S P D I S C U S S I O N P A P E R NO. 0804 42752 Poverty Traps and Social Protection Christopher B. Barrett, Michael R. Carter and Munenobu Ikegami February 2008 Poverty Traps and Social Protection? Christopher B. Barrett1, Michael R. Carter2 and Munenobu Ikegami2 February 2008 Abstract This paper demonstrates that there are potentially large returns to social protec- tion policy that stakes out a productive safety net below the vulnerable and keeps them from slipping into a poverty trap. Much of the value of the productive safety net comes from mitigating the ex ante e¤ects of risk and crowding in additional investment. The analysis also explores the implications of di¤erent mechanisms of targeting social protection transfers. In the presence of poverty traps, modestly regressive targeting based on critical asset thresholds may have better long-run poverty reduction e¤ects than traditional needs-based targeting. JEL classi...cation: D91, I30, O12 Keywords: Poverty traps, Targeting transfers, Dynamic modeling ? The authors'names appear alphabetically; seniority of authorship is shared. We thank John Hoddinott, Valerie Kozel, Felix Naschold and seminar audiences at the International Food Policy Research Institute, Namur, Purdue, Wageningen, Wis- consin and the World Bank for helpful comments on earlier versions of this work. Generous ...nancial support was provided by the Social Protection Division of the World Bank and by a grant from the USAID O¢ ce of Poverty Reduction to the BASIS Collaborative Research Support Program. The ideas expressed are the re- sponsibility of the authors and should not be attributed to either sponsoring orga- nization. 1 Cornell University, USA 2 University of Wisconsin-Madison, USA Poverty Traps and Social Protection Poverty traps caused by the existence of multiple dynamic equilibria attract ever-growing attention, among both economic researchers and development policymakers.3 In this paper, we focus not on why or if poverty traps exist, but rather on the implications of poverty traps for the design and performance of poverty reduction policies. This topic remains remarkably underexplored even though the poverty traps concept underpins much current development policy discourse.4 As we explore, multiple equilibria can create stark tradeo¤s between helping those who are currently poorest versus preventing descents into poverty among an initially non-poor, middle class group. Not only is there a tradeo¤ between preventing and responding to poverty, but because bene...t levels associated with transfer programs operating on a ...xed budget are determined endogenously as people descend into or graduate from poverty, the most progressive transfer policies may trade o¤greater reductions in near- term poverty for higher future poverty rates. Over time, today's poor may actually bene...t from policies that protect the assets of a vulnerable but some- what better-o¤ middle class if such social protection stimulates investment by the poor and eventually reduces the size of the poor subpopulation needing support from transfer programs with a ...xed budget. Ultimately, we demon- strate that poverty traps can have a pronounced e¤ect on the performance and appropriate design of poverty reduction policies. This fundamental point appears to have gone unnoticed in the literature to date. This paper explores these issue with a stochastic dynamic programming model of individual asset accumulation in the presence of innate ability di¤erences, heterogeneous asset endowments, multiple production technologies and risk. As in many such models, multiple equilibria and an associated poverty trap are generated by assumptions of missing ...nancial markets and non-convexities in production (i.e., ...xed costs of investment and innovation). These assump- tions create a `Micawber Frontier'which divides the innate ability­initial asset space into multiple regions of distinct, dynamically optimal behavior.5 In- dividuals located above the Micawber Frontier ...nd it feasible to accumulate 3 Azariadis and Stachurski (2005), Bowles et al. (2006) and Carter and Barrett (2006) provide excellent overviews of the relevant literature. 4 For example, Sachs (2005) relies heavily on the poverty trap idea in making a case for massive increases in international development assistance to low-income countries, but without directly teasing out speci...c design implications. 5 As discussed by Carter and Barrett (2006), the phrase Micawber Threshold was ...rst used by Michael Lipton to describe a point below which it is di¢ cult for agents ever to accumulate assets. The idea was subsequently adopted by Zimmerman and Carter (2003) who give it a meaning similar to that used here. The image echoes the travails of Wilkins Micawber, the perpetually insolvent debtor in Dickens'David Copper...eld. 2 assets, adopt the improved production technology and eventually climb out of poverty. Those below the frontier do not. Because the frontier is in...nite for individuals below a minimum ability level, there is a region of what might be termed "intrinsic chronic poverty." The model thus captures the ability di¤er- ences that ...gure prominently in some empirical discussions of chronic poverty (Chronic Poverty Research Centre 2005, Santos and Barrett 2006), as well as the bifurcated wealth dynamics that ...gure prominently in the theoretical poverty traps literature.6 In addition to making clear the complex nature of chronic poverty, the model also shows that exposure to risk and shocks play especially pernicious roles when poverty traps exist. Ex post, realized shocks can have irreversible conse- quences for agents who get pushed below the critical threshold. In addition, the ex ante anticipation of shocks shifts out the endogenous threshold, mak- ing escape from poverty less likely as agents become less willing to sacri...ce current consumption to accumulate risky assets. Policies that compensate individuals for the e¤ects of realized shocks or insure them against future losses can crowd-in investment and have a major e¤ect on the incidence of chronic poverty, even taking into account agents'natural behavioral response to insurance (i.e., moral hazard). The remainder of the paper proceeds as follows. Section 1 presents the sto- chastic dynamic programming model of individual asset accumulation. Section 2 then uses this framework to form a stylized model of a poverty trap econ- omy. As a baseline for later analysis of alternative policy regimes, we simulate the stylized economy over a sixty year time horizon, tracking the evolution of GDP, technology adoption, inequality and standard Foster-Greer-Throbecke (FGT) poverty measures, as well as a new measure of unnecessary deprivation. Section 3 explores the design of programs intended to aid the poor, either by making progressive, needs-based transfers, or by o¤ering a productive social safety net that o¤ers insurance against potentially catastrophic asset losses. These experiments are perhaps best characterized as relief programs in that they are ex post and they are assumed to be unanticipated by agents in the economy.7 In the presence of poverty traps needs-based allocation rules can lead to a long-run "relief trap" for development assistance because agents fall into a poverty trap due to asset shocks, swelling the ranks of the poor and thereby ultimately reducing assistance to the poorest due to increased 6 This ...nding suggests that much of the empirical literature on poverty traps (in- cluding our own) has been misguided in imposing a single model of welfare dynamics on data generated by heterogeneous agents. Santos and Barrett (2006) is an excep- tion. 7 This does not strictly require that agents are ignorant of the possibility of trans- fers, merely that assistance is su¢ ciently unreliable that agents behave as if such policies do not exist. 3 competition for scarce relief resources. While in the near term the productive safety net implies regressive targeting among the subpopulation of poor and vulnerable agents, by preventing collapse into poverty by agents vulnerable to asset risk, it reduces poverty and leads to greater transfers to and higher welfare for the intrinsically poor in later years. Section 4 then explores what happens when a program of sporadic, unan- ticipated relief is replaced with a a systematic program of fully anticipated social protection. While anticipation of social protection creates an element of standard, output-reducing (and indemnity payment-increasing) negative moral hazard, it can also create what we term positive moral hazard, wherein individuals are induced to take on more risk and invest more. But rather than increasing the likelihood of subsequent indemnity payments, this induced risk taking behavior reduces that likelihood of indemnity payments and stimulates output growth. While the e¤ects of negative moral hazard appear potentially substantial under a naive program design, we show how modest changes in program structure can markedly shift the balance between negative and posi- tive moral hazard. Section 5 concludes the paper with implications for further research and for social protection policy design. 4 1 Poverty Traps: Assets, Ability, Risk and the Multiple Dimen- sions of Chronic Poverty The growing literature on poverty traps o¤ers a range of theoretical models that generate multiple dynamic welfare equilibria, at least one of which falls beneath a poverty line. Dercon (2003), Banerjee and Duo (2004), Azariadis and Stachurski (2005) and Bowles et al. (2006) provide excellent summaries of that literature. Our focus in this paper is on micro-(household-)level poverty traps, especially forward-looking agents'asset accumulation and welfare dy- namics in an economic environment characterized by credit constraints, a non- convex production technology set, heterogeneous agent ability and initial asset endowments, and non-existent labor and asset rental markets. Our model thus resembles other models of poverty traps in the sense that some households do not invest ­nor choose the more pro...table technology ­because the current cost of investment is large compared to the future returns to investment for those with low initial wealth when they cannot borrow against future expected earnings.8 In what follows we build on Buera's (2005) non-stochastic model of asset accumulation with two production technologies under credit constraints and heterogeneous agent ability. We extend Buera's model by adding asset shocks to allow for the importance of both ex ante awareness of risk and the ex post experience of shocks as key determinants of poverty dynamics (Elbers and Gunning 2005). We show that intermediate ability households dramatically change asset accumulation and production choices in response to ex ante asset risk and ex post realization of asset shocks. This section and that result help motivate our focus in subsequent sections on prospective safety net policies and associated moral hazard concerns. 