Tsukuba Economics Working Papers
No. 2011-006

Economic models of shifting cultivation: a review
byYoshito Takasaki
September 2011

UNIVERSITY OF TSUKUBA
Department of Economics
1-1-1 Tennodai
Tsukuba, Ibaraki 305-8571
JAPAN

Economic models of shifting cultivation: a review
Yoshito Takasaki
University of Tsukuba

Contact Information:
Yoshito Takasaki
Graduate School of Humanities and Social Sciences
University of Tsukuba
1-1-1 Tennodai, Tsukuba
Ibaraki 305-8571 Japan
Tel./fax: +81 29 853 6280
E-mail address: takasaki@sk.tsukuba.ac.jp

September 21, 2011

Abstract
This chapter reviews farm-level economic models of shifting cultivation and those of deforestationand soil conservation related to shifting cultivation. Although economists have made significant
progress in modeling shifting cultivation over the last two decades, extant economic models neither
clearly distinguish between primary and secondary forests nor address potential roles of on-farmsoil conservation in shifting cultivation. Developing a unified farm model of primary forest clearing,forest fallowing, and on-farm soil conservation is needed to examine effective policies forprotecting primary forest and maintaining sustainable secondary fallow forest. The chapter points topromising avenues for future modeling.
Key Words: Economic models; Shifting cultivation; Deforestation; Soil conservation
JEL Codes: O13, Q12, Q23, Q24.

1

Chapter Number
Economic models of shifting cultivation: a review
Yoshito Taksaki
University of Tsukuba
Japan
1. Introduction
Shifting cultivation is a dominant agricultural system in tropical forests. Shifting cultivators transform nutrients stored instanding forests to soils by slashing, felling, and burning forests (i.e., slash-and-burn); they regularly shift crop lands by
replacing depleted plots with cleared forest lands (Denevan & Padoch, 1987; Kleinman et al., 1995; Ruthenberg, 1980).
Approximately 300–500 million people practice slash-and-burn agriculture on almost one third of the planet’s 1,500
million ha of arable land (Giaradina et al., 2000; Goldammer, 1993). Shifting cultivation is central to the povertyenvironment nexus in the tropics. On one hand, shifting cultivation is a dominant livelihood activity among small-scale
tropical farmers with various cultural, ethnic, and social backgrounds, and thus it is tightly linked with poverty anddevelopment (Angelsen & Wunder, 2003; Byron & Arnold, 1999; Reardon & Vosti, 1995; Wunder, 2001). On the other
hand, not only is shifting cultivation one of the major causes of tropical deforestation, but also, the associated forestcover change leads to multiple environmental problems, such as soil degradation, biodiversity loss, and reduced carbon
sequestration (e.g., Kleinman et al., 1995; Myers, 1992). As such, shifting cultivation can conflict with various
conservation efforts, such as maintaining protected areas, engaging in community-based conservation, sustaining
integrated conservation-development programs (ICDPs), making payments for environmental services (PES), andreducing emissions from deforestation and forest degradation (REDD). A win-win goal of poverty alleviation andrainforest conservation in shifting cultivation systems is a global challenge of the first order. To design an effective policy
mix, it is crucial to develop a better understanding of shifting cultivators’ decision making; to that end, economic
modeling is a powerful tool.
This chapter reviews economic models of shifting cultivation and those of deforestation and soil conservation related toshifting cultivation developed by economists over the last two decades. My goal is not to offer a comprehensive review,
but to highlight key modeling approaches (what is modeled and what is not, and with what assumptions), clarify how
they are useful and incomplete in efforts to examine shifting cultivators’ behaviors, and point to promising directions for
future modeling. I encourage readers to see other reviews on economic models, such as Kaimowitz and Angelsen (1998)
and Barbier and Burgess (2001) for deforestation and Barbier (1997) for land degradation in developing countries. As far
as I know, no other reviews on economic models of shifting cultivation are available.
I focus on farm-level models that characterize individual farmers’ behaviors (endogenous variables) under certain
environmental and institutional conditions, such as resource stock, markets, and property rights (Binswanger & McIntire,1987). 1 Farm models allow modelers to examine how farmers’ behaviors are affected by policy parameters (exogenous
variables). Modelers usually focus on individual farmers’ key decisions that directly or indirectly determine
environmental outcomes of interest (e.g., forest clearing in deforestation models). Although no models fully capture thecomplexity of the real world, economic models highlight key aspects of the reality to better understand causal
mechanisms.

1

Kaimowitz and Angelsen (1998) review deforestation models other than farm-level models, such as regional-level
models and national and macro-level models, including general equilibrium models (see also Angelsen & Kaimowitz,
1999). Although tropical forests are often common property, soils are individual farmers’ private property; most soil
conservation models are farm-level models.

