Constraints on Labor and Land and the Return to Microcredit and Microinsurance∗ Alex Cohen† October 2016

Abstract How much do constraints on labor and land weaken the impact of microcredit and microinsurance? I answer this question using data from two experiments, which relaxed credit constraints for firms in Sri Lanka and uninsured risk for farms in Ghana. I combine observed changes in inputs in response to the experimental treatments with structural assumptions and a production function estimation approach that exploits variation induced by the experiments. I estimate that raising ceilings on constrained inputs by 10 percent would have increased the treatments’ impacts on profits by up to 61 percent in Sri Lanka and 82 percent in Ghana. Keywords: microcredit, microinsurance, financial constraints, labor markets, land markets, firms, farms, production functions, randomized experiments JEL codes: O12, O16, D12, Q12, D24

∗

This paper is a revised version of the first chapter of my Ph.D. dissertation. It was previously circulated under the title “Do Financial and Factor Market Frictions Interact to Constrain Growth? Evidence from Firms and Farms.” I am grateful to my advisors, Penny Goldberg, Mushfiq Mobarak, Mark Rosenzweig and Chris Udry, for their guidance and support. I thank Suresh De Mel, David McKenzie and Chris Woodruff for making the data from their experiment in Sri Lanka available and Dean Karlan, Robert Osei, Isaac Osei-Akoto and Chris Udry for sharing the data from their experiment in Ghana. I also thank Muneeza Alam, Treb Allen, David Atkin, Sabrin Beg, Claire Brennecke, Jessica Cohen, Saby Das, Cheryl Doss, Julia Garlick, Dean Karlan, Dan Keniston, Xiang Ma, David McKenzie, Melanie Morten, Sri Nagavarapu, Tommaso Porzio, Nick Ryan, Gabriella Santangelo, Meredith Startz, Russell Toth, Eric Weese and participants at several seminars for numerous helpful comments and suggestions. All errors are mine. † Contact information: Richard M. Fairbanks Foundation, Indianapolis, IN 46260. E-mail: [email protected].

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Introduction

Small firms and farms dominate employment in developing countries. As a result, researchers and policymakers have devoted substantial attention to relaxing financial constraints on these firms and farms by extending access to microcredit and microinsurance. The underlying theory is that relaxing financial constraints will raise investment and profits. Yet recent papers often find puzzlingly weak effects of credit and insurance (Cole et al. 2014a, 2014b, Angelucci et al. 2015, Attanasio et al. 2015, Augsburg et al. 2015, Banerjee et al. 2015, Crepon et al. 2015, Tarozzi et al. 2015). One explanation may be that firms and farms also face constraints in markets for factors of production like labor and land, which weaken the impact of these programs. For example, supervision or search costs for hired labor may make expanding labor beyond family members prohibitively costly (Feder 1985, Eswaran and Kotwal 1986, Benjamin 1992, Fafchamps 2003, Foster and Rosenzweig 2011, Bloom et al. 2013). For farms in particular, missing land markets may make it difficult to scale up land in response to improved access to credit or insurance (Goldstein and Udry 2008, Adamopoulos and Restuccia 2014). In this paper, I quantify the extent to which constraints on labor and land weaken the impact of relaxing financial constraints. I use two randomized experiments that relaxed financial constraints to varying degrees for small firms in Sri Lanka (De Mel et el. 2008) and farms in Ghana (Karlan et al. 2014). Using a simple model of production, I first develop a test for whether constraints on labor and land limited firms’ and farms’ ability to scale up production in response to the treatments provided by the experiments. I then use my model and estimates of production function parameters to quantify how much larger the effect of the treatments on firm and firm profits would have been if labor and land constraints were relaxed. My estimates indicate that factor market constraints severely limited the impact of relaxing financial constraints via the treatments. This has several implications for researchers and policymakers interested in the impacts of microcredit, microinsurance and other programs aimed at relaxing constraints on small-scale producers. Financial constraints are common in developing countries, as exemplified by the experiments reported in De Mel et al. (2008) and Karlan et al. (2014). De Mel et al. (2008) provide cash grants of varying sizes to small firms in Sri Lanka. They show that credit

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constraints limit firm investment and that their treatments relaxed this constraint. Karlan et al. (2014) provide discounted rainfall insurance, cash grants and a combination of both to small farms in Ghana. They show that uninsured risk limits farm investment and that their treatments relaxed this constraint. In both settings, however, there is reason to believe that constraints in factor markets may be at work, too. In both the Sri Lanka and Ghana samples, labor comes primarily from family members, consistent with high monitoring or screening costs associated with hiring non-family members. In the Ghana sample, land is either inherited or allocated by village chiefs or family heads, and there is virtually no renting of land, suggesting frictions in this market, too. To test whether labor and land market constraints weaken the effect of relaxing financial constraints, I first develop a model of firm or farm production. My model predicts that if factor markets are perfect, relaxing financial constraints through the treatments causes firms or farms to increase all inputs “in proportion,” such that the ratios of the marginal revenue products of these inputs are unchanged. If, however, there are ceilings on how much firms and farms can use of certain inputs, such as labor or land, relaxing financial constraints will cause firms or farms to distort their input mixes away from labor and land as they scale up. That is, they will increase these inputs “disproportionately less” than inputs that only face financial constraints, such that the ratios of the marginal revenue products of these two types of inputs increases. In both settings, I call inputs that are only subject to financial constraints “materials.” In Sri Lanka, materials are the raw materials used in production. In Ghana, these inputs are tractor rental and chemical inputs like fertilizer. These inputs are purchased in well-functioning markets and, as a result, are not likely to be subject to factor market constraints. The ratios of the marginal revenue product of inputs with factor market constraints (i.e., labor or land) to those that do not face factor market constraints (i.e., materials) capture the shadow prices of inputs with factor market constraints. These are the prices the firm or farm would be willing to pay for an additional unit of those inputs, taking into account financial constraints. An increase in the shadow price of labor or land as a result of the treatments suggests there are frictions in the market for that input that prevent firms or farms with relaxed financial constraints from buying inputs from firms or farms without relaxed financial constraints. I run this test by estimating the impact of treatments in the Sri Lanka and Ghana ex2

periments on the shadow prices of labor and land, measured by the ratios of the marginal revenue products of labor and land to the marginal revenue product of materials. Doing this requires calculating the ratios of the marginal revenue products of inputs and, hence, imposing a functional form on the production function. I assume a Cobb-Douglas production function in both settings. In the Sri Lanka experiment, I find that the smaller cash grant had no effect on the shadow wage. However, relaxing financial constraints even more with the larger cash grant, which was twice as big, led to a 46 percent increase in the shadow wage, suggesting firms hit constraints on labor. In the Ghana experiment, I find that insurance alone led to an 11 percent increase in the shadow wage but had no effect on the shadow rental price of land, suggesting that farmers were able to acquire enough additional land. However, the combination of insurance and cash, which provided the biggest relaxation of financial constraints, led to a 22 percent increase in the shadow price of land and an even greater increase in the shadow wage (36 percent). (The magnitude of the effects of cash only were weaker than the combination of cash and insurance, but the difference is not statistically significant.) These results suggest frictions in labor and land markets distorted firms’ and farms’ investment responses to relaxed financial constraints and prevented the reallocation of labor and land from firms and farms with lower shadow prices to those with higher shadow prices, particularly when the relaxation of financial constraints was the largest. To further quantify the results, I conduct a series of counterfactuals that answer the question: How much larger would the impact of the treatments on firm and farm profits have been if we relaxed constraints on labor and land? I do this by first estimating firms’ and farms’ Cobb-Douglas production function coefficients. I employ a version of the dynamic panel approach used in the literature on firm production function estimation, in which lagged inputs are valid instruments (Ackerberg et al. 2015), and also exploit the experimental treatments as additional instruments. Though this approach is traditionally applied to firms in developed countries, I argue firms and farms in developing countries provide an ideal setting to apply it because financial and factor market frictions provide the variation in shadow prices of different inputs necessary for identification. Next, using the estimated coefficients, I allow a representative firm or farm to reoptimize its input choices with the effect of the treatments on financial constraints intact 3

but with higher ceilings on labor and land. In Sri Lanka, I estimate that raising the ceiling on labor by 10 percent would have increased the effect of the larger cash grant on profits by 61 percent. In Ghana, I estimate that raising the ceiling on labor by 10 percent would have increased the effect of the combination of insurance and cash on profits by 33 percent, raising the ceiling on land by 10 percent would have increased the effect of the combination of insurance and cash on profits by 41 percent and raising the ceiling on both labor and land by 10 percent would have increased the effect of the combination of insurance and cash on profits by 82 percent. The results of this paper have a number of important implications for understanding the impact of insurance and credit in developing countries. Most obviously, programs that only relax financial constraints may have diminished effects, and resources spent on them will have a lower return, when there also exist frictions in labor and land markets. These frictions may at least partially explain the weak impact of microcredit and microinsurance products in many settings. For marketers and providers of credit and insurance, these products may have greater demand where labor and land constraints are weaker (e.g., in industries where workers are paid a piece-rate and monitoring is less costly) or when paired with other interventions, such as land tenancy reforms or programs that improve firms’ or farms’ ability to screen and monitor employees. When factor and financial market frictions interact, there may also be unintended consequences. For example, if labor market frictions prevent firms or farms from using non-family labor, relaxing financial frictions may increase the use of child labor (see, for example, Augsburg et al. (2015)). My results have implications beyond the realm of financial intervention as well: Any program designed to stimulate small firm and farm growth (e.g., improvements in market access or provision of productivity-improving technologies) will likely have the same deficits if factor market constraints are present. I also contribute to the growing literature on misallocation in developing countries (Banerjee and Duflo 2005, Hsieh and Klenow 2009). A major goal of this literature is to determine the causes of misallocation. In a recent contribution, Shenoy (2014) provides a clever approach for decomposing misallocation into misallocation from factor market frictions and misallocation from financial market frictions. I use a similar approach to shed light on how these frictions interact. My results suggest that relaxing financial frictions can worsen misallocation caused by factor market frictions. Failing to account 4

for this interaction will lead to overestimates of the effect of relaxing financial frictions on reducing misallocation. A key assumption underlying my test and counterfactual is that the production function is Cobb-Douglas. My production function estimation approach permits two tests of this assumption. First, I estimate the production function for just treated firms or farms and compare estimates from the full sample of firms or farms. This allows me to test whether my results are driven by firms or farms switching to less labor- or land-intensive production technologies as they scale up. Second, I conduct an overidentification test, using the additional instruments from the treatments, which allows me to test for deviations from Cobb-Douglas. With both tests, I fail to reject the null hypothesis that the CobbDouglas assumption is correct. However, the power of these tests is low, and I regard this assumption as a limitation of this approach. An alternative approach, which does not require assuming a functional form of the production function, would be to conduct a randomized experiment that relaxes both financial and factor market constraints. De Mel et al. (2013) attempt such an experiment by offering a matched savings program (to relax credit constraints), along with wage subsidies (intended to relax labor constraints), for a sample of Sri Lankan firms. They find that only 20 percent of firms add employees in response to wage subsidies and that the effect of wage subsidies on profits is zero (both on their own and combined with the savings program). These findings suggest the wage subsidy was not sufficient to relax labor constraints, perhaps because firms face such high costs of search, screening or monitoring that hiring a new employee is not optimal even with the subsidy.1 Their results highlight the difficulty in experimentally relaxing labor constraints and motivates using a more structural approach, like the one used in this paper, to infer interactions between constraints in financial and factor markets.2 1 Those 20 percent that do respond to the treatment may not face these hiring costs and, as a result, do not see an increase in profits when they add employees in response to the subsidies. In a companion paper, De Mel et al. (2010) show these firms tend to have higher sales, more talented managers and hired employees in the past, suggesting they may face lower hiring costs than the average firm. These firms also tend to be larger than the firms in the sample from De Mel et al. (2008), which I use in my analysis. 2 In a related paper, Hardy and McCasland (2015) find that providing small firms in Ghana with access to a pool of workers screened by a government job placement program leads to substantial increases in employment and profits, consistent with the intervention relaxing labor market constraints. Such an intervention could be paired with treatments designed to relax financial constraints to experimentally explore the interaction. However, finding settings to implement such an intervention is non-trivial, and more structural approaches can provide an alternative.

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As an additional methodological contribution, I show how experiments may be used to provide additional identification for estimating production functions. To the best of my knowledge, this is the first paper to combine standard instruments with instruments provided by experiments for production function identification.3 This method might prove helpful in future work on estimating production functions (e.g., by providing overidentification tests to check the assumptions underlying estimation approaches or by increasing the precision of estimates) and measuring productivity, misallocation and inefficiency. The rest of the paper proceeds as follows: In Section 2, I describe the two experiments, settings and datasets. In Section 3, I use a model of firm or farm production to derive tests for whether constraints on labor and land weaken the effect of relaxing financial constraints. I implement these tests in Section 4, using data from the two experiments. In Section 5, I describe and implement my production function estimation approach. In Section 6, I report results from counterfactuals where ceilings on labor and land are relaxed. I conclude in Section 7. I provide tests of the Cobb-Douglas assumption and additional results in the Appendix.

