Abstract
Whether the negative relationship between farm size and crop productivity that is confirmed in a large global literature holds in Africa is of considerable policy relevance. Plot-level data from Rwanda point toward constant returns to scale and a strong negative relationship between farm size and crop output per hectare that is robust across specifications and emerges also if profits with family labor valued at shadow wages are used but disappears if family labor is valued at market rates. In Rwanda, labor market imperfections, rather than other unobserved factors, seem to be a key reason for the inverse farm-size productivity relationship. (JEL O13, Q15)
I. INTRODUCTION
The existence of an inverse relationship between the size of a farm’s operated area and different measures of productivity in crop production has long been a puzzle to agricultural economists. The most common explanations for this finding, which is somewhat less pronounced in Africa as compared to other regions, are either a failure to properly measure key factors such as land quality or area, or small farmers’ application of more than the optimum amounts of certain inputs, possibly as a result of imperfections in markets for key factors such as labor, land, and insurance. The latter explanation is supported by the fact that the relationship generally weakens with technical progress and mechanization.
With the recent reemergence of interest in agriculture, the extent to which small farms use resources efficiently is particularly relevant for African countries that seek to modernize their agricultural sector and make the transition from subsistence-based to a market-driven rural economy. If small farmers use resources efficiently, policy should focus on attracting investment higher up in the value chain (e.g., in agro-processing) and on linking smallholders to key market channels, for example, via out-grower schemes while using the high poverty elasticity of smallholder agriculture (Ligon and Sadoulet 2008) to support growth and poverty reduction (Larson et al. 2012). If they do not, a strategy that aims to leapfrog directly to large-scale farming (Collier and Venables 2011) and a regulatory environment that reduces the scope for further subdivision and aggressively promotes land consolidation may be more appropriate.
In Rwanda, Africa’s most densely populated country, fragmentation and small farm sizes are considered a key issue by policy makers. The 2008 national agricultural household survey puts average holding size at 0.72 ha per household (in four parcels with 0.18 ha each on average), which with traditional technology will not generate enough revenue to allow the average household to meet subsistence needs (Republic of Rwanda 2009). To promote efficient and sustainable use of scarce land resources for agricultural development, the country put in place a three-pronged national land policy that (1) promotes land use planning to free up land for agricultural investors and nonagricultural development, (2) aims to consolidate land to achieve “economic” plot sizes, and (3) prohibits any subdivision that would result in parcel sizes below 1 ha. As such measures were not uncontroversial and proved to be difficult to implement in other settings, an empirical review of the underlying assumptions seems warranted.
Use of plot-level data allows us to analyze this issue and contribute to the literature in three respects. First, we explore the existence of an inverse relationship not only for output or gross revenue but also for profit per hectare, with family labor valued at market wages or an imputed household-specific shadow wage rate. Second, to reduce the possibility of the relationship being driven by measurement error and unobserved plot characteristics, we control for a wide range of time-variant and time-invariant characteristics including soil quality and unfavorable productivity shocks. Finally, as plot characteristics that prevent mechanization emerged as a key factor in overturning the relationship in India (Foster and Rosenzweig 2011), we conduct analysis both at plot and holding levels.
Descriptive statistics by tercile of the farm size distribution reveal three regularities. First, plot (and farm) size is inversely related to land quality, that is, smaller farms and plots have higher land quality and are less likely to be affected by crop shocks. Second, differences in output per hectare and input use intensity across farm size classes are pronounced: output value for farms in the bottom tercile is almost three times that of those in the top tercile ($860 and $298, respectively) with differences even more pronounced ($ 1,296 and $317, respectively) at plot level. But for profit per hectare, using actual input cost and valuing labor at market wages, the inverse relationship between size and productivity essentially disappears.
Econometric estimates allow us to infer on the underlying production technology, control for other factors such as land quality, and compute household-specific shadow wages to obtain profits to more accurately reflect the opportunity cost of labor. Results suggest that (1) technology is characterized by constant returns to scale; (2) even after controlling for land quality, yields, labor intensity, and shadow profits per hectare are all much higher on small farms; and (3) profit per hectare (with labor valued at market rates) is virtually identical across holding and plot sizes. Results thus point toward labor market imperfections as a main reason for the inverse relationship between farm size and productivity but suggest that with existing market imperfections, small farms are able to absorb large amounts of labor in a gainful way.
As long as farmers’ labor use responds to price signals, interventions (e.g., restrictions on subdivision or involuntary consolidation programs) may thus yield few benefits and could even be counterproductive. Efforts to reduce labor market imperfections and non-agricultural growth so that higher wages and nonagricultural employment opportunities pull labor out of agriculture may be more effective tools to improve rural welfare than land market interventions.
II. BACKGROUND AND LITERATURE
To frame the analysis, we discuss the conceptual basis, empirical evidence, and likely evolution of the farm size–productivity relationship over time. While one set of explanations focuses on unobserved land quality differentials, an alternative one focuses on labor market imperfections that make small producers either apply more effort than larger ones, or more than the optimum amount of family labor. Credit market imperfections and constraints on mechanization imposed by plot sizes below a certain size may counter this, providing advantages to large producers that may weaken the relationship as access to mechanization becomes more important, especially if labor market functioning improves.
