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\begin{document}
\title{Choosing to become a lost cause: the perverse effects of benefit
preconditions}
\author{\textbf{Paul Frijters}\thanks{%
Corresponding author. Free University Amsterdam and Tinbergen Institute.
Faculty of Economics, de Boelelaan 1105, 1081 HV Amsterdam, the Netherlands,
pfrijters@econ.vu.nl. \newline
I thank Jaap Abbring, Aico van Vuuren and Rob Alessie for helpful comments
on earlier versions of the paper.}\textbf{\ and Lisa Farrell} \\
%EndAName
\textit{Preliminary. Do not quote.}}
\maketitle
\date{}
\begin{abstract}
In this paper it is argued that preconditions for welfare benefit
entitlements based on labour market prospects can be counterproductive when
they create an incentive for individuals to abstain from any investment
earlier in life that could improve future prospects. Benefit entitlements
based partly on investments made prior to labour market entry are then
Pareto-improving.\newline
Keywords: benefits, job search, irreversible investments.\newline
Yel-codes: J20, J60
\end{abstract}
\section{Introduction}
In many OECD countries in the last few decades, there has been a tendency to
make benefits more and more contingent on low potential. Blundell and
McCurdy (1999) for instance mention that in many US states, total welfare
payments (including food stamps, child benefits and housing support) are
substantially higher for lone mothers with children than for single men in
unemployment. In Holland, unemployed individuals are ranked according to the
ease with which they would be able to find a job (=labour market potential)
and those with low labour market potential are not required to search for
jobs, effectively making them entitled to higher net benefits. Similar
arrangements hold in many EU-countries.
The basic argument for basing benefits (and taxes) on potential are in order
to avoid moral hazard problems (Akerlof 1978). Restricting benefit
entitlements can reduce the number of people in the poverty trap, i.e. the
number of individuals for whom looking for work pays less than remaining on
benefits. Such poverty traps are well-illustrated by Harris (1993, page
456-457) who argues that many households in US inner-cities regard benefits
as a career-choice. Having stringent benefit conditions reduces the number
of individuals that can do this. This moral hazard aspect of UB has been
extensively studied in the literature (e.g. Hopenhayn and Nicollini, 1997).
When we also consider choices that are made before the labour market and
that are furthermore irreversible (such as schooling or fertility), the
reliance on indicators of having a very low potential for obtaining and
maintaining good jobs can work counterproductive though. Faced with benefits
that are contingent on having no opportunities on the labour market,
individuals on the `margin' of the talent distribution face a stark choice
earlier in their lives. They can make investments that will give them some
chance of good future jobs, but that will cost them entitlement to welfare
benefits, or they can abstain from any such productive investment altogether
in favour of irreversible choices that actually make the future job market
prospects bleak. Looking forward, they may choose to become `a lost cause'
in order to be eligible for welfare payments.
The study of Harris (1993) also highlights this downside. Harris tries to
make plausible that the US inner city phenomenon of households with several
generations of child-rearing women without husbands can be partially
attributed to the fact that benefits are withdrawn if husbands would be
present. A similar forward-looking mechanism is implicit in studies that
look at the effect of welfare benefits on fertility choices of teenagers in
the US. Rosenzweig (1999) finds a positive response of out-of-marriage
fertility of women as a result of increases in benefit entitlements to the
AFDC program. Clarke and Strauss (1998) find elasticities of illegitimacy
with respect to levels of welfare payments of around 1.5. Looking at the
relationship between various human capital investments in the NLSY,
Klepinger et al. (1999), find that low fertility and low formal education
and low work experience all correlate positively with one another and reduce
future work opportunities. Havemann and Wolfe (2001) find further
indications that US youngsters do anticipate the effect of their actions on
future received benefits and change their fertility choices accordingly.
In this paper the possibility that irreversible choices earlier in life may
be negatively affected by benefits contingent on low potential is examined
in further detail. The focus on choices made before entering the labour
market sets the analysis apart from current models which highlight the
distortionary effect of benefits, such as that by Ljungqvist and Sargent
(1998) or the papers discussed in Blanchard and Wolfers (1999), where
unemployment benefits only have an effect on the characteristics of the
individuals \textit{after} entering the labour market.
A simple equilibrium model is developed where individuals on the labour
market choose a search effort that is unobservable. This search effort is
combined with labour market potential to produce a job-finding probability.
Given a level of labour market potential, we get the standard finding that
unemployment benefits reduce the incentives for finding jobs and reduce
search effort.
We then extend this standard set-up with a first, pre-labour market, period
in which individuals who differ in initial talent have to spend effort to
increase their future labour market potential. Governments are assumed to
give a benefit entitlement to all those with a labour market potential below
a certain cut-off point. The fact that benefits are only begotten if labour
market potential is low enough, has the effect that very high talented
individuals behave as if there were no benefits at all, whereas very low
talented individuals behave as if they were certain of benefit entitlement.
Individuals with talents in a certain middle range will however make less
effort to improve their labour market potential than they would have done if
there were no benefits or if there was a universal benefit. This reduces the
average labour market potential and increases actual unemployment rates.
