Social Protection in the Face of Climate Change:

Targeting Principles and Financing Mechanisms

Michael R. Carter and Sarah A. Janzen

June 2015

Abstract

It has long been recognized that climate risk is an important driver oflong-term poverty dynamics, especially in rural regions. We build a dynamic,multi-generation household model of consumption, accumulation and risk man-agement that allows us to draw out the full consequences of exposure to thisrisk (or vulnerability) by incorporating the long-term impacts of consumptionshortfalls (induced by the optimal “asset smoothing” coping behavior of thevulnerable) on the human capital and long-term well-being of families. Weshow that the long-term level and depth of poverty can be improved by in-corporating elements of “Vulnerability-targeted Social Protection” (VSP) intoa conventional, cash transfer-based system of social protection. If publiclyfunded, VSP implies less budget for other elements of social protection. In ane↵ort to mediate this implied tradeo↵, we then explore the degree to whichVSP can be implemented through an insurance mechanism. This mechanismnot only allows smoothing of public expenditures across time, the provisionof VSP as a partially subsidized insurance contract also encourages the vul-nerable themselves to pay a fraction of the cost. Our analysis shows that thislatter scheme dominates the other in terms of both poverty measures as well aseconomic growth measures. The relative gains brought about by this schemeof insurance-augmented social protection increase–at least for a while–underclimate change scenarios. However, if climage change becomes too severe, theneven this novel form of social protection loses its ability to stabilize the extentand depth of poverty.

Michael Carter is Professor, Department of Agricultural and Resource Economics at the Universityof California, Davis, and a member of NBER and the Ginanni Foundation. Sarah Janzen is AssistantProfessor, Department of Agricultural Economics & Economics, Montana State University.

1 Introduction

Climate shocks, which reduce incomes and destroy productive assets, can drive ruralhouseholds into poverty. Climate change, which increases the frequency and intensityof these shocks, threatens to make climate risk an ever more important contributorto poverty dynamics.

Against this backdrop, we ask two questions concerning the design of social pro-tection programs intending to reduce poverty and facilitate the upward mobility ofpoor and vulnerable households:

1. How should a given social protection budget be targeted or prioritized betweenthe already destitute and those who are vulnerable to becoming destitute?

2. Can public budget constraints be relaxed – and poverty impacts improved –through targeting social protection at the vulnerable with partial financingprovided by beneficiaries’ own private ‘premium’ contributions?

To gain purchase on these questions, we develop a theoretical, dynamic programmingmodel of multi-generation families or ’dynasties’ that in the face of risk allocatescarce resources between consumption and asset accumulation to maximize long-term family well-being. Loosely calibrated on the pastoral regions of East Africawhere climatic shocks already loom large and drive poverty, each dynasty in themodel begins with initial levels of physical assets and human capabilities or capital.Over time, shocks can not only drive vulnerable households into long-term poverty,they may also induce households to cut consumption and preserve physical assets asthey seek to avoid chronic poverty.

One novelty of the model developed here is that we allow consumption shortfalls(or undernutrition) to feedback and probabilistically reduce the human and economiccapabilities of the dynasty’s next generation. This feedback further increases the im-pact of vulnerability on long-term poverty dynamics, raising the stakes for addressingpoverty and vulnerability through carefully designed social protection programs.

Using this model, we explore the e↵ectiveness of di↵erent schemes of social pro-tection, ranging from conventional cash transfers, means-tested and targeted at thealready destitute, as well as novel schemes where a fraction of a fixed social protectionbudget is spent as contingent transfers that protect the vulnerable. Our key findingsare as follows: Gauged by standard poverty metrics, targeting some of the fixed socialprotection budget at the vulnerable can reduce both the extent and depth of povertyover time relative to a conventional cash transfer strategy. Climate change increasesrisk, which increases the importance and value of targeting vulnerable households for

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social protection provision. However, given budget constraints, targeting the vulner-able induces a tradeo↵ between the short-term and the long-term well-being of thepoor. This tradeo↵ can be partially mitigated if a fixed social protection budget isstretched by having the vulnerable privately fund a portion of the premium load foran insurance that functions as contingent social protection.

The remainder of this paper is organized as follows. Section 2 develops the dy-namic model of dynastic decisionmaking, illustrating how coping strategies interactwith the evolution of human capital to alter the mapping between initial endow-ments and long-term poverty. Section 3 then explores alternative schemes of socialprotection, including cash transfers, vulnerability-targeted social protection and in-surance models with mixed public and private financing of social protection. Section4 summarizes the impact of increased risk on the design of social protection. Finally,Section 5 concludes with thoughts on furthering the social protection conversationin an era of climate change-fueled increases in the number and intensity of shocks.

2 A Dynamic Model of Risk, Vulnerability & Long-

term Poverty Dynamics

We begin with our core theoretical model of household intertemporal decisionmak-ing and analyze it first under the simplifying assumption that human capital is anendowment that is fixed over time and is not influenced by a dynasty’s history ofconsumption and undernutrition. While this assumption is patently unrealistic overthe longer term, it provides the opportunity to fix key concepts and ideas concerningrisk, vulnerability and asset smoothing.

