Land Markets, Resource Allocation, and Agricultural Productivity

Transcription

1 Land Markets, Resource Allocation, and Agricultural Productivity Chaoran Chen University of Toronto Diego Restuccia University of Toronto and NBER Raül Santaeulàlia-Llopis MOVE, UAB, and Barcelona GSE December 2016 Abstract We study factor misallocation and its impact on aggregate agricultural productivity using detailed household-level micro data from Ethiopia. Land ownership resides with the state but use-rights are granted at the local level in an egalitarian basis. There are severe restrictions to land reallocation. In this context, it is not surprising we find substantial factor misallocation across farmers in agriculture. An efficient reallocation of resources can increase aggregate agricultural output and productivity by 144%. Exploiting the regional variation in land rentals which resulted from differences in the implementation of a land-certification reform, we find that more land rentals are associated with lower factor misallocation and higher agricultural productivity. On average, a one percentage point higher land rental is associated with an increase of 1.7 percentage points in aggregate agricultural productivity. Keywords: Aggregate productivity, land markets, land rentals, misallocation, micro data. JEL classification: O11, O13, Q12, Q15. Contact: Chaoran Chen, 150 St. George Street, Toronto, ON M5S 3G7, Canada, chaoran.chen@mail.utoronto.ca; Diego Restuccia, 150 St. George Street, Toronto, ON M5S 3G7, Canada, diego.restuccia@utoronto.ca; Raül Santaeulàlia-Llopis, Plaza Civica s/n, Bellaterra, Barcelona 08193, Spain, rauls@movebarcelona.eu. 1

2 1 Introduction Agriculture plays an important role in understanding income differences across countries for two reasons. First, labor productivity differences between rich and poor countries are much larger in agriculture than in non-agriculture. Second, poor countries allocate a larger share of employment in agriculture. 1 There is a considerable literature addressing differences in agricultural labor productivity across countries. 2 Within this literature, there is a recent emphasis in factor misallocation steaming from imperfect land markets as a major obstacle limiting agricultural productivity in poor countries. 3 In this paper, we use detailed household-level farm data from Ethiopia to study the aggregate impact of factor misallocation in agriculture. While land markets remain severely restricted in Ethiopia, a round of land certification has lead to variation in land rental-market activity across regions. We exploit this variation and find strong evidence that better functioning land rental markets facilitate resource allocation and improve agricultural productivity. In many poor countries land is hardly tradable across farmers. Land transactions can either be prohibited by law or face high transaction costs. Land institutions are such that property rights over land are ill defined, typically the ownership of land resides with the state or the collective and use rights of land are distributed by leaders of the community in a fairly egalitarian basis, with all members of the collective receiving amounts of land use rights that are based solely on the household size. As a result, to the extent that households are 1 See, for instance, Gollin et al. (2002) and Restuccia et al. (2008). 2 Among many others, see Gollin et al. (2002), Gollin et al. (2004), Gollin et al. (2007), Restuccia et al. (2008), Adamopoulos (2011), Lagakos and Waugh (2013), Gollin and Rogerson (2014), Donovan (2014), Gollin et al. (2014), Chen (2016b), Adamopoulos and Restuccia (2015), and Herrendorf and Schoellman (2015). 3 See, for instance, Adamopoulos and Restuccia (2014), Banerjee and Iyer (2005) and Restuccia and Santaeulàlia-Llopis (2015). 2

3 heterogeneous in their farming productivity and that land allocations are not based on these productivity differences, land misallocation is prevalent in poor countries. Ethiopia provides an excellent case to study. A communist government that was in power from 1974 until early-1990s expropriated and redistributed the majority of the land in the country. Land transactions were prohibited by the law. While ownership today still resides with the state and many of the restrictions to land transactions remain in place, since the early-2000s a series of reforms were implemented to grant land certificates to farmers and to partially allow land to be reallocated across farmers via rentals (up to a limit) of the use rights. Because the implementation of these reforms were decentralized to the level of local governments and the timing and extent has differed across regions, the extent of land rentals differs substantially across local regions. We exploit these regional differences of land rental markets to study how land reallocations affect aggregate agricultural productivity. We first study factor misallocation in agriculture at the nationwide level. In our analysis, family farms are the basic unit of production and we use the detailed household-level data of inputs and outputs across plots of land within these households to measure farm-level total factor productivity (TFP). Given these estimates of farm-level TFP, we use a span-ofcontrol model following Lucas (1978) and derive the efficient allocation of capital and land across farms, the is the allocation of factors that maximizes agricultural output. We then compare this efficient allocation of factors to the actual allocation and assess the extent and consequences of misallocation. We find that factors are severely misallocated in agriculture in Ethiopia. In particular, and given the institutional context it is not surprising that land allocations are essentially unrelated to farm-level TFP. We also assess the aggregate output and productivity gain from reallocating resources. By reallocating resources according to 3