2

1.1. Modeling approach
Three important choices in modeling approaches require attention: static vs. dynamic modeling, market conditions, andpolicies. Economic models are generally classified into static or dynamic models; whereas static models capture
economic agents’ decisions at a point in time, dynamic models consider the potentially changing path of their behaviors.
The choice depends on whether agents’ decisions at a point in time affect their future decisions. This dynamic linkage is
described by state equations, i.e., the law of motion of state variables, which can be the outcome of interest. Althoughstatic models characterize agents’ optimal decisions at a given point in time, dynamic models characterize the over-time
path of their optimal decisions (control variables) and corresponding state variables. For example, in a soil-conservation
model, the state variable can be soil stock (or fertility) and the control variables can be farmers’ choices that affect soil
fertility, such as cultivation intensity and soil conservation input. The simplest dynamic model is a two-period model,
although most dynamic models discussed below consider an infinite time horizon, while in this chapter, models are
considered to be static when agents make current decisions based only on the present value of the net benefit/coststream.
Although perfect markets enable an efficient allocation of resources, market imperfection is the norm in developing
countries, where most tropical forests are situated. Better understanding market imperfection and non-market
institutions has been a central theme of development economics over the last three decades (Bardhan & Udry, 1999; Ray,
1998). Although many shifting cultivation, deforestation, and soil conservation models in the literature assume perfectmarkets to examine price policies, such as those related to taxes and subsidies, some models consider imperfect factor
markets. In particular, although with a perfect labor market a market price (wage) supports a separation of farmhouseholds' consumption (labor supply) and production (labor demand) decisions, market imperfection can break thisseparation (Singh et al., 1986); here wage represents the opportunity cost of labor in the form of returns to any non-farmactivities (Benjamin, 1992). Not surprisingly, market imperfection commonly gives rise to ambiguous policy impacts. In
contrast, some models employ a framework that does not involve any factor markets (e.g., models focusing on fallowcultivation cycle).
Most models examine farm output price (mostly food price) and wage (opportunity cost of labor), which can be alteredby various macroeconomic policies; some models also examine input price other than wage, technological progress, andproperty rights. 2 Many dynamic models highlight the role of the discount rate, which can be altered by credit policies.
Some models that consider farmers’ decisions with uncertainty – especially in production and price – focus on the rolesof risk and risk aversion. Most deforestation models show that promoting farming through price and technology leads togreater forest clearing as the farmers augment farm production; in contrast, promoting non-farm activities discourages
forest clearing. Most dynamic models reveal that a lower discount rate encourages investment not only in soils (soilconservation), but also in land holdings (forest clearing). Other policy impacts are generally mixed, depending on
modeling specification (assumption). Specific theoretical predictions of each model are not reviewed in this chapter.
1.2. Organization of the chapter
The remainder of the chapter is organized as follows. Sections 2, 3, and 4 review deforestation, soil conservation, andshifting cultivation models, respectively. The main papers cited in these sections are listed in chronological order inTables 1, 2, and 3, respectively, which summarize decision variables, outcome variables, policy parameters, modelingframeworks (static vs. dynamic), and factor markets (perfect vs. imperfect vs. not modeled).
The tables also report whether the modeling work is accompanied with a substantial empirical analysis; an empiricalanalysis can be a case study, a descriptive analysis of micro data, simulation work based on micro data, or a regression
analysis (to test theoretical hypotheses). Whereas some models – especially those accompanied with an empiricalanalysis – consider specific empirical contexts (e.g., colonists in Amazonia), others are developed in general contexts.
Although this distinction is not always clear, it is clarified when needed. In some models I show mathematical equations
to highlight their key features in a concrete way; when I do so, I change original notations (and functions in some cases)
to uniform notations for clarity and clear comparisons across models.
Based on these reviews, Section 5 discusses major lacunae in extant shifting cultivation models and promising avenues
for future modeling. Section 6 concludes.

2 Welfare-augmenting policies are usually considered. It is a straightforward process to examine welfare impacts ofspecific policies in dynamic models by applying the procedure developed by Caputo (1990) (see Takasaki, 2006 for an
example).

3
Main decision variables

Main outcome variables

Main policy parameters

Forest-clearing labor, soil
conservation labor
Forest-clearing labor, soil
conservation labor
On-farm labor

Output price, wage, interest
rate
Output price, wage, interest
rate, technological progress
Output price, input price,
wage, cost of land clearing
Wage

Angelsen (1999)

Labor for firewood
collection
Cleared forest (distance)

Forest-clearing labor, soil
conservation labor
Forest-clearing labor, soil
conservation labor
Forest clearing (landvalue)
Firewood collection,
forest stock
Cleared forest (distance)

Barrett (1999)

Forest-clearing labor

Forest-clearing labor

Barbier (2000)

Forest-clearing labor

Cultivated land

Pendleton and Howe (2002)

Forest-clearing labor

Cleared forest

van Soest et al. (2002)

Forest-clearing labor

Cleared forest

Takasaki (2007)

Forest-clearing labor

Cleared forest

Delacote (2007)

Proportion of land
cultivated

Proportion of land
cultivatedSouthgate (1990)
Larson (1991)
DeShazo and DeShazo(1995)
Bluffstone (1995)

