Paper: Bane & Ellwood (1986)

Slipping into and out of Poverty: The Dynamics of Spells

Mary Jo Bane, David T. Ellwood

... journal, year, issue, etc.

## 0. Intro

Primary findings:

* Many people have very short spells of poverty
* Yet, the few with long spells account for the majority of the poor at any given time
* Some analyses of beginning and ending events of poverty spells

## 1. Describing Dynamics - previous research

Three primary approaches have used to describe the dynamics of various types of behavior (not just poverty). The bulk of research uses approaches 1 and 2; this paper uses approach 3.

### 1.1 Error structure

Any estimated longitudinal model implicitly or explicitly provides a model of intertemporal dynamics. Typically, the dynamics are subsumed in the error structure, allowing for both permanent and transitory components. Post-estimation, it is possible to examine the frequency and duration of poverty based on the estimated structure of earnings.

All deviations from permanent income tend to be treated as random and behaviorally equivalent in these models. Yet, not all disturbances lead to the same sort of paths/dynamics. Often, these disturbances are of interest in their own right; in the study of dynamics the changes themselves are the driving force. Hence, it is unfortunate to treat the poverty entry and exit events as homogeneous and largely unobservable disturbance terms.

### 1.2 Tabulations of frequency over fixed time frame

This method (e.g used by Duncan) looks at the proportion of people who are poor over a fixed time frame, usually 8 or 10 years. Then, one can tabulate how many people for poor for e.g. 1/10, 2/10, 3/10, ... 9 out of 10 years, etc. Quite simple to use.

But, again no attention on the events that lead people into and out of poverty. In addition, the measure can be misleading (see paper for example).

### 1.3 Spell durations and exit probabilities

Consists primarily of measuring spell lengths, and then producing the distribution? Simple and comprehensible way to summarize information.

In addition, the events associated with movements into and out of poverty can be investigated, which is of major interest in itself. The characterization of entry and exit events of poverty is a key innovation of this paper.

## 2. Methodology

Use PSID 1970-1982, basically in three steps: (1) identify spells---continuous periods during which income is below the poverty line, (2) calculate exit probabilities, and (3) use these exit probabilities to generate distributions of spell lengths.

### 2.A Definition of Spells

They classify a unit as poor if income is below a standard (calculated based on HH size). They:

* Include all cash transfers in the definition of income yet exclude in-kind transfers.
* The PSID provides such a need standard, that is essentially equivalent to the Census Bureau and OMB.
* Since the PSID finds more income than the CPS, inflate this standard by 25% to make numbers comparable to headline.
* Exclude those who began a poverty spell when 65 or older.
* Define a spell as beginning in the year that income is first below the line after having been above it, and ending when income is above it after it was below the line.
* One-year spells are eliminated if they begin or end with an income change of less than one-half the needs-level.

### 2.B Calculation of Exit Probabilities

* Use data on all spells whose start is observed
* Spells with an observed start but censored at the end were included in the calculation of exit probabilities in all but the censored year
* Since the unit of observation are spells, persons with multiple spells were included for each spell.
* Hence, sample sized large for short spells and decreasing in length of the spell. Calculate exit probabilities for 9 years, assume years 10-30 are stable, and assume no spells last longer than 30 years.

### 2.C Beginning and Ending Events

* For all spells for which and start or end was observed, they attempted to identify the beginning or ending event.
* Classify such events into mutually exclusive categories, looking for the primary cause of moving into poverty.
* They develop an hierarchical classification system: (1) look for change in head of HH within the previous two years, (2) determine if change in income/needs ratio was influence more by the income or needs.

## 3. Exit Probabilities

Table 1 shows the exit probabilities derived from the PSID. Clearly, the longer a person is poor the less likely it is that he or she will escape poverty. The probability of exiting fall from 45% in year one to 21% in year four.

These declining exit probabilities could be for two reasons: (1) poverty itself makes it more difficult to leave, or (2) this is simply a result of heterogeneity in the poverty population where those with persistent-poverty characteristics make up a larger and larger portion of the poverty population as the transitorily poor exit in the earlier years.

## 4. Calculation of Distributions

From the probabilities in section 3, three important distributions are calculated:

1. The distribution of spell lengths:

D
(
1
# )
p
(
1
)

{\displaystyle D(1)=p(1)}

,

D
(
2
# )
p
(
2
)
(
1
−
p
(
1
)
)

{\displaystyle D(2)=p(2)(1-p(1))}

,

D
(
3
# )
p
(
3
)
(
1
−
D
(
1
)
−
D
(
2
)
)

{\displaystyle D(3)=p(3)(1-D(1)-D(2))}

, etc. such that:

D
(
t
# )
p
(
t
)
[
1
−

∑

# j
1

t
−
1

D
(
j
)
]

{\textstyle D(t)=p(t)[1-\sum \_{j=1}^{t-1}D(j)]}

.
2. The distribution of completed spells for the poor at a given time: based on exit probabilities, calculate the (prospective) distribution of completed spell lengths of all those currently poor.
3. The distribution of uncompleted spells for the poort at a given time: the how long the currently-poor have been poor up to that time.

[I AM NOT CLEAR EXACTLY WHAT 2 AND 3 ARE???] (becomes clear from section 5)

## 5. The Persistence of Poverty

How long does poverty last? The answer depends on whether we're interested in the ever-poor group or currently-poor group. Only a small fraction of the population will be chronically poor, but people with long poverty spells make up a sizable part of the currently-poor at any given time.

(1) distribution of spell lengths, (2) distribution of spell lengths of the currently poor, (3) distribution of length of current spell of the currently poor.