Agriculture and Aggregate Produc0vity September 24, 2012
Modernization of Agriculture and Long-Term Growth Xiaodong Zhu University of Toronto Joint work with Dennis Tao Yang CUHK
World Per Capita GDP 10000 1000 100 0 250 500 750 1000 1250 1500 1750 2000
Per Capita GDP of China and Western Europe 100000 10000 1000 100 0 250 500 750 1000 1250 1500 1750 2000 Western Europe China
Literature on Stagnation to Growth Human capital and fertility choice: e.g., Becker et al. (1990), Tamura (1998), Lucas (2002) Endogenous technological change and population: e.g., Kremer (1993), Goodfriend and McDermott (1995), Jones (2001), Galor and Weil (2000) Adoption of modern technology: Hansen and Prescott (2002) This paper proposes a new explanation.
Three Concurrent Events: #1: Per capita GDP started modern growth Figure 1. Real Per Capita GDP: England, 1700-1909 1810-20 2 1.8 16 1.6 1.4 1.2 1 0.8 0.6 Index of Per Capita GDP 04 0.4 0.2 0 1700 1710 1720 1730 1740 1750 1760 1770 1780 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 Year Data source: Clark (2001), Mitchell (1988)
#2: Inception of Agricultural Mechanization 1810-20 1810-20
#3: Relative price falling until 1810-20, then stayed flat Figure 2. Price Ratio of Industrial Product to Agricultural Product: England, 1700-1909 2.5 1810-20 2.0 Relative pric ce (1820=1.0) 1.5 1.0 0.5 0.0 1700 1710 1720 1730 1740 1750 1760 1770 1780 1790 1800 Year Source: Clark (2002, 4) and Mitchell (1962, 468-73). 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900
Main Ideas of Our Model The three events are causally linked: Agricultural and nonagricultural (industrial) sectors: Growth in industry not sufficient for sustained growth Growth in industry leads to declines in relative price When relative price falls below a certain threshold, farmers start to use industry-supplied supplied modern inputs Agricultural modernization triggers structural changes g gg g Embark on the takeoff to sustained growth Ag. modernization is a necessary condition for growth
More on Related Literature Role of agriculture in growth: Johnston and Mellor (1961), Jorgenson (1961), Schultz (1964), Johnson (1997) Gollin, Perante and Rogerson (2002, 2007): food constraint; multiple ag. technologies, international income differences This paper: Effects of industrial growth on agricultural modernization Central role of relative price Empirically supported mechanisms of transition to modern growth Quantitative analysis of the English economy, 1700-1909
The Model Triggering mechanism of modern growth: changes in the relative price, and choice of agricultural technologies Time paths of aggregate variables under stagnation, transition, and growth Two sectors: agriculture and nonagriculture (industry) Population: N t, non-overlapping generations Population growth: N t 1 g y t N t, hump-shaped growth i g c 1; ii g. increasing over 0, y, y c; iii g. decreasing over y,, and lim y g y 1 Land endowment: fixed Z; equal distribution, z t N 1 t Z
Income: y t w t r t z t where w t for wage, r t rental price of land Prices: Price of agricultural good: numeraire Price of nonagricultural good: p t Consumption: Agricultural good: c at c, subsistence food Nonagricultural good: c nt p 1 t y t c
Production Technologies Nonagricultural production: Y nt A nt L nt Agricultural technologies: Traditional: Modern: Y T at Z 1 t A at L at, 0 1 Y M at Z 1 t A at L at 1 X t, 0 1 One unit of industrial product produces one unit of intermediate input Note: A n and A a grow exogenously
Choice of Technology in Agriculture Farmer s problem: max Z T t,z M t,l T at,l M at,x t Z T t 1 A at L T at Z M t 1 A at L M at 1 X t p t X t r t Z t w t L at Resource constraint: Z t T Z t M Z t, and L T at L M at L at Condition for choosing modern technology: / 1 1 pt 1 High price of industrial product p t discourages adopting modern technology; p t endogenous
Competitive Equilibrium (1) Farmers only use traditional technology, if: A nt A at Z/N t 1 l, or p t p In the steady-state of traditional economy (stagnation): A nt l A a where A a Aat Z/N t 1 is a constant Rise in A nt ultimately triggers the use of modern technology When p t falls to a critical value, adoption of modern technology will occur, since p t c 1 Aa /Ant