We then generalize the model and incorporate a feedback loop between consump-tion, nutrition and the evolution of human capabilities or capital. This feedback loopincreases the probability that vulnerable households will collapse into long-term des-titution. Section 3 will then explore the implications of this feedback loop for thedesign of social protection programs.

2.1 Poverty Dynamics with Exogenous Human Capital

We model an infinitely lived household dynasty d, which is comprised of a sequenceof generations g = 0, 1, 2, ... . Each generation lasts for 25 years (t = 1 � 25).Each dynasty enjoys initial endowments of physical assets, Ad0 and human capital,Hd0. We will initially assume that the dynasty’s human capital is fixed once andfor all. We will later relax this assumption and allow the next generation’s human

2

capital to evolve, in part in response to that generation’s ‘early childhood’ nutritionalexperience as reflected in the consumption levels of the prior generation.

We assume that the household dynasty manages its resources to solve the follow-ing problem:

maxc�!dgt

E✓

" 1X

g=1

25X

t=1

u(cdgt)

#

subject to :

cdgt Adgt + f(Adgt, Hdgt)

f(Adgt, Hdgt) = Hdgt max[A�h

dgt � F,A�l

dgt]

Adgt+1 = [f(Adgt, Hdgt) + (1� ✓dgt+1)Adgt]� cdgt

Hdgt+1 = Hd0

Adgt � 0

(1)

The first constraint restricts current consumption to cash on hand (the value ofcurrent physical assets plus income). As shown in the second constraint, dynastieshave access to both a high and a low productivity technology (�h > �`). Fixedcosts, F , associated with the high technology make it the preferred technology onlyfor households above a minimal asset threshold, denoted A. Thus, households withassets greater than A choose the high technology, and households below A choosethe low productivity technology. Note that human capital, Hdgt, augments the totalfactor productivity of both production technologies.

The third constraint is the equation of motion for physical assets. Assets aresubject to stochastic shocks (or depreciation), ✓it+1 � 0. The shock is exogenous,and realized for the households after decision-making in the current period (t), andbefore decision-making in the next period (t+ 1) occurs. Period t cash on hand thatis not consumed by the household is carried forward as period t+ 1 assets.

As shown by the fourth constraint, we assume for now that the dynasties’ humancapital is exogenously fixed at its initial level. Finally, the non-negativity restrictionon assets reflects the assumption that households cannot borrow. This assumptionimplies that consumption cannot be greater than current production and assets, butit does not preclude saving for the future.

As has been analyzed by others in similar models (e.g., Buera (2009) and Carter(2009)), the non-convexity in the production set can, but need not, generate a bi-furcation in optimal consumption and investment strategies (or what Barrett andCarter (2013) call a multiple equilibrium poverty trap). This bifurcation happens ifsteady states exist both below and above A. If they do, there will exist a critical

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Figure 1: Probability of Chronic Poverty (low level equilibrium)

asset threshold where dynamically optimal behavior bifurcates, with those below thethreshold deaccumulating assets and moving towards the low steady state, and thoseabove it investing in an e↵ort to reach the high steady state. The former group areoften said to be caught in a poverty trap. Following Zimmerman and Carter (2003),we label the critical asset level where behavior bifurcates as the Micawber threshold,and denote it as AM .

Using the parameter values given in the Appendix, numerical dynamic program-ming analysis of the household problem 1 shows that multiple equilibria exist for arange of human capital levels. The solid blue line in Figure 1 graphs the probabilitythat a dynasty with a fixed intermediate level of human capital will end up in thelow-level, poverty trap equilibrium as a function of its initial level of physical assets,Ad0. As can be seen, for a fixed level of Hd0, an asset level of about 14 units marksthe Micawber threshold as dynasties with initial assets below that level will, withprobability one, end up at the low level equilibrium.

The “chronic poverty map” shown in Figure 2a graphs across the full endowmentspace of initial physical and human capital assets the probability that a dynasty willend up at the low level equilibrium. The light region across the northeast corner ofthe figure are those asset combinations for which this probability is zero, whereasthe dark region across the southwest corner of the figure are those combinations

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with probability one of the low level equilibrium. As can be seen, in this model,dynasties with initial human capital above 1.35 units will always escape the povertytrap, whereas those with human capital below 1.05 never will, irrespective of theirinitial level of physical assets. We refer to this latter group as the chronically pooror Destitute.

Between those two critical human capital levels, dynasties are subject to multipleequilibria, and their probability of ending up poor depends on their initial endowmentof physical assets. We label dynasties in the intermediate multi-color band as theVulnerable - households that face a probability between zero and one of ending upin the poverty trap.

As analyzed further by Janzen, Carter, and Ikegami (2015), a key implication ofthis model is that incremental physical assets carry an extremely high shadow valuefor these vulnerable households.1 Incremental assets not only create an income flow,they also give the option of advancing to the high equilibrium in the long-run, or,conversely, avoiding falling into a poverty trap. As discussed by these authors andby Carter and Lybbert (2012), it is this jump in the shadow value of assets that leadshouseholds in this asset neighborhood to smooth assets, and destabilize consumptionwhen hit with a shock.