1.1 A Model of Asset Dynamics and Heterogeneous Ability Consider an economy in which each individual i is endowed with a level of innate ability ( ) as well as an initial stock of capital (ki1). Preferences are i unrelated to the individual's innate ability. In what follows, we treat i as ...xed. We conceptualize the agents in this economy as adults and i as cap- turing the e¤ectively immutable physical stature, cognitive development and educational attainment with which they enter adulthood and thus the econ- omy. This obviously ignores the origins of such innate ability. Exploring the 8 Related previous papers include Becker and Tomes (1979), Loury (1981), Banerjee and Newman (1991, 1993), Galor and Zeira (1993), Ray and Streufert (1993), Aghion and Bolton (1997), Piketty (1997), Carter and Zimmerman (2000), Ghatak, Morelli and Sjostrom (2001) and Ghatak and Jiang (2002). 5 multigenerational extension to the present model, by endogenizing i, seems a promising topic for future research, not least of which because it would directly address the economic growth and poverty reduction e¤ects of early childhood nutrition, health and education interventions. In this paper, however, we set those questions aside in order to concentrate on exploring social protection policy design in the presence of poverty traps. Each period the individual has to choose between two alternative technologies for generating income. Both technologies are capital using and skill-sensitive (i.e., for both technologies, more able people can produce more than less able people). One technology (the "high " technology) is subject to ...xed costs, E, such that the technology is not worth using at low amounts of capital. Speci...cally, we assume that expected income, f, for individual i in period t is given by f( ; kit) = i 8 > fH( ; kit) = kit E under the high technology H i where 0 < < :< 1. The individual interested in maximizing income will L H optimally employing the high technology if and only if kit equals or exceeds the critical level kb( ) = fkjfL( ;k) = fH( ;k)g.9 i i i If an individual had access to only one technology, she or he would accumulate capital up to a unique steady state values kL( ) for the low technology or i kH( ) for the high technology. The key question is then what happens when i the individual has access to both technologies. In particular, will an individual whose initial capital stock is below kb( ) gravitate toward the high or the low i technology and, relatedly, toward the higher or lower income level associated with the di¤erent technologies? Consider the case of an individual who begins life with kL( ) < ki0 < kb( ): Note that because this individual is beyond i i the low level steady state, incremental returns to further investment are low and discourage further investment. Will this individual optimally accumulate assets over time, and ending up at kH( ) and a non-poor standard of living? i Alternatively, will the individual settle into a poor standard of living with capital stock kL( )? More formally, is there an initial asset threshold, which i we will denote ke( ); below which individuals stay at the low equilibrium i (remaining chronically poor), and above which she or he will move to the high equilibrium (eventually becoming non-poor)? We analyze this question with a model of dynamic choice. Given the income 9 By construction, this formulation favors adoption of the high technology by as- suming away information problems and all other obstacles to adoption other than ...nancing. These simpli...cations merely eliminate inessential factors that reinforce this e¤ect. 6 generation process shown above, assume that in every period individuals al- locate the income they earn between consumption and the accumulation of productive assets: ct + it f( ; kit); i where ct is household consumption in period t and it is household investment in period t. The household's stock of accumulated capital evolves over time according to the following rule: kit+1 = t t [i + (1 )kit]; where is the asset depreciation rate and t is a random variable realized every period t.10 Individuals cannot borrow against future earnings to build up capital and can only pursue autarchic accumulation strategies. Note that = 1 indicates that there is no shock, whereas < 1 indicates a negative shock that destroys some fraction of assets. While in principal > 1 might be allowed, such events seem unlikely and we will restrict the analysis to the case where only negative shocks are possible, i.e., t 2 [0;1]. The cumulative density function of t is denoted by ( ) and we assume that every household knows ( ). The decision-maker's allocation choice at period is therefore represented by the following problem: X 1 max E t 1 u(ct) (1) t= s.t. ct + it f( ; kit) i kit+1 = t t [i + (1 )kit] ki given where E is expectation at the start of period , is the time discount fac- tor, and u( ) is the utility function de...ned over consumption ct and has the usual properties. Denote the investment rule in the presence of asset shocks as i (ktj ; ).11 10This asset shock is the only source of stochasticity considered here. Incorporating income shocks would make the choice of technology more complicated, but will not fundamentally change the nature of our results as long as the income risk is stationary. 11More precisely, i (ktj ; ) is the policy function of the following Bellman equation: V (kt) max fu(f( ; kt) it where E [V (kt+1jkt;it)] = Zit) + E [V (kt+1jkt; it)]g V ( [i + (1 t t )kt])d ( ) t where ( ) is cumulative density function of t. 7 1.2 The Micawber Frontier and the Two Dimensions of Chronic Poverty As in Buera (2005), this model identi...es a critical asset level, denoted ke( ); for each level of skill or ability. An individual with ability level i will attempt to accumulate the assets needed to adopt the high technology if she enjoys capital stock ki > ke( ). Otherwise, she will only pursue the low technology, i accumulating the modest stock of capital that it requires. Note that this frontier, a generalization of what Carter and Barrett (2006) call the Micawber Threshold, divides those who have the wealth needed to accumulate from those Figure 1, created through numerical analysis of the dynamic programming who do not. We label ke( ) the Micawber Frontier. model, illustrates the Micawber Frontier.12 Along the horizontal axis are innate ability or skill levels, ranging from least to most able. The vertical axis measures the stock of productive assets. The solid curve is the Micawber Frontier for the basic model. To ease discussion and link it to more conventional poverty analysis, Figure 1 also includes an "asset poverty line," illustrated as the dashed downward sloping line. For each ability level, this asset poverty line indicates the stock of assets the individual must have in order to produce a living standard exactly equal to a money metric poverty line, yp. We de...ne this poverty line as the level of income that a reference middle ability person ( = 1:12) would produce were she in steady state equilibrium at the low technology. This assumption is of course arbitrary,13 but it has the advantage of rendering most individuals poor unless they craft a pathway to the high technology. This is desirable in our stylized model as it creates a strong linkage between improved technology adoption, income and poverty measures. Note that the Micawber Frontier has a behavioral foundation and thus di¤ers from from the asset poverty line, which is based on a standard (and there- fore somewhat arbitrary) income poverty line.14 Those agents whose initial 12 Buera provides a formal proof for his non-stochastic model. Appendix 1 details the parameterization used to implement the numerical analysis of the stochastic model discussed in the remainder of the paper. The piece-wise linear shape of the Micawber Frontier arises from the discretization of : The ...ner grained ;the smoother the frontier. 13 Standard poverty lines are of course inherently arbitrary. In contrast, the Micaw- ber Frontier has a behavioral foundation, as well as strong behavioral implications, as Hoddinott (2006) discusses, and can be thought of as a dynamic asset poverty line (Carter and Barrett 2006, Carter and Ikegami 2007). 14 As discussed by Carter and Ikegami (forthcoming), this characteristic of the Mi- cawber Frontier makes it an interesting candidate as the base for chronic poverty measures. 8 Fig. 1. Risk and the Micawber Threshold ability-asset endowment places them above the Micawber Frontier but be- neath the asset poverty line will be initially but only transitorily poor as they naturally accumulate their way out of poverty. By contrast, those whose ini- tial ability-asset endowment situates them beneath the Micawber Frontier but above the asset poverty line will not be poor initially, but will steadily eat into their asset holdings and will eventually become poor. These movements repre- sent structural transitions across the poverty line. There can also be stochastic movements around the asset poverty line among the subpopulation that ...nds itself above the Micawber Frontier. For those individuals, small asset shocks may temporarily leave them beneath the asset poverty line without driving them o¤their growth path toward the high equilibrium. Of course, individuals could ...nd themselves above (below) both the Micawber Frontier and the asset poverty line, in which case they would be always non-poor (poor). This simple depiction of the Micawber Frontier and the asset poverty line thereby captures the full range of conventional static and dynamic poverty measures.15 As illustrated in Figure 1, the numerical analysis identi...es three distinct re- 15See Carter and Barrett (2006) for a discussion of distinct generations of poverty analysis that encompass these di¤erent ideas. 