Linking common property resource management to human capital outcomes

Ecological Economics 105 (2014) 139–153

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Linking common property resource management to human capital outcomes Ram Ranjan ⁎ Dept. of Environment and Geography, Faculty of Science, Macquarie University, NSW 2109, Australia

a r t i c l e

i n f o

Article history: Received 10 December 2013 Received in revised form 1 May 2014 Accepted 8 June 2014 Available online xxxx Keywords: Human capital Common pool resources Climate change, repeated droughts, social norms Forestry management Optimal forest harvesting Soil erosion Soil degradation

a b s t r a c t In regions where common pool resources provide significant support to their surrounding communities, any climate change related shock could produce multiple livelihood repercussions. In this paper, a model explores how the health of common pool resources could impact upon human capital outcomes for communities that struggle to find alternate livelihood options when traditional means such as agriculture become unsustainable. The management of common pool resources is modeled as a strategic interaction process between two heterogeneous communities that are directly or indirectly dependent upon it. An unconstrained harvesting of common resources such as forestry not only depletes its stocks, but it also indirectly affects crop output through soil degradation. A number of situations are constructed where communities are able to successfully finance human capital accumulation through proper management of their common pool resources. However, results also warn that communities that are faced with limited opportunities towards accumulating human capital must plan ahead to prevent the depletion of their common resources below critical levels. When non-linear feedbacks to soil degradation emanate from low levels of common pool stocks, human capital outcomes as well as future livelihoods of such communities are threatened. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Common pool resources (CPRs) face the ‘tragedy of the commons’ problem (Hardin, 1968). When adequately maintained, however, they could provide additional support towards rural livelihoods. Marginal farmers and landless labor types are most directly affected by the depletion of CPRs as CPR based income comprises a higher proportion of their consumption. Then, there are agricultural farmers who may not need to rely directly on the CPRs but still benefit indirectly through the ecological services provided by CPRs. Dense forests can protect against soil erosion during heavy rainfall and flooding. Forests may also provide fodder to support farmers' livestock, where livestock is often used as a hedging strategy to cope with prolonged droughts. In the absence of property rights, social norms may endogenously evolve over how much CPRs to exploit and over the optimal maintenance of their stock, as has been argued in the literature (for instance, see Ostrom, 1990; Sethi and Somanathan, 1996). Ostrom (1996) lays out a number of circumstances where such social norms could evolve for the betterment of forestry resources. Some of these conditions relate to low discount rates of users, higher importance of forests to their survival, common interests, etc. Social norms may evolve to punish the harvesters or alternatively, those who do not contribute towards enforcing

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norms could themselves be punished (see Sethi and Somanathan, 2006 for a model incorporating the latter). The type of social norms that may evolve towards the management of CPRs such as forests also depends upon the level of heterogeneity amongst communities that are dependent upon it. For instance, Kant (2000) points out that landed households with ruminants would depend upon the forests to sustain their livestock as well as to provide agricultural inputs such as composts, whereas landless and poor communities would be more concerned with direct consumption of forest resources for their survival (also see Poteete and Ostrom, 2004). In some societies government may step in to enforce harvesting rules. For instance, Copeland and Scott Taylor (2004) describe three types of CPR economies — namely ‘Hardin’, ‘Ostrom’ and ‘Clark’. This classification ranks communities on their ability to sustainably manage their common pool resources as a function of the price at which such resources are traded. Specifically, Hardin economies do not exhibit any control over their resources even if the price of such resources becomes very high, whereas Clark economies are very responsive to price changes in terms of their ability to manage resources efficiently (Copeland and Scott Taylor, 2004). Bray et al. (2006) provide examples from Mexico, where democratization of the forestry sector in the late 20th century led to the emergence of community forest economies (CFEs) which were conducive towards the generation of social and natural capitals in such environments. While, De Blas et al. (2011) provide an example of significant internal and external conflicts in Cameroonian community forests that have led to less than desired outcomes.

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Very often, the interests of those who directly benefit from CPRs are found to be at loggerheads with those who indirectly depend upon such resources. For instance, landed farmers stand to lose from soil erosion caused by uncontrolled flooding, the effect of which can be mitigated through maintaining a dense forestry. Whereas, when faced with prolonged droughts and reduction in employment opportunities, landless wage earners tend to intensify their reliance on CPRs as their immediate survival is at stake. In this particular context, an optimal arrangement would be where the landed farmers participate in planting additional trees, whereas the landless are required to reduce grazing intensity of their small ruminants and reduce reliance on forest products for sustenance. However, differences in goals between different user groups often lead to conflicts and inequitable outcomes under such circumstances. Adhikari et al. (2004) provide evidence from common forestry in Nepal pointing to the fact that poorer households have reduced access to forestry products whereas well-off households are able to appropriate a larger share of the same. Pradhan and Patra (2013) also find evidence relating to higher difficulties encountered in join forestry management when communities differ in their socioeconomic conditions. Climate change could add to the mix of the above challenges by reducing forest cover and changing the composition of species within. The economic consequences of such changes have been estimated to be immense globally (see Hanewinkel et al., 2013; Thuoller et al., 2011). Climate change could lead to forest dieback, which will not only provide feedback carbon emissions to the atmosphere, but also change the nature of the soils (Peterman and Bachelet, 2012). The impact of climate change on forests in Asia has been particularly predicted to be high (Somaratne and Dhanapala, 1996; Zhao et al., 2005). Forest degradation in the Asia Pacific region has already contributed to low soil quality thereby reducing its ability to provide high quality or quantity crop yields (FAO, 1999). Furthermore, by reducing the carrying capacity of the CPRs, climate change will exacerbate the existing conflicts over CPR usage norms. Climate change would also reduce agricultural output and hence the demand for landless labor, thereby resulting in intensification of their reliance upon the CPRs. In this paper, we explore another aspect of CPR management challenges, which has not been touched upon in the literature thus far. This concerns exploring the linkages between human capital and CPR stocks and how the maintenance or depletion of the latter could affect future human capital outcomes in small scale societies. The key question that is being posed in this paper is how those rural economies, which are struggling to transition out of sustenance based livelihoods through investment in human capital, will be affected by climate change related shocks to the CPRs? Further, how do social norms evolve under climate change related stress and what are the conditions under which such successful transitions may not materialize? These questions are addressed in the context of common pool resources in Asian economies. Following Becker's seminal work on human capital (see Becker, 1964), a vast body of literature has emerged linking human capital outcomes to growth at national levels as well as associating it with differences in wages and national incomes of various countries. Human capital in the context of rural areas has been studied by Huffman (2001) and Taylor and Martin (2001). The roles of different types of institutions in different societies have also been explored recently by Acemoglu and Dell (2010) with respect to their impact on making schooling accessible and cheaper. However, how human capital outcomes are affected amongst CPR based communities, especially when climate change threatens the sustainability of such CPRs, is a question that has remained unexplored thus far. In order to take up and address these important questions, a dynamic optimization model is developed that links crop output to the health of the CPRs. One community (the landed farmers) invests in human capital augmentation of their children and hence needs to have profitable agriculture to finance such human capital investments. The other community (the landless group) directly relies upon the CPR for their

