رشد بهره وری و مهاجرت خارجی محصولات کشاورزی در ایالات متحده

In the 20th century U.S., the average annual decline in the relative farm share of employment was 3.6%. Despite this rapid reallocation of labor, a large wage gap persisted between the farm and non-farm sectors that declined only slowly over time. We develop a model of farm out-migration with three driving forces: (i) absolute farm productivity growth in conjunction with subsistence food consumption, (ii) relative farm productivity growth in conjunction with a low elasticity of substitution between farm and non-farm goods, and (iii) endogenously declining wage gaps. Quantitative features of the model accord well with the U.S. experience during this period.

Throughout the world, gradual but massive migration from the farm to the non-farm sector has accompanied industrialization and capitalist development. The U.S. experience is especially remarkable. In the 20th century, coinciding with an acceleration of farm productivity growth, the average annual decline in the farm share of employment relative to non-farm employment was approximately 3.6%. Yet despite considerable and steady off-farm migration, the 20th century U.S. economy was characterized by a significant gap between farm and non-farm real wages that declined only gradually over time. Fig. 1 presents these striking trends.1 A key puzzle involves how to explain the relationship between these rapid labor flows and the slow change in the farm–non-farm wage gap over time. In answer to this puzzle, we show that both of these phenomena are ultimately caused by the patterns of absolute and relative productivity growth in the 20th century U.S. Our main contribution is two-fold: (i) we develop endogenously determined, persistent wage gaps that experience a secular (and gradual) decline and, simultaneously, (ii) we account for the reallocation of labor from the farm to the non-farm sector in an internally consistent fashion.The traditional account of off-farm migration has emphasized absolute farm productivity growth in conjunction with the subsistence consumption of agricultural goods. 2 This explanation is quite intuitive. As productivity in agriculture rises, supply outstrips demand due to the low income elasticity of demand for farm goods. As a result, labor moves out of agriculture. This explanation is empirically appealing as well. Absolute farm productivity growth in the U.S. accelerated at the same time that farm out-migration accelerated, and the low income elasticity of demand for farm goods is one of the few undisputed facts in economics. This is the first driving force of farm out-migration that we identify. The second driving force of farm out-migration is relative farm–non-farm productivity growth, which has also been a remarkably important feature of the U.S. data in the 20th century. This observation hinges critically on a non-unitary elasticity of substitution between farm and non-farm products. In the special case of unitary elasticity, a productivity growth differential across sectors leads to offsetting income and substitution effects, and so does not influence the relative demand for farm goods. As a result, relative productivity growth by itself does not create any incentives for labor to move out of the farm sector. By contrast, in the empirically relevant case of a low demand elasticity of substitution between farm and non-farm goods (i.e., the goods are gross complements), relatively high technological progress in the farm sector results in a relative increase in the demand for non-farm goods and an unfavorable shift in the agricultural terms of trade, which exert additional pressure on labor to move out of farming. To gauge the quantitative importance of both absolute and relative productivity growth for structural change, we provide a detailed reinterpretation of the changes in the sectoral labor shares in the 20th century U.S. In particular, we use a baseline general equilibrium model to calibrate sectoral labor shares. The baseline model allows for instantaneous sectoral reallocation of labor in response to a change in relative wages. We decompose the changes in these calibrated series into the contributions of absolute and relative farm productivity growth. We find that, depending on the relative importance of subsistence food consumption, between one-fifth to one-third of the observed reallocation of labor from the farm to the non-farm sector is due to relative productivity growth. The third driving force of farm out-migration that we study is related to the “transfer problem” (of moving labor out of agriculture and into industry) as well as recent accounts of regional convergence.3 The focal point of this literature has been persistent sectoral wage and income gaps which were interpreted as indicative of a significant misallocation of labor.4 Specifically, despite the substantial transfer already taking place, many contemporary commentators felt that the 20th century U.S. off-farm migration rate was too low based primarily on the size and persistence of the wage gap in favor of industry. The baseline model with zero migration costs is unable to account for the transfer problem. We therefore extend the model so that workers have to incur fixed and sunk costs when they move between sectors. This creates a degree of inertia in sectoral allocations of labor. In this case, migration decisions follow (S, s) rules whereby relocation is triggered only when sectoral wage gaps exceed S (or s) percentage points. We characterize these relocation thresholds analytically. In particular, we show that, as incomes increase and as the share of food consumption in total expenditures declines, sectoral wage gaps also decline endogenously. The ultimate reason for the decline in wage gaps is because rising incomes move individuals further away from subsistence, lowering their aversion to risk, and thus decreasing the wage premium they require before committing to migration. Declining risk aversion is linked to non-homotheticity in preferences resulting from the subsistence nature of food consumption. At higher levels of income, individuals are less susceptible to slipping below subsistence for a given pattern of shocks and, as such, are less risk averse. 5 This framework allows us to assess whether the wage gaps observed in the U.S. (and elsewhere) in fact imply a “large misallocation” of labor across sectors. Our calibration results suggest that the “shortfall” in farm out-migration was in fact relatively small. However, the elimination of that shortfall comprised a third, albeit transitory, source of farm out-migration. Although our analysis is related to a voluminous literature on structural change (as surveyed in Syrquin (1988)), let us briefly mention here two of the most recent complementary studies that explicitly attempt to match the declining employment share of agriculture. Kongsamut et al. (2001) model very long-run economic growth with three sectors in which relative employment shares vary over time. They assume a unitary elasticity of substitution across goods and invoke identical productivity growth rates across sectors. As a consequence of these two assumptions, all structural change is driven by absolute productivity growth in their theoretical model. Caselli and Coleman (2001) model regional convergence over the medium- to long-run, and allow for differential productivity growth rates across farm and non-farm sectors. They also assume a unitary elasticity of substitution between farm and non-farm goods, so their analysis also has the feature that all structural change is driven by absolute productivity growth. Although the economic significance of these assumptions is ultimately an empirical matter (as we discuss in detail below), our simulations indicate that they are important for the 20th century U.S. experience.6 The rest of our paper is organized as follows. Section 2 outlines our two-sector model. Section 3 presents the quantitative implications of our model for changes over time in sectoral labor shares and endogenously declining wage gaps. Section 4 concludes.

