Insect Population Dynamics, Pesticide Use, and Farmworker Health

David Sunding and Joshua Zivin

We address the impacts of regulations designed to reduce pesticide poisoning of farmers and farm laborers. Attention is concentratedon pre-harvest interval regulations that impose a time interval between pesticide application and harvest. The incidence of poisoning is determined by aggregate pesticide use, worker exposure, and toxicity. A dynamic, stochastic model of insect population growth is developedandusedtomeasure the incentives for pesticideuse. Increasing the pre-harvest interval has an ambiguous effect on the number of harvest worker poisonings. Pesticide taxation unambiguously reduces the number of worker poisonings. Theoretical results are quantiﬁed in a case study of mevinphos application on leaf lettuce in California’s Salinas Valley.

Key words: farmworker health risk, interval regulation, pesticides, population dynamics, taxation.

Regulators andthe public are becoming andthe dateworkers can re-enter the field increasingly concernedwith the adversepub- to perform various tasks (e.g., installing lic health consequences of agricultural chem- irrigation equipment). Since pesticides typi- ical use. One of the most serious concerns cally decay when exposed to sunlight, rain, motivating pesticide regulation is the impact andother environmental factors, a suffi- of these chemicals on the health of farm- ciently long interval will reduce the chemi- ers andfarmworkers. While there are a large cal’s toxicity. number of potential regulations to address While there is now a relatively large lit- this problem, the typical response of state and erature on the economic effects of banning federal regulators to concerns about farm- pesticides (see for example Zilberman et al.; worker poisoning is to ban the use of the Lichtenberg, Parker, andZilberman; and product in question. This paper considers less Sunding), there has been less analysis of the extreme interventions, anduses a dynamic, impacts of regulating the timing of pesticide stochastic model to assess their impacts on applications. One notable exception is the pesticide productivity, pesticide use, and, ulti- pioneering 1993 study of Lichtenberg, Spear, mately, worker health levels. andZilberman, which presents a methodfor One potentially important type of agricul- finding efficient re-entry intervals.1 As a part tural chemical regulation that has received of their analysis, Lichtenberg, Spear, andZil- little attention in the economics literature is berman consider farmer response to regu- interval regulation. Two notable examples of lating the timing of pesticide applications. interval regulation are the pre-harvest inter- They assume a pest infestation of predeter- val (PHI) andthe re-entry interval (REI). minedsize andallow the farmer to choose The former governs the time between chem- between applying pesticides early (preven- ical application andharvest, while the latter tively) or on the last feasible day, defined sets the time between chemical application as the desired harvest date minus the re- entry interval (reactively). They conclude that farmers may respondto increases in the David Sunding is director, Center for Sustainable Resource Development, andmember, Giannini Foundationof Agricultural re-entry interval by applying pesticides pre- Economics, University of California at Berkeley. Joshua Zivin ventively. Furthermore, they conclude that is assistant professor, Joseph Mailman School of Public Health, increasing the re-entry interval unambigu- andsenior research fellow, International Center for Health Out- comes andInnovation Research, Columbia University. ously reduces the number of farmworker This research was supportedby a Cooperative Agreement with poisonings. the California Department of FoodandAgriculture’s Office of Pesticide Consultation and Analysis. The opinions expressed in this paper do not necessarily reflect those of the funding agency. 1 The econometric analysis of Hubbell andCarlson considers We wish to thank Andrew Gutierrez, Bob Spear, Janet Spencer, the effect of pre-harvest intervals on insecticide choice and the andDavidZilberman for helpful comments. choice of application rate. Amer. J. Agr. Econ. 82 (August 2000): 527–540 Copyright 2000 American Agricultural Economics Association 528 August 2000 Amer. J. Agr. Econ.