2

Experiments, Settings and Data

In this section, I provide background on the experiments and settings I use, including information on financial and factor markets, and I describe the data.4

2.1 2.1.1

Firms in Sri Lanka Experiment and Setting

The first experiment I use provided cash and in-kind grants to small firms in Sri Lanka (De Mel et al. 2008). The firms in the sample were chosen so that they had less than 100,000 Sri Lankan rupees (roughly 1,000 U.S. dollars) in physical assets, not including land and buildings, and no paid employees. The firms are split across two broad industries: manufacturing/services (e.g., producing clothing and food products) and retail (mostly small

3

Keniston (2011) compares estimates of the return to capital from structural production function estimation and experimental variation, using the De Mel et al. (2008) experiment. However, he does not exploit the extra identification provided by the experiment. 4 Further details can be found in De Mel et al. (2008) and Karlan et al. (2014).

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grocery stores). The firms are spread across three districts in southern and southwestern Sri Lanka. The experiment provided four treatments: (i) a cash grant of 10,000 LKR (100 USD), (ii) a cash grant of 20,000 LKR (200 USD), (iii) an in-kind grant of 10,000 LKR (100 USD) and (iv) an in-kind grant of 20,000 LKR (200 USD). Firms receiving in-kind grants could redeem the grant for either raw materials or physical capital (but not labor). De Mel et al. (2008) use the effect of the treatments on profits to argue that the firms in the sample face severe credit constraints. However, there is reason to believe that the firms in the sample may also face frictions in markets for factors of production— specifically, labor. The firms in the sample use very little hired labor. 76 percent of labor hours come from the owner, and 21 percent comes from family members, leaving 3 percent from hired (non-family) labor. Hiring labor may be costly due to the costs of supervision to prevent theft or shirking or search costs to find trustworthy employees. The observation that firms use very little non-family labor does not necessarily mean there are labor market constraints that constrain hiring. It could simply be the case that firms’ demand for labor is small and, thus, there is no need for hired labor. The tests that I implement in Section 4 exploit the relaxation of financial constraints, which should increase the demand for labor, to determine whether labor market constraints exist and constrain firms’ response to, say, access to credit. A priori there may be less reason to believe there are frictions in markets for raw materials and physical capital (i.e., small machines and tools), the other two factors of production for the firms in the sample. Firms who received in-kind grants were notified that they would receive the grants in the evening, then went with research assistants to markets of their choosing to purchase the raw materials or physical capital they wanted the following day. This provides some suggestive evidence that there do not exist frictions in these factor markets, such as shortages or high transportation costs, that might also constrain investment in materials and physical capital. Furthermore, given the small size of these firms and the types of physical capital they use, it is unlikely that they face the type of adjustment or time-to-build costs that are normally incorporated in firm investment problems.

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2.1.2

Data

De Mel et al. (2008) collected data on firm production over nine waves, conducted every four months, from April 2005 to April 2007.5 In the empirical portion of the paper, I use data on firm inputs and output. Output is total revenue by the firm over the past month. The three inputs are labor, raw materials and physical capital. Labor is the sum of hours worked by the owner, family members and hired labor over the past month.6 Raw materials are firms’ total expenditure on raw materials over the past month.7 Physical capital is the value of business tools, furniture, vehicles and other physical assets, not including land or buildings. Output, raw materials and physical capital are deflated to April 2005 levels using the Sri Lankan CPI. Table 1 reports summary statistics for inputs and output for my preferred sample. This sample includes 360 firms and 2,850 firm-year observations. To create my preferred sample, I start with the preferred sample used by De Mel et al. (2008), which excludes firms directly affected by the tsunami that took place in December 2004 and those with absolute profit changes in the outer 0.5 percentiles. I limit the sample to firms who use positive amounts of labor, raw materials, physical capital and output so that I can use a Cobb-Douglas production function.8 Finally, I Winsorize inputs and output at the 2nd and 98th percentiles to weaken the effect of outliers.

2.2 2.2.1

Farms in Ghana Experiment and Setting

The second experiment I use provided access to rainfall insurance and cash grants to small farms in northern Ghana (Karlan et al. 2014). The farms in the sample were chosen so 5

All firms were interviewed at least once before treatment and several times post treatment. Some of the treated firms received treatment after the first wave, and some received treatment after the third, due to logistical reasons. 6 The questionnaire asks owners to report labor from the past week, so I multiply by 4.2 to create monthly labor. This re-scaling has no effect on the test (since the multiplier falls out when we take logs). I choose to report the re-scaled (monthly) labor simply because the counterfactual requires putting all inputs in monthly terms. 7 A better way to define this would be to use raw materials used over the past month. However, this measure is not available for the first wave of the survey, which provides the only pre-treatment round for roughly half of the treated firms. Re-running the analysis with this alternative measure of raw materials yields similar results. These results are available upon request. 8 This eliminates 363 observations, or roughly 11 percent of the sample. 5 percent of observations report zero labor hours, 2 percent report zero raw materials and 1 percent report zero physical capital.

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that they had less than 15 acres of landholdings. The experiment provided three treatments: (i) an offer of rainfall insurance for free or at a subsidized price, (ii) a cash grant and (iii) a combined treatment that provided both access to rainfall insurance and a cash grant. The cash grants provided 112 Ghanaian cedis (approximately 85 U.S. dollars) per acre for an average cash grant of 553 GHC (420 USD) per farmer. The rainfall insurance had an expected payout of 62 GHC (47 USD) per acre. The insurance policy paid out if rainfall was above or below “trigger” levels chosen based on historical rainfall data. Karlan et al. (2014) use these different treatments to argue that uninsured risk constrains investment for farmers in the setting. Is there any a priori reason to believe there are frictions in labor and land markets might also constrain investment and weaken the impact of relaxing uninsured risk? Among farmers in the sample, farm labor comes primarily from family members. The share of farmers’ own labor and labor from family and friends is 77 percent on average in the sample. The remaining labor comes from communal labor (13 percent)—that is, labor exchanged among households—and hired labor (10 percent). Non-family labor (hired or communal labor) may be subject to supervision costs. Farmers report paying hired laborers based on time worked on the farm. When farmers are paid time wages, rather than a piece-rate, the scope for moral hazard from unobservable effort is greater and so is the need for supervision. For communal labor, there is no explicit wage, as farmers repay labor from their neighboring farmers by working on their neighbors’ farms. Of course, farmers may use a small share of hired labor because their labor needs are small, not because they face frictions in labor markets. The tests in Section 4 provide a way to determine whether there exist labor market constraints and how strong they are by measuring how much farmers are able to adjust labor in response to a shock that should raise their demand for labor (in this case, relaxing financial constraints). Turning now to land, in northern Ghana, as in many places in Sub-Saharan Africa, land markets are thin. In the survey, farmers report that they obtained nearly 100 percent of the plots they cultivate through inheritance or “allocation free of charge” by village chiefs or family heads. While there is no formal land market, the allocation of land provided through informal mechanisms may achieve the same allocation as the market would by reallocating land to farmers who have their financial constraints relaxed via the treatments. 9

Again, this is exactly what I test in Section 4. The final factor of production that farmers in the sample use, outside of labor and land, is what I call materials. These include both tractor rental for plowing and chemical inputs, such as fertilizer and weedicide. In northern Ghana, tractors are rented at the beginning of the season from a “tractor man.” Fertilizer and other chemical inputs are purchased from local sellers. Since these inputs are purchased in fairly well-established markets, I argue it is not likely that they face frictions to the extent that labor and land do. 2.2.2

Data

Karlan et al. (2014) collected data on farm production during the harvest period of each of the three years of the experiment (2009-2011).9 I use input and output data as the main variables in my empirical analysis. Output is the total value of crop production. I value physical output from each crop at the median market price and sum across all crops. I aggregate inputs into labor, land and materials. Labor is days of labor employed on the farm and includes the farmer’s own labor, family labor, communal labor and hired labor. Land is the cultivated area, measured in acres. Materials are the sum of expenditures on chemical inputs, bullocks and tractor costs. Chemical inputs are calculated as the chemical quantity used multiplied by the median price. Chemical inputs include fertilizer, weedicide/herbicide, insecticide and fungicide. Bullocks value is calculated as the median cost per acre for bullocks services multiplied by the number of cultivated acres. Bullock cost per acre is defined as the median plow cost per acre for farmers who reported using bullocks. Tractor value is the cost per acre for tractors multiplied by the number of cultivated acres. Tractor cost per acre is defined as the median plow cost per acre for farmers who reported using tractors. Materials are roughly evenly split between chemicals 9

The treatments varied by year. In the first year, Karlan et al. (2014) split farmers into four groups: farmers who received a cash grant only, farmers who received access to free rainfall insurance only, farmers who received both the cash grant and free rainfall insurance and farmers who received neither. In the second year, they provided the same treatments. However, this time they offered rainfall insurance at randomly varying prices below the actuarially fair price, instead of providing it for free. In the third year, they only provided access to subsidized rainfall insurance but at a new range of prices. Karlan et al. (2014) do not include inputs and output from 2011 in their analysis. I include 2011 because it provides additional data and is important for the production function estimation results in Section 5, since identification relies on lagged inputs. The results in Section 4, however, are unchanged if I limit the analysis to the 2009-2010 sample Karlan et al. (2014) use. These results are available upon request.

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and plowing (bullocks and tractors). The share of materials from chemicals is 44 percent on average (with most coming from fertilizer), and the share of materials from plowing is 56 percent on average (with most coming from tractors). For output and materials, prices are measured in GHC and deflated to 2010 levels. I aggregate all inputs and output to the household level by summing across plots. Table 2 presents summary statistics for farmers in my preferred sample. My preferred sample includes 1,341 farmers and 3,448 farmer-year observations. I limit the sample to farmers who use positive amounts of labor, land, materials and output so that I can use a Cobb-Douglas production function.10 Finally, I Winsorize inputs and output at the 2nd and 98th percentiles to weaken the effect of outliers.

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Model

In this section, I provide a model of firm or farm production with financial constraints (either credit constraints or uninsured risk) and potentially constraints in factor markets (namely, labor and land). I use the model to derive a test for whether constraints in factor markets weaken the impact of relaxing financial constraints. I will also use the model to estimate the impact of relaxing financial constraints in counterfactual scenarios where factor market constraints are weakened. While the model encompasses both settings, I split this section by setting for clarity.

3.1

Firms in Sri Lanka

Firms in Sri Lanka solve a standard firm production problem with two potential frictions: constraints in labor markets and a credit constraint. Each period, firms choose inputs (labor, Lt , raw materials, Mt , and physical capital, Kt ), consumption, ct , and savings, At+1 , to maximize expected utility from consumption. The price of labor is w. The price of materials is p. The price of physical capital is q. The interest rate is r. The physical capital depreciation rate is δ. Output is a function of productivity, ωt , which is unknown before production. The production function is Cobb-Douglas.

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This eliminates 85 observations, or roughly 2 percent of the sample.

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Firms face a credit constraint that limits the amount they can borrow for inputs. However, they do not face uninsured risk. In their study, De Mel et al. (2008) find that the credit constraint, not uninsured risk, is the binding financial friction. To show this, they do the following: They use the cash and in-kind grants as an instrument for capital stock—that is, physical assets, excluding land and buildings, plus inventory. They then use the increase in capital stock induced by the grants to estimate the return to capital. They find returns to capital that exceed prevailing market interest rates. This suggests firms face either a credit constraint or uninsured risk, which limits investment. They then show that these effects do not vary with firm owners’ risk preferences, which suggests that it is likely not uninsured risk that is limiting investment but rather a credit constraint. The experiment provided cash grants, zt , of varying sizes, meant to relax the credit constraint.11 I model the credit constraint as a ceiling, H(At , zt , Kt ), which is a function of assets coming into the period, the cash grant and physical capital. The idea is that firms can use each of these as collateral for a loan.12 Firms also potentially face a ceiling on the amount of labor they can hire, L. This is meant to capture limits on the amount of labor firms can hire due to the cost of supervising workers to prevent shirking or theft or the cost of searching for trustworthy employees. For example, these costs may limit owners to hiring just family members or, consistent with what we observe in Sri Lanka, just themselves.13 The firm’s problem is   X max E  β t u(ct )

(1)

t≥0

s.t. ct + At+1 = exp(ωt )Lβt l Mtβm Ktβk + (1 − δ)qKt − (1 + r)(wLt + pMt + qKt )

(2)

+ (1 + r)At + zt wLt + pMt + qKt ≤ H(At , zt , Kt )

(3)

Lt ≤ L.