9 gions in the space of ability and initial asset holdings. Irrespective of their cap- ital endowment, high skill individuals with H i > will always move toward shift asset threshold kb( ) they will optimally switch to the higher technology. the high equilibrium as kei( ) = 08 H i > . When they reach the technology Irrespective of their starting position, these Upwardly Mobile agents steadily converge to the steady state asset value for the high technology. They may be poor over some extended period as they move toward their steady state value, but eventually they should become non-poor by virtue of the optimal accumulation behavior induced by their high ability endowment.. In contrast, those with an innate ability level below the critical level L will never move toward the high technology irrespective of their initial asset en- dowment. This critical skill level de...nes a region of intrinsic chronic poverty, made up of individuals who lack the ability to achieve a non-poor standard of living in their existing economic context.16 Finally, those in the intermediate skill group with L < H i< have positive but ...nite values ke( ). If su¢ ciently well-endowed with assets (ki0 > ke( )), these intermediate ability individuals will accumulate additional assets over time, and would be expected to adopt the high technology and eventually reach a non-poor standard of living. If they begin with assets below ke( ), however, these individuals will no longer ...nd the high equilibrium attainable and will settle into a low standard of living. Like those in the region of intrinsic chronic poverty, intermediate ability individuals initially endowed with less than ke( ) will be chronically poor. Unlike the intrinsically chronically poor, the chronic poverty of the intermediate skilled individuals is needless in the sense that they could be helped to lift themselves out of poverty with appropriate social protection policies, as we discuss below. The total number of chronically poor in any society will thus depend on the distribution of households across the ability-wealth space. 1.3 The Ex-post and Ex-ante E¤ects of Asset Shocks The Micawber Frontier is a function of the economic environment in which individuals ...nd themselves. In particular, the stochastic term fundamentally shapes investment behavior. We now explore the impact of ex ante risk and ex post shocks on investment and the long-term evolution of poverty. The ex post e¤ect of realized shocks comes about simply because negative events may destroy assets, knocking people o¤ their expected path of accumu- lation. For upwardly mobile individuals, such shocks may delay their arrival 16 CPRC (2004) gives examples of individuals who su¤er such fundamental disabil- ities. 10 at the upper level equilibrium, or knock them down from it, necessitating a period of additional savings and asset reaccumulation. But it does not set them on a di¤erent accumulation path. Similarly, shocks have no long-term e¤ect on the equilibrium toward which the low ability intrinsically chronically poor gravitate. In contrast, the ex post consequences of shocks can be rather more severe for households of intermediate ability. Consider the case of a household that is initially slightly above the Micawber Frontier. A shock that knocks it below that frontier will banish the household into the ranks of the chronically poor as in the wake of the shock, the household will alter its strategy and move toward the low equilibrium (divesting itself of assets). While these ex post e¤ects of shocks are important, the anticipation that they might take place would be expected to generate a "sense of insecurity, of potential harm people must feel wary of-- something bad can happen and `spell ruin,'"as Calvo and Dercon (2005 p.5) put it. Numerical analysis of the model shows that this sense of impending ruin indeed discourages forward-looking households from making the sacri...ces necessary to reach the high equilibrium. The Micawber Frontier shifts to the southwest once asset risk is removed, as shown in Figure 1. The dashed curve is the Micawber Frontier in the absence of risk. The boundaries marking the critical skill levels at which households move between the di¤erent accumulation regimes also shift out, meaning more intrinsically upwardly mobile households and fewer intrinsically chronically poor households when we eliminate the ex ante e¤ects of risk. The most dramatic e¤ects of risk are seen by considering a household whose skill and capital endowments place it between the two frontiers. Consider a household whose skill and initial asset endowments are represented by the solid circle in the middle of Figure 1. Absent the risk of asset shocks, such a house- hold would strive for the upper equilibrium and eventually escape poverty. In the presence of risk, such a household would abandon this accumulation strat- egy as futile and settle into a low level, chronically poor standard of living. In the face of asset risk, the extraordinary sacri...ce of consumption required to try to reach the high equilibrium is no longer worthwhile, and the household will optimally pursue the low level, poverty trap equilibrium. By contrast, the shift has no signi...cant behavioral e¤ect on either intrinsically chronically poor households (represented by the solid diamond on the left side of Figure 1) or intrinsically upwardly mobile households (the solid triangle on the right side of Figure 1). To explore the di¤erential e¤ects of risk and shocks on these di¤erent sub- populations, we simulated the income streams generated in three distinct set- tings: 11 A non-stochastic economy in which agents repeatedly apply the optimal investment rule, inr(ktj )17 , i An economy characterized by risk without realized shocks in which agents follow the risk-adjusted optimal accumulation rule, i (ktj ; ), but never i actually experience shocks (a scenario that allows us to isolate the ex ante e¤ects of risk); and, A fully stochastic economy, meaning that individuals not only follow the risk-adjusted optimal investment rule but each period they are subject to a random asset shock generated in accordance with the probability structure . These simulations show that for the intrinsically chronically poor (low i) and the upwardly mobile (high i) groups, the e¤ects of risk are relatively mod- est and attributable almost entirely to the disruptive, ex post e¤ects of asset shocks. By contrast, for the intermediate ability group, the ex ante behavioral (i.e., investment disincentive) e¤ects of uninsured risk account for most of the welfare e¤ects due to asset stochasticity. These e¤ects are also large in magnitude. While the discounted income streams for the other two groups fall only 5-10 percent in the fully stochastic scenario, the drop is approxi- mately 25 percent for the intermediate ability group, with roughly 90 percent of the losses due to the ex ante risk e¤ect exclusively.18 The di¤erence arises because while risk slightly reduces the desired steady state capital stock for low and high ability agents, mainly it forces them to regularly rebuild assets in order to reattain the desired steady state capital stock. In sharp contrast, intermediate ability agents may fundamentally shift their investment strategy in the presence of risk, eschewing any attempt at trying to reach the high-level equilibrium open to them, creating added avoidable chronic poverty. Among other things, these simulations show that in the presence of critical as- set thresholds, risk takes on particular importance for those individuals subject to multiple equilibria. Social protection policies could in principal generate large returns for such individuals, as the next two sections describe. Further- more, this response to risk adds an important twist to the moral hazard that naturally results from any policy that attempts to reduce risk exposure, as we discuss in section 4. 17Subscript nr represents no-risk. inr(ktj ) is policy function of the following Bell- man equation: Vnr(kt) max fu(f( ; kt) it it) + Vnr(kt+1jkt; it)g = max fu(f( ; kt) it) + Vnr(it + (1 it )kt)g 18Details on these simulation results are available from the authors by request. 12 2 Accumulation, Growth and the Evolution of Poverty in the Ab- sence of Social Protection The analysis in the prior section has shown that both the anticipation and the experience of economic shocks have a fundamental e¤ect on behavior and welfare in the presence of poverty traps, expanding the portion of the endow- ment space from which people do not escape poverty through their own e¤orts. This observation suggests that social protection policies have a fundamental role to play in stimulating poverty reduction and economic growth. But how should social protection be designed in a world of poverty traps? As a ...rst step towards answering this question, this section uses the model of individ- ual decisionmaking developed above as the basis for analyzing accumulation, growth and poverty in a stylized economy lacking any social protection poli- cies. Section 3 will then take a careful look at the impact of alternative social protection schemes on this economy. 2.1 The Stylized Economy and Measures of Performance Consider now an economy comprised of agents whose livelihood choices are described by inter-temporal maximization problems (2). To keep things sim- ple, we will assume that all shocks are idiosyncratic and that prices in the economy are una¤ected by shocks and by individuals'decisions. While these assumptions are clearly at odds with the real world, they permit us in the ...rst instance to clarify basic principles and tradeo¤s in the design of social protection policies.19 For purposes of the numerical analysis, we assume that there are 100 agents, each described by a skill and initial capital stock pair. We allocated agents along the skill continuum, with 25% each in the intrinsically chronically poor and upwardly mobile ranges, and half the agents in the intermediate ability range where endowments matter to their accumulation and welfare trajecto- ries. Each agent was then assigned a random initial capital stock drawn from a uniform distribution over the zero to ten range. While in any existing econ- omy we would expect there to be a correlation between skill and observed capital stock, this random assignment of capital creates an experimental envi- ronment in which to study asset dynamics under alternative social protection schemes. 