Our paper takes a different approach. PHI gives farmers greater incentive to apply We formalize farmer response to interval the pesticide preventively, and benefits work- regulations in a model with explicit insect ers by giving the chemical additional time population dynamics. In particular, we con- to decay. The Lichtenberg, Spear, and Zilber- sider the impact of increasing the interval man result, by construction, ignores the possi- between chemical application andharvest bility that increasing the PHI can increase the (i.e., PHI) on pesticide productivity and the aggregate amount of pesticide use, thereby corresponding incentives for pesticide use. counteracting, to some degree, the salutary Indeed, a main goal of our work is to give effect of increasing the decay interval. micro-foundations to pesticide productivity We also apply our model to another impor- by explicitly considering insect population tant intervention: pesticide taxes. We mea- growth. The impacts on pesticide use are sure the impact of taxation on worker health then tracedthrough a health risk generation levels, andindicateits effectiveness rela- model to measure the ultimate effect of inter- tive to changing the pre-harvest interval. val regulation on harvest worker health. This Conceptually andempirically, we demon- approach yields substantially different results strate that pesticide taxes reduce pesticide than the work of Lichtenberg, Spear, and use and the incidence of pesticide poison- Zilberman. ing. The interesting empirical question is the Insect growth rates are modeled as a geo- magnitude of these impacts, and how they metric Brownian motion process. This for- compare to the sensitivity of worker safety mulation captures the well-establishedinflu- to pre-harvest interval regulation. This com- ence of stochastic weather conditions on parison is a first step towarda more gen- insect reproduction and development. Given eral determination of efficient worker safety initial insect population levels andweather, regulations that compares health impacts and as well as market andregulatory condi- social welfare costs. tions, farmers form expectations about future Our paper contains a case study in which insect populations andhence crop damage. the theoretical model is applied to an Using this framework, it is possible to dis- actual case of pesticide regulation: control- entangle the various effects of changing the ling worker poisoning from the insecticide PHI.2 Increasing the time between pesticide mevinphos in California’s Salinas Valley. This application andworker contact with pesti- case study demonstrates how the model can cide residue gives the chemical more time be made operational and discusses the types to decay, thus benefiting workers. However, and sources of data needed to quantify the increasing the PHI also alters the productiv- economic, biological, andtoxicological com- ity of the chemical andchanges the optimal ponents of the overall framework. The case amount of pesticide application. study measures the impact on worker poison- We show that there are cases in which ings of changing the length of the pre-harvest increasing the PHI may increase total pesti- interval for mevinphos, as well as imposing cide use. The ultimate effect of changing the pesticide taxes. The case study is significant PHI is then ambiguous theoretically andrests because it demonstrates that the integrated on the relative magnitudes of the pesticide approach to farmworker protection proposed use and pesticide decay effects. An extreme in this paper can be usedto designpolicies in result of our model is that increasing PHI a practical andaccurate way. may actually increase the number of pesticide poisonings. This discussion shows a clear distinction between our approach and that The Model of Lichtenberg, Spear, andZilberman. Their analysis precludes the result that increasing The model is sequential and the major stages the PHI increases pesticide use in that they are presentedin Figure 1. In the initial assume farmers only choose when to apply period, the farmer observes the initial insect pesticides, but not whether to apply pesti- population, market parameters such as pes- cides at all. In their framework, increasing the ticidecost andoutput price, andregulations including the length of the pre-harvest interval. Using this information, the farmer forms 2 Note that we are considering the problem of harvest worker expectations about profits at the date of poisoning. In this case, there is effectively no difference between harvest with andwithout pesticideapplica- a REI anda PHI. In other applications, the two types of interval regulations may not be equivalent. Our theoretical results apply tion. He then chooses, in the secondperiod, to these other cases as well. whether or not to apply chemicals. In the Sunding and Zivin Pesticide Use and Farmworker Health 529