sustenance. Both crop output and the CPRs are faced with the risk of climate change related shocks materializing in the future. Social norms endogenously evolve within this heterogeneous community over management of the CPR, as CPR depletion can indirectly and adversely affect crop output. The literature addressing the evolution of social norms and capital supports this endogeneity assumption. For instance, Krishna (1994) provides an example from South India where social norms and social capital endogenously evolve with increasing resource scarcity. Water supply uncertainty promotes better water management through formation of collectives (that self-impose sustainable water use practices) whereas regions with relatively less water scarcity see no such endogenous institutional formations (Krishna, 1994). Group size also affects the successful enforcement of rules for governing CPRs, as smaller groups are found to be more effective towards harnessing collective action compared to larger groups. In smaller groups, the tendency to free ride is absent, whereas in the case of larger groups, collective action can be enforced only through punishments and coercion (Olson, 1965). In the context of joint forestry management, Ostrom (1996) argues that group heterogeneity can lead to differences in interests of the users and therefore agreeing upon and enforcing a common set of rules can be difficult and costly. The next section provides the model outline. A formal dynamic optimization model is presented following the model outline. Results are derived through a numerical example. The paper concludes by discussing some of the insights that emerge through the modeling of the complex inter-linkages between climate change related threats to the sustainability of CPRs as well as the livelihoods and human capital outcomes of the communities that are directly and indirectly dependent upon it.

2. Model Outline The model presented in this paper draws from cases of several farming districts in South India (in particular from Anantapur, see Conroy, 2001 for a background) where farming and forestry based communities have co-existed historically and were well supported by the surrounding common pool forestry resources. However, over time, as repeated droughts have made water scarce, it has affected the crop outputs of the landed communities. This has also adversely affected the demand for casual labor that was earlier supplied by the landless communities. When faced with reduced employment opportunities, the landless communities have increased their reliance upon common pool resources for sustenance thereby leading to its rapid depletion. This in turn has led to rapid soil erosion (from uncontrolled runoffs) and set off further feedback effects through significantly reducing crop outputs and demand for casual labor. This necessitated the need for stricter forestry management in order to prevent further soil erosion and improve the livelihood of the communities. There are examples from elsewhere of similar problems arising due to excessive forest degradation. Forestry is mostly relied upon by rural households for fuel wood consumption and livestock grazing in Kenya (Muchena et al., 2005). This has led to unsustainable rates of deforestation. In general, as result of deforestation, the rate of soil degradation in developing countries of Central America, Asia and Africa has been very high (Scherr, 1999). In this section, we develop a modeling framework that incorporates some of the key challenges faced by two heterogeneous communities relying upon a CPR. Consider that there are two types of farmers, the landed and the landless categories. Additionally, assume that there are only two farmers, each representing their respective communities. The landed farmer grows a composite crop and the derived income is used to finance consumption and educational expenses of their children. The landless farmer relies upon the CPR for their livelihood sustenance such as through collecting fuel wood and grazing of small ruminants in the common lands.

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We wish to explore how human capital investment decisions are affected by various factors including CPR health, and concentrate only on the landed type farmer with respect to schooling decisions. The child of the landless farmer is assumed to be assisting the family in generating sustenance income through harvesting forestry products and does not go to school. Schooling is subsidized and incentive programs, such as mid-day meals, exist to prevent school dropouts. While there are no direct costs of schooling, there are indirect opportunity costs of schooling time for the children of the landed farmer. For the landed farmer, the opportunity cost is the reduced output in agriculture, whereas for the landless farmer, if their children went to school, it would be the reduced CPR based income. Investment in education yields rewards by providing assured employment outside of agriculture. In reality, farmers may not encourage schooling of their children if employment after completion of schooling is not assured. Here we assume that while education will lead to some form of employment after schooling, there is a threshold level of education that needs to be crossed before the wages become significant. Next, introduce the evolution of social norms related to CPR harvesting. The amount of CPR harvesting per time period is a function of social norms in the society which comprises these two categories of farmers. Further, it is assumed that it is only the landless type that is reliant upon the CPR for their sustenance and that the landed group does not directly access the CPR. While social norms and its dynamics has been a widely researched topic, it is still a gray area. Social norms could be endogenous to the conflicting financial and non-financial interests of various factions in the society. The dynamics of social norms in the present context are affected by the ability of groups to successfully enforce a set of regulations to manage the CPR. In the absence of effective regulation, social norms could dissipate leading to depletion of the CPR. Here we make the evolution of social norms endogenous to human capital accumulation objectives of the landed farmer. When CPR health is essential for ensuring steady source of revenues, social norms will evolve to protect CPR. However, when different groups rely differentially upon the CPR and are affected in varying degrees by its depletion, social norm dynamics may not be linear and could exhibit path dependence or hysteresis. In our particular model, the landed farmer needs to conserve CPRs to avoid loss in agricultural productivity from soil erosion from uncontrolled flooding in the absence of dense forestry. The cost of education of the landed farmer's child can be financed through agricultural income and the farmer is only indirectly dependent upon CPRs. That is, the landed farmer has an income buffer. The landless labor relies more intensively and directly on CPRs and has no such buffer. The landed farmer is assumed to be the dominant of the two types (owing to higher wealth and caste based status) and dictates the norms with respect to harvesting. If the landless type does not harvest as dictated, they suffer a cost. The cost of harvesting CPRs, therefore, comprises the direct cost of searching for and harvesting forestry products as well as the costs imposed by the landed farmer for harvesting the CPR. The landed farmer accomplishes this punishment enforcement indirectly through investing in accumulation and maintenance of social norms which must be obeyed by the CPR harvesters. Since, time spent in accumulating norms is time lost in farming, the landed farmer suffers as well while trying to maintain CPR health. We formalize the above outline through a dynamic optimization framework next. 3. A Model of CPR Health and Human Capital Outcomes Consider that a small scale economy owns natural resources, the stock of which is given by x(t), which are mainly in the form of a forest ecosystem. The rate of growth of this CPR stock is given as:


 xðt Þ −hðt Þ; x˙ ðt Þ ¼ ρ  xðt Þ  1− k

ð1Þ

141

where ρ is the intrinsic growth rate of CPR, h(t) is the annual harvest rate of CPR and k is its maximum carrying capacity. The landed farmer who depends upon farming for their main source of subsistence income faces the following crop production function, q(t), with respect to soil quality, s(t), labor input, l(t), and water, w(t):
qðt Þ ¼ sðt Þ  lðt Þ  ηw 

 wðt Þα 0 ; wðt Þα0 þ α 1

ð2Þ

where α0 and α1 are the parameters that lead to a non-linear relation between water applied and crop output, and ηw is the maximum crop output that could be produced when applying any amount of water on one unit of land using one unit of labor and when the soil quality is one unit as well. The landed farmer also spends a part of their time enforcing social norms, N(t), with respect to harvesting in the CPR. Assuming that they have one unit of total time available per year, the time left for enforcing norms would be 1 − l(t). Soil quality degrades with the depletion of the CPR stock. The soil quality dynamics is modeled as: s˙ðt Þ ¼ srenew −ηs 