This effect also leads to the possibility of multiple equilibria of poverty
levels at constant levels of the government budget: in equilibria with
stringent benefit entitlement requirements, these stringent requirements can
lead to very low levels of prior investments, which leads to high
unemployment and poverty later. In equilibria with less stringent benefit
entitlement requirements, individuals invest more effort in previous periods
and subsequent unemployment and poverty are lower.
Governments can improve the outcome by conditioning benefits not only on
actual labour market potential, but also on invested effort, such as school
attendance. Under quite general conditions, giving benefit entitlements
conditional on minimum effort requirements is Pareto-improving. The higher
the labour market potential, the higher the minimum effort requirements.
Equivalently, given a certain level of labour market potential, the higher
the reward for having low initial talents, which is an argument for positive
discrimination (Coate and Lowry 1993).
Then we look at what would be the optimal allocation of benefits under
welfare maximization. The finding there is that under most search
technologies benefits should increase with previous effort in order to give
individuals incentives to increase their labour market potential. Only when
previous effort and search effort are perfect substitutes, any conditioning
on earlier effort is ineffective because individuals will then substitute
later search effort for previous effort without altering their job-finding
probabilities.
As a final model exercise, the results of the simple two-period model are
generalised to an infinite horizon dynamic environment, which is not found
to qualitatively alter the previous results.
The pen-ultimate section then discusses possible candidates as indicators of
early life effort, i.e. truancy, school effort and teen pregnancy, and
discusses the empirical facts known about them. Although truancy and school
effort would be prime candidates to base benefits on, it appears that there
is virtually no reliable historical data available on them. On teenage
fertility, much more is known. We add to the knowledge on US data by looking
at fertility choices and welfare payments in the UK. It turns out that there
does appear to be a strong correlation between both the level and dynamics
of teenage fertility and benefit preconditions that effectively bar young
women without children from benefits.
The final section concludes.
The contribution of the model to existing theoretical literature on moral
hazard and benefits is subtle: the model of Heckman et al. (1998) is one of
many that explicitly looks at the relation between human capital formation
and later uncertainty. However, in their model uncertainty is homogeneous
and not subject to choice. Niccolini and Hopenhayn (1997), in much simpler
framework, already provide a model with which one can calculate one-shot
optimal benefit paths that take account of current moral hazard. This model
was extended by Zhao (2000) to allow for benefits to depend on full labour
market histories, including earlier effort that affected both employment
risks and income risks. Although Zhao's model is only solved analytically
for the very restrictive case that there are only two possible effort level
choices, it can in principle be extended quite easily to be able to compute
optimal benefits for any parametrisation of the model in this paper also.
Hence, this papers theoretical contribution is that it analytically solves
the problem of the effect of benefits conditional on low labour market
potential when effort levels are continuous. Contrary to any of the
mentioned papers, this paper also analyses what pareto-improvements are
possible under current circumstances, quite apart from what would be optimal
in a more abstract welfare maximising sense. The empirical contribution is
that it uses macro-data to argue that teenage fertility is related to
benefit preconditions.
\section{The Model}
\subsection{The second period}
Consider a continuum of individuals with an observable labour market
potential $\alpha >0$ which has a cumulative probability distribution
function $A(\alpha )$.
Individuals search for jobs and have a probability of finding a production
site equal to 1$>g(\alpha ,s)>0,$ where $s>0$ can be seen as the effort put
into search the second period. The standard search assumptions apply: $%
g(0,0)=0,$ $g(\infty ,\infty )=1,$ $g_{\alpha },g_{s}\geq 0,$ $%
g_{ss},g_{\alpha \alpha }<0$. Throughout, $s$ will be regarded as
unobservable and is the source of a moral hazard problem. If individuals
find a production facility, they produce and receive an income net of taxes
equal to P.\footnote{%
An important alternative to this type of economy with production sites (such
as the island analogy of Galor and Lach, 1990), is to have a search model in
the vein of Pissarides (1990). In those latter models, search frictions also
matter for wages and individual behaviour has macro-economic spillover
effects through matching. Hence such a set-up creates two extra market
distortion, namely wage distortions and search externalities. Wanting to
focus on moral hazard as the main source of market imperfection, we abstract
from these other distortions, as is also done by for instance Moen (1997).}
Jobs are thus homogeneous, which means we abstract from any
productivity-increasing effect that benefits may have when jobs are not
homogeneous and benefits improve incentives for looking for the right jobs
(such as in Acemoglu and Shimer 1999, 2000, or Marimon and Zillibotti, 1999).
Individuals maximize:
\begin{eqnarray*}
U(y,e,s) &=&u(y)-s-e \\
e,s &\geq &0
\end{eqnarray*}
where $u(y)$, ``financial utility'', is strictly concave, increasing and
with $u(0)<0$; $y$ denotes monetary income; $e$\ denotes an effort level
made earlier in life and is for now taken constant and unobservable.
As in Gruber (1997) and Acemoglu and Shimer (1999, 2000), we assume that the
basic motivation behind benefits is risk-aversion on the part of
individuals. Here, this is labelled as poverty relief: the government has a
fixed budget M to spend on poverty relief that can be spent on entitlements
to unemployment benefits b. Poverty is defined as having a financial utility
less than a fixed level, say 0. Minimizing poverty then means that benefits
are such that those on benefits are exactly on a financial utility of 0.
