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Salaries or piece rates: on the endogenous matching of harvest workers and crops.

I. INTRODUCTION

Why are some workers paid piece rates based on output while others are paid salaries for their input?1 We will try to answer this question using the confidential version of the National Agricultural Workers Survey (NAWS) data by focusing on agricultural workers who harvest different crops for which they are paid either piece rates or hourly rates. The question straddles two of the main research areas of the modern personnel economics that are tightly related: incentives and hiring. A firm should choose its hiring policy corresponding to the incentive structure it has in place and should select an incentives structure in line with people it strives to hire. The theoretical foundation of the incentives literature is the agency model which has been very useful in explaining pay-for performance relationships and the empirical literature has repeatedly shown that financial incentives do change behavior in organizations. The fundamental economic problem in hiring is one of matching with costly search and bilateral asymmetric information. Job seekers have varying abilities, risk aversions, skills, and motivations and firms have varying needs for these traits. Economic efficiency requires that the labor market identify the best matches of workers to firms. (2)

In the core of the agency theory is the principal-agent model (e.g., Holmstrom and Milgrom 1987) which provides the solution for the optimal contract that strikes a balance between the provision of incentives and insurance for the risk-averse agents. The shape of the optimal contract should depend inversely on the agent's risk aversion and the riskiness of the contracted task. This model generates three key predictions. First, the stronger the incentives, the harder the agent will work. Second, there is a trade-off between incentives and the agent's risk aversion: everything else equal, more risk-averse agents will always face lower powered incentive schemes (those that provide more income insurance) and less risk-averse agents will face higher powered schemes (less income insurance). Third, there is a trade-off between incentives and the riskiness of the task. In situations where factors beyond the agent's control have a relatively large effect on output, incentives will be weaker. However, the pay-for-performance incentives do not improve organizational performance in all contexts. For example, Gibbons (1987) showed that when workers have private information about the difficulty of the task and when the firm cannot commit not to use the information it learns about the difficulty of the task, workers will restrict output, that is, the ratchet effect will arise. In a multitasking setting, Holmstrom and Milgrom (1991) demonstrated that providing incentives for some tasks could induce a misallocation of effort across tasks, and when this is sufficiently severe, the theory predicts that incentive pay should not be used. There is also ample evidence that problems with performance measurement can lead agents to game the measures by selecting inefficient actions (e.g., Baker 1992).

Regarding the provision of incentives in firms, empirical research has convincingly shown that people respond to incentives. For example, Lazear (2000) using the payroll data for automobile windshield installers at Safelite Glass Corporation (Columbus, OH) showed that a switch from hourly to piece rate led to a 44% increase in output per worker. About half of this was the pure productivity effect, the rest was due to the fact that the piece-rate scheme led to self-selection of more productive workers into the company and less productive workers out. Shearer (2004), using the data from a field experiment where a treatment group of tree planters was randomly assigned to be paid a piece rate while a control group was paid an hourly wage, showed that piece-rate workers were ~20% more productive than those paid by the hour. (3)

Regarding the risk/incentive trade-off, as Prendergast (1999, 2002a, 2002b) pointed out, empirical research offers a rather weak support for this theory. Among large empirical literature in areas such as sharecropping, executive compensation, franchising, and so forth, very few papers have confirmed the negative relationship between pay for performance and observed measures of uncertainty, while the majority of them either discovered a positive or no significant relationship between the two phenomena. This challenge has led many empirical researchers to look for new evidence in support of this theory but has also led to the development of models that lead to the predictions that incentives and risk could be positively related. (4) One surprisingly common characteristic of most empirical papers in this area is the fact that they ignore the possibility of endogenous matching between principals and agents. Despite the fact that the data usually come from markets which consist of heterogeneous principals and agents, they test predictions which emerge from the single principal-agent pair model. It is easy to see that if one allows workers to be different with respect to their risk aversion, and also allows projects (tasks, jobs) to be different with respect to their riskiness, then perhaps from the social welfare point of view it would be best if agents with low risk aversion work on more risky projects and workers with high risk aversion work on less risky projects. If this endogenous equilibrium materializes in the economy and either the agents' risk aversion or the riskiness of the projects is unobservable, one could end up with a spuriously positive relationship between risk aversion and the pay structure (power of incentives). This could be the case if, for example, workers with low risk aversion matched with high risk projects and ended up signing low powered incentive contracts, resulting in a positive relationship between the power of incentives and risk aversion (Ackerberg and Botticini 2002).

Unlike in the literature on risk/incentives tradeoff, matching (sorting) of workers with firms (as well as matching workers with jobs within the firms) is central to the entire research program of the hiring literature. Important theoretical contributions fit into two areas: models of efficient matching with symmetric learning and game theoretic models of asymmetric information. In learning models (see Jovanovic 1979) a worker's expected productivity in any given period depends on where she works. Hence, in terms of economic efficiency it is important to maximize the firm/worker match quality. The asymmetric information problem has been addressed from two angles. In the pioneering work of Spence (1973) employers rely on costly signals to infer the ability of the job seekers. Signalling solves selection problem, that is, a separating equilibrium is obtained, only when acquiring the signal (education) is sufficiently costly and when the cost to an individual of acquiring the signal is inversely related to her ability. Another way to separate people of different abilities is to use self-selection. Salop and Salop (1976) has shown that if some attribute of the employment relationship (say compensation) differs in its value to prospective employees, and this difference in value is related to productivity, then more productive employees will self-select into this firm. Lazear (1986) ties self-selection to monitoring (measuring) cost. If measurement is costly enough, those with relatively low productivity are not willing to pay to be separated from those with the lowest productivity. Consequently, some firms pay a fixed salary for all employees and attract workers with relatively low ability. Other firms use piece rates and measure workers. Even if performance pay has no effect on workers' effort, when workers are heterogeneous in terms of abilities, it can be profitable for firms to incur the monitoring cost and attract more able workers by paying them a wage that better reflects their productivity (see also Lemieux, MacLeod, and Parent 2009).

The main objective of this paper is to revisit the question of risk/incentives trade-off in an approach that combines the flavors of the incentives and hiring strains of the personnel economics literature. A similar model which combines moral hazard and matching is used by Courty and Marschke (2008) in their empirical study of matching physicians and medical occupations. Another example of a model of matching and incentives provision is used by Bandiera etal. (2011b) who study the match between firms and managers. As will be shown later, the type of matching between agricultural workers and crops they harvest that emerges in equilibrium critically depends on the underlying traits and can be positive assortative (PAM) or negative assortative (NAM). (5) In our context PAM would be the situation when low risk-averse (or high ability) workers match with crops that exhibit low risk in harvesting and workers with high risk aversion (or low ability) match with crops that exhibit high risk in harvesting. NAM is characterized by the exactly opposite situation.

Our matching model is a modified version of Series (2005) who derived the equilibrium relationship between the principal's risk and the power of incentives, whereas we derive the relationship between the agents' risk aversion (ability) and incentives. When matching on risk aversion, the model generates the well-known unique prediction of a negative relationship between risk aversion and incentives only in case of PAM. However, in case of NAM, the theory gives no definitive prediction and the relationship between agents' risk aversion and the power of incentives becomes an empirical question. On the other hand, when it comes to matching on ability, the equilibrium matching is always NAM and the relationship between the agents' ability and the power of incentives is always positive such that high ability agents always sort themselves into high powered incentives contract.

Our empirical results show strong evidence of matching between agricultural workers and the crops they harvest based on workers' risk aversion but no matching based on ability. We show that matching occurs across counties and that the effect is completely exhausted within counties as a result of much less variation in crops within a county. This information is crucial for the correct econometric specification of the contract choice equation, which will suffer from the endogeneity problems if the econometrician does not properly control for the matching that occurs, in this case by including county fixed effects in the contract choice equation. When controlling for matching, we find strong evidence that high risk-averse workers choose hourly rates and low risk-averse workers choose piece rates. We also found that high ability types choose piece rates and low ability types choose hourly rates but the evidence is weaker.

II. UNDERLYING THEORY

Consider a simple principal-agent model where a risk-neutral principal contracts a risk-averse agent to perform a certain task. The production function for this task is given by [y.sub.p,a] = [e.sub.a] + [[epsilon].sub.p] where ea is the agent's effort and [[epsilon].sub.p] ~ N (0, [[sigma].sup.2.sub.p]) is the i. i.d. productivity shock. The agent's effort is unobservable hence there is a moral hazard problem. The choice of subscripts {a, p}, subsequently dropped to avoid notational clutter, specifies the distribution of inputs in the production function such that the agent supplies effort and the principal supplies only the productivity shock which can be thought of as the riskiness or the complexity of the task (project). The agent's cost of effort is given by C = (c/2)[e.sup.2] and she is assumed to have constant absolute risk-aversion (CARA) preferences with the utility function given by V = 1 - exp[- [lambda](w - (c/2) [e.sup.2])], where w represents the compensation and [lambda] is the Arrow-Pratt measure of the agent's absolute risk aversion. The principal's profit (utility) function is simply [pi] = y - w. Both players have zero reservation utilities.

The compensation scheme in the above set-up is linear in output (see Holmstrom and Milgrom 1987) such that w = [alpha] + [beta]y where [alpha] is the fixed salary and [beta] is the piece rate. Utilizing the fact that [epsilon] is normal, the agent's utility function can be expressed in the mean-variance form and the agent's optimal effort becomes [e.sup.*] = [beta]/c. As seen, the optimal effort depends positively on the power of incentives and negatively on the cost of effort. Now we are in the position to solve for the optimal contract parameters by maximizing the agent's expected utility subject to the agent's incentive compatibility and principal's zero expected profit constraints. The optimal piece rate becomes:

(1) [beta] = 1 / 1 + c [[lambda].sub.a] [[sigma].sup.2.sub.p].

The model has two key predictions. First, there is a trade-off between incentives and the agent's risk aversion. Everything else equal, the stronger the agent's risk aversion, the weaker the incentives. Second, there is a trade-off between incentives and the riskiness of the task. In situations where factors beyond the agent's control have a relatively large effect on output, incentives will be weaker.

Next, using the above results it is easy to solve for the expected total surplus function:

(2) [PI] = 1 / 2c (1 + c [[lambda].sub.a] [[sigma].sup.2.sub.p]).

To rule out uninteresting cases, we assume that [PI] > 0 because otherwise the contracting between the principal and the agent would have not taken place to begin with. (6) By differentiating Equation (2) with respect to the degree of agent's risk aversion and using the envelope theorem, one can easily show that the expected total surplus is decreasing in the agent's risk aversion. This means that an agent with low risk aversion can tolerate more risk and therefore can be exposed to stronger incentives ([beta]) which increases the total surplus. Similarly, one can show that Equation (2) is decreasing in the variance of the productivity shock ([[sigma].sup.2]). Hence, the aggregate gain from contracting (employment) is inversely related to the riskiness of the task. Given that the productivity of an agent is inversely related to the degree of her risk aversion, we should expect principals (who offer employment contracts) to compete with each other for low risk-averse agents. The question that naturally arises in the industry setting with multiple principals and many agents is who ends up hiring low risk-averse agents, that is, it becomes obvious that one needs to study the equilibrium matching patterns between industry participants.

To derive the equilibrium matching conditions between workers and firms we start by defining positively assortative matching (PAM) when good (high) type principals match with good (high) type agents and bad (low) type principals match with bad (low) type agents (the matching curve has a positive slope). Similarly, we define negatively assortative matching (NAM) when good type principals match with bad type agents or the opposite (the matching curve has a negative slope). Conventionally, we define good type agents by low degree of risk aversion ands good type principals by the low variance of tasks and bad type of agents by high degree of risk aversion and bad type of principals by high variance of projects. (7)

To simplify, we follow Series (2005) and focus on monotone (globally assortative) matching and assume a continuum of principals and agents with uniform distributions. In particular, the model is based on the following primitives: a continuum of principals (employers) which are uniquely identified by the riskiness (variance) of their tasks (projects) and are uniformly distributed on the interval [[sigma].sup.2.sub.L], [sigma].sup.2.sub.H]; a continuum of agents (workers) which are uniquely identified by the degree of their absolute risk aversion and are uniformly distributed on the interval [[[lambda].sub.L], [[lambda].sub.H]]; and a set of possible contracts (payment schemes) that workers and firms can sign, defined by a fixed hourly compensation and the slope of the performance based compensation (piece rate). We are only interested in the relationship between agent's risk aversion and the power of incentives (the slope coefficient). (8) We ignore the potential impact of the market clearing condition on rents that agents with different degrees of risk aversion can possibly receive in equilibrium. Finally, we assume that one principal has to match with exactly one agent (and vice versa) to produce output.

