The importance of economic variables v. household characteristics

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Smallholder decision-making under uncertainty

In order to assess the role of fire risk in smallholder decision-making we first develop a suitable household subsistence framework. Decision-making by the subsistence household assumes an expected utility maximization framework comprised primarily of on-farm own labor allocation between various productive activities and time allocated to leisure (Jacoby, 1993). Central to econometric applications of household models when labor markets are found to be incomplete is the estimation of a ‘shadow wage,’ which expresses the opportunity cost of time of adult labor to household production. Jacoby (1993) shows that the empirical realization of the shadow wage is simply the value marginal product of labor as allocated to on-farm labor activities. We assume incomplete labor markets in our sample because smallholders routinely have difficulty obtaining off farm work given that settlements are spread over large areas, and transportation costs and infrastructure are such that off-farm wage employment opportunities are extremely limited in the FLONA. In most cases, off farm work is accomplished via the smallholder traveling to the relatively distant city of Santarém during the off-season to work for extended periods. The estimation of a shadow wage rather than use of a market wage becomes necessary under these circumstances.
Many household studies have addressed how varying degrees of integration into formal labor markets affect household decisions such as level of forest clearing and the corresponding effects on household income and welfare (Shively, 2001a; Pendleton and Howe, 2002; Shively and Fisher, 2004; Angelsen, 1999). The application of household models to examine effects of market characteristics, land policy, technological change and conservation initiatives on subsistence households provides us with a starting point to assess the ways in which accidental fire, fire prevention, and slash-and-burn agriculture enter into the household decision-making process.
The introduction of fire risk into the traditional agricultural household model framework presents itself as a natural extension of the existing literature. Subsistence households face diverse risks including illness (Amacher et al., 2004), crop loss (Kochar, 1999; Fafchamps, 1993), price stochasticity (Barrett, 1999 & Saha, 1994), land confiscation (Amacher et al., 2004) and environmental disasters (Takasaki et al., 2004; Rosenzweig and Binswanger, 1993). It has been demonstrated that household behavior diverges from that of profit maximization in the presence of risk (Barrett, 1999), and subsistence households are therefore assumed to be risk averse. Tradeoffs associated with risk mitigation are reflected in smallholder reluctance to adopt newer or riskier technologies (Shively, 2001b Amacher et al., 1992), and in risk aversion to potentially productive but less secure economic opportunities (Morduch, 1995 & Rosenzweig and Binswanger, 1993).
Household responses to risk are diverse and include household saving and asset accumulation (Behrman et al., 1997), diversification of production (Rosenzweig and Binswanger, 1993), or increased labor market participation (Bluffstone, 1995 & Rose, 2001). Additionally, households may receive gifts or loans in response to an adverse shock from friends or family members in a sort of informal credit arrangement (Howe, 2003). Sales of assets such as livestock (Fafchamps, 1998), increased forest clearing (Pendleton and Howe, 2002; Anglesen, 1999; Amacher et al., 2004), non-timber forest product collection (Pattanayak and Sills, 2001 & McSweeney, 2004) or increases in hours of work (Kochar, 1999) are other methods employed by the small farm household to hedge against the presence of risk.
 

A household model with risk of accidental fire

As previously discussed, our purpose is to develop a model to be investigated empirically that expands upon a classic household expected utility maximization problem to include exogenous risk of accidental fire. We are primarily interested in examining the household choice variables of labor spent in fire prevention, land area burned to create agricultural plantations, and labor allocated to non-timber forest product collection in the presence of accidental fire risk. Assume that household decisions are made ex-ante to the realization of accidental fire in a given year. Let the exogenous probability of an accidental fire occurring be denoted P , such that (1 − P) is the probability that a smallholder does not experience accidental fire in the next year. The expected level of household utility is defined by the probability that the household experiences a fire multiplied by the utility obtained in the case of fire (U ^F ) plus the probability that the household does not experience a fire multiplied by the utility obtained where utility is derived from consumption of agricultural goods, Q_c , non-timber forest products, N , and other goods , X , as well as from leisure time, l , which is equivalent to the total time allocation to the household minus time spent in household labor activities (l = T − L ), where T is total time and L is a vector of labor time spent in agriculture, non-timber forest product collection, and in fire prevention. Smallholder utility also depends on a vector of household-specific characteristics, Ω .
Production of non-timber forest goods is a function of household labor time allocated to collection of non-timber forest goods ( L_N ), of forested area available to the household ( A_F  ), and household characteristics, Ω . In the case of an accidental fire we introduce an additional term to represent protection afforded by fire prevention exercised by the household. Fire prevention, α , increases household production possibilities should a fire occur and is assumed to be an increasing function of household labor spent in fire prevention, ≡ α ( L _p ) , where α ( L _p ) represents some protection to non-timber forest goods afforded by fire prevention, and where α ‘ ( L _p ) > 0 and α ‘ ‘ ( L _p ) < 0 . Non-timber forest production by the household in non-fire and fire cases is then written:
Agricultural production in the case of accidental fire (Q_p^F  ) and without (Q^O_p ) depend positively on family agricultural labor ( L_A ) and hired labor ( L_H  ), on agricultural capital, K , and on the area of land burned for agriculture, A_B , as well as on household characteristics, Ω . For purposes of the model, we assume land area burned for agriculture is equivalent to the area planted by the household.² As in the case of non-timber forest production, we include level of fire prevention, α ( L _p ) , in the agricultural production function in the case of accidental fire, so that:
Fire prevention represents an opportunity cost to both smallholder production and to leisure. This opportunity cost of time spent in fire prevention enters directly through the household time constraint (l ≡ T − L_A  − L _p  − L_N  ), and indirectly through the household land available for production, A_B ≡ A − A_F − A_E ), where A is the total endowment of land in hectares, A_B is area burned for agriculture, A_F is land area in forest, and A_E is area cleared as a firebreak, or ‘aceiro’. A_E is simply a direct function of labor allocated to fire prevention ( A_E ≡ A_E ( L _p ) ) because this activity is largely labor dependent.

Abstract
Acknowledgements
Table of Contents
List of Tables and Figures
I. Introduction
II. Smallholder decision-making under uncertainty
III. A household model with risk of accidental fire
IV. Data and descriptive statistics
V. Results
VI. The importance of economic variables v. household characteristics
VII. Conclusions
Literature Cited
Appendix A: Household Survey Instrument
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SMALLHOLDER FIRE PREVENTION AND BURNING ACTIVITIES UNDER THE THREAT OF ACCIDENTAL FIRE: A HOUSEHOLD MODEL APPLICATION FROM THE TAPAJÓS NATIONAL FOREST IN THE STATE OF PARÁ, BRAZIL