Hence b solves $u(b)=0.$
For the optimal level of search intensity of an individual there has to hold
\begin{equation*}
\lbrack u(P)-u(b\ast B(\alpha ))]g_{s}-1=0
\end{equation*}
where $B(.)$ is one if an individual is entitled to benefits and zero
otherwise. From this condition it directly follows that search intensity
will be lower when an individual is entitled to benefits.
We assume policy to be to give benefit entitlements first to individuals
with the lowest labour market potential and upwards until the available
budget runs out, which occurs at $\alpha ^{\ast },$ which has to solve
\begin{equation}
\alpha ^{\ast }=\arg \{b\int_{0}^{A(\alpha ^{\ast })}[1-g(\alpha ,s(\alpha
))]dA(\alpha )=M\} \label{e2}
\end{equation}
Hence $B(\alpha )=I_{\alpha ^{\ast }>\alpha }.$ Whether this is actually
minimizes the number of individuals living in poverty for a given
distribution of $\alpha $ is unknown\footnote{%
In the appendix it is shown that this policy minimizes the number of people
in poverty only for specific forms of $g:$ it is only poverty minimizing if $%
0\geq \frac{d\{g(\alpha ,s|B=0)-g(\alpha ,s|B=1)\}}{d\alpha }$ which will be
the case iff $0\geq \frac{d\frac{\partial g(\alpha ,s(\alpha ,b))}{\partial b%
}}{d\alpha }$ which is the case iff $g_{\alpha s}\geq g_{s}\frac{g_{ss\alpha
}}{g_{ss}}$ which for instance arises when $\alpha $ and $s$\ are perfect
substitutes. When they are complements, $\frac{d\frac{\partial g(\alpha
,s(\alpha ,b))}{\partial b}}{d\alpha }>0$ and it would actually be poverty
minimizing to give benefit entitlements to those with high potential. Then
the justification for giving benefits to those with lower $\alpha $ would
have to depend on other considerations, such as valuing equal \textit{%
expected} utility.} but the level of $\alpha ^{\ast }$ is common knowledge
and individuals can take account of this in a previous period.
\subsection{The first period: endogenous $\protect\alpha $}
Suppose individuals live two periods. The second period is as described
above. In the first period, labour market potential is produced, i.e. $%
\alpha =q\ast e.$ Here $q$ denotes an non-negative innate talent or quality
q which is drawn from a cumulative distribution $Q$ with $Q$(0)=0. In this
first period individuals must choose their effort level $e$, which can be
interpreted as school attendance, time spent making homework, making sure to
use contraceptives, etc.
We find the rational expectations equilibrium by solving individual
behaviour for a given $\alpha ^{\ast }$. In equilibrium, the outcome of
these choices, i.e. A($\alpha |\alpha ^{\ast }$), must solve (\ref{e2}).
Such an $\alpha ^{\ast }$ is termed a feasible $\alpha ^{\ast }$.
Given $\alpha ^{\ast },$ individuals have to take account of the fact that
when they choose an $e$ that is very high, they may become ineligible for
benefits the second period. If benefits were not dependent on $\alpha ,$ the
envelope theorem tells us that individuals would set $e$ such that
\begin{eqnarray}
qFg_{\alpha } &=&1 \label{e10} \\
s.t.\text{ e} &\geq &0 \notag
\end{eqnarray}
with $F=u(P)-u(b)$.
Denote the resulting level of $\alpha $ by $\alpha _{F}(q)$ whereby the
subscript denotes that this is the level of $\alpha $ when the utility
difference between work and unemployment is F. The level of $\alpha $ when
the utility difference between work and unemployment without benefits is $%
E=u(P)-u(0)$ is likewise denoted by $\alpha _{E}(q).$ Because $g_{\alpha
\alpha }<0,$ in an interior solution there holds $\alpha _{F}(q)<\alpha
_{E}(q).$
Now, for the range of $q$ for which there holds that $\alpha ^{\ast }\geq
\alpha _{F}(q),$ the optimal level of effort is obviously given by (\ref{e10}%
). Because $\alpha _{F}(q)$ is increasing in q, there is a unique level of $%
q $ at which $\alpha _{F}(q)=\alpha ^{\ast }$ which we denote by $q_{0}.$
For individuals with $q>q_{0},$ there holds that $\alpha _{F}(q)>\alpha
^{\ast }.$ For these individuals, the option of reducing effort in order to
remain eligible for benefits is relevant. For individuals with $q>q_{0}$ who
decide to reduce their effort such that they remain eligible for benefits,
it is immediate that their optimal level of effort will be to obtain exactly
$\alpha ^{\ast }.$ For those individuals that decide to have an effort level
such that they become ineligible for benefits, optimal $\alpha $ and $e$ are
given by $\alpha =\alpha _{E}(q)$ and $e=\arg _{e}\{qEg_{\alpha }=1\}$.