Given that in this case the only coalitions that matter are of size two, assuming transferable utilities and no externalities across coalitions, any reasonable solution concept to the matching problem should maximize aggregate surplus (see Legros and Newman 2002). The sufficient conditions for assortative matching are obtained by looking at the cross-partial derivatives of the surplus function to determine whether it is supermodular or submodular. If the surplus function is supermodular, the principals' and agents' traits are complements and matching is PAM. If the surplus function is submodular, the traits are substitutes and the matching is NAM. (9) The result shows (see Appendix A) that if the product of the low ends of the supports of the principals' and agents' distributions is relatively high, that is, in the market where the degrees of risk aversion and/or the riskiness of the projects are high, agents with high degrees of risk aversion are matched with principals who own high risk projects and vice versa (PAM). Conversely, if the product of the high ends of the supports of the types distributions is relatively low, that is, in markets where the degrees of risk aversion are low and/or the riskiness of the projects are low, agents with low degrees of risk aversion should efficiently match with high risk principals and vise versa (NAM). (10)

The intuition for the above results is best provided by referring to the risk-neutrality case. If all agents are risk-neutral, then the matching problem would be trivial in the sense that any principal-agent match would be efficient (first-best) because of the absence of the trade-off between incentives and insurance. When agents are risk averse, however, such trade-off exists and the optimal assignment maximizes the sum of all principals' second-best profits. In the two principals by two agents case, when the variances of traits are relatively high (complements), the higher variance principal is very far from the efficient frontier and hiring the lower risk-averse agent is not going to increase his profit as much as it would if this agent was hired by the lower variance principal. In case of substitute traits, since variances are low, the lower variance principal is very close to the efficient frontier and therefore does not gain as much as the higher variance principal would by employing the lower risk-averse agent. The reason for possible co-existence of substitutable and complementary traits is that the profit function (2), in general, exhibits non-monotonic marginal products. This is the reason why the general matching patterns are not easily characterized. (11)

Once we know the type of equilibrium matching that would emerge between the principals and the agents, we can derive the relationship between their traits and the equilibrium contract form. Starting with PAM and using a measure consistency condition (see Legros and Newman 2002) which says that, since each principal is matched with exactly one agent and vice versa, the mass of principals has to be equal to the mass of agents:

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

After some straightforward manipulation, Equation (3) yields the equilibrium relationship between the riskiness of the principal's project (asset) and the degree of agent's risk aversion: [[sigma].sup.2] = [[lambda].sub.H] [[sigma].sup.2.sub.L] + [[lambda].sub.L] [[sigma].sup.2.sub.H] / [[lambda].sub.H] - [[lambda].sub.L] + [lambda] ([[sigma].sup.2.sub.H] - [[sigma].sup.2.sub.L] / [[lambda].sub.H] - [[lambda].sub.L], which after inserting it into Equation (1) yields:

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The differentiation of (4) with respect to [lambda] gives:

(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Since the denominator is always positive, the sign of Equation (5) depends on the sign of the numerator which can be rewritten as c ([[lambda].sub.H] - [[lambda].sub.L]) (-[[lambda].sub.H] [[sigma].sup.2.sub.L] + [[lambda].sub.L] [[sigma].sup.2.sub.H] L) - 2 [lambda] [[sigma].sup.2.sub.H]) + 2[lambda] [[sigma].sup.2.sub.L]. Since c([[lambda].sub.H] - [[lambda].sub.L]) > 0, the sign of the numerator depends only on the sign of the expression in the parentheses, which can be rewritten as: -[[sigma].sup.2.sub.L] ([[lambda].sub.H] - [lambda]) + [[sigma]sup.2.sub.H] ([[lambda].sub.L] - [lambda]) + [lambda] ([[sigma].sup.2.sub.L] - [[sigma].sup.2.sub.H]) < 0, which is obviously negative since all three elements of the sum are negative. Hence, in case of a PAM, the resulting equilibrium relationship between agents' risk aversion and the power of the contract incentives is always negative. Agents with high degree of risk aversion will sort themselves into low powered incentives contracts, and vice versa.

Combining the above results with the corresponding equilibrium matching we obtain a rather interesting result. Since the equilibrium matching is positively assortative, agents with high degrees of risk aversion are matched with principals who own high risk projects but they pick low powered incentives schemes. Conversely, agents with low degrees of risk aversion are matched with principals owning low risk projects but they pick high powered incentives schemes. This result is interesting because it gives the same prediction about the relationship between risk aversion and the power of incentives as in the case of a single principal-agent pair (1), but which is based on a counter-intuitive risk matching result where the traits (agents' risk aversion and the riskiness of the tasks) are complements. On the other hand, when traits are substitutes (as economists intuitively believe), the theoretical model gives no definitive empirical prediction about the relationship between risk aversion and the power of incentives. The equilibrium relationship can be positive, negative, or U-shaped (see Appendix B for details).

The same model can be adapted to explore the relationship between agents' abilities and the power of incentives. For this purpose the production function can be written as [y.sub.p,a] = [e.sub.a] [[theta].sub.a] + [[epsilon].sub.p] where [[theta].sub.a > 0 represents agent's inherent ability. We will assume that] agents' abilities are observable by both sides hence there is no adverse selection. With this specification, the agent's optimal effort, [e.sup.*] = [beta][theta]/c, depends positively on the power of incentives and the agent's ability and negatively on the cost of effort.12 With this specification the optimal piece rate is given by [beta] = 1/1 + (c[lambda][[sigma].sup.2]//[[theta].sup.2]) and the expected total surplus becomes [PI] = [[theta].sup.4]/2c([[theta].sup.2] + c[lambda] [[sigma].sup.2]). By differentiating with respect to ability and using the envelope theorem, one can easily show that the expected total surplus is increasing in agent's ability ([theta]) meaning that an agent with higher ability can be exposed to higher incentives to exert effort. This is a well-known result in the personnel economics literature; for an overview see for example Lazear and Oyer (2012).

To keep the analysis tractable we continue focusing on the single dimensional matching patterns, that is, we develop equilibrium matching conditions between workers and firms based on the workers' abilities (ignoring their preferences towards risk) and the riskiness of firms' projects. (13) Again, we define good type agents by high ability and good type principals by the low variance of tasks and bad type agents by low ability and bad type principals by high variance of projects. We assume a continuum of agents (workers) who are uniquely identified by their inherent ability and uniformly distributed on the interval [[[theta].sub.L], [[theta].sub.H]].

Same as before, the sufficient condition for assortative matching is obtained by looking at the cross-partial derivative of the surplus function. As it turns out, [partial derivative][PI]/[partial derivative][[sigma].sup.2] = -2 [[theta].sup.3] c[[lambda].sup.2][[sigma].sup.2]/( ([[theta].sup.2] + c[lambda] [[sigma].sup.2]).sup.3], which is clearly always negative for all [[sigma].sup.2] and [theta] in the support of the distributions and the total surplus function is submodular and we always obtain NAM. That means the agent's ability and the riskiness (complexity) of the principal's task are always substitutes. Therefore, when matching on ability, in equilibrium, good type (high ability) agents will always match with bad type (high risk task) principals and bad type (low ability) agents will always match with good type (low risk task) principals. Implementing the same procedure as before, we can now show (see Appendix C) that the equilibrium relationship between agents' ability and the power of contract incentives is always positive. This means that high ability agents will always sort themselves into high powered incentives contracts and low ability agents will always pick low powered contracts.

III. EMPIRICAL TESTING

Based on the presented theoretical framework we can derive two empirically testable propositions. First, when considering matching on agents' risk aversion, we can only make a qualified prediction: if the underlying equilibrium matching is positive assortative, highly risk-averse workers should end up choosing hourly rates whereas low risk-averse workers would choose piece rates. If the underlying equilibrium matching is negative assortative, the relationship is ambiguous and no definitive prediction is possible. Whether the underlying matching process is PAM or NAM is an empirical question. Second, when the agents' trait of interest is ability and the principals' trait is the riskiness of the task, the underlying equilibrium matching is always negative assortative and in market equilibrium we should find high ability agents working under high powered incentives (piece rates) and low ability agents working under low powered incentives (hourly rates).

The empirical testing proceeds in two steps. In the first step, we estimate the matching equation. This serves two purposes. First, it determines the type of matching between workers and crops that will emerge in market equilibrium. Knowing whether the underlying equilibrium matching is PAM or NAM is important for deriving the precise theoretical prediction about the contract choice. Second, knowing if either type of matching emerges in market equilibrium is important because via principal-agent matching the riskiness of the task (job) becomes endogenous to the agent (employee) and needs to be addressed econometrically. In the second step, we estimate the contract choice equation by relating the incidence of piece rates versus hourly rates to the measures of workers' risk aversion and ability (as well as their other characteristics) and the measures of risk associated with harvesting various crops. The test hinges on the signs of the coefficients associated with measures of workers' risk aversion and ability.

A. Data

The empirical work in this paper is all done using confidential individual-level data on undocumented harvest crop workers from the NAWS for a period of 10 years--from 1999 to 2008. The data set does not have a panel structure but it rather consists of independent annual cross sections. The difference between the confidential data and the public release version of the NAWS is in the details provided for each individual worker in terms of the location of their employer (down to the county level in the confidential data, but only down to six aggregate regions [East, Southeast, Midwest, Southwest, Northwest, California] in the public release version), and the crops which they harvest (down to the actual crop [e.g., oranges] in the confidential data, but only down to five crop aggregates [Field Crops, Fruits and Nuts, Horticulture, Vegetables, and Miscellaneous] in the public release data). The NAWS is the only nationally representative survey of demographic and employment characteristics of hired crop workers. To reflect the seasonality of agricultural production and employment, the crop workers are surveyed in three cycles each year. The information is obtained directly from farm workers through face-to-face interviews.

We use data on undocumented harvest farm workers, that is, crop workers who are not U.S. citizens, do not have permanent U.S. residence, and who are not otherwise legally authorized to work in the United States. There are two reasons for this choice. First, not surprisingly, most harvest farm workers in the United States are undocumented--about 70% of all harvesters during the 1999-2008 period in the NAWS are undocumented. Second, the distribution of risk aversion across U.S. citizens and permanent residents, who are legally allowed to work in the United States, is likely quite different from the distribution of risk aversion across undocumented workers. While the baseline results shown here use only undocumented workers, similar results obtain using both undocumented workers and legal permanent residents. In one of our robustness checks, we use data on all harvest workers--both undocumented and documented.

Table 1 presents the summary statistics for all undocumented harvest crop workers surveyed in the NAWS between 1999 and 2008. The data shows that 40% of workers are paid by the piece (piece rate) as opposed to by the hour (hourly rate), and that their average hourly wage is $7.94 (constant 2006 U.S. dollars). (14) Only 11% of all workers are female. About half of all harvesters are married, but only 18% have children in the family. At an average age of 28.85 years, these farm workers are fairly young, and while undocumented, they have spent an average of 6.07 years in the United States. Given their farm work experience in the United States of 5.62 years, their predominant form of employment in this country is farm work--only 9% were ever employed outside the agricultural sector in the United States. This may not be surprising as they have fairly low levels of education with an average of 6.04 years of schooling. Many of them do not speak English well. Their average proficiency in spoken English on a scale of 1 (worst) to 4 (best) is only 1.38. Most workers in this population (79%) are full-time employees with an average of 41.66 hours per week, and about one-third are employed by a farm labor contractor as opposed to directly by the farm. Half of all harvesters live within 9 miles of their place of employment, and nearly 90% live within 25 miles. For the vast majority of them (97%), Mexico is their home country. More than half of all workers (53%) harvest various fruits and nuts, and 34% pick vegetables. Not surprisingly, a large fraction of all harvest workers are employed in California (41%); the second largest region in terms of employment is the Southeast (22%).