19 When shocks are correlated across households, asset and other prices will begin to covary with household income. The implications of this covariance can be important as Carter, Little, Mogues and Negatu (2007) discuss empirically in the case of Ethiopia. Zimmerman and Carter (2003) theoretically examine the implications of such asset price covariance, showing that it can create another type of poverty trap. 13 Initial Distribution Year 50 Autarchy 8 8 6 6 Capital4 Capital4 2 2 0 0 0.9 1.0 1.1 1.2 0.9 1.0 1.1 1.2 Intrinsic Ability, Intrinsic Ability, Year 50 Needs-based Year 50 Triage 8 8 6 6 Capital4 Capital4 2 2 0 0 0.9 1.0 1.1 1.2 0.9 1.0 1.1 1.2 Intrinsic Ability, Intrinsic Ability, Fig. 2. Asset Evolution with and without Social Protection The diagram in the northwest corner of Figure 2 shows the initial distribution of ability and wealth in this stylized economy. Each symbol on the graph represents an individual agent. The solid line is the Micawber Threshold under the stochastic environment, while the dashed line is the asset poverty line. We employ the following core measures to track economic performance of the stylized economy under alternative social protection regimes:20 (1) Production Measures, including household income, national income (de- ...ned as the sum of the incomes of the 100 agents) and technology adop- tion (de...ned as the fraction of agents who adopt the higher yielding 20In work not reported here, we also analyzed the impacts of the di¤erent policies using a conventional Benthamite social welfare function as well as the dynamic poverty measures suggested by Calvo and Dercon (2007). The qualitative story told by these measures is similar to that which can be gleaned from the measures discussed here. 14 technology). Under the initial asset distribution, the GDP of this styl- ized economy is 187, with 60% of individuals initially using the high yielding technology. (2) Standard static poverty measures based on the Foster-Greer-Thorbecke (FGT) family of measures: 1 X yp Py = (2) n yi1 placing greater weight on larger underperformance relative to potential. In our subsequent calculations, we report only the =1 variant. Thus, de...ne Dy as 1 X f( ; k ( )) Dy = i i (3) n yi yp). Instead, the "potential gap" captures mainly those of intermediate skill who are trapped in a low-level equilibrium or those who are presently far from their long-run equilibrium (e.g., upwardly mobile 15 individuals with very low initial endowments). This measure is impractical in empirical work, since it relies on an estimate of steady-state capital holdings conditional on unobservable ability; it is nonetheless helpful as a conceptual tool for distinguishing unnecessary poverty from that which is unavoidable given individuals'immutable endowments and the economic environment in which they operate. These core, period-by-period measures permit us to capture both the social costs (foregone output and unexploited technological opportunities) and the human costs (low standards of living and unnecessary deprivation) of poverty traps. 2.2 Baseline Case of No Social Protection The northeast panel of Figure 2 shows the asset distribution after 50 years of simulated history for our stylized economy. As can be seen, the asset distribution (which was originally randomly distributed independently of the ability distribution) has bifurcated, with a strong positive correlation between innate ability and wealth. One set of individuals has comfortably settled above the Micawber Frontier at the high technology steady state. The other group is at the low level steady state, below the asset poverty line. There are quite a few poor individuals in the middle ability group whose potential to reach the high equilibrium has been blocked by their low inherited (or realized) asset levels that lock them below the Micawber Frontier. In this long-run state, the bifurcation is such that there is no transitory poverty ­reected in the absence of observations between the Micawber frontier and the asset poverty line. With no exogenous technical change or growth in productive inputs to stimu- late growth and modest investment incentives for a large portion of the popu- lation, GDP in this baseline economy is relatively stagnant over time (Figure 3, northwest quadrant). This reects the fact that the positive accumulation and associated productivity gains of those above the Micawber Frontier is o¤- set by the lost potential ­and wealth deaccumulation and productivity decline ­of many of those trapped below it. The decline among some sub-populations is manifest in the disadoption of the high technology, use of which falls from roughly 60% to only 40% of the population. Further reection of this eco- nomic bifurcation is found in the increasing levels of poverty, measured both as a poverty headcount (northeast quadrant) as well as by the poverty gap indicator (southwest quadrant) and our new unnecessary deprivation measure (southeast quadrant). Income inequality (not shown) declines modestly over the ...rst decade of the simulations, then increases above the initial level by year 25 as households converge on their -conditional long-run equilibria. The 16 GDP Poverty Headcount 210 0.4 195 0.2 10 30 50 10 30 50 year year Triage Poverty Gap Needs-based Autarchy Unnecessary Deprivation 0.08 0.10 0.04 0.04 0.00 10 30 50 10 30 50 year year Fig. 3. Evolution of Economy-wide Indicators under Alternative Forms of Relief lackluster performance of the base case poverty trap economy illustrates both the human and aggregate economic costs of poverty traps. The next sections consider alternative policy regimes that might lead to better outcomes. 3 Designing Unanticipated Social Relief to Manage the Ex Post E¤ects of Shocks This section examines the impact of alternative social relief policies on our stylized economy. We use the term "social relief" to signal that these poli- cies are implemented ex post of shocks and we (unrealistically) assume away agents'anticipation of the resulting transfers and the behavioral response that follows from such anticipation. In section 4 we explore "social protection" poli- cies that are properly anticipated by households, who adjust their behaviors accordingly. The purpose of the present, intermediate step is to make clear the value of addressing the purely ex post e¤ects of asset shocks, even if agents 17 cannot or do not expect transfers. For all alternatives, we assume that the operational agency21 has access to an annual income stream or budget of B = 5, which amounts to 2.5% of initial GDP.22 This amount was chosen because it is insu¢ cient to lift all initially poor individuals above the poverty line, though it is enough to substantially close the poverty gap. We further assume that the operational agency has access to full information, including household ability and asset holdings, re- alized shocks and knowledge of the production technology. While these are strong assumptions (and underwrite unrealistically perfect targeting), using them to explore targeting of this limited assistance budget helps further illus- trate the workings of the poverty trap economy. Based on those ...ndings, we explore alternative regimes that can e¤ectively link relief to development. 3.1 Poverty and Aid Traps under Needs-based Assistance Under the needs-based scenario, the agency uses its budget only for humani- tarian transfers. After each production cycle, it calculates the total poverty shortfall for the economy, S = Pyi 1), then all poor individuals are given transfers to increase their income to the level of the poverty line. If B < 1, then each poor individ- S ual is given transfers that move them to an income level equal to yp. Note B S that this targeting methods makes the largest transfers to the least well-o¤. This analysis also arti...cially assumes that individuals do not anticipate in- come transfers. That is, once individuals receive the transfer, they make their consumption versus investment decision according to maximization of prob- lem (2) above and (myopically) assume that future transfers will never occur. Section 4 relaxes this strong assumption, but for now it helps to understand the di¤erent e¤ects of alternative designs based on this extreme simplifying assumption. The impact of this needs-based assistance regime on asset distribution can be seen in the southwest diagram in Figure 2. The ...gure is quite similar to that under autarchy, except that asset levels are somewhat higher for those below the poverty line, especially among lower ability persons (reecting a transfer rule based on realized income levels). Turning to Figure 3, we see that the 21We use the broad term "operational agency" to encompass local or national gov- ernment as well as non-governmental organizations (NGOs) that might respond to shocks. 22We ignore the source of taxation that generates these resources and the associated distortionary e¤ects on the economy. They could be conceptualized as either ex- ternal resources (brought in by a donor, an NGO or a relief agency), or as domestic tax resources transferred from another sector of the national economy. 18 poverty headcount and unnecessary deprivation measure under needs-based assistance follows a trajectory nearly identical to that under autarchy. The FGT(1) poverty gap measure is substantially lower under needs-based assis- tance than without the assistance, reecting the added resources introduced into the system exogenously. But we can also see that the FGT(1) steadily rises after year 10 of the simulation. GDP is higher in the economy with needs- based transfer, but purely due to the extra 2.5% of GDP assumed available each year. In a world where budgets for transfers are available exogenously (e.g., via unrequited transfers associated with overseas development assistance), needs- based transfers plainly reduces income and asset poverty, if only because there are added resources in this scenario. However, these transfers do not funda- mentally alter the economy's dynamics. Indeed, the troubling irony is that poverty grows in this economy in spite of these transfers as some agents su¤er asset shocks that drop them into poverty but then receive insu¢ cient transfers to enable them to climb back out of poverty on their own. Transfer policies that are not designed to respond to the poverty trap mechanism systemati- cally fail to prevent more people from inadvertently falling into the trap over time. These results signal what might be termed a relief trap. By failing to stem the ow of intermediate ability individuals below the Micawber Frontier, the ...xed aid budget becomes less and less able to meet the needs of those below the poverty line. If the operational agency (or the international community) were intent on holding poverty at, say, year 10 levels, then increasing fractions of total public expenditures would need to be devoted to aid budgets. We abstract here from the standard public ...nance problems of raising revenues, but clearly the growing demands for transfers would have to be met either through increasingly distortionary taxation or through reducing funds avail- able for developing new technologies, building schools and infrastructure, or other interventions (not modeled here) that are aimed at boosting productiv- ity. Poverty traps can thus, in a very direct way, create relief traps. In their analysis of food aid, Barrett and Maxwell (2005) present evidence that such a relief trap may be emerging at a global scale. Current O¢ cial Development Assistance (ODA) ...gures from the OECD show that even though real ODA increased more than 60% since the mid-1970s, the share of ODA devoted to emergency assistance had increased far faster, ten-fold, from only 1% of total ODA to 10% over the same period. 