testing the farm size-productivity relationship over a

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Zambia is an interesting case for the present paper because the country has been experiencing major ... The aforementioned paper rejects sample selection bias ...... _Inverse_Farm_Size_Productivity_Relationship/file/3deec5255aa9f2f5ff.pdf. Jayne ..... No formal education; 2 = basic education (Grade 1-9); 3 = high school.
TESTING THE FARM SIZE-PRODUCTIVITY RELATIONSHIP OVER A WIDE RANGE OF FARM SIZES: SHOULD THE RELATIONSHIP BE A DECISIVE FACTOR IN GUIDING AGRICULTURAL DEVELOPMENT AND LAND POLICIES IN ZAMBIA?

Chewe Nkonde1, Thomas S. Jayne1, Robert B. Richardson1, and Frank Place2 Michigan State University, East Lansing, MI, USA1 International Food Policy Research Institute, Washington DC, USA2 [email protected]

Paper prepared for presentation at the “2015 WORLD BANK CONFERENCE ON LAND AND POVERTY” The World Bank - Washington DC, March 23-27, 2015

Copyright 2015 by author(s). All rights reserved. Readers may make verbatim copies of this document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies.

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Abstract There is growing interest by development scholars to revisit the inverse farm size-productivity (IR) hypothesis to guide policy on land and agricultural development strategies. However, it is remarkable that existing empirical studies, particularly in sub Saharan Africa (SSA), have been derived from data with few farms outside the zero to ten-hectare range, yet their findings have been extrapolated beyond this range. Moreover, the definition of productivity has mainly been limited to yield or other land productivity measures to explore this highly contested hypothesis. Using data from Zambia, this study addresses these shortcomings and explores the reasons for potential differences in productivity within and between farm size categories, so as to provide practical guidance for relevant policy formulation. Results from our carefully constructed measures of productivity -- accounting for all production costs including less commonly considered costs such as family labor and fixed costs -- reveal that the farm size-productivity relationship is not uniform across the four measures of productivity. While relatively large farms (medium-scale farms) enjoy labor productivity efficiency, they do not exhibit a superior efficiency advantage over small farms when other productivity measures are considered. With a multiple set of considerations to be made in setting land and agricultural policy, these findings indicate that prioritizing unutilized land for medium- over small-scale farms on efficiency grounds are unwarranted.

Key Words: Inverse relationship (IR), Production costs, Productivity measures, Farm size, Agricultural development, Zambia.

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1.0

Introduction

Although agriculture in sub-Sahara Africa (SSA) has recently experienced gains in productivity ever since the early 1980s (Block, 2010), there remain lingering doubts whether an African “green revolution” can be ushered in given the patchy progress in African smallholder agriculture (Mosley, 2002). Recent pessimism about smallholder-led agriculture stems from evidence of: (1) slow productivity growth and uptake of modern inputs (Diao et al., 2007); (2) shrinking size of most smallholder farms due to rural population growth and rising land scarcity (Hazell, 2005; Jayne et al., 2012), and; (3) widespread land degradation (Lal, 1995). At the same time, recent evidence shows a meteoric rise in farmland acquisitions by medium-scale farms and, to a lesser extent, large-scale acquisitions, leading to a greater concentration in both landholdings and marketed agricultural output in a number of African countries (Jayne et al., 2014). Are these important changes in farm structure promoting national goals of agricultural productivity, food security and poverty reduction? To shed light on this question, this paper explores two important policyrelevant research questions. In light of changes in farm structure experienced in parts of SSA, does the inverse farm size-productivity relationship hold? And if productivity is associated with scale of farming operation, what should be the focus of land institutions and policies to accelerate agricultural development and poverty reduction in SSA? We explore these questions by revisiting the farm size-productivity relationship hypothesized to have an inverse relationship in literature and is therefore commonly abbreviated as IR. The IR hypothesis has been part of the agricultural development discourse for nearly a century, first noted in Russian agriculture (Chayanov, 1926) and later examined in Indian agriculture (Sen, 1962; Mazumdar, 1965; Bardhan, 1973) The hypothesis posits that output per unit of land tends to be greater on small farms than on large farms (Berry & Cline, 1979). A number of studies have found a strong negative relationship between farm size and productivity suggesting that small farmers are more productive per unit of land than large farmers (Bhalla & Roy, 1988; Barrett, 1996). As a consequence, findings of an inverse relationship have been a celebrated empirical discovery so much so that proponents of smallholder agriculture have argued for agricultural strategies that emphasize smallholder-led development. In SSA, smallholder agriculture has remained an integral part the region’s agricultural development strategies and as such, development scholars have also taken an interest to examine the farm sizeproductivity relationship in the region (e.g. Carletto et al., 2011; Larson et al., 2012; Ali & Deininger, 2014). However, it is remarkable that existing empirical studies have been derived from data with few farms outside the zero to ten-hectare range, yet their findings have been extrapolated beyond this range.

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Findings from such studies cannot address the salient policy questions related to desired land allocation patterns given the rapid rise of medium-scale farm landholdings between 5 and 100 hectares observed in some SSA countries such as Ghana, Kenya and Zambia (Jayne et al., 2014). Therefore, tests of the IR hypothesis in Africa covering a wide range of farm scales, take on even greater policy importance in light of recent papers questioning the viability and even the objectives of promoting small-scale agriculture in Africa (e.g., Dercon & Gollin, 2014; Collier & Dercon, 2014). Given this background, the current study makes two important contributions. First, the IR hypothesis is explored over a much wider range of farm sizes using a statistically representative sample of small- and medium-scale farming households with landholding size between 1 and 100 hectares from central and southern Zambia. In this study, small-scale farmers are defined as agricultural households owning land less than or equal to five hectares. The relatively large landholders are classified as medium-scale farmers whose landholding size ranges between 5 and 100 hectares.1 Including this wide range of farms in our analysis can inform current policy discussions about how governments should allocate unutilized/underutilized land in order to achieve national equity and productivity goals. Second, the paper examines the relationship between farm size and productivity using alternative measures of productivity. A number of related studies have exclusively used yield or value of output per unit area -- both measures of land productivity -- to investigate the farm size-productivity relationship. While land productivity is an important measure that can be used to assess differences in farm efficiency, consideration of other measures gives a more comprehensive picture especially when findings from such studies are used to draw implications for land policies and agricultural development strategies. Therefore, we address this shortcoming in the extant IR literature by constructing four measures of productivity. While a more detailed explanation of each measure is provided in the “Data and Methods” section of this paper, we briefly note here how we define each measure. The first measure of productivity, a land productivity measure, is the net value of total crop production per unit of area planted computed as the net value of crop production (variable input and fixed costs netted out from total value of crop production) divided by total area planted. Net value of crop production per family labor day (labor productivity) is the second measure that captures the total value of crop production net of variable input (excluding opportunity cost of family labor) and fixed costs divided by the number of days taken for crop production activities by family labor. Our third measure of productivity is the cost of maize production per metric ton produced computed by dividing the sum of variable input 1

In Zambia, medium-scale farmers are alternatively referred to as emergent farmers. This term became popularized in the 1970s when it was used to describe farmers that leave subsistence farming sufficiently far behind to sell at least half their produce to the market in an average year (Lombard & Tweedie, 1972).

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costs and fixed costs by the number of tons of maize produced. Our final measure of productivity is the Total Factor Productivity (TFP) indicator determined by dividing the gross value of crop production by the product of three factors of production: value of capital; total number of labor days, and; the total amount of land used for crop production. Each factor in the TFP indicator is raised to the power of factor output elasticities. Our study has the advantage of accounting for fixed costs when computing the cost of production, which may produce results different from prior studies that have typically ignored fixed production costs (and which therefore may have overstated the productivity of farms with high fixed costs). For each measure of productivity, we use econometric techniques (controlling for household-specific heterogeneity) to explore reasons for potential differences in productivity within and between farm size categories, so as to provide practical guidance for formulation of relevant policies. Zambia is an interesting case for the present paper because the country has been experiencing major changes in farm structure, the most salient of which is a major increase in cultivated area under the control of farms cultivating between 5 and 100 hectares (Sitko et al., 2013; Jayne et al., 2014). These changes in farm structure has warranted an empirical review of the IR hypothesis that covers the relevant range of farm sizes with the goal of informing policy makers on how land policies can be harmonized more compatibly with other national policy objectives. The rest of the paper is organized as follows. Section 2 presents the conceptual background relevant to this study while the data and the estimation strategy used in this study are presented in section 3. The study findings are outlined and discussed in section 4 and the paper concludes with section 5 drawing out implications for policy. 2.0

Conceptual background

We develop the conceptual basis for our study by synthesizing empirical IR hypothesis literature according to the following three themes: (1) main explanations for the hypothesis; (2) productivity measures and range of farm sizes, and; (3) empirical evidence from sub-Saharan Africa. 2.1

Explanations for the Inverse Farm Size – Productivity Hypothesis

The key reason why research and policy opinion leaders have continued to debate and investigate the relative efficiency of small farmers implied by the IR hypothesis is because results for the main explanations of the existence of the inverse relationship have been mixed and thus inconclusive. For the rest of section 2.1, we discuss the three main explanations that have been examined in an appreciable number

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of studies for why an inverse relationship is predominantly observed in developing countries. We also discuss how the empirical literature has had mixed results pertaining to each of the main explanations. The first explanation relates to market imperfections in factor markets such as labor, insurance and credit with imperfections in labor markets being the main focus. In an imperfect labor market, the cost of searching and supervising hired labor (transactions costs) is relatively high. Therefore, this creates an advantage for small farms who mainly rely on family labor for most farming activities. Large farms, on the other hand, depend substantially on hired labor to help with farming operations. According to Eswaran & Kotwal (1986), hired labor have a propensity to “shirk” if not supervised, and therefore, the labor that can be hired on the market is an imperfect substitute for one’s own time. Using data from Pakistan, Heltberg (1998) finds an inverse relationship between farm size and productivity explained by the presence of a supervision constraint with regard to labor, where outside workers are imperfect substitutes for family labor. Toufique (2005) compares two regions in Bangladesh with differences in transactions costs in rural labor markets. For a region with high transaction costs, output per acre on smaller farms is found to be higher than on larger farms. However, the study generates the opposite conclusion in a region with lower transactions costs – output per acre on small farms is lower than on large farms. Another study of Nicaraguan agriculture has shown that empirical evidence cannot rule out labor market imperfections as the driving force behind the oft-observed inverse relationship even if one controls for technical and allocative efficiency (Henderson, 2014). A related explanation to imperfect factor markets attributes the IR to what is referred to in the literature as a “peasant mode of production” (Carter, 1984). Carter’s study explains this by stating, “small farms use far more inputs per hectare than do large farms, producing the observed inverse relationship given the estimate of constant returns to scale” (ibid, p144). The aforementioned paper rejects sample selection bias or village factors correlated with farm size as possible explanations for the IR. Cornia (1985) corroborates the peasant mode of production explanation in a study of 15 developing countries. The study ascribes the IR to higher factor inputs and a more intensive use of land on small farms. However, other studies question the imperfect factor markets and peasant mode of production as rationale for the existence of an IR. Assunção & Braido (2007) argue that the imperfect factor markets explanation does not explain the inverse farm size-productivity relationship based on evidence from India. To control for imperfect factor markets, their study analyzes data that contains households cropping multiple plots in each season. This allows them to investigate the inverse relationship across different plots managed simultaneously by the same household. They find that the inverse relationship remains virtually unchanged implying that the content of the inverse relationship is not related to imperfect factor markets.

