, % 100 100

Average duration, years 3.7 3.2

Note: Hazard rates and the implied distribution of years poor is for the representative person in the new sample including left censored spells

(averages over all person years, except age, which is the average age at spell start )

33


Compared with the estimations and simulations in paragraph 5.3, inclusion of the left-censored

cases has only little impact on the estimated parameters. Many exit parameters are still

insignificant, but the significant re-entry rates are close to the parameters in Table 8. The

simulated distribution deviates somewhat from the new actual distribution. The average duration

is estimated to be 3.2 years, while the new actual duration is 3.7. Compared to the actual

distribution in the case without the left-censored observations (Table 3), the inclusion of leftcensored

spells does not give poorer predictions. The estimated duration of 3.2 years is thus close

to the actual distribution of 3.3 years in Table 3. Effects of variables (not shown) are also close to

the effects presented in Table A9. This insensitivity to inclusion of left censored spells is also

found in Stevens (1999).

34

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