metadata: authors: 0: author: Rijkers,Bob
1: author: Soderbom,Mans Martin
count: World
docna: 0: docna: Market integration and structural
            transformation in a poor rural economy
docty: Policy Research Working Paper
subtopic: Nutrition,International Trade and Trade Rules,Food Security,Inequality
teratopic: Agriculture,Macroeconomics and Economic Growth,Industry,Poverty Reduction
abstracts: cdata!: By developing a simple theoretical model
            of the impact of market integration on sectoral output and
            employment in a poor rural setting, this paper demonstrates
            that trade can induce asymmetric growth. Under certain,
            plausible, assumptions, the non-farm sector will grow much
            faster than the agricultural sector when markets become
            integrated. Promoting market integration may thus be an
            effective way of encouraging diversification beyond
            agriculture and catalysing structural change in poor rural economies.
repnme: repnme: Market integration and structural
            transformation in a poor rural economy
display_title: Market integration and structural
            transformation in a poor rural economy
listing_relative_url: /research/2009/03/10330167/market-integration-structural-transformation-poor-rural-economy
topicv3: Education, Skills Development and Labor
            Market m1326135 1484,Agriculture and Food Security m1326205 435,Poverty m1326687 695,Trade m1326924 698,Malnutrition m1627088 4737
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Agriculture,Macroeconomics and Economic Growth,Industry,Poverty Reduction
no_of_pages: 21
author_keys: 0: author_key: 906035
1: author_key: 667817
model_extractions: WPS4856 Policy ReseaRch WoRking PaPeR 4856 Market Integration and Structural Transformation in a Poor Rural Economy _Måns Söderbom Bob Rijkers_ The World Bank Poverty Reduction and Economic Management Network Poverty Reduction Group March 2009
Policy ReseaRch WoRking PaPeR 4856

# **Abstract**

By developing a simple theoretical model of the impact of market integration on sectoral output and employment in a poor rural setting, this paper demonstrates that trade can induce asymmetric growth. Under certain, plausible, assumptions, the non-farm sector will grow much faster than the agricultural sector when markets become integrated. Promoting market integration may thus be an effective way of encouraging diversification beyond agriculture and catalysing structural change in poor rural economies.

This paper—a product of the Poverty Reduction Group (PRMPR), Poverty Reduction and Economic Management Network—is part of a larger effort in the group to understand how access to markets and opportunities, especially productive employment opportunities, faciliate poverty reduction. Policy Research Working Papers are also posted on the Web at http:// econ.worldbank.org. The authors may be contacted at brijkers@worldbank.org and mans.soderbom@economics.gu.se.

_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
# **Market Integration and Structural Transformation in a Poor Rural Economy**

**Måns Söderbom**<sup>**1**</sup> **Bob Rijkers**<sup>**2**</sup>

## **JEL Classification:** O13, O14, O18.

**Key words:** Market integration, trade, structural change, rural transformation

**Acknowledgements:** We thank Arne Bigsten, Luc Christiaensen, Paul Collier, Stefan Dercon, Catalina Gutierrez, Helena Hwang, Varun Kshirsagar, Alice Kuegler, Peter Lanjouw, Josef Loening, Remco Oostendorp, Pierella Paci, Johan Stennek, Ana Revenga and Francis Teal for helpful comments and discussions.

1Department of Economics, School of Business, Economics and Law, University of Gothenburg, E-mail: mans.soderbom@economics.gu.se 2The World Bank, Washington D.C. E-mail: brijkers@worldbank.org
# 1 Introduction

Economic development is an uneven process, characterized by severe inequalities in growth patterns across sectors and across space (Harris, 1985). Theories of structural change typically explain the shift from agriculture to manufacturing and services that accompanies the development process as being triggered by increases in agricultural productivity ("push"), manufacturing productivity ("pull") or a combination of both (for an overview of the literature, see Matsuyama, 2008). This paper contributes to the literature by demonstrating that, even in the absence of technological progress, asymmetric sectoral output growth and employment shifts can be induced by trade. Such shifts result in spatial disparities in economic activity that are qualitatively similar to those conventionally associated with rural transformation. By highlighting the possible role of preferences as part of the explanation for these disparities, the paper also aims to contribute to the New Economic Geography literature (see Krugman, 1998, for an overview of this literature).