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An empirical study of rice producers in Madagascar also concludes that only a small portion of the inverse farm size-productivity relationship is explained by market imperfections (Barrett et al., 2010). Ghose (1979) debunks the peasant mode of production explanation by asserting that the inverse relationship exists independently of production relations and thus reflects only a static superiority of small-scale over large-scale production. The said paper concludes: “[a]n essential precondition for this superiority, however, is a backwardness of technology. With technological progress involving the introduction of chemical fertilizers, labor-saving machinery and modern irrigation equipment, the inverse relationship is, therefore, likely to disappear” (Ghose, 1979, p27). The second explanation for the often-observed inverse relationship is the omission of important variables such as land quality in estimation equations. Since the estimation of the relationship between farm size and productivity is operationalized using econometric procedures, omission of relevant variables might lead to a biased coefficient on the variable of interest. If small farms have better (poorer) quality land, omitting important control variables for land quality might amplify (diminish) the inverse relationship between farm size and productivity. Bhalla & Roy (1988) find that when exogenous land quality variables are accounted for, the inverse relationship observed weakens, and in many cases, disappears. Other studies also show that failure to account for unobserved plot level characteristics such as soil and land quality can overstate the inverse relationship (Lamb, 2003; Assunção & Braido, 2007). Using a unique data set that includes detailed soil quality measurements, Barrett et al. (2010), however, find that none of the inverse relationship is explained by the omission of soil quality measurements. In essence, their study suggests that the inverse relationship may not be attributed to differences in land quality among rice producers in Madagascar. The third explanation examined in the literature relates to the role of measurement error (Lamb, 2003; Carletto et al., 2011; Holden & Fisher, 2013). Measurement error, in this case, is considered as the inaccuracy in the variable measuring farm size (Lamb, 2003). De Groote & Traoré (2005) is an example of a study conducted in southern Mali set out to compare the accuracy of area measurement with the accuracy of farmers estimates, assisted by enumerators. Their findings suggest that the observational error, the difference between the area measured and the area estimated, is strongly related to plot size, with smaller plots being overestimated and larger plots underestimated, in an approximately negative linear relationship. Therefore, because farm size data available in developing countries are usually selfreported, some scholars have attempted to see if use of such data yield biased estimates. Using econometric techniques that control for measurement error inherent in farmer self-reporting of their farm size, it has been observed that a statistically significant IR, reported prior to the aforementioned

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estimation adjustments, completely disappears (Lamb, 2003). Recent studies (e.g., Carletto et al., 2011; Holden & Fisher, 2013) have addressed the issue of measurement error by using rich data that include selfreported land size information complemented by plot measurements collected using Global Position System (GPS) devices. Carletto et al. (2011) test the hypothesis that the inverse relationship may just be a statistical artifact linked to problems with land measurement error. They reject this hypothesis and instead find that using an improved measure of land size strengthens the evidence in support of the existence of the inverse relationship. Findings by Holden & Fisher (2013) also confirm that more reliable GPS-estimated plot and farm sizes lead to estimates of a stronger IR than basing estimation on unreliable self-reported estimates by farmers. 2.2

Productivity Measures and Range of Farm Sizes

While the bulk of research has focused on the three aforementioned explanations for the existence of the IR in developing countries, it is remarkable that the empirical literature rarely uses a comprehensive set of productivity measures to study the farm size-productivity relationship. Table 1 (column 2) shows that most IR studies use only one measure of productivity and that there are few cases when more than one measure of productivity is used. In some studies, yield or output per unit of land area is used as a measure of productivity (e.g., Sen, 1962; Carter, 1984; Kimhi, 2006; Assunção & Braido, 2007; Barrett et al., 2010; Chen et al., 2011). These studies focus on yield of a single crop (usually a staple or main cash crop) and how this measure of land productivity relates to farm size ceteris paribus. Gross or net value of output per unit land area is another way that productivity is measured in IR empirical studies (e.g., Mazumdar, 1965; Bardhan, 1973; Ghose, 1979; Bhalla & Roy, 1988; Heltberg, 1998; Dorward, 1999; Toufique, 2005; Carletto et al., 2011; Holden & Fisher, 2013). Net value of output per unit area allows the researcher to account for multiple crop production and nets out input costs. The use of a combination of productivity measures such as land and labor productivity is less common (e.g., Ali & Deininger, 2014; Lamb, 2003). Evidently, a number of studies use only one measure of productivity -- land productivity -- to explore the farm size-productivity relationship. Other measures of productivity such as labor productivity, TFP, technical and allocative efficiency are rarely used. Further, when accounting for cost of production, a number of studies fail to account for fixed costs when constructing productivity measures. In our review of the literature, we are only aware of one study (in China, by Li et al., 2013) that has used a comprehensive set of productivity measures to reexamine the IR hypothesis: land productivity, labor productivity, profit ratio, TFP, and technical efficiency. Like most studies, however, the main shortcoming of the aforementioned study is that it covers a narrow range of farm sizes, zero to seven hectares, when exploring the farm size-productivity relationship.

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Although farm size is not explicitly defined in most IR studies, it is commonly treated as the area of land that the farmer operates or utilizes for agricultural production. In the current study, agricultural land is characterized in four distinct ways: (1) operated farm size -- cleared land that is cultivated/planted for crop production; (2) cleared land not cultivated -- includes grazing and fallow land); (3) uncleared land -forested land, and; (4) total landholding size -- the sum of (1), (2) and (3). Ironically, the range of farm sizes considered in most studies have been confined to a range of relatively small farms and generally exclude larger farms over ten hectares (Collier & Dercon, 2014). The last column in Table 1 presents the operated farm size ranges reported in selected IR studies. While some studies do not report detailed descriptive statistics, the studies where such statistics are available reveals that very few include farms outside the 0 – 10 hectare range. Therefore, a number of studies that make conclusions about relative efficiency based on operated farm size do so by extrapolating their findings outside the range of the data available. [TABLE 1 ABOUT HERE] 2.3

Empirical Evidence and Implications for Policy in Africa

Although empirical evidence in Africa examining the inverse relationship between farm size and productivity is fairly limited, there has been a gradual increase in recent years in the number of IR studies. The changes in farm structure have brought to bear the question of whether or not smallholders are still competitive based on relative efficiency. As a result, the need for evidenced-based policy formulation in Africa has become even more pronounced in light of “the active current debate about the future of small farms in the developing world” (Barrett et al., 2010, p. 95). Latest IR studies conducted in SSA likewise test the three main explanations outlined in the section above with the primary objective of informing policy. Barrett et al. (2010) revisit the conventional explanations of the inverse farm size-productivity relationship using data for rice producers in Madagascar. Their study finds that only a modest share of the inverse relationship is explained by apparent factor market imperfections that drive variation in household- or village-specific shadow prices, and that none of the inverse relationship seems attributable to the omission of soil quality measurements. They conclude that the results highlight the possibility that measurement error causes most of the inverse relationship observed in their data. Carletto et al. (2011) and Holden & Fisher (2013) explore the measurement error explanation using GPS farm size data in Uganda and Malawi respectively. Both studies find evidence of measurement error in self-reported farm sizes but reject the hypothesis that farm size measurement error creates the inverse relationship. With accurate farm size data, the inverse relationship is actually strengthened.

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Other notable IR studies in Africa include a four-country study (Kenya, Malawi, Tanzania and Uganda) by Larson et al. (2012) which explores a research design conundrum that encourages researchers who study the relationship between productivity and scale to use surveys with a narrow geographic reach, when policy would be better served with studies based on wide and heterogeneous settings. They estimate a model using multiple datasets of varying granularity and geographic scope and find that the inverse productivity hypothesis holds up well across a broad platform of data, despite obvious shortcomings with some components. Another study by Verschelde et al. (2013) uses a non-parametric approach to investigate the relationship between farm size and productivity in two Northern provinces in Burundi. Although their study does not reject the findings of an inverse relationship between farm size and productivity, they find that size returns vary substantially with farm size, that is, between 0.2 for the smallest farms and 0.8 for the largest farms. Ali & Deininger (2014) revisit the IR issue and examine its potential causes in Rwandan data where policy makers consider land fragmentation and small farm sizes to be key bottlenecks for the growth of the agricultural sector. They find that the inverse relationship continues to hold if profits with family labor valued at shadow wages are used, but disappears if family labor is rather valued at village-level market wage rates. Their findings imply that, in Rwanda, labor market imperfections, rather than other unobserved factors, seem to be a key reason for the inverse farm size-productivity relationship. Kimhi (2006) is the only notable IR study we are aware of on Zambia. When considering plot size of maize as exogenous, Kimhi finds a monotonic positive relationship between yield of maize and plot size but they 2

find a U-shaped relationship when they correct for endogeneity of plot size. The study suggests that market imperfections should be targeted by any policy aimed at increasing maize productivity in Zambia. One important thing to note is that the study uses data from the crop year of 1993 – 1994. The crop year corresponds to a period when Zambia’s economy was undergoing major structural changes during which free market policies were becoming entrenched and government’s involvement in input and output markets had significantly reduced. Also, the study uses yield as the only measure of productivity and addresses the research question using data with 86 percent of the sampled households having farm sizes under 3 hectares. With recent changes in farm structure, a burgeoning agribusiness sector, and reintroduction of government input subsidies and maize output price support, our study brings contemporary insights to the IR debate in Zambia. Similar to previous studies, we assess the relationship between farm size and productivity and control for other factors that drive productivity. Our study uses a dataset that includes 2

The U-shaped relationship is because the paper finds that the inverse relationship dominates the economies of scale in all plots up to three hectares while economies of scale in maize become operative above the three-hectare threshold.

