metadata: authors: 0: author: Barbier,Edward B.
count: World
docna: 0: docna: Structural change, dualism and economic
            development : the role of the vulnerable poor on marginal lands
docty: Policy Research Working Paper
subtopic: Rural Settlements,Coastal and Marine Resources,Food Security,Energy and Natural Resources,Agricultural Growth and Rural Development,Inequality,Global Environment
teratopic: Environment,Macroeconomics and Economic Growth,Poverty Reduction,Finance and Financial Sector Development
abstracts: cdata!: Empirical evidence indicates that in
            many developing regions, the extreme poor in more marginal
            land areas form a "residual" pool of rural labor.
            Structural transformation in such developing economies
            depends crucially on labor and land use decisions of these
            most-vulnerable populations located on abundant but marginal
            agricultural land. Although the modern sector may be the
            source of dynamic growth through learning-by-doing and
            knowledge spillovers, patterns of labor, land and other
            natural resources use in the rural economy matter in the
            overall dynamics of structural change. The concentration of
            the rural poor on marginal lands is essentially a barometer
            of economy-wide development. As long as there are abundant
            marginal lands for cultivation, they serve to absorb rural
            migrants, increased population, and displaced unskilled
            labor from elsewhere in the economy. Moreover, the economy
            is vulnerable to the "Dutch disease" effects of a
            booming primary products sector. As a consequence,
            productivity increases and expansion in the commercial
            primary production sector will cause manufacturing
            employment and output to contract, until complete
            specialization occurs. Avoiding such an outcome and
            combating the inherent dualism of the economy requires both
            targeted polices for the modern sector and traditional
            agriculture on marginal lands.
repnme: repnme: Structural change, dualism and economic
            development : the role of the vulnerable poor on marginal lands
display_title: Structural change, dualism and
            economic development : the role of the vulnerable poor on
            marginal lands
listing_relative_url: /research/2013/05/17744048/structural-change-dualism-economic-development-role-vulnerable-poor-marginal-lands
topicv3: Agriculture and Food Security m1326205 435,Natural Resources m1326446 1979,Poverty m1326687 695,Environment, Natural Resources and Blue
            Economy m1327391 566,Rural Development m1504505 2667
publishtoextweb_dt: 2013-05-01T00:00:00Z
historic_topic: Environment,Macroeconomics and Economic Growth,Poverty Reduction,Finance and Financial Sector Development
no_of_pages: 38
author_keys: 0: author_key: 582939
model_extractions: WPS6456 Policy Research Working Paper 6456 Structural Change, Dualism and Economic Development The Role of the Vulnerable Poor on Marginal Lands _Edward B. Barbier_ The World Bank Development Research Group Environment and Energy Team May 2013
Policy Research Working Paper 6456

# **Abstract**

Empirical evidence indicates that in many developing regions, the extreme poor in more marginal land areas form a “residual” pool of rural labor. Structural transformation in such developing economies depends crucially on labor and land use decisions of these mostvulnerable populations located on abundant but marginal agricultural land. Although the modern sector may be the source of dynamic growth through learning-by-doing and knowledge spillovers, patterns of labor, land and other natural resources use in the rural economy matter in the overall dynamics of structural change. The concentration of the rural poor on marginal lands is essentially a barometer of economy-wide development. As long as there are abundant marginal lands for cultivation, they serve to absorb rural migrants, increased population, and displaced unskilled labor from elsewhere in the economy. Moreover, the economy is vulnerable to the “Dutch disease” effects of a booming primary products sector. As a consequence, productivity increases and expansion in the commercial primary production sector will cause manufacturing employment and output to contract, until complete specialization occurs. Avoiding such an outcome and combating the inherent dualism of the economy requires both targeted polices for the modern sector and traditional agriculture on marginal lands.

This paper is a product of the Environment and Energy Team, Development Research Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at ebarbier@uwyo.edu. .

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Structural change, dualism and economic development: The role of the vulnerable poor on marginal lands**

# Edward B. Barbier

John S. Bugas Professor of Economics, ebarbier@uwyo.edu Department of Economics and Finance, University of Wyoming, Laramie, WY, USA 82071 Keywords: structural change, rural poverty, marginal lands, dualism, primary products. JEL codes: O13, O44, Q15 Sectors: Environment, Agriculture, Poverty
# **Introduction**

In recent years there has been renewed interest in how the structure of an economy influences its development. According to this perspective, economic growth in developing countries is intrinsically related to the dynamics of production structures and to the specific policies and institutions implemented to enhance structural transformation.<sup>1</sup> Consequently, "high-growth countries are those that are able to undertake rapid structural transformation from low-productivity ('traditional') to high-productivity ('modern') activities” (Rodrik 2010, p. 90). As these leading production activities have the inherent capacity to innovate with laboraugmenting technology through learning-by-doing, they create sector-wide knowledge spillovers that sustain growth (Lin 2011; Ocampo et al. 2009; Rada 2007; Stiglitz 2011). The conclusion is that in developing economies “productivity growth is closely associated to dynamic structural change toward industry and modern services” (Ocampo et al. 2009, p. 122).

In contrast, the traditional and predominantly rural sector of developing economies is viewed as being relatively unproductive and incapable of dynamic structural change through learning-by-doing and knowledge spillovers. Instead, the rural economy absorbs any excess supply of labor when overall economic growth is weak, and serves as a source of surplus labor to facilitate dynamic growth in the highly productive modern sector.<sup>2</sup> As a result, “when labor and other resources move from less productive to more productive activities, the economy grows even if there is not productivity growth _within_ sectors” (McMillan and Rodrik 2011, p. 1). Such an emphasis on modern sector expansion as the engine of dynamic structural change and growth suggests that the structure of production within the rural economy, and especially natural resource and land use, has little significance to the overall development process.<sup>3</sup> However, as Kreuger (2011, p. 223) has pointed out, “ignoring the importance of increased productivity of the large fraction of the labor force (and of land) in rural areas” is a flawed approach to economic development. According to this view, structural change in 1 See, for example, Lin (2011), McMillan and Rodrik (2011), Ocampo (2005), Ocampo et al. (2009), Rada (2007), Rodrik (2007) and (2010), Stiglitz (2011), Taylor (2004) and Wade (2009).

2 However, some proponents of this view do concede that agricultural productivity can have an important influence on overall economic development, but its role is limited: “One key aspect of growth in the poorest countries is that agriculture dominates the economy. Therefore, agricultural productivity growth is crucial, as in sub-Saharan Africa now. But productivity increases in the sector are significantly constrained by lack of access to modern technology, natural factors such as low fertility land, and mostly by its intrinsic inability to offer increasing returns. Hence, per capita output growth at 2 percent requires even higher growth rates of labor productivity in leading sectors (assuming that the ratio of employed labor to the population is fairly stable).” (Ocampo et al. 2009, p.9).

3 For example, Lin (2011, p. 200) argues: “Following the tradition of classical economics, economists tend to think of a given country’s endowments as consisting only of its land (or natural resources), labor, and capital (both physical and human). These are in fact factor endowments, which firms in an economy can use in production. It should be noted that the analysis of new structural economics focuses on the dynamics of the capital/labor ratio. This is because land is exogenously given in any realistic discussion of a country’s development and natural resources, such as mining resources, exist underground in fixed quantity and their discovery is often random.” 2
developing countries requires policies and investments aimed specifically at improving the productivity and livelihoods of rural areas. Empirical evidence on the intractability of rural poverty in developing regions is often cited in support of this perspective. Rural poverty rates in developing economies have declined over the past decade but remain high in South Asia (40%) and Sub-Saharan Africa (51%), and where reductions in rural poverty have occurred, they are largely due to rural development and not rural-urban migration (World Bank 2008). In general, poverty incidence is greater in rural areas with less favored land, which suggests that “the extreme poor in more marginal areas are especially vulnerable, and until migration provides alternative opportunities, the challenge is to improve the stability and resilience of livelihoods in these regions” (World Bank 2008, p. 49).

