Tsukuba Economics Working Papers
No. 2013-003	
 Deforestation, forest fallowing, and soil conservation in shifting cultivationbyYoshito Takasaki	 July 2013

UNIVERSITY OF TSUKUBA
Department of Economics
1-1-1 Tennodai
Tsukuba, Ibaraki 305-8571
JAPANDeforestation, forest fallowing, and soil conservationin shifting cultivation
Yoshito Takasaki*
University of Tsukuba
July 9, 2013

Acknowledgements
An earlier draft of this paper benefited significantly from the suggestions of Brad Barham,
Michael Carter, Jean-Paul Chavas, Oliver Coomes, and Bill Provencher. I gratefully
acknowledge the generous financial support of my research by the following
organizations: Foundation for Advanced Studies on International Development, theMellon Foundation, the Institute for the Study of World Politics, the MacArthur
Foundation, the Graduate School of the University of Wisconsin-Madison, the Matsushita
International Foundation, Japan Society for the Promotion of Science, and Ministry of
Education, Culture, Sports, Science and Technology in Japan. Any errors ofinterpretation are solely the author’s responsibility.
*Corresponding author. Faculty of Humanities and Social Sciences, University ofTsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571 Japan, Tel./fax: +81 29 853 6280.
E-mail address: takasaki@sk.tsukuba.ac.jp.

1Deforestation, forest fallowing, and soil conservation in shifting cultivation
Abstract
To design effective policies for rainforest conservation in shifting cultivation systems, itis crucial to have a better understanding of shifting cultivators’ decision making. This
paper develops a unified dynamic farm model of shifting cultivation, addressing two
lacunae in extant theoretical works: taking into account differences between primary andsecondary forests and potential roles of on-farm soil conservation. The model unifies
shifting cultivator’s decisions about primary-forest clearing, forest fallowing, and onfarm soil conservation by incorporating new soils acquired from cleared
primary/secondary forest land into on-farm soil dynamics. I examine how three distinct
policies – forest protection (e.g., protected areas), fallow management (e.g., improved
fallow), and on-farm soil management (e.g., biochar in Amazonia) – alter primary-forest
clearing (deforestation) and fallow length. The analysis reveals that although all threepolicies reduce deforestation, only on-farm soil management leads to longer fallow, i.e.,sustainable secondary fallow forest.
Keywords: shifting cultivation; deforestation; forest fallowing; soil conservation
JEL classification: Q23; Q24.
1. Introduction
Shifting cultivation is a dominant agricultural system in tropical forests. Shifting
cultivators transform nutrients stored in standing forests to soils by slashing, felling, andburning forests (i.e., slash-and-burn) [1, 2]. Not only is shifting cultivation one of the
major causes of deforestation and forest degradation, but also, the associated forest-coverchange results in other environmental problems, such as soil degradation, biodiversity
loss, and reduced carbon sequestration [e.g., 1, 3-6]. To design effective policies for
rainforest conservation in shifting cultivation systems, having a better understanding ofshifting cultivators’ decision making is crucial. This paper develops a new shiftingcultivation model to address two major lacunae in the literature [see 7 for an extensive
review].
First, extant theoretical works do not distinguish between primary and secondary
1,2
forests. 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 tosecondary fallow forest. 3 In particular, short fallow results in less matured secondary
1