φ

ðk−xðt ÞÞ 0 ; ðk−xðt ÞÞφ0 þ φ1

ð3Þ

where srenew is the natural rate of annual soil replenishment and the φ0

ðk−xðt ÞÞ represents a non-linear rate of decline in soil qualterm ηs  ðk−x ðt ÞÞφ0 þφ 1

ity with CPR stock depletion. Soil regeneration rate is usually very slow, at about 0.025 mm to 0.125 mm per year, and is highly variable (Parikh and James, 2012). The decline in soil quality becomes much more rapid and increases non-linearly as the difference between the maximum carrying capacity and the current CPR stock level increases. Parameters φ0 and φ1 determine the sensitivity of this relationship between the difference in the maximum carrying capacity and current CPR stock and the rate of annual soil erosion. A higher value of φ1 implies that a much higher difference would be needed to make a sharp upward jump in soil loss rate (so high φ1 signifies more resilient soil), whereas a higher value of φ0 would imply a much steeper increase in the rate of soil degradation as this difference increases (so a high φ0 would signify low soil resilience). When the stock of CPR is depleted beyond a certain threshold (captured by the degree of separation of the current stock from the carrying capacity of the CPR), there is a significant increase in soil erosion rate leading to a complete loss in agricultural productivity. For instance, when CPR is totally depleted, soil quality erodes at a maximum annual φ0 rate of, srenew −ηs  kφk0 þφ , which can be further written as srenew − ηs 1 when k is large. Whereas, when the current stock of CPR is at its maximum sustainable level of k, the soil quality is augmented annually at srenew. We further assume that srenew ≪ ηs, so that under complete depletion of the CPR stock, soil erosion is very high. ˙ð Þ, for the landed farmer is given as: The financial wealth dynamics,mt m˙ ðt Þ ¼ π  qðt Þ−cðel ðt ÞÞ þ ð1−el ðt ÞÞ  iðt Þ−cðt Þ;

ð4Þ

where m(t) is the stock of accumulated wealth, π is the fixed price of the composite agricultural crop, c(el) is the annual cost of acquiring education as a function of the educational effort el(t), and (1 − el(t)) ⋅ i(t) is the wage income earned by the landed farmer's child. Annual wages are defined as i(t) and are a function of the accumulated stock of education, E(t), which evolves according to the equation: E˙ðt Þ ¼ f ðeðt ÞÞ−δ  Eðt Þ;

ð5Þ

where the term δ ∙ E(t) reflects the fact that acquired human capital (or the stock of education) could be lost gradually if not continually augmented. The variable f(e(t)) is the annual rate of transformation of educational effort into stock of human capital E(t).

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Wages evolve non-linearly with human capital, so that a threshold level of human capital must be crossed before wage earnings become substantial. This relationship between wages and human capital is given as: Eðt Þχ 0 ; iðt Þ ¼ ηh  Eðt Þχ 0 þ χ 1

U ðt Þ ¼ logðcðt ÞÞ:

ð7Þ

Next, we derive the CPR harvesting rules. The time spent by the landed farmer in enforcing social norms has implications for the harvesting of the CPR by the landless wage earning household. The CPR is primarily relied upon by the landless type farmer for meeting their sustenance needs. Let us assume that the CPR is in a mildly degraded state which makes harvesting for meeting sustenance needs costly. There is an additional cost associated with harvesting, which comes in terms of the social norms being enforced by the landed farmer. The landless farmer derives non-linear benefits, log(h(t)), from the CPR, where the cost of harvesting is non-linear in harvesting effort as well as in the stock of social norms, N(t), the dynamics of which is given as: γ

N ðt Þ 0 −δN  N ðt Þ: N ðt Þγ0 þ γ 1

N˙ ðt Þ ¼ vð1−lðt ÞÞ þ ηn 

ð8Þ

In Eq. (8), v(1 − l(t)) is a function relating time spent enforcing norms into its effect on the accumulation of stock of norms and δN is the annual decay in norms, which implies that norms need to be conγ0 stantly enforced to keep their stock constant. The term, ηn  NðNtÞðγt0Þ þγ , 1

provides a positive feedback boost to social norms once they have been accumulated beyond a certain level and parameters γ0 and γ1 determine the level of stock at which this feedback effect becomes significant. The cost of CPR harvesting, c(h(t), N(t)), is multiplicative in harvesting and the stock of social norms established by the landed community, which tries to prevent any harvesting to avoid further forestry and soil degradation, and is given as: β1

cðhðt Þ; Nðt ÞÞ ¼ β 0  hðt Þ

ϕ

 Nðt Þ 1 ;

ð9Þ

where β0 and β1 are the parameters determining non-linear harvesting costs and ϕ1 is the effectiveness of social norms in imposing punishment for a given level of harvesting. The above form of the cost function also implies that when social norms are non-existent there would be no harvesting costs incurred. This form has additional implications that when the landless farmer harvests too much, a higher social norm will lead to higher punishment compared to when the norms are lower. The landless farmer simply optimizes their utility from per period consumption and acts as a myopic agent in the sense that they do not plan for the future. Another way to put this is that they exhibit high time discounting given their poor livelihood status. Their first order optimization condition with respect to harvesting choice leads to: β1 −1

ϕ1

 Nðt Þ

hðt Þ ¼

( )1 N ðt Þ−ϕ1 β1 : β0  β1

ð11Þ

ð6Þ

where χ0 and χ1 are the parameters that determine the minimum human capital needed before its impact on wages could become significant. Also, ηh is the maximum possible wage that a farmer's child is projected to earn for any level of human capital acquired. Parameter η h itself could increase over time, but here we avoid this complication. The landed farmer maximizes utility, U(t), from consumption, c(t), which takes a logarithmic form to reflect risk aversion:

β 0  β1  hðt Þ

which upon further simplification yields harvesting effort as a declining function of the stock of social norms:

¼

1 ; hðt Þ

ð10Þ

The landed farmer can incorporate this relationship in their optimization problem with respect to human capital, social norm and wealth accumulation. The current value Hamiltonian problem for the landed farmer is written as:

logðcðt ÞÞ þ μ 1 ðt Þ  π  s  ðlðt ÞÞ  ηw 

  α wðt Þ −cðel ðt ÞÞ þ ð1−el Þ  iðt Þ−cðt Þ wðt Þα þ α 0   γ N ðt Þ 0 −δN  Nðt Þ þμ 2 ðt Þ  f f ðeðt ÞÞ−δ  Eðt Þg þ μ 3 ðt Þ  vð1−lðt ÞÞ þ ηn  γ0 N ðt Þ þ γ 1 8 )1 9
 ( −ϕ < xðt Þ N ðt Þ 1 β 1 = þμ 4 ðt Þ  ρ  xðt Þ  1− þ μ 5 ðt Þ − : ; β0  β1 k   ðk−xðt ÞÞφ0 ; ð12Þ  srenew −ηs  ðk−xðt ÞÞφ0 þ φ1

where μ1(t), μ2(t), μ3(t), μ4(t) and μ5(t) are the shadow prices of stocks of financial wealth, human capital, social norm, CPR and soil quality respectively. First order condition with respect to consumption decision gives: 1 ¼ μ 1 ðt Þ: cðt Þ

ð13Þ

Eq. (13) simply requires that marginal utility from consumption be equated to the shadow price of financial wealth along an optimal path. However, since financial wealth is needed for both consumption as well as human capital accumulation, and is affected by decisions with respect to social norm and soil quality preservation, consumption decisions will also be tied to the same constraints. First order condition with respect to agricultural labor time allocation by the farmer yields: 
μ 1 ðt Þ  π  sðt Þ  ηw 

wðt Þα wðt Þα þ α 0



0

¼ μ 3 ðt Þ  v ð1−lðt ÞÞ:

ð14Þ

The shadow prices of stock of financial wealth and that of the stock of social norms are inter-linked by the above condition. A marginal input of labor put into farming enhances crop output, but it also affects the stock of social norms as the time spent in farming is time lost not augmenting social norms. The marginal productivity of labor in agriculture is a function of soil quality and water. So, at lower water availability or lower soil quality, the marginal productivity of labor in agriculture will be lower. This will affect the tradeoff derived in the above equation — that between crop income and social norm augmentation. First order condition with respect to educational effort of the child yields:  0  0 μ 1 ðt Þ  c ðel ðt ÞÞ þ iðt Þ ¼ μ 2 ðt Þ  f ðeðt ÞÞ:

ð15Þ

The farmer's child's level of educational effort ties the shadow prices of financial wealth to that of stock of human capital. Earlier we saw that shadow price of wealth was related to that of social norms, thereby making the shadow prices of stocks of human capital and social norms interlinked. This inter-linkage could again turn out to be complex to predict as the dynamics of both social norm as well as human capital are assumed non-linear. Human capital needs to be augmented continuously given its depreciation rate which increases in the stock of human capital. When human capital based wages are higher, the shadow price of human capital will be higher, therefore requiring higher current consumption sacrifices and use of financial wealth towards educational expenses. This creates a tradeoff between current income generation activities to finance education and maintaining future sources of income

R. Ranjan / Ecological Economics 105 (2014) 139–153

through wage income as well as crop income. Investment in social norms ensures that crop income does not decline in the future; however, if future crop income is expected to be lower than the future wage income, investment in social norms could be discounted. There are a number of scenarios where social norm investment could take a back seat. First, when the financial wealth level of farmers seeking human capital is higher, which mitigates the reduction in crop income to a certain extent allowing them a buffer time period within which to augment skills and become employable outside of agriculture. Second, future climate change related water scarcity could reduce the carrying capacity of the CPRs, thereby indirectly threatening reduced crop income through lower soil quality and also directly affecting crop productivity through lower rainfall. When faced with such a possibility, the incentive to invest in CPR augmentation through social norms or even through direct investments may be absent. This is evident from looking at the noarbitrage condition over the shadow price of stock of CPR, which yields: μ˙ 4 ðt Þ ¼ −


    d xðt Þ ðk−xðt ÞÞφ0 þ μ 5 ðt Þ  −ηs  μ 4 ðt Þ  ρ  xðt Þ  1− φ0 ðk−xðt ÞÞ þ φ1 dxðt Þ k

þr  μ 4 ðt Þ:

ð16Þ

Shadow price of stock of CPR is a function of its own stock, as a relatively higher stock leads to higher growth, as well as it is affected by the shadow price of stock of soil quality. The latter leads to lower crop income at lower soil quality stock thereby also reducing the shadow price of the CPR stock. No-arbitrage condition with respect to the shadow price of stock of social norms yields: 8 8 ( ) 1 99   < d < Nðt Þγ0 N ðt Þ−ϕ1 β1 == μ ðt Þ  ηn  −δN  Nðt Þ þ μ 4  − μ˙ 3 ðt Þ ¼ − : ;; dNðt Þ : 3 N ðt Þγ0 þ γ1 β 0  β1 þr  μ 3 ðt Þ:

ð17Þ

Further, the no-arbitrage condition with respect to the stock of soil quality yields: 

 α d wðt Þ μ 1  π  sðt Þ  ðlðt ÞÞ  ηw  μ˙ 5 ðt Þ ¼ − þ r  μ 5 ðt Þ: ð18Þ α dsðt Þ wðt Þ þ α 0

Let us briefly explore the steady state condition for the stock of CPR. In the steady state we can write: )1  ( xðt Þ Nðt Þ−ϕ1 β1 ¼ 0; − x˙ ðt Þ ¼ ρ  xðt Þ  1− β0  β1 k


ð19Þ

and also from Eq. (8), we get: N˙ ðt Þ ¼ vð1−lðt ÞÞ þ ηn 

Nðt Þγ0 −δN  Nðt Þ ¼ 0: Nðt Þγ0 þ γ1

143

If we re-define social norm enforcement effort (1 − l(t)) as n(t), one can also derive a steady state relationship between the stock of CPR and the optimal social norm enforcement effort as:

vðnðt ÞÞ ¼ δ  Nðt Þ−ηn 

 
  1 N ðt Þγ 0 xðt Þ β1 −ϕ1 ¼ δ  β 0  β 1  ρ  xðt Þ  1− γ0 k N ðt Þ þ γ 1

n n  oβ o−γϕ0 1 1 β 0  β 1  ρ  xðt Þ  1− xðktÞ −ηn  n : γ0 n  oβ o−ϕ 1 1 β0  β 1  ρ  xðt Þ  1− xðktÞ þ γ1