Explanations and Evolution of the Farm Size-Productivity Relationship
A negative relationship between farm size and output per hectare, first noted in Russia (Chayanov 1926) and in Indian farm management studies (Bardhan 1973; Sen 1975; Srinivasan 1972), has been confirmed empirically so frequently as to almost be perceived as a stylized fact in the literature (Eastwood, Lipton, and Newell 2010; Lipton 2009). Analytically, many studies find agricultural production to be characterized by constant economies of scale, implying that a wide range of farm sizes can coexist. As residual claimants to profit, owner-operators will be more likely to exert effort than wage workers who require supervision, which, in light of the spatial dispersion of agricultural production processes, is costly (Frisvold 1994). Owner-operators’ knowledge of local soil and climatic conditions, often accumulated over generations, also gives them an edge over wage workers (Rosenzweig and Wolpin 1985).
Under constant returns to scale and with well-functioning factor markets or imperfections in one market only, output and intensity of input use will be identical across farm sizes. Imperfections in more than one factor market will lead to a systematic relationship between the size of cultivated area, inputs, and yields (Feder 1985). Small farmers’ advantages in labor supervision, knowledge, and organization can be offset by their difficulty in accessing capital and insurance, which arises from the high transaction cost of providing formal credit in rural markets, possibly exacerbated by the difficulty of small farms to provide collateral. Frictions in labor market participation and land markets (e.g., due to transaction costs) could motivate small farmers who are unable to rent but are likely to rationally apply family labor to cultivate their fixed land endowment more intensively than with perfect markets. An inverse relationship can also emerge if labor and credit market imperfections are combined with a fixed-cost element for production (Eswaran and Kotwal 1986) or if there is heterogeneity in farmers’ skills in the presence of credit market imperfections (Assuncao and Ghatak 2003). Land and insurance market imperfections can prompt small farmers who are net buyers of food to use family labor more intensively in an attempt to reduce potentially adverse effects of price fluctuations (Barrett 1996). The lumpiness of certain inputs (e.g., machinery, draft animals, and management skills) plus advantages in getting access to working capital or small farmers’ capacity to diffuse risk may in practice lead the relationship between farm size and productivity to be U-shaped (Heltberg 1998). Thus, with few exceptions,1 agricultural production in practice thus relies on owner-operated firms (Allen and Lueck 1998; Deininger and Feder 2001).2
Empirically, it has long been noted that part of the reason for cross-sectional evidence supporting an inverse farm size–productivity relationship (Berry and Cline 1979; Cornia 1985) is likely to have been the failure to fully capture land quality (Bhalla and Roy 1988; Chen, Huffman, and Rozelle 2011). However, the relationship is robust to inclusion of broad soil quality measures in cross-sectional estimates, more sophisticated panel data estimation techniques (Assuncao and Braido 2007; Benjamin 1995), and inclusion of a wide array of soil characteristics such as pH, carbon, clay, and sand content (Barrett, Bellemare, and Hou 2010). Measurement error for land size may explain part of the relationship (Lamb 2003), and use of GPS, though not without challenges, suggests that indeed farmers’ area estimates may be biased (Carletto, Savastano, and Zezza 2013). It has also been argued that proper measures of efficiency should be based on profits rather than gross output (Binswanger, Deininger, and Feder 1995). In post–green revolution India, use of profits has either weakened the relationship (Rosenzweig and Binswanger 1993) or made it disappear entirely (Carter 1984; Lamb 2003).
The empirical literature also suggests that rising nonagricultural wages and new technology will affect factor price ratios, supervision requirements, and the presence and extent of market imperfections that might have led to an inverse relationship in the first place. The earliest example of this was in India, where the green revolution increased the importance of knowledge and capital, weakening the size-productivity relationship in predictable ways: large farmers emerged as more productive in districts suited to new technology, while small farms continued to be most efficient where traditional methods prevailed (Deolalikar 1981). More recently, continued subdivision in the context of generational change and the limits on the scope for mechanization by small plot sizes may have contributed to a reversal of the inverse relationship so that, with land market imperfections preventing consolidation, some farms (or, more precisely, plots) may be too small for efficient cultivation (Foster and Rosenzweig 2010). In fact, for rice farms in Japan, where factor markets work well, a strongly positive relationship between farm size and productivity has been found (Kawasaki 2010). Recent innovations in crop breeding, tillage, and information technology also make it easier to supervise labor, thus tending to attenuate or eliminate large operations’ disadvantages3 in a way that may have altered or even reversed the traditional farm size–productivity relationship in Eastern Europe and South America (Helfand and Levine 2004; Lissitsa and Odening 2005).