4 their productive uses in agriculture, aggregate agricultural output and TFP can increase by a factor of 2.4-fold (an increase of 144 percent). The efficiency gain associated with an efficient allocation of factors in agriculture in Ethiopia is much larger than what Hsieh and Klenow (2009) find for the manufacturing sectors of China and India but smaller than what Restuccia and Santaeulàlia-Llopis (2015) find for the agricultural sector in Malawi (around 3.4-fold increase). We then quantify the extent of misallocation across local regions and correlate it with the prevalence of land rentals across regions. We find that land rentals differ substantially across regions. Among 69 zones (counties) where we have data, the percentage of rented land varies from 0 to 64.4%. Among 233 woredas (districts), this percentage differs from 0 to 87.1%. These differences in land rentals reflect a substantial variation of local land market institutions. Furthermore, we also find that the prevalence of land rentals is negatively correlated with the extent of misallocation. This correlation is significant both at the zone level and at the woreda level. On average, aggregate agricultural productivity is 2.7 percentage points higher in a zone where land rental is one percentage higher. This elasticity remains significant even if we control for farmers TFP within zones. An important feature of the data is that we have measures of inputs and outputs in each plot of land operated by a family farm. Therefore, we exploit this feature of the data to measure farm-level inputs, outputs, and TFP more accurately relative to related studies. First, because households operate on average 9 plots of land and our farm-level inputs and outputs are the sum of the inputs and outputs of all the plots operated by the household, classical measurement error at the plot level is mitigated by the aggregation. Second, the plot-level data allow us to construct alternative measures of farm-level TFP for robustness. 4

5 We use the plot-level inputs and outputs to estimate plot-level TFP (as opposed to farm-level TFP in our baseline) to construct an alternative measures of farm-level TFP, in particular we look at the mean, the median, and the sum of plot-level TFP for all the plots operated by the household farm. We find that our results are robust to using these alternative farm-level TFP measures. Whereas household farms produce several different crops, plots are typically used to produce a given crop and therefore, we also explore the plot-level data to quantify misallocation within crops. We find that factor misallocation is more severe in cash crops than in food crops. Our plot-level data also enable us to compare the land quality between rented land plots and other plots. We find that on average rented land has better quality, although the causality is undetermined. Our paper is related to the macro development literature on the differences in agricultural productivity across countries. We specifically follow Adamopoulos and Restuccia (2014) in highlighting land institutions and factor misallocation as key elements in accounting for low agricultural productivity in poor countries. Our paper is also related to the macro development literature connecting quantitative frameworks with micro data to assess the role of misallocation. 4 The closest paper to ours is Restuccia and Santaeulàlia-Llopis (2015), which use micro data from Malawi to assess the extent of misallocation in agriculture and the connection with land market restrictions by assessing the extent of misallocation for households operating market land relative to those households with no marketed land. While we use a similar framework, we study a different country Ethiopia, which has implemented a land certification reform and hence allows us to exploit regional differences in the implemen- 4 See, for instance, Hsieh and Klenow (2009), Midrigan and Xu (2014), and Adamopoulos and Restuccia (2015), among others. 5

6 tation of the reform to identify the productivity impact associated with improvements in land markets. We further differ from Restuccia and Santaeulàlia-Llopis (2015) by exploiting the available plot-level data in Ethiopia to show the robustness of the results to potential measurement error and crop composition choices. Our paper also contributes to the micro development literature studying the role of institutions as an obstacle of economic development. 5 We differ from this literature by taking a macro approach and focusing on the impact of institutions on aggregate productivity, rather than the household-level productivity. The paper proceeds as follows. Section 2 describes the data we use. In section 3, we perform the quantitative analysis by presenting the basic framework, the calibration, and the main results on factor misallocation and aggregate efficiency gains. Section 4 shows the relationship between land rentals and misallocation, at the household level, woreda level, and zone level. We exploit differences in the implementation of the land certification reform to identify the impact of land rentals on aggregate productivity. Section 5 performs robustness checks and discusses the relevance for our results crop composition and land quality differences. We conclude in section 6. 2 Data We use household-level data from the World Bank, the Ethiopia Integrated Survey of Agriculture (ISA) 2013/14. This survey provides information over the entire process of crop production, including physical measures of farm inputs and outputs. In the original data, 3,629 households are sampled to be representative of the population, among whom 88.4% 5 See, for instance, Acemoglu et al. (2001), Banerjee et al. (2002), and Banerjee and Iyer (2005), among others. 6