Individuals with $q>q_{0}$ will take this latter option if and only if
\begin{eqnarray*}
W(E,q) &\equiv &u(0)+g(\alpha _{E}(q),s(\alpha _{E}(q)))\ast
(u(P)-u(0))-s(\alpha _{E}(q))-\arg _{e}\{qEg_{\alpha }=1\}\geq \\
W(F,q) &\equiv &u(0)+g(\alpha ^{\ast }(q),s(\alpha ^{\ast }(q)))\ast
(u(P)-u(0))-s(\alpha ^{\ast })-\arg _{e}\{qe=\alpha ^{\ast }\}
\end{eqnarray*}
Now, because there holds that $\frac{\partial W(E,q)}{\partial q}>\frac{%
\partial W(F,q)}{\partial q},$ there is a unique quality level $q_{1}$ above
which individual behaviour leads to an $\alpha >\alpha ^{\ast }.$ This point
$q_{1}$ solves
\begin{equation*}
q_{1}=\arg _{q}[W(E|q>q_{0})=W(F|q>q_{0})]
\end{equation*}
The behaviour of the individuals with $q>q_{1}$ is in effect the same with
and without the existence of benefits contingent on $\alpha ^{\ast }\geq
\alpha $.
Individuals with a quality between $q_{0}$ and $q_{1}$\ will choose their
effort levels such that $eq=\alpha ^{\ast }.$ From this, it follows that
those with higher quality levels, but with quality levels still below $%
q_{1}, $ have to reduce their effort more than those with lower quality
level as a result of the dependence of benefit entitlement on a level of
labour market potential. This is the perverse effect of allocating benefits
only to those with low labour market potential.
An anticipated minimum labour market potential level of $\alpha ^{\ast }$
hence leads to an endogenous distribution of $\alpha $ that will have a
mass-point at $\alpha ^{\ast }.$ One question is now whether there is only
one feasible $\alpha ^{\ast }$. We can look at this issue by looking at the
change in the number of individuals receiving unemployment benefits as a
result as a result of a change in $\alpha ^{\ast }.$ If this change is
always positive, there can be only one $\alpha ^{\ast }$ that exactly uses
up the available budget for poverty relief and that is hence feasible. There
now holds that
\begin{eqnarray*}
d\frac{\int_{0}^{A(\alpha ^{\ast })}(1-g(\alpha ,s^{1}))dA(\alpha |\alpha
^{\ast })}{d\alpha ^{\ast }} &=&-[Q(q_{1})-Q(q_{0})]\ast \lbrack \frac{%
dg(\alpha ^{\ast },s^{1}(\alpha ^{\ast }))}{d\alpha ^{\ast }}] \\
&&+\frac{dQ(q_{1})}{dq}\frac{dq_{1}}{d\alpha ^{\ast }}\ast (1-g(\alpha
^{\ast },s^{1})) \\
&=&-[Q(q_{1})-Q(q_{0})]\ast \lbrack g_{\alpha ^{\ast }}-g_{s}\frac{g_{\alpha
s}}{g_{ss}}] \\
&&+\frac{dQ(q_{1})}{dq}\frac{dq_{1}}{d\alpha ^{\ast }}\ast (1-g(\alpha
^{\ast },s^{1}))
\end{eqnarray*}
The first term on the right hand side denotes the reduction in the benefit
take-up as a result of the fact that the group of individuals with $%
q_{0}q_{1}.$ Hence, for any
given distribution below $q_{1}$ and a given feasible solution $\alpha
^{\ast },$ we can pick a $\frac{dQ(q)}{dq}|^{q_{1}}$ such that $d\frac{%
\int_{0}^{A(\alpha ^{\ast })}(1-\alpha s^{1})dA(\alpha |\alpha ^{\ast })}{%
d\alpha ^{\ast }}=0$ in which case we have a continuum of feasible $\alpha
^{\ast }$.}
Given the strategy of giving benefits to those with lowest labour market
potential, the optimal poverty relief policy is obviously to take the
highest feasible $\alpha ^{\ast }.$ The possibility of many feasible $\alpha
^{\ast }$ however means that a government that does not have all the
information necessary to calculate all the feasible $\alpha ^{\ast }$ and
that for instance uses trial-and-error to see if $\alpha ^{\ast }$ turns out
to be feasible in practice may be stuck at a higher level of unemployment
and poverty than necessary under the same budget.
\subsection{Can the outcome be improved upon?}
We take here the most informative case of the model, i.e. an interior
solution where $0<\alpha ^{\ast }$ and $0\alpha ^{\ast }$ which reduces unemployment and increases
welfare. Because $q$ is only indirectly observable through $\alpha $ and $e,$%
\ this means that individuals with an $\alpha $ above $\alpha ^{\ast }$ can
be given benefit entitlement if they have higher levels of effort $e$ than
the individuals with $\alpha ^{\ast }.$ The more above $\alpha ^{\ast }$ an
individual is, the higher $e$ should be to be entitled. The intuition is
that individuals with higher labour market potential than $\alpha ^{\ast }$
have to prove to nevertheless be of low quality ($qq_{1}
\end{equation*}
Whether this is actually the poverty minimizing level depends on whether the
distortionary effect of benefits on the job-finding rates is actually lower
for those with low quality. Conditioning benefit entitlement on $q$ through
conditioning it on the observed $\alpha $ and $e,$ Pareto improves the
current outcome under very general circumstances however.
The results of this model sofar can be summarized in Figure 1.