While the NAWS does not record the value of personal assets, it offers a very detailed classification of all assets an agricultural worker can possess. In particular, workers indicate if they own land, a business, a house, or other assets in their home country, which is Mexico for 97% of the sample, and in the United States. (15) In our analysis, we use these eight indicator variables as empirical proxies of harvest workers' wealth. The summary statistics in Table 1 reveal that undocumented harvest workers own few assets in the United States. Only 0.2% of this population own land in the United States, and only 0.1% own a business or other assets. Also, a small fraction of workers (1.7%) own a house in the United States. When it comes to assets in their home country, a much larger fraction of the harvesters own land (11.2%) or a house (46%). A smaller number of workers own a business (0.02%) or other assets (0.02%) in their home country.

Using these eight wealth indicators, we also compute two additional wealth measures. The first measure is a simple sum of the eight wealth indicators. It varies between 0 and 8 and shows how many different assets (in the United States or in the worker's home country) a worker has. The sample average of this wealth measure is 0.589, indicating that a given worker is expected to own about half of one of the eight different types of assets discussed above. The second wealth measure is the weighted sum of the eight wealth indicators with their respective population-wide average values (in U.S. dollars) used as weights. (16) This wealth measure has a mean of $23,489 (2006 U.S. dollars) and a standard deviation of $46,627 in our sample. Notice that the standard deviation is about twice the size of the mean, indicating that there is substantial variation in wealth among undocumented harvest workers. While neither of the two additional wealth proxies measures is perfect, each combines the available information differently--the first proxy weights all eight types of assets equally, while the second one gives more weight to assets that are in general more valuable as revealed by their population (United States and Mexico) averages.

Finally, in our robustness checks we also use data on worker's smoking behavior and legal status. While the publicly released version of the NAWS data does not provide any information on smoking, the confidential version of the NAWS that we employ does contain such information for the 5-year period from 1999 until 2003. In the survey, workers were asked if they have smoked at least 100 cigarettes in their lifetime. If the answer is "yes," we consider the worker to be a smoker.

B. Measuring Unobservable Traits

In order to establish the correspondence between the presented theory and the available data, we need to explain how the principals' and agents' characteristics (traits) are defined and measured.

First, it is important to realize that the riskiness of the principals' assets (projects) in this context is the riskiness associated with harvesting a particular crop and not the riskiness of producing (growing) that crop (although there could be some commonalities between the two). It is the first that matters and not the second, because here we deal with harvesting contracts rather than, for example, sharecropping contracts. To fix ideas, imagine two crops being harvested with two types of equipment, one prone to frequent malfunctioning and stalling and the other very primitive but always functioning flawlessly. Some harvesters may prefer the second job, albeit physically more strenuous, because it could be perceived as less risky. Another situation may be weather related. Imagine that harvesting a certain crop is easily done when it rains whereas harvesting another crop is very difficult or impossible. For the latter, if it rains during harvest, the piece-rate workers are wasting their time because they could hardly earn any money, whereas the hourly rate workers do not mind rain as they get paid regardless of whether they are active or idle. Finally, the riskiness of growing a crop, as typically represented by its yield, can also play a role in harvesting. When the yields are low, the harvesters may use more time to pick a certain quantity compared to harvesting when yields are high. The hourly paid workforce would be indifferent between the two yield scenarios whereas the piece-rate crew would always prefer to harvest a bumper crop.

Second, the fact that agents' (farm workers') risk aversion or risk tolerance is not directly observable presents a challenge for empirical work. In our approach we rely on Guiso and Paiella (2008) who used survey data on households' willingness to pay for a hypothetical risky security to recover a measure of the Arrow-Pratt index of absolute risk aversion of the consumer lifetime utility. Their findings show that risk aversion (risk tolerance) is a decreasing (increasing) function of consumers' resources (wealth), thus rejecting the CARA preferences. They also estimated the elasticity of absolute risk tolerance to consumers' resources to be below unity as implied by the constant relative risk aversion (CRRA) preferences which then suggests that risk tolerance is a concave function of wealth. Wealth was used as a proxy for risk aversion in many other studies, for example, Laffont and Matoussi (1995) and Ackerberg and Botticini (2002).

Using the personal wealth indicators discussed in the data section, we construct two different proxies for risk aversion. First we use the entire vector of workers resource endowments. This measure is coded as eight dummy variables that indicate if a harvest worker owns land, a house, a business, or other assets in the United States or their home country. The second proxy uses the five principal factors that are retained after we perform a principal factor analysis using the eight wealth indicators. In line with all existing literature, we postulate that wealthier individuals are less risk averse.

Because wealth is an imperfect measure of risk aversion, we also use two other alternative proxies: worker's smoking habits and legal status. Both smokers and undocumented workers are likely to be less risk averse than non-smokers and documented workers. Recent research by Anderson and Mellor (2008), who conduct a large-scale experimental study, shows that controlling for demographic and economic characteristics, risk aversion is negatively and significantly associated with cigarette smoking. Also, in a recent empirical contribution, Jaeger et al. (2010) show direct evidence that individuals who are more willing to take risk, that is, individuals who are less risk averse, are also more likely to migrate.

Table 2 presents the sample correlations across the type of compensation (piece rate vs. hourly), the eight different wealth indicators, the two alternative wealth measures, and the two other proxies for risk aversion--the indicator for being a smoker and the indicator for being an undocumented worker. The first column of Table 2 implies that risk aversion as proxied by wealth, smoking behavior, or undocumented status, is not really correlated with piece-rate pay--the coefficients are of rather small magnitude, with some being positive, and some being negative.

Finally, similarly to risk aversion, the inherent ability of workers is also not observed and difficult to measure. An elegant solution to this problem is typically found in the panel data setting where individual abilities can be estimated as person-specific fixed effects in some performance measure (output or cost) regression (e.g., Lazear 2000; Levy and Vukina 2004). Since our data set consist of independent annual cross-sections, this approach is ruled out. Instead, we had to rely on two less ideal measures of ability. First, we use education as a proxy for ability and argue that more able people are more likely to obtain more schooling than less able people. Second, we use language proficiency and argue that among non-native English speakers (undocumented immigrants), those who speak English more proficiently are likely to be of higher ability than those who do not speak English at all or speak it rather poorly.

C. Matching Equation

Based on the previously presented theoretical model, an obvious first step in the empirical analysis would be to determine the type of matching between workers and crops that will emerge in market equilibrium. This is important not only for deriving the theoretically correct predictions but also for important econometrics reasons. As shown by Ackerberg and Botticini (2002), the problem here is that whereas the riskiness of the crop may be exogenous to the farmer (principal) it is endogenous, via principal--agent matching, to the agricultural worker (agent) that has chosen that job. If the workers' risk aversion were perfectly observed by the researcher, the endogeneity problem could be solved by regressing the contract choice (power of incentives) on the riskiness of the crop and worker's risk aversion. However, since the degree of risk aversion is never perfectly observed, using proxies in such regressions will not solve the endogenous matching problem. With endogenous matching, the riskiness of the crop variable will be correlated with the error term through the proxy error, that is, the unobserved component of risk aversion. Because matching always generates correlation between possibly observable traits of one party and proxy errors from unobservable traits of the other party biasing the estimated coefficients of interest, exactly the same problem arises when matching on ability is considered. A potential solution to this problem is the estimation of a matching equation to check if and how principals and agents are matched with each other.

Unfortunately, since there is really no meaningful way to ascribe or compute the risk associated with harvesting each particular crop, it is impossible to estimate the slope of the matching equation by simply regressing the risk associated with the principal's task on the agents' measure of risk aversion in one case or agents' ability in the other case. However, utilizing the detailed information on the type of crop each harvester chooses, we can still test if any kind of matching between workers and tasks exists. This is accomplished by estimating a multinomial logit model, where the left-hand-side variable is the probability that harvest worker i chooses crop k, [P.sub.ik] and the right-hand-side includes the measure of the worker's risk aversion and ability. Workers can potentially select from a set of 106 available crops. In addition to the worker's wealth, [W.sub.ik], which is used as a proxy for risk aversion, the regressors include a vector of personal characteristics, [X.sub.ik], a full set of yearly dummies, [Year.sub.t], and a full set of county dummies, [County.sub.j]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6)

The vector of personal characteristics, [X.sub.ik], for worker i, harvesting crop k includes controls for schooling and English proficiency as measures of ability, but also gender, marital status, children, age, time spent in the United States, a linear and a square term in U.S. farm work experience, and indicators for non-farm employment, full-time status, and employment by a farm labor contractor. (17) For identification and without loss of generality, one of the crop choices (k = 1) is treated as the base category (the correspondent coefficients are constrained to equal 0). In our case the base crop is oranges. At the very basic level, this model provides evidence of matching between harvest workers and the crops they harvest.

D. Contract Choice Equation

In order to empirically test our two propositions we need to estimate the contract choice equation. The empirical representation of the optimal contract slope is the relationship that relates the incidence of piece rate vs. hourly rate to the measures of workers' risk aversion and ability, their other characteristics (notably, the disutility of effort reflected in the parameter c), the measures of the risk associated with harvesting various crops and different cross-products of the above variables, see Equations (4) or (11).

Same as in the matching equation (6), individuals' risk aversion will be proxied by various indicators of workers' personal wealth, residency status, and smoking; ability will be proxied by education and English proficiency; and the individuals' disutility of effort will be proxied by the vector of other personal characteristics which includes the same controls as in Equation (6). Because exact measures of the riskiness of harvesting various crops do not exist, they are proxied by a full set of crop, county, and harvest year dummy variables. Crop fixed effects capture the differences in harvesting technology. Harvesting of some crops is much more likely to require hourly pay than piece-rate pay--for example, table grapes require much more careful harvesting (in order to avoid squishing the grapes) than do wine grapes. As a result, harvesting table grapes is likely to pay predominantly by the hour, while harvesting wine grapes by the piece. Consistent with differences in harvesting technology, Table 3 provides evidence that harvesting table grapes has an incidence of piece rates of 0.21, while the incidence of piece rates for wine grapes is 0.65. Another good example are cut flowers which are always paid by hour because they need to be harvested carefully to look nice when they arrive at the market. However, we also see beets and cauliflower which are always paid by hour and where the same type of monitoring or measuring paradigm fails in explaining the contract choice. (18)

Controlling for the county of employment is important because the same crop produced in two different regions may require somewhat different harvesting practices. More importantly, knowing the precise job location down to the county level allows us to use county fixed effects to control for (a) alternative employment opportunities that exist across locations, (b) political and institutional differences across states and counties (as related to the labor market [such as minimum wage laws] as well as eligibility and generosity of welfare programs), (c) differences in the public's attitude towards (undocumented) immigrants (Hanson, Scheve, and Slaughter 2007) and the immigration environment in general. In practice, it is quite difficult to control for all of these factors because there is really no micro-level data on variables that capture variation in these factors across location (or over time). (19) Assuming that all of these factors vary mostly geographically within the 10-year period of our study, we can effectively control for all of them by incorporating county dummies in the contract choice equations. Finally, year dummies account for the differences in weather, yields, infestations, market conditions, and so forth, that could possibly cause the variation in the payment mechanism offered from one year to the next.

The theoretically correct specification of the econometric model that can be estimated is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (7)

The dependent variable [R.sub.ik] is an indicator equal to one if individual i, harvesting crop k, is paid by the piece rate, and zero if he is paid by the hour. The vector of personal characteristics [X.sub.ik] includes the same controls as it did in the matching equation (6) and risk aversion is proxied by a vector of variables [W.sub.ik]. The matrix of dummy variables measuring the riskiness of harvesting various crops [Z.sub.k,j,t] consists of the vectors of dummies for each crop k, county j, and year t.