To demonstrate these e¤ects, we use a simple theoretical model to analyze the e¤ects of market integration on food and non-food production and the sectoral composition of employment in a poor rural setting, where utility is highly sensitive to food consumption. Our motivation for focusing on poor rural areas is twofold. At the inception of the industrial revolution, most societies were rather poor and dominated by agriculture. Currently, diversi...cation beyond agriculture is often considered a promising way out of poverty for poor rural economies. Yet, in many countries, market fragmentation constrains the growth of the rural nonfarm sector (see e.g. Loening et al, 2008). If people cannot trade, they have no choice but to produce what they need to eat.<sup>1</sup> We analyze the bene...ts of

> 1See e.g. de Janvry et al. (1991) for an analysis of peasant household behaviour when markets

1
market integration and show that, under certain plausible assumptions, as trade is facilitated, output and employment in the non-food sector grow more quickly than output and employment in the food sector as trade. Sectoral growth patterns are thus asymmetric. A related result is that the non-farm sector may bene...t more from market integration than the farm sector.

# 2 The Model

We consider a setting in which there are two representative agents (communities) who are potential trading partners. We assume they produce, and consume, food and non-food products, and that they have Cobb-Douglas utility functions: where CF<sup>i; C</sup> NF<sup>idenoteconsumptionoffoodandnon-foodproducts,respectively,</sup> for agent i, and a is a preference parameter bounded between 0 and 1. In rural areas of developing countries, where poverty is widespread and a substantial proportion of the population is malnourished, we think of a as being closer to 1 than 0, re‡ecting a relatively high sensitivity of utility to changes in food consumption.<sup>2</sup> Each producer has a vector of product-speci...c productive skills denoted (A<sup>i</sup> F<sup>; Ai</sup> NF<sup>),andproductionoffood(F)andnon-food(NF)productsisgivenby</sup> where �i is the time (bounded between 0 and 1) agent i allocates to food production, which we shall refer to as the employment share of sector i. Thus there are missing.

> 2Dasgupta and Ray (1986; 1987) discuss how physical wellbeing is highly sensitive to changes in nutritional intake at low nutrition levels, in their analysis of the e¤ects of inequality on malnutrition. Private consumption expenditure on food accounts for the bulk of consumer spending in the least developed countries (Grigg, 1994).

2
are constant returns to scale in both sectors.

Under autarky, each agent has to produce the products to be consumed. It is straightforward to show that, in our model, the optimal amount of time allocated to producing food in autarky is �i = a. Thus, if the preference parameter a is high, each agent will allocate most of his or her time producing food, independent of the underlying skills vector (A<sup>i</sup> F<sup>; Ai</sup> NF<sup>).</sup> Now consider the e¤ects of integrating the market, enabling the two producers to trade with each other. Suppose that community 1 has a comparative advantage in the production of food, so that This assumption is maintained throughout the analysis. We assume that the agents bargain over the total utility surplus generated by trade. The outside option in the bargaining game is the utility under autarky, denoted U i: In equilibrium, the Nash product is maximized with respect to inputs �1; �2. The solutions for �1; �2 are summarized in Proposition 1.

Proposition 1 Optimal time allocation under trade is determined by preferences and productivity di¤erentials as follows: 3
Proof: See Appendix. Clearly, small changes in preferences can result in sharply discontinous patterns of spatial specialization, as preferences a are a key determinant of which solution will be optimal and thus of the sectoral composition of employment across communities.

# 3 Application: A poor rural economy

Subject to the assumptions made, the results summarized in Proposition 1 are general. In the context of a poor rural economy, it seems reasonable to assume that utility is quite sensitive to food consumption (a close to 1), and that heterogeneity in productivity levels (skills) across agents is modest (A<sup>1</sup> F<sup>=A2</sup> F<sup>close to 1).We thus</sup> focus on the solution scenario where A<sup>1</sup> F<sup>=A2</sup> F<sup><a= (1 �a).Itthenfollowsfrom</sup> Proposition 1 that, under trade, community 1 will specialize in food production while community 2 will adopt a mixed production strategy. Now consider some implications for output and sectoral employment shares under this scenario.