7 live in rural areas and participate in agricultural production. Each household is surveyed twice in a year: the first round is during the planting season and the second round is during the harvest season. Almost all farms in Ethiopia are family farms. Therefore, we treat a family farm operated by a household as our basic unit of production. We construct our measures of inputs, outputs, and TFP at the farm (household) level. A farm operated by a household typically consists of several different parcels of land; we therefore aggregate the inputs and outputs of these parcels to the household level. We also explore in a robustness section parcel-level variation in productivity. We next detail how we measure inputs and outputs from the data. Agricultural output. Farm output is recorded in physical quantities (kilogram) of different crops. The most common crops in Ethiopia are maize, sorghum, teaf, coffee, wheat, and barley, which are planted on 11.1%, 9.1%, 7.8%, 7.1%, 4.7%, and 4.4% of all land plots, respectively. 6 To aggregate farm production of different crops we use common crop prices. For our purposes, what is key is that aggregate production at the farm level reflects physical variation in output and hence valuing output at common prices across farms achieves that. Less important is what common price we use. We observe the prices of crops traded at local markets. For each crop, we compute the median price among all transactions and use it as the common price of this crop. The value of crop production of a farm is estimated by multiplying its physical quantity produced with its common price. We then sum up the values of all crops produced in the farm to obtain the value of gross output of each farm. We also use common prices to estimate the value of intermediate inputs used by farms in 6 We restrict our analysis to crops only and hence abstract from livestocks as the production cycles of livestocks are usually longer than one year, which is our data period. 7

8 a similar way. These intermediate inputs include different kinds of fertilizers and seeds. Note that some fertilizers and seeds are from the farmers home production; we evaluate these home-produced goods using common market prices as well. Again, the key in these assumptions is that the aggregate measure of intermediate inputs used in a farm tracks as best as possible physical variation in inputs. We subtract the value of intermediate inputs from the value of gross output and the remaining is the value added of a farm. We use this measure of value added in our analysis as the net farm output. Rain. Since we measure productivity from cross-sectional data, it is important to exclude transitory variation in output from value added. 7 In the agricultural production, the most important shock is precipitation. Rainfall information is provided in the data, recorded as the annual precipitation in millimetres, and we can use it to identify the shocks of rainfall. We create 10 dummies representing different levels of rainfall. Then we regress value added on those dummies and obtain the residual of this regression as the value added excluding the shock of rainfall. This is the measure of value added we will use in our analysis. Capital. Farm capital has three components: agricultural tools, transportation tools, and some livestocks. Agricultural tools include sickles, axes, pick axes, traditional or modern ploughs, and water pumps. We observe the physical quantity of these tools owned by each farmer, as well as their prices at local markets. Again, we construct common prices, defined as the median of sell prices, to evaluate these agricultural tools. Transportation tools include hand-pushed or animal-drawn carts and bicycles. The price of transportation tools are not directly available in the data, so we estimate their values using local prices from the internet. 8 7 An earlier round of ISA is available which in principle would allow us to exploit a panel dimension, but we are not able to use the earlier data as a key variable (farm gross output) was not recorded in that round. 8 We assign the prices of transportation tools as follows: one hand-pushed cart is worth about 6 traditional ploughs; one animal-drawn cart is about 9 traditional ploughs; one bicycle is about 17 traditional ploughs. 8

9 The livestocks are a bit more complicated though. The survey records three most common species in Ethiopia, cattle, goats, and sheep, as well as the usage of these livestocks. In our measure of capital, we include cattle that are for agricultural or transportation purposes only, while we exclude goats and sheep, which are mainly used for meat, wool, or milk. We also observe the prices at which farmers sell their cattle. Then we construct common prices of cattle, male and female separately, to evaluate the value of these cattle. Finally, we sum up the values of agricultural tools, transportation tools, and cattle as our measure of farm capital. Labor. The data provide labor input for every plot of land of a farm, in both the planting season and the harvest season. Labor input includes farmers family labor, hired labor, and unpaid labor from other households. Family labor is recorded in hours (the data reports hours per day, days per week, and the number of weeks); hired labor and unpaid labor, however, are only recorded in days. We assume hired males work the same hours per day as family members, while hired females and children work fewer hours, consistent with their lower wage bills per day. 9 We also assume that unpaid labor from other households work the same hours per day as hired workers of the same identity: for example, unpaid males work the same hours per day as hired males. Finally, we construct farm labor input as the sum of hours from all the three kinds of labor for all land plots of this farm in both seasons. We find that out of the total labor input, 77.6% is supplied by household members, 13.6% by hired labor, and 8.8% by unpaid labor from other households. Land. Land input of a farm, or farm size, is the sum of the size of all land plots Note that very few farmers have these transportation tools, so excluding them in the measure of capital would only change our results slightly. 9 We assume the ratio of hours worked by hired women and hired men equals the daily wage ratio between them. We also estimate hours per day of hired children in the same way. 9