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both small- and medium-scale farming households across a wider range of farm sizes and uses different measures of productivity to explore the IR hypothesis. 3.0

Data and Methods

3.1

Description of the Data

The study uses two main sources of household survey data collected in Zambia. The first source of data is the Agricultural Commercialization Survey (ACS) of emergent farming households in Zambia conducted in 2013. The Indaba Agricultural Policy Research Institute (IAPRI) of Zambia conducted the survey for this primary source of data. Medium-scale farming households in this study were defined as farmers owning land between 5 and 100 hectares. The survey was conducted in six administrative districts of Zambia out of 72 districts: Chibombo, Choma, Chongwe, Kalomo, Mpongwe and Mumbwa (see Appendix 1 for the map). The aforementioned districts were purposively selected based on the concentration and number of farmers owning over five hectares of land. Using the nationally representative Rural Agricultural Livelihoods Survey (RALS) of 2012, districts with at least three percent of all farmers owning over five hectares, were purposively selected. The proportion of medium-scale farming households was 27 percent, 22 percent, 20 percent, 17 percent, 12 percent and 5 percent for Mumbwa, Kalomo, Choma, Chibombo, Mpongwe, and, Chongwe respectively. The main objective of the ACS was to understand the characteristics, behavior, land use patterns and outputs of medium-scale farmers who are a growing category in Zambia. Farms between 5 and 100 hectares now account for more than half of the total area owned among farms less than 100 hectares in Zambia (Jayne et al., 2014). The survey instrument captured information according to the following themes: demographic information, family history and settlement; employment record and off-farm income sources; land ownership, land markets and future plans; land use and crop management; draft power use and costs; hired labor and costs; sales and marketing from own production; endowments and assets, and; livestock and poultry management. A total of 482 households were randomly selected from a list of emergent farming households generated in consultation with the Zambia National Farmers’ Union (ZNFU) and the Ministry of Agriculture and Livestock (MAL) district offices (see Table 2 for breakdown by district). The Ministry of Agriculture and Livestock (MAL) block areas were identified as the sampling units with help from local district offices. Whereas the sampling procedure was supposed to ensure reasonable representativeness of farmers in the 5-100 hectare category within the selected districts, the sample may have not been statistically representative of all medium-scale farmers in Zambia. This is because medium-scale farmers were not

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sampled from the other 65 districts. But we can say that the chosen districts are understood to contain the highest proportions of farms in this size class. We augment the ACS data with a second source of data called the Rural Agricultural Livelihoods Survey (RALS) of small- and medium-scale farming households in Zambia conducted in 2012.3 The RALS was implemented by IAPRI in collaboration with the Central Statistical Office (CSO) of Zambia and the Ministry of Agriculture and Livestock (MAL). The purpose of this survey was to provide policy relevant information that is not practical to collect annually from the government agricultural surveys. The survey collected data on the following main themes: demographic characteristics of household members; farmland and use; crop sales from own production; input and credit acquisition; livestock ownership and marketing; off-farm income sources; food security indicators, and; other themes such as kinship ties of the household head. While the RALS is a nationwide survey, we restrict our analysis in this paper to the six districts where the ACS was conducted (see Appendix 2 for the location of households interviewed during the two surveys). Therefore, the number of households in the sub-sample from the RALS is 1000 households bringing the total number of households in our pooled sample to 1482 (see Table 2 for the breakdown of the sample by district). For the analysis in this study, we focus on 1429 households because 53 households either reported that they did not cultivate/plant any part of their land or had missing values on some of the key variables necessary for computing the measures of productivity. [TABLE 2 ABOUT HERE] Both surveys captured the Geographical Positioning System (GPS) coordinates of surveyed households. This made it possible to generate Geographical Information Systems (GIS) for land and land quality variables included in our analysis.4 While these variables are deserving of caution as they are coarse estimates and may not correspond to local conditions, they are generally good proxies for dealing with the omitted variable problem prevalent in such studies. The data on soil were collected from the Harmonized World Soil Database v 1.2 (Nachtergaele & Batjes, 2012). In this study, we extracted data on soil nutrient availability that combines soil characteristics such as soil texture, soil organic carbon, soil pH and total exchangeable bases. We were able to also extract data for the length of the growing period (LGP) from the GIS data – LGP combines information on temperature and available moisture to determine the length of time for adequate crop growth (Fischer et al., 2000). Elevation and slope variables were extracted from

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Please note that the RALS includes both small- and medium-scale farms up to 20 hectares of land while the ACS has medium-scale farms between 5 and 100 hectares. 4 We would like to thank Jordan Chamberlin for extracting all the GIS data used in this study.

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the Shuttle Radar Topography Mission (SRTM) data.5 Finally, the extracted rainfall data is a time-series of dekadal estimates collected from 1983 to 2013.6 Using these data, we defined rainfall as the total amount of estimated rainfall, in millimeters, received during the crop production season for each survey. 3.2

Empirical Framework and Estimation Strategy

The empirical framework we use is similar to the standard model used in numerous studies discussed in previous sections for testing the existence of the IR. We estimate the following relationship at the household level using Ordinary Least Squares (OLS) regression: 𝒀𝒊 = 𝛽1 + 𝛽2 𝐴𝑖 + 𝒁𝒊 𝜷𝟑 + 𝑿𝒊 𝜷𝟒 + 𝜀𝑖

(1)

where 𝒀𝒊 represents a vector of measures of productivity for each household i, 𝐴𝑖 is the operated farm size at household level, 𝒁𝒊 is a vector of exogenous variables such as household head characteristics, land and soil conditions and district fixed effects, 𝑿𝒊 denotes a vector of crop management practices that influence crop production, the 𝛽′𝑠 are the parameter estimates, and; 𝜀𝑖 is the error term. Table 3 lists and defines all the variables used in the estimation for the models specified in this study. [TABLE 3 ABOUT HERE] The key difference between our paper and previous studies is in the way we construct the dependent variable, 𝒀𝒊 . The dependent variable is defined using four distinct measures of productivity: (1) net value of crop production per hectare planted (land productivity); (2) net value of crop production per family labor day (labor productivity); (3) cost of production of maize per metric ton produced (cost efficiency), and; (4) Total Factor Productivity. Valuation of input costs and output values is in Zambian Kwacha based on 2011/2012 agricultural season prices.7 The first measure of productivity, net value of crop production per hectare planted (𝑌1 ), is computed as follows:

𝑌1𝑖 =

∑ 𝐺𝑉1𝑖𝑗 −∑ 𝑉𝐶1𝑖𝑗 −∑ 𝐹𝐶1𝑖𝑗 ∑ 𝑎1𝑖𝑗

(2)

where 𝐺𝑉1𝑖𝑗 is the gross value of production, 𝑉𝐶1𝑖𝑗 is the measure of variables costs, 𝐹𝐶1𝑖𝑗 is the measure of fixed costs, 𝑎1𝑖𝑗 is the area planted to each crop and all these components are measured 5

The SRTM data are available here: http://srtm.csi.cgiar.org/ Precipitation data are available from: http://www.cgiar-csi.org/data/climate/item/104-cru-ts-31-climate-database 7 The average exchange rate prevailing at the time was US$ 1 = ZMW 5.3. 6

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across each household i and crop j. Variable costs include the opportunity cost of family labor, imputed hired labor costs, seeds, fertilizers, chemicals, and rental costs for draught power. The opportunity cost of family labor is computed by multiplying the number of prime age (15 – 59 years) household members working on each farm by the median days allocated to farming by the median daily agricultural wage rate prevailing in each district. Imputed hired labor costs are computed by multiplying the district level median daily agricultural wage rate by the number of hired labor days. Fixed costs are computed for owned agricultural-related assets used during the production season captured by the survey data. To compute fixed costs, we use the rental rate for assets with an active rental market. For example, if a household owns a tractor and uses it for land preparation, the tractor fixed cost is the land preparation rental rate per hectare multiplied by the number of hectares cultivated. If the household used the tractor multiple times in a year, e.g., for land preparation, harvesting, etc., we valued all the uses of the tractor to get the fixed cost attributable to the tractor for each household. While the fixed cost measure is computed mainly using the rental rate approach, an alternative approach is also used for fixed assets with no rental market e.g. irrigation equipment, pumps. For the ‘no rental market’ approach, the fixed cost of an asset is computed as follows: 𝐹𝐶 = 𝑐⁄𝑛 + (𝑐 ∗ 𝑟)

(3)

where FC is the fixed cost of an asset; c is the price or cost of an asset when it is new; n is the estimated asset’s usual life, and; r is the annual straight line depreciation rate. Appendix 3 lists all the assets included in the computation of fixed costs (rental and non-rental market approach). The second measure of productivity, net value of crop production per family labor day (𝑌2 ), is computed as:

𝑌2𝑖 =

∑ 𝐺𝑉2𝑖𝑗 −∑ 𝑉𝐶2𝑖𝑗 −∑ 𝐹𝐶2𝑖𝑗 ∑ 𝐿2𝑖𝑗

(4)

where 𝐿2𝑖𝑗 is the number of days taken for crop production activities by adult family labor during the crop production season for household i and crop j. All other components are defined in a similar way as explained for the net value of crop production per hectare planted. However, please note that 𝑉𝐶2𝑖𝑗 excludes the opportunity cost of family labor. The third measure of productivity, cost of production of maize per metric ton produced (𝑌3 ), is computed as:

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𝑌3𝑖 =

∑ 𝑉𝐶3𝑖𝑀 +∑ 𝐹𝐶3𝑖𝑀 ∑ 𝑀𝑇3𝑖𝑀

(5)

where 𝑉𝐶3𝑖𝑀 measures the variables costs of maize production, 𝐹𝐶3𝑖𝑀 measures the fixed costs of maize production, 𝑀𝑇3𝑖𝑀 metric tons of maize produced and all these components are measured across each household i. Our fourth measure of productivity, Total Factor Productivity (TFP), comprehensively reflects the efficiency of the whole crop production process. Based on the approach used by Li et al. (2013), which they adapt from Fan (1991) and Zhang & Carter (1997), we use the Cobb-Douglas production function to calculate TFP using the following functional form: 𝛼𝑀 𝐺𝑉𝑖 = 𝐴0 𝑒 𝜂𝑡 𝐾𝑖𝛼𝐾 𝐿𝛼𝐿 𝑖 𝑀𝑖 exp⁡(𝜀𝑖 )

(6)

where 𝐺𝑉𝑖 is the gross value of crop production of farm i, 𝐾𝑖 , 𝐿𝑖 and 𝑀𝑖 represent the value of capital (all costs of production except imputed family labor costs), total number of labor days (hired and family labor), and land inputs (operated farm size) of farm i, respectively, 𝛼𝐾 , 𝛼𝐿 , 𝛼𝑀 are the output elasticities for capital, labor and land, correspondingly, t is the time trend term, and 𝜂 is the rate of technological progress. Using natural logarithm, equation (3) is estimated as follows: 𝑙𝑛𝐺𝑉𝑖 = 𝑙𝑛𝐴0 + 𝜂𝑡⁡ + 𝛼𝐾 𝑙𝑛𝐾𝑖 + 𝛼𝐿 𝑙𝑛𝐿𝑖 + 𝛼𝑀 𝑙𝑛𝑀𝑖 + 𝜀𝑖 ⁡

(7)

Given that this production function is estimated with cross sectional data, the time trend variable is t=1 and thus the 𝑙𝑛𝐴0 + 𝜂𝑡⁡term becomes the constant term. To get the TFP indicator, we first compute the returns to scale (RTS) coefficient, which is the sum of factor output elasticities (𝑅𝑇𝑆 = ⁡ 𝛼𝐾 + 𝛼𝐿 + 𝛼𝑀 ). ∗ We then normalize each factor’s output elasticity and obtain 𝛼𝐾∗ = 𝛼𝐾 /𝑅𝑇𝑆, 𝛼𝐿∗ = 𝛼𝐿 /𝑅𝑇𝑆, and 𝛼𝑀 =