(4)

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I discuss the in-kind grants below. Notice that I allow physical capital to be used as collateral. This follows work by Fernandes and Pakes (2008) and Szabo (2015), who find that firms in India and Ghana, respectively, tend to over-use physical capital, consistent with physical capital being valuable not just as a productive input but as a form of collateral. 13 An alternative way to model labor market imperfections would be allow the wage to be an increasing function of the amount of labor hired. This yields similar predictions. 12

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The first-order conditions yield the following formulas for the marginal revenue products of each input: βl E[exp(ωt )]Lβt l −1 Mtβm Ktβk = (1 + r + µ)w + λ

(5)

βm E[exp(ωt )]Lβt l Mtβm −1 Ktβk = (1 + r + µ)p

(6)

βk E[exp(ωt )]Lβt l Mtβm Ktβk −1 = (r + δ + µθ)q,

(7)

where µ is the multiplier on the constraint in (3) divided by u0 (ct ), λ is the multiplier on the constraint in (4) divided by u0 (ct ) and θ ≡ 1 − HK (At , zt , Kt ) captures the effect of physical capital on the credit limit. We can use the changes in the ratio of the marginal revenue product of labor to the marginal revenue product of raw materials in response to the treatments to test whether the labor market constraint weakened the impact of relaxing the credit constraint through the treatments. Suppose first that there is no constraint in labor markets, i.e., the ceiling on labor does not bind with or without the cash grant. The cash grant relaxes the credit constraint (i.e., µ falls). This shows up as a lower “wedge” from the credit constraint in the FOCs. Firms will increase both labor and raw materials (and potentially physical capital). However, the ratio of the marginal revenue product of labor to the marginal revenue product of raw materials remains unchanged. Now, suppose the labor market constraint does bind, either after receiving the cash grant or both before and after receiving the cash grant. Again, the cash grant will relax the credit constraint, leading to a lower “wedge” from the credit constraints in the FOCs. This time the labor market constraint will prevent firms from increasing labor. As a result, the ratio of the marginal revenue product of labor to the marginal revenue product of raw materials will rise. Recall that De Mel et al. (2008) provide cash grants of different sizes. Higher cash grants should relax financial constraints even more. As a result, firms should be more likely to run into constraints in labor markets (or be more severely constrained by a ceiling that bound before receiving the cash grant). This should lead to larger changes in the ratios of the marginal revenue product of labor to the marginal revenue products of raw materials. These predictions are formalized in the following propositions:

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Proposition 1 Suppose the credit constraint binds. If the ceiling on labor does not bind, then providing a cash grant, zt , has no effect on the ratio of the marginal revenue product of labor, Lt , to the marginal revenue product of raw materials, Mt . Proposition 2 Suppose the credit constraint binds. If the ceiling on labor binds, then providing a cash grant, zt , increases the ratio of the marginal revenue product of labor, Lt , to the marginal revenue product of raw materials, Mt . Proposition 3 Suppose the credit constraint binds. If the ceiling on labor binds, then providing z2t > z1t increases the ratio of the marginal revenue product of labor, Lt , to the marginal revenue product of raw materials, Mt , even more than providing z1t . Another way to interpret the ratio of the marginal revenue product of labor to the marginal revenue product of materials is the shadow wage. Since materials are valued at a price of 1, this ratio tells us the implicit price of an additional unit of labor. When there are frictions in the market for labor, relaxing financial constraints raises the shadow wage. That is, firms who have their credit constraints relaxed through the treatment will be willing to pay more for labor than firms in the control group. Labor market constraints are what prevent labor reallocation from occurring. The size of this increase in shadow price gives us a measure of the magnitude of factor market constraints. A large gap in shadow wage across firms with and without credit constraints tells us there exist large frictions that make such a trade unprofitable, despite the apparent gains.14 Note that I do not include predictions related to physical capital. Since physical capital enters the credit constraint, the predictions on its marginal revenue product, relative to the marginal revenue product of other inputs, are ambiguous. Note also that I have ignored the in-kind grants. Recall that the in-kind grants can be spent on raw materials (or physical capital) but not labor. If the in-kind grants are perfectly liquid, then we can treat them just like cash grants in the model. If, however, these grants cannot be costlessly liquidated, then they will lower the effective price of raw materials more than labor. As a result, firms who receive in-kind grants will have a higher 14

This interpretation follows the literature on misallocation of factors of production across firms or farms in developing countries (e.g., Banerjee and Duflo 2005, Hsieh and Klenow 2009). Finding large differences in shadow prices indicates a high degree of misallocation. In the language of Hsieh and Klenow (2009), the financial friction acts as a “tax” that affects all inputs (like a tax on output), whereas factor market constraints are specific to certain inputs.

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ratio of the marginal revenue product of labor to the marginal revenue product of raw materials, even when there are no frictions in labor markets. Therefore, the in-kind grants do not provide a clean test for labor market constraints, and I focus on the cash grants, though I present results for the in-kind grants as well in Section 4.

3.2

Farms in Ghana

Farms in Ghana solve a standard firm production problem with two potential frictions: constraints in labor and land markets and uninsured risk. Each period, farms choose inputs (labor, Lt , materials, Mt , and land, Kt ), consumption, ct , and savings, At+1 , to maximize utility from consumption. The price of labor is w. The price of materials is p. The price of land is q. The interest rate is r. The land depreciation rate is δ. Output is a function of productivity ωt , which is unknown before production. The production function is Cobb-Douglas. Farms face uninsured risk but no credit constraint. In their study, Karlan et al. (2014) find that uninsured risk is present but the credit constraint does not bind. They note that if insurance alone leads to an increase in investment, then it must be the case that there is uninsured risk but no credit constraint. If the credit constraint does bind, then farmers will not be able to find additional funds to finance increases in investment in response to lowered risk. Their finding that rainfall insurance alone led to an increase in investment indicates uninsured risk is the primary financial friction in this setting. The experiment provided both cash grants and insurance against shocks. I model these as pay outs that are allowed to be state-contingent, zt (ωt ). In the case of pure cash grants, which are not dependent on productivity shocks, this collapses to zt . Firms also potentially face a ceiling on the amount of labor and land land they can employ in production. These ceilings are denoted by L and K, respectively. For labor, the ceiling captures limits on hiring labor due to supervision or search costs, as in the Sri Lanka case. For land, the ceiling captures analogous imperfections in the land market. These ceilings could arise due to transaction costs, which make it prohibitively expensive to rent in additional land. We could also think of the ceilings as being set by a village leader or other “social planner,” who allocates land among farmers. The ceiling may bind—leading to a higher shadow price of land among some farmers vs. others—if the social planner does not allocate land to maximize efficiency among farmers, for example, 15

because of imperfect information, political connections or equity considerations.15 Asking for more land from village leaders or family heads may also entail costs, such as social capital costs or costs of begging for additional land, which may constrain the amount of land they can use in production.16 The farm’s problem is   X max E  β t u(ct )

(8)

t≥0

s.t. ct + At+1 = exp(ωt )Lβt l Mtβm Ktβk + (1 − δ)qKt − (1 + r)(wLt + pMt + qKt )

(9)

+ (1 + r)At + zt (ωt ) Lt ≤ L

(10)

Kt ≤ K.

(11)

The first-order conditions yield the following formulas for the marginal revenue products of each input: βl E[exp(ωt )]Lβt l −1 Mtβm Ktβk = ψ(1 + r)w + λ

where ψ ≡

1

βm E[exp(ωt )]Lβt l Mtβm −1 Ktβk = ψ(1 + r)p

(13)

βk E[exp(ωt )]Lβt l Mtβm Ktβk −1 = ψ(r + δ)q + κ,

(14)

cov(u0 (ct ),exp(ωt )) t )]E[exp(ωt )]

1+ E[u0 (c

(12)

is the wedge from uninsured risk, λ is the multiplier on the

constraint in (10) multiplied by constraint in (11) multiplied by

1 1 cov(u0 (ct ),exp(ωt )) E[u0 (ct )] 1+ E[u0 (c )]E[exp(ω t t )] 1 1 cov(u0 (ct ),exp(ωt )) E[u0 (ct )] . 1+

and κ is the multiplier on the

E[u0 (ct )]E[exp(ωt )]

We can use the changes in the ratio of the marginal revenue products of labor and land to the marginal revenue product of materials in response to the treatments to test whether the labor market constraint weakened the impact of relaxing uninsured risk through the treatments. Consider labor markets first. Suppose first that there is no constraint in labor markets, 15

For example, Goldstein and Udry (2008) show that political connections affect allocation of land among farmers. 16 Understanding land allocation in settings without formal land markets has been the subject of extensive research in anthropology. For a recent contribution from an area near the sample of farmers from the Ghana experiment, see Lentz (2013).

16

i.e., the ceiling on labor does not bind with or without treatments. The treatments relax uninsured risk by lowering the covariance between consumption and productivity and, hence, cov(u0 (ct ), ωt ). This shows up as a lower “wedge” from uninsured risk in the FOCs. Insurance does this by providing payoffs in “bad” states, where productivity is low. The cash grant does this as long as farmers have decreasing absolute risk aversion, such that cash makes farmers less risk-averse by making them richer. In either case, farms will increase both labor and materials (and potentially land). However, the ratio of the marginal revenue product of labor to the marginal revenue product of materials remains unchanged. The same logic holds for land markets. Now, suppose the labor market constraint does bind. Again, the treatments will relax uninsured risk, leading to a lower “wedge” from uninsured risk in the FOCs. This time the labor market constraint will prevent farms from increasing labor by as much as they would otherwise. As a result, the ratio of the marginal revenue product of labor to the marginal revenue product of materials will rise. Again, the same logic holds for land markets. The different treatments provided by Karlan et al. (2014) should relax uninsured risk to varying degrees. In particular, they find the combination of cash and insurance provided the biggest reduction in financial constraints. In the model, this could be because of the additive effect of cash and insurance. However, they argue it could also be because bundling insurance with cash increased farmers’ (unmodeled) trust that insurance would pay out. In either case, farmers should be even more likely to run into constraints in labor and land markets—or be more severely constrained by the ceiling—when they receive the combination of insurance and cash. As a result, the ratio of the marginal revenue product of labor and land to the marginal revenue product of materials should increase even more. These predictions are formalized in the following propositions: Proposition 4 Suppose there is uninsured risk but the credit constraint does not bind. If the ceilings on labor and land do not bind, then providing zt (ωt ) has no effect on the ratios of the marginal revenue products of labor, Lt , materials, Mt , and land, Kt . Proposition 5 Suppose there is uninsured risk but the credit constraint does not bind. Consider three cases: • Case 1: If the ceiling on labor binds but the ceiling on land does not, then providing zt (ωt ) increases the ratio of the marginal revenue product of labor, Lt , to the marginal 17

revenue product of materials, Mt , and the ratio of the marginal revenue product of labor, Lt , to the marginal revenue product of land, Kt . The ratio of the marginal revenue product of land, Kt , to the marginal revenue product of materials, Mt , is unchanged. • Case 2: If the ceiling on land binds but the ceiling on labor does not, then providing zt (ωt ) increases the ratio of the marginal revenue product of land, Kt , to the marginal revenue product of materials, Mt , and the ratio of the marginal revenue product of land, Kt , to the marginal revenue product of labor, Lt . The ratio of the marginal revenue product of labor, Lt , to the marginal revenue product of materials, Mt , is unchanged. • Case 3: If the ceilings on both labor and land bind, then providing zt (ωt ) increases the ratio of the marginal revenue product of labor, Lt , to the marginal revenue product of materials, Mt , and the ratio of the marginal revenue product of land, Kt , to the marginal revenue product of materials, Mt . The effect on the ratio of the marginal revenue product of labor, Lt , to the marginal revenue product of land, Kt , is ambiguous. Proposition 6 Suppose there is uninsured risk but the credit constraint does not bind. Consider two insurance policies z1t (ωt ) and z2t (ωt ), where z2t (ωt ) lowers cov(u0 (ct ), ωt ) more than z1t (ωt ). Consider three cases: • Case 1: If the ceiling on labor binds but the ceiling on land does not, then providing z2t (ωt ) increases the ratio of the marginal revenue product of labor, Lt , to the marginal revenue product of materials, Mt , and increases the ratio of the marginal revenue product of labor, Lt , to the marginal revenue product of land, Kt , more than providing z1t (ωt ). The ratio of the marginal revenue product of land, Kt , to the marginal revenue product of materials, Mt , is unchanged in either case. • Case 2: If the ceiling on land binds but the ceiling on labor does not, then providing z2t (ωt ) increases the ratio of the marginal revenue product of land, Kt , to the marginal revenue product of materials, Mt , and increases the ratio of the marginal revenue product of land, Kt , to the marginal revenue product of labor, Lt , more than

18

providing z1t (ωt ). The ratio of the marginal revenue product of labor, Lt , to the marginal revenue product of materials, Mt , is unchanged in either case. • Case 3: If the ceilings on both labor and land bind, then providing z2t (ωt ) increases the ratio of the marginal revenue product of labor, Lt , to the marginal revenue product of materials, Mt , and the ratio of the marginal revenue product of land, Kt , to the marginal revenue product of materials, Mt , more than providing z1t (ωt ). The effect on the ratio of the marginal revenue product of labor, Lt , to the marginal revenue product of land, Kt , is ambiguous in either case. Again, we can interpret the ratio of marginal revenue products of labor and land to the marginal revenue product of materials as the shadow prices of labor and land. Finding a gap in the shadow prices of labor and land between insured and uninsured farmers tells us that farmers with insurance would be willing to pay more than farmers without insurance for an additional unit of labor or land. The larger this gap, the greater the gains for trading labor or renting in and out land among farmers and, hence, the larger the frictions preventing this reallocation. One final note: A key assumption for both the Sri Lanka and Ghana models is that the inputs that I have assumed are frictionless (i.e., materials) are in fact frictionless. I argue in Section 2 that interpreting these inputs as frictionless seems plausible. However, what if this assumption is incorrect? Constraints in markets for inputs I have assumed are frictionless would cause weaker changes in these inputs relative to labor and land. In this case, my estimates of the effect of relaxing financial constraints on the ratios of the marginal revenue products of labor and land to the marginal revenue product of materials would be underestimates. In the extreme, where constraints in markets for materials are the same as those for, say, labor, relaxing financial constraints would lead to no change in the ratio of the marginal revenue product of labor to the marginal revenue product of the“frictionless” input.