10 operated by this farm. For 96.5% of land plots, their size is accurately measured by GPS at a precision of 0.05 hectares, while the size of the remaining plots is reported by farmers. Farms are in general very small in Ethiopia. The average farm size in our sample is around 1.5 hectares, compared to hectares in the United States as reported in 2007 U.S. Census of Agriculture. The farm size distribution is very skewed to very small sizes: 54.7% of households in our sample operate farms smaller than 1 hectare, 79.7% of households operate farms smaller than 2 hectares, only 2.9% of households operate farms larger than 5 hectares. We note that a plot of land is treated as a part of a particular farm if it is operated by that farmer, regardless of whoever has the use rights of the land. In other words, the size of the farm is the operational scale and not the ownership or use rights of land so when we compute farm size we include rented-in land plots and exclude rented-out plots for each household. The land rental market is, however, relatively under-developed in Ethiopia as only 22.9% of households rent in any land. Among the households that operate any rented in land, only 6.6% operate on rented land only. The data has information on how farmers acquire land plots that they are operating. The vast majority of land plots feature use rights that are either inherited or granted by a local leader (39.2% and 41.5%, respectively). On average, 12.0% of land plots are rented from other households, and this number differs substantially across regions. We will use this information on geographical differences in land rentals to assess the impact of land markets on factor misallocation. Land quality. The data also record land quality and other geographical variables for each plot of land. For each plot, the data records its elevation, slope, terrain roughness, nutrient availability, nutrient retention, rooting conditions, excess salts, toxicity, and workability. We construct a measure of land quality as follows. We regress the log value added 10

11 per labor hour on these variables indicating land quality, controlling for log capital and land input per labor hour. This regression estimates how each dimension of land quality affects the value added per labor hour. Then we take the coefficients from this regression to evaluate the land quality index q for each farm. This is an upper bound measure of land quality as some inputs may be correlated with the quality of the land. We have constructed our measures of value added, capital, labor, and land. These measures summarize inputs and outputs of farms, and are used in our quantitative analysis in the next section. 3 Quantitative Analysis In this section we first describe the framework for the analysis and our calibration strategy. Then we use this framework to quantify the extent of misallocation in agriculture in Ethiopia, and compare our results with related studies. 3.1 Framework and Calibration We start by describing our framework for the analysis, which closely follows Restuccia and Santaeulàlia-Llopis (2015). Consider a farmer with productivity s i S with the following production function: y i = s 1 γ i [k α i (q i l i ) 1 α ] γ, (1) where y i is the net output of this farm (measured as value added excluding transitory components), k i is the capital input, q i is land quality, and l i is the land input. The parameter 11

12 γ governs the return to scale at the farm level, and α determines the share of capital. In our analysis, we focus on the allocation of capital and land across farms. As a result, we follow Restuccia and Santaeulàlia-Llopis (2015) and Adamopoulos et al. (2016) and abstract from the labor input in our production function other than the productivity of the farmer. For this reason, when we confront this production function with data, we normalize our measures of output (value added), capital, and land in the data by labor hours. In other words, the production function is in per-hour form. The farmer earns the profit, which is a fraction 1 γ of the farm output; therefore, 1 γ can be interpreted as the labor share. Given the actual inputs and output (value added) of a farm from the data, the farm-level productivity s i can be solved out as We further denote s 1 γ i [ s i = k αγ i y i as the farm-level TFP. (q i l i ) (1 α)γ ] 1 1 γ. (2) Let s consider the social planner s problem first. The planner allocates total capital K and land L endowments among farmers who are heterogeneous in their ability s i S. Given the span-of-control technology specified in (1), the efficient allocation of factors among farms is non-degenerate. In particular, one can show that the efficient allocation of capital and land among farms should satisfy k e i = s i i s K and li e = s i i i s L, (3) i where k e i and l e i denote the efficient allocation of capital and land (as opposed to the actual 12

13 allocation k i and l i ). The efficient output (value added) of this farm is given by y e i = s i (K α L 1 α ) γ ( i s i) γ. Then aggregate output is given by Y e = i y e i = ( i s i ) 1 γ (K α L 1 α ) γ. Here Y e is the aggregate output from the social planner s solution. Therefore, it is the maximum output this economy can obtain given the aggregate amount of resources (capital, land, and number of farmers). The planner s solution has the following two properties: Proposition 1. The efficient allocations of capital and land are proportional to farmer s ability: ke i k e j = s i s j, le i l e j = s i s j. Proposition 2. The efficient allocation equalize the marginal products of capital and land across farms: MPK i = MPK j, MPL i = MPL j, i, j. In general, the actual allocation of capital and land from the data (k i and l i ) are not identical to the efficient allocation from the planner s solution (k e i and l e i ). The difference indicates resource misallocation. Furthermore, aggregate output in the data Y d = i yd i = i s1 γ i (ki α l 1 α i ) γ is lower than Y e. The difference between the actual aggregate output Y d and the efficient aggregate output Y e provides a summary statistics of the impact of 13