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” [8, p.86].
2
As an exception, Pendleton and Howe [9] address making the choice between primaryand secondary forests as a pure forest-clearing problem; they neither model the role ofsecondary fallow forest as a soil builder nor consider soil addition through primary-forest
clearing.
3
Smith et al. [8] show that the relative importance of secondary forest to primary forest
increased over time among Amazonian colonists. Coomes, Grimard and Burt [10] and2forest with limited biomass accumulation and poor protection of erodible soils, as well as
low biodiversity, weak carbon sequestration, and limited timber and non-timber forest
products [4-6, 12, 13].
The second lacuna is the investigation into potential roles of on-farm soil
conservation. Among poor shifting cultivators, forest-based soil-management options –forest clearing and fallowing – outweigh on-farm soil conservation [14]. This is because
when degraded land can be easily replaced, farmers have little incentive to adopt
expensive, input-based soil-conservation measures. Although developing locallyadoptable, effective on-farm soil-conservation measures in tropical forests has been adaunting task [15], soil scientists' recent growing interest in biochar in Amazonia maylead to a significant improvement in soil fertility and soil carbon sequestration in shifting
cultivation systems [16-19]. 4 At the same time, various management measures toimprove fallows by planting species that replenish soil nutrient stocks faster than plants
in natural succession are available and have been practiced across the tropics [e.g., 20,
21, 22]. 5
To fill these two lacunae, the paper unifies shifting cultivator’s decisions about
primary-forest clearing, forest fallowing, and on-farm soil conservation. I do so byextending the land-replacement-modeling approach, which explicitly captures shifting
cultivators’ motive for clearing forests: to acquire new fertile soils [7, 27]. As labor is a
key scarce factor among shifting cultivators in land-abundant tropical environments [28],the model highlights the tradeoff in labor allocations associated with primary/secondaryforest clearing and on-farm soil management; cleared primary forest is more fertile thansecondary forest land, but the former clearing is more labor intensive, and the alternative“slash-and-char” system is also labor intensive [29]. In particular, the model incorporates
new soils acquired from cleared primary/secondary forest land into on-farm soil
dynamics. Although my model best reflects shifting cultivation practices amongAmazonian peasants [e.g., 10, 11], the modeling framework can be widely applied toother shifting cultivation systems in the tropics.
This unified model allows me to examine how policies can alter shifting
cultivators’ decisions about primary-forest clearing and fallow length, which determine
the two key outcomes of rainforest conservation: protecting primary forest andmaintaining sustainable secondary fallow forest [they are a key for reducing emissions

Coomes, Takasaki and Rhemtulla [11] also find this pattern over a longer time spanamong Amazonian peasants (in their study village in Peru, primary forest has virtuallydisappeared).
4
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 organicmatter content, higher nutrient levels, and a better nutrient retention capacity thansurrounding infertile soils [17].
5Enriched fallows, which involve planting tree species with economic benefits (e.g.,
fruits, medicines) [e.g., 23, 24], may also enhance nutrient recovery, as shown by Unruh[25] in the Peruvian Amazon. An alternative approach to speed up soil regeneration underfallow is to accelerate secondary forest regrowth, for example, by canopy removal [e.g.,26].

3from deforestation and forest degradation (REDD), e.g., 30]. I compare three policies –soil management interventions for fallow and cultivated land, respectively, as discussed
above, and forest-protection measures [e.g., protected area, 31]. 6 Although many
empirical studies show that protected areas can significantly reduce tropical deforestation[e.g., 32, 33-35], systematic empirical works on the roles of fallow and on-farm soil
management for rainforest conservation in shifting cultivation systems are lacking. The
comparative static analyses reveal that although not only forest protection but also fallow
and on-farm soil management reduces deforestation in the long run, only on-farm soil
management increases fallow length.
As is any theoretical model, my unified model is built on various assumptions(detailed below). In particular, a fixed land size is assumed. This assumption isrestrictive, because cleared primary forest usually adds to land holdings [as emphasizedby 7]. Then, it is possible that better on-farm soil management encourages shifting
cultivators to clear more primary forest to expand land holdings in response to increased
returns to farming. The theoretical literature, however, has not yet fully integrated
shifting-cultivation practices and land accumulation [see, for example, 11 for such an
empirical work]. 7 The paper is a first attempt to model shifting cultivation in a way that
addresses the two major lacunae in the literature discussed above; developing a morecomprehensive model, especially one endogenizing land accumulation, is an important
agenda for future research.
The rest of the paper is organized as follows. Section 2 develops the dynamic
farm model, derives the optimal path of labor allocations, and characterizes the steadystate equilibrium. Section 3 conducts comparative static analyses on policy impacts. The
last section concludes.
2. The model
Let us consider a representative farmer who cultivates agricultural land with thesize of 1. Let a and b (0 < a, b < 1, a + b < 1) denote the land that is replaced with newly
cleared primary and secondary fallow forest lands, respectively. Cleared forests bringnew soils. Secondary forest is less fertile but easier to clear than primary forest [37].
Primary forest land is homogeneous in terms of soil fertility, and the soil stock per unit
forest land is assumed to be 1, with no loss of generality. Contrarily, the fertility of
secondary forest land is determined by fallow length [e.g., 38]. Following Larson andBromley [39], I assume a fixed land allocation between swidden and fallow. Then, thesize of fallow forest land is written as θ(1 – a), where θ is the fixed ratio of fallow land to
swidden land 1 – a. Fallow length N is given by θn, where n = (1 – a)/b, i.e., the ratio of
swidden land to the land switched between swidden and fallow (n > 1, because a + b <1). 8 Thus, fallow length is determined by both primary- and secondary-forest clearings: If
6