The term [PI][W.sub.ik] [Z.sub.k,j,t] represents all cross-products between the indicators of workers' risk aversion, ability, and crops' harvesting risks.

The central interest of this paper is to determine the signs of the coefficients associated with the measures of individuals' risk aversion and ability. Since wealthier workers are less risk averse, they should be more likely to choose piece rates as opposed to hourly pay and, therefore, we should expect positive coefficients on all wealth indicator variables. However, this negative relationship between incentives and risk aversion is only theoretically correct if the underlying matching relationship between workers' risk aversion and the riskiness of harvesting various crops is positive assortative (PAM). On the other hand, if matching is NAM, no definitive prediction is possible as the equilibrium relationship between risk aversion and the power of incentives can be positive, negative or U-shaped. The signs of the coefficients associated with ability measures should be unambiguously all positive reflecting the fact that high ability workers should choose piece rates.

The signs of the coefficients associated with other personal characteristics of harvest workers depend on their relationship to the disutility of effort. The inspection of the optimal compensation formula in Equation (4) or Equation (C1) reveals that the disutility of effort parameter c is in the denominator. This means that the larger disutility of effort reduces the intensity of the payment mechanism and hence would reduce the likelihood of observing the piece rate relative to the hourly rate. Hence, to the extent that a particular personal characteristic is associated with the cost (disutility) of effort in a positive fashion, then it should have a negative impact on the choice of piece rates relative to the choice of hourly rates. For example, if women have higher cost of effort than men, we should expect, ceteris paribus, that they would prefer hourly rates to piece rates and vice versa.

Finally, the signs of the various measures of the riskiness of harvesting different crops (i.e., crop, county, and harvest year dummies) and that of the cross-product terms are generally undetermined as they depend on the base category (crop, county, year) omitted from the analysis. They are used only for the purpose of correctly specifying the empirical model and per se do not contribute to the empirical falsification of the presented theory.

IV. RESULTS AND DISCUSSION

Following the structure of the exposition so far, we first discuss the empirical results from the matching equation and then the findings from the contract choice model.

A. Matching Results

As mentioned before, there are two possibilities for matching between workers and crops, depending on the traits (attributes). Crops are always differentiated by the riskiness or complexity of their harvesting and workers can be differentiated either by their risk aversion or ability. In this section, the base crop category is oranges and all estimates are relative to those of oranges. Because there is a very large number of estimates--105 different set of estimates for the 106 different crops--to conserve space we only present one of the crops--strawberries. (20) The estimation results from Equation (6) are presented in the first column of Table 4. The second column presents the results with aggregate region fixed effects and the third column presents the estimates with detailed county fixed effects.

The results in the first column show that a number of the estimated coefficients on the personal characteristics are statistically significant. They suggest that women and workers who have children in the family are more likely to harvest strawberries than oranges. On the other hand, those employed by a farm labor contractor (and not directly by the farmer) are less likely to harvest strawberries. More importantly, we also see that some of the risk aversion (wealth) indicators are statistically significant at the 5% level, providing evidence of matching based on the project riskiness (harvesting of a particular crop) and the agent's risk aversion (wealth). For example, if a worker owns land in their home country, they are significantly less likely to harvest strawberries (relative to oranges). However, neither one of the ability measures (education and English proficiency) are statistically significant, indicating no matching based on ability. Adding aggregate region (six regions) fixed effects to the matching equation changes the results little. A few of the estimated coefficients which were significant at the 5% level in the first column are no longer significant; still a number of the coefficients remain statistically significant, providing evidence that some matching between projects (crops) and workers does exist even within aggregate regions.

Finally, consider the third column in Table 4. This specification includes detailed county fixed effects in the matching equation (6) and this fundamentally changes the previous results. As seen from column (3), none of the within-county estimated coefficients on the personal characteristics (including those that measure ability) are statistically significant at the 5% level. The only one that comes closest is the coefficient on the indicator for employment by a farm labor contractor (and not directly by the farmer). However, note that this coefficient is more than three times smaller in magnitude than its counterpart in column (1). (21) Similarly, none of the estimated coefficients on the eight wealth indicators are statistically significant, and compared to their counterparts in column (1), these estimates are much smaller in magnitude and are all very close to zero.

Similar results hold for the other 104 crops relative to oranges. Without county dummies, some of the risk (wealth) indicators are statistically significant at the 5% or the 10% level. For some crops (relative to oranges), wealth has a positive effect, while for others, it has a negative effect. (22) Once the county fixed effects are added to the matching equation the significance completely disappears. All of these results imply that matching on risk aversion does occur across counties by harvest workers moving to counties with crops that they would prefer to harvest. However, once the county of employment is determined, matching is exhausted, that is, within a county there is no longer any evidence of matching between harvest workers and crops based on the crop's risk in harvesting and the worker's risk aversion. When it comes to matching on ability, all estimates reveal that there is no evidence of matching between crops and workers based on a worker's ability across or within counties--the estimated coefficients on schooling and English proficiency are always small and statistically insignificant.

Because there is no meaningful way to ascribe or compute the risk associated with harvesting each crop, we cannot sign the slope of the matching equation between workers and crops, that is, we can establish that matching exists but we cannot further determine whether the underlying matching is of PAM or NAM type. In this regard, the obtained matching results do not help in narrowing down the predictions of the theoretical model. However, the confirmed presence of endogenous matching across counties between workers based on their risk aversion and crops is critical from an econometrics point of view. Estimating a matching equation such as this is in fact what Ackerberg and Botticini (2002) suggest as a check for endogeneity when regressing the contract choice on the worker's wealth, where wealth is an imperfect proxy for risk aversion. Because we find clear evidence of matching between workers based on their risk aversion and crops across counties, and no evidence of matching within counties, the estimation of the contract choice equation has to include controls for the county of employment. Otherwise, the identification strategy will suffer from the endogeneity problem driven by endogenous matching.

Finally, the obtained results are also helpful in refining the specification of the empirical model (7). The empirical result showing that matching between workers and crops is fully exhausted across counties suggests that there is no need to include the crop dummies into the contract choice equation as the riskiness of harvesting different crops is adequately captured by the characteristics of the county in which they are grown.

B. Contract Choice Results

The estimates from the contract choice model (7) are presented in Table 5. We estimate a linear probability model instead of a probit or a logit model because employing a maximum likelihood estimator with a large number of fixed effects (indicator variables) is computationally challenging. (23) Additionally, the mean of the left-hand-side variable [R.sub.ik] is about 0.4, far away from the end points of the [0, 1] interval, implying that the linear probability model will deliver results that are very close to those of a probit or a logit specification.

For simplicity, we start by estimating the specification which includes none of the fixed effects or the cross-product terms from regression Equation (7). The results presented in the first column of Table 5 reveal a number of interesting findings. First, it appears that none of the ability variables matter for contract choice as neither of the two variables (education and English proficiency) is significant. The same is true for sex, marriage status, time spent in the United States, U.S. farm work experience, and non-farm employment. On the other hand, having children and being older has a large, economically and statistically significant negative impact on the likelihood of piece-rate pay. In particular, having children decreases this likelihood by 8 percentage points, and 40-year-old harvesters have a 6% lower probability of being paid by the hour than do 20-year-old workers (=(40-20) x 0.003).

Next, we find that employment by farm labor contractor has a very large and statistically significant positive impact on the probability of piece-rate contract. In fact, being employed by a farm labor contractor, and not directly by the farm, increases the likelihood of piece-rate pay by 25% points. (24) Given the average incidence of 40% (see Table 1), this represents an increase of 63%. Further, we find that full-time employment (40 or more hours per week) is associated with 18% point lower likelihood of piece-rate pay.

The estimated coefficients in column (1) of Table 5 associated with risk aversion (wealth) indicators are mixed with some large, positive, and statistically significant coefficients, some large negative and statistically significant coefficients, and some small and statistically insignificant estimates. For example, owning a business in the United States has a large negative impact on the likelihood of piece-rate pay, while owning a business in the worker's home county has a large positive impact. Except for owning a business, generally, the same type of asset (e.g., land) has the same qualitative impact regardless of its location. For instance, ownership of land both in the United States and in the worker's home country has a positive effect on piece-rate pay. Overall, the results from this simple specification do not tell very much about the validity of the proposed theories of contract choice. This is really not that surprising given the fact that the model is not correctly specified. The theoretically consistent econometric model, Equation (7), requires that we include county dummies in order to avoid issues with endogenous matching, which we showed occurs across counties, and also in order to control for differences in local (labor market) institutions and attitudes toward undocumented immigrants. Theoretically, one also needs to include interactions between the wealth indicators and all county and year dummies. Note that the overall (composite) effect of wealth on contract choice theoretically depends on the direct effect of wealth and the indirect effect via the interaction terms between the wealth indicators and the measures of riskiness of harvesting different crops (the set of dummies). As it turns out, the direct effects (no interactions) and the overall effects (with interactions) are statistically very similar so we present the substantially more parsimonious (and easier to interpret) model with no interaction effects. (25)

We begin by augmenting the basic specification in column (1) of Table 5 with year dummies which account for the fact that aggregate macroeconomic fluctuations, weather patterns, yields, etc., may impact the optimal contract choice over time. Almost none of the estimated coefficients in column (2) of Table 5 change from their respective counterparts in column 1 pointing to the importance of spatial matching, for which we have not yet accounted. In specification (3), we additionally include the six aggregate region dummies. These fixed effects control for region of employment. However, being fairly aggregate in nature with not enough resolution, they do not change the estimates appreciably. We next use the detailed information on harvester's county of employment available only in the confidential version of the NAWS. The specification in column (4) of Table 5 includes both year and county of employment fixed effects. The inclusion of the county fixed effects significantly increases the [R.sup.2] to 0.39. The much higher [R.sup.2] in column (4) signals that the county fixed effects have indeed accounted for a large portion of the unexplained variation in either column (2) or column (3) where the [R.sup.2] was 0.12 and 0.20 respectively.

Here, we note several significant changes in parameter estimates. First, one of the two ability variables (English proficiency) became significant but has the wrong (negative) sign. The theory predicts that more able workers should choose piece rates over hourly rates. Second, farm work experience in the United States became positive and significant. This result can be interpreted as supportive of the ability to perform paradigm to the extent that people with more experience can be seen as more productive. Third, the effect of being employed by a farm labor contractor has now diminished substantially from 0.25 in column (1) to 0.15 in column (4) which is not all that surprising because employment by a farm labor contractor is primarily determined by location-and crop-specific factors. (26)

Finally, consider the coefficients on the wealth indicators. The impact of owning a business in the United States has turned from negative, as it was in the previous three specifications (columns 1-3), to positive. The estimate now implies that harvest workers who own a business in the United States are 8 percentage points more likely to be paid by the piece. Second, we record a large change in the coefficient on the other assets in the home country, which has now jumped to 0.31 in column (4) from 0.14 in column (2). The new coefficient suggests that owning other assets in the home country increases the likelihood of piece-rate employment by 31 percentage points, or about 78% at the mean of 0.40 (see Table 1). The rest of the estimated coefficients do not differ very much from their respective counterparts in column (3). Overall, we see that the estimated effects of all different types of assets (wealth), both in the United States and in the worker's home country, are positive. The only exception is ownership of a house either in the United States, or in the worker's home country--the estimated coefficients on those assets are negative but ownership of a house in the home country is statistically insignificant and its economic effect is nearly zero. All of the other six asset types in the United States and the home country are large and positive, with five of them (land in the United States, other assets in the United States, land in the home country, business in the home country, and other assets in the home country) also statistically significant.

Another interesting point to note is that for two out of the three assets with estimated positive effect on piece-rate pay, the impact is larger for assets located in the United States--owning land or other assets in the United States have a larger positive impact on piece-rate pay than owning land or other assets in the worker's home country. This may be due to the fact that these assets are likely to have a higher value in the United States than in Mexico (the native country for about 97% of all harvest workers). Hence, workers owning such assets in the United States are most likely wealthier (and hence less risk averse) than workers owning such assets in their home country.