𝛼𝑀 /𝑅𝑇𝑆 and define TFP (𝑌4 ) as:

𝑌4𝑖 =

𝐺𝑉𝑖

𝛼∗ 𝛼∗ 𝛼∗ 𝐾𝑖 𝐾 𝐿𝑖 𝐿 𝑀𝑖 𝑀

(8)

In sum, the relationships between operated farm size (𝐴𝑖 ) and the four outlined measures of productivity, conditional on control variables that potentially explain productivity differences, is the main interest of this study. For three measures of productivity -- net value of crop production per hectare planted, net value of crop production per family labor day worked and TFP -- a statistically significant negative coefficient on the operated farm size variable upholds the IR while a positive coefficient suggests otherwise. However, the interpretation of the coefficient on operated farm size when the measure of productivity is cost of maize production per metric ton is the opposite of the other three measures. With

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this measure of productivity, the IR is upheld when the coefficient on the operated farm size variable is positive while a negative coefficient would imply otherwise. Finally, our empirical strategy for establishing the relationship between farm size and alternative measures of productivity is specified in three ways. For each measure of productivity, we first estimate a bivariate regression that includes only operated farm size and its squared term as regressors. The squared term is included because we hypothesize that the farm size-productivity relationship is non-linear. Our second specification is a parsimonious or restricted regression where each productivity measure is regressed on regresssors from the first specification and additional variables such as household head characteristics, land and soil conditions, and district fixed effects. Third, we specify the full model that estimates the relationship between each measure of productivity with covariates from the second specification and crop management variables (input intensity, crop composition, etc.). The main reason for specifying the full model in addition to the parsimonious specification is that the former approach has been used in a number of past IR studies despite the prospective endogeniety of crop management practices which are choice variables for the farmers (Barrett et al., 2010; Carletto et al., 2011). The empirical strategy outlined above is important for two reasons. First, proceeding this way helps us to establish whether the farm size-productivity relationship is consistent across the four measures of productivity given the wide range of farm sizes in our data. Does the relationship depend on the measure of productivity and what does that imply in a broader policy context? Second, within each measure of productivity, do we see a switch in the sign, magnitude and level of statistical significance of the coefficient on operated farm size when we compare the parsimonious versus the full model? Is the observed farm size-productivity relationship a result of the omitted variable problem or other factors? These issues are discussed in our econometric results in section 4.2. 4.0

Results and Discussion

4.1

Descriptive Results

The descriptive results are presented by four landholding size categories: (1) five hectares and below (0 – 5 ha); (2) above five hectares to twenty hectares (5 – 20 ha); (3) above twenty hectares to fifty hectares (20 – 50 ha), and; (4) above fifty hectares to one hundred hectares (50 – 100 ha). This categorization is intended to mirror the way the Ministry of Agriculture and Livestock (MAL) in Zambia categorizes different scales of farming households, although in their case the categorization is based on area cultivated.

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Table 4 presents demographic, land and input use descriptive characteristics for the four categories of farms as well as for the full sample. The average age of household heads increases with landholding size with household heads belonging to the 50 – 100 ha category having an average age of 53.14 years and are on average older by eight, five and two years than household heads in the first, second and third categories respectively. While there is no clear pattern with respect to the number of years that the household has lived in the current settlement and how that relates to landholding size, household heads with landholding size between five and twenty hectares have on average lived the longest in the current settlement (32.94 years). This finding suggests that household heads with relatively longer years in current settlement do not necessarily have the largest landholding size. As expected, more than 80 percent of the full sample is male-headed households and only the first category (0 – 5 ha) has the proportion of male-headed households (77.41 percent) less than the full sample average. The other landholding size categories have 90 percent or more of the households headed by a male. Household heads with secondary or tertiary education have comparably large landholdings. On average, about 16 percent of household heads in the 0 – 5 ha category have secondary education or higher while 50 percent of households in the 50 – 100 ha category have similar level of education. An important aspect about the changes in farm structure currently being experienced in parts of SSA is that a significant proportion of medium scale farmers comprise landowners who have or have had a salaried job besides farming. The results indeed confirm this, with more than 30 percent of household heads with landholding size greater than 20 hectares indicating that they were previously or are currently employed in a formal job. Less than 25 percent of household heads with landholding size less than 20 hectares said that were previously or currently employed in a formal job. Similarly, the proportion of household heads involved in off farm business activities is increasing with landholding size. One of the survey questions asked the respondents to state whether they were local or non-local in their current settlement. A household head is considered local if he or she has family ties in the area and is most likely ethnically part of the people in that settlement. The enumerator manual for the RALS describes the concept of local as follows. “[A] HH head is local if he/she is CONSIDERED local. In many cases people will consider themselves as non-local if they are denied certain benefits as a result of having migrated into the area. In other cases migrants will still consider themselves as local if they feel that they have been accepted into the community and have the same basic rights as other residents” (CSO/MAL/IAPRI, 2012, p. 77). Interestingly, 40 percent or less of household heads with landholding size greater than 20 hectares said that they considered themselves ‘local’ in their current settlement. This result is less than the averages observed for the first and second landholding size categories of 78 and 73 percent respectively. This finding supports the hypothesis that most medium-scale farms in Zambia are

15

owned by people mostly based in urban areas or retirees who worked in the civil service (Sitko & Jayne, 2014). The average landholding size for farms in the fourth category is more than twice that for farms belonging to the third category (74.29 hectares versus 34.24 hectares), approximately seven times more than the second category (74.29 hectares versus 10.59 hectares) and more than thirty times that for the first category (74.29 hectares versus 2.31 hectares). Average operated farm size is also increasing with landholding size but one thing clear from the results is that the proportion of landholding that is operated reduces with increasing landholding size. Operated farm size is 86%, 60%, 31% and 25% of landholding size for the first, second, third and fourth categories correspondingly. On the other hand, the two other land characteristics “cleared land not cultivated” and “uncleared land” are increasing in both levels and respective proportions with increasing landholding size. Results for input use characteristics by landholding size categories illustrate some interesting patterns. The proportion of households applying basal and top dressing inorganic fertilizer is increasing in landholding size. Households in the fourth category applying basal fertilizer use twenty three-, eighteenand three- kilograms more fertilizer than households in the first, second and third categories correspondingly. For top-dressing inorganic fertilizer, the average amount of fertilizer applied per hectare by households in the fourth category is approximately eighteen-, fourteen- and one- kilogram(s) more than households in the first, second and third categories respectively. In general, the average application rates for both basal and top dressing fertilizer for all landholding size categories, are lower than the nationally recommended fertilizer application rates of 200 kg/ha for each type of fertilizer. The number of crops grown is increasing with landholding size suggesting that households with larger farms are diversifying their crop production portfolio relative to the smaller farms. The main activities carried out by family and hired labor which we account for when computing labor days per hectare are land preparation, planting, fertilizer application, weeding and harvesting. On average, about 100 family labor days per hectare and six hired labor days per hectare are spent to perform the aforementioned tasks when the full sample is considered. Larger farms tend to use more of animal draught power and less of manual draught power. Use of mechanical draught power is relatively low although the proportion of households in the third and fourth categories using this source of draught power is higher than the first and second categories. Both herbicide and insecticide use show a positive relationship between the proportion of households using the two productivity enhancing technologies and landholding size. [TABLE 4 ABOUT HERE]

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Table 5 presents findings for crop production characteristics of five main crop categories by landholding size categories. The table focuses on four main aspects: (1) proportion of households planting each crop category; (2) land allocation to main crop categories; (3) gross value per hectare of main crop categories, and; (4) contribution of main crop categories to total gross value of crops produced. The five crop categories analyzed in this study include: (1) maize; (2) beans and oilseeds (groundnuts, soya beans, mixed beans, bambara nuts, cowpeas, velvet beans); (3) other cereals (sorghum, rice, millet, popcorn); (4) traditional cash crops (seed cotton, tobacco, coffee, sugarcane), and; (5) roots and tubers (sweet potatoes, potatoes, cassava). More than 98 percent of all the households plant maize while 66.48 percent plant beans and oilseeds. Traditional cash crops and roots and tubers are planted by slightly over 20 percent of the households and less than five percent of the households plant other cereals. About 70 percent of the area planted by the sample households is under maize production, which demonstrates its dominance in Zambia. Households in the first category allocate 71.65 percent of their land to maize production, which is more than three percent higher than the area allocated to maize by households in the other three categories. Beans and oilseeds are a distant second in terms of the amount of land allocated with the average land allocated to this category of crops for the full sample at 13.24 percent. Traditional cash crops get the third highest allocation (10.38 percent) in terms of area planted while about three percent of area planted is with roots and tubers. The crop category that has the least amount of land allocated for its production is other cereals, which is less than one percent of area planted. The gross value of crop production per hectare produced is highest for maize followed by traditional cash crops, and thereafter roots and tubers. Beans and oilseeds, and other cereals have the least gross value per hectare respectively. Three main patterns emerge with respect to gross value per hectare of main crop categories when analyzed across landholding size categories. The first pattern shows that the gross value per hectare increases with landholding size like in the case of maize. The second pattern emerging is that gross value per hectare reduces as one moves from the first through to the third category but increases from the third to the fourth category. The crop categories that exhibit this U-shaped pattern are other cereals and roots and tubers. The third pattern exhibited by beans and oilseeds and traditional cash crops shows that gross value per hectare oscillates as one moves from one landholding size category to the next. Maize contributes about 75.66 percent to gross value of crop production followed by traditional cash crops at 14.57 percent and thirdly by beans and oilseeds at 10.09 percent. Roots and tubers and other cereals contribute a combined total of approximately five percent to gross value of crop production. The

17

contribution of maize and traditional cash crops to gross crop value increases while the other crop categories fluctuate across landholding size categories. [TABLE 5 ABOUT HERE] Table 6 reports crop production costs and four indicators of productivity by landholding size categories. In our study, we account for seven individual cost items that build up the cost of crop production across farms in Zambia. The cost items include land rental, hired animal and machine use, hired labor, seed, fertilizer, family labor and fixed costs. Total production cost per hectare planted increases across landholding size categories, which provides the first indication that small farms are, on average, cost efficient relative to large farms in Zambia. On average, households in the third category incur crop production costs that are 80 and 35 percent more than those in the first and second categories correspondingly. This pattern is evident for most cost components except for hired animal and machine use, and seed. Our study also focuses the analysis on Zambia’s main staple, maize, and we find that the cost of producing maize per hectare increases across landholding size categories. The net value of crop production per hectare planted and the total factor productivity average values do not show a clear pattern across landholding size categories. On the other hand, the net value of production per family labor day results show a monotonic positive relationship across landholding size categories. This implies that large farms are more productive than small farms when the measure of productivity under consideration is family labor productivity. The cost of maize production per metric ton increases across landholding size categories. Put another way, smaller farmers are cost efficient compared to larger farmers when it comes to maize production. [TABLE 6 ABOUT HERE] To conclude the descriptive findings section, we discuss the graphs (Figure 1) that show changes in factor input ratios across landholding size. The factor input ratios considered are capital-labor, capital-land, labor-land and labor-capital ratios. The components of these ratios are defined as follows. Capital is the sum of all costs of production excluding imputed family labor costs; labor is the number of prime age members, between 15 and 59 years, living and participating in farming activities in a given household, and; land is the operated farm size. Both capital-labor and capital-land ratios exhibit a positive relationship while the labor-land labor-capital ratio have a negative relationship when graphed against landholding size. Two main observations are made from these graphs. First, farms become more capitalintensive as landholding size increases. Second, farms become more land using/labor saving as farm size