While highly stylized, this model has rich implications concerning the impact ofshocks:

• Shocks Can Have Irreversible Consequences for the VulnerableA shock that pushes a household below the critical asset level, AM , has ir-reversible consequences as the household becomes mired in chronic poverty.Vulnerability, as defined in Figure 1 thus matters as those who fall below AM

become candidates for conventionally conceived schemes of social protection.

• Shocks Can Induce Asset Smoothing by the VulnerableWhile households near either steady state will tend to smooth consumptionin the spirit of the Deaton (1991) model, highly vulnerable households in theneighborhood of AM will asset smooth when hit with a shock. In contrast,those near the threshold drastically cut consumption in an e↵ort to preservecapital and avoid the collapse into chronic poverty. While this coping behav-ior is understandable, it potentially has deleterious long-term consequences asconsumption doubles as investment into future human capital. We will later

1Janzen, Carter, and Ikegami (2015) show the shadow value of assets is non-monotonic withrespect to assets, and, for a typical level of human capital, swells around approximately 14 assetunits.

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Figure 2: Chronic Poverty Maps

(a) Fixed Human Capital (b) Endogenous Human Capital

explore the implications of this behavior for long-term poverty dynamics.2

In addition, as we will explore later in Section 4, climate change that increasesthe severity or probability of shocks will redraw the poverty map, increasing bothdestitution and vulnerability. However, before turning to the analysis of climatechange, we need to further probe the logic of asset smoothing and vulnerability.

2.2 Asset Smoothing by the Vulnerable as IntergenerationalAsset Shifting

Consistent with our theoretical model, there is an emerging body of evidence thatpoorer households tend to hold on to their (modest) assets and smooth consumptionless e↵ectively than they might, and certainly less e↵ectively than wealthier house-holds do.3 While asset smoothing by the vulnerable thus has both theoretical and

2**May be worth saying something about single equilibrium models having somewhat similarimplications to points 3; and also if shocks are AR-1 as in Deaton**

3Townsend (1994), Jalan and Ravallion (1999) and Kazianga and Udry (2006) note that poorhouseholds less e↵ectively smooth consumption than do wealthier neighbors. In later work, Hod-dinott (2006) provides evidence that in the wake of the 1994-1995 drought in Zimbabwe, richerhouseholds sold livestock in order to maintain consumption, while poorer households did not, desta-

6

empirical foundations, the full welfare consequences of asset smoothing are less ex-plored. Hoddinott (2006) points out, even though asset smoothing is an attempt topreserve assets, consumption itself is an input into the formation and maintenance ofhuman capital, and hence “[t]he true distinction lies in households’ choices regardingwhat type of capital–physical, financial, social or human (and which human)–thatthey should draw down given an income shock.” While asset smoothing strategiesmay be rational, they come at the cost of immediately reduced consumption, withpotentially irreversible losses in child health and nutrition.4 Relatedly, Jacoby andSkoufias (1997) present evidence that households in rural India cope with shocks byreducing child school attendance, although their estimates of the long-term conse-quence suggest that the overall e↵ects are modest. In short, while the logic of assetsmoothing is unassailable, it sets the stage for the intergenerational transmission ofpoverty. The implications for poverty dynamics, and ultimately the design of socialprotection–especially in the face of climate change–warrant attention.

While asset smoothing protects the dynasty from immediate danger of permanenteconomic collapse, it may also impinge on future capabilities and human capital of thefamily. To explore the longer-term implications of asset smoothing by the vulnerable,we modify the equation of motion for human capital for inter-temporal choice model1 as follows:

Hdgt =

8

<

:

Hdgt�18t 6= 1n

wHd(g�1),25 + (1� w)Ho

�⇢

�P5

t=1 1(z > cd(g�1)t)⇣

(z�cd(g�1)t)

z

⌘2�

if t = 1

(2)This somewhat tortuous notation indicates that human capital within a generation isfixed at its starting value for that generation. However, when the generation changes(and when the children of the prior generation take over as dynasty leaders), humancapital resets based on the realized capabilities of this next generation.

As shown by Equation 2, two forces shape this human capital update. The

bilizing consumption instead. Similar evidence is found by Carter et al. (2007) (for Ethiopia) andCarter and Lybbert (2012) (Burkina Faso). Exploiting a randomized controlled trial in Kenya,Janzen and Carter (2014) find evidence not only of di↵erential asset smoothing by the poor, butalso evidence that insurance allows the poor to improve consumption smoothing, while the im-pacts for the wealthier allow them to hold on to assets that they would otherwise sell to smoothconsumption.

4The outcomes of undernutrition and malnutrition are well known. In children, these conditionscan lead to muscle wastage, stunting, increased susceptibility to illness, lower motor and cognitiveskills, slowed behavioral development, and increased morbidity and mortality (Martorell, 1999).Those that do survive su↵er functional disadvantages as adults, including diminished intellectualperformance, work capacity and strength (Alderman, Hoddinott, and Kinsey (2006)).