Table 1. Deforestation models

Output price, wage,transport cost, discount rate,
population
Output price - mean andstandard deviation
Output price, wage
Market integration(generated from price andwage), technologicalprogress
Technological progress,
output priceOutput price, wage, land
price, discount rate
Risk, risk aversion,
population, forest
profitability

Static vs.
dynamic
StaticFactormarkets
Perfect

None

StaticPerfect

None

StaticPerfect

None

Dynamic

Perfect,
imperfectNone,
perfect

Nepal(simulation)
None

StaticPerfect

Dynamic

Perfect

Dynamic (2periods)

Perfect

Madagascar (casestudy)
Mexico, Ghana(case study)
Bolivia(regression)

StaticPerfect,
imperfect
Perfect,
imperfect
Not
modeledStaticDynamic (2periods)
StaticEmpirics

None
None
None

4

McConnell (1983)
Barbier (1990)
Barrett (1991)
Clarke (1992)
LaFrance (1992)
Krautkraemer (1994)
Barrett (1996)
Grepperud (1997a)

Grepperud (1997b)

Bulte and van Soest (1999)
Grepperud (2000)
Lichtenberg (2006)
Graff-Zivin and Lipper(2008)

Main decision variables

Main outcome variables

Main policy parameters

Soil loss, non-soil input
Soil-degrading input,
soil-conserving input
Soil loss, non-soil input
Farm input, soil
investment
Cultivation input, soilconservation input
Soil loss
Soil loss, soilconservation input
Farming labor, soilconservation labor

Soil depth
Soil depth

TenureOutput price, input price

Soil depth
Soil quality

Farm input, investment
in soil-conservation
structure
Soil loss, farming labor
Farming intensity (soildepleting/conserving)
Soil loss, farming labor
Soil carbon-sequestration
investment

Table 2. Soil-conservation models

Static vs.
dynamic
Dynamic
Dynamic

Factormarkets
Perfect
Perfect

Empirics

Dynamic
Dynamic

Perfect
Perfect

Soil stock

Output priceOutput price, input price,
discount rate
Output price

None
Indonesia(descriptive)
None
None

Dynamic

Perfect

None

Soil fertility
Soil depth

Population
Output price, discount rate

Dynamic
Dynamic

Perfect
Perfect

None
None

Farming labor, soilconservation labor

StaticPerfect

None

Soil stock

Farming support, soilconservation support, offfarm support
Output price, discount rate

Dynamic

Perfect

None

Soil depth

Output price

Dynamic

None

Soil fertility

Risk aversion

Dynamic

Perfect,
imperfect
Perfect

None

Soil depth
Soil carbon-sequestration
investment

Output price
Sequestration cost, output
price, discount rate, risk
aversion

Dynamic
Dynamic

Perfect
Perfect

None
None

5
Main decision variables

Main outcome variables

Main policy parameters

Cultivation length, fallow
lengthProportion of land
cultivatedCleared forest

Fallow-cultivation cycle

Output price

Fallow length

Output price, wage, discountrate, population
Output price

StaticFactormarkets
Notmodeled
Perfect

Dynamic

Perfect

Tachibana et al. (2001)

Proportion of uplandland cultivated, uplandforest cleared

Perfect

Fallow length

Dynamic

Sylwester (2004)

Proportion of land
cultivatedFallow-cultivation cycle

Lowland technologicalprogress, lowland farm area,
output price, forest-clearing
cost, tenure security
Return to fallow, discountrate
Income transfer, output
price, population
Output price

Dynamic

Batabyal and Lee (2003)

Proportion of uplandcultivated, shifting
cultivation area, uplandforest cleared
Fallow length

NotmodeledNot
modeledNot
modeledBarrett (1991)
Jones and O’Neill (1993)
López (1997)

Willassen (2004)

Takasaki (2006)

Proportion of land
clearedPascual and Barbier (2006)

Farming labor (clearing
and on-farm labor with afixed proportion)
Farming labor (clearing
and on-farm labor with afixed proportion)
Cultivation length

Pascual and Barbier (2007)

Balsdon (2007)
Brown (2008)

Proportion of land
cultivated

Table 3. Shifting cultivation models

Cleared forest

Land quality
Fallow-cultivation cycle,
soil fertility (present
value of gross output)
Proportion of land
clearedStatic vs.
dynamic
Dynamic

Dynamic
Dynamic

Empirics
None
None
Ghana
(regression)
Vietnam(regression)

None
None
None

Output price, wage, discountrate, soil-regeneration rate,soil erosivity
Population

Dynamic

Perfect

None

Dynamic

Perfect

Mexico(simulation)

Fallow soil fertility,
forest clearing

Output price

Dynamic

Perfect

Mexico(simulation)

Cultivation length

Output price, non-farmincomePreference, spatial
dependency

Dynamic

Not
modeled
Perfect

None

Fallow soil fertility,
forest clearing

Proportion of land
cultivatedDynamic

Cameroon(regression,
simulation)