ð24Þ

4. CPR and Human Capital Outcomes under Climate Change Risk Now consider that there exists a risk of climate change related shock to the CPR in the near future. This risk is exogenous in that the local farmers are unable to mitigate it. Further assume that the hazard rate of this climate event,λ˙ðt Þ, follows an exponential distribution (for similar risk formulation, see Clarke and Reed, 1994; Feinerman and Tsur, 2014; Tsur and Zemel, 1995). The climate change related shock could arrive in two forms, one through reduced rainfall, or two, through directly and abruptly reducing the carrying capacity of the CPR. One may even assume that both these possibilities are likely to occur simultaneously or could be inter-related. For simplicity, let us first begin with only the risk of a reduced carrying capacity being present in the near future. In the post-climate event scenario, the stock dynamics of the CPR will be given as:

x˙ ðt Þ ¼ ρ  xðt Þ 

! xðt Þ −hðt Þ; 1− kpost

ð25Þ

where kpost is the reduced carrying capacity of the CPR. After this event, the landed farmer faces the same optimization problem as before, but now with a reduced carrying capacity of the CPR. Let Vpost(x(t), s(t), m(t), E(t)) be the value function obtained after making optimal choices with respect to labor, education, consumption and social norm investment decisions in the post-climate change scenario where the CPR carrying capacity has been adversely affected. To solve for this value function, the utility levels obtained after optimizing over the control choices need to be calibrated for each possible combination of the stock variables that remain at the beginning of the post-event optimization problem. This value function, once solved for, can then be inserted into the following optimization problem, which is to maximize: ∞

ð20Þ

∫ log ðcðt ÞÞ  expð−r  t Þ  expð−λðt ÞÞ þ λ˙ ðt Þ  expð−λðt ÞÞ 0

 expð−r  t Þ  ðV ðxðt Þ; sðt Þ; mðt Þ; Eðt ÞÞ dt;

ð26Þ

Eqs. (19) and (20) can be further simplified to: )1  ( xðt Þ N ðt Þ−ϕ1 β1 ; and ρ  xðt Þ  1− ¼ β0  β1 k


vð1−lðt ÞÞ þ ηn 

Nðt Þγ0 ¼ δN  N ðt Þ; Nðt Þγ0 þ γ1

ð21Þ

subject to the previously defined equations of motions for all stock variables. Note that since V(x(t), s(t), m(t), E(t)) already incorporates the reduced carrying capacity, Eq. (26) uses the original carrying capacity of the CPR in the CPR stock dynamic equation. This is because Eq. (26) is maximizing optimal decisions where the expected utilities before and after the climate change event are separately incorpo∞

ð22Þ

rated. Specifically, the term ∫ log ðcðt ÞÞ  expð−r  t Þ  expð−λðt ÞÞd t, 0

maximizes utility until the climate change event arrives and the term

which gives a relationship between the steady state stocks of natural capital and social norms as:

∞

∫λ˙ ðt Þ  expð−λðt ÞÞ  expð−r  t Þ  ðV ðxðt Þ; sðt Þ; mðt Þ; Eðt ÞÞdt , maximizes 0

 Nðt Þ ¼


  1 xðt Þ β1 −ϕ1 : β0  β1  ρ  xðt Þ  1− k 

ð23Þ

utility outcomes in the post-event time periods. Eq. (26) represents a simplified form of the overall optimization problem (refer to Clarke and Reed, 1994 for setting up of optimization problems involving

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R. Ranjan / Ecological Economics 105 (2014) 139–153

similar hazard functions). The current value Hamiltonian (cvh) in the presence of climate risks is written as: logðcðt ÞÞðt ÞÞ  expð−r  t Þ  expð−λðt ÞÞ þλ˙ ðt Þ  expð−λðt ÞÞ  expð−r  t Þ ( ðV ðxðt Þ; sðt Þ; mðt Þ; Eðt ÞÞ þ μ 1 ðt Þ 
 ηw 

π  ðsðt Þ  ðlðt ÞÞ

)  wðt Þα −c e ð ð t Þ Þ þ ð 1−e ð t Þ Þ  i ð t Þ−c ð t Þ l l wðt Þα þ α 0

arrives at a time when the current stock of CPR is low, it will adversely affect the post-event value function as it may no longer be optimal to try to invest effort towards preserving the CPR through social norm reinforcement. A farmer may be better off spending all their time farming and augmenting their human capital at a quicker rate. On the other hand, if the climate change event mainly affects the future rainfall patterns and leaves the carrying capacity un-altered, the shadow price of stock of CPR will be mostly influenced by the last term in Eq. (28) n o ðk−xðt ÞÞφ0 , which is the shadow price of under brackets, μ 5  −ηs  ðk−x φ ðt ÞÞ 0 þφ 1

þμ 2 ðt Þ  f f ðeðt ÞÞ−δ  Eðt Þg þ μ 3 ðt Þ   N ðt Þγ0 −δN  N ðt Þ þ μ 4 ðt Þ  vð1−lðt ÞÞ þ ηn  γ0 N ðt Þ þ γ 1 8 )1 9
 ( < xðt Þ Nðt Þ−ϕ1 β1 = þ μ 5 ðt Þ −  ρ  xðt Þ  1− ; : β0  β1 k   ðk−xðt ÞÞφ0 þ μ 6 ðt Þ λ˙ ðt Þ;  srenew −ηs  φ0 ðk−xðt ÞÞ þ φ1

ð27Þ

the stock of soil quality. Low rainfall adversely affects the crop output whereas a better soil quality augments it, so a reduction in rainfall could be balanced by a higher CPR investment as along as the marginal costs of labor time dedicated to increasing soil productivity through social norm augmentation are not exceeded by the direct marginal productivity of labor in agriculture. We take recourse to a numerical example to further explore and illustrate these tradeoffs. 5. A Numerical Example

where μ6(t) is the shadow price of the stock of the cumulative hazard function. Deriving the no-arbitrage condition over the shadow price of stock of CPR leads to:

f

g

0 λ˙ ðt Þ  expð−λðt ÞÞ  expð−r  t Þ  ðV x ðxðt Þ; sðt Þ; mðt Þ; Eðt ÞÞ 
   d xðt Þ ðk−xðt ÞÞφ0 μ˙ 4 ðt Þ ¼ − þ μ 5  −ηs  þμ 4 ðt Þ  ρ  xðt Þ  1− φ dxðt Þ k ðk−xðt ÞÞ 0 þ φ1

þr  μ 4 ðt Þ:

ð28Þ

Compared to the no-risk case, now the dynamics of the shadow price of stock of CPR incorporates the effect a marginal change in its own stock has on the post-climate value function. If climate change event

The intrinsic growth rate of the forest ecosystem is assumed to be 0.1. At this rate, when the initial stock of forestry is 10% of its maximum carrying capacity of 100 (thousand tons), it takes roughly 25 years to reach half the carrying capacity and when the initial stock is half the carrying capacity at 50, it takes 25 years to reach about 90% of its maximum carrying capacity. The value for the annual rate of soil regeneration is chosen at 0.025 mm per year. Annual rainfall is randomly generated in GAMS using a mean of 400 mm and a standard deviation of 100 mm. The farmer, however, is aware of this pattern of rainfall and hence rainfall is not stochastic for the farmer. The maximum total time available to the farmer for allocating towards farming and social norm accumulation is 1 unit per year. The farmer's child also has one unit of time per year which is allocated

3

Harvest (Thousand Tonnes/Year)

2.5

2

1.5

1

0.5

0

1

3

5

base case

phi1=.5

phi1=.9

x0=50

x0=100

s0=75

s0=30

m0=400

chi1=50

v=.5

v=.25

low rain

7

9

11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 Time Fig. 1. Time paths of CPR harvesting under all scenarios.

