How complete are labor markets in sub-saharan Africa? Evidence from panel data in four countries

Transcription

1 How complete are labor markets in sub-saharan Africa? Evidence from panel data in four countries Work in progress. Please do not cite or circulate. Comments welcome. Brian Dillon Peter Brummund Germano Mwabu April 25, 2017 Abstract We develop and implement new tests for the completeness of rural labor markets. Our approach builds on the seminal work of Benjamin (1992) and requires panel data with changes in household labor endowments over time. We show how the possibility of asymmetric responses to increases and decreases in labor endowments leads to tests of necessary conditions for a shortage or surplus in the labor market. The tests are based on strictly exogenous changes in the household labor endowment and allow for variation in labor market conditions across phases of the cultivation cycle. We implement the test using nationally representative panel data from Ethiopia, Malawi, Tanzania, and Uganda. Results differ across countries. In Ethiopia there is strong evidence of a labor shortage. In Malawi, the evidence is strongly in favor of a labor surplus. For Tanzania the results suggest a labor surplus at all times other than planting, when the pattern is less clear. In Uganda there is no evidence of non-separation in the panel, and therefore no labor market shortcoming. The paper shows that labor markets are not efficiently allocating labor in the study economies, with the possible exception of Uganda. But the underlying labor market imperfection varies across settings, highlighting the importance of tailoring policies to the circumstances of each country. We thank the Institute for the Study of Labor (IZA) and the UK Department for International Development for funding through the GLM-LIC program. Preliminary work on this project took place as part of the Myths and Facts in African Agriculture project of the World Bank and African Development Bank. For comments and helpful discussions we are grateful to Chris Barrett, Taryn Dinkelman, Dave Donaldson, Andrew Foster, Louise Fox, Markus Goldstein, Doug Gollin, Rachel Heath, Joe Kaboski, Supreet Kaur, David Lam, Simone Schaner, Tavneet Suri, and seminar participants at the Pacific Development Conference and CSAE Conference in Oxford. We thank Joshua Merfeld, Reuben Mutegi, and Audrey Royston for excellent research assistance. All errors are the responsibility of the authors. University of Washington, Evans School of Public Affairs. bdillon2@uw.edu. University of Alabama. pbrummund@cba.ua.edu University of Nairobi, Department of Economics. gmwabu@gmail.com. 1

2 1 Introduction The performance of labor markets has been central to the study of economic development since Lewis (1954) and Harris and Todaro (1970). Labor is a primary endowment of the world s poor households, and poverty reduction is inextricably linked to increases in the returns to labor. As a key input to agriculture, labor also contributes to the majority of output in rural areas of low-income countries. Understanding the process that determines the returns to labor in rural areas is critical for designing policies to increase agricultural productivity and reduce poverty (Teal, 2011). The goal of this paper is to shed light on the functioning of rural labor markets in four countries of sub-saharan Africa: Ethiopia, Malawi, Tanzania, and Uganda. We build on a classic line of literature in development economics that uses the resource allocation problem of family farms to test the completeness of rural markets (REFS). The intuition behind this test is simple and powerful. In the standard model of the agricultural household, the profit-maximization problem of the farm is embedded in the household s utility maximization problem. If markets for inputs, outputs, and other relevant goods are complete and competitive, the household s consumption and production problems are separable. The family farm can be analyzed as a profit-maximizing firm. This implies that household endowments should have no impact on the input demand functions of the farm. Hence, testing whether there is a relationship between household endowments and farm inputs is tantamount to testing the complete markets assumption. A common way to implement this separation test is to regress farm labor utilization on the household s labor endowment. A significant relationship indicates that households with more (fewer) members use more (less) labor on their farms a violation of separation, and hence of the assumption of complete markets. In a seminal paper, Benjamin (1992) shows in cross-sectional data from Indonesia that labor demand on farm does not depend on the number of workers in the household, leading to non-rejection of the complete markets assumption. Numerous other studies have implemented a similar test in cross-sectional data, with mixed findings (REFS). In an important advance, LaFave and Thomas (2016) use panel data from the same setting as Benjamin to effectively overturn the result. In both 2