7

first term in curly brackets is the next generation’s genetic potential expressed as aweighted average of the parent generation’s human capital endowment and a randomdraw, H, from the overall population capabilities distribution. Numerically, H isdistributed with expected value of 1.35. Note that this term will generate a regressionto mean genetic potential.

The second term in curly brackets is a penalty that pushes an individual belowgenetic potential if she or he su↵ered consumption shortfalls (cdgt < z, where z isthe nutritional poverty line) in the first critical five years of life. This specificationis meant to capture the idea that undernutrition en utero and in the first 4 yearsof life can have irreversible damage on the physical and cognitive development ofthe child. Note that a dynasty that avoids nutritional penalties will regress towardsmean human capital potential, E[H].

After replacing the fixed human capital specification in model 1 with the new hu-man capital equation of motion 2, we used the same parameter values to reanalyzethe implications of the dynasty intertemporal problem for long-term poverty dynam-ics.5 For this analysis, we assume that households ignore these long-term feedbacksinto its long-term human capital.6 Figure 2b displays the modified frontier thatevolves across the generations when human capital is nutritionally sensitive. Thecolor contours again mark the probability of chronic poverty as a function of thedynasty’s initial human capital and asset endowments.

The results are quite striking. Comparing Figures 2a and 2b, we see that theMicawber Frontier has moved to the northeast. Initial endowment positions in thelower right of the diagram, which used to have some probability of escape fromlong-term poverty have seen those prospects drop to zero. Moreover, vulnerabilityhas increased for a broad range of dynasties that used to be able to rely on rapidaccumulation and asset smoothing to ensure a near certain escape from poverty.

Figure 3 allows further insight into the forces that lead undernutrition to lead tothis unfavorable redrawing of the chronic poverty map. The color contours that formthe base of this figure are those for the chronic poverty map in the case in whichhuman capital is treated as fixed. The arrows superimposed on top of these contours

5The Appendix also reports the parameters needed for equation 2.6While we make this assumption for now primarily to keep the problem manageable mathemat-

ically, the assumption could perhaps also be justified based on lack of nutritional knowledge. Notethat simple discounting will also tend to lead the current decisionmakers to largely, but not com-pletely, ignore impacts that occur in the distant future. We leave it to future work to incorporatenutritional awareness in this model. Note also that for the asset smoothers, choice even with fullknowledge of its long-term consequences, may be no di↵erent than that which modeled when thishuman capital feedback is ignored. For these households, failure to consumption smooth wouldmean an immediate dissent into chronic poverty as opposed to putting it o↵ for a generation.

8

Figure 3: Malnutrition and the Intergenerational Transmission of Chronic Poverty

show the evolution of endowments over four generations when human capital evolvesaccording to 2. The base of each arrow marks the initial endowment position for agiven dynasty, while the head of the arrow marks the position of the dynasty afterthe four generations have passed. As can be seen dynasties that begin in the centralpart of the endowment space and who would have had some chance of escaping long-term poverty, experience a deterioration of human capital across the generations andbecome locked in at low levels of human capital and physical assets. In addition,dynasties whose initial assets placed them in the northwest corner of the endowmentspace (high human capital, but low physical capital) su↵er a long-term deteriorationof human capabilities and end up either poor or highly vulnerable.

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3 Social Protection Tradeo↵s: Targeting the Des-

titute or the Vulnerable?

As analyzed in the prior section, undernutrition worsens the poverty map by deepen-ing the intergenerational transmission of poverty as the children and grandchildrenof initially poor and vulnerable households tend to su↵er a long term deteriorationin their realized levels of human capital. This result is strikingly illustrated in Figure3 where we see that after 4 generations, initially disadvantaged dynasties fall shortof their potential human capabilities, whereas initially better o↵ dynasties oscillatearound the population potential level (set at 1.35 in our simulations).

This concern that long-term poverty sometimes deepens and perpetuates itselfby diminishing the human capital of the next generation motivated the outpouringof conditional (and unconditional) cash transfer programs that have been largelyfocussed on helping poor families invest in the nutrition, health and education oftheir children. Note that at least in principle, cast transfers could help avoid thedeterioration of human capital and thereby alter poverty dynamics. The goal of thissection is to explore the impact of a stylized, means-tested, cash transfer programon long-term poverty dynamics in a world with risk and poverty traps.

After exploring the e�cacy of such a program in terms of its impacts on the evo-lution of both the poverty headcount and the poverty gap, we consider the tradeo↵s(in terms of the core poverty measures) that are induced if a proportion of a givensocial protection budget is targeted at the vulnerable rather the destitute.

To explore these social protection tradeo↵s we analyze a stylized economy com-prised of D dynasties that are uniformly distributed across the domain of the endow-ment space shown in the preceding poverty maps. This distributional assumption ismeant to illustrate the workings of the model from the full range of possible originalpositions. Over time, as dynasties move to the stochastic steady states associatedwith this model, certain portions of the endowment space will of course become lessdensely populated. Subsequent dynamic simulation results are then best consideredas illustrations of the underlying economic mechanisms, and not as a prediction ofimpacts on any actually existing economy (found in mid-history).