19 3.2 Triage or Threshold-targeted Social Relief As the prior simulations make clear, risk in our model poverty trap econ- omy creates an ever increasing amount of unnecessary poverty that eventually overwhelms the capacity of needs-based assistance to provide relief. This ob- servation suggests that a social relief scheme targeted at the threshold de...ned by the Micawber Frontier ­i.e., a safety net designed to stem the increase in needless poverty ­can potentially generate a win-win-win scenario, with higher rates of improved technology adoption and GDP growth, reduced poverty (es- pecially for intermediate ability groups), and less stress on the operational agency's budget. To explore this idea, we initially analyze an admittedly harsh triage policy regime in which the agency provides transfers to households according to the following rule: (1) The budget, B, is ...rst allocated to individuals recently pushed below the Micawber Frontier. Denote these threshold-based transfers as productive safety net (PSN) transfers. An individual is eligible for a PSN transfer of PSNi = k~( ) i it it [i + (1 )kit] if iit + (1 )kit > k~( ) and i it it [i + (1 )kit] < k~( ). In words, if an individual was above the i Micawber Threshold prior to the most recent asset shock, but below it afterward, the agency provides a transfer to move the household back to the Micawber Frontier. If the total budget (PSN = Pi=1 PSNi) exceeds the total eligible transfers, then all individuals pushed below the threshold are given an asset transfer to lift them back to it. If the budget is insu¢ cient, then it is allocated ...rst to those closest to the Micawber Frontier so as to minimize the increase in the headcount of needless poverty. (2) If there is any remained budget after step 1 (i.e., if B > PSN), then those mid-ability individuals already below the Micawber Frontier (due to low initial inheritance or prior bad luck not stemmed by a PSN transfer) are given priority for cargo net transfers that lift them over the Micawber Frontier.23 Analogous to stage 1, total potential spending on cargo net transfers is calculated (denote this total amount as CN). If CN > B PSN, then the budget is again prioritized in order to minimize headcount poverty, by ...rst helping those closest to the Micawber Frontier. (3) If B > PSN + CN, then the residual budget is allocated according to the needs-based formulation discussed in the previous sub-section. 23The term "cargo net" was coined by Barrett (2005) and refers to transfers in- tended to lift people above ­or help people climb over ­thresholds at which ac- cumulation dynamics bifurcate, as distinct from safety nets, which prevent people from falling beneath those same thresholds. 20 Figure 3 again illustrates the results of this assistance regime for our styl- ized poverty trap economy. The results stand in strong contrast to autarchy and needs-based assistance simulation. By year 50, all needless poverty is eliminated and the headcount of total poverty levels o¤ at 25%, the share of the population that is intrinsically chronically poor by construction. Technol- ogy adoption is high, as is GDP (and GDP growth). In the longer-run, this triage approach to development assistance plainly outperforms needs-based assistance by any of these metrics. However, the southwest diagram in Figure 3 illustrates one of the major chal- lenges associated with this form of development assistance. The FGT(1) poverty gap measure is lower under needs-based assistance for the ...rst 10- 15 years of the simulation because needs-based assistance is targeted to the least well-o¤while the stylized triage policies are targeted to those nearest the Micawber Frontier. After 10-15 years, the remaining poor are better o¤under PSN design because it reduces the number of people needing assistance, allow- ing the ...xed budget to provide more generous support to those who inevitably need it. However, prior to that time, individuals who are poor, and especially the poorest, are better o¤ under needs-based targeting. The results for (asset or income) inequality (not shown) are qualitatively similar, with needs-based transfers generating lower inequality in the economy over the ...rst nine years, but threshold-based transfers generating lower inequality over longer hori- zons. These results underscore the di¢ cult tradeo¤s inherent to the design of social relief policy, both over time ­do we care for the poor better today or tomorrow? ­and across sub-populations of the poor ­do we focus on helping those who, with a bit of assistance, can then pull themselves out of poverty by their bootstraps or on those who will su¤er low living standards in the absence of assistance of inde...nite duration? In the presence of poverty traps, these tradeo¤s become especially sharp. Policymakers need to weigh these tradeo¤s and design social relief policy accordingly.24 24In additional simulations not reported here, we considered whether these tradeo¤s could be mitigated by mixing di¤erent kinds of transfers and/or by reallocating budgets intertemporally through borrowing. While these alternatives can reduce the magnitude of the tradeo¤s reported here somewhat, they cannot be eliminated entirely. This underscores the unavoidable nature of the targeting tradeo¤s in both cross-section (between di¤erent sub-populations of the poor and vulnerable) and over time in a poverty trap economy. 21 4 Using Safety Nets to Reduce the Ex Ante E¤ects of Risk in the Presence of Moral Hazard In the previous section we assumed that households do not react to social relief interventions. However, one would naturally expect agents to adapt their behaviors to a known transfer regime. Indeed, Hubbard, Skinner, and Zeldes (1995) show that social insurance programs discourage precautionary savings in the United States. In this section we therefore relax the previous assumption and consider households'response to safety net transfers and the implication of such endogenous response for the design of productive safety nets. We do not consider households'endogenous response to needs-based transfers, both in the interests of brevity and because the induced behavioral e¤ects are conceptually simpler than those with respect to safety net transfers, for reasons we explain below. 4.1 Positive and Negative Moral Hazard We expect two kinds of household response to safety net transfers. First, since safety net transfers mitigate asset risk, households are willing to accu- mulate more assets ceteris paribus. This is canonical moral hazard, in that the provision of some insurance induces increased risk taking.25 In this model, accumulation of assets subject to stochastic shocks is the only risk-taking be- havior available to agents. But asset accumulation is socially desirable in this setting, as it increases productivity and adoption of improved production tech- nologies, increases GDP and reduces poverty. We therefore call this incentive e¤ect "positive moral hazard." Second, because the safety net transfers are conditional (on pre- and post- shock asset holdings) and given the standard intertemporal tradeo¤ between current consumption and saving for future consumption, ceteris paribus house- holds have an incentive to satisfy the transfer condition as often as possible so as to receive extra transfers. If the agency will insure them against falling into a poverty trap, households do not need to self-insure through asset accumu- lation to the same degree, thereby creating a disincentive to invest that runs counter to social objectives. We therefore label this e¤ect "negative moral hazard". The trick in designing safety net policy is to maximize the positive moral haz- ard e¤ects and minimize the negative ones. In the remainder of this subsection, 25Recognize that risk is increasing in asset holdings because is a multiplicative shock and independent of k: Therefore, stochastic losses are greater when k is larger. 22 we explore the behavioral consequences of the simple PSN triage policy out- lined in the previous section. We show that awareness of the safety net shifts the Micawber Frontier in a complex way due to the dual e¤ects of positive and negative moral hazard, expanding the share of ability-wealth space from within which lower-intermediate ability households naturally gravitate toward the higher level technology and equilibrium. But it also induces signi...cant negative moral hazard, as households that would otherwise accumulate as- sets and adopt the high technology become far more likely to settle around the Frontier, maximizing current consumption and the likelihood of indem- nity payments from the operational agency's transfer scheme. In the next subsection we modify the safety net design slightly and show how this can substantially mitigate negative moral hazard. Assume that the productive safety net (PSN) design is as before, with the var- ious strong assumptions about perfect information on agents'ability, wealth and experience of shocks.26 The agency publicly (and credibly) announces that it will insure against potentially catastrophic asset loss by making in- demnity payments to any household that experiences a negative shock that drives its asset holdings below the autarchy Micawber Frontier k~( ), with the amount of the transfer exactly the amount that restores the household's wealth to k~( ).27 As before, each household maximizes its expected lifetime utility given agency policy, that is, given k~( ): X1 max E1 t 1u(ct) ct t=1 s.t. ct + it f( ; kt) kt+1 = 8 <~tk( ) if it + (1 )kt > kg and [i + (1 t t )kt] < k~( ) (4) : [it + (1 )kt] otherwise k1; k~( ) given This is the same as the problem speci...ed in section 1 except for the important change in the law of motion governing kt+1 now that households are aware of and respond to the agency transfer policy.28 The main result is that the anticipated safety net transfer induces some house- 26If the government cannot observe or verify ; an adverse selection problem arises too. We abstract from that possibility here. 27The existence of anticipated social insurance will of course endogenously change the Micawber Frontier so that the true threshold under insurance will be di¤erent than the insured capital stock. 