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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 Do not quote.}} \maketitle \date{} \begin{abstract} In this paper it is argued that preconditions for welfare benefit entitlements based on labour market prospects can be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 %%%%%%%%%%%%%%%% BudQbj@@@@@@@XC@@@@J@@@@EH@@@D\@@@P@@`A@@@@@@@ahJ@`sN@@@X{@@@@@@@@@@@@@@                            @|        C@@@@@@@|    C@@@@@@@@@@@|                Cp       O@@@pO@@@p     O@@@p               O@        @@@@@@@@    @@@@                @|       C@@@| C@@@|    C@@@|            C@@@|   Cp        O@@@pO@@@p    O@@@p          O@@@@@@@@@@@p  O@@@p    O@       @@@@@@@@@@@@@@@@ @@@@    @@@@@@@@@@@@@@@@          @@@@  @@@@    @|       C@@@|C@@@|C@@@|    C@@@| C@@@|         C@@@|  C@@@|    Cp       O@@@p O@@@pO@@@p    O@@@pO@@@p          O@@@@@@@@@@@pO@@@p  O@@@p    O@       @@@@@@@@@@@@@@@@@@@@@@@ @   @@@@@@@@@@@@@@@ @@@@@         @@@@@@@@@@@@   @@@@   @|  C@@@@@@@|     C@@@| C@@@@@@@|C@@@|C@@@|    C@@@|C@@@@@@@|C@@@@@@@@@@@|          C@@@|C@@@|  C@@@|    Cp  O@@@pO@@@p     O@@@pO@@@pO@ @@@@@@p   O@@@p O@@@pO@@@p         O@@@p O@@@pO@@@@@@@@@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@p    O@ @@@@@@@@      @@@@@@@@    @@@@@@@@   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@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@         @@@@                @|  C@@@|C@@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@|        C@@@|                Cp  O@@@p O@@@@@@@@@@@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@p                        O@  @@@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@                         @|  C@@@| C@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@|    C@@@|                    Cp  O@@@p O@@@@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@@@@@@@p   O@@@p                     O@  @@@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@    @@@@    @@@@                @|  C@@@|  C@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@|    C@@@|    C@@@|                Cp  O@@@p O@@@@@@@@@@@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@p   O@@@p                    O @ @ @@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ @@@@@   @@@@@@@@@@@@@@@@                    @|  C@@@|  C@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@|   C@@@| C@@@|                    Cp  O@@@p O@@@@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@p   O@@@p                    O@  @@@@  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