The purpose of the following paper is to show that structural transformation in developing economies depends crucially on how production in the rural economy is characterized. That is, even if one accepts that the modern sector is the source of dynamic growth through learning-by-doing and knowledge spillovers, the pattern of labor and land use (including natural resources) in the rural economy matters to the overall dynamics of structural change. To illustrate this point, the paper develops two versions of a “dual” developing economy model that differ in their portrayal of the rural sector. In both versions, the modern sector of the dual economy remains the same, but the rural sector exhibits distinctively different patterns of production, labor and land use.

The first dual economy model depicts a traditional rural sector as conventionally portrayed in most current analyses of structural transformation in developing economies. As indicated above, the usual assumption is that the rural sector displays the classical labor surplus conditions as initially described by Lewis (1954), which are normally associated with traditional subsistence agriculture on a fixed agricultural land base (e.g., see Ocampo et al. 2009; McMillan and Rodrik 2011; Rada 2007). With a labor surplus rural sector, the real wage is equal to the average product of labor. The equilibrium wage and the allocation of labor in the dual economy are determined where the average productivity of workers in the labor-surplus rural economy equals the marginal productivity of workers employed in the modern sector. Because workers in the rural economy are paid according to their average rather than marginal productivity, the equilibrium wage is too high and the rural labor supply is larger than it would be if labor surplus conditions were not present. As a result, any shift of labor from the less productive laborsurplus rural economy to the more productive and dynamic modern sector leads to structural change toward industry and modern services, and ultimately, to the establishment of a fully modernized and growing economy.

However, the problem with the labor surplus characterization of the rural sector is that it ignores two key stylized facts of the rural economy in most developing economies: first, there is a “residual” pool of rural poor located on abundant but marginal agricultural land, and second, considerable land use conversion and resource exploitation are occurring through expansion of a commercial primary products sector. That is, the rural economy comprises two separate sectors 3
that exhibit distinctly different patterns of labor, land and natural resource use. One sector consists of commercially oriented activities that convert and exploit available land and natural resources for a variety of traded primary product outputs. The other sector contains smallholders employing traditional methods to cultivate less favorable agricultural lands. As a consequence, the rural economy displays Ricardian land surplus conditions, as first identified by Hansen (1979). Because there is an unlimited supply of marginal land with negligible productivity, smallholders practicing traditional agriculture earn no rents. Real wages are invariant to rural employment and determined by the average product of labor. As a consequence, the modern sector competes with the commercial primary production sector for available labor, with marginal land absorbing the residual. The concentration of the rural poor on marginal lands is essentially a barometer of economy-wide development. As long as there are abundant marginal lands for cultivation, they serve to absorb rural migrants, population increases and displaced unskilled labor from elsewhere in the economy. Moreover, the economy is vulnerable to the type of “Dutch disease” effects of a booming primary products sector first analyzed by Matsuyama (1992). In a small open economy, productivity increases in a traded agricultural or primary producing sector will cause manufacturing employment and output to contract while the primary sector expands, until complete specialization occurs. Avoiding such an outcome and combatting the inherent dualism of the economy requires both targeted polices for the modern sector and traditional agriculture on marginal lands.

The paper is organized as follows. The next section provides evidence on the two key stylized facts of land use and rural poverty in developing countries. The subsequent sections develop the two versions of the dual economy model, with the first version assuming classical Lewisian "labor surplus" conditions for the rural sector and the second assuming Ricardian “land surplus” conditions. The influence of primary product price booms and the implementation of targeted policies for the modern sector and traditional agriculture on marginal land are then analyzed. The paper concludes by summarizing the key implications of patterns of land, resource and labor use for the design of policies for structural transformation in developing economies.

# **Land use and rural poverty in developing countries**

Land use change is critically bound up with the pattern of economic development in low and middle income countries. Most developing economies, and certainly the majority of the populations living within them, depend directly on natural resources. For many of these economies, primary product exports account for the vast majority of their export earnings, and one or two primary commodities make up the bulk of exports (Barbier 2005, ch. 1). Agricultural value added accounts for an average of 40% of GDP, and nearly 80% of the labor force is engaged in agricultural or resource-based activities (World Bank 2012). Further adding to these disparities, by 2025, the rural population of the developing world will have increased to almost 4
3.2 billion, placing increasing pressure on a declining resource base (Population Division of the United Nations 2008).

Over the past 50 years, the pattern of land use change in developing as opposed to developed economies has been dramatically different (Barbier 2011; FAO 2006; Lambin and Meyfroidt 2011; Ramankutty and Foley 1999; World Bank 2012). In developed countries, cropland area slowed its growth, eventually stabilized and is now declining. As a result, the decline of forest and woodland has halted in developed countries in aggregate, and since 1990, total forest area has increased (FAO 2006). Not only has primary forest area recovered but also the growth in plantations has been strong. In contrast, in developing economies cropland area has continued to expand. In the developing regions of Africa, Asia and Latin America, tropical forests were the primary sources of new agricultural land in the 1980s and 1990s (Gibbs et al. 2010). From 1990 to 2005, cropland in developing countries increased at the rate of 5.5 million ha per year, suggesting that at least 135 million ha of forests, wetlands and other non-cultivated land will be converted to cropland by 2030 (Lambin and Meyfroidt 2011). Developing countries will also require new land for biofuel crops, grazing pasture and industrial forestry, and also to replace land lost to degradation (Lambin and Meyfroidt 2011).

Consequently, development in low and middle-income economies is accompanied by substantial resource and land exploitation, especially the expansion of the agricultural land base through the conversion of forests, wetlands and other natural habitat. But more importantly, the current pattern of resource and land use has two unique structural features.

First, expansion of less-favored agricultural lands is occurring primarily to meet the subsistence and near-subsistence needs of poor rural households. This is not a new phenomenon; as noted by Coxhead et al. (2002, p. 345), “the land frontier has long served as the employer of last resort for underemployed, unskilled labor”. Yet, this process has become a major structural feature of most poor economies. Many of the world's rural poor continue to be concentrated in the less ecologically favored and remote areas of developing regions, such as converted forest frontier areas, poor quality uplands, converted wetlands, and similar lands with limited agricultural potential (Barbier 2005 and 2010; Comprehensive Assessment of Water Management in Agriculture 2007; CPRC 2004; Dercon 2009; Fan and Chan-Kang 2004; Hazell and Wood 2008; IFAD 2010; World Bank 2003 and 2008). Population increases, rural migration and other economic pressures mean that marginal land expansion continues to absorb the growing number of rural poor in developing economies (Barbier 2011; Carr 2009; Chen and Ravillion 2007; Dercon 2009; Hazell and Wood 2008; Population Division of the United Nations 2008). The result is that the rural poor located on marginal and low productivity agricultural land typically employ traditional farming methods, earn negligible land rents or profits, and have inadequate access to transport, infrastructure and markets (Barbier 2005 and 2010; Banerjee and Duflo 2007; Barrett 2008; Coxhead et al. 2002; Dercon 2009; Hazell and Wood 2008; IFAD 2010; Jalan and Ravallion 1997 and 2002; Maertens et al. 2006; Pichón 1997).