E¤ects of shifting from autarky to trade on output. We highlight two striking results. The ...rst is that total volume of food produced is the same under 4
trade as under autarky: Total consumption of food will thus not change as a result of market integration.

The second result is that total volume of non-food produced is strictly higher under trade than under autarky: hence the percentage growth in non-food output is where R = A<sup>1</sup> <u>F</u> A<sup>2</sup> <u>NF</u><sup>1measuresthecomparativeadvantageofcommunity1in</sup> A<sup>2</sup> F A<sup>1</sup> NF<sup>></sup> food production. Thus, subject to A<sup>1</sup> F<sup>=A2</sup> F<sup><a= (1 �a),themorepronounced</sup> the comparative advantage in agriculture for community 1, and the higher the relative non-food productivity of community 1 to that of community 2, the higher the output gain from trade in the non-food sector. This e¤ect arises because the increase in the relative e¢ ciency with which non-food is produced resulting from trade exceeds the increase in the e¢ ciency with which non-food goods are produced.

5
Shifting from autarky to trade thus results in asymmetric growth: food output does not change; non-food output increases.

E¤ects of shifting from autarky to trade on sectoral employment shares.

The e¤ects on sectoral employment shares depend on absolute advantages. It follows from part 1 in Proposition 1 that if community 1 has an absolute advantage in food production, i.e. A<sup>1</sup> F<sup>=A2</sup> F<sup>>1,totalemploymentinagricultureinthe</sup> economy falls, and total non-farm employment increases. Conversely, if A<sup>1</sup> F<sup>=A2</sup> F<sup><</sup> 1 (agent 1 has an absolute disadvantage in food production), total employment in agriculture in the economy increases, and total employment in the non-farm sector falls. If A<sup>1</sup> F<sup>=A2</sup> F<sup>=1,thereisnochangeinemploymentintheagricultural</sup> vs the non-farm sector.

Both the increase in non-farm output and the increase in the employment in the non-farm sector are consistent with historically documented patterns of rural transformation. Also note that the average productivity with which both farm and non-farm goods are produced rises.

# 3.1 A numerical example

We now illustrate these e¤ects by means of a simple numerical example. Suppose A<sup>1</sup> F<sup>=0:6,A1</sup> NF<sup>=0:4,A2</sup> F<sup>=0:4,A1</sup> NF<sup>=0:6; a=0:8.Community1thushasa</sup> comparative (and absolute) advantage in the production of food, and community 2 a comparative (and absolute) advantage in the production of the non-food product. In autarky, we have �i = 0:8 for i = 1; 2, hence total production is as follows: 6
Once the communities are allowed to trade, we obtain �1 = 1 and �2 = a � (1 � a)(A<sup>1</sup> F<sup>=A2</sup> F<sup>)in equilibrium (see proposition 1).In this particular example,we</sup> obtain �2 = 0:5. The total output volume in equilibrium is as follows: Thus, as a result of allowing the agents to trade with each other, the volume of non-food products grows by 50%, whereas the volume of food products does not change at all. Furthermore, since in this example A<sup>1</sup> F<sup>=A</sup> F<sup>2>1,morelaboris</sup> allocated to non-food production and less is allocated to food production.

These e¤ects are depicted in Figure 1. The solid straight lines indicate the production possibility curves for the two agents, under autarky, and the indi¤erence curves are drawn for the Cobb-Douglas utility function with a = 0:8. Optimal production and consumption in autarky for producers 1 and 2 are indicated in the graph by the hollow small circle, and the hollow small diamond, respectively. Once the agents engage in trade, the solution to the bargaining problem is such that production occurs in the points indicated by the solid large circle for producer 1, and the solid large diamond for producer 2. The terms of trade are determined as part of the bargaining process, and are shown in the graph by the gray dashed lines. Producer 1 thus consumes in the point indicated by the solid small circle, and producer 2 consumes in the point indicated by the small solid diamond. Both agents increase their consumption of nonfarm goods, and so total production of nonfarm products increases. The total level of food production and consumption is unchanged compared to autarky.