4

Test

In this section, I implement tests for whether constraints on labor and land weakened the effect of relaxing financial constraints, using the experiments with firms in Sri Lanka and

19

farms in Ghana.

4.1

Firms in Sri Lanka

I first implement the test using the randomized experiment from De Mel et al. (2008) that provided cash and in-kind grants to small firms in Sri Lanka. In this setting, I want to test whether frictions in labor markets weakened the effect of relaxing financial constraints with the grants. 4.1.1

Specification

To implement this test, I estimate the following regression: yit = γ0 + γ1 Cash100it + γ2 Cash200it + γ3 In-kind100it + γ4 In-kind200it + γi + γt + ψit . (15) Cash100it (Cash200it ) is 1 if firm i received the 100 USD (200 USD) cash grant before wave t. In-kind100it (In-kind200it ) is 1 if firm i received the 100 USD (200 USD) inkind grant before wave t. Since all treated firms were surveyed at least one round before receiving treatment, I include firm fixed effects. Identification of the effect of treatment on outcomes, yit , comes from variation within firm across time. I also include wave fixed effects to capture any shocks that are common across firms. This specification follows De Mel et al. (2008). The outcome variables, yit , that I use are log inputs, log output and, most importantly, the ratio of the marginal revenue product of labor to the marginal revenue product of materials. To measure the ratio of the marginal revenue product of labor to the marginal revenue product of raw materials, I use the Cobb-Douglas assumption. Under Cobb-Douglas, the log of the ratio of the marginal revenue product of labor to the marginal revenue product of raw materials is  mrplit − mrpmit = ln

βl βm

 + mit − lit .

(16)

Notice that production function coefficients are simply constants that affect the level of the marginal revenue products or their ratios. Thus, I do not require estimates of 20

the production function to estimate the effect of treatments on the ratio of the marginal revenue product of labor to the marginal revenue product of raw materials. I will test whether constraints in labor markets limit the impact of the treatments by estimating the impact of the treatments on the log ratio of raw materials to labor. 4.1.2

Results

Table 3 presents estimates of (15). I consider the cash treatments first then discuss the in-kind treatments. The first row of Table 3 shows the effect of the smaller, 100 USD, cash treatment. In columns (2)-(4), we see that this treatment had a small effect on investment. The only input that sees a significant increase from the treatment is labor hours (coefficient = 0.11, se = 0.05), though the effect on labor is not statistically different from the effects on materials and physical capital and the point estimate on materials is higher. To test whether frictions in labor markets weakened the impact of relaxing financial constraints via the treatment, I impose the Cobb-Douglas functional form assumption and estimate the effect of the 100 USD cash treatment on the ratio of the marginal revenue product of labor to the marginal revenue product of materials. If frictions in labor markets distort firms’ responses to relaxed financial constraints, then this ratio should rise with the cash grant. As shown in Column (5), I find no significant effect on this ratio (coefficient = 0.05, se = 0.14). These results suggest that the smaller cash grant did not cause firms to run into labor market constraints. Now, consider the effect of the larger, 200 USD, cash treatment, given in the second row of Table 3. We now see significant effects on raw materials (and physical capital) but no significant effect on labor. This treatment increased materials by 50 percent (coefficient = 0.41, se = 0.12). The point estimate of the effect on labor is 4 percent and not statistically significant (coefficient = 0.03, se = 0.07), though not statistically different from the effect of the 100 USD cash treatment on labor. Turning to the effects on the ratio of the marginal revenue product of labor to the marginal revenue product of materials in Column (5), we see that the large effects on raw materials relative to labor imply that the ratio increased by 46 percent for firms who received the 200 USD cash grant (coefficient = 0.38, se = 0.14). These results suggest that while firms do not run into labor market constraints with 21

the smaller grant, when that grant is doubled to 200 USD, firms are unable to adjust labor in proportion to the adjustment in raw materials. The fifth row of Table 3 shows the p-value for the test of whether the estimated effect of the larger cash grant is equal to the estimated effect of the smaller cash grant. I find that the effect of the 200 USD treatment on the ratio of the marginal revenue product of labor to the marginal revenue product of materials is significantly greater than the effect of the 100 USD treatment (pvalue = 0.08). This result supports the prediction that factor market constraints become more important when financial constraints get relaxed even more. Next, consider the effects of the in-kind treatments, given in the third and fourth rows of Table 3. The in-kind treatments provided 100 USD or 200 USD grants that had to be spent on raw materials or physical capital. As discussed in Section 3, if raw materials and physical capital are perfectly liquid, so that they can be re-sold at the purchase price by firms, then the effect of the in-kind grant should be the same as a cash grant. The third and fourth rows of Table 3 show the effects of the in-kind grants. In both cases, the grants induce firms to increase raw materials disproportionately more than labor hours, leading to significant increases in the shadow wage. I cannot reject the null hypothesis that the increase in the shadow wages is the same for either of the in-kind grants relative to the 200 USD cash grant. However, it may not be reasonable to assume the in-kind grants are perfectly fungible. For example, if firms can only re-sell raw materials (and physical capital) at some fraction of the purchase price, then the in-kind grant will lower the effective price of raw materials (and physical capital) more than labor, whether there are frictions in labor markets are not. Such a story may explain why the 100 USD in-kind grant had a greater effect on physical capital than the 100 USD cash grant. As a result, the cash grants provide a clearer test of whether labor market constraints weaken the impact of relaxing financial constraints. Overall, these results suggest labor market constraints weakened firms’ response to relaxed financial constraints by distorting their input mix away from labor and toward raw materials and physical capital. The 46 percent gap in ratio of the marginal revenue product of labor to the marginal revenue product of materials for firms that received the 200 USD cash grant, relative to firms in the control group, who did not have their financial constraints relaxed via the grant, suggests these frictions are sizable and prevented 22

reallocation of labor to those firms from firms in the control group.

4.2

Farms in Ghana

I also implement the test using the randomized experiment from Karlan et al. (2014) that provided access to rainfall insurance and cash grants to farmers in Ghana. In this setting, I want to test whether frictions in labor and land markets weakened the effect of relaxing financial constraints through rainfall insurance and cash grants. 4.2.1

Specification

To implement this test, I use the following instrumental variables regression: yit = α0 + α1 Insuranceit + α2 Bothit + α3 Cashit + α4 Wit + φit .

(17)

Cashit is equal to 1 if farmer i received a cash grant in year t. Insuranceit is equal to 1 if farmer i took up rainfall insurance in year t. Bothit is equal to 1 if farmer i took up rainfall insurance in year t and received a cash grant. Since insurance takeup is endogenous, I instrument Insuranceit using a set of indicators for whether farmer i received an offer of rainfall insurance at each price in year t. I instrument Bothit using the same indicators interacted with whether farmer i also received a cash grant in year t. Wit is a set of sample frame-year fixed effects. Identification of the effects comes from variation across farmers within sample frame and year. This specification follows Karlan et al. (2014). The outcome variables, yit , that I use are log inputs, log output and, most importantly, the ratios of the marginal revenue products of labor and land to the marginal revenue product of materials. With a Cobb-Douglas production function, these ratios are  βl + mit − lit mrplit − mrpmit = ln βm   βk mrpkit − mrpmit = ln + mit − kit . βm 

(18) (19)

Since the coefficients are constant, they fall out of the regression above, so I can measure the ratios of marginal revenue products using the log of the ratios of inputs.

23

4.2.2

Results

Table 4 presents estimates of (17) using two-stage least squares. I consider the effect of insurance and cash alone first, then discuss the effect of the combination of insurance and cash. The first row of Table 4 shows the effect of insurance alone. As shown in columns (2)-(4), insurance alone increased materials (tractor rental plus chemical inputs) by 11 percent (coefficient = 0.11, se = 0.05) and cultivated land area by 12 percent (coefficient = 0.12, se = 0.06) but had no significant effect on labor (coefficient = 0.02, se = 0.05). To test whether factor market constraints weakened the effect of relaxing financial constraints, I impose the Cobb-Douglas functional form assumption and look at the effect of insurance only on ratio of the marginal revenue products of labor and land to the marginal revenue product of materials. Recall that if there are frictions in labor or land markets, then relaxing uninsured risk should increase the ratios of the marginal revenue products of labor and land to the marginal revenue product of materials. Column (5) shows that insurance alone led to an 11 percent (coefficient = 0.10, se = 0.05) increase in the ratio of the marginal revenue product of labor to the marginal revenue product of materials. This suggests frictions in labor markets distorted farmers’ response to insurance alone and weakened its impact on investment. In column (6), however, we see insurance alone had no effect on the ratio of the marginal revenue product of land to the marginal revenue product of materials (coefficient = 0, se = 0.03). This suggests farmers did not hit constraints in land markets and were thus able to adjust land commensurately with materials. Now, consider the effect of cash alone, given by the third row of Table 4. Recall that if farmers face uninsured risk but no credit constraint and have decreasing absolute risk aversion, cash should increase investment by making farmers richer and less risk averse. Consistent with this, cash alone increases investment in materials by 13 percent (coefficient = 0.12, se = 0.06). There is no statistically significant effect on land or labor. Columns (5) shows the effect on the ratio of the marginal revenue product of labor to the marginal revenue product of materials. The increase in this ratio is high (coefficient = 0.22, se = 0.06), but this is driven by the negative (but statistically insignificant) coefficient on labor.

24

Since cash alone did not increase land but did increase materials, the ratio of the marginal revenue product of land to the marginal revenue product of materials also rose, as shown in column (6). It is surprising that cash alone did not increase land used. The effect of insurance alone suggests that farmers have some scope for increasing land used. Thus, we would expect cash alone to increase land used as well. One possible explanation for this result is that farmers face some fixed cost of adjusting land. For example, farmers may face a fixed cost from asking village leaders or other members of their community for additional land. If the cash only treatment relaxed financial constraints less than the insurance only treatment, as Karlan et al. (2014) suggest, then the cash only treatment may not provide enough incentive for farmers to pay this fixed cost. Finally, consider the effect of both insurance and cash in combination, shown in the second row of Table 4. In columns (1)-(4), we see that relaxing financial constraints with insurance and cash led to a 13 percent (coefficient = 0.13, se = 0.06) increase in land, 41 percent (coefficient = 0.34, se = 0.07) increase in materials and no significant increase in labor (coefficient = 0.03, se = 0.07), leading to a 21 percent (coefficient = 0.19, se = 0.08) increase in output. As shown in columns (5)-(6), these changes in the mix of labor and land to materials suggest the combination of insurance and cash led to a 36 percent (coefficient = 0.31, se = 0.06) increase in the ratio of the marginal revenue product of labor to the marginal revenue product of materials and a 22 percent (coefficient = 0.20, se = 0.04) increase in the ratio of the marginal revenue product of land to the marginal revenue product of materials. These estimates suggest frictions in both labor and land markets distorted the impact of relaxing financial constraints via the combined treatment. Recall that the model predicts that the combination of insurance and cash should relax financial constraints the most and thus lead to the biggest changes in the ratio of the marginal revenue products, relative to insurance or cash alone. The fourth row of Table 4 shows the p-value for the test of whether the estimated effect of both insurance and cash is equal to the estimated effect of insurance only. I find that the increase in the ratios induced by the combination of insurance and cash is significantly greater than the increase in these ratios induced by insurance alone (p-values < 0.01 for both the ratio of the marginal revenue products of labor and land to the marginal revenue product of materials). The fifth row of Table 4 shows the p-value for the test of whether the estimated effect of the combined treatment is equal to the estimated effect of cash only. While the 25

point estimate of the effect on the ratio of the marginal revenue product of labor to the marginal revenue product of materials is higher for the combined treatment, relative to the cash only treatment, the difference is not statistically significant (p-value = 0.18). However, the effect on the ratio of the marginal revenue product of land to the marginal revenue product of materials is significantly greater in the combined treatment relative to the cash only treatment (p-value = 0.08). Taken together, these results show a similar pattern to the results from the Sri Lanka experiment. Relaxing financial constraints to a large degree—through the combination of both insurance and cash—led to substantial increases in the ratios of the marginal revenue products of inputs that potentially face constraints (in this case, labor and land) to the marginal revenue product of materials. On the other hand, treatments that relaxed financial constraints to a lesser degree—by providing insurance or cash alone—led to somewhat smaller increases in these ratios. The estimated changes in these ratios suggest substantial gaps in shadow prices. In particular, the combination of insurance and cash led to a 36 percent increase in the shadow wage and a 22 percent increase in the shadow rental price of land. These imply substantial frictions preventing reallocation of labor and land from uninsured to insured farmers.

5

Production Function Estimation

In this section, I estimate the parameters of firms’ and farms’ Cobb-Douglas production function. I will use these parameters when I estimate the counterfactuals in the following section. I also use the production function estimation approach to conduct some tests of my Cobb-Douglas functional form assumption, which I discuss in the Appendix.