(2) Farmers only use modern technology, if: A nt A at Z/N t 1 h (3) Farmers use both technologies, if: A l nt A at Z/N t 1 h where l 1 1 1 c 1 and h 1 1 l
Stagnation (T) to Transition (X) Threshold for transition: T p t X p t c 1 Aa /Ant p 1 1 p Persistent growth in A nt eventually triggers transition Once reaching the threshold, begins agricultural modernization During transition, relative price p t stays constant
Inception of agricultural modernization: T X Z t M Z 0 Z t M Z 1 A nt A at Z/N t 1 Structural break in per capita income: T y t 1 c 1 Aat Z/N t 1 c l 1 1 1 X y t 1 1 Ant 1 1 1 A at Z/N t 1 A nt 1 Per capita income takes off during transition
Features of Modern Growth In the modern economy: Relative price declines continuously Per capita income rises, driven by the growth of A at and A nt Agricultural labor share converges to zero in the long-run Real wage rises, driven by the growth of A at and A nt Rental price of land rises with population growth
Compilation of English Historical Data: 1700-1909 Two criteria: reliability and completeness Starting year: prices of industrial products, earliest 1700 Ending year: statistical sources switched to UK after 1913; some earlier data only available for England Data coverage: 21 decennial data points for all key aggregate variables relative price, agricultural mechanization, real per capita GDP, labor share in agriculture, real wages, and rental price for land
Major Data Sources Clark (2001): historical estimates of GDP, price deflators Clark (2002, 2004): history of agriculture, ag. prices Mitchell (1962, 1988): British historical statistics Crafts and Harley (1992): British industrial production Wrigley and Schofield (1981): population history of England Walton (1979), Thompson (1968): modern ag. Inputs
Calibration of the Model Technology parameters: Labor share in traditional agriculture: σ=0.6, Hansen-Prescott (2002), Ngai (2004) Share of modern inputs: α=0.4, Restuccia, Yang and Zhu (2008) TFP growth rates: In industry A nt : Crafts-Harley (1992), Matthews et al. (1982) In agriculture A at : Clark (2002) Initial values: Normalization: initial income, y 0 = 1 Initial population N₀ : England and Wales population in 1700 A a0 : set to match L a0 = 0.55 A n0 : pinned down by labor share and timing of mechanization Subsistence food consumption c: y 0 =[1-σ+σ(L a0 /N 0 )]c
Exogenous variables: Simulation of the Model TFP growth in industry and agriculture: A at and A nt Industrial, traditional and modern agricultural technologies Land, subsistence food consumption, population growth profiles A set of parameters: e.g., α, σ, c Solutions to the time paths of: Per capita income y t Relative price p t Employment share in agriculture L at Agricultural mechanization: share of land devoted to modern technology Z M t Real wage and rental price of land Account for English growth experience, 1700-1909
Incorporating Trade We follow closely the assumptions used by Stokey (2001) England as a small open economy: exogenous terms of trade Balanced trade: importing food and exporting industrial products Food import relaxes subsistence constraint
Concluding Remarks Modernization of agriculture is essential for sustained growth Great historical innovations outside agriculture; not sufficient to generate modern growth Yet, these innovations caused the decline in relative price Low relative price triggers ag. modernization Agricultural modernization leads to structural change Economy escapes from Malthusian trap to modern growth
Some startling numbers In 1985, the average GDP per worker in the richest 5% countries is 34 0mes that in the poorest 5% countries The difference in agriculture is even larger: 78:1 The difference in non- agriculture is smaller: 5:1 Yet, poorest countries allocate 84% of labor in agriculture, compared to only 4% in the richest countries
Agriculture s rela0ve produc0vity by income deciles
Intermediate input share in agricultural output
Intermediate input use and agricultural produc0vity In the special case when a=0
What determines the intermediate input use? In the special case when a=0
Barriers to intermediate input use
Results