The Relevance of the Debate for Rwanda’s Context
Whether small farms make efficient use of resources at their disposal is particularly relevant for African countries aiming to modernize their agricultural sector and make the transition from a subsistence-based to a market-driven rural economy. A belief in large holdings’ superior performance led influential observers to urge policy makers to abandon “smallholder romanticism” and aim to leapfrog to “efficient” large-scale farming based on industrial methods (Collier and Venables 2011). Others claim that once conditions are accounted for, small farmers remain the most efficient (Larson et al. 2012) so that a strategy based on the traditionally high poverty elasticity of smallholder agriculture (Ligon and Sadoulet 2008), possibly supported by investment up in the value chain, will be appropriate.
Empirical evidence from Africa on this issue remains ambiguous, partly due to vast variation of relative land scarcity, capital access, and mechanization across countries. If investment is important and poor farmers’ access to finance and insurance constrained, difficulties in accessing financial markets may lead to a positive relationship between farm size and productivity, as in Sudan (Kevane 1996). In Kenya, profits per acre were also found to increase monotonically with farm size, while the relationship between output per acre and size was U-shaped with a minimum at about 5 ha, a finding partly attributed to crop composition changing across farm sizes (Carter and Wiebe 1990). Detailed grouped farm survey data for Malawi in the 1980s point toward a significant positive relationship between farm size and output per hectare, apparently driven by constrained capital access (Dorward 1999). A positive relationship between output per hectare and farm size also is found in Zambia, although it becomes U-shaped if endogeneity of plot size is considered (Kimhi 2006).
By contrast, in situations with little mechanization, a strong negative relationship between output and farm size is often found even after adjusting for other factors. For example, in Malagasy rice farms, inclusion of household fixed effects and controls for soil nutrients that are generally not observable does not reduce the negative relationship (Barrett, Bellemare, and Hou 2010). Similarly, data from Rwanda in the 1990s point toward higher intensity of labor use by small farmers who farm land more intensively (e.g., by reducing fallowing) but also invest more in soil conservation (Byiringiro and Reardon 1996). Farm household survey data from four countries (Malawi, Tanzania, Kenya, Uganda) also point toward a negative relationship between farm size and output (Larson et al. 2012).
Detailed empirical study of productivity by farm size will be of relevance for Rwanda, where efforts to promote agricultural development prompted adoption of policies to encourage consolidation and prohibit subdivision of plots almost entirely.4 Such efforts have been controversial and difficult to implement even in countries with higher levels of per capita income. Consolidation efforts in Eastern Europe have a mixed record, partly because they failed to address key institutional factors (Deininger, Carletto, and Savastano 2012). In Mexico, subdivision restrictions had little impact on the ground and merely drove farmers into informality (World Bank 2002). They could thus easily undermine sustainability of Rwanda’s recent, and in many respects exemplary (Ali, Deininger, and Goldstein 2014), effort to demarcate and register all of the country’s 10.3 million land plots.
III. DATA, DESCRIPTIVE STATISTICS, AND ECONOMETRIC APPROACH
Detailed plot-level data from Rwanda allow us to explore determinants of agricultural production and the presence of a farm size–productivity relationship using output as well as measures of profit consistent with types of labor market imperfections at holding and plot level. Descriptive data and graphs point toward large differences in intensity of input use and gross value of output across farm sizes, in line with the notion of small producers using inputs more productively. This relationship disappears if profits that value family labor at market wages are considered.
Data
We use data from a 2010/2011 survey of 3,600 rural households in 300 randomly selected villages of Rwanda to provide evidence on the relationship between farm size and output and profit per unit of cultivated land. The main purpose of the survey, conducted by the World Bank with support from the U.K. Department for International Development and the International Growth Center, was to use the results as a baseline to assess impacts of a program of land tenure regularization. A three-stage stratified cluster sampling strategy was adopted to select study villages from a complete list of enumeration areas provided by the National Institute of Statistics of Rwanda. First, 100 sectors nationwide (4 in each of the 25 districts) were randomly selected from all sectors.5 Three enumeration areas and 12 households were then chosen randomly in selected sectors and enumeration areas. The distribution of the sample, together with the boundaries of the country’s main regions, is illustrated in Figure 1. In addition to land characteristics, detailed information was collected on inputs and outputs to compute revenue and profit at plot level and on households’ demographics, resource endowments, and participation in land, credit, and other markets.
Location of Sampled Cells (Villages)
Plot-level data on labor and nonlabor inputs and output from crop production are for the March–August 2010 agricultural season. Plot size measures are based on owners’ estimates.6 Appendix Figures A1 and A2 illustrate that Rwandan farms are, with a mean of 0.37 ha (or a median of 0.17 ha) and a maximum of about 2 ha, small by global standards, with most plots smaller than 0.25 ha. To control for unobserved plot-level heterogeneity, we use subjective information on plot characteristics including soil type and topography, as well as self-reported land values. After dropping plots that were either temporarily left fallow or lacked information, we are left with a sample of 7,477 plots in 3,080 house-holds.7 Furthermore, to prevent them from confounding our analysis, we exclude from the analysis some 15% of plots that are rented.8
Household-level descriptive statistics, displayed in Table 1, point toward clear differences between terciles of cultivated area (measured by a simple t-test, with significance denoted by asterisks). With 0.37 ha on average, own cultivated area ranges between 0.05 ha for the bottom and 0.88 ha for the top tercile.9 Owing to the 1994 genocide, the incidence of female headship is, at 27%, high. Female-headed households are more prevalent in the south (32%) and are more likely to cultivate smaller areas; some 33% of those in the bottom but only 20% in the top tercile are female headed. Farmers of smaller holdings have less secondary education and family labor endowments and are somewhat younger than farmers of large holdings, possibly due to accumulation over the life cycle. Variations in crop mix by size are less pronounced, though large farms have slightly less land under grain or vegetables and more under tubers or trees.