3 both pooled cross-section and fixed effects regressions, LaFave and Thomas find a significant relationship between labor endowments and labor utilization on farm, leading them to reject the complete markets assumption. A key limitation of the standard test is that a rejection of separation does not generally identify the specific pattern of underlying market failures. Although the test is implemented using data on labor endowments and labor utilization, separation can fail even if labor markets are complete (Feder, 1985; Udry, 1999). This is a concern for both panel and crosssectional data. Interpretation is especially difficult in a cross section, where time invariant factors such as heterogeneity in managerial skill or preferences for working on one s own farm can lead to non-separation. Hence, while the standard test provides insights into the completeness of markets, and is informative for model selection, its practical use as a guide for policymakers is limited. In this paper we develop an extension to the standard separation test that allows us to make inferences about the underlying pattern of market failures (see Section 2). Our test is only implementable in panel data. The intuition is simple. From one year to the next, household labor endowments can change for a variety of reasons: in-migration, out-migration, divorce, death, children aging into the workforce, elders aging out. Some households see an increase in labor endowments, others a decrease. We show that in a labor market characterized by excess labor (downward sticky wages), the expected response of farm labor utilization to changes in the labor endowment is asymmetric. A decrease in the labor endowment has a smaller expected effect on farm labor utilization than an increase, because for some households a decrease leads to a situation in which the ration on the labor demand side no longer binds. In a labor market characterized by excess demand, the opposite is expected. Hence, by allowing for possible asymmetries in the response of farm labor utilization to changes in the household labor endowment, we can test necessary conditions for specific labor market failures. We show that failures in other markets do not generally predict the same asymmetries. In particular, if the market for labor is complete but those for land and insurance are not a distinct possibility in much of sub-saharan Africa there is no a priori reason to expect an asymmetric response. Of course, we could find asymmetric responses due to labor market 3

4 failures, while other markets are also incomplete. Our test cannot rule out the possibility of complex and geographically variable patterns of market failures, but it can provide specific insights about the state of labor markets. In implementing our test of labor market failures we make a number of other empirical advances. We conduct the analysis separately for the four study countries, using recently collected, nationally representative panel data (see Section 4 for details). 1 This allows us to make comparisons across countries. The use of household fixed effects controls for a number of confounding interpretations that might arise in cross-sectional data (LaFave and Thomas, 2016). Because we use nationally representative data, our findings provide a characterization of the average state of rural labor markets across the country, rather than a finding specific to a particular area. We also allow for the possibility that labor markets could be in different states during different periods of cultivation. This is important when production is dominated by agriculture, which is subject to short-term spikes in labor demand at planting and harvest. In Section XX we discuss the possibility of endogenous adjustments to household labor endowments, and argue based on the necessary sign of any endogenous adjustment that the key results are identified by exogenous changes in endowments. Finally, in Section 4 we provide a rich descriptive characterization of the state of labor in the four countries farm labor force participation rates, analyses of the intra-annual time path of labor utilization, geographical patterns of net increases and decreases in labor endowments, and others that simultaneously guide our empirical choices and provide an updated set of stylized facts for the study countries. We find an intriguing pattern of results, which we describe in Section 5. In pooled cross sectional analyses, separation is rejected everywhere. This pattern holds when we include household fixed effects, except in Uganda, where we cannot reject non-separation in the panel. The implication is that rural markets are reasonably complete in Uganda, and that non-separation in the cross-section is due to fixed differences between household types, perhaps from preferences for working on one s own farm. When we further allow for asymmetric responses to increases and decreases in the labor endowment, the results in the 1 The data were collected by the national statistics offices of the study countries, with technical support from the World Bank as part of the Living Standards Measurement Study - Integrated Surveys on Agriculture (LSMS-ISA). More details are at [[Link to LSMS-ISA website]]. 4

5 other three countries look markedly different. In Ethiopia the positive correlation between changes in farm labor usage and and changes in the household labor endowment is driven entirely by the decreases. That is, when a worker moves out of the household, there is a significant drop in per-acre labor use on the farm but there is no analogous response when someone moves in. This is consistent with labor markets that are characterized by excess demand, on average. In Malawi, we find the opposite pattern: non-separation in the panel arises from increases in endowments, but not from decreases. This is consistent with an average pattern of excess supply. In Tanzania the results are broadly similar to those from Malawi. This pattern of labor market failures is surprisingly consistent across the phases of agricultural production. In Ethiopia and Malawi, the above patterns hold during both the harvest and pre-harvest periods. In Tanzania, where the data are more finely disaggregated by activity, we find evidence of excess labor during weeding and harvest, but a (weakly) symmetric response of changes in labor usage to changes in labor endowments during the planting period. Although this symmetric result does not lend itself to a single interpretation, it suggests that input markets are least efficient in Tanzania during the planting phase. As a field, we know surprisingly little about how labor markets function in sub- Saharan Africa, in part because of how difficult it is to develop sharp tests. Farming households are on many sides of the market. They both buy and sell labor, and may also barter labor with neighbors through systems of reciprocal exchange (Feder, 1985; Reardon, 1997; Barrett, Reardon and Webb, 2001; Teal, 2011). Additionally, labor supply to the market is partly determined by the shadow wage of labor on the family farm, which is difficult to observe (Benjamin, 1992; Jacoby, 1993; Skoufias, 1994). The seasonality and inherent riskiness of agricultural production add additional complexity. Early season shocks, or anticipation of late-season labor market bottlenecks, may dynamically alter the household s position in the labor market (Fafchamps, 1993; Kochar, 1999; Dillon, 2014). Finally, nominal wage rigidity due to hold-up problems, norms against wage reductions, or other sources of incomplete adjustment may reduce the effectiveness of the price-setting mechanism in allocating labor efficiently across households and sectors (Dreze and Mukherjee, 1989; Osmani, 1990; Kaur, 2014). 5