5.1

Estimation Framework

I assume a Cobb-Douglas production function. The log production function is qit = β0 + βl lit + βm mit + βk kit + ωit + it ,

26

(20)

where qit , lit , mit and kit are the log of output and the log of each input, respectively, for firm or farm i in period t. ωit is unobserved productivity, and it is an i.i.d. error term. Estimates of (20) using ordinary least squares will generally be biased due to unobserved productivity, ωit . For firms, ωit may capture machine breakdown or demand shocks. For farms, ωit may capture growing conditions, such as soil moisture and nutrient levels, pests or crop disease. Since firms and farms at least partially observe these conditions when they choose inputs, input choice will be endogenous. For farms, the econometrician can also at least partially observe productivity. Farm surveys often provide measures of growing conditions. The survey used by Karlan et al. (2014) provides farmers’ self-reported percentage of output loss due to too much or too little rain, birds and other pests and crop disease. To remove these shocks, I “deflate” output using farmers’ self-reported percentage of output lost to shocks. That is, if a farmer reported 50 percent of his output was lost to these types of shocks, then I double the output I observe for that farmer. However, farmers may fail to perfectly report all shocks to growing conditions on their farm in the survey. As a result, I allow farmers’ selfreported measures of growing conditions to only partially capture unobserved productivity. For farms, I call ωit the portion of farm productivity not captured by farmers’ self-reported shocks. That is, ωit represents productivity that is unobserved to the econometrician but is known to the farmer, and qit is output after deflating out the observed shocks. Given the endogeneity of ωit , how can we estimate firms’ and farms’ production functions without getting biased estimates from ωit ? One option is to assume ωit is fixed over time. However, if productivity varies over time, this assumption will be too restrictive. Furthermore, fixed effects estimation has a well-known attenuation bias, especially when estimating production functions (Ackerberg et al. 2007). Instead, I follow a version of the dynamic panel approach described by Ackerberg et al. (2015). First, I assume ωit follows an AR(1) process: ωit = ρ0 + ρ1 ωit−1 + ξit .

(21)

That is, each firm or farm’s productivity this year is a linear function of his productivity last year plus some unforeseen shock. This law of motion is often used in the literature on “proxy” approaches to estimating firm production functions (Olley and Pakes 1996,

27

Levinsohn and Petrin 2003, Ackerberg et al. 2015, De Loecker et al. 2014).17,18 Given the law of motion for productivity, we can quasi-difference the production function to get qit − ρ1 qit−1 = constant + βl (lit − ρ1 lit−1 ) + βm (mit − ρ1 mit−1 )

(22)

+βk (kit − ρ1 kit−1 ) + ξit + eit , where constant ≡ β0 (1 − ρ1 ) + ρ0 and eit ≡ it − ρ1 it−1 . The error term is now ξit + eit . eit is independent of current and lagged inputs by assumption. ξit captures unforeseen changes in productivity this period relative to last period. For example, for firms, ξit may capture unexpected machine breakdowns or increases in demand. For farms, it may capture changes in soil moisture due to temperature fluctuations before planting. This shock may be known when firms and farms choose inputs this year and may thus be correlated with today’s inputs. However, this shock will not be correlated with last year’s input use. This suggests the following moment conditions: E [(ξit + eit ) · (qit−1 , lit−1 , mit−1 , kit−1 )] = 0.

(23)

That is, we can estimate (22) via GMM by instrumenting current inputs and output with their lags. The estimated parameters are ρ1 , βl , βm and βk . Identification comes from input-specific costs that cause inputs to persistently vary across firms and farms, separately from unobserved productivity. Among the Sri Lankan firms and Ghanaian farms in my sample, and similar settings with various market imperfections, such variation might come from financial constraints and frictions in specific 17

Like the dynamic panel approach, the proxy approach uses a law of motion on productivity and the timing of input choice relative to innovations in productivity to estimate coefficients. However, the proxy approach requires a proxy input that is monotonic in unobserved productivity. For firms and farms in developing countries, especially in the settings I look at, it is difficult to imagine such an input in an environment with numerous market imperfections. For example, monotonicity is violated if there are financial constraints on all inputs. 18 Researchers using the dynamic panel approach often also include a fixed effect in the law of motion for productivity (Anderson and Hsiao 1982, Arellano and Bond 1991, Blundell and Bond 2000). Adding a fixed effect not only introduces attenuation bias but also reduces the number of years available for estimation because the instruments in this case are based on two lags. Again, for these reasons, dynamic panel approaches using fixed effects often perform poorly in practice (Ackerberg et al. 2007). This is especially problematic in the Ghana data, where I only have three years of data.

28

markets, like labor and land, which vary the “cost” of inputs across firms and farms and across inputs within firm and farm. This structural source of identification therefore fits the current settings well. However, the two experiments I use provide another, experimental source of identification. Since the cash and insurance experiments conducted by De Mel et al. (2008) and Karlan et al. (2014) affect shadow prices for different inputs differently, as shown in Section 4, they provide an additional source of identification. Note that the treatments are exogenous to both ξit and ωit . Denote the vector of all treatments—offers of insurance at all prices, cash grants and their interactions for the case of Ghana and the four different cash and in-kind grant treatments for the case of Sri Lanka—by treatmentit . We can use the following moment conditions:   E Z0it rit = 0,

(24)

where  rit = 

ξit + eit ωit + it

 (25)



and  Zit = 

(1, qit−1 , lit−1 , mit−1 , kit−1 , treatmentit )

0

0

(1, treatmentit )

 .

(26)

The residual ξit + eit comes from (22) and the residual ωit + it comes from (20).

5.2

Production Function Estimates

Table 5 and Table 6 shows the estimates of the production function for firms in Sri Lanka and farms in Ghana, respectively. In neither case can I reject the null that the returns to scale are 1. (This will motivate assuming constant returns to scale in the counterfactual.) Table 5 and Table 6 also compare the estimates to OLS and fixed effects. In both settings, we see that fixed effects gives production function coefficients that imply decreasing returns to scale, consistent with attenuation bias often observed when estimating production functions using fixed effects. In Sri Lanka, the point estimate on the returns 29

to scale is 0.65, and the p-value for the test of constant returns to scale is less than 0.01. In Ghana, the point estimate on the returns to scale is 0.78, and the p-value for the test of constant returns to scale is 0.06. Finally, Table 5 and Table 6 compare estimates using the dynamic panel approach with and without the additional instruments. In both cases, we see adding the instruments improves the precision of the estimates. The extra precision afforded by incorporating these extra instruments is valuable, especially in noisy datasets, and may be helpful in future research estimating production functions in developing countries.

6

Counterfactuals

In this section, I estimate what the effect of relaxing financial constraints via the treatments would have been if we relaxed ceilings on labor and land markets by a small amount. These counterfactuals help quantify the extent to which constraints on labor and land weaken the impact of relaxing financial constraints.19

6.1

Firms in Sri Lanka

In Section 4, I showed that the large cash grant led to increases in the ratio of the marginal revenue product of labor relative to the marginal revenue product of materials. This indicates that constraints on labor prevented firms from fully responding to this cash grant. In this section, I ask: What would the effect of the large cash grant have been if we relaxed the ceiling on labor by some percent? 6.1.1

Approach

To do this, I consider a representative firm. I maintain the large cash grant’s effect on credit constraints but raise the ceiling on labor the firm can hire.

19

I relax ceilings by these relatively small amounts for two reasons. First, with non-decreasing returns to scale, removing both financial constraints and factor market constraints would cause firms and farms to grow without bound. Second, relaxing ceilings on labor and land by a small amount reduces concerns about general equilibrium effects. If firms and farms with relaxed financial constraints were allowed to expand, say, labor, then the market wage would rise, which would offset the counterfactual impacts on profits that I calculate (see, for example, Mobarak and Rosenzweig (2014)). Of course, while raising ceilings by a small amount reduces this concern, my counterfactuals are overestimates to the extent that they do not account for these general equilibrium effects in labor and land markets.

30

I assume that the large cash grant completely relaxed the credit constraint. This is consistent with De Mel et al.’s (2008) finding that firms do not appear to spend the entire large cash grant. If the credit constraint still bound, we would expect firms to spend the entire grant. This assumption is also consistent with my finding that the large cash grant drove the marginal revenue product of raw materials close to what it would be if the financial “wedge” were completely removed. (I discuss this in detail in Appendix A.2.) Removing the ceiling on credit, I keep a ceiling on the amount of labor the firm can hire but raise it by some percent, v. Then I allow the representative firm to optimally choose materials and physical capital. Denote the counterfactual inputs for the representative firm as Lcf , Mcf and Kcf . These inputs will solve the following system of equations: Lcf = Ltr (1 + v) βm −1 βk βm E[exp(ωcf )]Lβcfl Mcf Kcf = (1 + r)p βm βk −1 = (r + δ)q. Kcf βk E[exp(ωcf )]Lβcfl Mcf

(27) (28) (29)

With these inputs, I can calculate the counterfactual output: βm βk Qcf = exp(ωcf )Lβcfl Mcf Kcf .

(30)

Finally, I can use this to calculate counterfactual profits: πcf = Qcf − (r + δ)qKcf − (1 + r)(wLcf + pMcf ).

(31)

I can compare these to the average inputs we observe for the control (Lco , Mco , Kco ) and treatment groups (Ltr , Mtr , Ktr ) and the associate output and profits. To estimate this counterfactual, we need the following parameters: βl , βm , βk , E[exp(ωcf )], r, δ, p, w and q. I calculate βl , βm and βk using the production function estimation approach from the previous section. Recall that the point estimates for the production function coefficients in Sri Lanka suggest increasing returns to scale, though I cannot reject the null hypothesis of constant returns to scale. To be conservative, I impose constant returns to scale by re-scaling the estimated coefficients by the estimated returns to scale. 31

I set r = 0.015, following survey evidence from De Mel et al. (2008), who estimate a monthly interest rate of 1-2 percent. I set q = 1 and p = 1, since materials and physical capital are measured in currency units. There are no reliable wage data in the Sri Lanka survey (since there is little hiring of labor), so I estimate the wage, w, using the ratio of the marginal revenue product of labor to the marginal revenue product of materials in the control group. The FOCs for the representative control firm are: βm βk βl E[exp(ωt )]Lβcol −1 Mco Kco = (1 + r + µ)w

(32)

βm −1 βk βm E[exp(ωt )]Lβcol Mco Kco = (1 + r + µ)p

(33)

βm βk −1 Kco = (r + δ + µθ)q. βk E[exp(ωt )]Lβcol Mco

(34)

Thus, the wage is simply the ratio of the marginal revenue product of labor to the marginal revenue product of materials, since p = 1. To calculate δ, I use the FOCs for treated firms. The FOCs for the representative treated firm are: βl −1 βm βk βl E[exp(ωt )]Ltr Mtr Ktr = (1 + r)w

(35)

βm −1 βk βm E[exp(ωt )]Lβtrl Mtr Ktr = (1 + r)p

(36)

βm βk −1 βk E[exp(ωt )]Lβtrl Mtr Ktr = (r + δ)q,

(37)

The FOC for physical capital, combined with assigned values for r and q, let us back out δ.20 I calculate inputs for the representative control firm by using the inputs corresponding to the average of the log of inputs among control firms. I do this in order to match the estimated effects of the treatments on inputs in Table 3. I then calculate inputs for the representative treatment firm by adding the estimated effect of the large cash grant on labor, materials and physical capital to the representative control firm’s labor, materials and physical capital. Finally, I calculate the expected productivity, E[exp(ωcf )], using the FOC for materials 20

I estimate δ ≈ 0.03, which is in line with estimates for capital depreciation in the Sri Lankan setting cited by De Mel et al. (2008).

32

for the representative treated firm.21 Notice that we cannot back out E[exp(ωcf )] using the production function estimates. This is because the residual in the production function is ω + . Taking the average of the exponential of this residual would give us an estimate of E[exp(ω + )], which is not generally equal to E[exp(ω)]. Notice also that we could have use the FOCs for the representative control firm to estimate this parameter. 6.1.2

Results

Table 7 shows the counterfactuals for firms in Sri Lanka.22 Columns (1)-(2) of Table 7 provide the inputs, output and profits for the representative control and treated firms, respectively. Columns (3)-(5) provide estimates of inputs, output and profits under counterfactuals where I relax the ceiling on labor by 5 percent, 10 percent and 15 percent, respectively. Relaxing the ceiling on labor causes firms to use more labor, materials and physical capital. This translates to increases in outputs and profit. When I relax the ceiling on labor by 5 percent, the effect of the treatment on monthly profits increases by 31 percent (from 163 LKR to 212 LKR). When I relax the ceiling by 10 percent, the effect of the treatment on profits increases by 61 percent (from 163 LKR to 262 LKR). And when I relax the ceiling by 15 percent, the effect of the treatment on profits increases by 92 percent (from 163 LKR to 312 LKR). Table 7 also reports borrowing costs under these counterfactuals. We might be concerned that, with higher ceilings on labor, firms with the large cash grant would run into a new credit constraint, once they spent the entire cash grant. However, we see that even when we relax the ceiling on labor by 15 percent, borrowing is 10,644 LKR higher than for the representative control firm. This is just over half the amount of the 20,000 LKR grant, which suggests that the counterfactual representative firm would not have run into a credit constraint.

21

I could also use the FOC for materials for the representative control firm, since productivity should not change as a result of treatments. Consistent with this, I find that using the representative control firm gives similar estimates. 22 The parameters are in Appendix Table A6.