5
Second, less favorable and marginal lands may be an important outlet for the rural poor, but increasingly it is commercially oriented economic activities that are responsible for much of the resource exploitation and expansion of the agricultural land base through the conversion of forests, wetlands and other natural habitat that is occurring in developing economies (Boucher et al. 2011; Chomitz et al 2007; Deininger et al. 2011; DeFries et al. 2010; FAO 2006; Rudel 2007). The primary product activities responsible for extensive land conversion include plantation agriculture, ranching, forestry and mining activities, and often result in export-oriented extractive enclaves with little or no forward and backward linkages to the rest of the economy (Barbier 2005 and 2011; Bridge 2008; van der Ploeg 2011). In addition, developing countries have been actively promoting these commercial activities as a means to expanding the primary products sector, especially in the land and resource abundant regions of Latin America and Africa (Deininger and Bayerlee 2012; Rudel 2007). The result is that most developing economies remain highly dependent on the exploitation of natural resources and are unable to diversify from primary production as the dominant economic sector.

These two structural features of the rural economy of developing countries, the tendency of the rural poor to be clustered in marginal areas and the high dependency on primary product exports, are highlighted in Table 1 and Figure 1. For example, Table 1 indicates the link between low levels GDP per capita, rural poverty and the share of populations concentrated in fragile areas. The table includes 89 developing economies that have, on average, at least 20% of their populations located on fragile lands. Across all economies, the average real GDP per capita is $1, 613 and the rural poverty rate is 47.3%. In addition, several important trends emerge from the table. First, more than half (48) of the countries are low-income economies with real GDP per capita of less than $1,000. Second, none of the economies with GDP per capita greater than $4,000 have more than 50% of their populations located in fragile areas. Finally, the table confirms that lower income economies generally have more of their populations concentrated in fragile areas and higher rural poverty rates.

Figure 1 confirms that the developing economies in Table 1 are also highly resource dependent; i.e., primary products account for a large share of total merchandise exports.<sup>4</sup> These economies, which have at least 20% of their population living in “fragile” environments, have on average 69% of their exports consisting of primary products. Resource dependency is even greater for the economies with higher concentrations of their populations on marginal land. Developing countries with 20- 30% or their populations in marginal areas typically have around 65% of their exports from primary products. But for those economies with more than 50% of their populations located in fragile areas, resource dependency can rise to 75% to 80%. The concentration of the rural poor on marginal land and resource dependency are clearly important structural attributes of many poor countries.

> 4 The Solomon Islands and Uzbekistan were excluded from Figure 1 due to the lack of data on the composition of their exports. Thus, Figure 1 includes 87 of the 89 economies depicted in Table 1.

6
The consequence of these two structural features of land use and expansion in developing economies is that they are symptomatic of a _dualistic rural economy_ . That is, the rural economy contains both a traditional sector that converts and exploits available land to produce a nontraded agricultural output, and a fully developed, commercially oriented sector that converts and exploits available land and natural resources for a variety of traded outputs. The latter includes plantation agriculture, ranching, forestry and mining activities. In addition, the traditional agricultural sector is dominated by farm holdings that occupy marginal or ecologically fragile land with poor land quality and productivity potential. Although these two types of economic activities differ significantly and may also be geographically separated, they are linked by labor use, as the rural poor on marginal land form a large pool of surplus unskilled labor that can be employed in commercial primary production activities. This linkage is important not only to the dynamics of land expansion and use within developing economies but also to the pattern of overall economic development (Barbier 2005 and 2010; Carr 2009; Coxhead et al. 2002; Hansen 1979; Maertens et al. 2006; Pichón 1997).

# **Labor Surplus Rural Economy**

In this version of the dual economy model, it is assumed that the rural sector displays classical Lewisian "labor surplus" characteristics. This condition is represented in the normal way, assuming that agricultural labor is sufficiently abundant so that its average productivity equals the wage rate. In comparison, the modern or leading sector employs capital and labor, innovates through learning-by-doing technological change and generates knowledge spillovers.<sup>5</sup> There is perfect labor mobility between the two sectors. This means that, given the presence of labor surplus conditions in the rural sector, any increase in the labor force is absorbed by modern sector activities and not agriculture. Given that much of today’s developing world is experiencing agricultural land expansion, the following analysis considers explicitly the role of an increase in the fixed factor, land. Under labor surplus conditions, an increase in the availability of land is the only way that a rise in agricultural output per worker will occur. As this increases the real wage, labor shifts from the modern to the rural sector, and growth is adversely affected.

_Labor surplus rural sector_ Assume a rural sector that produces a homogeneous agricultural good under perfect competition and constant returns to scale production from land _N_ 1 and labor _L_ 1

> 5 These assumptions replicate the basic conditions found in economic models of structural transformation in developing economies. For example, Ocampo et al. (2009, p. 122) state: "The modern sector basically comprises industry along with parts of agriculture and services.  It will be contrasted...with a 'subsistence,' or informal, sector with production assumed to rely on  (low-wage) labor only....the modern sector is characterized by increasing returns while constant or decreasing returns dominate subsistence."

7
As there is no unemployment, and labor is abundant relative to the amount of land available for agriculture, people living in the rural area appropriate all the arable land for production until rent is fully dissipated; i.e., the land rent is completely subsumed in the wage income of rural households. Thus, letting _p_ 1 be the price of the agricultural product and _w_ the nominal wage, total profits are π = _L_ 1 _p_ 1 _f_ ( _n_ 1 ) − _wL_ 1 = 0, _n_ 1 = _N_ 1 _L_ 1 , _f_ ( _n_ 1 ) = _F_ ( _N_ 1 _L_ 1,1 ) , which yields The real wage is equal to the average product of labor. As average productivity declines with respect to _L_ 1 and _p_ 1 is given, the nominal wage _w_ is a decreasing function of rural employment. The marginal productivity of labor is therefore less than the average productivity. This implies that the wage is higher, and the rural labor supply is larger, with averageproductivity compared to marginal-productivity remuneration of labor. These conditions constitute the classic Lewisian _labor surplus_ conditions for the rural sector of a dual economy (Fields 2004).

# _Modern sector_

The modern sector, which includes industry but also technically advanced agriculture and services, has labor-augmenting technology that benefits from learning by doing and knowledge spillovers. Production in the sector depends on both unskilled labor and capital, which could also comprise human capital (skills). For the representative firm, an increase in the firm’s capital stock leads to a parallel increase in its stock of knowledge. Each firm’s knowledge is a public good, however, that any other firm can access at zero cost. For the representative _i_<sup>th</sup> firm, output _Q_ 2 _i_ is produced by hiring capital _K_ 2 _i_ and labor _L_ 2 _i_ , and _A_ 2 _i_ is the amount of labor-augmenting technology available to the firm. But, with the presence of learning by doing and knowledge spillovers _A_ 2 _i_ = _K_ 2 = ∑ _K_ 2 _i_ and the representative _i_ firm’s production function is Production of the firm displays diminishing returns to its own stock of capital _K_ 2 _i_ , provided that _K_ 2 and _L_ 2 _i_ are constant. However, if each producer in the sector expands its own capital, then _K_ 2 will rise and produce a spillover benefit that increases the productivity of all firms, which is the increasing returns effect. Each firm’s production is nonetheless homogeneous of degree one with respect to its own capital _K_ 2 _i_ and labor _L_ 2 _i_ , and if _K_ 2 _i_ and _K_ 2 expand together by the same amount while _L_ 2 _i_ is fixed, production also displays constant returns to scale.

8
For each firm, the total capital stock _K_ 2 of the modern sector is exogenously determined. In addition, assume that the output of each firm is a homogenous product with a given price _p_ 2. If all firms make the same choices so that _k_ 2 _i= k_ 2 and _K_ 2 _= k_ 2 _L_ 2, then profit-maximizing by each firm yields where use is made of the following expressions for the average product of capital _h_  ( _L_ 2 ) and private marginal product of capital _hK_ ( _k_ 2, _K_ 2 ) , respectively Condition (4) indicates that the value marginal productivity of capital for a modern sector firm equals the interest rate, _r_ . Condition (5) indicates that the value marginal productivity of labor employed by a modern sector firm equals the real wage rate. As labor can move freely between the traditional and modern sector, the nominal wage is determined by the labor market equilibrium of the dual economy.