Although protecting primary forest as the common often faces enforcement problems inpractice, such problems are much smaller in the incentive-compatible measures affecting
shifting-cultivators’ management of soils as their private asset.
7
Although Tachibana, Nguyen and Otsuka [36] endogenize the evolution of uplandholdings among Vietnamese farmers who combine upland shifting cultivation andlowland paddy cultivation, they do not distinguish or specify the type of cleared forest.
8
For example, if θ = 5, a = 1/4, and b = 1/3, then n = 3 and N = 15.

4both clearings diminish, fallow becomes longer; if the diminished and augmented
clearings coexist, their net effect on fallow length is generally ambiguous. With a fixed θ,
the fertility of fallow land is determined only by n: The fallow-land fertility per unit ofland is ηk(n), where k’ > 0, k” < 0, and η is a fixed productivity parameter of soil
regeneration under natural fallow. ηk’ measures the rate of soil regeneration per unit offallow length. Secondary fallow forest land never becomes more fertile than primary
forest land, i.e., ηk(∞) < 1.
The farmer’s soil regeneration technology on the cultivated land uses labor as an
unique input [as modeled by 40, 41]. Letting m denote the labor per unit land allocated to
on-farm soil management, the total regenerated soil is a concave function of non-replaced
land 1 – a – b and labor input on the non-replaced land m(1 – a – b). With a constantreturns-to-scale regeneration function, the total regenerated soil is written as αh(m)(1 – a– b), where αh(m) is the regenerated soil per unit land, such that h’ > 0, h” < 0, and α is a
fixed productivity parameter of on-farm soil regeneration. The regenerated soil on the
non-replaced land never becomes more fertile than primary forest land, i.e., αh(∞) < 1.
The farmer’s cultivation intensity also affects soil dynamics; the more labor-intensive thecultivation, the more soil is lost. Total soil loss is given by βl, where l is labor allocated tocultivation and β is constant soil loss per unit of cultivation labor.
An example of the fertility profile across plots (for given a and b) is depicted by
the solid line ABCDEF in Figure 1, where each plot is displayed in the decreasing orderof fertility. The total soil stock x, the area below ABCDEF, consists of a on the newly
cleared primary forest land OG, ηkb on the cleared secondary forest land GH, and the soilon the remaining plots HK. The fertility profile after cultivation and the replacement andabandonment of the infertile plots IJ and JK, respectively, is depicted by the broken line
LM. 9 The area between ABCDEF and LMIK is total soil loss resulting from cultivation
βl. The revised fertility profile of OI after regeneration is given by the dotted line NP(LM has shifted upward by αh). In the next cultivation, NP becomes old plots and shifts
rightward by a + b (at a steady state, NP and EF are the same). Hence, the evolution ofsoil stock x on the farm land is written as: 10
1− a (1)x = a + ηk 
b + αh(m )(1 − a − b ) − βl , 0 < x(0 ) = x0 .
 b 
The farmer acquires new soil a and loses regenerated soils on the abandoned plots
αh(m)a. Thus, 1 – αh(m), which is positive, represents the net soil addition per unit crop
land through primary-forest clearing. Similarly, ηk(n) – αh(m) captures the net soil
addition through secondary-forest clearing, which is also shown to be positive below.

9

The remaining soils on the replaced and abandoned plots (which are not specified in
Figure 1) do not affect the soil dynamics on the farm land. In particular, it is assumed that
1) the former soil stock does not affect the fertility of fallow forest, or the soil on theformer land is used up before replacement, and 2) the latter plot is not added to fallow
land (i.e., θ is unaltered).
10
A perfect substitutability between regenerated soils through fallow and on-farmmanagement is assumed; in particular, the nutrient accumulation process in these two is
assumed not to be substantially different from each other. This assumption is consistent
with biochar in Amazonia [17-19].