6 Our analytical approach combines many of the strengths of previous papers in this area. Like Benjamin (1992), our tests are based only on characteristics of the input demand equations that prevail under a null hypothesis of complete and competitive markets. In this way we avoid structural estimation and the large set of required assumptions. Also, we use panel data to control for unobserved household characteristics (LaFave and Thomas, 2016), and we theoretically link potential wage rigidities (non-clearing labor markets) with the household response to exogenous in- or out-migration (Kaur, 2014). In this sense our findings align with recent evidence of persistent gaps between rural and urban wages (Gollin, Lagakos and Waugh, 2014; McCullough, 2015), which are indicative of significant structural barriers to fully clearing labor markets. What do our results suggest for policymakers? First, different approaches are called for in different countries. This may sound simplistic, because policies should always be tailored to local conditions. Here, however, we find results that appear to be similar across settings upon the initial analysis. There is a cross-sectional correlation between labor endowments and labor use on farm in all four countries (Dillon and Barrett, 2014) and a positive correlation in the panel for Ethiopia, Malawi, and Tanzania. Only when we allow for asymmetric adjustment do we see that the underlying labor market failure in Ethiopia is the opposite of that in Malawi and Tanzania. For Ethiopia, where the results indicate a labor shortage, it would be beneficial to expand programs that match workers to farmers or that promote adoption of labor-saving technologies (herbicides, tractors). In Malawi and (for the most part) Tanzania there is evidence of a labor surplus. Possible policy responses to this situation are the expansion of jobs programs or government spending to increase aggregate demand. Finally, we find little evidence that labor market conditions change from one agricultural phase to the next. The conditions that prevail during planting appear to persist through the end of the harvest, despite noticeable spikes in demand at certain times. This result is surprising, and contravenes both our expectations and assumptions that are commonplace in the literature. The rest of the paper proceeds as follows. In Section 2 we develop the theoretical framework and associated empirical tests. Section 4 describes the data sets and sample, as 6

7 well as a number of descriptive statistics that clarify the setting and rationalize some of the choices we make in the empirical implementation. In Section 5 we present our main results and a series of extensions and robustness checks. The paper concludes with a discussion in Section 6. 2 Theory and empirical framework In the first part of this section we develop a dynamic version of the standard agricultural household model (Sen, 1966; Singh et al., 1986; Benjamin, 1992). Our model is similar to that in LaFave and Thomas (2016). We then develop the tests that associate specific labor market failures with asymmetric responses to changes in labor endowments. We discuss identification in the third subsection, and then conclude the section with a description of the empirical specifications that we bring to the data. 2.1 A dynamic agricultural household model Consider a farming household endowed with L t units of labor in year t. The household divides its labor endowment between leisure L l t, work on the household farm L h t, and supply of labor to the market, L m t. The household has preferences over consumption C t and leisure L l t, represented by the strictly increasing and concave utility function U(C t, L l t). The household farm produces the single consumption good C using strictly increasing, concave production technology F (L t ), where L t represents total labor application, and other inputs are subsumed in the production function (we discuss one key input, land, in Section??). Total output is y = F (L t )ɛ t, where ɛ t is an exogenous production shock representing pest pressure, rainfall, and other agro-climatic factors. The household can hire labor on the market, represented by L d t. Let w t be the market wage rate, with the price of the output normalized to 1. The household has access to credit markets in which it can borrow or lend at interest rate r t. Hence, liquid wealth W t+1 is equal to 1 + r t times the difference between wealth at the start of period t, W t, and net income in period t. If markets are complete and competitive, and utility is inter-temporally separable, 7

8 then the household s utility maximization problem takes the following form: [ ] max E β t U(C t, L l t ɛ t, ρ t ) t=0 subject to: C t w t L m t r (W t+1 W t ) F (L t )ɛ t w t L d t (2) L t = L h t + L d t (3) L t = L h t + L m t + L l t (4) L l t, L h t, L d t, L m t, C t, 0 (5) (1) where the utility function is conditioned on the stochastic output shock and a parameter ρ t that represents preferences and endowments. The equality in (2) will hold at the solution. Under current assumptions, the model is recursive, and the consumption and production sides of the household problem can be solved separately. In period t, household members first choose L t to maximize expected farm profit, which is on the right-hand side of (2). They then maximize utility, conditional on expected farm income. The solution is characterized by the following: Π = max E [ ] F (L t )ɛ t w t L d t (6) L D t L S t L t = L h t L h t + L d t = L D (w t, r t ɛ t ) (7) + L m t = L S (w t, r t ρ t ) (8) where equation (6) is the expected profit function, equation (7) is the farm labor demand function, and (8) is the household labor supply function. The complete markets assumption imposes the testable exclusion restriction that labor demand is not a function of the household labor endowment, L t, which is a component of ρ t. With complete markets, L t depends only on prices and ɛ t. If all markets but one are complete, then separation holds, because relative prices can adjust to accommodate one non-tradable (Feder, 1985). In Figure 1, panels A and B show two possible cases under separation. 2 In panel A, the marginal rate of substitution at L t, the point at which the marginal revenue product of labor on farm is equal to the wage, is such that the household would rather work less than 2 The graphs in Figure 1 are based on figures in Benjamin (1992), with only minor modifications. 8