Finally, we further augment the contract choice equation by including detailed crop fixed effects. Note, however, that given our results from the matching equation in Table 4, there is no need to include the crop dummies into the contract choice equation as the riskiness of harvesting different crops is adequately captured by the characteristics of the county in which they are grown. To check the validity of excluding the crop fixed effects as suggested by the results of the matching model, we re-estimate the specification in column (4) including detailed crop fixed effects (column (5) of Table 5). The inclusion of the crop fixed effects significantly increases the [R.sup.2] to 0.55, but the coefficients on the wealth indicators do not change very much. While two of the wealth effects (land and other assets in the United States) are somewhat smaller than those in specifications (3) and (4), both have the same sign as before and both are still statistically significant. This is not surprising--once we account for the endogenous matching between workers and crops by including county fixed effects, the inclusion of the crop dummies should not influence the impact of risk aversion (wealth) on the choice of payment type. (27)

In summary, the econometric results convincingly show that once we overcome the endogenous matching between workers based on their risk aversion and crops, which occurs across counties, by including county fixed effects in the contract choice equation, the estimates coefficients on risk aversion, that is, the eight wealth indicators, point to an inverse relationship between risk aversion and the intensity of the payment scheme in that wealthier (less risk averse) harvest workers prefer to get paid by the piece rather than by the hour.

When it comes to testing the relationship between ability and the power of incentives, the results are weaker. Given our finding of no statistically significant matching between workers and crops based on ability, we should see no improvement in the estimation results across columns in Table 5 because the endogeneity should not be a problem even if traits are measured with errors. However, strictly speaking, this is misleading because the endogenity could still cause problems in estimation of ability coefficients due to endogenous matching based on risk aversion. Since the estimated contract choice equation contains the proxies for risk aversion and proxies for ability, it is possible that the estimates of the ability coefficients could change as a result of addressing the endogenous matching (endogeneity) on the risk aversion side. The inspection of the results in Table 5 show that the education coefficient is positive and significant at the 5% level. This is consistent with the theory and suggests that more educated, that is higher ability, workers choose high powered incentives, that is piece rates. The effect of English proficiency, on the other hand, has a negative sign, but the impact is practically zero and it is not statistically significant.

C. Robustness Checks and Alternative Risk Aversion Measures

In this section, we perform a number of robustness checks and re-estimate the contract choice equation using two alternative risk aversion measures. All of these specifications confirm our baseline results. We start in column (1) of Table 6, by re-estimating our baseline specification in column (5) of Table 5 by weighting it based on the number of workers surveyed in each county. The estimated coefficients on the wealth indicator dummies are very similar to those reported in the last column of Table 5. In the second column of Table 6, we augment our baseline specification by including county-by-year effects, instead of only county and year fixed effects. The estimates are again very similar to those reported column (5) of Table 5 despite the use of much finer fixed effects. In column (3) of Table 6, we re-estimate our baseline specification but additionally include county-level employment in the non-agricultural sector in order to control for alternative employment opportunities in other sectors of the local economy. The estimated coefficients on the wealth indicators are again very similar to those in column (5) of Table 5.

Next, in Table 7, we continue with the robustness checks and introduce a number of alternative risk aversion measures--some based on wealth (in columns (1)--(4)) and some based on workers' smoking behavior and legal status (in columns (5) and (6)). All of the alternative wealth measures are based on the eight asset indicators that we used in the baseline specification in column (5) of Table 5 and all of them attempt to reduce the dimensionality of these eight wealth indicators. All specifications in Table 7 include year, county, and crop fixed effects, and as such they are comparable to the richest specification in column (5) of Table 5. In column (1) of Table 7, we employ only the five principal factors that are retained after we perform a principal factor analysis using the eight wealth indicators. The estimates are quite similar to those in the last column of Table 5. In particular, four out of the five principal components of the eight wealth indicators are positive, with three of them also statistically significant at the 5% level. The only one principal component whose effect is negative has an impact that is nearly zero and it is not significant. These estimates continue to confirm that less risk averse (wealthier) workers tend to choose piece rate.

In the second column of Table 7, we use only one wealth variable which combines all eight assets into one variable by simply counting them. The estimates show that the worker's wealth, a proxy for risk aversion, has a positive impact on piece-rate pay--just as theory predicts. In column (3) we use the single wealth variable obtained by weighting all the eight assets by their average value. The estimated coefficient on the wealth index is positive and statistically significant at the 5% level confirming the earlier result. In particular, the estimated coefficient on the wealth index implies that as the worker's wealth rises by $100,000, the likelihood of piece-rate pay increases by 1.6 percentage points, or 4% at the mean of 0.40 (see Table 1). In the following specification, in column (4), we add a square term of the wealth index to test for concavity, which previous research has documented (e.g., Guiso and Paiella 2008). The coefficient on the linear wealth term remains positive and significant whereas the coefficient on the square wealth term is negative, but not statistically significant. However, when we test the joint hypothesis that both the linear and the square wealth terms are zero, we reject it at the 10% level of significance, providing some evidence of the concavity of wealth.

As we already discussed, wealth is an imperfect measure of risk aversion. Hence, in the next two robustness checks, we employ two alternative proxies. In column (5) we use smoking behavior as a proxy for risk aversion. The estimates show that smokers are 3.9 percentage points (or 9.8% at the mean of 0.40) more likely to be paid by the piece. Given that smokers are less risk averse (Anderson and Mellor 2008), the results imply that less risk-averse workers are more likely to choose piece-rate pay, as expected. This again is consistent with the baseline estimates in column (5) of Table 5.

Finally, in column (6), we use yet another empirical proxy for risk aversion---worker's undocumented status. For this exercise, we employ an expanded sample--both undocumented and documented (U.S. citizens and permanent residents) harvest workers. Here we compare undocumented harvest workers, the large majority of whom (97%) have migrated from Mexico without proper documentation and who we presume are less risk averse, to U.S. citizens and permanent U.S. residents. The estimates show convincingly that undocumented workers are 2.3 percentage points (or 5.8% at the mean of 0.40) more likely to be paid by the piece. This finding again implies that less risk-averse workers choose high powered incentives and it is consistent the baseline estimates in column (5) of Table 5. In summary, all of the robustness checks lead to the same conclusion--less risk-averse individuals choose high powered incentives (piece rates).

Regarding the relationship between ability and the power of incentives, the results are also very similar to those in column (5) of Table 5. The English proficiency coefficient became positive as predicted by the theory, yet remained statistically insignificant. The schooling coefficient is positive and significant, in support of the theory. Farm work experience in the United States, as another possible indicator of ability, is also positive and statistically significant as it was in Table 5. Overall we can say that we found some empirical evidence in favor of the theory that high ability workers sort themselves into high powered incentives schemes and therefore prefer piece rates over hourly rates.

V. CONCLUSION

There has a been a great deal of empirical studies looking at the determinants of contractual choice in a variety of situations ranging from historical and modern agricultural contracts, to franchising, executive compensation, and payroll. When it comes to investigating the importance of risk or risk aversion for contract choice, a surprising fact about most of this literature is that theoretical hypotheses underlying the empirical work are almost always based on the results from the model of an isolated principal--agent pair. In this paper, we focus on the theoretical and empirical implications of endogenous matching of heterogeneous principals and agents and argue that the results from the single pair model do not necessarily extend into the market setting with multiple participants. This has potentially important consequences for empirical work.

With two simple matching models we showed that the equilibrium matching depends on the principals' and agent's traits. If the traits are risk-aversion and project risk, then both PAM and NAM are possible and there is no clear prediction about the relationship between risk aversion and the power of incentives. However, if the traits are ability and the project risk (complexity), then the equilibrium matching is unequivocally NAM and the prediction about the relationship between ability and contract choice is unique: high ability agents will always pick piece rates and low ability agents will always pick hourly rates.

Our empirical exploration into the payment mechanisms used in agricultural labor contracts was motivated by the observation that hired labor for harvesting of different crops is paid either by piece rates or hourly rates. Some crops exhibit high degree of uniformity with respect to the payment selection but most of them do not. For example, harvesting of olives is exclusively paid by the piece, harvesting of Christmas trees is always paid by hourly rates, whereas harvesting of nearly everything else is sometimes paid by piece rates and sometimes by hourly rates. Our objective is to see whether the choice of payment schemes can be systematically explained by the risk aversion or ability of the workers who select them. To estimate the relationship between the workers' risk aversion (ability) and the power of contract incentives, we use confidential, individual-level data on harvest farm workers from the NAWS from 1999 to 2008.

Our estimation strategy consists of two steps. In the first step, we estimate a matching equation between workers and crops. Because there is really no meaningful way to compute the risk associated with harvesting various crops, it is impossible to determine whether the matching is PAM or NAM. Instead, we are only able to assess whether the likelihood of choosing one particular crop over some other crop is influenced by workers' risk aversion or ability. The results show strong evidence of matching between workers and crops across counties based on risk aversion but not ability. However, this effect has been entirely exhausted at the county level. This information is crucial for the correct econometric specification of the contract choice equation. It implies that if we do not control for location (i.e., include county fixed effects) in the contract choice equation, the endogeneity will bias the results. The fact that endogenous matching between workers and employers (crops) is completely captured by controlling for the county of employment means that counties are internally homogenous in terms of the crops they grow. Most counties are geographically small enough not to exhibit significant within-county variations in climate, soils, infrastructure, tradition, and so forth, which all jointly determine the type of agriculture that would emerge.

In the second step we estimate the contract equation relating the workers' payment mechanism choice to their risk aversion and ability. The central result of this paper is that, controlling for county of employment, that is after accounting for endogenous matching between workers and crops, the estimated impact of risk aversion, as proxied by wealth, smoking behavior or undocumented legal status, on the probability of choosing a piece rate relative to an hourly rate is positive. This result confirms that workers' risk aversion and the power of incentives are negatively related. Less risk-averse individuals would choose piece rates whereas more risk-averse individuals would choose hourly rates. These results cast new light into the previously tenuous trade-off between risk and incentives. The theory that more able individuals would sort themselves into high powered incentives schemes is also upheld although the empirical evidence is somewhat weaker than that for the risk aversion/incentives tradeoff.

doi: 10.1111/ecin.12231

ABBREVIATIONS

CARA: Constant Absolute Risk Aversion

CRRA: Constant Relative Risk Aversion

NAM: Negatively Assortative Matching

NAWS: National Agricultural Workers Survey

PAM: Positively Assortative Matching

APPENDIX A

The cross-partial derivative of (2) is given by:

(A1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Since the denominator is always greater than zero, the sign of (A1) depends on the sign of the numerator. The derivative is positive if [lambda][[sigma].sup.2] [greater than or equal to] 1/c, and negative if [lambda][[sigma].sup.2] [less than or equal to] 1/c. Therefore, if [[lambda].sub.L] [[sigma].sup.2.sub.L] 1/c, then (Al) is guaranteed to be positive for all [lambda] and [[sigma].sup.2] in the support of the distributions and the surplus function is supermodular and we obtain PAM. On the other hand, if [[lambda].sub.H] [[sigma].sup.2.sub.H] [less than or equal to] 1/c, the function is submodular and we obtain NAM.

APPENDIX B

When matching on agents' risk aversion, in case of NAM, the measure consistency condition is

(B1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Going through the same sequence of steps as with PAM we can determine the effect of the change in agent's risk aversion on the power of incentives by evaluating the sign of the following derivative:

(B2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

In case of a NAM, the resulting equilibrium relationship between agents' risk aversion and the power of the contract incentives is:

A. positive if [[lambda].sub.L] [greater than or equal to] [[lambda].sub.H] [[sigma].sup.2.sub.H]/2 [[sigma].sup.2.sub.H] - [[sigma].sup.2.sub.L].

B. negative if [[lambda].sub.H] [greater than or equal to] [[lambda].sub.L] [[sigma].sup.2.sub.L]/2[[sigma].sup.2.sub.L] - [[sigma].sup.2.sub.H] and 2[[sigma].sup.2.sub.L] [greater than or equal to] [[sigma].sup.2.sub.H].