\FRAME{ftbpFU}{2.7726in}{2.4111in}{0pt}{\Qcb{The relation between q, e, $%
\protect\alpha ,$ and $\protect\alpha ^{\ast }$.}}{}{hopeless.bmp}{\special%
{language "Scientific Word";type "GRAPHIC";maintain-aspect-ratio
TRUE;display "USEDEF";valid_file "F";width 2.7726in;height 2.4111in;depth
0pt;original-width 5.3852in;original-height 4.6769in;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename
'graphics/hopeless.bmp';file-properties "XNPEU";}}The thick lines
denote a hypothetical correspondence between quality and $\alpha $ and $e$
respectively. In this figure, a government interested in minimizing poverty
sets a minimum labour market potential level $\alpha ^{\ast }$ above which
individuals are not entitled to benefits in order to give them maximum
incentives to search. Individuals with $qq_{1}$ are going to supply effort in both periods as if there was no
benefit system at all. Hence, at $q_{1}$ both effort and $\alpha $ make a
discontinuous jump.
The thin lines in figure 1 denote the possible Pareto-improvement. For $e$
and $\alpha $, the Pareto-improvement of conditioning on e has the same
effect on the individuals in the range $q\in \lbrack q_{0},q_{1}]$ as
unconditional benefit entitlement. This increases their job-finding
probabilities, their utility levels, and decreases the amount of money
needed to finance this system of unemployment benefits. Note though, that
even after the Pareto-improvement, there is a discontinuous jump in $\alpha $
and $e$ at $q_{1},$\ because individuals with $q>q_{1}$ do not have benefit
entitlement and hence provide more effort than those with entitlement.
\subsection{Welfare maximizing benefits if $\protect\alpha $ and $e$ are
observable}
Poverty minimization bounds benefits from below at the poverty-avoiding
level. Welfare maximization does not impose this constraint and does not
have to neglect the utility effect of effort. The question is hence what $b$(%
$q,e$) would be under social welfare maximization.
If we denote the Lagrangian multiplier of the budget constraint by $\lambda
, $ in a welfare optimizing program $\frac{dU(b,q,e)}{db}$ has to be
constant for all combinations of $q$ and $e$. Using the envelope theorem, we
have
\begin{eqnarray*}
\frac{dU(b,q,e)}{db} &=&(1-g(\alpha ,s))u^{\prime }(b)-\lambda \ast
\{(1-g(\alpha ,s))-b\frac{\partial s}{\partial b}\ast \frac{\partial
g(\alpha ,s)}{\partial s}\} \\
&\equiv &0
\end{eqnarray*}
where the term with $\lambda $ denotes the externality of individual
behaviour on the budget constraint. We can hence write $\lambda =\frac{%
(1-g(\alpha ,s))u^{\prime }(b)}{(1-g)-b\ast \frac{g_{s}^{2}u^{\prime }(b)}{%
g_{ss}F}}0$.
For these findings to be applicable in any practical scheme however, we
would need detailed information on $u(.)$ and $g,$ of which at least $u(.)$
is considered immeasurable by many economists. This severely reduces the
empirical usefulness of the welfare maximizing benefit scheme. For the
Pareto-improvement above to be implemented, all that is needed is
information on $\alpha $ and $e$.
\section{A dynamic model}
So far, employment was taken to be a one-shot game. Here we briefly examine
whether the qualitative findings of the previous model carry over when
individuals live infinite periods in which they can search, maintain and
loose jobs in continuous time.
Employed individuals become unemployed at an exogenous separation rate $%
\delta $. Individuals choose an $e$ in the first period and, from the second
period till infinity onwards, search in continuous time for jobs while
unemployed. We do not allow for individual income smoothing because one of
unemployment benefits' main role is to help individuals to smooth income
(see Gruber, 1997). The value of a job and of unemployment are denoted as $%
V^{J}$ and $V^{U}$ respectively. Taking a discount rate of $\rho ,$ these
values equal
\begin{eqnarray*}
(\rho +\delta )V^{J} &=&u(P)+\delta V^{U} \\
(\rho +g(\alpha ,s))V^{U} &=&u(b)+g(\alpha ,s)V^{J}-s
\end{eqnarray*}
substituting $V^{J}$ in the equation for $V^{U}$ and re-arranging leads to
\begin{equation*}
\rho V^{U}=\frac{g(\alpha ,s)}{(\rho +\delta +g(\alpha ,s))}u(p)+(1-\frac{%
g(\alpha ,s)}{(\rho +\delta +g(\alpha ,s))})u(b)-\frac{(\rho +\delta )}{%
(\rho +\delta +g(\alpha ,s))}s
\end{equation*}
Now, if we define $s^{\ast }=\frac{(\rho +\delta )}{(\rho +\delta +g(\alpha
,s))}s$ and $g^{\ast }=\frac{s^{\ast }g(\alpha ,s)}{(\rho +\delta )},$ we
have
\begin{equation*}
\rho V^{U}=g^{\ast }(\alpha ,s^{\ast })u(p)+(1-g^{\ast }(\alpha ,s^{\ast
}))u(b)-s^{\ast }
\end{equation*}
Because at any optimal solution there has to hold $\frac{\partial g^{\ast }}{%
\partial s^{\ast }}>0$ and $\frac{\partial ^{2}g^{\ast }}{\partial
^{2}s^{\ast }}<0,$ the maximization of $\rho V^{U}$ with respect to $s^{\ast
}$ has the same properties in equilibrium as the maximization of utility
with respect to $s$ in the previous section. If there is again an initial
period in which individuals choose $e$ and if a government conditions
benefit entitlement on low $\alpha ,$ then the same Pareto-improvement as in
the two-period model is possible in the infinite period case also. Optimal
benefits can be calculated analogue to (\ref{eg}).