Both the private marginal product of capital and average product of capital are invariant with respect to the capital-labor ratio because learning by doing and spillovers eliminate diminishing returns to capital. As (6) indicates, the private marginal product of capital is less than the average marginal product of capital. The private marginal product of capital is increasing in _L_ 2, given _h_ ′′( _L_ 2 ) < 0 . These results (4)-(6) for production and input use involving learning by doing and spillover are standard for these types of relationships (Barro and Sala-IMartin 2004).

# _Growth dynamics and labor market equilibrium_

household’s assets per person, _r_ is the interest rate, _w_ the wage rate, ρ is the rate of time preference, and θ is the intertemporal elasticity of substitution. As shown in the Appendix, the growth dynamics of the modern sector and thus the economy are governed by 9
Equation (7) is the usual condition for capital accumulation in an economy. If output per capita, valued at the price _p_ 2, exceeds consumption, capital per person will increase. Condition (8) indicates that per capita consumption is proportional to capital per person. Consequently, as (9) depicts, capital and output per worker in the modern sector grow at the same (constant) rate as consumption per capita. The per capita growth rate, γ, is determined by the total number of employed in the sector, _L_ 2. An expansion (contraction) in the aggregate modern sector labor force, _L_ 2, therefore increases (decreases) per capita growth in this sector.

The solid lines in Figure 2 depict one such labor market equilibrium in the dual economy, and thus the corresponding growth rate for the modern sector. The equilibrium wage and the allocation of labor in the dual economy are determined where the average productivity of workers in the labor-surplus rural economy equals the marginal productivity of workers employed in the modern sector. Note that, because workers in the rural economy are paid according to their average rather than marginal productivity, the equilibrium wage is too high and the rural labor supply is larger than it would be if labor surplus conditions were not present. As the figure indicates, once the labor market determines the allocation of labor between the modern sector _L_ 2 and the rural sector _L - L_ 2, the amount of labor employed in the modern sector determines the per capita growth rate of the economy γ.

The equilibrium outcome depicted by the solid lines in Figure 2 is highly optimistic. It also supports the view that, with the shift of labor from the less productive labor-surplus rural economy to the more productive and dynamic modern sector, the resulting productivity growth leads to dynamic structural change toward industry and modern services (Lin 2011; McMillan and Rodrik 2011; Ocampo 2005; Ocampo et al. 2009; Rada 2007; Rodrik 2007 and 2010; Stiglitz 2011; Taylor 2004). For example, the solid lines in Figure 2 depict an employment equilibrium for the modern sector _L_ 2 that generates a positive growth rate γ > 0 . Consequently, from (9), capital per person will be increasing in this sector. With _L_ 2 initially determined by the labor  market equilibrium this implies _K_ 2 > 0 . However, from (9), an increase in the capital stock of the modern sector will shift out its marginal productivity curve for labor. More workers will 10
shift from the rural economy to the modern sector, and the growth rate γ will increase further. This process becomes self-reinforcing, the labor-surplus rural economy will shrink, and the modern sector expands. Eventually, all labor will be re-allocated from the labor-surplus sector and a fully modern economy will emerge.

However, the equilibrium outcome may not be as favorable to modern sector growth and development as depicted by the solid lines in Figure 2. If there is a rise in the agricultural price _p_ 1 in the rural economy or more land is used in cultivation _N_ 1 the value of the average productivity of labor will increase, as will the equilibrium wage and the number of rural workers. As represented by the dotted lines, the new equilibrium will lead to less employment and growth in the modern sector. Although not shown in the figure, if the employment equilibrium in the latter sector _L_ 2 is too low, it will generate a negative growth rate γ < 0 . Capital per person in the will now be falling, which implies a declining capital stock _K_ 2. In this case, the marginal productivity of labor in the modern sector will decline, causing more labor to shift to the rural economy. Although wages will eventually decline, growth in the modern sector will continue to fall until it completely disappears, and the economy reverts to the classical Lewisian state of underdevelopment and labor surplus. Avoiding this undesirable outcome explains the importance placed on long-term industrial policies as a means to ensuring modern sector expansion (Lin 2011; Ocampo 2005; Rodrik 2007 and 2010; Stiglitz 2011; Taylor 2004).

Although this view of the dual economy is compelling, it does not account for some of the key structural features of land use and rural poverty in most developing countries today. As we shall see in the following model, a land surplus rural economy that contains both a commercial primary production sector and a sizable population cultivating less favorable lands yields very different conditions for labor allocation and growth.

# **Land Surplus Rural Economy**

This version of the model assumes that the rural economy displays land surplus, rather than labor surplus, characteristics. In addition, the rural economy comprises two separate sectors that exhibit distinctly different patterns of labor, land and natural resource use. One sector consists of commercially oriented activities that convert and exploit available land and natural resources for a variety of traded primary product outputs. Land and other natural resources are sufficiently abundant for use in primary production, but can only be appropriated through employing increasing amount of labor for this purpose. The sector rural sector contains smallholders employing traditional methods to cultivate less favorable agricultural lands. For smallholders engaged in traditional agriculture in marginal areas, land is also abundant but is of extremely poor quality for agricultural production. There is perfect labor mobility throughout the dualistic rural economy.

Although the rural economy is characterized differently, the modern sector is the same as in the previous version of the model. Production depends on both unskilled labor and capital, 11
and for the representative firm, output is still determined by (3). Profit-maximizing by each firm also yields conditions (4) and (5) for the value marginal productivity of capital and labor, respectively. Learning by doing and spillovers in the modern sector ensure that the marginal and average product of capital are invariant with respect to the capital-labor ratio but instead vary with the amount of labor employed _L_ 2 (see (6)).

# _Commercial primary production_

In this rural sector, production of the primary product (plantation crops, timber, beef, mineral, etc.) depends directly on inputs of land and/or natural resources _N_ 1 and labor _L_ 1; any capital input is fixed and fully funded out of normal profits. Primary production _Q_ 1 is determined by a function with the normal concave properties and is homogeneous of degree one _Q_ 1 = _F_ ( _N_ 1, _L_ 1 ) , _Fi_ > 0, _Fii_ < 0, _i_ = _N_ , _L_ . (11) The commercial activity can obtain more land or natural resources (hereafter referred to as “resources”) for primary production, but only by employing and allocating more labor for this purpose. It is assumed that increasing _N_ 1 incurs a rising input of _L_ 1 ′ ′′ _L_ 1 = _z_ ( _N_ 1 )<sup>,</sup> _z_ > 0, _z_ ≥ 0, , (12) where _z_ ′( _N_ 1 ) is the marginal labor requirement of obtaining and transforming a unit of the resource input, which is a convex function of the amount of _N_ 1 appropriated.

in resources appropriated for primary production in response to proportionately more labor devoted to this purpose. It is assumed that the normal case is 0 < ε( _N_ 1 ) < 1 .<sup>6</sup> Condition (13) indicates that labor will be used in commercial primary production activities until its value

> 6

> As shown by Barbier (2012), the case ε( _N_ 1 ) = 1 implies ∂ _L_ 1 ∂ _N_ 1 = _L_ 1 _N_ 1 = _z_ , which is a violation of the convex properties of (12).  It also corresponds to the case first suggested by Domar (1970), where natural resources and land are so abundant that they essentially comprise a limitless "frontier" that they can be appropriated proportionately with increases in labor.  In contrast, if ε( _N_ 1 ) = 0<sup>, then resources are no longer abundantly available</sup> but fixed in supply.

12
marginal productivity equals the wage rate. As labor is used for both appropriating resources and production, the wage rate will be higher than if resources are fixed in supply and thus labor was used only for production( ε( _N_ 1 ) = 0 ). Because in (13) the value marginal productivity of labor declines with respect to _L_ 1, the wage rate is a decreasing function of labor employed in the primary product sector.