3.1 Poverty Dynamics under Conventional Cash Transfers

We begin by considering a stylized social protection program that o↵ers cash transfers⌧dgt with the following characteristics:

• Means Tested

10

Eligible households are those for whom cdgt < z, where z is the consumptionpoverty line.

• Contingent TransfersSubject to budget constraints, each household receives the transfer needed tocompletely close the poverty gap – i.e., ⌧dgt = z � cdgt. Note that underthis specification, transfers are contingent in the sense that a dynasty thatexperiences asset losses and hence lower consumption, will receive a largertransfer from an otherwise identical dynasty. We assume that all transfers arechanneled directly into consumption and that they are not anticipated andhence do not influence the decision to accumulation physical capital.7

• Government Budget ConstraintWe assume that the government has a fixed social protection budget, B, that isinitially just large enough to close the poverty gap for all destitute households.At any point in time in which the budget becomes insu�cient, then we assumethat transfers are adjusted so that all destitute dynasties receive transfers thatclose an equal fraction of their poverty gap.

• Varied E�ciencyTargeting of conventional cash transfer programs is often a significant practicalchallenge, and administrative costs can be quite high. To account for thesechallenges, we also allow for some of the allocated budget to dissipate.

More specifically, define the total social protection need at each point in time as:

Bgt =DX

d=1

(z � cdgt)1(z > cdgt)

and define the available budget adequacy as:

�gt =B

Bgt

.

Individual transfers are thus given by:

⌧dgt=

8><

>:

z � cdgt if �gt � 1

�gt(z � cdgt), otherwise.

7Using a similar model, Barrett, Carter, and Ikegami (2013) analyze what happens if transfersare anticipated.

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Figure 4: Chronic Poverty Map with and without Cash Transfers

(a) Without Cash Transfers (b) With Cash Transfers

We assume that households use the transfer for consumption. Figure 4 displaysthe chronic poverty map for the case of cash transfers. For ease of comparisonwith the case without cash transfers, panel 4a duplicates Figure 2b. We see thatcash transfers have some impact on poverty dynamics as the area of certain chronicpoverty in the southeast corner of the map shrinks modestly. Vulnerability, however,remains high in certain portions of the endowment space.

A sharper way to engage the e↵ectiveness of di↵erent social protection schemesis to define a set of standard poverty measures, whose evolution over time can betraced under di↵erent policies. Specifically, we consider headcount and poverty gapmeasures using realized consumption (optimal consumption plus a cash transfer whenappropriate) defined as follows:

Hgt =DX

d=1

1(z > cdgt)

D

Ggt =1

DHgt

DX

d=1

(z � cdgt)1(z > ccgt)

Note that the poverty gap measure, Ggt, measures the average depth of povertyacross poor dynasties.

12

In addition to these headcount and gap measures based on realized consump-tion, we can also define variants of these measures based on a dynasties’ potentialearning given its current holdings of physical and human assets.8 These potentialearnings measures will of course be smoother than those based on realized consump-tion. Notice that since we assume the cash transfer goes directly to consumption, acash transfer doesn’t increase production in a given period. The potential earningsmeasures also allow us to see how potential earnings and economic capacity evolvesunder any particular policy regime.

Figure 5 traces the evolution of the headcount and poverty gap measures acrossfour generations and allows us to see the aggregate impact of these changes in thepoverty map for the stylized population with a uniform distribution of initial en-dowments of physical and human assets. The generational transition years–whena dynasty’s human capital is updated according to equation 2–are marked by grayvertical lines. The top two figures display poverty measures based on realized con-sumption, whereas the bottom two illustrate the poverty headcount and gap measuresbased on potential earnings. In all figures, the solid blue line traces out the povertymeasures for the autarchy case with no social protection, whereas the solid green linetracks these measures for a cash transfer program in which 100% of the budget goesdirectly to the targeted population. The dashed green line considers an alternativecash transfer program with 30% of the budget “lost” to administrative costs.9 Wewill discuss the other two lines, which correspond to alternative social protectionschemes, momentarily.

As illustrated by the solid blue line, under autarchy, poverty increases markedlyupwards over the generations. Despite this increase in poverty, the simulated econ-omy grows very modestly across the generations, as shown by Figure 6. The increasein poverty does not reflect an aggregate economic collapse, but rather a process ofbifurcation in which some dynasties succeed economically, while others do not.

The green line shows the impact of cash transfers on this scenario. As the uppergraphs in Figure 5 illustrate, cash transfers eliminate all consumption-based povertyin the short-term. Over the longer term, the extent and depth of poverty drift up overtime as those who have collapsed because of shocks become eligible for cash transfers,reducing the amount available for other indigent households. Given the fixed budget,this increase in the number of cash transfer-eligible households in turn pushes up theaverage depth of poverty. As can be seen in the lower two graphs in Figure 5,

8The poverty line for the potential earnings measure is defined as that level of earnings thatwould, under optimal behavior, yield a consumption level equal to the consumption poverty line, z.

9For potential earnings measures, the blue autarchy line coincides with, and is hidden by, thecash transfer line for the first generation.