33

6.2

Farms in Ghana

In Section 4, I showed that rainfall insurance and cash grants combined led to substantial increases in the ratio of the marginal revenue products of both labor and land to the marginal revenue product of materials for farmers in Ghana. This indicates that constraints in labor and land markets limited farmers’ ability to expand production and increase profits in response to relaxed uninsured risk. I further quantify this effect by asking: What would the impact of the combination of insurance and cash have been if we relaxed the ceiling on labor, land or both by some percent? 6.2.1

Approach

To do this, I follow a similar approach to the case with Sri Lankan firms above: For a representative farmer, I maintain the effect of insurance and cash on uninsured risk but raise the ceilings on the amount of labor and land the farm can use in production. I assume the combination of insurance and cash completely removed uninsured risk. This assumption is useful because it frees me from having to estimate a host of parameters related to the farmer’s utility function and perception of shocks. It is also consistent with my finding that the combination of insurance and cash drove the marginal revenue product of materials close to what it would be if the financial “wedge” were completely removed. (I discuss this in detail in Appendix A.2.) Removing uninsured risk, I maintain a ceiling on the amount of labor and land the farm can use in production, but I raise the ceiling on labor by v percent and land by n percent. I then allow the farm to optimally choose material inputs, along with labor and land. In the counterfactuals I consider, farms will find it optimal to use both labor and land up to their ceilings. As a result, the counterfactual inputs will solve the following system of equations: Lcf = Ltr (1 + v) βm −1 βk βm E[exp(ωcf )]Lβcfl Mcf Kcf = (1 + r)p

Kcf = Ktr (1 + n).

(38) (39) (40)

As in the Sri Lanka case, I can use these inputs to calculate counterfactual output and

34

profits. I then compare these to the inputs, output and profits I observe for control and treated farms. In this case, I calculate the inputs for “treated” farms using the estimated IV effects on labor, materials and land in Table 4. To estimate this counterfactual, we need the following parameters: βl , βm , βk , E[exp(ωcf )], r, δ, p, w and q. I calculate βl , βm and βk using the production function estimation approach from the previous section. Again, to be conservative, I impose constant returns to scale by re-scaling the estimated coefficients by the estimated returns to scale. I set r = 0, following survey evidence from Ghana, which indicates that farmers rarely report paying interest in loans. I set p = 1, since materials are measured in currency units. I use the FOCs for the representative control farm to calculate w and δq, since there are no reliable wage data (due to lack of hiring labor), land rental price data (due to lack of land rental) or land depreciation estimates. These FOCs are βm βk βl E[exp(ωt )]Lβcol −1 Mco Kco = ψ(1 + r)w

(41)

βm −1 βk βm E[exp(ωt )]Lβcol Mco Kco = ψ(1 + r)p

(42)

βm βk −1 Kco = ψ(r + δ)q. βk E[exp(ωt )]Lβcol Mco

(43)

I calculate w as the ratio of the marginal revenue product of labor to the marginal revenue product of materials in the control group. I calculate δq as the ratio of the marginal revenue product of land to the marginal revenue product of materials, since r = 0. Note that I do not need to separately identify δ and q, since I only use these to calculate profits and, given r = 0, the “cost” of land reduces to δq. I calculate inputs for the representative control farm by using the inputs corresponding to the average of the log of inputs among control farms. I do this in order to match the estimated effects of the treatments on inputs in Table 4. I then calculate inputs for the representative treatment farm by adding the estimated effect of the combination of insurance and cash on labor, materials and land to the representative control farm’s labor, materials and land. Finally, I calculate the expected productivity, E[exp(ωcf )], using the FOC for materials for the representative treated farmer, as in Sri Lanka.

35

6.2.2

Results

Table 8 shows the counterfactuals for farms in Ghana.23 Panel A of Table 8 shows the counterfactual effect of relaxing the ceiling on labor alone. Panel B shows the results for relaxing just the ceiling on land. Panel C shows the results for relaxing both the ceilings on labor and land. Columns (1)-(2) provide the inputs, output and profits for the representative control and treated farms, respectively. Columns (3)-(5) provide estimates of inputs, output and profits under counterfactuals where I relax the ceilings by 5 percent, 10 percent and 15 percent, respectively. Relaxing the ceilings on labor and land induce the representative farmer to expand all inputs, output and profits. Relaxing the ceiling on labor alone by 10 percent increases the effect of the combination of insurance and cash on profits by 33 percent (from 16 GHC to 21 GHC). Relaxing the ceiling on land alone by 10 percent increases the effect of insurance and cash on profits by 41 percent (from 16 GHC to 23 GHC). Relaxing both the ceiling on land and labor by 10 percent increases the effect of insurance and cash on profits by 82 percent (from 16 GHC to 29 GHC).

7

Conclusion

The goal of this paper has been to show that factor market constraints, such as supervision costs for hired labor or thin land markets, weaken the effect of policy changes or interventions which relax financial constraints. I do this using two randomized experiments: one that provided cash grants to small firms in Sri Lanka and another that provided access to rainfall insurance and cash grants to farmers in Ghana. I develop a model that provides a test for whether constraints on labor and, for farms, land weakened the impacts of these interventions by distorting firms’ and farms’ input mixes away from labor and land toward inputs that are not subject to factor market constraints. Implementing these tests in both settings, I find evidence that factor market constraints limited firms’ and farms’ ability to increase investment in response to relaxed financial constraints and that relaxing constraints on labor and land would have substantially increased the effect of the treatments on firm and farm profits. These results suggest that in settings with labor and land market constraints, relaxing 23

The parameters are in Appendix Table A7.

36

financial constraints alone may be ineffective. More broadly, the results suggest that any intervention that seeks to promote firm or farm growth—for example, by providing access to more productive technology or relaxing constraints on access to markets and trade—may be weakened by frictions in labor and land markets. Methodologically, this paper provides an alternative approach to testing for overlapping constraints. I show that imposing some structure allows researchers to use a singlearmed experiment—in this case, one that relaxes financial constraints—to test whether other constraints weaken the effect. In cases where the constraints of interest are difficult to randomize, such as labor or land market constraints, this approach may be particularly useful.

37

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Lentz, C. (2013). Land, Mobility and Belonging in West Africa. Indiana University Press. Levinsohn, J., and A. Petrin (2003). “Estimating Production Functions Using Inputs to Control for Unobservables.” Review of Economic Studies 70 (2), 317-341. Mobarak, M., and M. Rosenzweig (2014). “Risk, Insurance and Wages in General Equilibrium.” Working Paper. Olley, G. S., and A. Pakes (1996). “The Dynamics of Productivity in the Telecommunications Equipment Industry.” Econometrica 64 (4), 1263-1297. Shenoy, A. (2014). “Market Failures and Misallocation: The Costs of Factor and Financial Market Failures in Thailand.” Working Paper. Szabo, A. (2015).“Measuring Firm-level Inefficiencies in Ghanaian Manufacturing.” Working Paper. Tarozzi, A., J. Desai and K. Johnson (2015). “The Impacts of Microcredit: Evidence from Ethiopia.” American Economic Journal: Applied Economics 7 (1), 54-89.

40

Table 1: Summary Statistics (Sri Lanka)

Log Output (LKR) Log Labor (hours) Log Materials (LKR) Log Physical Capital (LKR) Output (LKR) Labor (hours) Materials (LKR) Physical Capital (LKR) Firm-wave obs. Firms

Control

Cash 100

Cash 200

In-kind 100

In-kind 200

All

9.148 (1.222) 5.713 (0.580) 8.630 (1.529) 9.042 (1.466)

9.579 (1.242) 5.681 (0.584) 9.036 (1.517) 9.695 (1.329)

9.718 (1.146) 5.701 (0.518) 9.354 (1.332) 9.590 (1.352)

9.211 (1.196) 5.586 (0.576) 8.678 (1.535) 9.182 (1.172)

9.683 (1.154) 5.714 (0.520) 9.261 (1.480) 9.688 (1.131)

9.315 (1.230) 5.688 (0.571) 8.813 (1.530) 9.259 (1.397)

17,698.66 (19,902.56) 352.45 (187.30) 13,466.40 (17,427.00) 17,746.48 (18,574.82)

25,411.43 (22,962.98) 343.26 (190.01) 17,653.71 (18,296.73) 28,244.43 (23,429.34)

28,430.41 (27,875.36) 336.02 (152.00) 22,254.51 (23,321.42) 28,880.83 (27,095.43)

18,146.25 (19,505.97) 309.30 (157.95) 13,691.07 (17,156.08) 16,275.42 (15,500.40)

27,274.02 (25,705.49) 342.07 (164.37) 21,884.30 (22,686.98) 26,320.93 (22,715.49)

20,623.74 (22,040.03) 342.24 (179.21) 15,586.54 (18,871.99) 20,726.78 (20,757.35)

1,518 346

404 63

256 40

434 71

238 37

2,850 360

Notes : Means of inputs and outputs, with standard deviations in parentheses. Output, materials and physical capital deflated to April 2005 LKR (Sri Lankan rupees). Inputs and output Winsorized at the 2nd and 98th percentiles.

Table 2: Summary Statistics (Ghana)

Log Output (GHC) Log Labor (days) Log Land (acres) Log Materials (GHC) Output (GHC) Labor (days) Land (acres) Materials (GHC) Farm-year obs. Farms

Control

Insurance

Both

Cash

Total

6.514 (0.941) 5.314 (0.771) 1.995 (0.662) 5.400 (0.816)

6.545 (0.997) 5.401 (0.792) 2.084 (0.654) 5.576 (0.796)

6.728 (0.874) 5.374 (0.815) 2.145 (0.634) 5.750 (0.676)

6.606 (0.941) 5.277 (0.742) 2.022 (0.634) 5.555 (0.744)

6.557 (0.965) 5.362 (0.785) 2.057 (0.655) 5.534 (0.795)

1,054.10 (1,291.02) 268.29 (208.49) 9.07 (6.08) 299.58 (235.47)

1,159.10 (1,520.98) 296.12 (229.27) 9.88 (6.57) 350.16 (260.21)

1,231.41 (1,382.96) 294.13 (238.63) 10.26 (6.14) 386.37 (246.67)

1,171.33 (1,504.41) 257.31 (209.20) 9.17 (6.03) 328.31 (224.11)

1,132.22 (1,434.51) 284.37 (222.76) 9.60 (6.35) 335.69 (250.32)

1,143 787

1,755 1,016

343 316

207 191

3,448 1,341

Notes : Means of inputs and outputs, with standard deviations in parentheses. Output and materials deflated to 2010 GHC (Ghanaian cedis). Inputs and output Winsorized at the 2nd and 98th percentiles.

Table 3: Effect of Treatments on Inputs, Output and Ratio of Marginal Revenue Products (Sri Lanka) (1)

Log Output

Cash 100

(2)

Log Labor

(3)

Log Materials

(4)

Log Physical Capital

(5) Log Ratio MRP Labor to MRP Materials (Log Materials Log Labor)

0.194 (0.107) 0.279 (0.132) 0.213 (0.105) 0.366 (0.117)

0.107 (0.0544) 0.0348 (0.0667) 0.0857 (0.0598) 0.106 (0.0727)

0.174 (0.126) 0.408 (0.123) 0.31 (0.141) 0.358 (0.136)

0.0605 (0.0877) 0.408 (0.127) 0.318 (0.0922) 0.583 (0.179)

0.0539 (0.136) 0.379 (0.141) 0.225 (0.137) 0.238 (0.121)

Cash 100 = Cash 200 In-kind 100 = In-kind 200 Cash 100 = In-kind 100 Cash 200 = In-kind 200

0.61 0.31 0.89 0.62

0.36 0.81 0.77 0.43

0.16 0.80 0.45 0.77

0.02 0.18 0.03 0.41

0.08 0.94 0.34 0.42

Firm-wave obs. Firms R2

2,850 360 0.816

2,850 360 0.649

2,850 360 0.783

2,850 360 0.934

2,850 360 0.729

Cash 200 In-kind 100 In-kind 200

Notes : Estimates of the regression in (15). Column (5) shows effects of treatments on the ratio of the marginal revenue product (MRP) of labor to the marginal revenue product of materials, assuming a Cobb-Douglas production function. The fifth, sixth, seventh and eighth rows show the p -value for tests of whether the coefficients on different treatments are equal. denotes natural log. All specifications include firm and wave fixed effects. All dependent variables Winsorized at the 2nd and 98th percentiles. Standard errors, clustered at the firm level, in parentheses.

Table 4: IV Effects of Treatments on Inputs, Output and Ratios of Marginal Revenue Products (Ghana) (1)

Log Output

Insurance

(2)

Log Labor

(3)

Log Land

(4)

Log Materials

(5)

(6)

Log Ratio MRP Labor to MRP Materials

Log Ratio MRP Land to MRP Materials

(Log Materials Log Labor)

(Log Materials Log Land)

0.0735 (0.0690) 0.193 (0.0810) 0.0414 (0.0773)

0.0222 (0.0534) 0.0255 (0.0684) -0.0977 (0.0601)

0.107 (0.0496) 0.126 (0.0586) -0.0106 (0.0510)

0.115 (0.0578) 0.341 (0.0652) 0.124 (0.0608)

0.102 (0.0516) 0.309 (0.0639) 0.22 (0.0598)

0.000482 (0.0325) 0.198 (0.0386) 0.125 (0.0389)

Both = Insurance Both = Cash Insurance = Cash

0.08 0.10 0.71

0.96 0.10 0.07

0.69 0.03 0.05

0.00 0.00 0.89

0.00 0.18 0.05

0.00 0.08 0.00

Farm-year obs. Farms R2

3,448 1,341 0.015

3,448 1,341 0.011

3,448 1,341 0.028

3,448 1,341 0.051

3,448 1,341 0.030

3,448 1,341 0.041

Both Cash

Notes : Estimates of the regression in (17). "Insurance" instrumented using indicators for whether farmer offered insurance alone at various prices. "Both" instrumented using indicators for whether farmer offered insurance at various prices and a cash grant. Columns (5)-(6) show IV effects of insurance, cash and both insurance and cash on the ratios of marginal revenue products (MRPs), assuming a Cobb-Douglas production function. The fourth, fifth and sixth rows show the p -value for tests of whether the coefficients on different treatments are equal. "Log" denotes natural log. All specifications include sample frame-year fixed effects. All dependent variables Winsorized at the 2nd and 98th percentiles. Standard errors, clustered at the farm level, in parentheses.