6

2. Deforestation models
Most farm-level deforestation models examine forest-clearing labor as a key decision variable. Assuming a simple
function of forest clearing with labor as a unique input (which is valid among small-scale farmers who do not use
chainsaws), cleared forest is directly captured by forest-clearing labor.
2.1. Static deforestation models
Early deforestation models are static. Southgate (1990), which is elaborated by Larson (1991), considers not only forestclearing labor, but also soil-conservation labor among colonists in the forest frontier; 3 these two labors separately
determine the present value of agricultural production (cropping and livestock) and soil conservation. DeShazo and
DeShazo (1995) apply an agricultural household model (Singh et al., 1986) to forest clearing with a perfect labor market,
though they capture forest clearing through the value of land (rent), not forest clearing itself. van Soest et al. (2002)
directly extend the agricultural household model to forest clearing, comparing effects of farm technological progress onforest clearing under perfect and no labor-market conditions.
Barrett (1999) and Delacote (2007), respectively, examine influences of price and production risk in farming on forest
clearing in their static models; Delacote (2007) also addresses effects of risk aversion and returns to standing forest in theform of non-timber forest products (NTFPs). 4
2.2. Discrete dynamic deforestation models
Static deforestation models effectively treat cleared land as a variable input (produced by labor) for farming. This setup
is valid if tropical farmers replace their old infertile plots with newly cleared forest lands every agricultural season or do
not consider future production on their cleared lands because of insecure tenure. This is not a common practice amongshifting cultivators, because (1) forest clearing is very costly to them (especially with no use of chainsaws), (2) they canemploy a variety of traditional soil management techniques (in particular fallowing), and (3) forest clearing andcultivation often give them some claims to the land (Takasaki, 2007). Instead, shifting cultivators crop their cleared lands
for more than one agricultural season over time.
Takasaki (2007) treats forest clearing as both an input for current production and an investment in future production in
his two-period model. Quality-adjusted land for cultivation at period t is given by:A1

a L1 ,(1.1)

A2

1  U A1  a L 2 ,(1.2)

where Lt is labor allocated to clear forest at period t, a is forest-clearing function, and ǒ captures fertility decline throughcultivation (depreciation rate). van Soest et al. (2002) use the same forest-clearing function as in equation (1.1); equation(1.2) is a state equation of crop land. Takasaki (2007) considers not only labor-market conditions, but also land-market
conditions, comparing four distinct market institutions (Latin America vs. Sub-Saharan Africa), including the effects ofland price.
Some static models, such as Southgate (1990), Larson (1991), and Angelsen (1999), jointly address input and investment
aspects of forest clearing by considering the benefit/cost stream over time generated by current forest clearing; suchmodels capture neither farmers’ behaviors over time nor the evolution of land assets. 5

3 Although conflicts over property rights are central issues among colonists in the forest frontier (e.g., Alston et al., 2000;
Anderson & Hill, 1990; Hotte, 2001; Mueller, 1997), related theoretical modeling is not reviewed in this chapter.
4
The potential role of NTFPs for sustainable development and poverty alleviation in the tropics is often emphasized (e.g.,
Arnold & Perez, 2001; Coomes et al., 2004; Wunder, 2001); at the same time, overexploitation of forest resources as local
commons among poor populations has been a major concern (i.e., poverty-environment trap) (Barbier, 2010; Dasgupta,
1993, 2001; Jodha, 1986). In particular, firewood collection and associated forest degradation have received muchattention. Bluffstone (1995), for example, examines firewood/fodder collection and forest biomass evolution.
5 The key decision variable in Angelsen’s model (1999) is the distance to forest cleared. Such spatial modeling, which iscommon among geographers, is not reviewed in this chapter (other examples of spatial farm-level deforestation models
developed by economists include Angelsen, 1994; Chomitz & Gray, 1996; Mendelsohn, 1994). Angelsen (1999) compares
four models under distinct modeling assumptions and property rights, not market conditions, in a unified framework.

7

Pendleton and Howe (2002) develop a two-period model for Amerindians in Bolivia, capturing forest clearing in the dry
season (period 1) for production in the wet season (period 2). Distinct from other modeling works, Pendleton and Howe
(2002) distinguish between primary and secondary forests; they also construct a measure of market integration frommarket prices.
2.3. Continuous dynamic deforestation models
Following a standard capital model, dynamic farm-level deforestation models consider forest clearing as a pureinvestment in land capital for future production. This modeling is commonly used to examine a society's optimal
deforestation – i.e., exploitation of tropical forests as the commons – in the literature (e.g., Barbier & Burgess, 1997; Ehuiet al., 1990; López, 1994; López & Niklitschek, 1991); most models employ control theory in a continuous time framework(e.g., Kamien & Schwartz, 1991; Seietstad & Sydsaeter, 1987).
Assuming that a fixed proportion of arable land (ǅ) is fallowed in each time period, Barbier (2000) considers thefollowing state equation:Awhere time index is suppressed and Aa L  GA ,(2)dA dt . The depreciation rate ǅ is effectively the same as ǒ in equation (1) in thediscrete-time framework.