9 C t IC 2 C t IC 2 IC 1 slope = w t IC 1 F(L t ) F(L t ) slope = w t L t S L * t = L D t L L * t = L D t A. Separation with hiring B. Separation with market work L t S L F(L t ) C t slope = w t C t F(L t ) IC slope = wt * F(L t ) - w t L t θ IC slope = w t * F(L t ) + w t H t slope = w t w t L t θ L t S L (Farmer) w t H t L t D L (Farm) L tθ +L ts = L t D L t * L (Farm) L * t L ts = L td +H t L (Farmer) C. Non-separation with supply constraint D. Non-separation with demand constraint Put the notes here. Figure 1: Household labor supply and farm labor demand L t. This household provides L S t units of labor to the farm, and the farm hires additional workers up to the point L t. Panel B shows the opposite case. The household prefers to work beyond the point L t, hence it provides additional work to the market after supplying the optimal amount of labor to its own farm. This characterization of separation suggests that a household would not both buy and sell labor in the same season. In fact, we can allow for that possibility with only minor adjustments. One option would be to add to the model a utility value from sometimes working on others farms, possibly related to learning, socializing, or maintaining group cohesion to support coinsurance. An empirically tractable and plausible alternative would be to allow for variation across phases of production. A household s position in the labor market might be different during periods of peak demand (planting, harvest) than during 9

10 other cultivation periods, if wages and the shadow value of farm labor vary between periods. With access to panel data, we can test the exclusion restriction implied by equation (4) while controlling for household fixed effects (LaFave and Thomas, 2016). If non-separation in a cross-section is due to time invariant (or very slowly evolving) factors, such as managerial skill or preferences for working on one s own farm, then we should find that violations of separation in the cross-section disappear in the panel. 2.2 Non-separation and incomplete labor markets In this subsection we build on the dynamic model of the previous subsection to consider the implications of an incomplete labor market for household labor supply and farm labor demand. To fix ideas, assume that land markets are also incomplete, so that separation does not hold (we will discuss land explicitly, below). Benjamin (1992) extensively develops the theory governing household labor allocation decisions under non-separation for the two types of labor market failures of primary interest in this section. The first scenario is one in which the household faces a ration H t on the number of hours it can provide to the market, perhaps because of a downwardly sticky wage. The second is one in which the household farm faces a hard limit, L θ t, on the labor that it can hire in the market, perhaps because local markets do not adjust quickly enough to spikes in demand related to certain activities (planting, harvest). Panels C and D of Figure 1 show the implications of these two different scenarios for household labor supply and farm labor demand. In panel C, preferences are such that the household does not want to provide the additional labor required to reach L t, on top of the maximum amount that it can hire from the market (L θ t ). The household optimizes by providing only L S t to its own farm, and the shadow value of labor is wt, which is above the market wage. In panel D, preferences are such that even after providing H t labor to the market and working on the family farm, household members would prefer to work more. They cannot do so in the market, so instead they supply additional labor to the farm, up to the point L S t. At this optimum, wt is below w t. Benjamin (1992) shows that under either of these types of non-separation, the critical question is: How does the shadow wage vary with the household labor endowment? That is, 10

11 what is the sign of dwt /dl t in the cross-section? He further shows that under the plausible assumption that equilibrium labor supply increases with the labor endowment i.e., the addition of a household member does not raise the utility value of leisure so substantially that total household labor supply falls, hence dl S t /dl t > 0 then dwt /dl t < 0 in either case. This leads to the testable prediction that labor utilization on farm is increasing in the household labor endowment under either of these types of non-separation. In a cross-section, these predictions are based on infinitesimal changes in labor endowments, evaluated through differentials. The key comparative static, dl S t /dl t, is equivalent to dl D t /dl t, and both are symmetric by construction. In panel data, however, we observe discrete changes in household labor endowments from one period to the next. This introduces the possibility of asymmetric responses to changes in endowments. The potential asymmetries differ depending on which of these two labor market failures underlies non-separation. To see this, suppose first that a non-separating household in period t 1 experiences an increase in labor endowment from period t 1 to period t, i.e., L t > 0. Under the analogous assumption to Benjamin, that total desired household labor supply cannot fall when the labor endowment increases, this has the effect in panels C and D of Figure 1 of tilting the indifference curve (IC) to the right (in either case). The marginal rate of substitution at the previous optimum is now lower, and the new optimum moves to the right, with increases in labor supply by the household, labor demand on the farm, and consumption. In the panel D case, this discrete shift serves only to exacerbate the effect of the ration H t, and L D t increases 1-for-1 with L S t. However, if the household is initially like the one in panel A, then the increase in L t may relieve the worker shortage, so that the supply constraint no longer binds. In that case, the household sets L D t = L t, and supplies any additional labor to the market. The increase L t has made separation possible, and the new equilibrium looks like that in panel B. By an analogous line of reasoning, when the labor endowment falls from one year to the next ( L t < 0), L D t and L S t for a supply-constrained household (panel C) fall together. But for a household facing labor demand constraint H t in period t 1 (panel D), the reduction in the labor endowment may be such that the constraint no longer binds and separation becomes possible. For this household, the new optimum is like that in panel A. 11