C. U-shaped if one of the following two conditions are met:

a. [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

b. [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Since the denominator of (B2) is always positive, the sign of the derivative depends only on the numerator. In fact, since c([[lambda].sub.H] - [[lambda].sub.L]) > 0, the sign of the numerator depends only on the sign of the expression in the parentheses. (A) The expression in parentheses is positive if [lambda] > [[lambda].sub.H][[sigma].sup.2.sub.H] - [[lambda].sub.L][[sigma].sup.2.sub.L]/2[[sigma].sup.2.sub.H] - 2[[sigma].sup.2.sub.L], from which it is obvious that [lambda] [greater than or equal to] [[lambda].sub.L] [greater than or equal to] [[lambda].sub.H][[sigma].sup.2.sub.H] - [[lambda].sub.L][[sigma].sup.2.sub.L]/2[[sigma].sup.2.sub.H] - 2[[sigma].sup.2.sub.L], solving for [[lambda].sub.L] gives the stated condition. (B) The expression in parentheses is negative if [lambda] < [[lambda].sub.H][[sigma].sup.2.sub.H] - [[lambda].sub.L][[sigma].sup.2.sub.L]/2([[sigma].sup.2.sub.H] - [[sigma].sup.2.sub.L], from which it is obvious that [lambda] [less than or equal to] [[lambda].sub.H] [less than or equal to] [[lambda].sub.H][[sigma].sup.2.sub.H] - [[lambda].sub.L][[sigma].sup.2.sub.L]/2([[sigma].sup.2.sub.H] - [[sigma].sup.2.sub.L]. Solving for [[lambda].sub.H] produces the first condition, whereas the second condition is simply the requirement that the denominator of the first condition be positive (C.a.). This case is simply the opposite from the previous two (C.b.). [[sigma]sup.2.sub.H] > 2[[sigma].sup.2.sub.L] makes [[lambda].sub.H] < [[lambda].sub.L][[sigma].sup.2.sub.L]/2[[sigma].sup.2.sub.L] - [[sigma].sup.2.sub.H] trivially satisfied and hence not needed.

APPENDIX C

Using a measure consistency condition, we can derive the equilibrium relationship between the riskiness of the principal's asset (task) and the agent's ability which upon substitution into [beta] = 1/1 + (c[lambda][[sigma]sup.2]/[[theta]sup.2]) yields the optimal slope equation as a function of agents' abilities:

(C1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The differentiation of (C1) with respect to [theta] gives:

(C2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

the sign of which will determine the effect of the change in agent's ability on the power of incentives in the principal--agent contracts.

The denominator of (C2) is obviously always positive and hence the sign of the derivative will depend on the sign of the numerator which can be reduced to (2[a.sub.H] - a) [[sigma].sup.2.sub.H] + (a - 2[a.sub.L]) [[sigma].sup.2.sub.L]. Because [[sigma].sup.2.sub.H] > [[sigma].sup.2.sub.L], (2[a.sub.H] - a) [[sigma].sup.2.sub.H] + (a - 2[a.sub.L]) [[sigma].sup.2.sub.L] [greater than or equal to] (2[a.sub.H] - a) [[sigma].sup.2.sub.L] + (a - 2[a.sub.L]) [[sigma].sup.2.sub.L] = (2[a.sub.H] - 2[a.sub.L]) [[sigma].sup.2.sub.L] [greater than or equal to] 0. Hence, the equilibrium relationship between agents' ability and the power of the contract incentives is always positive. High ability agents will always sort themselves into high powered incentives contracts, and vice versa.

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(1.) Lazear (1986, 406) asks this question in the context of two illustrative examples: "Unskilled farm labor often is paid in the classic piece-rate fashion: an amount of payment per pound or piece harvested is specified in advance. Near the other extreme are middle managers of major corporations whose annual salaries are specified in advance, and who are then paid exactly that amount, independent of output."

(2.) For most recent surveys of personnel economics literature see Lazear and Oyer (2012), and Oyer and Schaefer (2011).

(3.) Field experiments are becoming a research tool of choice in empirical economics because of their capacity to exogenously control certain features of complex relationships within or across firms which helps researchers to uncover various causal relationships. For an extensive survey of field experiments with firms see Bandiera, Barankay, and Rasul (2011a).

(4.) Oyer and Schaefer (2011) provide a detailed survey of this literature and argue that the weakness of the empirical evidence in support of the risk/incentives trade-off is largely due to insurmountable challenges related to measuring the necessary ingredients (risk, risk aversion, marginal return to effort, agent's responsiveness to incentives) for devising a test of this relationship.

(5.) The heterogeneity of firms and workers leads to match-specificity in productivity if there is some complementarity between firms' and workers' attributes (traits). The assumption of such complementarities underlies the large literature on assortative matching in labor markets (see Oyer and Schaefer 2011).

(6.) Because of the zero profit condition used to solve for the optimal slope parameter, the expected total surplus coincides with the indirect expected utility of the agent.

(7.) In his famous marriage market paper, Becker (1973) defines PAM as the situation when tall women marry tall men and short women marry short men and NAM as the situation when tall women marry short men and short women marry tall men.

(8.) In the empirical part of the paper, we only try to predict whether [beta] = 0 or [beta] [not equal to] 0.

(9.) For formal definitions of supermodularity and sub modularity see Milgrom and Roberts (1990).

(10.) A closer inspection of the result in Appendix A reveals that for some values of [[lambda].sub.a] and [[sigma].sup.2.sub.p], the optimal assignment can be simultaneously negatively and positively assortative (not globally assortative).

(11.) A complete treatment of endogenous matching in principal-agent markets using the assignment game of Shapley and Shubik (1972) is contained in Series (2008).

(12.) The result in which optimal effort depends on ability is the consequence of the production function specification where effort and ability enter multiplicatively. If effort and ability enter additively, the marginal product of effort does not depend on ability, and the optimal effort exerted by any agent is the same regardless of her ability.

(13.) A recent and rare example of multi-dimensional matching is found in Bandiera et al. (2011b).

(14.) Some workers are also paid by combination of piece rate and hourly rate (5% of the total) and about 1% of workers are on non-hourly salaries. Both categories are excluded from the analysis currently reported in the paper. If the combination workers are treated as piece-rate employees and the salaried workers are treated as hourly employees, the contract equation (piece-rate equation, see Section III.D) estimates (available from authors upon request) are almost identical to those reported here.

(15.) Among other assets in the United States, respondents specified "bicycle/motorcycle," "building," "cattle," and "part of a farm/hunting camp." Other assets in the respondent's home country include "cattle," "horses/donkey," and "apartment."

(16.) The information on the values of the four different types of assets workers hold in the United States--(farm) land, house, business, and other assets--comes from a number of sources. First, the median value of a U.S. house is taken from the U.S. Census ($119,600 in year 2000). The value of farm land for the average U.S. farm is $533,610, given that the average farm size is 433 acres (2002 Census of Agriculture) and the value of an acre of farmland is $1,210 (as of January 2002, Economic Research Service, U.S. Department of Agriculture, USDA). The average value of a small business in the United States ($872,753) is calculated as the ratio of the average annual sales of a small business in the United States ($43,638 in 2002, U.S. Census) and the interest/discount rate of 5%. The modal answer given for the "other assets" category is a small herd of cows. We assume there are five cows in a small herd. Information from the USDA indicates that the price per 100 lbs. (of steer) is $64 (as of January 2002). Given that the average steer weighs in at 1,363 lbs. (also as of January 2002), this implies that the value of a small herd of cows is about $4,362. Unfortunately, such precise information on these four different types of assets in Mexico is not available. To approximate the values of these four types of assets in Mexico, we deflate their U.S. value by the ratio of the U.S. GDP per capita ($36,797 current U.S. dollars in year 2002) to the Mexican GDP per capita ($6,491). Naturally, this valuation calculation assumes that the ratio of the two GDP per capita figures reflects the price differences between the two countries. The calculations imply that on average, the value of a house in Mexico is $21,097, the value of (farm) land is $94,129, the value of a small business is $153,954, and the value of "other assets" is $770.

(17). As mentioned before, the data set is not a panel, so each harvest worker i is observed only once, that is, a worker is never observed harvesting two different crops at different times.

(18). As seen from Table 3, most of the crops are paid by both piece rates and hourly rates, which represents an important evidence that the contract choice cannot be determined by crop attributes (like measuring cost) alone. Lazear (1986, 406) is aware of this fallacy when he writes: "When it is costly to measure output, it is sometimes argued, workers are paid salaries. When monitoring costs are low piece-rate payment is appropriate. Although there surely is much truth to this, it leaves a number of issues unresolved."

(19). Note that changes in the immigration environment within counties over time may result in workers moving to counties with more favorable immigration policy.

(20.) The estimation results for the other 104 crops relative to oranges are available from authors upon request.

(21.) While being employed by a farm labor contractor appears to be a choice at first glance, this really is not the case. Farm labor contractors operate only in certain locations and hire workers for harvesting only particular crops, that is, the variation in employment by a farm labor contractor (and not directly by a grower) across workers is almost entirely explained by the variation in location and crop attributes, likely driven by historic geographic or crop-specific patterns. In particular, when we estimated a linear probability model with employment by a farm labor contractor as a dependent variable and only year, county, and crop dummies on the right-hand side, the [R.sup.2] was 0.52, indicating that the majority of the variation in employment by farm labor contractor is due to location-and crop-specific factors. When we further added all personal characteristics, such as education, gender, experience, and wealth, on the right-hand side of the specification, the [R.sup.2] did not change at all, suggesting that personal characteristics do not play a role when it comes to employment by a contractor versus directly by the grower.

(22.) The signs of the estimated parameters change depending on whether harvesting the crop in question is more or less risky relative to the reference crop, hence there is no unique way to interpret these results. Since our goal is only to establish whether there is matching between workers and crops, it does not matter whether one particular crop is riskier than the others. We are only interested in the statistical significance of the parameters and not their signs.

(23.) In our preferred specification, we include more than 300 county fixed effects and more than 100 detailed crop fixed effects.

(24.) The relationship between labor contracting and wages of agricultural workers in California has been studied by Vandeman, Sadoulet, and de Janvry (1991), although they did not distinguish between hourly rates and piece rates. They found that wages paid by contractors are lower than wages in direct hiring, net of differences in the distribution of jobs or workers between the two contract types.

(25.) Notice that because of the very large number of dummies and eight personal wealth indicators, the estimation of the full set of cross-product terms is rather cumbersome. The estimation results of the model with cross-products of eight wealth indicators and six aggregate regional dummies are available from the authors upon request.

(26.) Once we include the county and crop fixed effects, the impact of farm labor contractors on piece-rate employment should disappear, which is exactly what we show in column (5) of Table 5.

(27.) We have also estimated a specification in which, in addition to year, county, and crop fixed effects, we have included region-specific time trends that are added to capture any differences in trends in market conditions, weather patterns, yields, and so forth, across the six aggregate U.S. regions. The estimates are almost identical to those reported in column (5) of Table 5.

IVAN KANDILOV and TOMISLAV VUKINA *

* We are thankful to Pierre Dubois, Atsushi Inoue, Dean Lueck, Thayer Morrill, Xiaoyong Zheng, and the participants of the Toulouse School of Economics research seminar for their helpful comments and suggestions. We are also thankful to Daniel Carroll, Office of Policy Development and Research, Employment and Training Administration, U.S. Department of Labor, for allowing us access to the NAWS confidential data.