# _Traditional agriculture on marginal land_

Production of non-traded agricultural output on marginal land also involves two inputs, land _N m_ and labor _Lm_ ; any capital input is fixed and fully funded out of normal profits. Both ( ) ( ) land and labor are required for traditional agricultural production, _Qm_ , which is determined by a function with the normal concave properties and is homogeneous of degree one _m m m Q_ = _G_ ( _N_ , _L_ ) , _Gi_ ≥ 0, _Gii_ < 0, _i_ = _N_ , _L_ (14) Note that the marginal productivity of land is not necessarily positive. This Ricardian surplus land condition follows from the assumption that poor quality marginal land is unproductive in cultivation (Hansen 1979). That is, for traditional agriculture on marginal land _GN_ = 0 , and because (7) does not apply to marginal land conversion, equilibrium is determined by The result is that there are no diminishing returns to labor in the use of marginal land for agricultural production. Real wages are invariant to rural employment (the number of farmers and/or labor input on marginal land) and determined by the average product of labor. Moreover, the condition of zero marginal productivity fixes the land-labor ratio on marginal land, which can _m_ be designated as _n_ . Given the average product of labor relationship in (15), the fixed land-labor ratio will determine the nominal wage rate _w_ for the predetermined output price _p_<sup>_m_</sup> . Thus, the best that farmers and their families on marginal land can do is either to sell their labor to each other and obtain an equilibrium real wage _w p_ 2 , or alternatively, farm their own plots of land and earn the same real wage. Since there is little advantage in selling their labor, farmers will tend to use their and family labor to farm their own land. Hence, under this marginal land condition, small family farms consuming their own production will predominate. Unless the population increases, no more land will be brought into production and there will be surplus land of marginal quality.

# _Primary production trade, growth dynamics and labor market equilibrium_

Because the fixed land-labor ratio on marginal land _n_<sup>_m_</sup> determines the nominal wage rate _w_ , the rural economy is recursive with respect to resource use, labor and output in the primary production sector. If the elasticity of resource conversion ε( _N_ 1 ) is constant, _p_ 1 given and _w_ known, then (13) yields the resource-land ratio _n_ 1 for primary production. With _n_ 1 determined, 13
′ the relationship ε = 1 _z n_ 1 can be solved for resource conversion and use _N_ 1. Employment _L_ 1, and from (11), primary production _Q_ 1 can then be found.

Primary products are exported by the small open economy, and thus _p_ 1 is the world price for these commodities. These products are exchanged for imports _M_ , which are substitutes for consumption of domestic output from the modern sector. The balance of trade for the economy is where _p_ is the terms of trade for the economy, expressed in terms of modern sector commodities as the numeraire. Note that, because _p_ is given and _Q_ 1 known, imports to the small economy are recursively determined.

If there is no population growth, the representative household seeks to maximize its  budget constraint _a_ = _ra_ + _w_ − _c_ , and where _m_ is per capita imports. However, as imports are determined by primary products trade, the household is free to choose only its per capita consumption.<sup>7</sup> Thus, the growth dynamics are the same as previously and governed by (7)-(9).

With the nominal wage determined by the fixed land-labor ratio on marginal land, the value marginal productivity condition (5) for the modern sector must equal _w_ . However, suppose that initially capital in the sector is some given level _K_ 20. Equilibrium employment must ′ therefore be the unique solution to _h_ ( _L_ 2 ) = _w p_ 2 _K_ 20 . It is possible that this level of employment is large enough so that growth of the modern sector is positive, i.e. γ > 0 . But this requires a relatively large initial stock of aggregate capital for the modern sector, as the equilibrium employment condition implies that more _L_ 2 requires a higher _K_ 20. For most developing economies, the initial stock of aggregate capital in the modern sector is likely to be small and not large. Thus, it follows that employment _L_ 2 will also be small, and if this is the case, it is more likely that (9) will yield γ ≤ 0 . If it turns out that γ < 0 , then the capital-labor ratio and aggregate capital will decline, employment will fall and the modern sector will contract.

Of course, it is also possible that the modern sector neither contracts nor declines. For example, with _w_ predetermined and for a given _K_ 20, the equilibrium _L_ 2 that satisfies (5) is just sufficient to ensure γ = 0 in (9). This outcome ensures constant employment and aggregate capital in the modern sector, and thus an equilibrium output level _Q_ 2. Such a steady-state result is depicted in Figure 3.

7 Note that the representative household now has the choice to work either in the modern sector or in commercial primary production. Households employed in traditional agriculture on marginal land consume all production within that sector and do not accumulate assts. Thus, the relevant population that the household represents comprises _L_ 1 + _L_ 2 . As we shall see presently, this population is determined by the labor market equilibrium, which is in turn based on the pre-determined nominal wage _w_ in the economy. Hence, if _M_ is known, then per capita imports are also determined exogenously to the household's welfare-maximizing decision.

14
_m_ The total labor force in the developing economy is _L_ = _L_ 1 + _L_ 2 + _L_ . With employment in primary production and the modern sector known, the residual labor on marginal lands _L_<sup>_m_</sup> can be found. As _n_<sup>_m_</sup> is already known, the total marginal land used in traditional agriculture _N_<sup>_m_</sup> is determined. Thus the full labor market equilibrium corresponds to As described previously, the average productivity of labor on marginal land determines the equilibrium wage rate in the economy, and employment in both the primary production and modern sectors equates their respective marginal productivities with _w_ . In addition, the amount of labor employed in the modern sector _L_ 2 must correspond to γ = 0 . The solid lines in Figure 3 depict the labor market equilibrium for the economy and the corresponding zero growth rate for the modern sector.

However, compared to the labor-surplus dual economy, the equilibrium outcome indicated in Figure 3 is much less optimistic. Although a substantial amount of labor may be employed in the modern sector, a constant capital stock eliminates any productivity gains from spillover and learning by doing in the sector. As a consequence, the modern sector competes with the commercial primary production sector for available labor, with marginal land absorbing the residual. Without the dynamic productivity effects of positive growth, the modern sector does not generate the self-reinforcing labor absorption process that leads workers to shift from the rural economy to this sector. The developing economy remains fundamentally dualistic; commercial primary production and a static modern sector are the two principal sectors, with marginal lands absorbing the remaining rural poor. This latter process is a key structural feature of the land-surplus rural economy. The concentration of the rural poor on marginal lands is essentially a barometer of economy-wide development. As long as there are abundant marginal lands for cultivation, they serve to absorb rural migrants, population increases and displaced unskilled labor from elsewhere in the economy.

On the other hand, the rural poor on marginal lands can also be thought of as a large pool of unskilled surplus labor that, under the right conditions, could potentially be absorbed by the commercial primary production and modern sectors. These conditions are explored in turn.

# **Primary product price boom**

Rising commodity prices frequently lead to expansion of the commercial primary product sector of developing countries (Barbier 2005 and 2012; Deininger and Byerlee 2012; van der Ploeg 2011). In such instances, commodity price booms can provide some employment opportunities for low-skilled labor, and thus alleviate the pressure on marginal lands less suitable for agriculture by smallholders. For example, in Southeast Asia, commercial agricultural activities in the lowlands rely on labor from marginal uplands, and thus lowland agricultural development significantly impacts land use and deforestation in the uplands (Barney 2009; Coxhead et al. 2002; Maertens et al. 2006). Oil palm expansion on the Malaysian and Indonesian frontiers has depended on off-farm labor provided by agricultural smallholders and poor migrants (McCarthy and Cramb 2009). If such employment opportunities are sufficiently large and sustained, they can actually reduce long-term marginal land expansion. In Columbia, since 1970 high-input, intensified, highly mechanized cropping on the most suitable land, as well expansion in cattle grazing has drawn labor from more traditional agriculture, so that areas of 15
marginal land are slowly being abandoned and re-vegetating (Etter et al 2008). These effects of commodity price boom are reflected in the land-surplus model.