12 Without knowing the exact shapes of the production function and the preference map, we cannot make predictions about the relative magnitudes associated with these changes. But if preferences and production are smooth in the neighborhood of the initial optimum, then in a large sample of households facing supply constraint L θ t we expect to see a larger average response of L D t to endowment decreases ( L t < 0) than to endowment decreases ( L t > 0), because some of the increases in L D t will be truncated at L t. Indeed, if L D t 1 is close to L t 1 for many households like that in panel C, then the response of L D t to a discrete increase in L t is unlikely to be statistically different from zero. Similarly, if L D t 1 is close to L t 1 for many households like that in panel D, then the response of L D t to a decrease in L t will be difficult to detect. 2.3 Failures in other markets It is well understood that non-separation identified in the labor dimension can stem from various underlying patterns of market failures, even when labor markets are complete. In this subsection we discuss those possibilities and consider whether other patterns of market failures could generate asymmetric predictions like those derived above Any two non-labor goods Suppose first that the labor market is complete, but the markets for any two other relevant goods or services, including outputs, are not complete and competitive. This is akin to a standard general equilibrium model with at least two non-tradables. In such a situation, relative prices cannot adjust to clear markets. Hence, households could face supply constraint L θ t or demand constraint H t simply because markets are not clearing generally, rather than because of a specific feature of the labor market. For example, a downwardly sticky wage could be due to some fundamental, such as social norms against wage decreases or strategic interaction between In one sense, this situation is not problematic for the empirical strategy implied by the arguments in Section 2.2. The labor market is still not clearing, and the pattern of asymmetric responses to changes in labor endowments can still potentially reveal whether 12

13 the average household faces a labor supply or labor demand constraint. Such an insight is important and policy relevant regardless of whether a specific feature of the labor market is the fundamental cause of non-clearing. However, the possibility that a non-clearing labor market could be a side effect of some other shortcoming serves as a cautionary note for the interpretation of results. The test underlying our main results can (in some cases) identify non-clearing labor markets and reveal whether the average household is supply- or demandconstrained, but it cannot distinguish between possible root causes of the incomplete labor market Credit Suppose the labor market is complete, but the markets for credit (and some other good) are not. A separating household like that in panel A of Figure 1 uses its liquid resources to hire L d t units of labor in the market. However, without a complete credit market the shadow value of cash to the household may be above the market interest rate, in which case the household cannot hire L d t and achieve L D t = L t. In that situation the household effectively faces a labor supply constraint, and looks like the non-separating household in panel C of Figure 1, even though labor markets are complete. Note that this is prediction is not symmetrical: there is no general reason that a household for whom the shadow value of cash is below the market interest rate should over-supply labor to its own farm. The implication is that even with complete labor markets we might still see the asymmetry associated with binding supply constraint L θ t : significant changes in L D t when L t is negative, but smaller or statistically insignificant changes when L t is positive. This is a potential challenge to the interpretation of the test proposed in Section 2.2. If we see this pattern, we can distinguish a labor supply constraint from a credit constraint if we test for heterogeneity by some proxy measure for liquid wealth. If households across the wealth spectrum exhibit this pattern of asymmetric responses, that is an indication that the shortcoming is in the labor market. If the asymmetric response is concentrated among households that are more likely to be credit-constrained, that suggests that the main driver is an incomplete credit market. Note that this test cannot provide insights into whether the entire structure of the 13