Kandilov: Associate Professor, Department of Agricultural and Resource Economics, North Carolina State University, Raleigh, NC 27695-8109. Phone 919-513-3713, Fax 919-515-6268, E-mail itkandil@ncsu.edu

Vukina: Professor, Department of Agricultural and Resource Economics, North Carolina State University, Raleigh, NC 27695-8109. Phone 919-515-5864, Fax 919-515-6268, E-mail tom_vukina@ncsu.edu

TABLE 1
Summary Statistics: Undocumented Harvest
Crop Workers

Variable                                Mean        SD

Piece rate (vs. hourly rate)            0.40      0.49
Average hourly wage                     7.94      2.08
(2006 U.S. dollars)
  Female                                0.11      0.31
  Married                               0.51      0.50
  Children                              0.18      0.38
  Age                                  28.85      9.60
Time in the United States               6.07      6.44
  (since first entry)
Schooling (years)                       6.04      2.94
Employed by farm labor contractor       0.30      0.45
  (vs. directly by grower)
English proficiency                     1.38      0.63
  (speaking, scale of
  1 = worst to 4 = best)
Farm work experience in                 5.62      5.44
  the United States
Non-farm employment                     0.09      0.28
Weekly hours (farm employment)         41.66     12.02
Full-time                               0.79      0.41
Assets in the United States
  Land                                 0.002     0.042
  House                                0.017     0.131
  Business                             0.001     0.016
  Other assets                         0.001     0.016
Assets in the home country
  Land                                 0.112     0.315
  House                                0.460     0.498
  Business                             0.002     0.035
  Other assets                         0.002     0.042
Number of different assets
  (between 0 and 8)                    0.589     0.647
Value of all assets
  (in 2006 U.S. dollars)              23.489    46,627
Smoker                                  0.30      0.46
Undocumented (as a
  fraction of all harvest               0.70      0.47
  workers)
Distance between current
residence and current
job (miles)
  Located at the job                    0.17      0.37
  Within 9 miles                        0.32      0.47
  10-24 miles                           0.39      0.49
  25-49 miles                           0.11      0.31
  50-74 miles                           0.01      0.09
  75+ miles                                0      0.03
Country of birth
  Mexico                                0.97      0.18
  Central America                       0.02      0.18
  Elsewhere                             0.01      0.06
Crop at the time
of the interview
  Field crops                           0.07      0.26
  Fruits and nuts                       0.53      0.50
  Horticulture                          0.03      0.16
  Vegetables                            0.34      0.47
  Miscellaneous                         0.03      0.17
Region at the time
of the interview
  East                                  0.14      0.33
  Southeast                             0.22      0.42
  Midwest                               0.08      0.27
  Southwest                             0.03      0.17
  Northwest                             0.12      0.33
  California                            0.41      0.49
No. of observations                    3,980

Notes: Authors' calculations based on confidential undocumented
harvest crop workers data from the NAWS, 1999-2008. Data on
smokers is from 1999 until 2003

TABLE 2
Correlation Matrix among Different Measures of Risk Aversion

                                    Land in   House in   Business in
                            Piece   United     United      United
                            Rate    States     States      States

Piece rate                   1
Land in United States       -0.04     1
House in United States      -0.08     0.27       1
Business in United States   -0.03     0.07       0.07          1
Other assets in
                            0.02      0.00      -0.01          0.00
Land in home country        0.05      0.01      -0.05         -0.01
House in home country       -0.01    -0.07      -0.16         -0.01
Business in home country    0.02      0.00      -0.01          0.00
Other assets in
  home country              0.01      0.00      -0.01          0.00
Number of different
  assets                    -0.03     0.25       0.35          0.08
Value of all assets         -0.05     0.81       0.56          0.38
Smoker                      0.01      0.00      -0.02          0.00
Undocumented                0.11     -0.13      -0.35         -0.03

                            Other Assets   Land in   House in
                             in United      Home       Home
                               States      Country   Country

Piece rate
Land in United States
House in United States
Business in United States
Other assets in
                                   1
Land in home country               0.00      1
House in home country             -0.01      0.20       1
Business in home country           0.00     -0.01       0.00
Other assets in
  home country                     0.00     -0.01      -0.03
Number of different
  assets                           0.01      0.55       0.75
Value of all assets               -0.01      0.30       0.06
Smoker                            -0.01      0.02       0.04
Undocumented                       0.01      0.06       0.14

                                        Other
                            Business   Assets    Number of
                            in Home    in Home   Different
                            Country    Country    Assets

Piece rate
Land in United States
House in United States
Business in United States
Other assets in

Land in home country
House in home country
Business in home country       1
Other assets in
  home country                 0.00      1
Number of different
  assets                       0.03      0.02        1
Value of all assets            0.04     -0.01        0.59
Smoker                         0.02      0.01        0.03
Undocumented                   0.02      0.01       -0.05

                               Value
                            of AH Assets   Smoker   Undocumented

Piece rate
Land in United States
House in United States
Business in United States
Other assets in

Land in home country
House in home country
Business in home country
Other assets in
  home country
Number of different
  assets
Value of all assets                1
Smoker                             0.00     1
Undocumented                      -0.20    -0.05    1

Notes: Authors' calculations based on confidential undocumented
harvest crop workers data from the NAWS, 1999-2008.

TABLE 3
Important Crop Characteristics--Examples

                  Piece-Rate   Employed by   Regional
Crop              Incidence    Contractor    Distribution

Olives                1           0.90       CA
Oranges              0.95         0.60       SE, CA, SW
Lemons               0.93         0.78       CA
Parsley              0.86         0.50       CA, SW, MW
Grapefruit           0.85         0.27       SE, SW
Beans, fresh         0.83         0.75       SE, CA
Kale                 0.80           0        SE
Pears                0.75         0.30       NW, CA
Cantaloupe           0.75           0        CA, SW
Grapes, wine         0.65         0.17       CA, E
Apricots             0.55         0.55       CA
Grapes, raisin       0.50         0.57       CA
Cucumbers            0.44         0.42       E, SE, MW, SW, NW
Tomatoes             0.38         0.43       SE, MW, CA, E
Peppers, sweet       0.36         0.32       SE, CA, MW, E
  and hot
Spinach              0.32           0        CA, SW, MW
Strawberries         0.26         0.01       CA, SE, NW, MW, E
Grapes, table        0.21         0.73       CA
Sugar cane           0.13         0.13       SE
Peaches              0.11         0.20       CA, E, NW, SE, SW, MW
Turnips              0.07           0        CA, MW
Broccoli             0.01         0.27       CA, SW
Cut flowers,          0           0.03       CA, SW, E, MW, NW
  florist grade
Christmas trees       0           0.25       E, SE, MW, CA
Beets                 0           0.50       CA, E
Cauliflower           0           0.35       CA
All crops            0.40         0.30       CA, SE, E, NW, MW, SW

Notes: Authors' calculations based on confidential
undocumented harvest crop workers data from the NAWS,
1999-2008. There are six regions--E (East), SE (Southeast),
MW (Midwest), SW (Southwest), NW (Northwest), CA (California).
The regions are listed in order of the size of the sample of
workers harvesting that crop.

TABLE 4
Multinomial Logit: Probability of Choosing to Harvest
Strawberries versus Oranges

                                 Strawberries vs. Oranges

Variable                          (1)              (2)

Schooling                        -0.04             -0.02
                                 -0.03             -0.03
English proficiency              -0.06              0.14
  (speaking)                     -0.16             -0.17
Female                            1.62 ***          1.23 ***
                                 -0.29             -0.33
Married                           0.18              0.26
                                 -0.19             -0.21
Children                          0.56 **           0.28
                                 -0.27             -0.32
Age                              -0.005             0.003
                                 (0.012)           (0.013)
Time in United States            -0.018             0.019
                                 (0.033)           (0.036)
Farm work experience             -0.086            -0.024
  in United States x 10          (0.059)           (0.064)
[(Farm work experience            0.006 ***         0.002
  in United                      (0.002)           (0.003)
  States).sup.2] x 10
Employed by farm                 -2.43 ***         -1.49 ***
  labor contractor               -0.24             -0.31
Non-farm employment               0.53 *            0.44
                                 -0.28             -0.34
Full-time                         0.24             -0.04
                                 -0.19             -0.21
Land in United States           -35.44            -16.00
                                (39.78)           (12.51)
House in United States            1.64 **           1.52 **
                                 -0.76             -0.78
Business in United States         1.93              1.05
                                 -9.78             -8.03
Other assets in                  -2.82             -2.45
  United States                  -5.81             -5.45
Land in home country             -0.50 **          -0.28
                                 -0.22             -0.31
House in home country             0.27 **           0.12
                                 -0.13             -0.20
Business in                      -3.76             -1.97
  home country                   -6.51             -3.98
Other assets in                  87.46              6.66
  home country                  -79.62            -73.32
Year FE                         Yes               Yes
Region FE                        --               Yes
County FE                        --                --
Log likelihood              -13,211.82        -11,218.50
No. of observations           3,989             3,989

                             Strawberries
                              vs. Oranges
Variable                          (3)

Schooling                       -0.01
                                (0.05)
English proficiency              0.05
  (speaking)                    (0.32)
Female                           0.54
                                (0.50)
Married                          0.02
                                (0.38)
Children                         0.02
                                (0.50)
Age                             -0.003
                                (0.020)
Time in United States            0.005
                                (0.07)
Farm work experience            -0.082
  in United States x 10         (0.90)
[(Farm work experience           0.001
  in United                     (0.04)
  States).sup.2] x 10
Employed by farm                -0.68 *
  labor contractor              (0.40)
Non-farm employment              0.04
                                (0.59)
Full-time                        0.11
                                (2.40)
Land in United States            0.07
                                (8.98)
House in United States           0.32
                                (0.96)
Business in United States        0.24
                                (4.60)
Other assets in                 -1.26
  United States                 (4.32)
Land in home country            -0.02
                                (0.55)
House in home country            0.03
                                (0.39)
Business in                     -0.47
  home country                  (4.32)
Other assets in                  1.15
  home country                 (16.22)
Year FE                        Yes
Region FE                       --
County FE                      Yes
Log likelihood              -6,694.23
No. of observations          3,989
Notes: Authors' calculations based on confidential
undocumented harvest crop workers data from the NAWS,
1999-2008. Robust standard errors reported in parentheses.
FE, fixed effects.

* Statistical significance at the 10% level, ** statistical
significance at the 5% level, ***statistical significance at
the 1% level.

TABLE 5
Contract Equation Estimates: Linear Probability Model

                                      Piece Rate

Variable                         (1)             (2)

Schooling                      -0.002          -0.001
                               (0.004)         (0.005)
English proficiency            -0.02           -0.03
  (speaking)                   (0.02)          (0.02)
Female                         -0.02           -0.01
                               (0.05)          (0.06)
Married                         0.01            0.01
                               (0.02)          (0.02)
Children                       -0.08 ***       -0.08 ***
                               (0.03)          (0.03)
Age                            -0.003 ***      -0.003 ***
                               (0.001)         (0.001)
Time in United                  0.004           0.003
  States                       (0.003)         (0.003)
Farm work experience            0.034           0.062
  in United States x 10        (0.029)         (0.038)
[(Farm work experience         -0.001          -0.002
  in United States)            (0.001)         (0.001)
  .sup.2] x 10
Employed by farm                0.25 ***        0.24 ***
  labor contractor             (0.04)          (0.05)
Non-farm employment            -0.03           -0.03
                               (0.04)          (0.04)
Full-time                      -0.18 ***       -0.17 ***
                               (0.03)          (0.03)
Land in United States           0.26 ***        0.24 ***
                               (0.08)          (0.08)
House in United States         -0.07           -0.07
                               (0.04)          (0.05)
Business in United States      -0.37           -0.41 ***
                               (0.09)          (0.11)
Other assets in                 0.43 ***        0.41 ***
  United States                (0.09)          (0.07)
Land in home Country            0.11 ***        0.12 ***
                               (0.02)          (0.02)
House in home country          -0.05 **        -0.05 **
                               (0.02)          (0.02)
Business in home country        0.39 ***        0.40 ***
                               (0.14)          (0.14)
Other assets in                 0.15            0.14
  home country                 (0.17)          (0.18)
Year FE                        --             Yes
Region FE                      --              --
County FE                      --              --
Detailed crop FE               --              --
[R.sup.2]                       0.11            0.12
No. of observations         3,989           3,989

                                       Piece Rate

Variable                         (3)             (4)