Descriptive Statistics at Household Level
Structural similarities notwithstanding, variable input use varies markedly across farm size groups. With about 450 days/ha, labor input is well above that of neighboring countries (Larson et al. 2012).10 Labor intensity varies significantly with farm size: small farms use almost four times as much own labor per hectare as large farms (765 vs. 207 days/ha). By comparison, cross-group differences in hired labor shares are marginal, with less than 10% of total labor demand covered by hiring labor (although large farms are three times more likely to use any hired labor than small ones). At 16% and 9% (22% and 12% in the top and 12% and 7% the bottom tercile), respectively, use of fertilizer and pesticide remains low. Regional disaggregation, in columns 5–8 of Table 1, points toward interregional differences in input use; while in the north and west some 82% apply manure, only 52% do so in the east. Similar differences emerge for fertilizer (25% and 22% in north and west vs. 7% in east) and pesticide (14% and 10% vs. 5%) use. With an average of $550, the value of monetary output per hectare varies enormously across farm-size classes, with $860, $492, and $298 for the bottom, middle, and top farm-size terciles, respectively.
As finding an inverse relationship between farm size and output per hectare may be due to failure to properly account for inputs, especially own labor, we complement the above with an analysis of profit (or gross revenue) per hectare by subtracting the value of purchased inputs and hired labor.11 Family labor is treated in three ways, namely, (1) not accounted for (equivalent to assuming missing labor markets), (2) valued at a household-specific shadow wage rate as discussed below (equivalent to labor market access varying by household, e.g., due to transaction costs); and (3) valued at the mean village wage rate (assuming perfectly competitive labor markets). Table 1 illustrates that the negative farm-size relationship is robust to the first two but that the measure of net profit obtained by valuing family labor at village wage rates shows little variation across farm sizes. It also suggests that marginal products of labor, computed as by Jacoby (1993), differ significantly across farm-size groups, with rates for the first and second terciles less than half and about three-fifths of the rate of the top tercile, which is not statistically different from the market rate. Assumptions regarding the nature of labor market imperfections and the resulting valuation of family labor will thus affect the nature of the relationship between farm size and output.
Kernel-weighted nonparametric regressions for the logarithms of crop output value against holding or plot size, in Figure 2, and labor use, in Figure 3, illustrate this descriptively. They point toward a pronounced decrease in yield from some $1,100/ha to less than $100/ha and labor use intensity (from close to 2,000 to 45 days/ha) with both holding and plot size, similar to what has been found elsewhere (Assuncao and Braido 2007). Figures 4 and 5, based on profit computed using shadow and market wages at plot level and holding level, respectively, show how different ways of valuing family labor can change this: shadow profit (dashed lines) still declines monotonically with farm size, except for extremely small holding sizes (less than 0.007 ha) where the relationship is very imprecisely estimated.12 By contrast, profit net of family labor valued at market prices (solid lines) remains virtually constant for all plot/holding sizes above 0.02 ha. If supported by parametric results, this would suggest no benefits from policies to promote consolidation. Gains from measures to prevent subdivision, if existent, would be of small magnitude and at most affect the very smallest plots (note that 25.8% of plots are below 0.02 ha).
Inverse Farm Size–Productivity Relationship: Yield
Farm Size and Intensity of Labor Use
Inverse Farm Size–Productivity Relationship at Plot Level: Net Profit
Inverse Farm Size–Productivity Relationship at Holding Level: Net Profit
Plot-level data in Table 2 suggest that small plots are of higher quality (16% in the bottom vs. 8% in the top tercile are wetland and 8% vs. 3% in a valley), a conclusion supported by higher self-assessed land values of $19,070/ ha for the bottom versus $8,387 in the top plot-size tercile.13 The relationship between farm size, yield, and gross and shadow profits per hectare remains similar to what was found earlier, namely, a negative relationship between plot size and output value that disappears once net profit valuing family labor at market wages is considered.