14 misallocation on aggregate output and TFP: e = Y e 1. Y d e measures the efficiency gain this economy can achieve if factors are reallocated efficiently. We focus on this efficiency gain e as our main measure of misallocation in our analysis. We also construct a summary measure of misallocation as the dispersion of the farm-level revenue productivity. We follow Hsieh and Klenow (2009) and Adamopoulos et al. (2016) and define the revenue productivity ( TFPR ) as TFPR i yd i k α i l1 α i. It is straightforward to verify that the efficient allocation (k e i, l e i ) will equate TFPR across farms. Therefore, we can use the dispersion of TFPR across farms (var(log TFPR i )) to measure how distinct the actual allocation is from the efficient one. Note that in our framework, the only structure we impose is the farm-level production function specified in Equation (1). Therefore, we only have two parameters to calibrate: α and γ, governing the factor income shares of the production function. Estimation of factor income shares in agriculture varies in the literature. Valentinyi and Herrendorf (2008) find that in the U.S., the capital, labor, and land shares in agriculture are 0.36, 0.46, and 0.18, respectively. Restuccia and Santaeulàlia-Llopis (2015) use micro data from Malawi and estimate the capital, labor, and land shares to be 0.190, 0.419, and 0.391, respectively. This discrepancy may arise from the fact that Malawi has lower level of mechanization in 14

15 agriculture compared to the U.S. In fact, Chen (2016a) argues that capital-output ratio (and therefore the capital income share) in agriculture tends to increase as an economy develops. Ethiopia is typically considered to be at a stage of development similar to Malawi. We therefore assign factor shares according to the estimation of Restuccia and Santaeulàlia- Llopis (2015), which results in the parameter values α = and γ = Given values of α and γ, together with farms actual inputs and outputs observed in the data (k i, l i, and y i ), we can use Equation (2) to solve out farm level productivity s i. We trim farms whose TFP fall in the top or bottom one percentile of the farm TFP distribution as these possible outliers may reflect measurement errors in inputs and outputs in the data. 10 Then we can use Equation (3) to solve out the efficient allocation of capital and labor (k e i and l e i ), and contrast it with the actual allocation (k i and l i ). We detail this comparison in the following subsection. 3.2 Misallocation and Efficiency Gain We now use this framework to quantify the extent of misallocation in the agricultural sector in Ethiopia. We start by describing four sets of facts about factor allocation from the data, the patterns of farm inputs, farm output, marginal products of factors, and farm TFPR. We contrast these patterns to the properties of efficient allocation discussed previously. We also compute the efficiency gain associated with factor reallocation as a summary measure of the cost of misallocation. Farm inputs. Figure 1 reports farm inputs (capital and land) against farm productiv- 10 Trimming observation at the tails of farm TFP distribution is conservative as our calculated efficiency gain is increasing in the farm TFP dispersion. 15

16 ity. Proposition 1 requires that the efficient allocation of capital and land be proportional to farm-level productivity (red dashed line in the figure). The actual allocation in our sample is, however, very different to this efficient allocation: capital input is negatively correlated with farm-level productivity and land input is virtually uncorrelated with farm-level productivity. Therefore, this Figure indicates severe factor misallocation in the agricultural sector in Ethiopia. Farm output. Figure 2 reports the farm output versus the farm productivity. The planner s solution requires that farm output should be proportional to farm productivity, which is the red dashed line in the figure. The actual farm output is also increasing in farm productivity, but the slope is much flatter. This means that, compared to the efficient allocation, low productivity farms tend to be larger than they should be, and high productivity farms tend to be smaller. This pattern suggests that farms face distortions that are correlated with their productivity. Marginal products of factors. Figure 3 shows the marginal products of capital and land at the farm level. Recall that Proposition 2 requires that the marginal product of capital (land) should be equalized across farms, independent of the farm level productivity. In our data of Ethiopia, however, we find a strong positive correlation between marginal product of capital (land) and farm level productivity. This is another piece of evidence of misallocation: farms with higher productivity are not able to obtain enough inputs and therefore their marginal products of factors are higher. In other words, farms with higher productivity are facing higher wedges. TFPR. As discussed before, if factors are allocated efficiently, TFPR should be the same across farms. As a result, we can use the dispersion of TFPR to measure the extent 16

17 of misallocation. Table 1 shows the dispersion of TFPR. The standard deviation of TFPR (log) is 1.22 in our sample. As a comparison, Hsieh and Klenow (2009) find this number to be 0.63 and 0.67 in the manufacturing sector of China and India. The ratio is 1.60 in our sample, compared to 0.82 and 0.81 of China and India. The ratio is also larger in our sample. This comparison indicates that the extent of misallocation is severe in Ethiopia. As will be discussed later, severe factor misallocation in Ethiopia is largely associated with obstacles to land reallocation. Figure 4 shows that farm TFPR tends to be increasing with farm productivity, confirming with our conjecture that more productive farms are facing more distortions. Efficiency gain. We also estimate the efficiency gain associated with reallocating resources efficiently. The efficiency gain, which equals the ratio between the maximum output (Y e ) and the actual output (Y d ), is 2.44 in Ethiopia. This means that if we reallocate resources according to the planner s solution, the aggregate output will be 2.44 times of the actual output. An efficiency gain of 2.44 is sizeable, compared to the literature quantifying misallocation in the manufacturing sector: for example, Hsieh and Klenow (2009) estimate that the efficiency gains are around 1.4 and 1.6 in the manufacturing sector of China and India. Our efficiency gain is, however, smaller than to Restuccia and Santaeulàlia-Llopis (2015), who find an efficiency gain of 3.6 in the agricultural sector of Malawi. Note that this does not mean the factor misallocation is less severe in Ethiopia than in Malawi. Efficiency gain depends on both misallocation and the dispersion of farm TFP (var(log TFP i )). Therefore, a lower efficiency gain in Ethiopia could be due to a smaller dispersion of farm TFP in our sample (0.73) than that of Malawi (1.44) in Restuccia and Santaeulàlia-Llopis (2015). 17