If _p_ 1 rises, then real wages in the commercial primary products sector _w p_ 1 fall. The result is increased demand for labor _L_ 1 in primary production. From (13), it follows that the land-labor ratio for primary production _n_ 1 must decline. However, from (12), attracting additional labor to the sector more will lead in turn to more land conversion. In order for _n_ 1 to fall, the rise in _L_ 1 must exceed the increase in _N_ 1. With real wages unchanged in the modern sector, the increase in _L_ 1 can come only from reducing labor on marginal land. The fall in _L_<sup>_m_</sup> must be accompanied by an equivalent decline in _N_<sup>_m_</sup> in order to keep the fixed land-labor ratio on marginal land. Thus, the increase in employment, land use and output in the primary production sector in response to the rise in _p_ 1 will reduce labor, cultivation and production on marginal land. In Figure 3, this outcome is represented by the dotted lines that indicate the shifting out of the marginal productivity curve for labor use in primary production.

Of course, if the price of primary products falls, the opposite occurs. The commercialoriented primary sector contracts, _L_ 1 falls and the resulting surplus labor is absorbed on marginal land. The result of _L_<sup>_m_</sup> rising is more land conversion until the land-labor ratio on marginal land returns to _n_<sup>_m_</sup> . Once again, marginal land expansion serves as an outlet for residual rural labor, in this case the unemployed displaced from commercial primary production as the result of a commodity price "bust". Unfortunately, such short-term boom and bust patterns of commercial primary products expansion occur frequently for many developing countries, including for commodities such as cattle, cocoa, coffee, grains, oil palm, soy, shrimp, sugar and other key primary products in various developing regions (Agergaard et al. 2009; Barney 2009; Ha and Shively 2008; Hall 2009; Knudsen and Folds 2011; Li 2011; McCarthy and Cramb 2009; Rodrigues et al. 2009).

However, even if the commodity price boom is sustained, it can have long-term consequences for the overall pattern of economic development. Suppose that commodity price rises continue to lower real wages in the primary product sector, so that the productivity curve in Figure 3 shifts further to the left until all the surplus labor on marginal land _L_<sup>_m_</sup> is absorbed as _L_ 1. Any further increases in the marginal productivity of labor in primary production will have an impact on the wage rate of the economy, as the labor market equilibrium is now Equilibrium condition (18) indicates that labor is allocated between primary production and manufacturing until its value marginal product in the two sectors are equalized. This equilibrium also determines the nominal wage.

As a consequence, as shown in Figure 4, any further shifting out of the value marginal product curve for _L_ 1 due to rising commodity prices will cause the nominal wage rate to rise. As _p_ 2 in the modern sector remains unchanged, real wages will rise and the demand for _L_ 2 declines. The unemployed labor will shift to the primary production sector instead. Although nominal wages have also risen for primary producers, the increase in _p_ 1 must be sufficiently large to − cause real wages in the sector to fall, in order for it to absorb the additional workers _L L_ 2 .

16
Similarly, resource conversion and use _N_ 1 will increase for primary production, but less than the increase in _L_ 1, so that the resource-labor ratio _n_ 1 still declines.

However, the shift in labor from the modern sector to primary production will also lead to dynamic changes to the economy. As indicated by the dotted lines in Figure 4, if workers leave the modern sector, then from (9), the fall in _L_ 2 causes the per capita growth rate in the modern sector to become negative γ < 0. Capital per person in the economy will now be falling, which implies a declining capital stock _K_ 2. In this case, the marginal productivity of labor in manufactures will decline, causing more labor to shift to primary production. Growth will continue to fall, primary production expands and manufacturing disappears, until the economy becomes fully specialized in primary production. This outcome is similar to the Dutch-disease "resource dependency" phenomenon first identified by Matsuyama (1992). In a small open economy, productivity increases in a traded agricultural or primary producing sector will cause manufacturing employment and output to contract while the primary sector expands, until complete specialization occurs.

# **Targeted policies for the modern sector**

The equilibrium outcome for the land-surplus economy depicted in Figure 3 indicates a static modern sector displaying zero per capita growth. Without the dynamic productivity effects of positive growth, the modern sector is unable to generate the self-reinforcing labor absorption process that causes workers to shift from the rural economy to this sector, and the overall developing economy remains dualistic.

However, as indicated in the Appendix, the growth outcome for the modern sector as represented by condition (9) is the result of the decentralized decisions made by competitive firms and households. Because individual producers in the modern sector do not internalize the learning by doing and spillover effects of capital accumulation, they base their decisions on the private marginal product of capital (see (4)). In contrast, as shown in the Appendix, the optimal growth for the modern sector should internalize learning by doing and knowledge spillovers across the sector. If so, then optimal modern sector growth is not determined by (9) but in accordance with the average product of capital, i.e.

* A comparison (9) and (19) indicates that γ > γ .  The optimal growth of the modern sector exceeds growth based solely on the decentralized decisions of consumers and firms.

As indicated in the Appendix, a targeted policy intervention could ensure that the decentralized economy of the modern sector can still attain the higher socially optimal growth

* rate γ .  Specifically, a lump sum tax on the wages of consumers could be used to subsidize purchases of capital goods, through mechanisms such as an investment tax credit, and thus effectively ensure that individual producers are making decisions based on the average product of capital. Such a targeted policy has the possibility of ensuring that the modern sector escapes the “zero growth” trap depicted in Figure 3.

17
> For example, if the growth rate γ = 0 in Figure 3 corresponds to the decentralized decision of producers based on the private marginal productivity of capital (4), then a subsidy of capital * purchases will raise the growth rate to γ > 0 .  However, as (19) indicates, this must correspond to a higher rate of modern sector employment<sup>_L_</sup> *2<sup>.  Workers will have shifted from the rural</sup> economy to the modern sector.  As depicted in Figure 5, the outcome generates a self-reinforcing process of growth and labor absorption. Positive growth in the modern sector implies that its capital-labor ratio is rising, and any corresponding increase in capital will shift out the marginal productivity curve for labor.  More workers will transfer from the rural economy to the modern sector, and the growth rate γ will increase further.  This self-reinforcing process ensures that the land-surplus rural economy will shrink, and the modern sector expands, until eventually a fully modern economy will emerge.

This outcome is in accord with the industrial and structural transformation policies that are frequently advocated to encourage modern sector growth in developing economies (Lin 2011; McMillan and Rodrik 2011; Ocampo et al. 2009; Rodrik 2007 and 2010). For example, as argued by Rodrik (2010, p. 90), "all successful countries have followed what one might call 'productivist' policies. These are activist policies aimed at enhancing the profitability of modern industrial activities and accelerating the movement of resources towards modern industrial activities", which include explicit industrial policies such as "tax and credit incentives" for investment.<sup>8</sup> Similarly, Ocampo et al. (2009, p. 132) maintain that, where successful, the overall goal for industrial and credit policies in developing economies has been "to induce firms 'to learn' or acquire 'specific assets' ...with the objective of building up technically advanced productive capacity." Similar industrial and structural transformation policies are increasingly advocated for Africa and other low-income and land-surplus economies (Aryeetey and Moyo 2012; Wade 2009).

# **Targeted policies for traditional agriculture on marginal land**

However, even if targeted policies in the modern sector succeed in raising the productivity of labor in that sector, the rising productivity does not translate into higher real wages for labor. The reason has to do with the key structural feature of the land-surplus rural economy; as long as there remains significant numbers of the rural poor rural farming marginal land, the Ricardian surplus land condition (15) ensures that the unchanging land-labor ratio for traditional agriculture on less favored land will determine the nominal wage rate for all sectors of the economy. Thus, as shown in Figure 5, although workers will shift from the rural economy to the modern sector, they will not necessarily be better off. Although eventually when a fully modern economy occurs, all workers will be paid their marginal productivity. However, in the transition to that outcome, with poor rural households still located in marginal areas, there may be a need for targeted policies to these households to raise real wages and alleviate widespread rural poverty.