14 rural economy, including the demand for labor outside of agriculture, is distorted by a lack of access to finance. Identification here is based on within-household variation in farm labor utilization as a function of the household labor endowment, and hence can only provide insights into whether non-separation, specifically, is driven by incomplete access to credit for the farming households in the data Land Dillon and Barrett (2014) use the same data employed here to show that land markets are clearly functioning in many areas of sub-saharan Africa. Yet, the existence of a rental market, sales markets, or other institution for temporary assignment of land use rights does not guarantee that such markets are complete or competitive. Incomplete land markets can clearly introduce rigidities that lead to non-separation. The specific concern is that an inability to adjust the amount of land under cultivation might prevent households from optimally responding to changes in the labor endowment. Furthermore, there is a potential asymmetry in how incomplete land markets impact separation. It is always possible to reduce the amount of land under cultivation, by leaving some of it fallow. 3 However, incomplete land markets might make it difficult to increase cultivated land from one period to the next. Following Benjamin (1992) and LaFave and Thomas (2016), we control for cultivated land in our main specifications (we include in the regression the change in log of land cultivated land). Hence, our results capture the relationship between the change in the household labor endowment and the change in labor-used-per-acre. The rationale for including a control for land, but not other physical inputs, is that land can be treated as fixed once the cultivation season begins. The concern with that, which is related to the concern in the previous paragraph, is that households might anticipate problems finding workers when deciding how much land to plant, which introduces a form of simultaneity into the land and labor decisions. To address these concerns we implement two robustness checks. The first is to exclude land entirely from the input demand equation for labor, as we exclude other inputs. 3 Though fallowing may be unwise in some settings, if it reduces future claims on the plot (Goldstein and Udry, 2008). 14

15 Under the null of separation, this should have no influence on results. The second is to instrument for changes in cultivated land with changes in owned land. While households do buy and sell agricultural land in some areas, sales are not commonplace. Farmers make year-to-year adjustment of cultivated acreage primarily through rental markets, borrowing for free, fallowing, or acquiring temporary usage rights over community land from a local leader (REF). Hence, if the relationship between L D t and L t is driven by incomplete land markets, it should disappear or be severely attenuated in the IV Insurance Finally, suppose that the labor market is complete, but the market for insurance is not (and there is at least one other missing or incomplete market). In this case the household bears all risk associated with ɛ in (1) and (2). Because ɛ represents the multiplicative effect of a general form of uncertainty over the value of output, it includes various types of untradable risk, such as that related to weather, pest pressure, or output prices. It is straightforward to see that the lack of an insurance market can lead to nonseparation and a correlation between labor usage on farm and the labor endowment (Udry, 1999). The intuition comes from examining the first order condition for the choice of farm labor L t, under the assumption that labor markets are complete but the household bears all risk associated with ɛ. Letting g(ɛ) represent the density function of ɛ, the condition that implicitly defines L t is: [ ] U Ct (Ct, L l t ) F (L t )ɛg(ɛ) w t = 0 (9) ɛ where U Ct is the derivative of the utility function with respect to consumption. If the household labor endowment increases from one period to the next, the optimal demand for labor on farm, L t, need not be directly affected, because the labor market is complete. But optimal leisure, L l t, changes with the increase in the labor endowment, and this impacts the marginal utility of consumption (the first term in (9)). The value of L t that solves (9) changes with the labor endowment, even though the labor market is complete, because the household cannot sell away its production risk and thereby predict the marginal value of 15

16 consumption with certainty. In this case there is no a priori reason to expect asymmetric adjustment to L + t and L t. As long as the utility function is smooth in the neighborhood of observed consumption and leisure, households respond to changes in either direction. There are no thresholds beyond which L t L D t ceases to adjust, as in the labor market case from Section 2.2. Hence, asymmetric responses to increases and decreases in the labor endowment are evidence that non-separation cannot be due exclusively to insurance market failures. 3 Identification and estimation In this section we first describe the empirical framework suggested by the above theory. We then discuss identification. 3.1 Empirical specification To test the theory developed in the previous section, we estimate the following empirical models using nationally representative panel data from the four study countries (separately): L D fht = F + β 1 L ht + β 2 FL ht + γa ht + γ 2 demog ht + ν t + ɛ fht (10) L D fht = F + β 1 L ht + β 2 F L ht + γ A ht + γ 2 demog ht + ν t + ɛ fht (11) L D fht = F + β 1 L + ht + β 2 L ht + β 4 F L + ht + β 5 F L ht +γ 1 A ht + γ 2 demog ht + ν t + ɛ fht (12) where t indexes year, h indexes household, and f indexes cultivation phase (planting, weeding, harvest); quantity of labor demanded (L D fht ), labor endowment (L ht), and cultivated acreage (A ht ) are entered as logs; F is a vector of dummy variables for cultivation phases; demog is a vector of controls for the demographic breakdown of the household; ν represent time effects interpretable as levels in equation (10) and differences in equations (11) and (12); and ɛ is a statistical error term. Equation (10) is a pooled model, and equation (11) is a household fixed effects model 16