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increases, but particularly in the range of 1-10 hectares – there is a lot of substitution of factor inputs within this range, but not so much after 10 hectares. [FIGURE 1 ABOUT HERE] 4.2

Econometric Results

Before delving into the econometric findings, we discuss the non-parametric locally weighted scatterplot smoothing estimator (lowess) graphs in Figure 2. The figure depicts four panels with the graphs showing the relationship between operated farm size and all the four productivity measures (see Appendix 5 for graphs showing the relationship between landholding size and productivity measures). For each measure of productivity, three curves are generated to represent the bivariate, restricted and full model specifications. The bivariate curve depicts the relationship between operated farm size and actual values of each productivity measure while both the restricted and full model curves depict the ceteris paribus relationship by graphing operated farm size against predicted values of productivity measures extracted from the relevant regression analysis. The top left panel shows a weakly positive relationship between operated farm size and the net value of crop production per hectare planted which reaches a maximum at around 20 – 25 hectares and declines thereafter. The top right panel shows the relationship between operated farm size and the value of crop production per family labor day. The graph illustrates that labor productivity is an increasing function of operated farm size and peaks at approximately 30 hectares. From 30 – 60 hectares, family labor productivity becomes a decreasing function of operated farm size. The relationship between maize area planted and the cost of producing one metric ton of maize is shown in the bottom left panel. As illustrated by the descriptive findings, the relationship is strongly positive up to 10 – 15 hectares but is negative for the rest of the maize area planted range. The TFP, captured in the bottom right panel, exhibits a monotonic but weakly negative relationship between operated farm size and the TFP indicator. Although the three curves are similar in all the four panels, the bivariate and restricted specifications are much more alike. This is expected because unlike the bivariate and restricted models, we control for crop management practices in the full model, which might cause minor deviations in the curves of the latter specification. Appendix 6 shows the correlation between operated farm size and other regressor variables used in our regression analysis as a first step to identifying potential reasons for why productivity differences might exist between small and relatively large farms. We note that there are a number of production technology related variables that are accounting for the differences between the bivariate and the restricted models, and the full model specification.

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[FIGURE 2 ABOUT HERE] Next, the econometric findings are discussed. Table 7 and 8 present estimates of the OLS regression analysis exploring the operated farm size-productivity relationship using four measures of productivity. For each measure of productivity, we report results for three model specifications: bivariate, parsimonious and full regressions. The measures of productivity have undergone logarithmic transformation using Inverse Hyperbolic Sine (IHS) transformation (Burbidge, Magee, & Robb, 1988) defined as: 1

sinh−1 𝑌𝑖 = log[𝑌𝑖 + (𝑌𝑖2 + 1)2 ]

(9)

where 𝑌𝑖 is the dependent variable (measure of productivity). This transformation is a standard solution for implementing logarithmic transformation when we have a dependent variable with extreme values as well as instances when the variable takes zero and negative values. We first focus on the estimates for net value of crop production per hectare planted presented in Table 7 (column 1 to 3). The results for all three specifications suggest a positive but insignificant relationship between operated farm size and the net value of crop output per hectare planted. The interpretation of these results is that while our data point to the fact that the IR is not upheld when the measure of productivity is net value of crop production per hectare planted, the alternative hypothesis that relatively large farms are more productive than small farms in Zambia is not supported. Muyanga & Jayne (forthcoming), in contrast, have found evidence that supports medium-scale farmers’ relative efficiency in terms of land productivity. In the present study, however, a number of other factors are associated with land productivity differences across farm sizes. According to the restricted specification results in column 2, a switch from female- to male-headed households is likely to increase land productivity by 59.7 percent. Our results also show that when we control for the household heads’ employment in a formal job, net value of crop production per hectare reduces by 39.3 percent. As expected, the length of growing period variable shows a positive association with our land productivity measure. We also find evidence that when farms are located on soils with somewhat severe constraints in terms of soil nutrient availability (Soil texture, soil organic carbon, soil pH, total exchangeable bases), this is negatively associated with our first measure of productivity. In column 3, we report estimates for the full model and find that all the significant variables remain relatively stable i.e. coefficients are similar in terms of magnitude and sign when compared with the parsimonious specification. In addition, increasing the share of land planted to beans and oilseeds, traditional cash crops, and roots and tubers has a positive effect on land productivity while a percent increase in other cereals is negatively associated with our measure of land productivity.

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The estimates for net value of crop production per family labor day are presented in columns 4, 5 and 6 of Table 7. The results show that there is a positive and significant relationship between operated farm size and our labor productivity measure in all three specifications. The estimated coefficients indicate that a one-hectare increase in the operated farm size increases the net value of crop production per family labor day by 38.6, 37.8 and 39.1 percent for the bivariate, parsimonious and full specifications correspondingly. When we compare the parsimonious with the full specification, the coefficient on operated farm size not only differs by barely 1.3 percent but also remains positive and significant. Our findings, in general, imply that the returns to labor are higher on large farms relative to small farms. These results imply that the IR does not hold when the measure of productivity is net value of crop production per family labor day. The square of operated farm size variable suggests that there is a significant non-linear relationship between operated farm size and labor productivity as shown by the negative and significant coefficient, in all three specifications, on the variable operated farm size squared. The point of inflection at which the relationship reaches its maximum happens at 27.57, 31.50 and 32.58 hectares for the bivariate, parsimonious and full specifications respectively. This suggests that labor productivity is an increasing function of operated farm size from zero to approximately thirty hectares, after which the relationship diminishes or is reversed beyond this operated farm size range. The parsimonious regression results for our labor productivity measure (column 5) suggest that there are a number of other factors that are associated with labor productivity. When we control for the gender of household heads, a change from female to male-headed households is associated with a 40 percent increase in labor productivity. Education is also an important explanatory variable in the labor productivity regression as evidenced by the positive and significant coefficients on the variables secondary education and tertiary education (base category is household heads with primary education). Similar to the net value of crop production per hectare planted, we find that length of growing period has a positive effect while formal employment and severely constrained soils are negatively associated with net value of crop production per family labor day. In addition, we also find that a switch from non-local household heads to those considered local, is likely to be associated with a 39.8 percent productivity increase and that rainfall is positively associated with labor productivity. Other than the education variable that is significant in the parsimonious but is not in the full specification for the labor productivity measure, the results remain relatively the same in terms of coefficient signs and levels of significance across the two specifications. The inclusion of crop management practices indicates that the share of land planted to maize, beans and oilseeds, traditional cash crops, and roots and tubers have a positive and significant effect on net value of crop production per family labor day. Increasing

21

family labor days worked per hectare by one extra day has a negative and significant effect while increasing hired labor days per hectare by an extra day has a positive and significant effect on our returns to labor measure. As expected, our results also suggest that the dummy variables mechanical draught power use and insecticide use have a positive and statistically significant effect on labor productivity. [TABLE 7 ABOUT HERE] The third measure of productivity analyzed is the cost of maize production per metric ton produced reported in Table 8 (columns 1 – 3). Estimates for all three specifications are found to be positive and statistically significant. The estimated coefficient on operated farm size reduces as one moves across specifications from the bivariate through to the full specification. The difference in the magnitude of the coefficient for operated farm size in the parsimonious and full model specification is 3 percent. Based on our explanation of how to interpret the estimates for our third measure of productivity, as outlined in section 3.2, the results uphold the IR in the case of the cost of maize production per metric ton produced. Therefore, this implies that small farms are cost efficient relative to large farms in terms of producing Zambia’s staple crop. The negative and significant coefficient on the operated farm size squared variable suggests a non-linear relationship between operated farm size and our third measure of productivity. The point of inflection at which the relationship reaches a maximum corresponds to the operated farm sizes at 13.83, 12.83 and 11.75 hectares for the bivariate, parsimonious and full specifications respectively. These results suggest that the cost of maize production per ton increases with operated farm size from zero to approximately 12 - 14 hectares, after which the cost advantage of small farms diminishes or is reversed beyond this range of operated farm size. According to the parsimonious regression estimates (column 2), factors that are positively associated with the cost of maize production per metric ton include the household head’s number of years in current settlement, whether he or she had a formal job, whether the farm is located on moderately constrained soils, and severely constrained soils. On the other hand, the household head attaining tertiary education, being considered local, length of growing period, and rainfall are factors that are negatively associated with the cost of maize production per metric ton produced. Results for the full specification (column 3) are comparable to the parsimonious specification i.e. they are similar in magnitude, signs and levels of significance of the estimated coefficients. The full model further shows that the top dressing fertilizer, share of maize area, share of beans and oilseeds area, share of traditional cash crops area variables are negatively associated with cost of maize production per metric

22

ton produced. An increase in the number of days per hectare for both family and hired labor are, on the other hand, positively associated with our third measure. To fully capture the comprehensive use of different inputs during the crop production process, we estimated the relationship between operated farm size and our fourth measure of productivity, TFP (Table 8, column 4 – 6). The results for all three specifications show a negative but insignificant relationship between operated farm size and TFP.8 These results fail to uphold the IR when the measure of productivity is TFP and leads to our conclusion that there is no adequate evidence to support the argument that small farms have a superior production efficiency relative to large farms. This finding is similar to that observed in China by (Li et al., 2013) where they found that while the relationship between their land size measurement and TFP was negative, it was not statistically negative. Without going through the details of similarities or differences between the parsimonious and full specifications, the pattern is similar to that observed for the other measures of productivity, in particular the signs and levels of significance of the coefficients on the explanatory variables. One concern about our study is that we used two surveys that differ by one year with potentially different rainfall patterns. We accounted for this by including a dummy variable Agricultural Commercialization Survey (1=yes). We found that the difference in the survey year did not have a significant effect on the net value of crop production per hectare and the net value of crop production per family labor day. However, the results indicate that the difference in survey year had an effect on the other two measures of productivity as shown by the significant coefficient on the survey variable at one percent confidence level (Table 8). Nevertheless, we have a degree of confidence in our overall results because they partially suggest that the difference in survey year has no effect on the relationship we are interested to explore in this paper. [TABLE 8 ABOUT HERE] 5.0

Conclusions and Implications for Policy

The interest by development scholars to revisit the IR hypothesis is mainly driven by the need to guide policy on whether smallholder-led agriculture remains a viable pathway to achieve the much-needed changes in the economic fortunes for the majority of SSA. Nevertheless, it is interesting to note that few studies have been comprehensive in terms of using alternative measures of productivity other than land productivity, to explore the relationship between farm size and productivity. Moreover, as observed by 8

Cobb-Douglas production function estimates used to compute TFP at household level are in Appendix 4.