\section{Policy options and empirical support}
Having an abstract model in which one looks at the theoretical relation
between some abstract concept of early life effort e and future labour
market outcomes, is really only useful if it is possible to empirically
measure aspects of e on which one could base benefit policy. Three prime
candidates for e come to mind.
1. Truancy. It would seem relatively easy to measure truancy fairly
accurately and to\ have benefits depend negatively on prior levels of
truancy. Unfortunately, however, no general national register of truancy
exists anywhere. The few case-studies of truancy that there are (...) do
suggest that truants are much more likely to become benefits applicants and
face lower wages and higher rates of crime. In this sense,truancy fits the
description of low previous effort.
There are several data problems with truancy. For one, truancy is
empirically related strongly to drop-out and expulsion, which in turn is
affected by school funding, changing laws and other matters not directly
related to later labour market outcomes: the strong rise in expulsions in
the UK of the last 10 years is probably more related to changing laws on
expulsion that on a dramatic increase in truancy leading to expulsions.
Because those who get expelled are often those with high incidences of
truancy however, this does cloud official figures on truancy. Another
problem is that much of truancy behaviour is unrecorded: the level of
truancy appears to be much smaller in official statistics than in
self-reported surveys. In official Dutch statistics for instance, truancy is
estimated to affect about 1 in 10 school attendants, whereas in surveys
about 40\% of school attendants claims to have been a truant now and then
(www.minsoza.nl). For truancy statistics to be used as a policy tool, much
would have to be done to improve their impartiality and accuracy in
measuring early effort.
2. School effort and homework. Although it would seem quite possible to base
benefits on effort levels in school, virtually nothing general is known
about it.
3. Teenage pregnancy. Teenage pregnancy is well-recorded in official
statistics in many countries and is also much analysed (e.g. Rosenzweig,
1999; Clarke and Strauss, 1998; Klepinger et al., 1999). The basic
experience of a selection of OECD countries is given in Figure 1.
Figure 1: historical experience in the OECD.
It is the case that female pregnancy in 1995 is about 10 to 20 times more
frequent in Anglo-Saxon countries (UK, US) than in Northern European
countries (The Netherlands, Denmark). Most other European countries have
slightly higher levels of teenage pregnancy than in Holland and Denmark,
though not very much (see white paper UK). Also, most other European
countries exhibit the same dynamic tendencies of increasing teenage
fertility in the early 60's, and great reductions in fertility since the
70's. The main difference with the US and the UK is that levels there have
not gone down and were historically also somewhat higher.
Now, we look at whether we can link fertility to the `child-premium', i.e.
the difference between benefits for those without children and the benefits
for those with children. Figure 2 shows the cross-sectional evidence for 20
OECD countries.
Figure 2: the OECD cross-section data.
Haveman and Wolfe (2001) review the empirical evidence for the US based on
state variation in benefits. They find strong positive effects on fertility
when the difference between benefits for those without children and the
benefits for those with children is greater. Adding to this US evidence, we
here add several additional sources of data.
figure with UK, US, the Netherlands, Denmark
The correlation between teenage fertility and the child-premium (defined as
the ratio between the benefits a teenage girl receives without children and
the benefits received with children) is about -0.6, but reduces to -0.2 if
we would ignore the US. Also we can clearly see that the other Anglo-Saxon
countries are outliers: England, New Zeeland, Australia and Canada all have
relatively very high levels of fertility, though the child-premium in these
countries is not dissimilar from the rest of the OECD. The child premium is
hence not the only relevant factor.
In order to see if changes in the child-premium are related to changes in
fertility, we show in Figures 3 and 4 the evolution of fertility in the UK
and in the Netherlands, together with indicators of the child premium. In
the Netherlands, where regional variation in benefits are very small, we
show the evolution of the general benefit level and of the child premium.
For the UK regional variation is much more important. Blundell and McCurdy
(1999) pointed out that many benefits are relevant for women without work
that each have their own preconditions and are often independent in their
functioning. Therefore, for the UK we have calculated the child-premium
indirectly fro calculating the median consumption level of teenagers on
benefits with and without children. For this, we've used the Family
Expenditure Surveys from 1970 onwards.
Figure 3 and 4.
In both Figures, we see a decline in fertility levels when general levels of
benefits go up and an increase when the child premium increases. Yet, it
must be conceded that whereas teenage fertility decreased to very low levels
in the Netherlands, teenage fertility in the UK did not, despite not too
dissimilar movements in the benefit structure. We are hence left with an
indication that forward looking choice behaviour is probably a component in
teenage fertility choices, but there is a clear and large remaining
`Anglo-Saxon teenage fertility puzzle'.