18 4 The Role of Land Markets Given above evidence of severe misallocation in Ethiopia, we now try to understand how poor institutions in land market affect the extent of misallocation. We focus on land market institutions as recent literature has shown that land misallocation can be an obstacle limiting agricultural productivity in poor countries 11. In this section, we explore the regional differences of land rental markets to study how land reallocations affect agricultural productivity. 4.1 Farmers With/Without Marketed Land Literature has illustrated how land market frictions distort the agricultural production. For example, Adamopoulos and Restuccia (2015) study a land reform in Philippine that imposed a ceiling on land holdings and severely restricted the transferability of the redistributed farm land. They find substantial productivity loss of this reform, and show that the key condition determining the extent of productivity loss is whether farmers are allowed to rent in/out the redistributed land. Chen (2016b) argues that most land in poor countries is hardly tradable or rentable, due to a lack of legal ownership. This friction leads to misallocation of land, as some farmers may hold extra land compared to their optimal operation scales while they cannot rent it out. In this section, we complement this literature by using our data to quantify the impact of land rentals in Ethiopia. Land market is underdeveloped in Ethiopia. There are 12,583 parcels of land in our sample, among which 41.5% are inherited, 39.2% are granted by local leaders, and only 11 See, for example, Adamopoulos and Restuccia (2014), Adamopoulos and Restuccia (2015), Restuccia and Santaeulàlia-Llopis (2015), and Chen (2016b), among others. 18

19 12.0% are rented from other households. These rented parcels are on average slightly larger than others (by 0.09 ha), but the difference is barely significant at the 10% level. In our sample, 76.1 percent of all household farms operate on non-marketed land only; 23.9 percent of households formally or informally rent in some land for production. We divide households into two groups accordingly: the first group of farmers have relatively little access to the land market, while the second group of farmers have some access. This division highlights the role of land rentals in determining the factor allocation and efficiency gain. Table 1 shows the dispersion of TFPR for the two groups separately. The dispersion of TFPR is larger in the first group (farmers with non-marketed land only). For example, the standard deviation of log TFPR is 1.24 in the first group while it is 1.13 in the second group. We compute the efficiency gain separately for these two groups, and Table 2 shows results. The efficiency gain among the first group of farmers, who operate on non-marketed land only, is 2.65, slightly higher than the aggregate efficiency gain (2.44). The efficiency gain is 1.78 among the second group of farmers who have some rent in land, which is much lower than the aggregate efficiency gain. This comparison provides direct evidence that land rentals help factor reallocation and alleviate misallocation. Although land rentals help reallocate resources, the extent of misallocation is still severe even among farms that operate on some marketed land. For example, the correlation between farm size and farm productivity is among the first group of farmers and among the second group of farmers, while the planner s solution requires this correlation to be 1. Therefore, even land rentals help reallocate land to more productive farms, overall farms are operating far from the efficient frontier, which suggests that land market are still limited and 19

20 subject to various frictions. Recall that both factor misallocation and farm TFP dispersion affect the efficiency gain of reallocation. Therefore, one potential concern of this comparison is that farm TFP may be more dispersed within those who have access to land market. To address this issue, we consider the following regression, which explicitly controls the farm level TFP when we compare the efficiency gains of farmers with and without rentals: log ye i y d i = β 0 + β 1 log s i + β 2 D i + ε i, where D is a dummy variable and D = 1 indicates that a farmer operates on some marketed land. We run an ordinary least square (OLS) estimation on our whole sample. Our estimation of β 2 has a coefficient of and it is significant at the 1% level. This means that, on average, having some access to land rental market reduces the efficiency gain by 19.0% even after controlling for farm level TFP. 4.2 Land Rental Markets across Locations So far our analysis of land rentals focus on individual farmers. We would also like to know how are the differences of land rentals across locations correlated with the extent of misallocation locally. We address this question in this section. Ethiopia is a good candidate to study misallocation versus local land market. Ethiopia has been implementing a land reform, which gives certification to land and partially allows farmers to rent their land up to a limit. This reform is implemented by local governments with different rules, instead of being implemented at the national level (Deininger et al., 20