Descriptive Statistics at Plot Level
Econometric Approach
To make inferences on scale of production and technical efficiency across farm-size classes and appreciate households’ patterns of resource allocation to crop production, we estimate Cobb-Douglas and translog production functions at holding and plot levels. The general form of the translog production function with no restrictions on cross elasticities of substitution is (Berndt and Christensen 1973)14
[1]
where Yij is the total value of crop output (in logarithms) on plot j cultivated by household i; α is household fixed effects; Xijk or Xijl are the logarithm of the quantity of variable inputs used (subscripts k and l stand for types of inputs, including the number of labor days, quantity of chemical fertilizer, pesticides, and manure used); Zij is a vector of plot characteristics that may affect production, for example, distance from homestead, years of possession, presence of irrigation or being located in wetland, soil type, topography, and incidence of crop shocks; β, γ, and δ are vectors of parameters to be estimated; and is a random error term. Fixed effects, αi, at plot or (for household-level regressions) village level include time-invariant unobserved factors affecting crop production at the relevant level. Computing the difference between villagelevel fixed effects and αi will provide a measure of farmers’ ability or technical efficiency (Deininger and Jin 2008).
Values of crop output and all inputs are normalized by dividing them by their sample means. In the empirical estimation, we also include dummies for zero values of nonlabor variable inputs (Battese 1997). Given symmetry conditions on all cross elasticities (i.e., γkl = γlk), the translog function is homogenous if ∑kγkl = 0 for all l, and it will have constant returns to scale if ∑kβk = 1. All these restrictions can be tested empirically. Shadow wage rates, that is, marginal products of different types of family labor, can be calculated by estimating the Cobb-Douglas version of [1] at holding level with family labor disaggregated by gender (Jacoby 1993).
To examine the relationship between productivity and farm size at plot or holding level, we estimate an aggregate yield equation, following the literature (Assuncao and Braido 2007; Barrett, Bellemare, and Hou 2010).15 If farms maximize profits and technology can be represented by a Cobb-Douglas production function with constant returns to scale, a reduced-form yield equation at the plot level can be specified as follows:
[2] where yij is the logarithm of the value of crop output per hectare or different profit measures as discussed above on plot j by household i, αi is a household fixed effect, Aij is the logarithm of plot area, Zij is a vector of plot characteristics that includes subjective land quality measures (soil type, topography, irrigation) and self-reported land values as well as crop dummies and an indicator variable for having experienced plot-specific crop shocks, β and δ are parameters to be estimated, and is a random error term. We first estimate a naive specification that omits Zφ and αi and then control for soil quality and possible market imperfections at the village or household level. The rationale for doing so is simple: if, as much of the literature seems to suggest, soil quality or market imperfections at the household or village level are the driving forces for the negative relationship between farm size and productivity, β would be significant in the naive specification but lose significance once additional elements are introduced, and δ as well as αi will be significant.
As more intensive use of labor on small holdings or plots was found to not only be a potential reason for the inverse relationship between output and size but also to result in the opposite relationship for profits (Carter 1984), we run [2] not only for yields and profits but also for labor demand. This is done by using the log of family labor days per hectare as a dependent variable at the plot and holding levels.
IV. ECONOMETRIC EVIDENCE
Various production function specifications support the notion of constant returns to scale at the holding level, a negative relationship between cultivated area and total value of crop output, and a strong positive link between farm size and labor used per hectare. Estimated shadow wages are in line with households’ level of market integration.While profits computed using shadow wages remain negatively related to farm size, the negative relationship disappears if a measure of profit that values family labor at mean wages is used. Small farmers’ superior levels of output can thus be attributed to higher intensity of (family) labor, consistent with the notion that they maximize profits in the presence of market imperfections.
Production Function Estimates
The top panel of Table 3 reports parameter estimates from the Cobb-Douglas and translog specifications at household (columns 1–3) and plot (columns 4 and 5) level, respectively. We note that all conventional factors are significant and positive, with elasticities of 0.31 for land, 0.41 for labor, 0.09 or 0.14 for fertilizer, 0.05 or 0.10 for pesticides, and 0.12 for manure at the holding level. We cannot reject constant returns to scale at the holding level, though there is some indication of increasing returns to scale (at 5% or 10% level of significance for translog and Cobb-Douglas functional forms, respectively) at the plot level. Crop shocks (drought, flooding, damage due to pests or insects) are estimated to reduce output by 21 percentage points, and soil type with loam soils increases output by some 20 percentage points. Plot-level regressions also point toward a negative impact of distance from the homestead; one minute of additional travel time is estimated to reduce output by about 0.4 percentage points.16
Parameter Estimates and Output Elasticities for Alternative Specifications of the Production Function
Estimates of technical efficiency from a stochastic frontier production function, plotted against holding size (Appendix Figure A3) together with a kernel-weighted local polynomial regression fitted through them, fail to support a systematic relationship between efficiency and size.17 Also, household- and village-fixed effects from plot-level regressions can be used to recover a measure of farmers’ ability as the difference between household- and village-level fixed effects. Plotting this variable and the regression fitted through it against cultivated area (Appendix Figure A4) points in the same direction.