\section{Conclusions and discussion}
Benefits for individuals who are not self-sufficient generate two moral
hazard problems. The first moral hazard problem is that it reduces
incentives to search for jobs while on the labour market. A second moral
hazard problem generated by welfare benefits is that it decreases the
incentives to make an effort earlier in life to have a high labour market
potential later in life. This second moral hazard problem interacts with the
first and leads to the possibility that preconditioning benefit entitlement
on being unable to find a job may help create a group of individuals who
really are unable to find a job and who would still have low
job-finding-probabilities (at least to well-paying jobs) if benefits would
be withdrawn at that moment.
An efficiency increasing change for a future generation is to condition not
only on labour market possibilities, but to condition on investments made
earlier in life also. Conditioning future benefits on school attendance and
`school effort' is one policy option to give incentives to make investments
earlier in life, whilst still allowing for the possibility that even school
attendance does not guarantee good labour market opportunities because of
heterogeneous talents.
Whether it is wise to condition (the height of) benefits on things like
prior school attendance and school effort depends on several so far
unmentioned effects of such conditioning. For one, conditioning future
benefits on prior school attendance will increase the leverage that schools
have on their students. It will furthermore crowd out the activities that
non-attending students currently perform. Whether the net effect is welfare
improving depends on a valuation of these effects also.\newline
\newline
\newline
{\large References}\newline
\begin{description}
\item Acemoglu, D., and R. Shimer (1999), `Efficient unemployment
insurance', \textit{Journal of Political Economy} 107, pp. 893-928.
\item Acemoglu, D., and R. Shimer (2000), `Productivity gains from
unemployment insurance', \textit{European Economic Review} 44, pp. 1195-1224.
\item Akerlof, G.A. (1978), `The economics of ``tagging'' as applied to the
optimal income tax, welfare programs, and manpower planning', \textit{%
American Economic Review} 68, pp. 8-19.
\item Blanchard, O.J., Wolfers, J. (1999), `The Role of Shocks and
Institutions in the Rise of European Unemployment: The Aggregate Evidence',
\textit{NBER working paper} 7282.
\item Blundell, A., McCurdy, T. (1999), 'Labour Supply: a review of
alternative approaches', Chapter 27 in Ashenfelter, O.C. and Card, D. (eds)
, \textit{Handbook of Labor Economics}, North Holland.
\item Burdett, K. (1979), 'Unemployment insurance payment as a search
subsidy: a theoretical analysis', \textit{Economic Inquiry}, 42, pp. 333-343.
\item Clarke, G.R.G., Strauss, R.P. (1998), `Children as income-producing
assets: the case of teen illegitimacy and government transfers', \textit{%
Southern Economic Journal} (64), pp. 827-56.
\item Coate, S., Loury, G.C. (1993), `Will affirmative action policies
eliminate negative stereotypes', \textit{American Economic Review} 83, pp.
1220-40.
\item Galor, O., Lach, S. (1990), `Search Unemployment in an
Overlapping-Generations Setting', \textit{International Economic Review} 31,
pp. 409-19.
\item Gruber, J. (1997), `The consumption smoothing benefits of unemployment
insurance', \textit{Amerian Economic Review} 87, pp. 192-205.
\item Harris, M., (1993), \textit{Culture, people, nature}, 5th edition,
HarperCollinsPublishers Inc.
\item Haveman, R., Wolfe, B. (2001), `', \textit{Quarterly Economic Review}.
\item Hopenhayn, G. and J.P. Nicolini, (1997), `Optimal unemployment
insurance', \textit{Journal of Political Economy} 105, pp. 412-438.
\item Klepinger, D., Lundberg, S., Plotnick, R. (1999), `How does adolescent
fertility affect the human capital and wages of young women?', \textit{%
Journal of Human Resources} (34), pp. 421-48
\item Ljungqvist, L., Sargent, T.J. (1998), 'The European unemployment
dilemma', \textit{Journal of Political Economy}, vol. 106(3), pp. 514-50.
\item Marimon, R., Zilibotti, F. (1999), 'Unemployment vs. mismatch of
talents: reconsidering unemployment benefits', \textit{Economic Journal}
109, pp. 266-291.
\item Moen, E.R. (1997), `Competitive search equilibrium', \textit{Journal
of Political Economy} (105), pp. 385-411.\newline
\item Pissarides, C.A. (1990), \textit{Equilibrium Unemployment Theory},
Oxford: Blackwell.