Schooling                       0.002           0.002
                               (0.003)         (0.002)
English proficiency            -0.04 ***       -0.02 **
  (speaking)                   (0.01)          (0.01)
Female                         -0.02            0.03
                               (0.07)          (0.06)
Married                         0.01            0.01
                               (0.02)          (0.02)
Children                       -0.06 ***       -0.07 ***
                               (0.01)          (0.01)
Age                            -0.003 ***      -0.002 ***
                               (0.001)         (0.001)
Time in United                  0.002           0.001
  States                       (0.002)         (0.002)
Farm work experience            0.087           0.092 **
  in United States x 10        (0.055)         (0.043)
[(Farm work experience         -0.002          -0.002 **
  in United States)            (0.001)         (0.001)
  .sup.2] x 10
Employed by farm                0 19            0.15 ***
  labor contractor             (0.05)          (0.05)
Non-farm employment            -0.04            0.01
                               (0.03)          (0.01)
Full-time                      -0.12 ***       -0.08 **
                               (0.03)          (0.03)
Land in United States           0.20 **         0.30 ***
                               (0.10)          (0.03)
House in United States         -0.05           -0.11 ***
                               (0.05)          (0.03)
Business in United States      -0.31 ***        0.08
                               (0.09)          (0.09)
Other assets in                 0.55 ***        0.63 ***
  United States                (0.05)          (0.04)
Land in home Country            0.08 ***        0.06 **
                               (0.03)          (0.02)
House in home country          -0.03           -0.02 **
                               (0.02)          (0.01)
Business in home country        0.28 **         0.14 *
                               (0.11)          (0.08)
Other assets in                 0.18            0.31 **
  home country                 (0.18)          (0.15)
Year FE                       Yes             Yes
Region FE                     Yes              --
County FE                      --             Yes
Detailed crop FE               --              --
[R.sup.2]                       0.20            0.39
No. of observations         3,989           3,989

                             Piece Rate

Variable                         (5)

Schooling                       0.003 **
                               (0.002)
English proficiency            -0.01
  (speaking)                   (0.01)
Female                          0.01
                               (0.03)
Married                         0.01
                               (0.01)
Children                       -0.06 ***
                               (0.01)
Age                            -0.001 ***
                               (0.001)
Time in United                 -0.001
  States                       (0.002)
Farm work experience            0.068 **
  in United States x 10        (0.030)
[(Farm work experience         -0.001 *
  in United States)            (0.001)
  .sup.2] x 10
Employed by farm                0.04
  labor contractor             (0.03)
Non-farm employment             0.01
                               (0.02)
Full-time                      -0.04
                               (0.03)
Land in United States           0.14 ***
                               (0.06)
House in United States         -0.08 **
                               (0.02)
Business in United States       0.11 **
                               (0.04)
Other assets in                 0.27
  United States                (0.05)
Land in home Country            0.05 **
                               (0.02)
House in home country          -0.01
                               (0.01)
Business in home country        0.08
                               (0.09)
Other assets in                 0.32 *
  home country                 (0.18)
Year FE                       Yes
Region FE                      --
County FE                     Yes
Detailed crop FE              Yes
[R.sup.2]                       0.55
No. of observations         3,989

Notes: Authors' calculations based on confidential
undocumented harvest crop workers data from the NAWS,
1999-2008. Robust standard errors reported in parentheses.
FE, fixed effects.

* Statistical significance at the 10% level, ** statistical
significance at the 5% level,  *** statistical significance
at the 1% level.

TABLE 6
Contract Equation Estimates: Linear Probability Model, Robustness
Checks

                                          Piece Rate

Variable                      (1)             (2)             (3)

Schooling                    0.008 **        0.005 ***       0.003 *
                            (0.003)         (0.002)         (0.002)
English proficiency         -0.027          -0.005           0.001
  (speaking)                (0.025)         (0.012)         (0.011)
Female                      -0.039           0.004          -0.001
                            (0.024)         (0.021)         (0.028)
Married                      0.049 **        0.021           0.014
                            (0.019)         (0.013)         (0.014)
Children                    -0.040 **       -0.051 ***      -0.055 ***
                            (0.016)         (0.010)         (0.007)
Age                         -0.002 *        -0.002 **       -0.001 *
                            (0.001)         (0.001)         (0.001)
Time in United              -0.001          -0.001          -0.002
  States                    (0.004)         (0.002)         (0.002)
Farm work experience         0.081           0.047           0.066 **
  in United                 (0.049)         (0.029)         (0.032)
  States x 10
[(Farm work experience      -0.002 *        -0.001          -0.001 *
  in United States)         (0.001)         (0.001)         (0.001)
  .sup.2] x 10
Employed by farm            -0.010           0.085 ***       0.031
  labor contractor          (0.023)         (0.019)         (0.029)
Non-farm employment         -0.003           0.022           0.006
                            (0.015)         (0.017)         (0.017)
Full-time                    0.029          -0.051 **       -0.037
                            (0.025)         (0.024)         (0.030)
Land in                      0.276 ***       0.052           0.141 **
  United States             (0.083)         (0.079)         (0.060)
House in                    -0.158 **       -0.094 **       -0.084 ***
  United States             (0.057)         (0.035)         (0.027)
Business in                  0.180 *         0.088 *         0.121 **
  United States             (0.100)         (0.051)         (0.051)
Other assets in              0.247 ***       0.235 ***       0.277 ***
  United States             (0.051)         (0.030)         (0.054)
Land in home country         0.057 **        0.041 **        0.051 **
                            (0.028)         (0.016)         (0.019)
House in home country       -0.017           0.004          -0.013
                            (0.028)         (0.010)         (0.012)
Business in home             0.196           0.063           0.083
  country                   (0.193)         (0.096)         (0.088)
Other assets in              0.220           0.261 *         0.316 **
  home country              (0.267)         (0.154)         (0.157)
Non-farm employment         --              --               0.727
  (millions)                                                (0.635)
Weights                    Yes              --              --
County * Year FE            --             Yes              --
[R.sup.2]                    0.575           0.63            0.555
No. of observations      3,989           3,989           3,989

Notes: Authors' calculations based on confidential
undocumented harvest crop workers data from the NAWS,
1999-2008. All specifications include year, county, and
detailed crop fixed effects. Robust standard errors reported
in parentheses. FE, fixed effects.

* Statistical significance at the 10% level, **statistical
significance at the 5% level, ***statistical significance at
the 1% level.

TABLE 7
Contract Equation Estimates: Linear Probability Model--
Alternative Proxies for Risk Aversion

                                     Piece Rate

Variable                       (1)             (2)

Schooling                     0.003 *         0.003 *
                             (0.002)         (0.002)
English proficiency          -0.01           -0.01
  (speaking)                 (0.01)          (0.01)
Female                       -0.01           -0.01
                             (0.03)          (0.03)
Married                       0.01            0.01
                             (0.01)          (0.01)
Children                     -0.05 ***       -0.05 ***
                             (0.01)          (0.01)
Age                          -0.002 ***      -0.001 ***
                             (0.001)         (0.001)
Time in United States        -0.002          -0.001
                             (0.002)         (0.002)
Farm work experience          0.060           0.066 **
  in United States x 10      (0.044)         (0.031)
[(Farm work experience       -0.001          -0.001
  in United                  (0.001)         (0.001)
  States).sup.2] x 10
Employed by farm              0.04            0.05 *
  labor contractor           (0.03)          (0.03)
Non-farm employment           0.01            0.02
                             (0.02)          (0.02)
Full-time                    -0.04           -0.04
                             (0.03)          (0.03)
Principal factor 1            0.09           --
                             (0.12)
Principal factor 2            0.15 **        --
                             (0.07)
Principal factor 3            0.05 **        --
                             (0.02)
Principal factor 4            0.02 **        --
                             (0.01)
Principal factor 5           -0.01           --
                             (0.01)
Number of different          --               0.009 *
  assets                                     (0.006)
  (between 0 and 8)
Value of all assets          --              --
  (in 100,000)
(Value of all                --              --
  assets [(in
  100.000)).sup.2]
Smoker                       --              --

Undocumented worker          --              --

[R.sup.2]                     0.55            0.55
No. of observations       3,989           3,989

                                     Piece Rate

Variable                       (3)            (4)

Schooling                     0.003 *         0.003 *
                             (0.002)         (0.002)
English proficiency          -0.01           -0.01
  (speaking)                 (0.01)          (0.01)
Female                       -0.01           -0.01
                             (0.03)          (0.03)
Married                       0.01            0.01
                             (0.01)          (0.01)
Children                     -0.06 ***       -0.06 ***
                             (0.01)          (0.01)
Age                          -0.001 ***      -0.002 **
                             (0.001)         (0.001)
Time in United States        -0.001          -0.001
                             (0.002)         (0.002)
Farm work experience          0.067 **        0.066 **
  in United States x 10      (0.031)         (0.031)
[(Farm work experience       -0.001          -0.001
  in United                  (0.001)         (0.001)
  States).sup.2] x 10
Employed by farm              0.05 *          0.05 *
  labor contractor           (0.03)          (0.03)
Non-farm employment           0.02            0.01
                             (0.02)          (0.02)
Full-time                    -0.04           -0.04
                             (0.03)          (0.03)
Principal factor 1           --              --

Principal factor 2           --              --

Principal factor 3           --              --

Principal factor 4           --              --

Principal factor 5           --              --

Number of different          --              --
  assets
  (between 0 and 8)
Value of all assets           0.016 **        0.023 *
  (in 100,000)               (0.007)         (0.014)
(Value of all                --              -0.002
  assets [(in                                (0.002)
  100.000)).sup.2]
Smoker                       --              --

Undocumented worker          --              --

[R.sup.2]                     0.55            0.55
No. of observations       3,989           3,989

                                     Piece Rate

Variable                      (5)             (6)

Schooling                     0.004 **       0.003 *
                             (0.002)        (0.001)
English proficiency           0.01           0.01
  (speaking)                 (0.01)         (0.08)
Female                        0.06 *        -0.01
                             (0.03)         (0.02)
Married                       0.02           0.01
                             (0.02)         (0.01)
Children                     -0.05 **       -0.04
                             (0.02)         (0.01)
Age                          -0.001         -0.001 ***
                             (0.001)        (0.001)
Time in United States        -0.001         -0.001
                             (0.002)        (0.001)
Farm work experience          0.059 *        0.063 **
  in United States x 10      (0.034)        (0.026)
[(Farm work experience       -0.001         -0.001 **
  in United                  (0.001)        (0.001)
  States).sup.2] x 10
Employed by farm              0.04           0.05 **
  labor contractor           (0.04)         (0.02)
Non-farm employment          -0.02           0.01
                             (0.03)         (0.02)
Full-time                    -0.06 **       -0.04
                             (0.03)         (0.03)
Principal factor 1           --             --

Principal factor 2           --             --

Principal factor 3           --             --

Principal factor 4           --             --

Principal factor 5           --             --

Number of different          --             --
  assets
  (between 0 and 8)
Value of all assets          --             --
  (in 100,000)
(Value of all                --             --
  assets [(in
  100.000)).sup.2]
Smoker                        0.039 **      --
                             (0.015)
Undocumented worker          --              0.023 **
                                            (0.009)
[R.sup.2]                     0.58           0.54
No. of observations       2,536          5,468

Notes: Columns (1)-(4) are based on confidential
undocumented harvest crop workers data from the NAWS,
1999-2008. Column (5) is based on confidential data for
undocumented harvest crop workers from the NAWS, 1999-2003.
Column (6) is based on confidential data for both
undocumented and documented harvest crop workers from the
NAWS, 1999-2008. All specifications include year, county,
and detailed crop fixed effects. Robust standard errors
reported in parentheses.

* Statistical significance at the 10% level, ** statistical
significance at the 5% level, *** statistical significance
at the 1% level.
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Author:Kandilov, Ivan; Vukina, Tomislav
Publication:Economic Inquiry
Article Type:Abstract
Geographic Code:1MEX
Date:Jan 1, 2016
Words:19169
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