Table 5: Production Function Estimates (Sri Lanka) (1)

(2)

(3)

(4)

All Instruments

Lagged Inputs Only

OLS

FE

0.284 (0.171) 0.76 (0.0470) 0.05 (0.0199)

0.280 (0.230) 0.766 (0.0625) 0.052 (0.0225)

0.277 (0.0453) 0.634 (0.0223) 0.0898 (0.0169)

0.156 (0.0332) 0.388 (0.0293) 0.103 (0.0386)

1.09 0.50

1.10 0.60

1.00 0.97

0.65 0.00

0.397 (0.0271)

0.404 (0.0299)

-

-

Hansen's J -statistic, χ2(8) p -value

4.218 0.84

-

-

-

Firm-wave obs. Firms

2,332 354

2,332 354

2,332 354

2,332 354

DP

Log Labor Log Materials Log Physical Capital Returns to scale p -value for null of CRTS Autocorrelation coefficient in productivity law of motion

Notes : Estimates of Cobb-Douglas production function. Column (1) presents dynamic panel (DP) estimates using lagged inputs and all treatments as instruments. Column (2) uses only lagged inputs as instruments. "Log" denotes natural log. "CRTS" denotes constant returns to scale. Inputs and output Winsorized at the 2nd and 98th percentiles. Standard errors, clustered at the firm level, in parentheses.

Table 6: Production Function Estimates (Ghana) (1)

(2)

(3)

(4)

All Instruments

Lagged Inputs Only

OLS

FE

0.255 (0.143) 0.368 (0.112) 0.441 (0.119)

0.516 (0.255) 0.170 (0.169) 0.426 (0.179)

0.194 (0.0290) 0.241 (0.0382) 0.525 (0.0456)

0.14 (0.0650) 0.241 (0.102) 0.402 (0.140)

1.065 0.21

1.112 0.12

0.960 0.18

0.783 0.06

0.091 (0.0153)

0.127 (0.0248)

-

-

Hansen's J -statistic, χ2(16) p -value

21.675 0.15

-

-

-

Farm-year obs. Farms

2,062 1,179

2,062 1,179

2,062 1,179

2,062 1,179

DP

Log Labor Log Materials Log Land Returns to scale p -value for null of CRTS Autocorrelation coefficient in productivity law of motion

Notes : Estimates of Cobb-Douglas production function. All specifications deflate farmers' output using farmers' self-reported losses due to shocks and drop observations where reported shock is 100 percent. Column (1) presents dynamic panel (DP) estimates using lagged inputs and all treatments as instruments. Column (2) uses only lagged inputs as instruments. "Log" denotes natural log. "CRTS" denotes constant returns to scale. Inputs and output Winsorized at the 2nd and 98th percentiles. Standard errors, clustered at the farm level, in parentheses.

Table 7: Counterfactuals for Large Cash Grant (Sri Lanka) (1)

(2)

(3)

Actual

(4) Counterfactual

(5)

Raise ceiling on Raise ceiling on Raise ceiling on labor by 5% labor by 10% labor by 15%

Control

Treatment

Labor (hours) Materials (LKR) Physical Capital (LKR)

302.68 5,599.74 8,446.46

313.40 8,420.93 12,701.85

329.07 8,841.97 13,336.94

344.74 9,263.02 13,972.04

360.41 9,684.06 14,607.13

Cost (LKR) Borrowing (LKR) Output (LKR) Profits (LKR)

8,181.59 16,138.73 9,013.90 832.32

11,308.69 23,289.41 12,303.53 994.83

11,874.13 24,453.88 12,918.70 1,044.58

12,439.56 25,618.35 13,533.88 1,094.32

13,005.00 26,782.82 14,149.06 1,144.06

-

162.52

212.26

262.00

311.74

Effect of Treatment on Profits (LKR)

Notes : Counterfactuals provide estimates of what effect of large cash grant on inputs, costs, borrowing, output and profits would have been if ceiling on labor were raised by 5%, 10% or 15%. See Section 6 for details.

Table 8: Counterfactuals for Combination of Insurance and Cash (Ghana) (1)

(2)

(3)

Actual Control

Treatment

(4) Counterfactual

(5)

Raise ceiling by Raise ceiling by Raise ceiling by 5% 10% 15%

Panel A: Raise Ceiling on Labor Only Labor (days) Materials (GHC) Land (acres)

203.23 221.44 7.35

208.48 311.43 8.34

218.90 317.05 8.34

229.33 322.50 8.34

239.75 327.79 8.34

Cost (GHC) Output (GHC) Profits (GHC)

640.26 754.91 114.65

769.85 900.44 130.59

783.33 916.68 133.34

796.65 932.44 135.78

809.82 947.75 137.93

-

15.94

18.69

21.13

23.27

Effect of Treatment on Profits (GHC)

Panel B: Raise Ceiling on Land Only Labor (days) Materials (GHC) Land (acres)

203.23 221.44 7.35

208.48 311.43 8.34

208.48 321.21 8.76

208.48 330.82 9.17

208.48 340.27 9.59

Cost (GHC) Output (GHC) Profits (GHC)

640.26 754.91 114.65

769.85 900.44 130.59

794.67 928.71 134.03

819.33 956.49 137.16

843.83 983.81 139.98

-

15.94

19.38

22.50

25.33

Effect of Treatment on Profits (GHC)

Panel C: Raise Ceiling on Both Labor and Land Labor (days) Materials (GHC) Land (acres)

203.23 221.44 7.35

208.48 311.43 8.34

218.90 327.00 8.76

229.33 342.57 9.17

239.75 358.14 9.59

Cost (GHC) Output (GHC) Profits (GHC)

640.26 754.91 114.65

769.85 900.44 130.59

808.34 945.46 137.12

846.83 990.48 143.65

885.32 1,035.50 150.18

-

15.94

22.47

29.00

35.53

Effect of Treatment on Profits (GHC)

Notes : Counterfactuals provide estimates of what effect of combination of insurance and cash on inputs, costs, output and profits would have been if ceilings on labor and land were raised by 5%, 10% or 15%. See Section 6 for details.

Appendix [For Online Publication] A.1

Alternative Explanations

In this section, I provide evidence against three potential alternative explanations for my results: (i) the Cobb-Douglas functional form assumption is wrong, (ii) labor and land are indivisible and (iii) farms in Ghana choose labor after other inputs. A.1.1

Cobb-Douglas Functional Form Assumption

I test whether constraints on labor and land limit the impact of relaxing financial constraints by looking at the effect of the treatments on the ratios of marginal revenue products. With Cobb-Douglas, this boils down to looking at changes in the log of ratio of inputs. Using changes in ratios to measure changes in marginal revenue products is valid under any homothetic production function. This follows from the fact that with homothetic production functions, the ratio of the marginal revenue products of two inputs is homogeneous of degree zero in the two inputs. Thus, observing a change in the ratio of inputs as a result of the treatments indicates factor market constraints, even if the Cobb-Douglas assumption is wrong, as long as the production function is homothetic. However, using the changes in the ratios of inputs to measure the magnitude of factor market constraints requires the production function to be Cobb-Douglas. Under other production functions—either homothetic or not—the change in the ratios may over- or underestimate the change in shadow prices.1 For example, suppose the firms in the Sri Lanka sample switch to a less labor-intensive or more materials-intensive technology as a result of the treatment. In terms of the Cobb1

Take the example of a constant elasticity of substitution (CES) production function: ν

ρ ρ ρ Qit = exp(ωit )(αLρit + βMit + (1 − α − β)Kit ) ,

where ρ ≤ 1. CES is homothetic but more general than Cobb-Douglas. (When ρ = 0, the CES production function is Cobb-Douglas.) With a general CES production function, the logged ratio of the marginal revenue product of labor to the marginal revenue product of materials, for example, is   α mrplit − mrpmit = ln + (1 − ρ)(m2it − l1it ). β If we use these measures of the log ratios of marginal revenue products, the direction of the effect would be the same, as long as ρ 6= 1, i.e., there is not perfect substitutability between the inputs. The only difference is that now the magnitude is affected by ρ. Specifically, if ρ < 0 (ρ > 0), i.e., inputs are less substitutable (more substitutable), I will underestimate (overestimate) the effect on the shadow price.

i

Douglas production function, this means firms choose a technology with a lower coefficient on labor and a higher coefficient on materials. In this case, observing the ratio of labor to raw materials rise when financial constraints are relaxed may simply capture firms moving to this new technology, not frictions in labor markets. In light of this concern, I implement two tests for whether my Cobb-Douglas assumption is incorrectly driving my results: a test for whether treatments change technology and an overidentification test. Do Treatments Change Technology? One concern is that firms or farms who receive treatments switch to less labor- and land-intensive products. In Sri Lanka, De Mel et al. (2008) report that firms do not respond to treatments by switching their line of business, suggesting my results are not driven by firms there switching to less labor-intensive lines of business. In Ghana, however, Karlan et al. (2014) show that insurance does induce farmers to switch to maize, which may be less labor- or land-intensive. When I control for crops in the regressions reported in (15), the results are unchanged.2 This suggests my results are not driven by households switching to a less labor- or land-intensive crop. However, it could still be the case that firms or farms produce the same products after they scale up in response to treatments but do so with a less labor- or land-intensive production function. I can test whether the production technology changes using the production function estimation approach described in Section 5. Specifically, I estimate the production function for treated observations only and compare the coefficients to those from estimating the production function with the full sample. When I estimate the sample with treated observations only, I cannot use the treatments as instruments, so I only use lagged inputs as instruments. I define a firm-wave or farm-year observation as “treated” if the firm or farm had an active treatment status in that wave or year and the wave or year before. I do this because the use of lagged inputs requires assuming the production function technology (i.e., the coefficients) is the same in consecutive years.3 Appendix Table A1 and Appendix Table A2 present the production function estimates for the Sri Lanka and Ghana experiments, respectively. Columns (1)-(2) replicate the estimates from columns (1)-(2) of Table 5 and Table 6. Column (3) estimates the production 2

These results are available upon request. Ideally, I would estimate the production function with the full sample and allow the production function coefficients to vary with treatment status, then test whether the interactions are significant. However, the results fail to converge with this specification. This may be because there are much fewer control observations, which makes estimating the production function coefficients for these observations difficult. 3

ii

function using only lagged inputs as instruments and limiting the sample to treated firms or farms. What we want to know is: How different are the ratios of coefficients for treated observations? For the Sri Lanka sample, we are interested in the ratio of the coefficient on labor to the coefficient on raw materials. This is because I use the ratios of the marginal revenue product of labor to the marginal revenue products of raw materials in my tests. The standard errors on these ratios are large in all specifications, and I cannot reject that the ratios in column (3) are equal to the estimates in column (1) or column (2).4 The point estimates, however, go in the direction of firms switching to technologies that have a higher intensity of labor, relative to raw materials. This would suggest the increases in the shadow wage I observe in Table 3 are underestimates. For the Ghana sample, we are interested in the ratio of the coefficient on labor to the coefficient on materials and the ratio of the coefficient on land to the coefficient on materials. This is because I use the ratios of the marginal revenue products of labor and land to the marginal revenue product of materials in my tests. Again, the standard errors on these ratios are large in all specifications, and I cannot reject that the ratios in column (3) are equal to the ratios in column (1) or column (2). For the ratio of the coefficient on labor to the coefficient on materials, the point estimate again goes in the direction of farms switching to technologies that have a higher intensity of labor, relative to materials. For land, the results are mixed. While the ratio of the coefficient on land to the coefficient on materials for treated farms is higher than the ratio using all instruments and the full sample, the ratio for treated farms is lower than the ratio using just lagged inputs as instruments and the full sample. Overall, I cannot reject that the treated firms and farms have different technology, relative to the full sample. However, in most cases, the direction of the change in technology implied by the estimates go against the story that firms or farms are switching to technologies that are less intensive in inputs that face factor market constraints. This suggests my results are not driven by changes in technology as a result of the treatments. Overidentification Test The additional moments I use in estimating the production function allow me to do an overidentification test. This test is an omnibus test of all the assumptions I have made 4 Again, what we really want to know is whether the ratios are different between treated and control observations, not treated and all observations, but estimations that split up the sample into control and treated observations fail to converge.

iii

in estimating the production function. One of the key assumptions is that the production function is Cobb-Douglas. Suppose instead the production function were more general: qit = β0 + βl lit + βm mit + βk kit + f (lit , mit , kit ) + ωit + it ,