21 2008). Therefore, we can exploit the variation of implementation across locations to study the impact of land rentals. Some existing literature also takes this approach and exploits regional differences using data from other countries, such as Banerjee and Iyer (2005), Deininger et al. (2011), and de Janvry et al. (2015). There are four levels of administrative divisions in Ethiopia: regions (states), zones (counties), woreda (districts), and kebele (wards). In our sample, we have records on each farmer s location down to the kebele level. We have in total 2,677 observations, located in 10 regions, 69 zones, and 233 woredas. We mainly focus on results at the zone level, since we have a reasonable number of zones and relatively large number of observations within each zone. We also present our results at the woreda level. For each zone z, we calculate the efficient output (Y e z = i z ye i ) and the actual output (Y d z = i z yd i ). The ratio e z = Yz e /Yz d gives the efficiency gain at the zone level. 12 We also compute the percentage of land rentals R z in each zone (defined as the ratio between the size of rented land and total land size); this ratio measures directly the land rental market in each zone. As mentioned before, the land reform is implemented by local government with different rules, so the variation of R z across zones contains information on how the reform is implemented across zones. Figure 5 shows the correlation between the efficiency gain of each zone e z and the percentage of land rentals in each zone R z. We only include zones with positive land rentals; as a result, 57 zones remain in this figure. We further exclude two zones with fewer than 20 observations. The correlation is weighted by the number of observations in each zone. Clearly 12 Note that yi e is the efficient output calculated as in our benchmark national level reallocation. In this case, it is possible to have e z < 1 for some zone z, while the national level efficiency gain e should always be greater than 1. 21

22 the efficiency gain e z is negatively correlated with the land rentals R z : a zone with more land rentals tend to have a lower efficiency gain (and therefore a lower degree of misallocation). In particular, the elasticity is , which is significant at the 1% level. Similar to the household level analysis, we consider the following regression form to address for any potential differences in farm TFP dispersion across zones: log e z = β 0 + β 1 log TFP z + β 2 log(r z ) + ε z, (4) where R z is the percentage of rented land in zone z and TFP z is the zone level efficient TFP defined as TFP z = ( ) 1 γ, s i i z which is independent of distortions. We include this zone level efficient TFP in the regression to control for the endogeneity of R z. Table 3 shows the results of this regression. We estimate the parameter β 2 to be , which is the elasticity between the efficiency gain and land rentals: β 2 = e z R z R z e z. Having estimated this elasticity, we can calculate the efficiency gain from one percentage more rental: e z = β 2 R z e z R z. (5) In our sample, on average 12.0% of land is rented in a zone; the average efficiency gain is 22

23 2.30 at the zone level. Applying Equation (5) we conclude that one percentage more rentals reduces the efficiency gain by 1.73 percentages. Recall that the efficiency gain is simply defined as the ratio between the actual output and the efficiency output; therefore, the result can also be interpreted as one percentage more rentals increasing the actual output by 1.73 percentages. The regression analysis confirms our conjecture that better access to land market is connected to less misallocation. This result is consistent with existing theoretical and empirical studies. It also highlights the importance of a proper land reform in developing countries, where the legal ownership of land is not clear. A land reform which grants tenure to farmers and facilitates land transaction or rental can potentially boost agricultural productivity, while a land reform which restricts land transaction or rental can be harmful. We also replicate this analysis at the woreda level. Figure 6 shows the correlation between the efficiency gain and the rental percentage at the woreda level. We also find a negative and significant correlation, although the slope is slightly different (-0.201). We also run the regression specified in Equation (4.2) at the woreda level. The results are in Table 3. The results are quantitatively similar to our zone level analysis: the estimated β 2 is , compared to at the zone-level regression. We do not choose the woreda-level analysis as our benchmark as a result of the following trade-off: although we have more woredas, we end up with much fewer observations (around 10) within each woreda. 23

24 5 Robustness and Extensions As we discussed earlier, a merit of the dataset we use is that it records inputs and outputs for each plot operated by all households. We exploit this feature to check the robustness of our results to different measures of farm TFP and to study the role of crop composition and land quality in the extent of misallocation. 5.1 Robustness We now explore the robustness of the quantitative results. Our quantitative results of misallocation are sensitive to the measure of farm productivity, while farm productivity is calculated from farm inputs and outputs, which could potentially suffer from classical measurement errors and therefore contaminate the measure of farm productivity. In this section, we provide several alternative ways to measure farm productivity, and conclude that our quantitative results still hold under these alternative measures of farm productivity. Recall that we have treated households as our basic unit of production. Since in the data a household operates a farm which contains several plots of land, in the case of Ethiopia an average of more than 9 plots, we have aggregated inputs and outputs to the household level. Then we assign a unique farm productivity to a household. Some classical measurement errors of inputs and outputs may have cancelled out in this aggregation. Nevertheless, we would like to take an alternative strategy as a robustness check: we treat each plot of land as a unique farm, and thus a household operates several different farms; the values of inputs and output are separately considered for each farm; each farm has a unique productivity computed from its inputs and output; finally we take the mean, median, or sum of these 24