Marginal products of male and female family labor together with market wages are displayed in the bottom of Table 3. To check the plausibility of the results, Appendix Figures A5 and A6 plot mean values and 95% confidence intervals of estimated shadow wages for male and female casual and semiskilled labor against four employment regimes, namely, those who are (1) full autarkic in labor markets, (2) only work off-farm but do not hire in any labor, (3) work in off-farm employment and hire in labor, and (4) only employ others but do not work off-farm.18 In all cases, and irrespective of gender, shadow wages for households who do not hire in (i.e., remain in autarky or hire out family labor for casual work) are significantly below those for households who hired in agricultural labor. Shadow wage rates for those employing workers are in most cases indistinguishable from the village wage rate. For semiskilled off-farm work, the situation is similar except that estimated shadow wage rates for households who at the same time hire in and out labor are estimated to be above those for households working only on their own farm (Figure A6). This points toward labor market imperfections and considerable seasonality of labor markets in rural Rwanda that would be worth exploring in more detail than is possible with our data.19
Evidence of the Farm Size–Productivity Relationship
Tables 4–7 report results from the regressions to explore the relationship between farm size and productivity in terms of yields (Table 4), labor use (Table 5), shadow profits (Table 6), and profits at market prices (Table 7) at holding and plot levels. In all cases, we start with a naive specification that includes only cropped area (columns 1 and 4 at holding and plot level, respectively) and successively add variables to control for soil quality (type, topography, location in a wetland or presence of irrigation, self-reported land value, length of possession, distance to homestead, and incidence of plot-level crop shocks). Village fixed effects are then added in columns 2–4 and 5–6, information on crop choice and household demography in columns 3 and 6, and finally household level fixed effects in column 7.
Farm Size-Productivity Relationship: Yield Approach
Farm Size and Intensity of Labor Use
Farm Size–Productivity Relationship: Net Profit Approach Using Shadow Wages
Farm Size–Productivity Relationship: Net Profit Approach Using Village Market Wages
Results from naive regressions, as reported in Table 4, point toward a strong negative relationship between the value of output per hectare and own cultivated area, with a doubling in cultivated area associated with a 38% or 48% decrease in the value of crop output per unit of cultivated land at the holding or plot level, respectively. Other attributes such as per-hectare value of land, distance from the homestead, soil type (loam), and having experienced a crop shock have all the expected sign and are highly statistically significant, and their inclusion improves the explanatory power of the regression (columns 2 and 5).20 Still, the magnitude of the estimated farm size–productivity relationship is hardly affected. This suggests that despite descriptive variation in plot attributes with size, as suggested by Table 2, land quality and villagelevel market imperfections are not at the root of the regularity. Including crop dummies (all negative compared to the base category of vegetables) and observed household characteristics such as head’s age and education or female headship provides interesting insights, for example, by suggesting that females may face difficulties in factor market participation, but yields essentially similar conclusions. Household fixed effects to control for unobserved heterogeneity, including householdspecific factor market imperfections that may affect the inverse relationship, do not alter the inverse relationship between plot size and output either, and results are not due to the fact that we restrict attention to owned plots.21
Table 5 presents results from the equivalent regression for labor demand, suggesting that use of labor per area declines steeply, with an estimated elasticity of about −0.45 in a household’s cultivated area (columns 1–3) and −0.58 in plot size (columns 4–7). Use of labor is also estimated to increase with land quality, as proxied by self-assessed land values and a plot being wetland, and to be higher for plots closer to the homestead. The high significance of coefficients on household composition (members 35–60 and less than 14 years old) and demography (female headship) suggest some frictions in labor markets.
If, as suggested by the above results, part of the superior output achieved by small farms (or on small plots) can be attributed to more intensive labor use, use of profit measures may result in a weaker, possibly even reversed, relationship. In light of this, Table 6 reports estimates of the relationship between farm size and per-hectare shadow profit net of purchased inputs and male and female family labor valued at their estimated marginal products. These estimates indicate that smaller farms are significantly more profitable; the magnitude of the (negative) per-hectare profit elasticity of land size is broadly equal to that obtained for per-hectare value of crop output. An inverse relationship between shadow profit and farm size emerges robustly at holding and plot levels, and is unaffected by inclusion of plot characteristics or village- and household-specific fixed effects.
However, results change if family labor is valued at village market wage rates rather than the estimated marginal products of labor (Table 7). With the exception of a marginally significant (negative) coefficient in the naive specification, all coefficients at the holding level are insignificant, and profit at market prices increases with self-assessed land values and soil quality (loam) while decreasing with incidence of crop shocks. At the plot level, cropped area becomes positive and highly significant when controlling for plot characteristics, although this significance disappears if household fixed effects are included (column 7). To explore if our specification may suppress heterogeneity in the data (e.g., an initial portion where profits increase with size), we reestimate the appropriate regressions allowing for differences in the size of the coefficients across terciles (Table 8). While results suggest differences between size groups in terms of yield (with the relationship being less negative for the first tercile in terms of cropped area and the second tercile in terms of plot size) and shadow profit, the hypothesis of any differences for net profits at market prices is rejected. As a further robustness check we also estimated a specification with land size squared. Average marginal effects from this specification, reported at the bottom of the supplementary online appendix Table 8,22 support our main result: the presence of an inverse relationship between farm size and yield and shadow profit that disappears when family labor is valued at market wages.