R. Ranjan / Ecological Economics 105 (2014) 139–153

145

7 base case

phi1=.5

phi1=.9

x0=50

x0=100

s0=75

s0=30

m0=400

chi1=50

chi1=45

v=.5

v=.25

6

Stock of Social Norms

5

4 low rain 3

2

1

0

1

3

5

7

9

11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 Time Fig. 2. Time paths of accumulated social norms under all scenarios.

between working and human capital accumulation. We further assume that the farmer's child can invest up to a maximum of half of their time each year in acquiring human capital and the remaining in earning wages from that human capital. That is, if the child chooses to work more than half the available time per year they can do so, this however,

will reduce the time available towards education. The equation for CPR stock dynamics is given as:
 xðt Þ −hðt Þ; x0 ¼ 75: x˙ðt Þ ¼ 0:1  xðt Þ  1− 100

120

CPR Stock (Thousand Tonnes)

100

80

60

40

20

base case

phi1=.5

phi1=.9

x0=50

x0=100

s0=75

s0=30

m0=400

chi1=50

chi1=45

v=.5

v=.25

low rainfall 0

1

3

5

7

9

11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 Time

Fig. 3. Time paths of stocks of CPR obtained under various scenarios.

ð29Þ

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R. Ranjan / Ecological Economics 105 (2014) 139–153

Price of the agricultural crop is assumed to be 20 rupees per kilo. Crop output is measured in tons per hectare with the representative farmer having one hectare of land. The modified crop production function can be specified as:

qðt Þ ¼ 10 

sðt Þ  lðt Þ  100

iðt Þ ¼ m0 

!

wðt Þ3 80 wðt Þ3 80 þ 20

;

Eðt Þ2 ; m0 ¼ 600: Eðt Þ2 þ 40

ð33Þ

ð30Þ Social norm dynamics are written as:

and 80 is a parameter value that converts rainfall into its effect on crop yield. Eqs. (31)–(36) present the rest of the equations with base case parameter values assigned to them as:

s˙ðt Þ ¼ 0:025−

Maximum wages based upon human capital are assumed to be 600 thousand rupees per year and wages increase non-linearly in human capital as:

N˙ ðt Þ ¼ ð1−lðt ÞÞ  1 þ 1 

Nðt Þ2 −0:1  Nðt Þ; v ¼ 1; ηn ¼ 1; Nðt Þ2 þ 20

and the cost of harvesting (in thousand rupees per ton) as a function of social norms is specified as:

3

ð0:1  ð100−xðt ÞÞÞ ; s0 ¼ 40: ð0:1  ð100−xðt ÞÞÞ3 þ 10

ð31Þ 2

0:75

cðhðt ÞÞ ¼ 0:2  hðt Þ  Nðt Þ

In Eq. (31), the starting value of soil quality is assumed to be 40 units with an annual regeneration capacity of 0.025 units. A reduction in CPR stock from its maximum carrying capacity increases soil erosion. Human capital declines in proportion to its stock as given by Eq. (32):

E˙ðt Þ ¼ eðt Þ−0:1  Eðt Þ:

ð32Þ

:

ð35Þ

The calibration of parameters governing the rate of harvesting of CPR is done so that when the value of ϕ1 is 0.75 and if the farmer were to spend all their time in enforcing social norms (which have a starting value of 1) instead of farming, the CPR harvesting would reduce to half its initial level (of 1.58) in about seven years' time. When ϕ1 is higher at 1, it takes only four years to reduce harvest by half from its starting level of 1.58. At ϕ1 equals 1.5, harvesting is reduced to 0.47 in 5 years' time when all of labor time is spent enforcing social norms.

100

90

80

base case

phi1=.5

phi1=.9

x0=50

x0=100

s0=75

s0=30

m0=400

chi1=50

v=.5

v=.25

low rainfall

70

Soil Quality

60

50

40

30

20

10

0

1

3

5

7

9

ð34Þ

11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 Time Fig. 4. Time paths of soil quality under various scenarios.

R. Ranjan / Ecological Economics 105 (2014) 139–153

147

4.1

3.6

3.1

Human Capital

2.6

2.1

1.6

1.1

base case

phi1=.5

phi1=.9

x0=50

x0=100

s0=75

s0=30

m0=400

chi1=50

v=.5

v=.25

low rainfall

0.6

0.1 1

3

5

7

9

11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

-0.4

Time Fig. 5. Time paths of human capital accumulated under various scenarios.

10 base case

phi1=.5

phi1=.9

x0=50

x0=100

s0=75

s0=30

m0=400

chi1=50

chi1=45

v=.5

v=.25

low rainfall

9

8

Crop Output (Tonnes/Hectare)

7

6

5

4

3

2

1

0

1

3

5

7

9

11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 Time

Fig. 6. Time paths of crop output generated under various scenarios.

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R. Ranjan / Ecological Economics 105 (2014) 139–153

The base case value of ϕ1 is chosen to be 0.75. Following this, the optimal harvesting effort (in thousand tons) for the landless farmer is given as: ( hðt Þ ¼

−0:75

Nðt Þ 0:2  2

)1 2

:

ð36Þ

We first run the model without the risk of any climate change. In the base case, the harvesting outcomes are depicted in Fig. 1. In Fig. 1 we also consider several scenarios that vary key parameters (one at a time) to assess how harvesting and other outcomes change. Since harvesting can only be indirectly influenced through social norms, we see increasing harvesting trends for certain periods and then a steep decline before the pattern repeats itself. The gradual increase in harvesting over time occurs due to declining social norms (social norms depreciate if not augmented periodically). Once harvesting has increased to a certain level, the landed farmer re-enforces social norms, thereby leading to its sharp decline as the stock of social norms increases. Note that the time spent reinforcing norms is time lost in farming and therefore there is an opportunity cost associated with enforcing social norms. Since we have assumed a linear effect of enforcement effort on social norm accumulation, we observe this kind of discontinuous enforcement pattern. When enforcement costs are non-linear, the farmer would be investing continuous efforts towards norm accumulation. Compared to the base case, several scenarios lead to higher harvesting patterns. For instance, when the accumulated social norms are less effective in delivering punishment to the harvester (see scenario named ‘phi1 = 0.5’, where phi1 refers to the parameter ϕ1), the harvesting pattern is higher as well. On the contrary, when the established social norms are very effective in punishing (see scenario named ‘phi1 = 0.9’), the harvesting pattern is lower than the base case. There are some other scenarios too that lead to lower harvesting than the base case. When the