28The household problem at period t can be represented in Bellman Equation form 23 holds to change their target capital level, from either the low or the high equilibrium levels, to the threshold at which the agency guarantees them insurance. This insurance equilibrium induces added asset accumulation by those at the low end of the intermediate ability range, but discourages asset accumulation and improved technology adoption by those in the upper end of the intermediate ability range. The northwest diagram in Figure 4 again shows the distribution of households in ability-asset space at t = 50 under autarchy and the Micawber Frontier by a solid line. The northeast diagram in Figure 4 shows the distribution under the safety net transfer scheme and adds the new, endogenous Micawber Frontier (the dashed line) to that which arises when agents do not adapt their behavior to the agency transfer policy. More intermediate ability households now move towards k~( ) instead of either the low or high equilibrium asset levels. Fewer households with ability in the low-intermediate range, rium asset level than under2autarchy; they increase their investment following [1:04; 1:06], remain at the low technology equilib- positive moral hazard. However, households in the upper-intermediate range, 2 [1:08;1:14]; become less likely to adopt the improved technology and hold less wealth when they anticipate the safety net transfers than when they do not. This reects the negative moral hazard created by a guaranteed transfer. For those intermediate ability agents who would, in the absence of the safety net, accumulate capital to the high-level equilibrium, the safety net reduces their need to sacri...ce current consumption in order to self-insure, thereby re- ducing savings and investment. The especially pernicious feature of negative moral hazard in this setting is thus that it not only increases agency indem- nity payments by inducing households to choose a steady state capital stock near the payout threshold, but it also reduces household risk-taking via asset accumulation. Figure 5 gives intuition for the emergence of this new behavior. Note that nature essentially acts as a tax collector in this model, probabilistically tak- ing away a fraction of assets every period. Absent safety nets, the nature's expected marginal tax rate in this model is 1.7%, as shown by the solid line in Figure 5. Under the safety net scheme, individuals exactly at the safety net point (k~( )) face a zero marginal tax rate as all asset losses are covered by safety net transfers. However, assets accumulated beyond the safety net trans- as: V (kt) max fu(f( ; kt) it it) + E [V (kt+1jkt; it)]g where E [V (kt+1jkt;it)] = V (kt+1(kt; it; ; kg; ))d ( ) t t )kt > kg and t t [i + (1 )kt] < kg kt+1(kt; it; ; kg; ) = t (kt[it Z g if it + (1 + (1 )kt] otherwise 24 Autarchy Standard Safety Net k 8 it k 8 it 6 6 Assets, 4 Assets, 4 ial ial Init 2 Init 2 0 0 0.9 1.0 1.1 1.2 0.9 1.0 1.1 1.2 Intrinsic Ability, Intrinsic Ability, Fuzzy Social Protection Temporary Fuzzy Social Protection k 8 it k 8 it 6 6 Assets, 4 Assets, 4 ial ial Init2 Init2 0 0 0.9 1.0 1.1 1.2 0.9 1.0 1.1 1.2 Intrinsic Ability, Intrinsic Ability, Fig. 4. Moral Hazard with Alternative Social Protection Policies fer point face a sharply increasing marginal tax rate. As shown by the dotted line in Figure 5, under the standard safety net the marginal tax rate abruptly jumps from zero to 10%, and then slowly decreases to the natural tax rate of 1.7%. It is this sharp and discontinuous elimination of social protection as the individual moves away from the insured point k~( ) that discourages accumulation and leads to a class of agents who become welfare dependent. There is an obvious analogy of this problem to that of an earlier generation of US welfare programs whose rapid elimination of bene...ts when an earned income threshold was crossed created extremely high e¤ective marginal tax rates on earned income. As with those program, a solution can be found by relaxing the rate at which the social protection bene...ts are eliminated so as to elminate the sharp jump in marginal tax rates. 25 10 Standard Safety Net Fuzzy Safety Net 8 No Safety Net (Autarchy) (%) Rate Tax 6 Marginal 4 Nature's 2 0 k~() Capital, kit Fig. 5. Nature's Marginal Tax Rates under Alternative Social Protection Schemes 4.2 Fuzzy Safety Nets The previous subsection demonstrated that when households naturally antic- ipate and react to the agency's implementation of safety net transfers, the resulting negative moral hazard sharply reduces asset accumulation, GDP, technology adoption and long-run poverty reduction (compared to what can be achieved when agents myopically do not anticipate social protection). This subsection outlines a way to overcome most of the negative moral hazard problem by modifying the simple safety net transfer scheme studied above. Our modi...cation is two-fold. First, we mitigate the negative e¤ects of the safety net transfer on incentives to accumulate more than the asset threshold the agency uses to determine transfer eligibility by using a "fuzzy"transfer scheme we describe in detail below. Second, the agency announces that safety net transfer scheme is temporary. If the policy period is long enough to permit some households to accumulate assets greater than the Micawber Frontier, be- fore the safety net policy lapses, they move to the high technology equilibrium asset level afterward but are thereafter vulnerable to catastrophic asset shocks against which the safety net previously protected them. This sort of sunset 26 clause to the policy is of course consistent with the well-known point that in the presence of multiple equilibria, temporary interventions can have perma- nent e¤ects. Short-lived productive safety nets can stimulate additional asset accumulation and technology adoption by those intermediate ability agents who would otherwise remain chronically poor without inducing dependence on safety net transfers. Turning to the ...rst modi...cation of the safety net, we can substantially mit- igate the distortions created by the high marginal tax rates discussed in the prior section by modifying the productive safety net scheme. We replace the variable transfer to a ...xed target asset level with a variable, fuzzy transfer to a variable ex post asset stock. Transfers now return the household to a convex combination of its pre-shock asset holdings, it +(1 )kt, and its post- shock realized wealth, [i + (1 t t )kt]. The technical details are presented in Appendix 2. But the essence of this fuzzy safety net scheme is that expected indemnity payments in the event of loss do not decline one-for-one as agents increase their asset holdings. While expected payments are still declining in wealth, they decline more slowly, thereby attenuating the increase in the im- plicit marginal tax on investment. The dashed line in Figure 5 depicts the resulting expected marginal tax rate under this fuzzy safety net transfer. As can be seen, the sharp jump in the marginal tax rate is eliminated and the im- plicit marginal tax rate on investment is now increasing rather than decreasing in wealth beyond the threshold, generating a more progressive scheme. The consequence of this change in e¤ective marginal taxation of asset accu- mulation is striking. The southwest diagram in Figure 4 depicts household distribution in ability-asset space after 50 years and the Micawber Frontier under the fuzzy safety net transfer. By comparing the southwest diagram with the northeast in Figure 4, we see that the positive moral hazard e¤ect is magni...ed by the fuzzy safety net, relative to the standard safety net, and that negative moral hazard is almost fully extinguished. There are no longer households settling at the insurance threshold k~( ), receiving transfers but not adopting the improved technology. A substantial cohort of intermedi- ate ability households now optimally accumulate more wealth, moving them comfortably above the Micawber Frontier, although the asset holdings of in- termediate ability households remain below those that obtain in the naive safety nets model under which households act as if the transfer scheme does not exist (depicted in the southwest diagram in Figure 4). The second re...nement we make is to put a sunset clause on the safety net scheme, i.e., the agency announces in the ...rst period that it will terminate safety net transfer scheme at t = Tg: We call this the temporary fuzzy safety net transfer policy. The southeast diagram in Figure 4 depicts the resulting household distribution in ability-asset space at t = 50 and the Micawber Fron- 27 tier under the temporary fuzzy safety net transfer with Tg = 20:29 By making a credible announcement that the safety net will not persist inde...nitely, agency can take advantage of the positive moral hazard (investment-inducing) e¤ects of the transfer scheme and, in the longer-term after Tg has passed, avoid the negative moral hazard e¤ects. The Micawber Frontier expands leftward and down during the life of the fuzzy safety net policy, giving more households an incentive to invest, to adopt improved technologies and thereby to grow their way out of chronic poverty. Of course, after the policy lapses, the Micaw- ber Frontier shifts back, and those who are subsequently shocked beneath the autarchic Frontier then collapse into chronic poverty. The gains of that policy thus become ...nite-lived. The termination of the safety net transfer thus inevitably involves a tradeo¤. If the agency does not terminate the policy, some households stay at asset levels which are ine¢ cient in the sense that they would accumulate more if the safety net did not attenuate accumulation incentives, in addition to the added costs to the agency of making indemnity payments in additional periods. On the other hand, if the agency terminates the policy, some households with moderate ability may subsequently experience negative asset shocks and be knocked beneath the Micawber Frontier and onto the undesirable path toward the low technology, poverty trap equilibrium. The northwest diagram in Figure 6 shows the GDP timepaths under the two di¤erent policy schemes as well as under autarchy (no safety net policy) and the needs-based social relief policy from section 3. GDP is ultimately markedly higher under either safety net program, as compared to the econ- omy in autarchy.30 But the GDP path under the temporary fuzzy safety net lies signi...cantly above that for the permanent fuzzy safety net transfer, imply- ing that the induced increase in asset accumulation ­due to the anticipation of safety net termination as much as by the event itself ­more than o¤sets the decrease in GDP due to households that subsequently su¤er shocks. The resulting gap is of course greatest at Tg (year 20) because the added invest- 29 We solve the resulting optimization problem backward: First, solve the problem at t Tg + 1 and obtain V (kt; t) and ir(kt; tj ; ) for t Tg + 1; which are the same as those under autarchy. Second, given V (kTg+1;Tg + 1), solve the problem at t = Tg and obtain V (kTg;Tg) and ir(kTg;Tgj ; ). Third, given V (kTg;Tg1)j, solve the problem at t = Tg 1 and obtain V (kTg ; Tg 1 1) and ir(kTg ; Tg 1 ; ). Iterate this backward until t = 1. 30 For almost 15 years, the needs-based relief scheme outperforms the other schemes illustrated here. However, as the southeast graph in Figure 6 shows, the amount of transfers under the needs-based scheme is almost double that under the other schemes. Given this budget di¤erence, it is remarkable that under the fuzzy safety net scheme, GDP catches up and eventually surpasses that under the needs-based scheme. This result clearly illustrates that the former schemes are working by crowding in private accumulation. 