Farm Size–Productivity Relationship: Variation by Farm Size
Taken together, these findings imply that although yield and shadow profits decrease significantly with farm or plot size, there is no need to resort to unobserved differences in land quality or measurement error to explain this phenomenon. To the contrary, the fact that profits are virtually unaffected by plot or farm size if family labor is valued at village level wage rates points toward imperfections in the operation of Rwanda’s rural labor markets as the main reason for the inverse relationship between farm size and gross output. As a result of this, Rwanda’s small farms use labor beyond the point where its marginal product equals the market wage. This would suggest that, as wages increase, farm sizes will adjust along the patterns observed in other countries and that interventions in the land market to eliminate the negative farm size–productivity relationship are unlikely to be successful.
V. CONCLUSION AND POLICY IMPLICATIONS
Heightened interest in African agriculture has led to a debate on the extent to which the negative relationship between farm size and productivity, documented in a large body of literature, is relevant for Africa, with implications for countries’ strategy in trying to increase sectoral productivity. We find a robust negative relationship between farm size and per-hectare gross output and shadow profit that does not disappear if plot characteristics or household attributes are controlled for. More intensive labor use by smaller farms is a key underlying reason. In fact, the relationship disappears (but does not reverse) if profit at market prices and wages rather than output or shadow profit is considered.
Rwandan farmers’ behavior seems in line with a scenario of labor market imperfection together with failures in other factor markets. Although nonagricultural development and investment higher up in the value chain may, in due course, lead to higher wages that would trigger farm-size growth through market-driven consolidation, the data fail to support administrative measures to prevent subdivision of holdings. The fact that results at the plot level are essentially identical and allow us to reject the notion of a positive relationship between plot size and net profits at market prices, even for the smallest size group, reinforces this conclusion. In terms of policy, it suggests that enforcing existing subdivision restrictions will at best yield insignificant benefits and, by forcing land transactions into informality and jeopardizing the sustainability of the country’s land regularization effort, could have high costs. Of course, farm sizes in Rwanda are very small by global standards, and further study from settings with larger variation in observed farm sizes may be of interest.
Given the importance of factor market imperfections emerging from our analysis, indepth analysis of key factor markets and their interactions will be desirable. However, our failure to find efficiency gains from larger holding or plot sizes even for Rwanda’s very small plot sizes cautions against sweeping generalizations in terms of determining the most appropriate policies to further the development of African agriculture. Instead it reinforces the need for policy recommendations to be based on careful analysis. Exploring whether similar results obtain in more land abundant African countries where mechanization and capital access will be more relevant would be of great interest to not only understand the role of imperfections in other markets but also the dynamics of farmers’ adaptation to nonagricultural economic development.
Acknowledgments
We gratefully acknowledge funding support from the U.K. Department for International Development and the Knowledge for Change Program and would like to thank Rodney Dyer, Sion McGeever, and Cyriaque Harelimana for initiating and supporting data collection, as well as the National Land Centre (now Rwanda National Resource Authority) in Kigali, especially Emmanuel Nkurunziza, Didier Sagashya, and Thierry Ngoga for their valuable comments. The authors are also grateful for the comments and suggestions of Hanan Jacoby, Will Martin, Keijiro Otsuka, and two anonymous reviewers, as well as seminar participants at the Center for the Study of African Economies at Oxford University and the World Bank’s 2013 Annual Conference on Land and Poverty. The views presented in this paper are those of the authors and do not represent those of the World Bank or its member countries.
APPENDIX
Distribution of Own Cultivated Area
Distribution of Own Plot Size
Farm Size and Technical Efficiency: Production Frontier Function Estimation
Farm Size and Technical Efficiency: Household Fixed Effects Approach
Shadow Wage Rate by Employment Regime with 95% CIs: Casual Labor Market
Shadow Wage Rate by Employment Regime with 95% CIs: Noncasual Off-farm Work
Footnotes
The authors are, respectively, economist and lead economist, World Bank, Washington, D.C. Additional material is available at http://le.uwpress.org.
↵1 A well-known exception to the advantages of owneroperated units of production over those relying on wage labor is in perishable plantation crops, where economies of scale in processing may be transmitted to the production stage (Binswanger and Rosenzweig 1986) and employment is often year-round so that the optimum size of a unit is determined by the factory’s processing capacity.
↵2 As of the end of 2009, only seven publicly listed farming companies existed worldwide, three in South America and four Ukraine and Russia (Deininger and Byerlee 2011). This contrasts with processing, input industries, and sometimes output markets, all of which are characterized by large fixed costs (e.g., for R&D or processing) that give rise to economies of scale and often a highly concentrated industry structure (Deininger and Byerlee 2012).