5
The following three assumptions are made. First, primary forest is locallyabundant, open-access, and unmanaged. Thus, forest stock is exogenous to the private
farmer. This institutional setup, which is common in the deforestation literature [e.g., 7,
42, 43], applies to many tropical areas, especially those where rapid deforestation is an
emergency problem, as in Amazonia. Second, all cleared lands, both farm land andfallow land, are secure under customary tenure (usufruct). This institutional setup applies
to peasants and indigenous populations in Amazonia. 11 Third, the farmer earns no income
from standing primary and secondary forests in the form of non-timber forest products.
Because to add such earning options would augment the benefit of maintaining standing
forests, the present model ignoring them is considered to be ‘conservative’ in the study offorest clearing. 12
With the fixed amount of primary forest land, more forest clearing requires longer
travel for clearing. Labor required to clear a primary forest land is given by πs(a), wheres(0) = 0, s’, s” > 0, and a fixed parameter π increases as the per-capita stock of primary
forest declines (e.g., through the establishment of protected areas). A linear clearing
function is assumed for secondary fallow forest with the proximity to the farmer’s plots:
The farmer allocates τb labor to clear b secondary forest, where τ is a fixed marginallabor cost, which is always smaller than that of primary-forest clearing, i.e., τ < πs’(0). 13
The farmer’s crop output is a function of soil stock and cultivation labor, f(x,l),
where f(0, l) = f(x, 0) = 0, fx, fl > 0, fxx, fll < 0, and fxl ≥ 0 (the subscripts represent
derivatives in a standard manner). Concavity is guaranteed by the non-negativity of thedeterminant of the Hessian matrix of f, i.e., d = f xx f ll − f xl2 ≥ 0 . The farmer hires labor lh
at a fixed wage w in a perfect labor market, and alternatively, the negative lh means thathe/she sells labor. 14 The farmer’s labor time constraint is

l + m(1 − a − b ) + τb + πs (a ) = L + l h ,11(2)

In practice, however, the customary tenure of fallow land can be insecure, and thistenure insecurity influences shifting cultivators’ forest clearing and fallowing decisions[36, 44, 45]. Conflicts over property rights are common among colonists in the forest
frontier [e.g., 46, 47-49].
12
Among Amazonian colonists, Smith et al. [8, p.95] find that secondary forest
management is determined primarily by soil regeneration considerations and isunaffected by such forest products; farmers regard those products as “a bonus obtained
during the fallow period.”
13
The more matured the secondary fallow forest, the more labor is needed for clearing.
Assuming that τ is positively related to fallow length does not alter the main results.
14
Wage represents the opportunity cost of labor in the form of returns to any non-farmactivities [50]. Although with a perfect labor market a market price (wage) supports a
separation of a farm household's consumption (labor supply) and production (labordemand) decisions, market imperfection can break this separation [51], often giving rise
to ambiguous policy impacts on its decisions [as shown by 52, 53 for forest clearing]. In
contrast, examining Amazonian peasants’ forest clearing in Peru, Takasaki et al. [28] findthat not only is their labor allocation efficient, as hired labor is combined with labor
sharing, but also, family, hired, and shared labor are perfect substitutes for each other.
This buttresses the assumption of labor-market perfection, which is common in extant
theoretical works [7].

6where L is his/her time endowment. With a perfect labor market, the farmer’s utility
maximization is recursive: The farmer maximizes the profit first [51].
The farmer chooses cultivation labor, soil conservation labor, and secondary- andprimary-forest clearing over time to maximize his/her discounted total profits:

[

∞

]

max ∫ e − rt pf (l , x ) − wl h dt

l ,m ,b ,a 0s.t., (1), (2),where p is a fixed crop price and r is a fixed discount rate (risk is ignored). The currentvalue Hamiltonian is given byH ≡ pf (x, l ) − w[l + m(1 − a − b ) + πs (a ) + τb − L ],
1− a + λ  a + ηk 
b + αh(m )(1 − a − b ) − βl 
 b 


where λ is the current-value costate variable for soil stock.
Given an internal solution, the first-order necessary conditions for optimality are(1) plus the following:(3)
H l = 0 ⇒ pf l = w + λβ ,(4)H m = 0 ⇒ λαh′ = w ,

1− a
,
b
H a = 0 ⇒ λ (1 − αh ) + wm = wπs ′ + ληk ′ ,λ = rλ − H = rλ − pf ,(7)

lim e λx = 0 , lim e λ ≥ 0 .

