Agricultural Productivity,, and Economic Growth Kiminori Krishna Teja Indian Statistical Institute April 12, 2016
This paper falls under the broad topic of Structural Transformation
Overview 1 2 3 4
This paper addresses the role of agricultural productivity in economic development in a two-sector endogenous growth model in which 1 are non-homothetic 2 Income elasticity of demand for agricultural good is less than unitary 3 In the manufacturing, the engine of growth is learning-by-doing For a closed economy, the model predicts a positive link between agricultural productivity, and economic growth For a small open economy, the model predicts a negative link
According to the conventional view(based on the British Industrial Revolution), there are positive links between agricultural productivity and industrialization. 1 Rising productivity in food production makes it possible to feed the growing population in the industrial sector. With more food being produced with less labor, it releases labor for manufacturing employment. 2 High incomes generated in agriculture provide domestic demand for industrial products. 3 It increases the supply of domestic savings required to finance industrialization.
Law of According to the Law of, there are negative links between agricultural productivity and industrialization 1 Manufacturing sector has to compete with agricultural sector for labor 2 Low productivity in agriculture implies the abundant supply of cheap labor which the manufacturing sector can rely on. Ex: Belgium, Switzerland were the first industrial countries in continental Europe, while the Netherlands lagged behind
The difference in explained The conventional view is based on the implicit assumption that the economy is an effectively closed system. In an open trading system, prices are determined by the conditions in the world markets 1 A rich endowment of arable land could be a mixed blessing. High productivity and output in agricultural sector may, without offsetting changes in relative prices, squeeze out the manufacturing sector 2 Economies which lack arable land and thus have the initial comparative advantage (not necessarily absolute) in manufacturing may successfully industrialize by relying heavily on foreign trade through importing agricultural products and raw materials and exporting manufacturing products. Ex:East Asia
Specific Factors model (Ricardo-Viner-Jones model) Only one mobile factor L(labor), with diminishing return to scale. T(Land) is used in Agricultural Industry only. K(Capital) is used in Manufacturing Industry only. The economy produces two goods using three factors of production, capital, land and labor in a perfectly competitive market. Labor is the mobile factor, and there are two specific factors, K and T. are non-homothetic and income elasticity of demand for agricultural good is less than unitary Manufacturing productivity rises over time because of learning-by-doing
outcomes Closed economy case: An exogenous increase in agricultural productivity shifts labor to manufacturing and thereby accelerates economic growth Open economy case: An economy with less productive agriculture allocates more labor to manufacturing and will grow faster. For a sufficiently small discount rate, it will achieve a higher welfare level than the rest of the world. The productive agricultural sector, on the other hand, squeezes out the manufacturing sector and the economy will de-industrialize over time, and, in some cases, achieve a lower welfare level. Hence, Openness in economies should be an important factor to be kept in mind when planning development strategies and predicting growth performances.
The economy consists of two sectors: 1 Manufacturing 2 Agriculture Population is constant, is equal to L Labor supply is constant and is normalized to one. Proposition The absolute size of the economy itself has no effect on this model.
Technologies in the two sectors are given by: X M t = M t F (n t ) F (0) = 0, F > 0, F < 0 (1) X A t = AG(1 n t ) G(0) = 0, G > 0, G < 0 (2) n t the fraction of labor employed in manufacturing as of time t A Agricultural productivity, constant over time and exogenous M t Manufacturing productivity (Knowledge capital as of time t, predetermined, but endogenous Both sectors operate under diminishing returns to scale Knowledge accumulates as a by-product of manufacturing experience,as follows: M t = δx M t, δ > 0 (3)
The Knowledge capital is purely external to the individual firms that generate them. Each manufacturing firm treats M t as given when making production and employment decisions. The competition for labor between the two sectors leads to the following equilibrium condition in the labor market: AG (1 n t ) = p t M t F (n t ) (4) p t relative price of the manufacturing good
Consumer I The Consumers maximize W wrt to a budget constraint: W = where, o [βlog(c A t γ)+log(c M t )]e ρt dt, β, γ, ρ > 0 (5) ct A consumption of the agriculture good as of time t ct M consumption of the manufacturing good as of time t γ subsistence level of food consumption
Consumer II γ satisfies the following condition: AG(1) > γl > 0 (6) The first inequality implies that the economy s agricultural sector is productive enough to provide the subsistence level of food to all consumers. With a positive γ, preferences are non-homothetic and the income elasticity of demand for food is less than unitary. Assumption: All Consumers have enough income to purchase more than γ units of food.