7
# 3.2 Generalized preferences

The above results are obtained under the assumption that the utility function is Cobb-Douglas. In cases where the elasticity of substitution is di¤erent from 1, the results will be di¤erent. Given our context, the substitutability between food and non-food products is probably rather limited. In the extreme case where the elasticity of substitution is zero (Leontief utility function), so that the ratio of food to non-food products consumed in equilibrium is constant, output in the two sectors will always grow at the same rate when shifting from autarky to trade. Suppose the utility function exhibits constant elasticity of substitution (CES), where r = (s � 1) =s and s is the elasticity of substitution. Suppose s = 0:5, so that there is some substitutability, but less than under Cobb-Douglas preferences. Using the same calibration as in the numerical example based on Cobb-Douglas preferences above, we then solve numerically for the e¤ects of trade on output. We ...nd that total food production grows by 5% (cf. 0% under Cobb-Douglas), and that non-food output grows by 30% (cf. 50% under Cobb-Douglas). Thus, there is still asymmetric growth - the non-farm sector grows more quickly - but, this is less pronounced than under Cobb-Douglas preferences. For completeness we also consider s = 2, implying high substitutability between the two products (of course, it seems unlikely that individuals in a poor rural economy are willing to substitute food for non-food consumption at such a rapid rate). In this case. the volume of food produced falls by 10%, whereas non-food production grows by 85%, when the economy shifts from autarky to trade.

8
# 4 Discussion

Our model is highly stylized. However, some of the mechanisms that we have abstracted from might enhance our results further. For example, Engel e¤ects, (which are often emphasized in the literature on structural change, see e.g. Matsuyama, 1992, Laitner, 2000, Caselli and Coleman, 2001) are likely to reinforce our results; if one of the e¤ects of market integration is to raise individuals’incomes and this in turn lowers the food preference parameter a (an Engel e¤ect)<sup>3</sup> , then this will enhance the pattern of asymmetric growth in non-farm production documented above. Alternatively, suppose the agents have Stone-Geary utility functions where S is the subsistence level of food consumption. It is easy to verify that this speci...cation would only reinforce our ...nding that trade stimulates the output of non-farm products and non-farm employment disproportionately (given reasonable choices of S). If in the numerical example above S = 0:35, the time allocation of producer 2 under autarky will change towards more production of food. The e¤ect of trade on total non-food production and non-farm employment will therefore be even greater than with conventional preferences.

Increasing returns to scale (Romer, 1987, Krugman, 1991), endogenous technological progress (Matsuyama, 1992), knowledge spillovers, pecuniary externatlities and other agglomeration economies are also likely to be important drivers of structural change (see e.g. WDR 2009 and the references therein for an overview of agglomeration economies). The contribution of our analysis is to show that, even

> 3That Engel-e¤ects cancontribute to asymmetric sectoral growth rates is well-known - see e.g. Caselli & Coleman (2001), Matsuyama (1992), and Laitner (2000).

9
in the absence of such auxiliary mechanisms which are probably very important in practice, trade could result in asymmetric sectoral output growth as well as employment shifts, and that small changes in preferences can result in sharply discontinuous patterns of spatial specialization. Since facilitating trade is likely to bene...t the non-farm sector most, market integration appears an e¤ective way of catalyzing economic development in economies dominated by agriculture, i.e. much of the developing world.

# References

Caselli, F. and Coleman II, W. 2001 "The US structural transformation and regional convergence" Journal of Political Economy 109, pp 584–616.

Dasgupta, P. and Ray, D. 1986 "Inequality as a Determinant of Malnutrition and Unemployment, 1: Theory." Economic Journal 96(4), pp 1011-1034.

Dasgupta, P. and Ray, D. 1987 "Inequality as a Determinant of Malnutrition and Unemployment, 2: Policy." Economic Journal 97(1), pp 177-188.

de Janvry, A., Fafchamps, M., and Sadoulet, E. 1991 “Peasant Household Behaviour with Missing Markets: Some Paradoxes Explained”Economic Journal 101(405) pp 1400- 1417.

Grigg, D. 1994 “Food Expenditure and Economic Development”GeoJournal 33(4), pp 377-382 Harris, D.J. 1985. "The theory of economic growth: from steady states to uneven development." In Contemporary Issues in Macroeconomics and Distribution, ed. G. Feiwel. London: Macmillan.