23

Collier & Dercon (2014) and demonstrated by our review of past empirical literature, a critical number of studies conducted in Africa have on one hand included very few farms outside the zero to ten hectare range while on the other hand have extrapolated their findings beyond this farm size range. The current study addressed these gaps in two specific ways. First, using data from two household surveys in six districts of Zambia, the study included small- and medium- scale farms with landholding size between 0 and 100 hectares and operated farm size ranging between 0 and 60 hectares. Second, the paper examined the relationship between farm size and productivity using four alternative measures of productivity: net value of crop production per hectare planted; net value of crop production per family labor day; cost of maize production per metric ton produced, and; Total Factor Productivity. With these carefully constructed productivity measures and a wider range of farm sizes, the analysis controlled for household-specific heterogeneity to explore the reasons for potential differences in productivity within and between farm-size categories, so as to provide practical guidance for formulation of relevant policies. The key findings that emerged from this study were the following. First, based on descriptive analysis, we found evidence that the proportion of households using productivity enhancing inputs such as inorganic fertilizers, pesticides and insecticides increased across landholding size. Second, we found that input intensity use for inputs where data on application rates were available increased with landholding size. For example, households in the fourth category of the landholding size distribution generated, applied an average amount of basal fertilizer which was twenty three-, eighteen- and three- kilograms more than households in the first, second and third categories correspondingly. This finding is contrary to other studies that have upheld the IR were input intensity use has been found to be negatively associated with farm size (Ali & Deininger, 2014). Third, we found that the pattern emerging with respect to the average number of labor days spent by family labor was different from what has been observed in a number of IR related studies. Past studies have shown that small farmers use family labor more intensively than large farmers and hence the number of family labor days employed for farm activities per unit area of land being negatively correlated with farm size (ibid). In this study, we found that farms in the 0 – 5 hectare landholding size range used approximately 80 days/hectare for farming activities compared to between 116 – 122 days per hectare employed by the top three categories. Perhaps not surprisingly, our fourth key finding was that the total cost of crop production per hectare increased across landholding size categories, which provides the first indication that small farms are, on average, cost efficient relative to large farms in Zambia. The fifth finding drawn from our econometric results was that the relationship between operated farm size and productivity is not uniform across the four measures of productivity used in our study i.e. our

24

relationship of interest was either uncorrelated, positively related or showed an inverse relationship. When we used net value of crop production per hectare (TFP) as our dependent variable, we found a positive (negative) but not significant farm size-productivity relationship. These results suggest that there is no strong evidence to uphold the IR hypothesis in the Zambian case when land productivity or TFP is the measure being considered. An important aspect of why the IR has been observed in past studies is related to the intensity of use of inputs, which has been found to be higher on small farms relative to large farms. As already explained above, the evidence from this study suggests that input use intensity is higher on relatively larger farms. This could probably explain why the IR is not upheld when the measure of productivity is either net value of crop production per hectare or TFP. When the outcome variable was net value of crop production per family labor day (labor productivity), we found a strong positive relationship between farm size and labor productivity similar to (Li et al., 2013). In the case of cost of maize production per metric ton produced, we found that the measure increased with operated farm size implying that small farms were more cost efficient (and therefore productive) relative to large farms. The upholding of the IR with respect to maize cost efficiency could be attributed to two main reasons. First, small sized farms are by nature subsistent farmers and their crop production focus is mainly on staple food crops like maize. Because small farms have low production costs accompanied by comparable maize yields, small sized farms are more cost efficient relative to farms at the top end of the farm size distribution. Second, the result could have been due to our analysis failing to account for some costs arising from market imperfections. Kimhi (2006) made the same argument of market imperfections as the possible reason for the existence of an inverse relationship between farm size and productivity in the study of maize productivity in Zambia. Overall, we glean the following insights from our findings. It is important that research that looks at relative productivity across farm sizes should extend beyond land productivity to include other measures of productivity and a wide range of farm sizes. As shown in this study, results emanating from using a more comprehensive set of productivity measures are not exactly identical. Our approach helps us to get a clear picture that shows that while larger farmers are productive in terms of labor productivity associated with aggregate crop production on farm, small farms are more cost efficient when it comes to maize production in Zambia. What do these findings imply especially at the time when smallholder-led agricultural growth strategies have been questioned? In truth, findings on the relationship between productivity and operated farm size, while important, should not be the decisive factor in guiding agricultural development and land policies in SSA because there are many other important considerations. The challenges of rural poverty that continue

25

to bedevil sub Saharan Africa are better addressed by pursuing broad based development strategies whose central focus should remain smallholder farmers. This entails promoting policies that would enhance productivity growth among smallholders, as this is crucial to poverty reduction and development. Moreover, an inclusive smallholder form of agricultural growth will clearly generate employment growth in both farm and non-farm sectors than a comparable rate of agricultural growth concentrated among a few large farms. This is very clear from the factor-intensity graphs in Figure 1 showing how labor-land and labor-capital intensities fall dramatically as farm size increases beyond five hectares. As suggested by Jayne et al. (2014, p48), “the employment effects and growth multipliers resulting from broadly based agricultural growth are likely to contribute much more to economic growth and poverty reduction”. Pioneering work by Mellor & Johnston (1984) contrasting employment effects from smallholder Asia versus Latifundia Latin America as well as more recent work (Christiaensen et al., 2011) show that inclusive forms of agricultural growth generate much greater growth and employment multipliers than agricultural growth concentrated among relatively few large farms. However, the challenges of achieving broad-based inclusive forms of agricultural growth remain daunting. While migration from farm to non-farm sectors, and from rural to urban areas will provide the brightest prospects for the transformation and modernization of Africa’s economies, it will happen only as fast as educational advances and growth in the non-farm job opportunities will allow. The rate of growth of nonfarm jobs in turn depends on the rate of income growth among the millions of families still engaged in smallholder agriculture. So there is a symbiotic relationship between inclusive agricultural growth, nonfarm growth, and poverty reduction.

26

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Table 1: Productivity Measures and Farm Sizes in Selected Past IR Studies Author

Measure of productivity

Carter (1984) Heltberg (1998)

Land productivity Land productivity

Dorward (1999)af Lamb (2003) Assunção & Braido (2007) Kimhi (2006)af Barrett et al. (2010)af Carletto et al. (2011)af Larson et al. (2012)af

Land productivity Land productivity Labor productivity Land productivity Land productivity Land productivity Land productivity Land productivity

Holden & Fisher (2013)af Verschelde et al. (2013)af

Land productivity Land productivity

Li et al. (2013)

Land productivity Labor productivity

Ali & Deininger (2014)af

Total factor productivity Technical efficiency Land productivity

How did they compute the measure of productivity?

Log of total annual farm output per hectare Net value of total farm output per operated holding size Net value of output per area planted Log of household profits Log total hours by gender Log output per acre Yield of maize Yield of rice Net agricultural revenues per area operated Yield of maize (Kenya) Yield of maize (Malawi) Yield of maize (Tanzania) Yield of maize (Uganda) Net agricultural return per unit area Net value of agricultural output per unit of land Value per unit area Value/working days of the labor or value/number of farm’s labor force Ratio of total output to total input Stochastic frontier analysis Logarithm of the value of crop output per hectare

Source: Authors’ own compilation from previous IR studies Notes: af = Studies conducted in an African country

30

Mean operated farm size (Hectares)

Operated farm size range (Hectares)

5.74 3.64

0 – 12 0 – 16

% of sampled households within the operated farm size range 67 100

1.12 3.58

0–2 0 – 40

85 100

5.30 1.78 0.16 0.91 1.74 0.95 2.24 2.01 0.34 1.1

0 – 34 0 - 10 0 – 1.5 0-9

~100 ~100 ~100 90

0–5 0-5

~100 > 90

0.38

0–7

100

0.37

0-2

~100

Table 2: Sample Size by District Number of respondents per household ACS RALS 108 200 61 160 42 160 39 200 117 120 115 160 482 1000

District Chibombo Choma Chongwe Kalomo Mpongwe Mumbwa Total

Total 308 221 202 239 237 275 1482

Source: ACS (2013) and RALS (2012)

Table 3: Variable Explanation Name Production costs Variable input costs: Land rental Hired animal and machine use

Fertilizer Seed Opportunity cost of family labor

Imputed hired labor Fixed costs

Productivity measures Net value of crop production per hectare Net value of crop production per family labor day Cost of maize production per metric ton

Description

Computed by multiplying the number of hectares rented by the district median land rental rate (2010/11 prices) Computed for main crop production activities where hired animals or machines were used. The main crop production activities include land preparation, planting, fertilizer application, weeding and harvesting. Multiplied each field area by 2010/11-district median cost per hectare for each activity and finally aggregated to household level. Computed amount of fertilizer used in each field and multiplied by total price to the farm gate Computed amount of seed used for each crop in each field and multiplied that by price to the farm gate Opportunity cost of family labor computed by multiplying three variables: (i) the number of prime age (15 – 59 years) household members working on each farm; (ii) family labor days allocated to crop production activities farming activities, and; (iii) district median daily agricultural wage rate. Hired labor costs computed by multiplying the district median daily agricultural wage rate by the number of hired labor days. The rental rate for assets with an active rental market was used to compute costs for fixed assets used in the production process. For example, if a household owned a tractor and used it for land preparation, the tractor fixed cost was the land preparation rental rate per hectare multiplied by the number of hectares cultivated. If the household used the tractor multiple times in a year, e.g., for land preparation, weeding, harvesting, etc., we valued all the uses of the tractor to get the fixed cost attributable to the tractor. Examples of other assets accounted for include: animal traction plows, tractor plows, oxen, planters, sprayers, carts and shellers.