25 plot-level productivity as alternative measures of household level productivity. Once we have these alternative measures, we again aggregate inputs and outputs to the household level, and redo previous analysis using these alternative measures of household productivity, instead the original measure calculated from household level inputs and outputs. The land and labor inputs and the value of output (value added) are available for each plot of land (a field in the data). The capital stock is, however, slightly more complicated. Capital stock is measured at the household level; furthermore, it is reasonable to assume that the capital (for example, a traditional plough) of a given household can be used in multiple plots owned this household. As a result, we cannot explicitly divide the capital into different plots. We assume the plot-level capital inputs are proportional to the size of plots: a larger plot uses more capital than a smaller plot. Then we treat a plot as a unique farm and calculate the plot-level productivity as we do in Section 2. We then construct three alternative measures of household level productivity. In section 2, we have assigned each household a unique household level productivity s i. Suppose this household i has several plots of land, and we have calculated plot-level productivities s ij for each plot as a separate farm. We now construct the following three alternative measures of the household level productivity: s 1 i = (Π j s ij ) 1 J, s 2 i = Median j (s ij ), s 3 i = j s ij. The first measure s 1 i uses the geometric mean of the plot-level productivity to approximate the household level productivity; the second measure s 2 i uses the median of the plot-level productivity as an approximation. These two measures are based on the assumption that 25

26 a household should have the same productivity across plots. Therefore, the variation of plot-level productivity within a household reflects measurement errors. We take the mean (median) of plot-level productivity to minimize these measurement errors. The third measure s 3 i uses the sum of the plot-level productivity as an approximation. This measure is based on the assumption that the productivity reflects the managerial time and ability of the household, and the household allocate its managerial time across different plots. A more talented household might be able to manage more plots of land. Therefore, we sum up the managerial time spent on each plot (plot-level productivity) to get the total managerial time of the household (household level productivity). These alternative measures of farm productivity are highly correlated with our benchmark farm productivity constructed in Section 3. The Spearman s rank correlation between our benchmark measure of household level productivity and these three alternative measures are 0.78, 0.74, and 0.55, respectively, and they are all highly significant at the 1% level. Having calculated these alternative measures, we replace the household level productivity s i in Section 2 with these three alternative measures and re-compute the efficiency gains. Note that we keep the inputs and outputs unchanged as in Section 2. The results are in Table 4. The efficiency gains corresponding to these three alternative measures are 2.11, 2.16, and 2.32, respectively. All these three numbers are fairly close to our original estimation of efficiency gain (2.44). Therefore, we conclude that the measurement errors of farm productivity are not driving our quantitative results. 26

27 5.2 Misallocation within Crops Farmers in Ethiopia cultivate a variety of crops: the most popular crops are maize, sorghum, teaf, coffee, wheat, barley, horse beans, and kales. In this section, we explore the misallocation within each crop using our plot-level data. For each plot of a household, the crop cultivated on that plot is recorded in the data. 13 We then focus on individual crops, say, maize. We keep all land plots with maize, and then we aggregate the inputs and outputs of these plots to the household level, and repeat the analysis in Section 3 and calculate the national level efficiency gain. Table 5 shows the results of eight different crops, which are the most widely cultivated crops in Ethiopia. The efficiency gain within crops are largely in line with our results in Section 3. Misallocation is in general less severe within most food crops, such as barley, sorghum, and wheat, while it is more severe within cash crops, such as coffee. This is because the dispersion of farmers ability is larger in those cash crops. Intuitively, more productive farmers may choose to specialize in cash crops, while less productive farmers may keep planting food crops. This is consistent with Adamopoulos and Restuccia (2015). 5.3 Differences in Land Quality Another interesting question is whether there are any land quality differences between the rented land and other land. For example, one may think that rented land tend to be land with better quality. We test this hypothesis using our plot-level data. We construct land quality at the plot level in the same way as described in Section 3 and then compare the 13 We focus on land plots with a single crop only, which account for 60% of all land plots. 27

28 land quality between rented plots and other plots. The Welch s t-test shows that the land quality q is similar between rented land plots and non-marketed land plots. As a result, we conclude that land quality does not differ significantly between rented land and other land. 6 Conclusion We studied the impact of factor misallocation on aggregate agricultural productivity in Ethiopia and connected this misallocation to the restrictive land markets in that context. We found that overall misallocation is severe in agriculture in Ethiopia and studied land misallocation at the regional level by exploiting differences in the implementation of a land certification reform that has lead to differences in the extent of land reallocation across farmers. We found that more land rentals are significantly correlated to less factor misallocation: one percentage point more rentals is associated to 1.7 percentage points higher output and aggregate productivity. We also used data at the plot level to corroborate that our estimates of efficiency gains are robust to measurement error on inputs and outputs, to crop composition, and to land quality differences. 28

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