3. Soil-conservation models
Soil-management measures are classified into two groups based on their costs: one with reduced current output levels,
such as less intensified cultivation, forest fallowing, and perennial systems, and the other with input use, which can takevarious forms, such as mulching, composting, terracing, and creating hedgerows, depending on agroecologicalconditions in specific locales. Although fertilizer is an essential input in other agricultural systems, fertilizer use is very
limited in shifting cultivation that relies heavily on forest-based measures (forest clearing and fallowing) (Nicholaides etal., 1983; Sanchez et al., 1982). Grepperud (1997a) examines how programs supporting farming, soil conservation, andnon-farm activities affect labor allocations for these three activities in his static model, in the same spirit as Southgate(1990) and Larson (1991).
All soil conservation models developed in the literature examine continuous cultivation with fixed land size.
3.1. Canonical soil dynamics
McConnell (1983) models the dynamics of soil depth x as follows:
x

D s,

(3)

where Dis natural soil regeneration and s is soil loss associated with cultivation; farm output is a function of soil loss,
soil depth (fertility), and non-soil inputs (evaluated at factor price). 6 This model captures only the adjustment ofcultivation intensity among soil-management measures.
3.2. Input-based soil-conservation models
Economists have extended McConnell’s (1983) dynamic model by incorporating input-based soil-conservation measuresin various ways. Clarke (1992) adds soil investment as a choice variable to equation (3); Barbier (1990) and LaFrance(1992) consider inputs for (soil degrading) cultivation and soil conservation separately; Barrett (1996) adds a soilconservation measure as a function of conservation input to equation (3); and Grepperud (1997b) considers aninvestment in soil-conservation structure, such as terraces, modeling the joint evolution of soil stock and conservation
structure.
Bulte and van Soest (1999) examine the soil dynamics with no labor market, using the following state equation:

6 Barrett (1991) compares McConnell’s (1983) models with and without non-soil inputs.

8x D l  s ,(4)where l is labor for soil conservation. Equation (4) captures labor-intensive soil conservation. 7
Grepperud (2000) examines how risk aversion influences soil conservation with production and price uncertainty. GraffZivin and Lipper (2008) examine the farmer’s decision on investment in soil carbon sequestration by explicitly modelingsoil carbon as well as soil fertility with production risk; they examine effects of sequestration cost and risk aversion, as
well as output price and discount rate.
3.3. Continuous vs. cyclical farming
Assuming stock-dependent soil regeneration (cf. equations 3 and 4),x D x  s ,(5)

Krautkraemer (1994) shows that in the presence of nonconvexity in the net benefit function, a non-continuous farming
strategy – periodic cycles of cultivation and fallow – can be an equilibrium (Lewis & Schmalensee, 1977, 1979) and that
population growth leads to a shift from cyclical cultivation to continuous cultivation (sensu Boserup, 1965).

4. Shifting cultivation models
Shifting cultivation models in the economics literature can be classified into four: the fallow-cultivation cycle model, theforest-fallow model, the cultivation-intensity model, and the land-replacement model. 8 Almost all models are dynamic;
all models except for Tachibana et al. (2001) assume a fixed land size.
4.1. Fallow-cultivation cycle models
Fallow-cultivation cycle models focus on fallow and/or cultivation length as decision variables, ignoring all otherdecisions, such as labor allocation. Barrett (1991) extends the optimal forest-rotation problem (Faustmann, 1995) tofallow-cultivation cycles by treating both fallow and cultivation lengths as choice variables. This rotation problem does
not explicitly capture soil dynamics. In contrast, Willassen (2004) models the cyclical evolution of soil fertility in thecultivation and fallow phases; the farmer chooses only the phase – binary choice q = 0 (fallow) or 1 (cultivation) – overtime, and distinct from soil conservation models (e.g., equation 3), soil dynamics under cultivation as well as fallow areassumed to be determined by soil fertility level x only.
In these cyclical models, the farmer does no cultivation in the fallow phase. This simplification is for analyticaltractability. Of course, in practice, shifting cultivators mix different stages of cultivation and fallow across plots.
Assuming fixed fallow length and on-farm soil dynamics characterized by equation (5), Balsdon (2007) focuses oncultivation length as a choice variable; distinct from other cyclical models, the termination of the cultivation phase in one
plot is instantly followed by cultivation on the next plot. Batabyal and Lee (2003), in contrast, focus on the choice of
fallow length.
4.2. Cultivation-intensity models
Cultivation-intensity models capture soil degradation resulting from shortened fallow through the cultivation-intensity
measure without explicitly modeling fallow dynamics. Although cultivation-intensity models differ depending on theirfocus, their common feature is to capture cultivation intensity through the proportion of land cultivated (b). For a given
land size, 1 – b is the proportion of fallow land and 1/b represents fallow length. For example, for b = .1, fallow length is
10 (years).

7 Using equation (4), Bulte and van Soest (2001) examine an environmental Kuznets curve for land degradation with nolabor market. Lichtenberg (2006) demonstrates that ambiguous impacts of output price found by Bulte and van Soest(1999) is not attributable to labor-market failure, but can occur depending on the labor supply's wage elasticity.
8 Batabyal and Beladi (2004) and Batabyal and Nijkamp (2009) apply stochastic modeling to shifting cultivation, which is
not reviewed in this chapter.