Krugman, P. 1991 "Increasing Returns and Economic Geography" Journal of Political Economy 99(3) pp. 483-499.

Krugman, P. 1998 "What’s New about the New Economic Geography" Oxford 10
Review of Economic Policy 14(2), pp7-17.

Laitner, J. 2000. Structural change and economic growth. Review of Economic Studies 67, 541–61.

Loening, J., Rijkers, B., and Soderbom, M. (2008) "Non-farm Microenterprises and the Investment Climate: Evidence from Rural Ethiopia" World Bank Policy Research Working Paper 4577.

Matsuyama, K. 1992. A simple model of sectoral adjustments. Review of Economic Studies 59, 375–88.

Matsuyama, K. 1999. "Structural Change" in The New Palgrave Dictionary of Economics, second edition. ed. Steven N. Durlauf. and Lawrence E. Blume.

Romer 1987 "Growth Based on Increasing Returns due to Specialization" American Economic Review 77, pp 57-62.

World Development Report (WDR) 2009 "Economic Geography", Washington D.C.

# Appendix

A1. Optimal time allocation under autarky. Individual i chooses the time share parameter �i so as to maximize utility: subject to 0 � �i � 1. The Cobb-Douglas functional form implies that corner solutions can be ruled out. The ...rst-order condition (f.o.c.) is : which implies a = �i: 11
Q=n( -— ) ( = ) a ,a <a< a ,a Qa ,a a ,a a ,a a ,a a ,a a a —-aaQ —-aaQ
OF, ON F, —0 —0 6 OF a,a ,ONF a,a —9@ a ,a —6 Qa ,a 0 —9@ a ,a a ,a Qa ,a Qa ,a aa ie @ J) - (ea -a J) a <a a a <a a
a a a <a a a [| -a —a | — [a —a -a - Qa — a —a -a - a a -a ~~—--~~ a —-— ~~—~~ a aa a ( -a ~~—-~~ a -— ~~—)~~ a -a ~~—~~ -a -— ~~—~~ a -a ~~—~~ -a — aa -a ~~—~~

a |
ae ~~ee~~ e ~~)~~ («a -a ~~—~~ ) - ( -« - - a - ~~—~~ ) ~~“da —( a —l(~~ - ~~=e -~~ ( ~~-—) = C—~~ ) ~~=e ()~~
Hence, if producer 1 has a comparative advantage in food production, B in Table A1 cannot be optimal. A corollary is that, if �1 is interior, then �2 must be a corner solution, and since producer 2 has a comparative advantage in non-food production, �2 = 0 must be the solution in this case; hence D cannot be optimal.

A2.3 Distinguishing between potential solutions The optimal solution will be such that it falls into one of the cells g,h,i shown in Table A2: Table A2 - Remaining solutions In regime i, we have where the latter equation follows from (2). In this regime, then, In regime g, we have thus Producer 1 has a comparative advantage in food production, hence: 16
- If (4) holds then (5) does not hold.

- If (5) holds then (4) does not hold.

Finally, suppose neither (4) nor (5) holds, so that In this case, neither g nor i can be optimal, leaving h (complete specialization) as the only remaining candidate solution.

This completes the proof of Proposition 1 in the text.

17
**Figure 1: The asymmetric effect of trade on production and consumption of the non-farm product**

<!-- Start of picture text -->
1.00<br>0.80<br>0.60<br>0.40<br>0.20<br>0.00<br>0 .1 .2 .3 .4<br>Non-farm product: Production & consumption<br><!-- End of picture text -->

Note: The solid straight lines indicate the production possibility curves for the two hypothetical individuals discussed in the text, under autarky. The indifference curves are drawn for the Cobb Douglas utility function discussed in the text, with _a_ = 0.8. Optimal production and consumption in autarky for individual 1 and 2 is indicated by the hollow small circle, and the hollow small diamond, respectively. Once the individuals engage in trade, the solution to the bargaining problem is such that production occurs in the points indicated by the solid large circle for individual 1, and the solid large diamond for individual 2. Individual 1 consumes in the point indicated by the solid small circle, and individual 2 consumes in the point indicated by the small solid diamond. The terms of trade are indicated by the gray dashed lines. Both individuals increase their consumption of nonfarm goods.