28 GDP Poverty Headcount 200 0.5 190 0.3 Autarchy Need Based 10 30 50 10 30 50 year Fuzzy Safety Net Temporary Fuzzy Safety Net year Unnecessary Deprivation Program Cost 7 0.10 3 0.05 10 30 50 10 30 50 year year Fig. 6. Evolution of Indicators under Alternative Social Protection Regimes ment incentives apply throughout the simulation but the absence of the safety net is only felt after that time. The GDP gap between the two safety net schemes steadily narrows thereafter as the loss of asset protection after safety net termination begins to slowly take a toll. That toll is most starkly reected by the poverty headcount and unnecessary deprivation indicators shown in the northeast and southwest diagrams of Fig- ure 6, respectively. The temporary fuzzy safety net outperforms the permanent fuzzy safety net by both measures up until the former policy terminates. After year 20 (Tg), poverty and unnecessary deprivation remain steadily low under the fuzzy safety net policy but trend upward in the economy whose safety net has lapsed. We do not impose budget constraints on the fuzzy safety net transfer policy since it is not easy to calculate the equilibrium in which household's expecta- tions of the timing and amount of transfer receipts are consistent with actual 29 timing and amount of transfer receipts and budgets constraints are satis...ed. But as the southeast diagram in Figure 6 indicates, the fuzzy safety net policy tends to cost the operational agency far less than the needs-based transfers under a ...xed budget explored in section 3. The time-discounted present value of actual spending for the permanent fuzzy safety net transfers is 43.6, less than half the 95.2 cost of the needs-based transfers. The discounted present value cost of the temporary fuzzy transfer policy is only 27.3 due to its shorter lifespan. Thus in cost-bene...t terms using any of our key indicators, social pol- icy based on productive safety nets outperforms either autarchy (no assistance to poor or vulnerable households) or needs-based social relief policy. 5 Conclusions This paper has put forward a stochastic dynamic programming model of a poverty trap economy in which asset risk plays a major role and heterogeneity of individual ability creates two types of chronic poverty. Some people are chronically poor because their innate ability condemns them to a low standard of living. Others su¤er unnecessary deprivation simply because they are born with insu¢ cient access to productive capital and are below the critical asset threshold needed to make it dynamically optimal to undertake the short-term sacri...ces inherent to long-term investment. Using this framework, we show that needs-based, unanticipated social relief policies can fall prey to an aid trap in which income support to the poorest of the poor ­predominantly the intrinsically chronically poor ­crowds out asset protection for those of intermediate ability and wealth who are vulnerable to shocks. Members of this latter group steadily fall into needless chronic poverty, adding to the pool of individuals needing income support. The result is that while the depth of poverty is initially reduced among the poorest of the poor, their lot deteriorates over time due to increasing competition for limited relief resources. Moreover, the numbers of people su¤ering poverty do not change appreciably, nor does wealth accumulation, economic output or adoption rates of improved technologies. We then show that an unanticipated triage policy that prioritizes threshold- targeted social protection for the intermediate wealth and ability group creates a "productive safety net"that largely eliminates needless chronic poverty and boosts growth through endogenous asset accumulation and adoption of im- proved technologies. While this triage policy still confronts important trade- o¤s among di¤erent poor people and over time, this theoretical exercise es- tablishes the potential gains to threshold-targeted social protection. As the Lucas critique famously showed, any policy naturally induces a be- 30 havioral response. We therefore go on to explore what happens when social protection is fully anticipated and demonstrate how safety nets have a complex e¤ect on individuals'investment behavior in the presence of poverty traps. In particular, an anticipated safety net induces some individuals to accumulate more assets than they would otherwise, which naturally stimulates economic activity and reduces poverty. But anticipated social protection also discour- ages others from investing beyond the range where they remain eligible for transfers, as externally-provided insurance e¤ectively displaces self-insurance through asset accumulation. This e¤ect retards economic growth, technology adoption and progress in the ...ght against poverty. We term these e¤ects pos- itive and negative moral hazard, respectively. The balance between them is manipulable through the design of the safety net. We show that by altering the payo¤ scheme slightly and by introducing a credible, known sunset clause to terminate the safety net program after a period of years, the positive e¤ects can be magni...ed and the negative ones e¤ectively extinguished. Of course, the price of these gains is the loss of safety net protection beyond the expiration of the policy, which leads to later increases in poverty. Ultimately, the key ...nding of this paper is that poverty traps can have a pronounced e¤ect on the performance and appropriate design of policy in- tended to stimulate poverty reduction, economic growth and uptake of im- proved production technologies. There are potentially large returns to devel- oping and using knowledge about critical asset thresholds to target assistance in economies characterized by poverty traps. Whatever its analytical com- plexity, the analysis here has nonetheless massively oversimpli...ed the real world. Improvements to the model are clearly possible, perhaps especially by endogenizing the ability parameter, : The more substantive research agenda, however, likely involves empirically identifying critical asset thresholds (the Micawber Frontier, as we have called it) and then seeing if threshold-targeted assistance can really liberate human potential to craft pathways from poverty. 31 Appendix 1: Parameters and Other Details for Numeri- cal Simulation This section provides additional detail on the formal model used to generate the results discussed in the main body of the paper. The functional speci...cation for the utility function u( ) is ct 1 1 u(ct) = 1 The probability density of tis assumed to be: 8 > > = 1:0 > 0:90 if t > > < 0:05 if t= 0:9 density of t= > >0:03 if > = 0:8 > t > : 0:02 if t= 0:7 The other structural parameter values are assumed as follows: = 1:5; = 0:08; = 0:95, = 0:3; = 0:45; E = 0:45. L H We discretize continuous variables k and as follows: k = f0:1;0:2;:::;15:0g and = f0:94; 0:96; : : : ; 1:22g. For the simulation of the stylized economy of 100 individuals we draw from N(1:08; 0:0742), with the mean and variance chosen so that ex ante proportion of low, middle, and high type individuals (de...ned relative to the stochastic Micawber Frontier) would be 25%, 50%, and 25%, respectively. We draw k1 from Uniform[0:1;10:0] and assume that k1 and are statistically independent from each other. We specify poverty line as follows. The asset level which generates income exactly equal to the poverty line satis...es the following equation: yp = f( ; kp): where yp is income-based poverty line. That asset level obviously depends on and we denote it by kp( ). We assume that an intermediate ability individual would fall below the income poverty line if he used the low technology and thus set poverty line by kp( = 1:12) = 3:4 and thus yp = 1:62. 32 Appendix 2: Fuzzy Safety Net Transfers Denote the safety net insurance threshold as kg. In order to decrease the negative moral hazard e¤ect of safety net transfers, i.e., the disincentive to accumulate assets beyond kg, we smooth kt+1 in (it + (1 )kt; kt+1) space. The best way to understand the idea is to draw ...gures in (it +(1 )kt; kt+1) space. Under section 3's assumptions, when a household gets t< 1, the kt+1 line is at in the region it + (1 )kt 2 (kg; kg= ): Thus the expected loss t due to a negative asset shock increases rapidly when a household increases it +(1 )kt from kg to kg= . This is why some households stick at the point t where kt = kg. In section 4, we modify safety net transfer so that kt+1is increasing in the region it + (1 )kt 2 (kg; kg= ) where t < 1 and thus the expected loss increases less rapidly when a household increases it + (1 )kt from kg to kg= tthan occurs under the previous PSN design. Under the new transfer scheme, kt+1 follows the following transition rule: 8 kt+1(kt; it; ; kg; ) = t > > [ ( ) + (1 > ( )) )][it + (1 t )kt] > > < if it + (1 )kt > kg (5) > > > and [i + (1 )kt] > kg > t t g > : t t [i + (1 )kt] otherwise where > 1 is a constant the agency sets (we let g g = 1:5) and ( ) 2 [0; 1] is a function of it + (1 )kt, more precisely 1 = 1 [it + (1 )kt]: kg g kg t Note that when a household receives a transfer under this smoothed safety net scheme, kt+1 is a convex combination of it +(1 )kt and [i + (1 t t )kt] and the following: 8 > > <= 1 if it + (1 )kt = kg > g t > :2 (0;1) if it + (1 )kt 2 (kg; kg= ) = 0 if it + (1 )kt = gkg= t The household problem at period t is: V (kt) max fu(f( ; kt) it it) + E [V (kt+1jkt; it)]g where E [V (kt+1jkt;it)] = Z V (kt+1(kt; it; ; kg; ))d ( ) t t where kt+1(kt;it; ;kg; ) is de...ned by (5). t 33 References Aghion, Philippe, and Patrick Bolton (1997) "A theory of trickle-down growth and development."Review of Economic Studies 64(2), 151­172. Azariadis, Costas, and John Stachurski (2005) "Poverty traps."In Handbook of Economic Growth, ed. Philippe Aghion and Steven N. Durlauf, vol. 1A (Elsevier) chapter 5. Banerjee, Abhijit V. and Duo, Esther, 2005. "Growth Theory through the Lens of Development Economics," in Philippe Aghion and Steven Durlauf (ed.), Handbook of Economic Growth, volume 1, chapter 7, pages 473-552 El- sevier. Banerjee, Abhijit V., and Andrew F. Newman (1991) "Risk-bearing and the theory of income distribution."Review of Economic Studies 58(2), 211­235. Banerjee, Abhijit V. and Andrew F. Newman (1993) "Occupational choice and the process of development." Journal of Political Economy 101(2), 274­298. Barrett, C.B. (2005) "Rural Poverty Dynamics: Development Policy Impli- cations," in David Colman and Nick Vink, editors, Reshaping Agriculture's Contributions To Society (Oxford: Blackwell). Barrett, C.B., M.R. Carter and P.D. Little, editors (2006), "Understanding and Reducing Persistent Poverty in Africa", special issue of Journal of Devel- opment Studies, 42(2). Barrett, C.B. and D.G. Maxwell (2005), Food Aid After Fifty Years: Recasting Its Role (London: Routledge). Barrett, C.B., P.P. Marenya, J.G. McPeak, B. Minten, F.M. Murithi, W. Oluoch-Kosura, F. Place, J.C. Randrianarisoa, J. Rasambainarivo and J. Wangila (2006), "Welfare Dynamics in Rural Kenya and Madagascar,"Journal of De- velopment Studies 42(2):248-277. Becker, Gary S., and Nigel Tomes (1979) "An equilibrium theory of the distrib- ution of income and intergenerational mobility."Journal of Political Economy 87(6), 1153­89. Bowles, Samuel, Steven N. Durlauf and Karla Ho¤ (2006) Poverty Traps Princeton University Press; Princeton, NJ. Buera, Francisco J. (2005) "A dynamic model of entrepreneurship with bor- rowing constraints: Theory and evidence."working paper, Northwestern Uni- versity. 