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cash transfers over the first generation have no impact on the potential earnings ofthe beneficiary population. While there is some (very) modest empirical evidencethat cash transfers spill over into investment and increase potential earnings, in oursimulation, we assume that cash transfer are unanticipated and delivered directly asin-kind additions to consumption.

Despite this assumption, we see that at the generational shift points, cash trans-fers do positively impact potential earnings, and therefore reduce the earnings-basedpoverty measures relative to the autarchy case. This improvement of course reflectsthe intention of cash transfers to enhance the human capital of the next generation.Note that the poverty reduction impacts of this improved human capital are rela-tively modest. This finding in part reflects the fact that in this model, human capitalgenerates income only when employed in conjunction with physical assets. As thepoor by definition have few physical assets, the impacts of improved human capitalis modest. Adding a second technology in which returns to human capital do notrequire physical assets would improve the economic impact of cash transfers.10

3.2 Poverty Dynamics under Vulnerability-targeted SocialProtection

The underlying dynamics of the system, which steadily add individuals to the aid-eligible population, undercuts the e�cacy of cash transfers scheme analyzed in Sec-tion 3.1. The pernicious e↵ects of the underlying system dynamics raise the questionas to whether there can be a more e↵ective deployment of the given social protectionbudget.

In this section, we consider adding vulnerability-targeted, contingent social pro-tection transfers (VSP) into the social protection system. There are two key elementsto the VSP scheme we model here:

• Vulnerability TargetedIssues payments to the “moderately vulnerable” (defined as the non-poor whoface between a 20 and 80% chance of collapsing into destitution) anytime theyare hit by a shock that could push them into chronic poverty. Note that likethe cash transfer program, we assume costless and perfect targeting. Note alsothat these VSP payments are contingent on the realized state of the world,meaning that these payments rise in bad years.

10For example, the next generation of individuals might exit this economy with prospects of urbanwage jobs proportional to their human capital.

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Figure 5: Evolution of Poverty Measures under Social Protection

(a) Headcount (realized consump-tion) (b) Gap (realized consumption)

(c) Headcount (potential earnings) (d) Gap (potential earnings)

15

Figure 6: GDP Growth with & without Social Protection

• TriageUnder this scheme, social protection resources are triaged by first making trans-fers to the vulnerable who have been hit by shocks, and then transferring theresidual social protection budget to the already destitute. We are not advo-cating this as an optimal scheme, but this assumption allows us to explore thepotential of VSP to alter poverty dynamics relative to a budget cash transferprogram which e↵ectively has the opposite prioritization, spending money firston the destitute.

This scheme can be considered an analogue to the restocking programs in the north-ern reaches in Kenya in which livestock lost to a drought are replaced by governmentprograms.

Returning to Figure 5, we can see the impact of this VSP on the evolution of theextent and depth of poverty. Looking first at the potential earnings-based povertymeasures, we can see the VSP scheme does a much better job than cash transfersin slowing the growth in the structurally poor. Over the four generations of thesimulation, the headcount and poverty gap measures decline by roughly a thirdunder VSP.

At the same time, the consumption based measures shown in the top half ofFigure 5 reveal an intertemporal tradeo↵ in the well-being of the poor. Over thefirst ten years of the simulation, the headcount and poverty gap measures based onrealized consumption are much lower for the cash transfer program. Put di↵erently,

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Figure 7: Budget Remaining for Cash Transfers to the Destitute

indigent households are unambiguously better o↵ over this initial time period undera social protection scheme that prioritizes their needs.

However, by the middle of the first generation, the situation becomes more com-plex. Headcount measures are often lower under the VSP triage scheme than they areunder the cash transfer scheme. Which scheme is better for the indigent is unclear,depending in part on how much the present versus the future poor are valued.

Figure 7 gives further insight into the workings and tradeo↵s of the VSP scheme.The red line in the figure shows how much of the fixed government social protectionbudget of 1200 is left over for cash transfers after VSP asset transfers have beenmade. Two things stand out in the picture. First, the VSP transfers on averageeat deeply into the available budget. Second, the amount of funds needed for VSPfluctuates wildly from year to year. In bad years, in fact, VSP transfers consumethe entire social protection budget, leaving nothing for transfers to the indigent suchthat the poverty gap skyrockets. Both of these observations suggest that even thoughsome vulnerability targeting has some potential to improve the overall situation forthe poor, there might be a better budgetary and social protection model.

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3.3 Using Insurance Mechanisms to Reduce the Social Pro-tection Tradeo↵: Mixed Public-private Financing of So-cial Protection

The tradeo↵s potentially induced by the system of VSP analyzed in section 3.2 mo-tivate the search for alternative financing mechanisms. The VSP scheme analyzed inSection 3.2 operates like a publicly funded insurance scheme: those su↵ering shocksreceive payments in the wake of a shock that drives them below the Micawber Fron-tier. This observation motivates the question as to whether vulnerability-targetedsocial protection could be o↵ered in the form of an insurance contract that is fundedin part by beneficiary contributions to the insurance premium.11

Janzen, Carter, and Ikegami (2015) explore this issue using a variant of model1 in which the household can also use its cash on hand to purchase units of indexinsurance. Intuitively, we might expect the vulnerable to voluntarily purchase insur-ance as they have the most to gain. As detail, while it is correct that insurance ishighly valuable to vulnerable households, it is also the case that these householdsare the most liquidity-constrained, and incremental assets are highly valuable (as aform of protection) for these households. Note that it becomes optimal for thesevulnerable households to purchase insurance as soon as they build up their assetstocks. In the end, the long-run prospects of vulnerable households is substantiallychanged by the availability of insurance. It does not, however, completely eliminatetheir vulnerability.