(8)

H b = 0 ⇒ λ (ηk − αh ) + wm = wτ + ληk ′

x

x

− rt

t →∞

− rt

t →∞

(5)
(6)

Equation (3) indicates that farming labor is chosen to the point where the value of themarginal product of labor equals wage, plus the marginal value of soil loss resulting from
cultivation. Equation (4) suggests that soil conservation labor is chosen to the extent thatthe value of the marginal product of on-farm soil regeneration equals forgone wage. In
equation (5), secondary fallow forest is cleared to the extent that the value of net soil
addition, plus the saved wage through a reduction in soil conservation labor (moreintensive secondary-forest clearing involves more land replacement), equals the forgone
wage through clearing, plus the value of the forgone marginal soil regeneration on thefallow land through shortened fallow. The interpretation of equation (6) with respect toprimary-forest clearing is analogous. Equation (7) is the standard costate condition,
giving the optimal evolution of the shadow value of soil stock. Transversality conditions
are given by equation (8). Because the Hamiltonian is jointly concave in the state andcontrol variables, these necessary conditions are sufficient for optimality. 15
The steady-state equilibrium, the existence of which is assumed, is shown to be
unique and stable, as follows. The steady-state equilibrium (x*, λ*) is given by x = λ = 0
in equations (1) and (7), and once the steady-state values for x* and λ* are known, thosefor l*, m*, b*, and a* are obtained recursively from (3)-(6). Substituting l, m, b, and a from
15

Considering corner solutions is a straightforward extension. In particular, if a = 0, i.e.,
no primary-forest clearing, for example, in highly deforested areas, equation (6) isirrelevant.

7equations (3)-(6), the canonical system is expressed by (1) and (7). Linearising thesystem at the steady state yields the following Jacobian matrix:
 βf xle2
ϕ 2 
β 2 α h′ 2γ

+
+
−
−
pf ll
λh′′
n 2 wπs′′  f ll
′
′
k
λη
,
J =
b
 pd

βf

 −
r − xl
f
f
ll
ll



where γ = 1 − a − b > 0 ; e = ηk − αh − ηk ′n ; ϕ = 1 − αh − (k − αh )n −1 > 0; J11 < 0, J12, J22> 0, and J21 ≥ 0, where Jmn is the (m, n) factor of matrix J. Because the x = 0 and λ = 0
loci, respectively, are upward and downward sloping in the λ-x space, the equilibrium (x*,λ*), which is determined as their intersection, is unique. Because J = J 11 J 22 − J 12 J 21 < 0
and (J 11 − J 22 ) + 4 J 12 J 21 > 0 , both characteristic roots are real and have opposite signs,
and thus the equilibrium is stable as a saddle point [54, p.253].
2

3. Policy analysis
The comparative statics of l*, m*, b*, a*, and x* with respect to exogenous
variables can be obtained from equations (3), (5), (6), (1), and (7) with the substitution of
λ from (4). The determinant of the Hessian matrix of the system of these five equations isgiven by:  h′′ 2
n2
1
n2 
h′′
n2 2 

′
′
′
′
′
′
+
D = p 2 d πs′′
−
e
k
k
k
β
η
πs′′Φ < 0 ,
η
γ
η
ϕ
+

2
b
b  α 2 h′ 3bα h′  αh′pwh′′(− βf xx + rf xl ) < 0 . Secondary-forest-clearing labor is assumed to bewhere Φ =αh ′ 2
greater than soil-conservation labor, i.e., τ > m; then, e > 0 (see equation 5).
I consider three policies: 1) forest protection (higher π); 2) improved fallow toaugment soil regeneration under fallow (higher η); and 3) on-farm soil management toaugment soil regeneration on non-replaced cultivated land (higher α). Key outcome
measures are primary-forest clearing a* and fallow length N* in the long run (the asterisks
represent the steady-state equilibrium). With a fixed θ, effects on N* are qualitatively thesame as those on n* = (1 – a*)/b*. To facilitate interpretations, soil conservation labor m*is also examined.
The comparative statics are reported in Table 1. Many results of the two soil
management measures, but not forest protection, depend on farming technology: Many
results are ambiguous when d > 0, but most ambiguities vanish when d = 0. This isbecause for the latter technologies, all adjustments in equations (3) and (7) aredetermined by the shadow value of soil stock, which unambiguously increases withaugmented soil conservation labor (see equation 4), because adjustments in cultivationlabor and soil stock cancel each other out (note that no other endogenous variables appear
in equations 3 and 7). With d > 0, this neutrality of farming technology vanishes becauseof the adjustments in crop production. Many empirical works that estimate the production
functions of shifting cultivation employ a Cobb-Douglas technology, for which d = 0[e.g., 55, 56, 57]. The summary of the comparative static results in Table 2 is based on