17 implemented in first differences. These two specifications provide baseline estimates for those in equation (12), a household fixed effects model that allows for possible asymmetry in the response of farm labor utilization to increases and decreases in the household labor endowment. This is the main specification of interest. The analysis in Section 2.2 suggests that when the average household faces the binding labor demand constraint H t, β 1 estimated in (12) will be positive and statistically different from zero with greater probability than β 2. In contrast, when the average household faces the binding labor supply constraint L θ t, we expect the opposite pattern. In large, nationally representative data sets, households in one area may face supply constraints while those in another are face demand constraints. The power of the test clearly weakens as the proportion of households facing each type of constraint becomes roughly similar. Additional work is needed to distinguish labor market failures from the other types of input failures discussed in Sections In section we argued that a credit constraint could look like a labor supply constraint, with β 1 positive and β 2 not different from zero. If we find this pattern, we interact the labor endowment variables with a binary variable for status as a household with above median wealth. If the asymmetry is concentrated among poor households, that suggests a credit constraint. If the asymmetry is general, the shortcoming is more likely in the labor market. 4 4 Data and descriptive patterns To test the predictions of the above model we use panel data from the Living Standards Measurement Study and Integrated Surveys on Agriculture (LSMS-ISA). These surveys are comprehensive household and agricultural surveys, conducted by the statistics offices of participating countries with cooperation and guidance of the World Bank. The data are nationally representative, span a wide range of topics, and are reasonably comparable across 4 The theory also suggests a test that compares the relative magnitudes of L S t and L D t to positive and negative changes in endowments. Unfortunately, such tests will not be possible in the data sets that we employ, because the survey module on household labor supply is incompatible with that on farm labor demand. Hence we follow the literature and focus on tests that use the farm labor demand equation. 17

18 countries. In Section 4.1 we describe the data and samples from the four study countries: Ethiopia, Malawi, Tanzania, and Uganda. Then in Section 4.2 we provide descriptive details about labor markets and labor endowments that are relevant for the analysis to follow. 4.1 Data and sample The four study countries are those for which at least two waves of LSMS-ISA panel data were available when we conducted the analysis. We use two waves of panel data from Ethiopia, two from Malawi, three from Tanzania, and four from Uganda, covering the following time periods: Ethiopia, and ; Malawi, and 2013; Tanzania, , , and ; Uganda, , , , and More details about the survey activities for each country are provided in Appendix A. Because our analysis is based on the input demand equation of the household farm, we restrict the samples to households that report cultivation of a positive number of acres in more than half of survey waves. For Ethiopia and Malawi this excludes all households that did not cultivate in both survey years. For Tanzania and Uganda, this excludes households that did not cultivate in more than one survey year. It is helpful for our cross-country comparisons that the survey questionnaires are based on a standard template, and hence are broadly similar across countries. Each survey begins with a household roster asking for the names of individuals who normally live and eat their meals together in the household. We use the list of such members to construct the variable for the labor endowment of household h in period t, L ht, by counting the number of working age household members. In the next subsection we provide a description and rationale for our definition of working age. The agriculture survey modules share some broad similarities across countries. Every survey allows for plot-specific reporting, though there is variation between countries in how plots are defined. Every survey also distinguishes between household labor and nonhousehold labor. In most cases there is more detail about household labor than hired labor. For example, the household labor module may ask the total number of weeks worked, average number of days per week, and average number of hours per day for each person who worked 18

19 on the plot, while the hired labor module may ask only about the total number of men from outside the household who worked on the plot and the average number of days a man was hired, and then repeat the those questions for women and children. 5 Where the agricultural labor surveys differ most is in the degree of disaggregation by activity. Questionnaires for Ethiopia and Malawi distinguish between non-harvest and harvest activities, which we use to form variables for labor demand during Cultivation and Harvest. The Tanzania data are even further disaggregated into Planting, which includes land preparation and planting, Weeding, which includes weeding and applying top-dressing fertilizer, and Harvest. The Uganda survey module does not allow for differential reporting by activity, hence we can only construct a single variable for all farming activities in Uganda. 6 Table 1: Summary statistics Ethiopia Malawi Tanzania Uganda (1) (2) (3) (4) (5) (6) (7) (8) Mean s.d. Mean s.d. Mean s.d. Mean s.d. Labor endowment, with kids Labor endowment, no kids Prime male share Prime female share Elderly male share Elderly female share Acres cultivated Acres owned Age of head (years) Education of head (years) Reference labor (person-days) Harvest labor (person-days) Weeding labor (person-days) Number of Obs Notes: Authors calculations from LSMS-ISA data. Labor endowment with kids uses adult equivalence scale for children aged 11-15, see Section Prime demographic groups are those aged 15-60; Elderly are aged 61+. The Reference agricultural phase is All non-harvest for Ethiopia and Malawi, Land preparation and planting for Tanzania, and All farming activities for Uganda. Table?? provides summary statistics for each country. Observations are captured 5 In Appendix A we provide details about variable construction for each country. 6 In a small number of cases, respondents report zero labor for one activity but a positive amount of labor for other activities. These zeroes may be measurement error, but they may also have an economic rationale, e.g., it is possible to apply zero weeding labor, or to apply zero harvest labor if the crop fails. We assign these zeroes a small, positive value, so that they are not dropped when we take logs. In our main tables this value is 0.1 person-days. All of our findings are robust to other reasonable replacement values, and to dropping these observations entirely. 19