Value of crop production net of variable input and fixed costs divided by the operated farm size (Kwacha/hectare) Value of crop production net of variable input (excluding opportunity cost of family labor) and fixed costs divided by the number of days taken for crop production activities by family labor (Kwacha/day) Sum of variable input costs and fixed costs divided by the number of tons of maize produced (Kwacha/metric ton)

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Table 3 Continued Name Productivity measures continued Total factor productivity indicator

Description

Value of crop production (𝑌𝑖 ) divided by the product of three factors of production: value of capital (𝐾𝑖 ), total number of labor days (𝐿𝑖 ) family and hired labor, and the total amount of land used for crop production (𝑀𝑖 ). Each factor was raised to the power of the normalized ∗ factor output elasticities (𝛼𝐾∗ , 𝛼𝐿∗ , 𝛼𝑀 ): =

Land measures Operated farm size (ha) Landholding size (ha) Fallow land (ha) Crop management practices Basal fertilizer per hectare Top dressing per hectare Maize Beans and oilseeds Other cereals Traditional cash crops Roots and tubers Family labor days per hectare Hired labor days per hectare Manual Animal Mechanical Herbicide Insecticide Land and soil characteristics Length of growing period Elevation Slope Rainfall Soil nutrient availability

Household head characteristics Male Age Household head education

𝑌𝑖 ∗ 𝛼∗ 𝛼𝐾 𝛼∗ 𝐾𝑖 𝐿𝑖 𝐿 𝑀𝑖 𝑀

Total area planted to crops during the reference year. Sum of uncultivated land (cleared and not cleared) and operated farm size during the reference year Cleared land not planted during the reference year

Amount of compound fertilizer (NPK) applied in kilograms per hectare planted (kg/ha) Amount of Nitrogen fertilizer applied in kilograms per hectare planted (kg/ha) Share of area planted with maize (%) Share of area planted with beans and oilseeds (%) Share of area planted with other cereals (%) Share of area planted with traditional cash crops (%) Share of area planted with roots and tubers (%) Imputed number of family labor days by prime age family members per hectare (days/ha) Imputed number of hired labor days per hectare (days/ha) 1 = used manual draught power 1 = used animal draught power 1 = used mechanical draught power 1 = used herbicide for weed control 1 = used insecticide for pest control

Number of months when moisture conditions are adequate for plant growth Meters above sea level Measure of steepness (degrees) Rainfall in millimeters received during the reference year Soil texture, soil organic carbon, soil pH, total exchangeable bases classified as: 1=No or slight constraints; 2=Moderate constraints; 3=severe constraints

1 = male head of household Age of household head (years) Level of education completed by the household head classified as: 1 = No formal education; 2 = basic education (Grade 1-9); 3 = high school education (Grade 10-12); 4 = tertiary education (higher education qualification)

32

Table 3 Continued Name Household head characteristics continued Employment Local Business Settlement Other variables Survey District fixed effects

Description

1 = Household head currently of previously involved in salaried employment 1 = Household head considered a local 1 = Household head involved in off farm business activities Number of years the head has lived in current settlement

1=Agricultural Commercialization Survey Unobserved effects captured by the six district dummy variables for our survey data

.

33

Table 4: Demographic, Land, and Input Use Characteristics by Landholding Size Categories Full 5 ha and Above 5 Above 20 Above 50 Variables sample below to 20 ha to 50 ha to 100 ha Means and percentages Farmer characteristics Age of household head Household head years in current settlement Household settled in the current settlement within the past 10 years (% yes) Male headed households (% yes) Household head’s education attainment (% yes) No formal education Basic (Grade 1 – 9) Secondary (Grade 10-12) Tertiary Household head previously or currently employed (% yes) Household head involved in off farm business activities (% yes) Household head considered local (% yes)

47.33 28.23 19.59

45.10 24.27 26.47

48.55 32.94 13.24

51.20 29.17 14.72

53.14 31.12 6.00

84.88

77.84

91.75

91.41

90.00

4.90 73.48 16.38 5.24 25.89

6.33 77.41 11.80 4.46 23.74

4.61 73.32 18.81 3.27 23.61

1.23 64.42 23.31 11.04 39.88

0 50.00 32.00 18.00 34.00

44.93

36.55

51.63

54.60

60.00

69.77

78.27

73.13

31.90

40.00

Land characteristics Operated farm size (hectares) Operated farm size (% of total landholding) Cleared land not cultivated (hectares) Uncleared land (hectares) Total landholding size (hectares)

5.19 45.17 2.99 3.12 11.49

1.98 85.71 0.22 0.13 2.31

6.45 60.91 2.45 1.60 10.59

10.68 31.19 9.96 12.79 34.24

18.67 25.13 24.39 29.04 74.29

Input use characteristics Used basal fertilizer (% yes) Quantity of basal fertilizer (kg/ha) Used top dressing fertilizer (% yes) Quantity of top dressing fertilizer (kg/ha) Number of crops grown per holding Number of fields per holding Used family labor (% yes) Family labor days/hectare Used hired labor (% yes) Hired labor days/hectare Used manual draft power (% yes) Used animal draft power (% yes) Used mechanical draft power (% yes) Used herbicide (% yes) Used insecticide (% yes) Number of observations by landholding size

78.59 72.16 80.20 70.61 2.47 2.26 92.02 100.15 32.54 6.38 20.00 82.29 5.95 25.12 28.20 1429

66.33 67.14 68.63 66.69 2.18 2.35 88.92 79.96 18.56 3.76 32.66 73.38 3.17 8.92 17.41 695

84.48 72.21 89.44 70.27 2.73 2.51 93.67 119.87 36.85 7.31 10.94 92.71 4.61 31.29 39.54 521

95.09 87.77 96.93 84.04 2.70 1.34 98.77 116.82 65.64 12.00 1.23 88.34 18.40 63.19 38.65 163

92.00 90.51 90.00 84.90 3.06 1.42 96.00 121.09 74.00 14.88 0 78.00 18.00 62.00 26.00 50

Source: Authors’ own computation from ACS (2013) and RALS (2012)

Table 5: Crop Production Characteristics of Main Crop Categories by Landholding Size Categories Full 5 ha and Above 5 Above 20 Above 50 sample below to 20 ha to 50 ha to 100 ha Means and percentages Households planting each crop category c (% of sampled households) Maize Beans and oilseeds Other cereals Traditional cash crops Roots and tubers

98.11 66.48 3.29 27.50 20.43

96.11 56.69 2.59 17.99 26.04

100.00 75.24 2.88 39.73 17.66

100.00 73.01 4.91 31.29 8.59

100.00 90.00 12.00 20.00 10.00

19.10

26.33

11.90

15.34

6.00

Land allocation to main crop categories c (% of area planted) Maize Beans and oilseeds Other cereals Traditional cash crops Roots and tubers

69.76 13.24 0.76 10.38 3.06

71.65 13.65 0.97 8.83 4.41

67.79 12.95 0.52 13.20 2.01

68.73 11.25 0.46 9.56 1.39

67.23 16.97 1.31 5.32 0.70

Gross value per hectare for households planting main crop categories c (ZMW/ha) Maize Beans and oilseeds Other cereals Traditional cash crops Roots and tubers

2527.24 1384.32 957.87 2401.76 2305.25

2184.09 1594.01 1066.76 2457.52 2785.11

2551.49 1144.69 963.97 2505.19 1618.53

3366.58 1521.55 563.32 983.28 878.75

4122.97 1272.92 1142.00 1698.23 1564.08

75.66 10.09 0.77 14.57 4.31 1429

73.63 10.85 0.74 10.59 5.02 695

75.63 8.60 0.62 19.83 2.65 521

82.73 10.21 2.05 23.03 6.73 163

80.99 13.30 5.36 23.79 2.66 50

Households planting maize only (% of sampled households)

Contribution of main crop categories c (% of gross crop value) Maize Beans and oilseeds Other cereals Traditional cash crops Roots and tubers Number of observations by landholding size

Source: Authors’ own computation from ACS (2013) and RALS (2012) survey data c Crop category/categories: 1 = Maize; 2=beans and oilseeds (groundnuts, soya beans, mixed beans, Bambara nuts, cowpeas and velvet beans); 3=other cereal grains (sorghum, rice, millet, popcorn); 4= traditional cash crops (seed cotton, tobacco, coffee and sugarcane); 5=roots and tubers (sweet potatoes, potatoes and cassava).

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Table 6: Crop Production Costs and Productivity Measures by Landholding Size Categories Full sample

5 ha and below

Above 5 to 20 ha Means

Above 20 to 50 ha

Above 50 to 100 ha

2174.30

2074.46

2166.50

2495.53

2596.19

2.24

2.01

2.30

2.71

3.14

8.66 33.21 261.54 185.86 418.83 302.15 115.69 1325.87

10.50 45.66 103.50 202.99 364.81 256.67 65.67 1049.81

5.31 20.83 332.21 167.51 458.84 346.77 165.70 1496.90

12.34 25.91 610.30 173.30 497.34 341.77 156.71 1817.43

6.05 13.20 585.09 179.84 496.95 340.00 156.38 1778.47

1311.76

1016.49

1461.06

1872.34

1873.57

1758.81

1377.93

1988.95

2385.58

2406.14

1901.51

1447.01

2194.99

2602.00

2632.15

1266.18

1347.00

1181.79

1176.34

1315.04

964.03

1090.33

835.02

834.80

974.09

848.43

1024.66

669.60

678.09

817.71

102.29

40.21

117.43

259.79

214.08

91.33

37.81

100.21

239.00

191.55

1191.03

766.28

1381.72

2028.32

2144.33

1674.03

1128.95

1896.84

2781.59

3017.46

1804.56

1187.52

2069.47

3026.99

3295.63

259.82 270.24 249.25 Total Factor Productivity indicator Number of observations by landholding size 1429 695 521 Source: Authors’ own computation from ACS (2013) and RALS (2012) survey data

254.36 163

255.16 50

Gross value of crop production per hectare (ZMW/ha) Maize yield (MT/ha) Cost of production per hectare – all crops (ZMW/ha) Land rental Hired animal and machine use Hired labor Seed Fertilizer Family labor Fixed costs Total production costs Cost of production per hectare – maize area only (ZMW/ha) Maize production costs (excluding family labor and fixed costs) Maize production costs (excluding fixed costs only) Maize production costs (all costs included) Land productivity measures (ZMW/ha) Net value of production per hectare (excluding family labor and fixed costs) Net value of production per hectare (excluding fixed costs only) Net value of production per hectare (all costs included) Labor productivity measures (ZMW/day) Net value of production per family labor day (excluding family labor and fixed costs) Net value of production per hectare (excluding family labor costs only) Maize cost efficiency measures (ZMW/MT) Cost of production per metric ton of maize (excluding family labor and fixed costs) Cost of production per metric ton of maize (excluding fixed costs only) Cost of production per metric ton of maize (all costs included)

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Table 7: Regression estimates of the relationship between operated farm size and measures of productivity (land and labor productivity) Explanatory variables

Operated farm size Operated farm size squared Male head (1=yes) Age of household head Years in current settlement Education of household head (base category: primary education) No formal education Secondary education Tertiary education Formal employment (1=yes) Local (1=yes) Length of growing period (months) Elevation (meters) Slope (degrees) Rainfall (millimeters) Soil nutrient availability (base category: no or slight constraints) Moderate constraints (1=yes) Severe constraints (1=yes) District fixed effects Agricultural commercialization survey (1=yes) Basal fertilizer (kg/ha) Top dressing fertilizer (kg/ha)

Dependent variable Net value of crop Net value of crop production per production per hectare family labor day (ZMW/day) (ZMW/ha) (1) (2) (3) (4) (5) (6) 0.022 (1.01) -0.001 (-1.11)

0.378*** (10.77) -0.006*** (-6.12) 0.403** (2.00) -0.007 (-1.10) -0.001 (-0.20)

0.391*** (9.83) -0.006*** (-5.54) 0.558*** (2.87) 0.005 (0.87) -0.001 (-0.15)

0.343 (1.13) 0.008 (0.05) 0.130 (0.45) -0.342** (-2.34) -0.016 (-0.11) 0.567** (2.02) -0.001 (-0.79) 0.169*** (2.72) 0.001 (0.60)