8those with d = 0 for soil-management measures; those for forest protection do not dependon the sign of d.
First, forest protection always reduces and increases primary- and secondaryforest clearing, respectively. As the former becomes more costly than the latter, this shift
is an obvious result of substitution. Although these two impacts counteract each other indetermining fallow length, the secondary-forest effect always outweighs the primaryforest effect, resulting in shorter fallow. Thus, protecting primary forest involves lesssustainable secondary forest as a tradeoff. In contrast, soil-conservation labor input isalways augmented. This is because the farmer offsets a decrease in the acquisition offertile soil from primary forest land, which is greater in magnitude than an increase in theacquisition of less fertile soil (as a result of shortened fallow) from secondary forest land.
Second, the results for improved fallow are qualitatively the same as those forforest protection. Secondary forest is substituted for primary forest in the farmer’s soil
management portfolio, as follows. On one hand, primary-forest clearing is reduced,
because with higher η, its marginal cost ηk’ – reduced soil regeneration under fallow –increases more than its benefit (see equation 6). On the other hand, secondary-forest
clearing is augmented, because higher η increases fallow soil minus the forgone marginal
soil regeneration on the fallow land, ηk – ηk’n (≡ g > 0 because e > 0) (see equation 5).
As the latter effect unambiguously outweighs the former, fallow always becomes shorter.
To offset the balance of these two forest-based soil managements, on-farm soil
management is intensified. Shortened fallow is not surprising at all, because this policy
speeds up the soil regeneration. The question is whether or not the fertility of fallow land
ηk(n) is improved. Although d (ηk (n )) dη = k (n ) + ηk ′(n ) dn dη is generally unsigned
even if d = 0, this comparative statics is likely to be positive, unless fallow length nbecomes very short. Whether and how much this policy mitigates adverse ecologicalimpacts of short fallow discussed above are empirical questions, the answers to which
depend on specific fallow-management measures. As such, although improved fallow
protects primary forest, it may do so at the cost of unsustainable secondary-fallow forest.
Third, enhanced on-farm soil regeneration always leads to the intensification of
on-farm soil management and thus more fertile soil on the cultivated land αh(m). It also
unambiguously reduces primary-forest clearing, because the net soil addition on crop
land through primary-forest clearing (1 – αh) decreases. In contrast, the impacts on
secondary-forest clearing are indeterminate even if d = 0, because the net soil addition
through secondary-forest clearing (ηk – αh) is ambiguously altered, depending on fallow
length. Fallow unambiguously becomes longer, because the former primary-forest effectalways outweighs the latter secondary-forest effect. An important difference of thispolicy from the other two policies is that although the latter two directly affect either oneof the two forest-based soil management options – primary- or secondary-forest clearing–, the former alters the benefit-cost comparisons of the on-farm option with both ofthem. 16
16

I also examine impacts of output price and wage, which can be altered by a variety ofmacroeconomic policies, such as price subsidies, exchange-rate policies, and trade
policies; alternatively, a higher p captures Hicks neutral technological progress infarming. Standard results are obtained: Regardless of the sign on d, promoting nonagricultural activities (higher w) always reduces primary-forest clearing and soil-

9

4. Conclusion
This paper developed a unified dynamic farm model of primary-forest clearing,forest fallowing, and on-farm soil conservation in shifting cultivation by incorporating
new soils acquired from cleared primary/secondary forest land into on-farm soil
dynamics. The comparative static analysis revealed that although forest protection (e.g.,protected areas), fallow management (e.g., improved fallow), and on-farm soil
management (e.g., biochar in Amazonia) all reduce primary-forest clearing(deforestation) in the long run, only on-farm soil management increases fallow length. A
caveat is that the model ignores land accumulation; with an additional motive for clearing
primary forest – land expansion – better on-farm soil management instead may lead toaugmented deforestation. Then, to attain the win-win goal of protecting primary forestand maintaining sustainable secondary fallow forest (longer fallow), an effective policy
mix is needed. These promising findings of the paper call for new empirical studies on
the roles of fallow and on-farm soil management for rainforest conservation in shifting
cultivation systems.
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conservation labor (and thus on-farm soil regeneration) and increases fallow length, as
they discourage farming itself (the impact on secondary-forest clearing is ambiguous);
the converse holds true for promoting agriculture (higher p).