This paper makes a case for three important mechanisms that together can account for the key stylized facts of the U.S. off-farm labor reallocation experience of the 20th century. We show the economic significance of three driving forces of farm out-migration during this period: (i) absolute farm productivity growth in conjunction with subsistence food consumption, (ii) relative farm productivity growth in conjunction with a low elasticity of substitution between farm and non-farm goods, and (iii) endogenously declining wage gaps. Although this paper deals with the U.S. experience, the structural changes discussed have occurred and will continue to occur in developing countries. The mechanisms we identify are general and significant. In particular, within a unified framework we demonstrate that the recognition of subsistence consumption in agriculture accounts for not only the pattern of off-farm migration, but also, in conjunction with fixed relocation costs, the secular trends in observed wage gaps. We have framed our analysis in the context of a closed economy. This is a reasonable framework for the U.S., especially for much of the long time period we examined. In our extended model without migration costs, because they are driven by identical demand and supply factors, agriculture's share of employment and consumption expenditures coincide as is commonly found in other structural change models (e.g., Echevarria, 1997 and Kongsamut et al., 2001) and historical accounts (e.g., Crafts, 1980). Naturally, in the presence of international trade, these two shares may evolve differently. Therefore, extending this class of models to an open economy context is important and left for future research. Finally, we have framed our analysis in the context of an infinite horizon economy with a constant population. This is also common to other structural change models, though it overlooks the demographic transformation that has also been central to earlier accounts of structural transformation (e.g., Kuznets, 1966). We leave this extension for future work as well.