94.2.1.

Early cultivation-intensity models

Larson and Bromley (1990) develop a dynamic model with a fixed cultivation intensity. Jones and O’Neill (1993) develop
a static model using cultivation intensity b as a key decision variable. 9
4.2.2.

Cultivation-intensity models with soil dynamics

In Sylwester’s (2004) model, the soil dynamics under cultivation follows equation (5), with soil loss s replaced with afunction of cultivation intensity b; distinct from other cultivation-intensity models, Sylwester does not model factor
markets as in fallow-cultivation cycle models.
Whereas Brown (2008) considers a binary choice between cultivation and fallow – on each plot over time – as in fallowcultivation cycle models, he solves the dynamic problem by treating this binary variable q as continuous; that is, heeffectively uses cultivation intensity b as a choice variable. His focus is to examine the roles of preference (measured by
the revealed preference approach) and spatial dependency in farmers’ forest clearing using simulation (see also Brown,2006).
4.2.3.

Cultivation-intensity models with land dynamics

Tachibana et al. (2001) develop a cultivation-intensity model that endogenizes the evolution of upland holdings (T)among Vietnamese farmers who combine upland shifting cultivation and lowland paddy cultivation:Ta  G ( b )bT ,(6)

where a is (upland) forest cleared and endogenized depreciation rate ǅ(b) (cf. equation 2) captures soil degradation
through shortened fallow (higher b captures depriving intensification). Note that distinct from equation (2), T is total
land holdings, consisting of cultivated land bT (=A) and fallow land (1-b)T (= T – A). Furthermore, fallow land is under
the risk of being grabbed by neighbors. Tachibana et al. (2001) examine how the proportion of cultivated upland land
(inverse of fallow length), shifting cultivation area, and upland forest clearing are affected by a rich set of policies, suchas lowland technological progress, lowland farm area, forest clearing cost, and upland tenure security, as well as output
price.
4.3. Forest-fallow models
4.3.1.

Forest-fallow models with communal fallow forest

Forest-fallow models endogenize the dynamics of biomass accumulation in fallow forest as a soil builder. Fallow forest is
explicitly or implicitly assumed to be communally owned by villagers. López (1997) introduces the following dynamics
of fallow biomass density ǈ:KJ¦iai K ,Q(7)

where Ǆ is the intrinsic growth of secondary vegetation, ai is cleared forest by household i, and Q is total land area –under both cultivation and fallow – of the village. Equation (7) assumes that fallow biomass density is determined by the
proportion of cleared forest land for cultivation, i.e., village-level cultivation intensity. 10
Assuming equation (7) and a simple conversion of biomass to soil fertility on cleared fallow forest, Pascual and Barbier(2006; 2007) derive the dynamics of soil fertility on cleared forest (Pascual & Barbier, 2006, equation 5). They assume thatin each period of time the farmer cultivates only the cleared land; then, on-farm soil conservation is irrelevant. In Pascualand Barbier (2006; 2007), the only decision variable is farm labor, which is assumed to be allocated between forest
clearing and cultivation with a fixed proportion. Pascual and Barbier (2006; 2007) examine impacts of population density(n/Q, where n is the number of households in the village) and output price on forest clearing and fallow soil fertility.

9 Jones and O’Neill (1993) extend their model to a spatial model.
10 In the forest-fallow model, adding NTFPs collected from secondary fallow forest as an additional benefit of fallowing

is a straightforward extension.

10

4.3.2.

Forest-fallow models with private fallow forest

Shifting cultivators commonly have usufruct of not only the cultivated land they have cleared, but also their fallow land;customary tenure of fallow land tends to be insecure, however, and this tenure insecurity influences their forest clearing
and fallowing decisions (Otsuka & Place, 2001; Place & Otsuka, 2001; Tachibana et al., 2001). It is straightforward torevise equation (7) to characterize such an alternative customary tenure setting; then, soil fertility of cleared fallow forest
is effectively determined by fallow length or the inverse of cultivation intensity, 1/b. In this way, the fallow-forest modelwith private fallow forest directly corresponds to the cultivation-intensity model; a key difference is that the former
focuses on fallow dynamics and the latter highlights other dynamics, such as on-farm soil or land holdings.
4.4. Land-replacement models
Fallow-cultivation cycle models assume a cyclical switch of the whole land between cultivation and fallow; fallow-forestmodels assume that the farmer cultivates cleared forest land only in each period of time. In practice, shifting cultivators
replace some depleted plots with cleared forest land each time, while continuing to cultivate the remaining plots;
replacing all plots simultaneously is a polar case.
This aspect is explicitly captured in the land-replacement model (with fixed land size) introduced by Takasaki (2006).
The key choice variable is the proportion of cultivated land, not total land, replaced with cleared forest land (c). Thismodeling approach highlights the tension between replaced (cleared) and non-replaced (remaining) plots – the former ismore fertile but clearing is costly. It also directly captures new soils on cleared forest land added to soils on remaining
plots. Specifically, the dynamics of on-farm soil stock is obtained by extending equation (3):x Mc  D 1  c  s ,(8)where Ǘ is soil stock (per unit of land) of cleared forest (see Takasaki, 2006, Figure 1 for derivation). Note that for c = 0(continuous cultivation), equation (8) is the same as (3); for c = 1 (complete replacement), equation (8) corresponds toforest-fallow models, though fallow dynamics is not modeled (Ǘ is not endogenized). Takasaki (2006) examines effects
on forest clearing (measured by c) of soil-regeneration rate D and soil erosivity altered by soil conservation programs, aswell as output price, wage, and discount rate.