Figure 1. The sequence of events thirdperiod,which is the periodof the lettuce, broccoli, cauliflower, andother crops. PHI, the insect population grows or declines. Making the model more general by working Finally, harvest occurs in the fourth period, at with a continuous, concave damage function which time the farmer realizes some level of does not change the basic comparative static profit. results that are central to this paper, but does make the analysis much more complex. Damage Function Damage has a probabilistic interpretation as the likelihoodthat the insect population at We suppose that the farmer operates in harvest exceeds a maximum allowable level, a competitive market. Insect damage is a in which case the harvest is a total loss. function of the number of insects at har- Formally, D = Pr(XH >XG ), where XH vest. Expectedprofits are determinedaccord- is the insect population at harvest and XG ing to the damage control specification of is the maximum allowable insect population. Lichtenberg andZilberman. In particular, We now turn to a discussion of insect popula- expectedfarm profits are equal to tion dynamics and more fully develop expectations about the terminal number of insects. (1) E() = PY(1 − D) − m Insect Population Growth where P is the output price net of production costs except the pesticide, Y is potential out- The insect population growth rate is modeled put, and m is the pesticide cost including any as an increasing function of the current insect taxes. The expectation is taken over the level population andtime. However, insect growth of insect damage, D. is a stochastic process, due in part to the Insect damage is a function of the size influence of random factors such as weather of the insect population. We adopt a binary on reproduction rates (Varley, Gradwell, and damage function where damage is zero if Hassell; Trumble; Minks andHarrewijn). the insect population falls below some pre- Formally, insect population growth is mod- determinedthresholdformarketability. This eledas a geometric Brownian motion process specification is accurate for many fresh and with a drift component as follows: frozen vegetable markets, including the case (2) dX = αX dt + σX dz of leaf lettuce studied in some detail in the empirical section. For example, the USDA where X is the current insect population, α is sets maximum allowable limits on the num- the intrinsic insect growth rate, dt is an incre- ber of aphids that can be present on fresh ment of time, σ is a variance coefficient, and 530 August 2000 Amer. J. Agr. Econ. √ H -PHI.3 Denote the effectiveness of the pes- dz = ξt dt is the increment of a Wiener process and ξt is standard normal. ticide as (1 − µ), so that the insect population The process in equation (2) has a num- after application is µX0. ber of features that make it appropriate for The decision rule is best understood as modeling insect population levels. The pro- a locus of parameter values for which the cess is such that per-periodgrowth rates farmer is indifferent between using the pesti- are normally distributed; as we discuss in cide or not. This locus is derived by equating the empirical section below, this property expectedprofit levels with andwithout appli- matches closely with experimental evidence cation of the pesticide. There are two damage relating insect growth rates to environmen- probabilities of interest in the derivation of tal conditions. Since percentage changes in these expectedprofit levels, one that attains X are changes in the natural logarithm of if the farmer applies the pesticide, and one X, population levels themselves are normally that attains if he does not. Let D denote distributed in this formulation. Thus, X is NA the probability that X >X if the farmer bounded from below by zero, so that popu- H G does not apply the insecticide, conditional on lation levels can never be negative. Another important property of this process is that government regulations (e.g., product mar- short-run changes in X are dominated by ketability, pesticide cost, and the length of the volatility component of (2), whereas long- the PHI), the initial insect population, and run changes are more influencedby the trend expectedpopulation growth rates. Similarly, component. the probability that the insect population at For our purposes, it is important to char- harvest exceeds the marketability standard if acterize the insect population at some future the farmer does apply the insecticide is DA. date t. If the farmer does not use the pesti- Equating expectedprofits with andwith- cide, the distribution of the insect population out pesticide application, it follows that the at time t is obtainedby applying Ito’s lemma thresholdlevel of the insect population above to equation (2) to obtain the following: which the farmer will apply the pesticide, X, is defined implicitly by the following αt 2 2αt σ2t (3) Xt ∼ LN X0e X0 e e − 1 equation: where X0 denotes the initial insect popula- m (5) DA + = DNA tion and Xt denotes the insect population at PY time t. In the following section, it will prove use- This decision rule is used to describe how ful to know the distribution of insects at har- the farmer’s pesticide application decision is vest time, H , taken prior to the pre-harvest alteredby changes in the policy parameters. interval, or at date H -PHI. This distribution Before proceeding, note that this basic follows directly from (3) as framework can be extended to the situation where the farmer is choosing between two αPHI 2 2αPHI (4) Xt ∼ LN X0e X0 e chemical alternatives, as opposedto the case considered in (5) where the choice is between σ2PHI × e − 1 a single pesticide and no treatment at all. It is straightforwardto show that (5) becomes For the remainder of this paper, X0 denotes the insect population at time H -PHI. m m (5)D+ 1 = D + 2 Equation (4) will now be usedto derive 1 PY 2 PY a grower’s chemical application rule conditional on his observation of the initial insect where the subscripts 1 and2 denotethe two population. alternative chemicals. As expected, pesticide choice hinges critically on relative effectiveness andrelative cost. Since the empirical Optimal Chemical Application example presentedlater is capturedby (5), we will pursue this formulation; note, how- This section derives a farmer’s decision rule for pesticide use. The basic structure of the pesticide application decision is straightfor- ward: apply the pesticide or not at date 3 This formulation assumes that the PHI constraint is binding. Sunding and Zivin Pesticide Use and Farmworker Health 531 ever, that many of the analytical results the derivative (6) can be rewritten as derived later go through with only obvious ∂zNA modifications if (5’) is used. dX (10) =−∂PHI dPHI ∂zNA Comparative Statics ∂X Taking the relevant derivatives and manipu- Consider first the marginal effect of chang- lating yields the following expression: ing the pre-harvest interval. Totally differen- tiating (5) andapplying the Implicit Function dX (11) =−αX Theorem yields dPHI 1 Xσ 2 Xe αPHI − ln XG ∂D ∂D + NA − A 2 σ2PHI − 1 dX ln XG e (6) =−∂PHI ∂PHI dPHI ∂D ∂D A sufficient condition to sign the equation NA − A ∂X ∂X above is for the expression in parentheses in the numerator to be less than or equal to As we demonstrated in the section on insect zero. This condition implies a negative sign for equation (11); i.e., increases in the pre- population growth, the insect population at harvest interval result in a decrease in the harvest time is distributed lognormally. When critical population level, thus implying more the farmer applies the pesticide, the number pesticide use. This result is worth emphasiz- of insects at harvest is distributed as ing: it is possible that increases in the PHI, which are designed to protect farmworkers, αPHI may actually provide incentives for increased (7) XH ∼ LN µX0e pesticide application. µ2X 2e2αPHI eσ2PHI − 1 Given the importance of this result, it 0 is useful to examine this sufficient condition more carefully. The negativity condi-