Consumer III Consumer budget constraint: We know the relative price of the manufacturing good is p t During any period t, the consumer budget constraint is as follows: c A t + p t c M t w During a given time period t, max βlog(c A t γ) + log(c M t ) s/t c A t + p t c M t w c A t = γ + βp t c M t Aggregation over all consumers yields, C A t = γl + βp t C M t (7) upper case letters denote aggregate consumption
Labor share between the two sectors I Assumption: is a closed System. C M t = X M t = M t F (n t ) C A t = X A t = AG(1 n t ) Combining the above equations with equations (4) and (7), we get: φ(n t ) = γl/a (8) where, φ(n) G(1 n) βg (1 n)f (n) F (n) Notice the following: 1 φ(0) = G(1) > 0 2 φ(1) < 0 φ(1) = G(0) βg (0)F (1) F (1) = 0 βg (0)F (1) F (1) < 0
Labor share between the two sectors II 3 φ < 0 φ (n) = G (1 n) + β G (1 n)f (n)f (n) F (n) 2 β (F (n)) 2 G (1 n) F (n) 2 + β F (n)g (1 n)f (n) F (n) 2 < 0 From equations (6) and (8), φ(n) has a unique solution in (0, 1)
Labor share between the two sectors This solution can be written as: n t = φ 1 (γl/a) = v(a), with v (A) > 0 This shows that there is an inverse relationship between agricultural production as a function of manufacturing employment,φ(n) and agricultural productivity per capita A/L Thus, the employment share of manufacturing is constant over time and positively related to A.
Consumption at v(a) Aggregate food consumption and production stay constant at: C A = X A = AG(1 v(a)) = γl + AβG (1 v(a))f (v(a)) F (v(a)) Observe that C A is also increasing in A. Intuition: Increase in agricultural productivity releases labor to manufacturing This increases the manufacturing output and accelerates its growth It also causes a permanent increase in the level of food production W increases for a consumer who consumes C A /L&C M t /L
Engel s Law Def: Engel s law states that as income rises, the proportion of income spent on food falls, even if actual expenditure on food rises. In other words, the income elasticity of demand of food is between 0 and 1. if γ = 0, then φ(n t ) is independent of A Agricultural Productivity has no effect on growth. If γ < 0, then food is a luxury good, then a rise in agricultural productivity slows down the economy.
Wage Rate The labor market is competitive and the wage rate is equalized across the two sectors. This is not the case in the modern manufacturing and traditional agricultural sectors. Common Argument: Labor migration from agriculture to manufacturing contributes to total productivity gains to the extent that the labor has higher productivity in manufacturing. The presence of wage gaps, if exogenous, will not cause labor market failure In reality, wage gaps and factor market distortions may be substantial, they are assumed away to simplify the exposition. Labor reallocation to manufacturing increases total productivity growth even in the absence of wage gaps, once productivity growth is endogenized
Country Size One might infer from the model that, ceteris paribus, a larger country(in term so labor force) has a bigger manufacturing sector, and thus, the model predicts that China or India would eperience a faster growth than South Korea or Taiwan,at least under autarky. This inference is unwarranted for two reasons: 1 A large country does not necessarily mean a large economy. It may simply consist of a large number of regional economies. 2 It depends on the nature of external effects of learning-by-doing. The density of manufacturing determines the speed of knowledge accumulation.
Constant share of Employment I Empirical evidence suggests that The share of agriculture in the labor force and total output declines as income per capita increases, both 8in cross section as well as time series. Extending this model to make it consistent with the empirical regularity: By introducing a continuous, exogenous improvement in agricultural productivity, A t, Instead of (4) and (8), we now have: A t G (1 n t ) = p t M t F (n t ) (4 ) φ(n t ) = γl/a t (8 )
Constant share of Employment II (8 ) As agricultural productivity rises over time, n t increases monotonically over time, and, if A t grows unbounded, then lim n t = n (0, 1) t, where φ(n) = 0 (4 ptm TF (nt) ) AtG(1 n t) = G (1 n t) F (n t) G(1 n t) F (n t), which is increasing in n t, so that the share of manufacturing in value of output also rises over time.
Relaxing closed economy assumption Consider two economies : Home and rest of the world Labor is immobile across the economies Learning-by-doing effects do not spill over economies Level of knowledge capital is region-specific
Home X M t = M t F (n t ) F (0) = 0, F > 0, F < 0 X A t = AG(1 n t ) G(0) = 0, G > 0, G < 0 Rest of the world Xt M = Mt F (n t ) F (0) = 0, F > 0, F < 0 Xt A = A G(1 n t ) G(0) = 0, G > 0, G < 0
Equilibrium condition in labor market A G (1 n ) M t F (n ) = p t A G (1 n ) = p t M t F (n ) (9) putting p t = AG (1 n t) M tf (n t) in the above equation gives us the equilibrium condition
the equilibrium condition we have is F (n t ) G (1 n t ) = AM t F (n ) A. M t G (1 n ) differentiating it w.r.t time gives us from M t n t [ G (1 n t) G (1 n t ) + F (n t) F (n t ) ] = δ[f (n ) F (n t )] Mt Mt M t = δf (n t ) and = δf (n t )
If the economy has comparative advantage in manufacturing, then > A M 0 n 0 > n A M 0 If the economy has comparative advantage in agriculture, then < A M 0 n 0 < n A M 0 n 0 n A M 0 A M 0
Complete Specialization lim t n t = 0 lim t n t = 1 if n 0 < n if n 0 > n Whether the economy will completely specialize in finite time depends on the properties of F and G at the origin.