Because the unwillingness of the vulnerable to purchase insurance is primarilydriven by liquidity constraints, it may be suspected that their demand would behighly price elastic and sensitive to partial subsidization of insurance. this intuition.When subsidies cut the cost of insurance in half, demand by the vulnerable respondsrapidly, with implied gains in reduced vulnerability. The insight from the Janzen,Carter, and Ikegami (2015) suggests that the vulnerable may be able to foot somesubstantial portion of the bill for their own social protection that might eventuallybenefit the already destitute. Note that in addition, the government’s share of aninsurance contract would be smooth over time, unlike the VSP program consideredin the prior sub-section.

11There are also questions about whether an insurance mechanism can be designed that resolvesthe moral hazard and adverse selection problems that have historically crippled the use of insuranceamongst poor populations. Index insurance seems to o↵er a potential solution to this problem (forrecent reviews, see International Fund for Agricultural Development and World Food Program(2010), Miranda, Farrin, and Romero-Aguilar (2012) and Carter et al. (2014)), but we leave deeperdiscussion of these issues to other work.

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Building on this intuition, we consider the impact now of a mixed social protectionscheme which relies on insurance mechanisms and a mixed public-beneficiary fundingmodel. For the analysis to follow we assume the following:

• Capped Insurance Subsidy for all DynastiesIn contrast to the precisely targeted cash and VSP transfers, we here assumethat the government simply o↵ers a 50% subsidy for the purchase of insurancefor anyone with fewer than 35 units of productive assets. This assumption ine↵ect means that benefits leak to non-vulnerable and non-destitute households.Sharper targetting could improve the relative performance of this insurance-based scheme.

• TriageAs with the VSP scheme analyzed in section 3.2, we assume here that thefixed government budget is first used to pay 50% of the cost of all voluntaryinsurance purchases. Remaining budget is then allocated to cash transfers.

As can be seen in Figure 5, the impacts of this scheme are quite impressive. Becauseindividuals purchasing insurance anticipate the protection it will provide in the eventof adverse events, the Micawber Frontier shifts to the northeast, and dynasties be-come more willing to invest (what we call the “risk reduction dividend”). Whencombined with the fact that insurance helps brake the descent into poverty by thevulnerable, this risk reduction dividend leads to substantial drops in both the extentand depth of poverty over the long-run. Figure 6 shows that the combined impact ofthese forces is a substantial growth in GDP, which ends up some 20% higher underthis insurance-based social protection scheme than it did under the budget neutralcash transfer scheme.

All this said, Figure 5 still reveals an intertemporal tradeo↵ in the well-being ofthe poor. For roughly the first 10 years of the simulation, poor dynasties are fewerand better o↵ under a pure cash transfer scenario. After year 10, they tend to bebetter o↵ under an insurance scheme that gives second priority to their needs.

The di↵erences between the insurance scheme and the VSP asset replacementscheme is visible not only in Figure 5, but also in Figure 7. As can be seen inthis latter figure, the budgetary draw down of the insurance based scheme is bothlower and more stable than the requirements of the VSP, restocking program. Thesesavings are of course good for destitute dynasties, and for the future human capitalof their children.

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4 Raising the Stakes: Poverty Dynamics and So-

cial Protection in the Face of Climate Change

The first graph in Figure 8 shows the baseline scenario our prior analysis has assumedin terms of the distribution of the covariant component of the stochastic mortalityor asset depreciation shocks faced by dynasties. A discretized approximation to thelivestock mortality data from northern Kenya used in the analysis Chantarat et al.(2012), this baseline risk scenario is meant to represent the extent and severity of riskfaced by pastoralist households circa the year 2000. While we do not have down-scaled climate change projections for this precise region, the other three graphsin Figure 8 show what we assume happens over time span of four generations todistribution of risk faced by these households. As can be seen, while in baseline,we assume that droughts occur only one year in five, at the end of our climatechange scenario that probability has increased to one year in three. In addition, weassume that shocks become increasingly severe, with proportionately larger increasesin the probability of severe shocks that may destroy as much as 60% of a dynastiesproductive assets.

To analyze the e↵ect of an increasingly unfavorable climate, we assume thatthe climate shifts discretely with the changing of each generation. While obviouslyunrealistic, this approach allows us to look carefully at the impacts of climate change.Importantly, we assume that each generation knows exactly the climate risk that itfaces and adapts consumption and investment rules to it. Insurance is also re-pricedto conform with the new risk levels at each generational transition. However, nogeneration anticipates the further deterioration in climate that will take place andbe confronted by its children, grandchildren, etc.. While this assumption departssomewhat from the economist’s usual rational expectations specification, it does notseem highly unrealistic in this case.