> 8 As outlined by Rodrik (2007, pp. 117-118), government could implement a broad range of incentive programs, including subsidizing costs of "self discovery" of profitable new products, developing mechanisms for higher-risk finance, internalizing coordination externalities, public R&D, subsidizing general technical training, and taking advantage of national abroad.

18
The introduction of new inputs, such as fertilizers or improved varieties, and other technical improvements on marginal land may be neutral, or biased in favor of either land or labor. But if any such technical progress fails to affect the zero marginal productivity condition indicated in (15), then the land-labor ratio for production on marginal land must therefore remain _m_ the same. However, the average productivity of labor _g_ ( _n_ 2 ) can rise as a result of technical improvements on marginal land, and if that is the case, real wages _w p_ 2 will increase. Since _p_ 2 is fixed, this implies a rise in the nominal wage.

As shown in Figure 5, an increase in the nominal wage for the entire economy has the _m m_ effect of shifting up the straight line represented by _p g n_ = _w_ . As condition (17) indicates, ( ) there will be a new labor market equilibrium. However, as depicted in Figure 5, if there are targeted modern sector policies in place, the implications of this new equilibrium will be different for the primary production as opposed to the modern sector.

The rise in the nominal wage leads to an increase in real wages _w p_ 1 in commercial primary production activities. Labor employment _L_ 1 declines and the resource-labor ratio increases. From (12), _N_ 1 must also decrease as employment in primary production falls. However, in order for _n_ 1 to rise, _L_ 1 must decline more than _N_ 1. Thus, the effect of technical progress on marginal land and the consequent rise in wages is a contraction in export-oriented primary production and employment.

Without modern sector expansion, there should also be contraction in employment in this sector, too. However, as outlined in the previous section and illustrated in Figure 5, targeted<sup></sup> ′ policies for the modern sector will cause the marginal productivity of labor (the _p_ 2 _K_ 2 _h_ ( _L_ 2 ) curve in Figure 5) to shift out, and thus some increase in _L_ 2. This will lead to positive growth in the modern sector and a rising capital-labor ratio, which means that the resulting increase in capital will cause the marginal productivity curve for labor to shift out continuously. Although as shown in Figure 5 rising nominal and real wages may reduce some of the labor absorption caused by the expanding modern sector, as long as the productivity curve for _L_ 2 shifts out, there will be some labor absorption by the sector. Eventually the self-reinforcing process of increasing growth, capital investment and labor employment in the modern sector will induce more workers to transfer from the rural economy to the modern sector, and the growth rate γ will increase further.

The self-reinforcing process of dynamic growth in the modern sector ensures once again that the land-surplus rural economy will shrink, and modern production activities expand, until eventually a fully modern economy will emerge.<sup>9</sup> However, by targeting investments and policies to improve the livelihoods and productivity of traditional agriculture on marginal land, now this process involves in higher real wages and reductions in rural poverty in the interim period before the emergence of the fully modern economy.

> 9 Note that Figure 5 depicts an interim period where residual labor still has to be absorbed on marginal lands. Although modern sector employment has expanded, it cannot absorb all the labor released from primary production. Some of the resulting unemployed labor must therefore be absorbed through greater traditional agricultural cultivation of marginal land.  As _Lm_ 2<sup>increases,</sup> _N_ 2 _m_<sup>must rise proportionately in order to keep the land-</sup> labor ratio fixed.

19
Such an outcome supports recent efforts to target investments directly to improving the livelihoods of the rural poor in remote and fragile environments (World Bank 2008). For example, in Ecuador, Madagascar and Cambodia poverty maps have been developed to target public investments to geographically defined sub-groups of the population according to their relative poverty status, which could substantially improve the performance of the programs in term of poverty alleviation (Elbers et al. 2007). A World Bank study that examined 122 targeted programs in 48 developing countries confirms their effectiveness in reducing poverty, if they are designed properly (Coady et al. 2004). A review of poverty alleviation programs in China, Indonesia, Mexico and Vietnam also finds evidence of “the value in specifically targeting spatially disadvantaged areas and households”, although the benefits are larger when programs, such as PROGRESA in Mexico, were successful in employing second-round targeting to identify households in poor locations and thus reducing leakages to non-poor households (Higgins et al. 2010, p. 20).

Appropriate targeting of research, extension and agricultural development has been shown to improve the livelihoods of the poor, increase employment opportunities and even reduce environmental degradation (Barbier 2005 and 2010; Carr 2009; Caviglia-Harris and Harris 2008; Coxhead et al. 2002; Dercon et al. 2009; Maertens et al. 2006). Empirical evidence of technical change, increased public investments and improved extension services in remote regions indicates that any resulting land improvements that do increase the value of homesteads can have a positive effect on both land rents and reducing agricultural expansion (Bellon et al. 2005; Coxhead et al. 2002; Dercon et al. 2009; Dillon et al. 2011; Maertens et al. 2006; Sills and Caviglia-Harris 2008).

Improving market integration for the rural poor may also depend on targeted investments in a range of public services and infrastructure in remote and ecologically fragile regions, such as extension services, roads, communications, protection of property, marketing services and other strategies to improve smallholder accessibility to larger markets (Barrett 2008; World Bank 2008). For example, for poor households in remote areas of a wide range of developing countries, the combination of targeting agricultural research and extension services to poor farmers combined with investments in rural road infrastructure to improve market access appears to generate positive development and poverty alleviation benefits (Ansoms and McKay 2010; Bellon et al. 2005; Cunguara and Damhofer 2011; Dercon et al. 2009; Dillon et al. 2011; Müller and Zeller 2002; Pattanayak et al. 2003;Yamano and Kijima 2010). In Mexico, poverty mapping was found to enhance the targeting of maize crop breeding efforts to poor rural communities in less favorable and remote areas (Bellon et al. 2005). In the Central Highlands of Vietnam, the introduction of fertilizer, improved access to rural roads and markets, and expansion of irrigation increased dramatically the agricultural productivity and incomes (Müller and Zeller 2002).

# **Conclusion**

The recent focus on structural transformation of developing economies has largely emphasized policies that promote growth of industries and highly commercialized agricultural and service activities (Lin 2011; McMillan and Rodrik 2011; Ocampo et al. 2009; Rodrik 2007 and 2010). This paper has attempted to show that, even if the modern sector is the source of dynamic growth through learning-by-doing and knowledge spillovers, the pattern of labor, land and natural resource use in the rural economy matters to the overall dynamics of structural 20
change. If the rural sector is characterized in the traditional labor-surplus way, with land and natural resources exogenously determined, then any shift of labor from the less productive laborsurplus rural economy to the more productive and dynamic modern sector leads to structural transformation of the developing economy. Such an outcome supports the importance placed on long-term industrial policies as a means to ensuring modern sector expansion (Lin 2011; Ocampo 2005; Rodrik 2007 and 2010; Stiglitz 2011; Taylor 2004).

However, the rural sector of most developing countries differs from classical Lewisian labor surplus conditions in two important respects. First, many economies have a “residual” pool of rural poor located on abundant but marginal agricultural land, and second, considerable land use conversion and resource exploitation are occurring through expansion of a commercial primary products sector. These Ricardian land surplus conditions can lead to a permanent “dualistic” outcome in the economy, where the modern sector competes with the commercial primary production sector for available labor, with marginal land absorbing the residual. In addition, the economy is vulnerable to primary product price booms and productivity increases, which will cause manufacturing employment and output to contract while the primary sector expands, until complete specialization occurs.