↵3 Pest-resistant and herbicide-tolerant varieties facilitated broad adoption of zero tillage and, by reducing the number of steps in the production process and the labor intensity of cultivation, allowed management of larger areas. The ability to have machinery operations guided by GPS technology rather than a driver’s skills makes close supervision of labor less relevant, while information technology can generate data to help better supervise labor. The scope for substituting crop and pest models and remotely sensed information on field conditions for personal observation also reduces the advantage of local knowledge and experience in tactical farm decisions, while climate change and the associated greater variability of climatic conditions reduces the value of traditional knowledge (Deininger and Byerlee 2012).
↵4 Article 20 of the Organic Land Law (Republic of Rwanda 2005) prohibits subdivision of agricultural plots of less than 1 ha and requires administrative approval for subdivision of plots of less than 5 ha. Per our data, 97.9% of plots are less than 1 ha and 99.9% are less than 5 ha, so that virtually everybody is affected.
↵5 Areas where the regularization program had already started by the time of data collection were dropped from the frame, implying that Kirehe district in the eastern province and Rubavu district in the western province, as well as Kigali city, were excluded.
↵6 While this may lead to some measurement error (Lamb 2003), measurement by GPS was not an option in light of the small plot sizes, which, with standard GPS receivers’ limited precision, could have been measured only with large errors (Carletto, Savastano, and Zezza 2013). GPS readings were taken for each plot’s centroid and the cultivator’s residence to provide information on plots’ location relative to each other and the homestead.
↵7 Plots were dropped because of unspecified response for crop type (3%), missing quantity of output, lack of prices or conversion factors for nonstandard units (4%), or because they were left temporarily fallow (4%) in the season under consideration.
↵8 The fact that they are operated under cash rent reduces the risk of confounding size- and tenancy-related factors, and substantive conclusions for the sample including these plots are indeed are almost identical, as can be verified from results for the expanded sample in the supplementary online appendix (available at http://le.uwpress.org).
↵9 As shown in the supplementary online appendix Table 1 (available at http://le.uwpress.org), there is little variation across farm size groups in the extent of land rental market participation: on average nearly 31% of the households rented in land during the season under consideration.
↵10 Average amounts of labor used on maize plots are about 310, 157, 116, and 106 days/ha in Malawi, Tanzania, Kenya, and Uganda, respectively (Larson et al. 2012).
↵11 In the absence of farm-gate price information and limited transactions at the village level, median unit sales value of each crop at the national level is used to estimate value of crop output. Note in particular that, as the average household cultivates more than two plots, we can estimate plotlevel regressions that control for unobserved heterogeneity at the household level. Smallholders in Rwanda are traditional farmers who use neither animal traction nor mechanization, and only 6% of plots are irrigated using traditional methods (i.e. drainage of marshlands or water from ponds or streams) (Republic of Rwanda 2008). The only capital inputs other than land used are hand tools and implements, which are difficult to value and thus not included in the production function or the computation of farm profits. Similarly, we control for access to irrigation using only a dummy variable.
↵12 Note that, in light of the paucity of observations, these are not very precisely estimated. Self-reported land values are in line with the notion that high-quality land is more likely to be subdivided (Lamb 2003), but land values may deviate from the net present value of future profits due to market imperfections. An anonymous reviewer, citing asset pricing theory, pointed out the inconsistency in the ranking of small, medium, and large plots on the basis of land values and net profits, which can be the case in an environment where markets work well.
↵13 Note that these values are very high by international standards, reflecting partly the lack of alternative assets.
↵14 We present the plot-level specification, noting that it is straightforward to translate this to the holding level, where j would index households in village i, and plot-level variables are aggregated at household level using plot size as a weight, and αi is a village-level fixed effect.
↵15 At the holding level, plot characteristics are aggregated using plot-size weights, and village fixed effects are used.
↵16 The signs of coefficients on dummy variables for zero use of nonlabor variable inputs (chemical fertilizer, pesticides, and manure) that are included to get unbiased estimates of the production function parameters cannot be determined a priori and could be affected by aggregation.
↵17 Results from estimating the stochastic frontier production function with a truncated normal nonnegative distribution component are available upon request from the authors.
↵18 For casual labor markets, 30% of sample households remained in autarky; 31% only hired out family labor; 8% hired out family labor and employed hired labor on-farm; and 31% only hired labor for farming. For semiskilled labor, 56% remained in autarky, 5% only hired out family labor, 7% hired out and hired in agricultural labor, and 32% only hired in.
↵19 Wage differentials between agricultural and nonagricultural sectors as well as the wedge between shadow and village wage rates may be due to adjustment costs that inhibit workers’ mobility (e.g., Richards and Patterson 1998), an issue that would be worth exploring more explicitly in future research.
↵20 Given that our data is cross sectional, heteroskedasticity could be a concern to the extent that those affected by plot-specific shocks had higher variation in yield or profit per hectare. We reestimated all specifications with robust standard errors to correct for any model misspecification and thus address this concern, but results remain the same and, hence, are not reported here, but they are available from the authors upon request.
↵21 The supplementary online appendix (available at http://le.uwpress.org) shows that very similar results are obtained if all plots are included in the analysis.
↵22 Available at http://le.uwpress.org.