5. Discussion
5.1. Primary vs. secondary forests
The review in the last section indicates two significant lacunae in the extant shifting cultivation models. The first lacuna
is that the extant models do not distinguish between primary and secondary forests. 11 This distinction is criticallyimportant for both environmental and economic reasons. First, in general, protecting primary forest with greater
biodiversity needs to be given a higher priority than secondary forest protection. At the same time, as primary forest
becomes scarce in the tropics, researchers and practitioners pay greater attention to secondary fallow forest (Coomes etal., 2000). In particular, short fallow results in less matured secondary forest with limited biomass accumulation andpoor protection of erodible soils, as well as low biodiversity, weak carbon sequestration, and limited timber and NTFPs(Brown & Lugo, 1990; Chazdon et al., 2009; Dalle & de Bois, 2006; Dent & Wright, 2009). Shifting cultivation models needto jointly address cleared primary forest and fallow length of secondary forest as key environmental outcomes.
Second, the choice between primary and secondary forest is determined by farmers’ decisions under specificenvironmental and economic conditions: In particular, secondary forest is less fertile but easier to clear than primary
forest (Scatena et al., 1996), and this comparison depends on fallow length (farmer’s decision) 'YRĢàk, 1992) and theavailability of primary forest (determined by population growth, etc.). This choice also has a direct implication for asset
accumulation: Although clearing secondary forest does not alter total land holdings (only the plot phase changes fromfallow to cultivation), clearing new primary forest augments land holdings. That is, although secondary forest brings
fertile soil, primary forest brings both more fertile soil and new land itself. Shifting cultivation models need to capture
these key differences.

11 Primary forest “has had little or no anthropogenic intervention” and secondary forest is “woody successional
vegetation that regenerates after the original forest cover has been removed for agriculture or cattle ranching” (Smith etal., 1999, p.86).

11

Pendleton and Howe (2002) address the choice between primary and secondary forests as a pure forest-clearing problem;
they neither model the role of secondary fallow forest as a soil builder nor consider soil addition through primary forest
clearing. No other deforestation models distinguish or specify the type of cleared forest; this is also true in dynamic
deforestation models, which necessarily involve land accumulation (Barbier, 2000; Takasaki, 2007). Not only all soil
conservation models but also most shifting cultivation models assume fixed land holdings, and thus implicitly focus onsecondary forest; Tachibana et al. (2001) do not distinguish or specify the type of cleared forest, either.
This lacuna in the theoretical literature is in contrast to the considerable number of empirical studies on primary andsecondary forests. Smith et al. (1999), for example, show that the relative importance of secondary forest to primary
forest increases over time among Amazonian colonists; Coomes et al. (2000; 2011) also find this pattern over a longer
time span among Amazonian peasants (in their study village in Peru, primary forest has virtually disappeared).
5.2. On-farm soil conservation in shifting cultivation
Supporting non-farm activities discourages farming, thereby releasing pressure on forests. This policy option becomes
available and significant only after non-agricultural sectors sufficiently develop, often following massive deforestationand forest degradation. What policies can slow down this trend along the development path?
The second lacuna not only in the extant theoretical works on shifting cultivation, but also in related empirical works is
the investigation into potential roles of on-farm soil conservation. Among poor shifting cultivators, forest-based soilmanagement options (forest clearing and fallowing) outweighs on-farm soil conservation (Barbier, 1997); when degraded
land can be easily replaced, farmers have little incentive to adopt expensive input-based soil-conservation measures.
Then, the question is whether policy makers can alter shifting cultivators’ benefit-cost calculations by introducing
effective soil-conservation programs, as discussed by Takasaki (2006) (see also Grepperud, 1997a).
Although developing locally adoptable, effective soil-conservation measures in tropical forests has been a daunting task(Lal, 1995), soil scientists' recent growing interest in biochar in Amazonia may lead to significant improvement in soil
fertility and soil carbon sequestration in shifting cultivation systems (Glaser, 2007; Marris, 2006; Steiner et al., 2004).
Biochar, also known as black carbon, is the residue of organic matter that has been pyrolyzed (partially combusted in a
low-oxygen environment). Research indicates that Amazonian black carbon (terra preta) has, on average, three times
more soil organic matter (SOM) content, higher nutrient levels, and a better nutrient retention capacity than surrounding
infertile soils (Glaser, 2007). How the labor-intensive alternative “slash-and-char” system, combined with sustainablecharcoal production, can be promoted among poor shifting cultivators is still an open question, however (Swami et al.,2009) (see Coomes & Burt, 2001 for charcoal production among Amazonian peasants).
Soil-conservation models extensively developed in the literature can well capture various input-based soil-conservation
measures; in particular, equation (4) or its variant can be applied to labor-intensive conservation like biochar.
5.3. Shifting cultivation regimes
It is very useful to differentiate two regimes of shifting cultivation. In regime 1, where primary forest is available,
farmers choose to clear primary or secondary forest. Although the extant deforestation and shifting cultivation models
effectively capture primary forest clearing and secondary fallow forest clearing (cyclical cultivation), respectively,
neither of them addresses the choice of these two. As primary forest becomes scarce (deforestation), cultivation shifts toregime 2, in which only secondary forest is cleared; in another words, primary forest has been so degraded that clearing
primary forest is too costly or simply not an available option. Policies effectively protecting primary forest (in particular,
protected areas with compliance) can also make this regime shift. 12 Although the extant shifting cultivation models
essentially focus on regime 2, protecting remaining primary forest and promoting sustainable secondary forest