0.318 (1.06) 0.362** (1.97) 0.923** (2.47) -0.694*** (-4.14) 0.398** (2.33) 1.099*** (3.24) -0.001 (-0.62) 0.207*** (2.99) 0.005** (2.49)

0.182 (0.63) 0.213 (1.26) 0.389 (1.12) -0.611*** (-3.85) 0.407** (2.56) 0.916*** (2.69) 0.000 (0.17) 0.179*** (2.69) 0.005** (2.53)

-0.121 (-0.67) -0.635*** (-3.01) Yes 1.848 (0.78) 0.003 (1.48) 0.004 (1.53)

-0.087 (-0.45) -0.557** (-2.32) Yes -1.665 (-0.65)

-0.121 (-0.71) -0.547** (-2.47) Yes 0.130 (0.05) 0.001 (0.36) 0.003 (1.21)

0.015 (0.62) -0.000 (-0.68) 0.597*** (2.85) -0.008 (-1.50) 0.001 (0.23)

0.016 (0.58) -0.000 (-0.67) 0.566*** (2.71) -0.002 (-0.43) 0.001 (0.26)

0.272 (0.86) 0.148 (0.84) 0.444 (1.49) -0.393*** (-2.64) 0.033 (0.22) 0.590** (1.99) 0.000 (0.02) 0.116* (1.95) 0.001 (0.44)

-0.114 (-0.62) -0.705*** (-3.30) Yes 1.591 (0.68)

0.386*** (12.06) -0.007*** (-6.70)

Table 7 Continued Explanatory variables

Dependent variable Net value of crop production per Net value of crop production per hectare (ZMW/ha) family labor day (ZMW/day) (1) (2) (3) (4) (5) (6)

Share of area planted with: Maize (%)

1.097 (1.54) 1.609** (1.98) -5.045*** (-2.74) 2.834*** (3.61) 2.278** (2.10) -0.001 (-1.06) -0.003 (-0.37) -0.088 (-0.37) -0.214 (-0.82) 0.424 (1.55) 0.181 (1.03) 0.024 (0.12) 6.211*** (2.67) -1382 0.135

Beans and oilseeds (%) Other cereals (%) Traditional cash crops (%) Roots and tubers (%) Family labor days per hectare (days/ha) Hired labor days per hectare (days/ha) Manual draught power (1=yes) Animal draught power (1=yes) Mechanical draught power (1=yes) Herbicide use (1=yes) Insecticide use (1=yes)

12.382*** 7.240*** 4.650*** (113.25) (3.01) (35.82) Inflection point (hectares) --27.57 Observations 1385 1382 1337 R2 0.001 0.063 0.184 Source: Authors’ computation from RALS (2012) and ACS (2013) t statistics in parentheses, significance levels as follows: * p < 0.10, ** p < 0.05, *** p < 0.01 Constant

38

-6.434** (-2.50) 31.50 1334 0.267

2.602*** (2.82) 3.714*** (3.72) 0.352 (0.25) 4.058*** (4.25) 4.175*** (3.54) -0.013*** (-11.02) 0.029*** (2.83) -0.203 (-0.87) 0.208 (0.80) 0.597* (1.86) 0.203 (1.15) 0.346* (1.76) -8.915*** (-3.29) 32.58 1334 0.389

Table 8: Regression estimates of the relationship between operated farm size and measures of productivity (maize cost efficiency and Total Factor Productivity) Explanatory variables

Operated farm size a Operated farm size squared Male head (1=yes) Age of household head Years in current settlement Education of household head (base category: primary education) No formal education Secondary education Tertiary education Formal employment (1=yes) Local (1=yes) Length of growing period (months) Elevation (meters) Slope (degrees) Rainfall (millimeters) Soil nutrient availability (base category: no or slight constraints) Moderate constraints (1=yes) Severe constraints (1=yes) District fixed effects Agricultural commercialization survey (1=yes) Basal fertilizer (kg/ha) Top dressing fertilizer (kg/ha)

Dependent variables Cost of maize production Total factor productivity indicator per ton (ZMW/MT) (1) (2) (3) (4) (5) (6) 0.095*** (6.16) -0.004*** (-4.79)

0.085*** (5.59) -0.004*** (-4.58) -0.099 (-1.54) 0.001 (0.85) 0.006*** (4.32)

0.054*** (3.40) -0.003*** (-3.44) -0.122* (-1.87) 0.001 (0.85) 0.005*** (3.25)

0.022 (0.19) 0.014 (0.24) -0.168* (-1.93) 0.221*** (4.13) -0.329*** (-5.87) -0.279*** (-3.14) 0.000 (0.53) 0.005 (0.20) -0.004*** (-5.62) 0.126** (2.14) 0.266*** (3.65) Yes 4.156*** (5.11)

-0.017 (-1.17) 0.000 (0.23)

-0.017 (-1.14) 0.000 (0.42) 0.408*** (3.26) -0.006* (-1.82) -0.007*** (-2.68)

-0.010 (-0.70) 0.000 (0.12) 0.366*** (3.09) -0.003 (-0.92) -0.005** (-2.16)

0.054 (0.50) 0.003 (0.05) -0.189** (-2.13) 0.183*** (3.44) -0.261*** (-4.60) -0.256*** (-2.88) 0.000 (0.63) 0.007 (0.27) -0.003*** (-4.92)

0.007 (0.03) 0.174* (1.65) 0.615*** (3.60) -0.467*** (-4.58) 0.415*** (4.22) 0.549*** (3.22) 0.000 (0.28) -0.017 (-0.31) 0.005*** (4.15)

0.090 (0.50) 0.045 (0.46) 0.365** (2.30) -0.381*** (-4.05) 0.299*** (3.24) 0.484*** (3.04) -0.001 (-0.81) 0.017 (0.36) 0.005*** (4.58)

0.121** (2.04) 0.231*** (3.20) Yes 3.887*** (4.81) 0.001 (1.10) -0.002** (-2.26)

-0.222** (-2.10) -0.480*** (-3.73) Yes -7.244*** (-4.55)

-0.232** (-2.37) -0.430*** (-3.60) Yes -8.185*** (-5.75) 0.000 (0.15) 0.007*** (4.91)

Table 8 Continued Explanatory variables

Dependent variables Cost of maize production per ton Total factor productivity indicator (ZMW/MT) (1) (2) (3) (4) (5) (6)

Share of area planted with: Maize (%) Beans and oilseeds (%) Other cereals (%) Traditional cash crops (%) Roots and tubers (%) Family labor days per hectare (days/ha) Hired labor days per hectare (days/ha) Manual draught power (1=yes) Animal draught power (1=yes) Mechanical draught power (1=yes) Herbicide use (1=yes) Insecticide use (1=yes)

-0.557** (-2.03) -0.982*** (-3.32) 0.061 (0.10) -0.516* (-1.66) -0.370 (-0.95) 0.002***

1.688*** (3.65) 2.555*** (5.18) 0.602 (0.71) 2.735*** (5.46) 2.640*** (4.05) -0.000

(3.90) 0.012*** (4.92) -0.138* (-1.81) 0.083 (0.97) -0.080 (-0.71) 0.060 (0.98) -0.137** (-2.04) 10.999*** (13.28) 9.00 1367 0.245

(-0.27) -0.004 (-1.04) 0.136 (0.99) -0.241 (-1.55) 0.029 (0.15) 0.179* (1.83) 0.290** (2.55) 0.941 (0.64) -1382 0.289

6.431*** 10.980*** 10.043*** 2.231 (157.98) (13.93) (150.40) (1.40) Inflection point (hectares) 11.88 10.62 --Observations 1370 1367 1385 1382 R2 0.041 0.207 0.002 0.147 Source: Authors’ computation from RALS (2012) and ACS (2013) t statistics in parentheses, significance levels as follows: * p < 0.10, ** p < 0.05, *** p < 0.01 a For the cost of maize production per metric ton measure, operated farm size and its square term refer to maize area only Constant

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Figure 1: Bivariate Relationships Between Factor Input ratios and Landholding Size

Figure 2: Relationships Between Operated Farm Size and Measures of Agricultural Productivity

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Appendix 1: Map of Zambia Showing Location of ACS Households

Appendix 2: Map of Zambia Showing Location of ACS and RALS Households

Appendix 3: List of fixed assets Asset Spray pump Animal traction plough and oxen Weighing machine Tractor Cart Trailer Water pump Irrigation equipment Ploughs for tractor Harrow/tiller Dam/well/water source Planter Truck Borehole Boom sprayer Sheller Ridger/weeder

Appendix 4: Production function estimates used for TFP estimation Estimated results 9.158*** 𝒍𝒏𝑨𝟎 + 𝜼𝒕 (28.71) 0.357*** 𝜶𝑲 (12.58) 0.007 𝜶𝑳 (0.27) 0.792*** 𝜶𝑴 (28.71) 1.156 𝑹𝑻𝑺 = 𝜶𝑲 + 𝜶𝑳 + 𝜶𝑴 𝜶∗𝑲

0.309

𝜶∗𝑳

0.006

𝜶∗𝑴

0.685

R2 F-statistic

0.634 826.18

Source: Authors’ computation from RALS (2012) and ACS (2013) t statistics in parentheses, significance levels as follows: * p < 0.10, ** p < 0.05, *** p < 0.01

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Appendix 5: Relationship between value of crop production per hectare and operated farm size across landholding sizes

Appendix 6: Estimates of correlations between operated farm size and other regressor variables used in the regressions Correlation p-value coefficient Operated farm size 1 0.143 0.000 Male head (1=yes) 0.062 0.021 Age of household head 0.106 0.000 Years in current settlement Education of household head (base category: primary education) No formal education - 0.104 0.000 0.081 0.003 Secondary education Tertiary education 0 .032 0.234 Formal employment (1=yes) 0.014 0.591 - 0.190 0.000 Local (1=yes) 0.071 0.008 Length of growing period (months) Elevation (meters) 0.137 0.000 - 0.064 0.017 Slope (degrees) Rainfall (millimeters) - 0.015 0.564 Soil nutrient availability (base category: no or slight constraints) Moderate constraints (1=yes) - 0.002 0.947 Severe constraints (1=yes) 0.025 0.356 Basal fertilizer (kg/ha) 0.043 0.109 Top dressing fertilizer (kg/ha) 0.031 0.250 Share of area planted with: - 0.071 0.009 Maize (%) Beans and oilseeds (%) - 0.010 0.702 Other cereals (%) - 0.002 0.945 0.045 0.090 Traditional cash crops (%) - 0.128 0.000 Roots and tubers (%) 0.240 0.000 Family labor days per hectare (days/ha) 0.279 0.000 Hired labor days per hectare (days/ha) - 0.249 0.000 Manual draught power (1=yes) 0.135 0.000 Animal draught power (1=yes) 0.176 0.000 Mechanical draught power (1=yes) 0.303 0.000 Herbicide use (1=yes) 0.155 0.000 Insecticide use (1=yes) Source: Authors’ computation from RALS (2012) and ACS (2013)

Highlighted variables are the most correlated (verified by the p-values) with operated farm size and have a significant effect on the productivity measures in Table 7 and 8.