20 at the household-wave level. Table?? shows that Tanzania households have the largest households, and that Malawian households have the least amount of labor demanded for their agricultural activities. Ethiopian households have the largest amount of labor demanded. The four countries have relatively similar shares of prime-age adults in their households (between 47% and 50%), though Ethiopia households have larger shares of elderly adults, 15% compared to 8, 8, and 10% for the other countries. Households in Malawi have the least amount of acres under cultivation, and also the youngest household heads. Household heads in Ethiopia have obtained the least amount of education. 4.2 Descriptive patterns In this subsection we present additional descriptive statistics that inform the empirical analysis and provide additional context about labor markets and labor force participation in the study populations. In some cases (as noted), details are relegated to the appendix Intra-annual time path of farm labor Farmers typically plant at the beginning of the rainy season. This leads to spatially correlated spikes in the demand for labor at planting time, and potentially again at harvest. If the supply side of the labor market does not adjust rapidly enough to meet demand during peak periods, which is all the more likely when the suppliers of market labor are farmers themselves, then separation may fail during some cultivation phases but not others. To examine the time path of farming labor, Figure 2 shows kernel regressions of labor demanded on farms (panels A and B) and labor supplied by households (panels C and D) across time, separately for the three regions of Malawi. The top two panels are based on the agriculture module from Malawi, which is the only data set in which we can match specific labor activities to dates. The data on farm labor utilization underlying these graphs is the same as that described in the previous subsection. There are three takeaways from panels A and B. The first is that the amount of household labor dwarfs that of hired labor (compare the vertical axes). The second is that the largest spike in labor demanded is associated with planting, which occurs toward the 20

21 5.3 Plot-level labor demand (person-days per half month) Plot-level labor demand (person-days per half month) August November February Month May August 0 August November February Month May August North Central South North Central South A. Farm use of household labor B. Farm use of hired labor 35 5 Household level labor supply (Hours per last 7 days) Household level labor supply (Hours per last 7 days) April 2010 July 2010 October 2010 Date January 2011 April April 2010 July 2010 October 2010 Date January 2011 April 2011 North Central South North Central South C. Household labor supply to own farm D. Household labor supply to local market Figure 2: Time path of labor demanded and supplied, Malawi Notes: Authors calculations from LSMS-ISA data. Top panel is from the long rainy season in the survey; bottom panel is from survey. All graphs are local polynomial regression using an Epanechnikov kernel. Panels C and D are local Additional details in Appendix A.3. end of the calendar year. Planting begins earlier in the South region than in the Central or the North, which matches the timing of the onset of the rains. The third takeaway is that labor utilization increases around harvest (May-July), but the spike is not as pronounced as that at planting, and is not present in all regions. This may reflect the fact that for some crops, farmers have more leeway with the timing of the harvest than they do with planting (though it may also reflect covariant production shocks leading to low yields that year). The lower two panels of Figure 2 are based on the household labor module from Malawi, which is the only survey with sufficient detail for us to examine the time path of labor supply over the year. 7 In the labor module of the household questionnaire, respondents reported the number of hours each household member spent on particular activities over the previous seven days. Panels C and D are kernel regressions of the responses for time spent 7 The sample in that year included 11,744 households, with interviews spaced uniformly across the year. 21

22 working on one s own farm and time spent supplying ganyu labor, or casual farm labor, in the local spot market. Note that the units of panels C and D (hours per last 7 days) are different from those of panels A and B (person-days per half month). Once again we see that labor supply to own farms is much greater than that to the market, at all times of year. Furthermore, intra-annual variation in labor supply to the market is less pronounced than that to own farms. The latter increases by % from peak to trough, while the former ranges from near-constant to at most a 50% increase from peak to trough. These two patterns are suggestive of non-separation: workers are ready and willing to supply additional labor on their own farm when needed, but do not (or cannot) exhibit a similar response in the labor market. Finally, the general pattern of intra-annual dynamics matches the labor demand side, with the peaks in own-farm labor supply occurring first in the South, then the Central region, then the North. While the patterns in Figure 2 are specific to Malawi, they underscore the importance of allowing for possible intra-annual variation in non-separation across phases of the cultivation cycle Defining the household labor endowment How do we measure the labor endowment of farming households? The main challenge in answering this question relates to choosing the age cutoffs at which someone enters or exits the labor endowment. It is clear in the data that some children and seniors supply labor to the market, participate in household chores, or work on the farm. Hence, there is no justification for arbitrarily excluding all such individuals from the labor endowment. To guide this decision, we examine own-farm labor supply by age across the data sets. Figure 3 shows kernel regressions of the own-farm labor force participation rate (LFP - the extensive margin) and the average number of days worked by those who are working (the intensive margin), plotted against age. Separate plots are shown for each farming activity. In all figures the axes are scale so that the LFP lines appear above those for days worked (the LFP axis is on the left). There are a number of interesting patterns in Figure 3. First, to our surprise, older people do significant work on farms. In all figures, the LFP rate for 70-year-olds is higher 22