12 Migration can also significantly affect the regime shift. Coomes et al. (2011) find that urban migration plays animportant role in lowering pressure on diminishing forest land among shifting cultivators in their study village. The
extensive migration option in the forest frontier, however, may allow farmers to clear forest – both primary andsecondary – without employing fallowing practices; this is possible among colonists in land-abundant areas in Latin
America, especially in locales where selling cleared lands is an additional motive for forest clearing (Barbier, 2004;
Binswanger, 1991; Takasaki, 2007). Conceptually, further regime shifts following regime 2 can be considered. Once
shifting cultivators start to employ continuous cultivation on some plots, regime 3 emerges; in this new regime, in
addition to forest fallow management, farmers make a key choice between shifting and continuous. Lastly, regime 3 isfollowed by the complete shift to continuous cultivation, i.e., abandonment of shifting cultivation (Krautkraemer, 1994).

12

management (long fallow) in regime 1 should be given a higher priority for conservation and development in shifting
cultivation systems.
5.4. Future modeling
It is now clear that a promising avenue for future modeling of shifting cultivation is to extend extant models forsecondary fallow forest in regime 2 by adding primary forest clearing to capture regime 1 and by endogenizing on-farmsoil conservation to examine its effects on forest outcomes. That is, a unified farm model of primary forest clearing, forest
fallowing, and on-farm soil conservation is needed to examine effective policies for protecting primary forest andmaintaining sustainable long fallow.
Two extensions toward such a unified model are suggested. The first is to augment a cultivation-intensity model so thatit captures the dynamics of both on-farm soil and land holdings (through primary forest clearing). Such an augmented
model could explicitly capture the mechanism of depriving intensification embedded in ǅ(b) in equation (6).
The second extension is to augment Takasaki’s (2006) land-replacement model by endogenizing cultivation intensity andcapturing acquisition of new land and soil through primary forest clearing. The proportion of total land, not cultivatedland, replaced with fallow forest is bc, and fallow length 1/bc determines the soil stock of cleared fallow forest Ǘ inequation (8).
5.5. Hypothetical effects of on-farm soil conservation
How does better on-farm soil conservation affect forest outcomes? On one hand, in regime 2 with no primary forest
clearing, it is expected that shifting cultivators intensify on-farm soil conservation and rely less on fallow soils (lessfrequent clearing), resulting in longer fallow. On the other hand, in regime 1, better on-farm soil conservation encourages
shifting cultivators to clear more primary forest with increased returns to farming; at the same time, primary forest
clearing (land accumulation) is balanced with secondary forest clearing (fallow management). A well-designed soil
conservation program might result in longer fallow at the cost of primary forest; then, it becomes crucial to combine thesoil program with other measures to protect primary forest, such as protected areas.
The unified farm model proposed above can dissect shifting cultivators’ benefit-cost calculations, shedding light on an
effective policy mix for conservation and development and pointing to promising avenues for empirical research.

6. Conclusion
This chapter reviewed farm-level economic models of shifting cultivation, as well as those of deforestation and soil
conservation related to shifting cultivation. Although economists have made significant progress in modeling shifting
cultivation over the last two decades, extant economic models neither clearly distinguish between primary andsecondary forests nor address potential roles of on-farm soil conservation in shifting cultivation. Developing a unified
farm model of primary forest clearing, forest fallowing, and on-farm soil conservation is needed to examine effective
policies for protecting primary forest and maintaining sustainable secondary fallow forest. The chapter pointed topromising avenues for future modeling.

7. Acknowledgment
This chapter has benefited significantly from the comments and suggestions of Oliver Coomes. This research has been
made possible through financial support provided by the Japan Society for the Promotion of Science and the Ministry of
Education, Culture, Sports, Science and Technology in Japan. Any errors of interpretation are solely the author’s
responsibility.

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