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13
Table 1. Comparative statics
Forest protection:
 h′′ 2
da*
n2 
n2 
1 
1

′
′
′
′
−
= − s'  p 2 d 
e
+
k
k
η
γ
β
Φ
η
<0
2
dπ
D 
b 
b 
α h′
 α h′
1
db* 1  2  h′′n n= s'  p d ηk ′′  > 0
eq + ηk ′′ γ  − βΦ
2
α h′
dπ
D 
b 
b
 α h′dn*h′′1 n= − ⋅ s' p 2 d
ϕe < 0dπ
D bα h′ 2dm* 1
n2 1= s' p 2 d⋅
ηk ′′ϕ > 0dπDb α h′
Fallow regeneration:
1
1
da * 1  2 n2 n 
ηk ′′ Ω  + βΦ 2 2 ηk ′′ k  < 0=  p d  eΘ +dη D 
α h′
b 
b 
α h′

1
1 
1
db* 1  2 n k =  p d  πs′′Ψ + qΘ +
ηk ′′ Ω  − βΦηk ′′  
 − gπs′′ +α h′
α h′ 
α h′dη D 
b 
b 

1 n
1
dn*

= − ⋅  p 2 d (πs′′Ψ + ϕΘ ) + βΦ
gπs′′ 
dη
D b
α h′


(

)


1
dm* 1 1  2 
n 
n2
2
′
′
′
′
′
′
′
′
= ⋅
Φ
p
d
π
s
ge
η
k
n
k
ϕ
η
k
k
β
η
k
πs′′ 
−
+
−



2
2
dη
D α h′ 
b 
b
α h′


On-farm soil regeneration:da * 1 
1
1n2 γ 
n2 
ηk ′′ Λ  + βΦ 2 2 ηk ′′ ⋅=  − p 2 d  eΓ +
dα D 
α h′b 1 − a 
b 
α h′

db* 1  2 
1
n 
1 
1
n γ 
=  p d  πs′′Π + qΓ +
ηk ′′ Λ  − βΦηk ′′ ⋅
 hπs′′ +
α h′
α h′ 
α h′dα D b 
b 1 − a  

1 n
dn*
h

= − ⋅  p 2 d (πs′′Π + ϕΓ ) − βΦπs′′ 
dαD b
α h′ 
11 
dm* 1 1 n2 b  
n2
2 
′
′
′
′
′
′


π
η
γ
ϕ
β
η
πs′′ 
1
Φ
−
= ⋅
−
p
d
s
eg
+
k
h
−
−
k
k

 



2
1 − a  dα
D αh′ b b
α h′ 
 αh′ 2< 0 , q = 1 − αh − ηk ′ > 0 (because q > e > 0),
h′′

 h′′
 h′′
γ 
h′′  γ
γ > 0 , Π = ϕχ + heχ + h γ > 0 ,− ϕ  , Λ = 
Γ=
e
2
2
2 ′3  1 − a
1− a 
α h
 αh ′
 αh ′

Note: χ = −h +

Θ=

 h′′
h′′
γ
h′′  k
qb + k > 0 , Ψ = −πs′′ekb + gγ > 0 .
 e + gq  < 0 , Ω =  −2n
α h′ 2 αh ′

α 2 h′3  n

14Table 2. Summary of comparative static results.

Forest protectionπPrimary
forestclearinga*-

Fallow regeneration

η-Secondaryforestclearingb*+

Fallow
lengthn*-On-farm soil
conservation
labor
m*
+

+

-

+

On-farm soil regeneration α?
++Note: Results for π do not depend on the sign of d; with respect to η and α, results with d= 0 are shown.

15
Figure 1. Soil fertility profile across plots.

1

Fertility

A

B
C

ηk

D
E

N
αh

L
P
G
O

a

H
a+b

M

F

J
K
1-a-b 1-a 1
PlotsI