Avoiding such an outcome can occur through the implementation of targeted modern sector policies. However, even if such policies succeed in raising the productivity of modern sector workers, the rising productivity does not translate into higher real wages for labor. Moreover, before the emergence of the fully modernized economy, there is likely to be an interim period during which poor rural households will remain on marginal lands. As long as this residual pool of labor exists, workers shifting from the rural economy to the modern sector will not necessarily be better off. During this transition period, targeted policies are required to raise real wages and alleviate widespread rural poverty in marginal areas. Such policies include investments to improve the livelihoods of the rural poor in remote and fragile environments, appropriate research, extension and agricultural development for marginal lands, and better market integration through extension service, roads, communication, protection of property, marketing services and other strategies to improve smallholder accessibility to larger markets.

Any policy strategy targeted at improving the livelihoods of the rural poor located in remote and fragile environments should be assessed against an alternative strategy, which is to encourage greater out-migration from these areas. As pointed out by Lall et al. (2006, p. 48), rural development is essentially an indirect way of deterring migration to cities, yet because of the costliness of rural investments, "policies in developing countries are increasingly more concerned with influencing the direction of rural to urban migration flows – e.g. to particular areas - with the implicit understanding that migration will occur anyway and thus should be accommodated at as low a cost as possible." Rarely, however, are the two types of policy strategies, investment in poor rural areas and targeted outmigration, directly compared. In addition, only recently have the linkages between rural out-migration, smallholder agriculture and land use change and degradation in remote and marginal areas been analyzed (Mendola 2008 and 2012; Gray 2009; Greiner and Sakdapolrak. 2012; VanWey et al. 2012). Researching such linkages will become increasingly important to understanding the conditions under which policies to encourage greater rural out-migration should be preferred to a targeted strategy to overcome poverty in remote and fragile areas. It may be, as argued by the World Bank (2008, p. 49), that “until migration provides alternative opportunities, the challenge is to improve the stability and resilience of livelihoods in these regions”. As this paper has pointed out, this may 21
become a critical feature in the design of structural transformation policies to overcome widespread rural poverty in many developing economies.

# **Appendix: Growth dynamics in the modern sector**

# _Decentralized solution_

In the decentralized economy of the modern sector, decisions are made by competitive firms and households. The representative household seeks to which yields the following optimization and transversality conditions respectively Setting _a = k_ 2 in (A.2), and using the marginal productivity conditions (4) and (5) to substitute for _r_ and _w_ , yields which is condition (7) for the accumulation of capital per person in the economy.

Similarly, using (4) in (A.3) Condition (A.6) defines the consumption growth path of the decentralized economy of the modern sector, which is constant if _L_ 2 is unchanging, and is positive if _p_ 2  _h_  ( _L_ 2 ) − _L h_ 2 ′( _L_ 2 ) > ρ . _t_ If γ is constant, then the per capita consumption path is _c_ ( _t_ ) = _c_ ( 0 ) _e_<sup>γ</sup> . Substituting the latter expression into (A.1) gives The integral (A.7) will converge to infinity unless ρ > ( 1 −θ)γ , which along with (A.6), implies  that _c c_ = γ > 0 iff 22
where _b_ is an unknown constant. Condition (A.8) implies that φ > 0.

Using _a = k_ 2 and (A.9) in the transversality condition (A.4) lower bound on convergence in condition (A.8) implies that γ – _r_ < 0. As _c_ (0) is finite and φ > 0, the second term inside the curly brackets in (A.10) converges toward zero. Hence, the transversality condition (A.10) requires the constant _b_ to be zero. Equation (A.9) therefore implies  _c_ ( _t_ ) = φ _k_ 2 ( _t_ ) , φ = _p_ 2 _h_ ( _L_ 2 ) −γ , (A.11) which is the same as (8) in the text. Along the path of the decentralized modern sector, consumption per capita is proportional to capital per person. Given that _q_ 2 = _h_<sup></sup> ( _L_ 2 ) _k_ 2 , then it follows that which is (9) in the text. Per capita consumption, capital and output grow at the same rate in the decentralized economy of the modern sector.

# _Optimal solution_

Unlike an individual producer, a benevolent social planner takes into account that each firm's increase in its capital stock adds to the aggregate capital of the modern sector via knowledge spillovers. That is, the social planner solves for (A.1) with respect to (A.5) and _k_ ( 0 ) = _k_ 0 , which yields the following optimization and transversality conditions  _t c_ 1  * − _rvdv c_<sup>=</sup> θ( _p_ 2 _h_ ( _L_ 2 ) − ρ) ≡ γ , lim _t_ →∞ _k_ ( _t_ ) _e_ ∫ 0 = 0 . (A.13) Condition (A.13) indicates that the optimal consumption growth path of the economy is constant if _L_ 2 is unchanging, and is positive if _p_ 2 _h_  ( _L_ 2 ) > ρ . If γ* is constant, then the optimal per capita 23
consumption path is _c_ ( _t_ ) = _c_ ( 0 ) _e_ γ * _t_ . This result implies that the integral (A.7) will converge to *  infinity unless ρ > ( 1 −θ)γ , which along with (A.13), implies that _c c_ = γ > 0 iff

* Condition (A.14) implies that φ > 0 and the transversality condition in (A.13) ensures that _b_ = 0 . It therefore follows from (A.15) that * *  * _c_ ( _t_ ) = φ _k_ 2 ( _t_ ) , φ = _p_ 2 _h_ ( _L_ 2 ) −γ . (A.16) Along the optimal path for the modern sector, consumption per capita is proportional to capital per person.  As _q_ 2 = _h_<sup></sup> ( _L_ 2 ) _k_ 2 , then it follows that optimal modern sector growth is determined by    _<u>qq</u>_ <u>22</u> = _kk_ <u>22</u> = _cc_ = γ *, γ * = 1 θ ( _p_ 2 _h_  ( _L_ *2 ) −ρ) , (A.17)

which is (19) in the text. Optimal growth of per capita consumption, capital and output occurs at the same rate in the modern sector, and the magnitude of this growth rate is determined by total

* * employment in the sector<sup>_L_</sup> 2<sup>.  As</sup> γ > γ , the optimal growth of the modern sector exceeds growth in the sector based solely on the decentralized decisions of consumers and firms. Because the social planner takes into account learning by doing and knowledge spillovers across the sector, the optimal growth rate is determined in accordance with the average product of capital _h_  ( _L_ *2 ) whereas the decentralized solution takes into account only the private marginal product of capital _h_  ( _L_ 2 ) − _L_ 2 _h_ ′( _L_ 2 ) .  Thus, the growth rate generated by decentralized decisionmaking in the modern sector is too low.

The decentralized economy of the modern sector can still attain the optimal growth rate * γ if capital goods purchased by individual producers are subsidized. For example, suppose that * ′ * producers receive a subsidy on interest payments equivalent to _s_ = _p_ 2 _L h_ 2 ( _L_ 2 ) . From (4), the private marginal productivity of capital would be _p_ 2  _h_  ( _L_ 2 ) − _L h_ 2 ′( _L_ 2 ) = _r_ − _s_ , which would ensure that in (9) the decentralized and optimal growth rate would be the same

* 1  * γ = γ = θ( _p_ 2 _h_ ( _L_ 2 ) − ρ) .  If the subsidy is funded through a lump-sum tax on the wages received by consumers _s_ = τ _w_ , then the budget constraint (A.2) of the representative consumer  becomes _a_ = _ra_ + ( 1 −τ) _w_ − _c_ .  However, maximization of utility (A.1) with respect to this new constraint does not change the optimization condition (A.3).  Thus, taxing consumer wages to pay for the subsidy for capital purchases by producers does not introduce any distortion in the model of the modern sector.

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