(A.1)

where f (lit , mit , kit ) is some higher-order polynomial in the inputs. If this is the true functional form, then the higher-order terms will be pushed into both residuals I use in the production function estimation, ωit and ξit . In this case, the overidentification test would produce a large test statistic and we would reject the null.5 Table 5 and Table 6 show the J statistic for the overidentification test for Sri Lanka and Ghana, respectively. In both cases, I fail to reject the overidentification test at conventional levels of significance. In Sri Lanka, the p-value for the overidentification test is 0.84. In Ghana, the p-value is 0.15. A.1.2

Indivisibilities in Labor and Land

Another potential explanation is that these increases in the shadow wage simply capture the fact that labor and land must be hired in indivisible units. For example, it might be unlikely to observe farmers renting less than an acre of land or hiring someone for just a few days per season or a few hours per week. We can get a sense of whether this story is plausible by estimating how much labor and land would have needed to rise in order for the shadow prices of these inputs to have stayed the same. For both Sri Lanka and Ghana, I do this by calculating taking the average of the log of each input for the control group, in Table 1 and Table 2, and calculating what the increase would have needed to be to match the impact of the treatment on materials. For Sri Lanka, the estimates in Table 3 imply that firms who received the large cash grant would have needed to hire approximately 142 more hours of labor per month, or roughly 34 hours of labor per week, to raise labor commensurately with materials. For Ghana, the estimates in Table 4 imply that farms who took up insurance and cash would have needed to use 77 additional days of labor per season and 2 acres of land area to increase these inputs commensurately with materials. These magnitudes suggest indivisibilities are not driving my results. 5

Another set of assumptions is that the law of motion for productivity is AR(1) and that lagged inputs are valid instruments. If these assumptions were invalid, we would also reject the null. Thus, the overidentification test is a joint test of the assumptions on both the law of motion and the functional form of the production function.

iv

A.1.3

Timing of Labor Choice in Ghana

An important assumption underlying the model and test for whether frictions in labor and land markets weaken the effect of relaxing uninsured risk is that all inputs are chosen before the unforeseen shock (in this case, rainfall) is realized and are thus equally subject to uninsured risk. For example, if labor or land were chosen after the shock was realized and materials were chosen before, then providing insurance would cause farmers to increase materials disproportionately more than labor or land even if labor and land markets worked perfectly, simply because materials are subject to uninsured risk and labor and land are not. It is reasonable to assume land and materials are chosen before the shock is realized. Land is chosen at planting, and materials, which include tractor rental for plowing and chemical inputs like fertilizer and weedicide, are chosen early in the year as well. If anything, since land is chosen first, relaxing uninsured risk should increase land more than materials under perfect factor markets. However, not all labor is chosen at the beginning of the year. The primary tasks for labor are land preparation, planting, weeding, fertilizer application and harvest. While land preparation, planting, weeding and fertilizer application occur before the rainfall shock is realized and at roughly the same time as materials, harvest labor is chosen at the end of the year, once the shock has already been realized. As a result, we might be concerned that the smaller effect of insurance and cash on labor is due to some portion of labor not being subject to uninsured risk.6 To address this issue, I re-run the analysis in Table 4 with pre-harvest labor (land preparation, planting, weeding, fertilizer application) only. The results, shown in Appendix Table A3, are nearly identical, which suggests that my findings do not depend on whether I use all labor or only labor used pre harvest.

A.2

How Much Did Treatments Reduce the Financial Wedge?

Assuming a functional form and estimating production function parameters enables us to measure the extent to which the treatments relaxed financial constraints. If the wedge on inputs that only face financial constraints falls to zero, then the treatment completely removed the financial constraint. 6

Note, however, that even in this case, we would expect harvest labor to increase with treatment in response to increase in farm output and the marginal revenue product of labor to be unchanged. However, in Table 4, I find no significant increase in labor and a statistically significant increase in the marginal revenue product of labor.

v

We can test this by estimating the effect of the treatments on the log of the marginal revenue product of materials. As before, with Cobb-Douglas, the log of the marginal revenue product of materials is mrpmit = ln βm + qit − mit ,

(A.2)

so the Cobb-Douglas coefficient does not affect estimates of the effect of the treatments on the log of the marginal revenue product of materials. However, we do need estimates of the coefficient to measure the level of the log of the marginal revenue product of materials for control firms or farms and determine if the treatment was enough to eliminate the financial wedge. Appendix Table A4 shows estimates for Sri Lanka. The large cash grant had a negative but statistically significant impact on the log of the marginal revenue product of materials (-0.11). The average log of the marginal revenue product of materials for control firms is 0.15 if we use the rescaled Cobb-Douglas coefficient on materials (normalized to impose constant returns to scale) and 0.24 if we use the non-rescaled Cobb-Douglas coefficient. If the treatments completed relaxed financial constraints (i.e., the ceiling on borrowing did not bind), then we would expect the marginal revenue product of materials to fall to log(1 + r)p, or approximately 0.015, given the assumptions that p = 1 and r = 0.015. The point estimate of the impact of the large cash grant on the log of the marginal revenue product of materials implies that this larger cash grant drove the log of the marginal revenue product of materials to 0.04 or 0.13 (depending on which Cobb-Douglas coefficient we choose). The 95% confidence interval on the treatment effect on the log of the marginal revenue product of materials is -0.32 to 0.10, which encompasses an effect that would correspond to driving the log of the marginal revenue product of materials to 0.015. Appendix Table A5 shows estimates for Ghana. The combination of both insurance and cash led a negative and statistically significant drop of -0.14 (se = 0.06) in the log of the marginal revenue product of materials. The average log of the marginal revenue product of materials for control firms is 0.05 if we use the rescaled Cobb-Douglas coefficient on materials (normalized to impose constant returns to scale) and 0.12 if we use the nonrescaled Cobb-Douglas coefficient. If the treatments completed relaxed financial constraints (i.e., there was no longer any uninsured risk), then we would expect the marginal revenue product of materials to fall to log(1 + r)p, or 0, given the assumptions that p = 1 and r = 0. vi

The point estimate of the impact of the combination of insurance and cash on the log of the marginal revenue product of materials implies that this combination drove the log of the marginal revenue product of materials to -0.09 or -0.02 (depending on which CobbDouglas coefficient we choose). These point estimates suggest the treatment did remove uninsured risk for farmers. The 95% confidence interval on the treatment effect on the log of the marginal revenue product of materials is -0.26 to -0.02, which encompasses an effect that would correspond to driving the log of the marginal revenue product of materials to 0.

vii

Appendix Table A1: Production Function Estimates by Treatment Status (Sri Lanka) (1) All Instruments

(2) (3) DP Lagged Inputs Only

All Observations All Observations Log Labor Log Materials Log Physical Capital Ratio of Coefficients on Labor and Raw Materials Firm-wave obs. Firms

Treated Only

0.284 (0.171) 0.76 (0.0470) 0.05 (0.0199)

0.280 (0.230) 0.766 (0.0625) 0.052 (0.0225)

0.33 (0.157) 0.757 (0.0447) 0.049 (0.0336)

0.374 (0.246)

0.366 (0.328)

0.436 (0.226)

2,332 354

2,332 354

1,063 208

Notes : Columns (1)-(2) repeat estimates from Columns (1)-(2) of Table 5. Column (3) replicates the estimation procedure from Column (2) with only observations where treatment status is 1 over two consecutive waves. "Log" denotes natural log. Inputs and output Winsorized at the 2nd and 98th percentiles. Standard errors, clustered at the firm level, in parentheses.

Appendix Table A2: Production Function Estimates by Treatment Status (Ghana) (1) All Instruments

(2) (3) DP Lagged Inputs Only

All Observations All Observations Log Labor Log Materials Log Land Ratio of Coefficients on Labor and Materials Ratio of Coefficients on Land and Materials Farm-year obs. Farms

Treated Only

0.255 (0.143) 0.368 (0.112) 0.441 (0.119)

0.516 (0.255) 0.170 (0.169) 0.426 (0.179)

0.616 (0.239) 0.146 (0.197) 0.33 (0.188)

0.693 (0.515) 1.12 (0.595)

3.03 (3.99) 2.50 (3.00)

4.22 (6.66) 2.27 (3.87)

2,062 1,179

2,062 1,179

1,566 984

Notes : Columns (1)-(2) repeat estimates from Columns (1)-(2) of Table 6. Column (3) replicates the estimation procedure from Column (2) with only observations where treatment status is 1 over two consecutive years. "Log" denotes natural log. Inputs and output Winsorized at the 2nd and 98th percentiles. Standard errors, clustered at the farm level, in parentheses.

Appendix Table A3: IV Effects of Treatments on Inputs, Output and Ratios of Marginal Revenue Products with Pre-Harvest Labor (Ghana) (1)

Log Output

Insurance

(2)

Log Labor

(3)

Log Land

(4)

Log Materials

(5)

(6)

Log Ratio MRP Labor to MRP Materials

Log Ratio MRP Land to MRP Materials

(Log Materials Log Labor)

(Log Materials Log Land)

0.0735 (0.0690) 0.193 (0.0810) 0.0414 (0.0773)

0.0386 (0.0575) 0.0156 (0.0746) -0.115 (0.0658)

0.107 (0.0496) 0.126 (0.0586) -0.0106 (0.0510)

0.115 (0.0578) 0.341 (0.0652) 0.124 (0.0608)

0.0773 (0.0559) 0.309 (0.0690) 0.241 (0.0667)

0.000482 (0.0325) 0.198 (0.0386) 0.125 (0.0389)

Both = Insurance Both = Cash Insurance = Cash

0.08 0.10 0.71

0.73 0.10 0.03

0.69 0.03 0.04

0.00 0.00 0.89

0.00 0.36 0.01

0.00 0.08 0.00

Farm-year obs. Farms R2

3,447 1,341 0.015

3,447 1,341 0.028

3,447 1,341 0.028

3,447 1,341 0.051

3,447 1,341 0.028

3,447 1,341 0.041

Both Cash

Notes : Replicates the estimates in Table 4 with pre-harvest labor only. "Log" denotes natural log. All regressions include sample frame-year fixed effects. All dependent variables Winsorized at the 2nd and 98th percentiles. Standard errors, clustered at the farm level, in parentheses.

Appendix Table A4: Effects of Treatments on Financial Wedge (Sri Lanka) Log MRP Materials (Log Output Log Materials) Cash 100

0.0222 (0.0867) -0.109 (0.104) -0.126 (0.0935) -0.0303 (0.108)

Cash 200 In-kind 100 In-kind 200 Cash 100 = Cash 200 In-kind 100 = In-kind 200 Cash 100 = In-kind 100 Cash 200 = In-kind 200

0.30 0.48 0.21 0.58

Firm-wave obs. Firms

2,850 360

R2

0.434 Average Log MRP Materials for Control Firms

With rescaled Cobb-Douglas coefficient on materials With non-rescaled Cobb-Douglas coefficient on materials

0.151 0.241

Notes : Estimates of the regression in (15). Dependent variable is log marginal revenue product (MRP) of materials, assuming a CobbDouglas production function. The fifth, sixth, seventh and eighth rows show the p -value for tests of whether the coefficients on different treatments are equal. "Log" denotes natural log. Specification includes firm and wave fixed effects. Dependent variable Winsorized at the 2nd and 98th percentiles. Standard errors, clustered at the firm level, in parentheses.

Appendix Table A5: IV Effects of Treatments on Financial Wedge (Ghana) Log MRP Materials (Log Output Log Materials) Insurance

-0.0324 (0.0510) -0.139 (0.0606) -0.0893 (0.0616)

Both Cash Both = Insurance Both = Cash Insurance = Cash

0.04 0.48 0.37

Farm-year obs. Farms

3,448 1,341

R

2

0.046 Average Log MRP Materials for Control Farms

With rescaled Cobb-Douglas coefficient on With non-rescaled Cobb-Douglas coefficient on materials

0.054 0.116

Notes : Estimates of the regression in (17). "Insurance" instrumented using indicators for whether farmer offered insurance alone at various prices. "Both" instrumented using indicators for whether farmer offered insurance at various prices and a cash grant. Dependent variable is log marginal revenue product (MRP) of materials, assuming a Cobb-Douglas production function. The fourth, fifth and sixth rows show the p -value for tests of whether the coefficients on different treatments are equal. "Log" denotes natural log. Specification includes sample frame-year fixed effects. Dependent variable Winsorized at the 2nd and 98th percentile. Standard errors, clustered at the farm level, in parentheses.

Appendix Table A6: Parameters for Counterfactual (Sri Lanka) Parameters

Value

Calculation

Cobb-Douglas coefficient on labor Cobb-Douglas coefficient on materials Cobb-Douglas coefficient on physical capital Expected productivity Interest rate Depreciation rate Wage Price of materials Price of physical capital

0.260 0.695 0.046 3.369 0.015 0.029 6.913 1 1

Production function estimation Production function estimation Production function estimation First-order conditions Assigned First-order conditions First-order conditions Assigned Assigned

Notes : Parameters for counterfactual for Sri Lanka, reported in Table 7.

Appendix Table A7: Parameters for Counterfactual (Ghana) Parameters

Value

Calculation

Cobb-Douglas coefficient on labor Cobb-Douglas coefficient on materials Cobb-Douglas coefficient on land Expected productivity Interest rate Wage Price of materials Price of physical capital x depreciation rate

0.240 0.346 0.414 14.272 0 0.755 1 36.090

Production function estimation Production function estimation Production function estimation First-order conditions Assigned First-order conditions Assigned First-order conditions

Notes : Parameters for counterfactual for Ghana, reported in Table 8.