\item Rosenzweig, M.R. (1999), `Welfare, marital prospects and nonmarital
childbearing', \textit{Journal of Political Economy} (107), pp. S3-32.%
\newline
\end{description}
{\LARGE Appendix 1: implication of specific functional forms for }$g${\LARGE %
.}\newline
\newline
We here look at optimal poverty policy in further detail. First we can note
that
\begin{eqnarray}
\frac{d\frac{\partial g(\alpha ,s(\alpha ,b))}{\partial b}}{d\alpha } &=&%
\frac{d(g_{s}\frac{ds}{db})}{d\alpha }=\frac{2g_{s}g_{\alpha s}u^{\prime }(b)%
}{g_{ss}F}+\frac{(g_{s})^{2}u^{\prime }(b)}{(g_{ss}F)^{2}}g_{ss\alpha }F \\
&&-\frac{g_{s\alpha }F}{g_{ss}F}[\frac{2g_{s}g_{ss}u^{\prime }(b)}{g_{ss}F}+%
\frac{(g_{s})^{2}u^{\prime }(b)}{(g_{ss}F)^{2}}g_{sss}F] \notag \\
&=&\frac{u^{\prime }(b)g_{s}}{g_{ss}F}\{g_{\alpha s}-g_{s}\frac{g_{ss\alpha }%
}{g_{ss}}\} \notag
\end{eqnarray}
We first look at possible $g(.)$ for a single index-function $g(x(\alpha
,s)) $ where, because of the boundedness of $g,$ there has to hold $%
g^{\prime \prime \prime }>0$ and $g^{\prime }g^{\prime \prime \prime
}=(g^{\prime \prime })^{2}.$ We can then look at some cases with
complementarity and substitutability between $\alpha $ and $s:$
\begin{itemize}
\item Complementarity with $g_{\alpha \alpha }<0$: $x(\alpha ,s)=\alpha s.$
Then $g_{s\alpha }=g^{\prime }+\alpha sg^{\prime \prime }$ and $g_{ss\alpha
}=\alpha (s\alpha g^{\prime \prime \prime }+2g^{\prime \prime }).$ Then $%
g_{\alpha s}-g_{s}\frac{g_{ss\alpha }}{g_{ss}}=-g^{\prime }<0.$ For $%
g(x)=1-e^{-bx}$ for instance$,$ this means that $g_{\alpha s}-g_{s}\frac{%
g_{ss\alpha }}{g_{ss}}=-be^{-bx}<0$ and $\frac{d\frac{\partial g(\alpha
,s(\alpha ,b))}{\partial b}}{d\alpha }>0$. \newline
For $g(x)=1-\frac{1}{1+bx},$ we have $g_{\alpha s}-g_{s}\frac{g_{ss\alpha }}{%
g_{ss}}=\frac{-b}{(1+bx)^{2}}<0.$ Hence $\frac{d\frac{\partial g(\alpha
,s(\alpha ,b))}{\partial b}}{d\alpha }>0.$
\item Complementarity with $g_{\alpha \alpha }<>0$: $x(\alpha ,s)=f(\alpha
)s $ with $f^{\prime }>0$ and $f^{\prime \prime }>0.$ Then $g_{s\alpha
}=f^{\prime }g^{\prime }+sff^{\prime }g^{\prime \prime }$ and $g_{ss\alpha
}=2ff^{\prime }g^{\prime \prime }+sf^{\prime }f^{2}g^{\prime \prime \prime
}. $ Then $g_{\alpha s}-g_{s}\frac{g_{ss\alpha }}{g_{ss}}=-f^{\prime
}g^{\prime }<0.$ Hence $\frac{d\frac{\partial g(\alpha ,s(\alpha ,b))}{%
\partial b}}{d\alpha }>0.$
\item Substitutability: $x(\alpha ,s)=\alpha +s.$ Then, $g_{s\alpha
}=g^{\prime \prime }<0$ and $g_{ss\alpha }=g^{\prime \prime \prime }$. Also,
$g_{\alpha s}-g_{s}\frac{g_{ss\alpha }}{g_{ss}}=0.$ Hence $\frac{d\frac{%
\partial g(\alpha ,s(\alpha ,b))}{\partial b}}{d\alpha }=0.$
\end{itemize}
For none-single index function we find different results.
\begin{itemize}
\item Additive substitutability: $g(.)=f(\alpha )+h(s)$ with $f,h,h^{\prime
},f^{\prime }>0,$ $f^{\prime \prime },h^{\prime \prime }<0$\ and $00$\ with single-index functions without perfect substitution.
For many cases where $s$ and $\alpha $ are complements, $\frac{d\frac{%
\partial g(\alpha ,s(\alpha ,b))}{\partial b}}{d\alpha }=0$. There are hence
no general results on $\frac{d\frac{\partial g(\alpha ,s(\alpha ,b))}{%
\partial b}}{d\alpha }.$\newline
\newline
{\Large Calculations on }$D=(g_{\alpha }-g_{s}\frac{g_{\alpha s}}{g_{ss}})%
\frac{g_{s}}{1-g}-\{g_{\alpha s}-g_{s}\frac{g_{ss\alpha }}{g_{ss}}\}:$
\begin{itemize}
\item $g=g(\alpha s).$ Then $D=g^{\prime }>0.$
\item $g=g(\alpha +s).$ Then $D=0.$
\item $g=g(f(\alpha )s).$ then $D=f^{\prime }g^{\prime }-\frac{(g^{\prime
})^{3}f^{\prime }}{g^{\prime \prime }(1-g)}>0$
\item $g(.)=f(\alpha )+h(s).$ Then $D=\frac{f^{\prime }h^{\prime }}{(1-g)}%
>0. $
\item $g(.)=f(\alpha )h(s).$ Then $D=(f^{\prime }h-h^{\prime }f\frac{%
h^{\prime }f^{\prime }}{fh^{\prime \prime }})\frac{h^{\prime }f}{1-fh}>0.$
\end{itemize}
We hence find in these examples that $D>0$ unless there is perfect
substitution, in which case $D=0$.
\end{document}
%%%%%%%%%%%%%%%%%%%%%% End /document/hopeless.tex %%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%% Start /document/graphics/hopeless.bmp %%%%%%%%%%%%%%%%
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