Negative link between agriculture and growth If A increases,the share of employment in manufacturing sector, n t decreases As n t decreases, the productivity rate of the manufacturing sector δf (n t ) decreases too This is quite opposite to the result obtained in the closed economy
Negative link between agriculture and growth With less productive agriculture, manufacturing sector attracts more labour and grows faster With productive agriculture sector, the manufacturing sector shrinks and the economy will de-industrialize over time
Welfare evaluations Suppose the initial level of knowledge capital in manufacturing is identical in all economies M 0 = M 0 Agriculture in home is less productive than rest of the world Let the national income be A < A Y t = AG(1 n t ) + p t M t F (n t ) Let the national expenditure be E t = C A t + p t C M t
Welfare evaluations From (5), the Consumers utility is W = o From (7), we have [βlog(c A t γ) + log(c M t )]e ρt dt, β, γ, ρ > 0 C A t = γl + βp t C M t The indirect utility of the representative agent, who consumes Ct A /L and Ct M /L is (1 + β) where, B = o o log(e t /L γ)e ρt dt + B p t log(βp t ) β ( 1 + β )1+β e ρt dt
Welfare evaluations In case of no international capital markets, Y t = E t for all t. The welfare measure is given by W 1 = (1 + β) o log(y t /L γ)e ρt dt In case of perfect capital markets, the Home economy can led and borrow at world interest rate, ρ(=discount rate) To smoothen consumption, the Home economy spends the constant amount, ρ Y t o L γ e ρt dt, at every moment Here, the welfare measure is given by W 2 = (1 + β) log(ρ ρ o Y t L e ρt dt)
Welfare evaluations If A = A, from (9), then Y = A G(1 n ) + G (1 n ) F (n.f (n ) ) W 1 = W 2 = (1 + β) log( Y ρ L γ)
Welfare evaluations If A < A, then Y t is not constant,then it suffices to show (1 + β) o log( Yt 0 A < A W 1 < W 2 L γ)e ρt dt > (1+β) ρ log( Y L γ) log (Y t γl) (Y γl) e ρt dt > 0 (10) But, Y t = AG(1 n t ) + p t M t F (n t ) grows unbounded. Thus, condition (10) is satisfied for a sufficiently small ρ.
Intepretations The model doesn t suggest that country s agricultre should be destroyed for sake of growth. It depends on the openess of the economy. The long run gain from faster growth outweighs the short run loss only when the agents are sufficiently patient.
Intepretations A > A need not imply that home economy is worse off than rest of the world. if A is large enough, then Y t > AG(1) Y Of course, if AG(1) < Y, then the Home economy is worse off than ROW for a sufficiently small ρ lim t Y t = lim t AG(1 n t ) + p t M t F (n t ) = AG(1) < Y from lim t n t = lim t p t M t = 0
Dutch Disease Adverse effect on the manufacturing sectory of a temporary boom in the natural resource sector Eg: Gold discoveries in Australia in the 1850 s, natural gas discoveries in the Netherlands in the 1960 s, and the effects of the North Sea Oil on British and Norwegian manufacturing Suppose a Home economy similar to that of ROW (A = A, M 0 = M 0 ) Employment manfucaturing is constant and its output grows at constant rate, δf (n ) Suppose there is a temporary increase in A (like discovery of natural resources)
Dutch Disease A temporary increase in A induces migration of labour from M, thereby reducing the rate of knowledge accumulation thorugh learning-by-doing Say, A returns to original level A at t = T At t = T, the economy has still comparitive advantage in A agricultre, i.e., M T = A M T > A MT : since manufacturing in the rest of world has grown faster (M T < MT ) Thus, n T < n, and the economy will continue to de-industralize
Conclusion of endogenous growth to demonstrate the realtion between agricultral productivity and growthperformance Extremely sensitive to the assumption concerning the openness of an economy Two key assumptions: low demand elasticity for the agricultural good and lack of complete spillover across economies
Conclusion can be extended with including a service sector, particularly when demand for is output has high income elasticity Exogenous nature of agricultural productivity. Spillovers from knowledge capital of manufacturing and learning-by-doing in agricultre can also be studied Omission of capital accumulation. Relaxation of this may help to do away with the assumption that all knowledge in manufacturing is disembodied.
Conclusion With international trade of capital goods, there could be a knowledge spillover across economies. In presence of certain financial market imperfections, domestic savings and export revenus generated by agricultre booms may be important in financing investment in capital goods. Openess of economies can be parameterized to examine how certain factors would affect the role of agricultural productivity in economic development
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