34 Calvo, C. and Dercon, S. (2007), "Chronic Poverty and All That: The Mea- surement of Poverty over Time,"working paper, Oxford University. Carter, M.R. and C.B. Barrett (2006), "The Economics of Poverty Traps and Persistent Poverty: An Asset-Based Approach,"Journal of Development Stud- ies 42(2): 178-199. Carter, M.R. and M. Ikegami (2007), "Looking Forward: Theory-based Mea- sures of Chronic Poverty and Vulnerability,"Chronic Poverty Research Centre Carter, Michael, Peter Little, Tewodaj Mogues and W. Negatu (2007). "Poverty Traps and the Long-term Consequences of Natural Disasters in Ethiopia and Honduras,"World Development. Chronic Poverty Research Centre (CPRC). (2004) "Chronic Poverty Report 2004-2005."http://www.chronicpoverty.org/resources/cprc_report_2004-2005.html Dercon, Stefan (2003) "Poverty traps and development: the e¢ ciency-equity trade-o¤ revisited." Elbers, Chris, and Jan Willem Gunning (2005) "Growth and risk: Analytical and empirical issues." Galor, Oded, and Joseph Zeira (1993) "Income distribution and macroeco- nomics."Review of Economic Studies 60(1), 35­52. Ghatak, M., M. Morelli, and T. Sjostrom (2001) "Occupational choice and dynamic incentives."Review of Economic Studies 68(4), 781­810. Ghatak, Maitreesh, and Neville Nien-Huei Jiang (2002) "A simple model of inequality, occupational choice, and development." Journal of Development Economics 69(1), 205­226. Hoddinott, John (2006) "Shocks and their consequences across and within households in rural zimbabwe,"Journal of Development Studies 42(2), 301­ 21. Hubbard, R. Glenn, Jonathan Skinner, and Stephen P. Zeldes (1995) "Precau- tionary saving and social insurance."Journal of Political Economy 103(2), 360­ 399. Loury, Glenn C. (1981) "Intergenerational transfers and the distribution of earnings."Econometrica 49(4), 843­867. Piketty, Thomas (1997) "The dynamics of the wealth distribution and the interest rate with credit rationing."Review of Economic Studies 64(2), 173­ 189. 35 Ray, Debraj, and Peter A. Streufert (1993) "Dynamic equilibria with unem- ployment due to undernourishment."Economic Theory 3(1), 61­85. Sachs, Je¤rey D. (2005) The End of Poverty Penguin Books: New York. Santos, Paulo, and Christopher B. Barrett (2006) "Heterogeneous wealth dy- namics: On the roles of risk and ability."Cornell University working paper. Zimmerman, Frederick J., and Michael R. Carter (2003) "Asset smoothing, consumption smoothing and the reproduction of inequality under risk and subsistence constraints."Journal of Development Economics 71(2), 233­260. 36 Social Protection Discussion Paper Series Titles No. Title 0804 Poverty Traps and Social Protection by Christopher B. Barrett, Michael R. Carter and Munenobu Ikegami, February 2008 0803 Live Longer, Work Longer: Making It Happen in the Labor Market by Milan Vodopivec and Primoz Dolenc, February 2008 (online only) 0802 Disability in Kazakhstan: An Evaluation of Official Data by Ai-Gul S. Seitenova and Charles M. Becker, February 2008 (online only) 0801 Disability Insurance with Pre-funding and Private Participation: The Chilean Model by Estelle James, Augusto Iglesias and Alejandra Cox Edwards, January 2008 0719 The Life-Course Perspective and Social Policies: An Issues Note by A.L. Bovenberg, November 2007 0718 Social Safety Nets and Targeted Social Assistance: Lessons from the European Experience by Chris de Neubourg, Julie Castonguay and Keetie Roelen, November 2007 (online only) 0717 Informality and Social Protection: Preliminary Results from Pilot Surveys in Bulgaria and Colombia by Franco Peracchi, Valeria Perotti and Stefano Scarpetta, October 2007 (online only) 0716 How Labor Market Policies can Combine Workers' Protection with Job Creation: A Partial Review of Some Key Issues and Policy Options by Gaëlle Pierre and Stefano Scarpetta, October 2007 (online only) 0715 A Review of Interventions to Support Young Workers: Findings of the Youth Employment Inventory by Gordon Betcherman, Martin Godfrey, Susana Puerto, Friederike Rother, and Antoneta Stavreska, October 2007 0714 Performance of Social Safety Net Programs in Uttar Pradesh by Mohamed Ihsan Ajwad, October 2007 0713 Are All Labor Regulations Equal? Assessing the Effects of Job Security, Labor Dispute and Contract Labor Laws in India by Ahmad Ahsan and Carmen Pagés, June 2007 0712 Convention on the Rights of Persons with Disabilities: Its Implementation and Relevance for the World Bank by Katherine Guernsey, Marco Nicoli and Alberto Ninio, June 2007 0711 Reaching the Poor and Vulnerable: Targeting Strategies for Social Funds and other Community-Driven Programs by Julie Van Domelen, May 2007 0710 The Macedonia Community Development Project: Empowerment through Targeting and Institution Building by Caroline Mascarell, May 2007 0709 The Nuts and Bolts of Brazil's Bolsa Família Program: Implementing Conditional Cash Transfers in a Decentralized Context by Kathy Lindert, Anja Linder, Jason Hobbs and Bénédicte de la Brière, May 2007 (online only) 0708 Globalization and Employment Conditions Study by Drusilla K. Brown, April 2007 0707 The Kosovo Pension Reform: Achievements and Lessons by John Gubbels, David Snelbecker and Lena Zezulin, April 2007 (online only) 0706 Measuring Disability Prevalence by Daniel Mont, March 2007 0705 Social Safety Nets in World Bank Lending and Analytic Work: FY2002- 2006 by Annamaria Milazzo and Margaret Grosh, March 2007 (online only) 0704 Child Labor and Youth Employment: Ethiopia Country Study by Lorenzo Guarcello and Furio Rosati, March 2007 0703 Aging and Demographic Change in European Societies: Main Trends and Alternative Policy Options by Rainer Muenz, March 2007 (online only) 0702 Seasonal Migration and Early Childhood Development by Karen Macours and Renos Vakis, March 2007 0701 The Social Assimilation of Immigrants by Domenico de Palo, Riccardo Faini and Alessandra Venturini, February 2007 (online only) 0616 Pension Systems in Latin America: Concepts and Measurements of Coverage by Rafael Rofman and Leonardo Lucchetti, November 2006 (online only). Also available in Spanish. 0615 Labor Market Outcomes of Natives and Immigrants: Evidence from the ECHP by Franco Peracchi and Domenico Depalo, November 2006 (online only) 0614 The Relative Merits of Skilled and Unskilled Migration, Temporary and Permanent Labor Migration, and Portability of Social Security Benefits by Johannes Koettl under guidance of and with input from Robert Holzmann and Stefano Scarpetta, November 2006 (online only) 0613 The Limited Job Prospects of Displaced Workers: Evidence from Two Cities in China by Gordon Betcherman and Niels-Hugo Blunch, October 2006 0612 Unemployment Insurance in Chile: A New Model of Income Support for Unemployed Workers by Germán Acevedo, Patricio Eskenazi and Carmen Pagés, October 2006 0611 Evaluating Social Fund Impact: A Toolkit for Task Teams and Social Fund Managers by Sarah Adam, October 2006 0610 Risk and Vulnerability Considerations in Poverty Analysis: Recent Advances and Future Directions by Carlo Cafiero and Renos Vakis, October 2006 0609 Comparing Individual Retirement Accounts in Asia: Singapore, Thailand, Hong Kong and PRC by Yasue Pai, September 2006 (online only) 0608 Pension System Reforms by Anita M. Schwarz, September 2006 (online only) 0607 Youth Labor Market in Burkina Faso: Recent Trends by Daniel Parent, July 2006 0606 Youth in the Labor Market and the Transition from School to Work in Tanzania by Florence Kondylis and Marco Manacorda, July 2006 0605 Redistributing Income to the Poor and the Rich: Public Transfers in Latin America and the Caribbean by Kathy Lindert, Emmanuel Skoufias and Joseph Shapiro, August 2006 (online only) 0604 Uninsured Risk and Asset Protection: Can Conditional Cash Transfer Programs Serve as Safety Nets? by Alain de Janvry, Elisabeth Sadoulet, Pantelis Solomon and Renos Vakis, June 2006 0603 Examining Conditional Cash Transfer Programs: A Role for Increased Social Inclusion? by Bénédicte de la Brière and Laura B. Rawlings, June 2006 (online only) 0602 Civil-service Pension Schemes Around the World by Robert Palacios and Edward Whitehouse, May 2006 (online only) 0601 Social Pensions Part I: Their Role in the Overall Pension System by Robert Palacios and Oleksiy Sluchynsky, May 2006 (online only) To view Social Protection Discussion papers published prior to 2006, please visit www.worldbank.org/sp. Summary Findings This paper demonstrates that there are potentially large returns to social protection policy that stakes out a productive safety net below the vulnerable and keeps them from slipping into a poverty trap. Much of the value of the productive safety net comes from mitigating the ex ante effects of risk and crowding in additional investment. The analysis also explores the implications of different mechanisms of targeting social protection transfers. In the presence of poverty traps, modestly regressive targeting based on critical asset thresholds may have better long-run poverty reduction effects than traditional needs-based targeting. HUMAN DEVELOPMENT NETWORK About this series... About this series Social Protection Discussion Papers are published to communicate the results of The World Bank's work to the development community with the least possible delay. The typescript manuscript of this paper therefore has not been prepared in accordance with the procedures appropriate to formally edited texts. The findings, interpretations, and conclusions expressed herein are those of the author(s), and do not necessarily reflect the views of the International Bank for Reconstruction and Development / The World Bank and its affiliated organizations, or those of the Executive Directors of The World Bank or the governments they represent. The World Bank does not guarantee the accuracy of the data included in this work. For free copies of this paper, please contact the Social Protection Advisory Service, The World Bank, 1818 H Street, N.W., Room G7-703, Washington, D.C. 20433 USA. Telephone: (202) 458-5267, Fax: (202) 614- 0471, E-mail: socialprotection@worldbank.org or visit the Social Protection website at www.worldbank.org/sp.