effect of human capital on wages is lower (see scenario ‘chi1 = 50’, where chi1 stands for the parameter χ1), harvesting is lower. Lower harvesting, obviously, must come through a higher social norm obtained under this scenario, and we will explore the reason for this soon. Also, a low mean rainfall of 300 mm as compared to the base case rainfall of 400 mm leads to lower harvesting pattern. Again, since we do not consider the effect of reduced rainfall on CPR stock health, it must be that the reduced harvesting is coming through a higher social norm established under this scenario. A lower maximum wage potential in the formal sector (m0 = 400) also leads to reduced harvesting through a higher social norm outcome. Finally, a lower starting level of soil quality (s0 = 30) as compared to the base case starting value of s0 = 40 also leads to higher social norms and therefore lower harvesting effort. Scenarios that lead to a higher harvesting pattern than the base case are where the initial soil quality is higher (s0 = 70) and when the relationship governing the norm establishing effort is less effective (v = 0.25 and v = 0.5 compared to the base case value of 1). The respective social norm stock outcomes are depicted in Fig. 2. The time path of social norms also follows a similar pattern as the harvesting pattern except with one difference — norms are initially declining under those scenarios whereas harvesting initially increases and vice versa. Fig. 3 depicts the stock of CPR under the same scenarios. As is evident from the graphs, all scenarios lead to an eventual long run increase in the stock of CPR. This reaffirms the beneficial linkage effect established in the model which the stock of CPR has on soil quality and hence on crop productivity. Fig. 4 depicts the time paths of soil qualities for these scenarios. Soil quality unlike the stock of CPR declines in the long run under all scenarios. Since we have assumed a non-linear feedback effect that CPR stock has on soil quality, a higher initial stock of CPR (x0 = 100) has a much better long run impact on soil quality as compared to a lower starting level of soil quality (s0 = 30). Since, soil quality outcomes are related to CPR health which in turn is linked to harvesting

200

180

160

Wages (Thousand Rupees Per Year)

140

120

100 base case

x0=50

x0=100

s0=75

s0=30

low rain

80

60

40

20

0

1

3

5

7

9

11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 Time

Fig. 7. Wages obtained based upon human capital accumulations.

R. Ranjan / Ecological Economics 105 (2014) 139–153

effort, the resulting outcomes seen for soil quality are merely a reflection of how social norms are established under these scenarios. When the acquired human capital is not effective in delivering wages in the formal sector (that is, it takes a higher human capital stock to achieve the same level of wage outcome), the farmer invests in higher social norm accumulating efforts instead. Note that formal sector wages provide an alternate source of revenue through the education of their children, so if farmers do not see much hope from educational investment, they would try to protect their only other source of income, the agricultural income. This explains a higher social norm investment (and a resulting higher CPR stock as well as a relatively higher soil quality) under this scenario. When the starting level of soil quality is low at (s0 = 30), we observe a low harvesting effort through a higher social norm investment and a resulting higher CPR level. However, the time path of soil quality still declines (though at a less steep rate). Human capital outcomes are presented in Fig. 5. Two broad patterns emerge — one where human capital increases over time and the other where it declines. Scenarios that lead to a decline in the human capital (implying no educational investment is undertaken) are ones where the maximum wages in the formal sector are lower (m0 = 400), or where a relatively higher level of human capital is needed to achieve the same level of wages. These scenarios could be thought of as representing those farming families who are relatively disadvantaged in terms of their human capital augmenting skills or other social networks that makes finding jobs with higher wages difficult. When such families foresee lower future wages from acquiring human capital, naturally, they will discount opportunities presented by human capital augmentation and concentrate on more traditional sources of income such as through agriculture. The time path of crop outcomes is depicted through Fig. 6. The annual fluctuations in output occur due to the rainfall pattern that has a base

case mean of 400 mm and a standard deviation of 100 mm. The highest crop outcome is possible under a higher soil quality scenario (s0 = 75), followed by the scenario where the CPR stock is at its maximum carrying capacity of 100. Notice the breaks in crop outputs in certain years. This happens when the farmer invests all their time in social norm accumulation rather than agriculture. In certain scenarios they split their times between farming and norm accumulation in each year. The lowest crop outputs are made possible when the soil quality is very low at s0 = 30 and when the CPR stock is low at x0 = 50. Figs. 7 and 8 depict the wages that materialize from human capital accumulations under the scenarios performed above. Note that (in Fig. 7) there is one scenario (low rainfall) that leads to zero wages. We observed earlier that this scenario led to no human capital accumulation. When rainfall is low, crop income is low too, which reduces cash availability to finance education. The fact that crop output is low also means that the farmer would need to spend more effort enforcing social norms in order to avoid any further soil erosion. That is the reason we see a very high level of social norm (as well as a low level of relative soil erosion) under this scenario. The scenarios that lead to high wage outcomes are where soil quality is higher to begin with (s0 = 75), and where starting level of forestry stock is lower (at x0 = 50). The latter result is surprising as one would expect low CPR stock to lead to high soil erosion and hence discourage educational effort. Soil erosion is indeed very high under this scenario and resulting crop income one of the lowest. However, the logistic growth function assumed for the CPR dynamics makes the difference in this case. Note that the starting low level of stock implies a relatively higher growth rate in forest stocks which leads to increasing stock of CPR (see Fig. 3). Therefore, even though the soil degradation is much higher, it eventually starts to slow down and the long run soil quality is not much different from most of the other scenarios. One of the lowest wages (ignoring the cases where

200

180

160

Wages (Thousand Rupees Per Year)

140

120 base case

chi1=50

chi1=45

v=.5

v=.25

chi1=50, s0=70

100

80

chi1=50, x0=100

60

40

20

0

1

3

5

7

9

149

11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 Time

Fig. 8. Time paths of wages compared under a combination of soil and CPR stocks and human capital effectiveness.

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wages are zero) is obtained when the soil quality is low at s0 = 30. A low stock of CPR only indirectly affects crop output through increasing soil erosion, however, a low level of soil quality does much more damage which is immediate. This explains a lower educational attainment and hence a lower long-term wages obtained under this scenario. Fig. 8 depicts a few more outcomes for wages where we explore the implications of the relative effectiveness of human capital in ensuring high wages in combination with soil and CPR stocks. Note that a higher value of chi1 (chi1 = 50) discourages educational investment as it takes too long to obtain a threshold level of human capital beyond which wages rise significantly. Having a higher endowment of CPR stock (see scenario x0 = 50, chi1 = 50) does not help with ensuring higher wages, as wages still turn out to be zero in the long term. However, having a higher endowment of soil quality leads to higher wages (even though they are the lowest in the category of cases where wages are positive in the long term). This once again emphasizes the relative importance of soil quality as compared to CPR stock in determining farmers' long-term livelihood outcomes. We next explore the implications of climate change risk in the model. Assume that the hazard rate λ˙ðt Þ of the climate event is 0.1. Given this rate, the probability that such a climate event would occur before 15 years would be 75% and the probability of the same happening before the next 8 years would be 50%. Calibrating the post-climate change value function comprising more than two state variables becomes challenging. Hence, we simplify a little by making assumptions of different types of risk that the farmer could face and then calibrate the value functions separately under these assumptions. The calibrated value functions are derived under various assumptions. In the first case when the carrying capacity of the CPR in the

post-climate change scenario is assumed to be reduced to 75, the post-climate change value function is given as:

V post ðxðt Þ; Eðt ÞÞ ¼ 75:98 þ 0:2999  xðt Þ þ 4:24  Eðt Þ−0:001548 2

90

80

CPR Stock (Thousand Tonnes)

70

60 base case

risk case_k=75

40

risk case_rain_mean=300mm

risk case_p=40

30

risk case_x0=40

20

10

0

1

3

5

7

9

ð37Þ

Under this scenario, it is assumed that there is an exogenous risk of climate change leading to a sudden reduction in the CPR carrying capacity, following which the farmer faces the challenge of re-establishing social norms as the accumulated norms are assumed lost in the sudden shock generated by the temporary loss of livelihoods for the landless category. In the post-shock event the landed farmer re-optimizes over their labor, education and norm accumulation decisions. The postevent value function is calibrated over starting values of human capital and the stock of CPR that the farmer has at the time the event materializes. We ignore the stock of financial wealth in the post-value calibration as wealth was found to have no effect in the pre-shock outcomes. The value function is calibrated by repeatedly solving for the obtained utility outcomes for various possible combinations of CPR stock and human capital stock that the farmer may have remaining at the time the climate event arrives. A polynomial function of degree two is used to fit a curve around the obtained outcomes (using the cftool option in MATLAB). In the next simulation, it is assumed that the climate change related shock pertains to a sudden reduction in mean rainfall to 300 mm (while the carrying capacity of the CPR remains unaffected). When the mean

100

50

2

 xðt Þ −0:006918  Eðt Þ  xðt Þ−0:1974  Eðt Þ :

11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 Time

Fig. 9. Stocks of CPR generated under climate change risk scenarios.

R. Ranjan / Ecological Economics 105 (2014) 139–153

151

8 base case

low rain

risk case_k=75

risk case_rain_mean=300

risk case_p=40

risk case_x0=40

7

6

5

Social Norm

no risk case_x0=40 4

3

2

1

0

1

3

5

7

9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 Time Fig. 10. Social norm outcomes under climate change risk.

rainfall is reduced to 300 mm, the new post-climate change value function is calibrated as:

Finally, when climate change leads to a CPR stock reduction to 60, the post-climate change value function is calibrated as:

V post ðxðt Þ; Eðt ÞÞ ¼ 80:72  0:01033  xðt Þ þ 4:997  Eðt Þ þ 0:0006844

V post ðnðt Þ; Eðt ÞÞ ¼ 84:9 þ 0:9846  Nðt Þ þ 4:124  Eðt Þ−0:05737

2

2

 xðt Þ −0:001757  Eðt Þ  xðt Þ−0:3123  Eðt Þ :

We also, try a positive risk scenario, where the farmer expects the arrival of an event which would double the crop price in the future. When there is a chance that future crop prices will double, the new postclimate change value function is given as: V post ðxðt Þ; Eðt ÞÞ ¼ 94:31 þ 0:02684  xðt Þ þ 1:903  Eðt Þ þ 0:0007215 2

2

 xðt Þ −0:0008314  Eðt Þ  xðt Þ−0:02302  Eðt Þ :

When future climate change leads to a reduction in stock of CPR to 40, the post-event value function is calibrated as a function of stock of social norms and human capital. Note that under this scenario we assume that the social norms are not lost upon arrival of a climate change related shock in the future which leads to a loss of CPR stock (instead of its carrying capacity as assumed earlier). The new post-climate change value function is calibrated as: V post ðnðt Þ; Eðt ÞÞ ¼ 83:76 þ 0:7982  nðt Þ þ 4:118  Eðt Þ−0:03878 2

2

 nðt Þ −0:05003  Eðt Þ  nðt Þ−0:2271  Eðt Þ :

2

ð39Þ

2

 Nðt Þ −0:07589  Eðt Þ  Nðt Þ−0:2225  Eðt Þ :

ð38Þ

ð40Þ

The resulting outcomes under risk are presented in Figs. 9 through 11. In Fig. 9, a risk of future reduction in carrying capacity to 75 leads to lower outcomes for the CPR stock over time. Similarly, when the risk involves a reduced mean rainfall of 300 mm, a lower CPR stock is maintained. A doubling of crop price in the future also does not encourage higher CPR stock. A lower CPR stock occurs due to lower investment in social norms (see Fig. 10). Since, the assumption under all these above scenarios involves a loss in accumulated norms with the arrival of a climate change related event, farmers do not invest in social norms as much as they would under the absence of risk. As Fig. 11 depicts, a higher agricultural price of 40 rupees per kilo leads to higher human capital as compared to the base case in the absence of any risks. However, when the possibility of prices doubling in the future is included as a risk, human capital investment declines. 6. Conclusion Common pool resources have been widely studied with respect to their sustainability aspects as well as the factors that lead to their destabilization or extinction. Climate change related events such as repeated droughts or frequent flooding can add to the challenges of managing CPRs as they could abruptly reduce their carrying capacity or their

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4.1

3.6

3.1

Human Capital

2.6

2.1 base case

risk case_p=40

p=40_no risk

1.6

1.1

0.6

0.1 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 -0.4

Time Fig. 11. Stocks of human capital compared for climate change risk scenarios.

stocks or both. Additionally, such changes could impact on the productivity and livelihoods of communities directly or indirectly dependent upon CPR. Climate change also directly stresses and challenges traditional forms of obtaining livelihoods in rural areas by adversely affecting agricultural productivity through causing repeated droughts. This forces large scale migration and occupational changes in rural communities. When faced with such challenging events, how should natural resources be managed and maintained so as to assist with short-term occupational adjustments while maintaining long-term livelihood resilience? This is the question we took up in this paper. Several interesting insights emerge from the theoretical model and the ensuing numerical example. First, when environmental degradation caused by CPR depletion affects crop productivity, optimal strategy requires that social norms be maintained high enough to discourage overharvesting of resources. However, when farmers cannot effectively enforce social norms, a reduced CPR stock results in lower crop incomes and hence welfare. Low rainfall discourages human capital investment as there is not enough cash available to pay for education. Whereas, a low level of CPR stock in some cases may not be detrimental to human capital accumulation. For farmers, who are less advantaged in terms of converting their human capital into tangible wages, it does make a difference whether they own a higher endowment of CPR stock or are having a higher soil quality. For such category of farmers, a higher endowment of CPR stock may not lead to high wages whereas a better soil quality can still ensure a livelihood transition. The presence of a risk of future loss to the CPR carrying capacity or its stock leads to lower enforcement of social norms thereby affecting crop income and human capital outcomes. Generally, it is found that a risk of reduced rainfall or a risk of reduced carrying capacity is detrimental to human capital outcomes and leads to lower welfare for the farming household.

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