In results available from the authors, we show that increasing risk of this sortshifts the Micawber Frontier to the northeast and causes a deterioration of the chronicpoverty map. Rather than focus on this maps, Figure 9 traces out the impact ofclimate change using the consumption-based poverty measures introduced earlier.While the first generation results are as in Figure 5 above, climate change kicksin beginning with the second generation (year 26 and beyond). As can be seen,without social protection, both the poverty headcount and poverty gap measuresworsen substantially in this stylized system in which risk is a major driver of poverty.

Importantly, under the climate change scenario, cash transfers become much lesse↵ective than the insurance-based subsidy scheme. Whereas without climate change,the insurance-based scheme modestly outperformed cash transfers, under climate

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Figure 8: Climate Change Scenarios

(a) Base Case (b) Generation 2

(c) Generation 3 (d) Generation 4

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Figure 9: Climate Change & Poverty Dynamics under Alternative Social ProtectionScenarios

(a) Headcount under Climate Change (b) Poverty Gap under Climate Change

change the insurance-based scheme has poverty rates and gaps that are roughly halfthose of the budget neutral cash transfer scheme. Interestingly, the insurance-basedscheme holds up quite well to climate change over generations 2 and 3 12 However,by generation 4, the insurance scheme begins to feel the pressure of climate changeand poverty rates begin to climb higher.

5 Conclusion

Climate-based risk and vulnerability have long been seen as key drivers of poverty,particularly in many rural areas of the developing world. In this paper, we havedeveloped a dynamic stochastic programming model of such an area. In such a model,the relatively poor, but vulnerable will tend to “asset smooth” – that is they choose toabsorb a larger fraction of any realized climate shock through reduced consumption.Unlike prior models, our analysis has drawn out the full consequences of this behaviorby the vulnerable by incorporating the long-term impacts of consumption shortfalls(induced by the optimal asset smoothing coping behavior of the vulnerable) on thehuman capital and long-term well-being of multi-generational family dynasties.

12Note also that the VSP restocking program also begins to perform relatively more favoablyfollowing moderate climate change.

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In the context of this model, we then explore how best to control poverty bya budget-constrained program of social protection. We first show that a standardprogram of conditional cash transfers, which target only the destitute, but not thenon-poor vulnerable, has limited e�cacy in the medium run as realized through con-stantly boosting the ranks of the destitute, diluting the amount of cash available foreach poor household. We then show that the long-term level and depth of povertycan be improved by incorporating elements of “Vulnerability-targeted Social Pro-tection” (VSP) into a national system of social protection. As modeled here, VSPe↵ectively operates as a restocking program, replacing the assets of the vulnerablepopulation so that they retain the ability to be non-poor into the future. However,these VSP payments, if publicly funded from the same fixed social protection bud-get, implies less funds for cash transfers targeted at the destitute. Moreover, thebudgetary requirements of VSP payments vary sharply across years. In the worstyears, they in fact absorb almost all the social protection budget, leading to a sharpuptick in the average depth of poverty amongst the poor.

In an e↵ort to mediate this tradeo↵ between the well-being of the destitute andthe need to keep the number of destitute from rising, we then explore the degreeto which an insurance mechanism can be used to implement vulnerability targetedprotection. Using this mechanism not only allows the public sector to smooth itsspending on helping the vulnerable, it also opens the door to having the vulnerablepay a portion of their own social protection. While we have shown in other work(Janzen, Carter, and Ikegami (2015)) that demand for market-priced insurance bythe vulnerable will be modest, we also show that their demand is highly price elastic.That is, the demand for insurance by the vulnerable responds strongly to partialprice subsidy.

Exploiting these insights, we then study the impact of having the public sectorfund 50% of the cost of a market-based insurance scheme, while the other 50% ispaid for privately by insured beneficiaries. Subsidies are again paid out of the fixedsocial protection budget. Unlike the simple VSP program, after the first few yearsof the simulation, insurance based vulnerability targeting performs at least as wellon poverty metrics as the cash transfer system. It also results in higher levels ofinvestment and 20% higher GDP in the simple model economy.

Finally, we ask what happens when climate change increases the frequency andseverity of shocks. While our baseline climate and risk scenario was calibrated onnorthern Kenya circa 2000, allowing for the sorts of changes expected with climatechange shows that the insurance-augmented social protection scheme strongly out-performs the budget neutral cash transfer scheme. Over the middle generations ofour simulation, poverty headcounts and gaps are some 50% lower under the insurance

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augmented social protection scheme compared to a standard cash transfer system.However, as climate change becomes ever more severe, even the insurance-basedsystem loses its ability to prevent a swelling in the number of destitute households.

While these results all emerge from a highly stylized model, they do strongly callour attention to the often overlooked intertemporal tradeo↵ between the well-beingof the poor in the present versus their well-being in the future. As such they suggestthat deviating some budget toward protecting the vulnerable but not the poor maypay o↵ big dividends in terms of reduced poverty rates, especially as climate changesmakes ever more people vulnerable.

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