Recognizing that Pr(XH >XG ) = Pr(ln tion amounts to a requirement that ln XG ≥ αPHI XH > ln XG ), we convert the damage prob- X0e . Noting that ln XG is the transformed abilities into z-scores utilizing the following government marketability standardandthat αPHI relationship: D = 1 − (z), where is X0e is the mean value of the insect popu- the standard normal distribution and z is a lation at harvest time, it follows that this con- z-score. Given pesticide application, the z- dition will be satisfied when a farmer expects to meet the marketability standard without score is pesticide application. Equivalently, this condition holds when the probability of crop fail- ln X − µX eαPHI G 0 ure is less than or equal to one-half. (8) zA = 2 2 2αPHI σ2PHI Alternatively, increasing the PHI could µ X0 e e − 1 result in less pesticide application if ln XG ≤ αPHI X0e andthe secondterm in expression Similarly, the z-score for the insect population (11) is greater in absolute magnitude than the at harvest given no pesticide application is first term. By similar logic, a necessary but not sufficient condition for this occurs when αPHI the probability of crop failure is greater than ln XG − X0e (9) zNA = one-half. 2 2αPHI σ2PHI X0 e e − 1 The basic intuition behindthese results hinges on the fact that, conditional on some For simplicity, consider the case where the initial insect population, lengthening the pre- harvest interval increases both the mean and pesticide is fully effective, or µ = 0. The com- the variance of the insect population at har- parative static results below go through with vest. Thus, when there is only a “slight” only obvious modifications if µ is positive. chance of failing to meet the marketability If a grower applies the pesticide in the full- standard, an increase in the mean and vari- effectiveness case, then all the mass of the ance is undesirable and induces more pesti- population density is concentrated at 0 and cide applications. However, when the chance 532 August 2000 Amer. J. Agr. Econ. of failing to meet the regulations is “large,” is defined as the probability of manifest- increases in the variance of the insect popula- ing a physical ailment as a result of contact tion (more specifically increasing the variance with a toxic substance usedin the workplace. faster than the mean) may increase the possi- If there is a pre-existing incidence of this ail- bility of meeting the standardandresultin a ment in the population, then risk refers to the reduction of pesticide applications. Therefore, incremental risk incurredby human exposure the ultimate impact of pre-harvest interval to the contaminant. Health risk is most com- regulation on pesticide applications remains monly representedas the productof three an open, empirical question. basic risk factors: (a) ambient contamination, Similar methods can be used to show how (b) human exposure, and( c) the manifesta- the farmer’s pesticide application decision tion of physical symptoms, termedthe dose– changes with respect to the other government response relationship. policy variables. For example, the change in This multiplicative formulation is reason- the thresholdlevel of insects as the cost of able when the increasedrisk is relatively pesticides changes, for example through a small, andis particularly germane to cases pesticide tax, is where there is pre-existing backgroundrisk (Van Ryzin, Crump andHowe, Krewski and dX X2eαPHI eσ2PHI − 1 Van Ryzin). In order to analyze the impacts (12) = dm PY ln X ϕ(z ) of government policies on health risk, it G NA is convenient to work with the following where ϕ(zNA) is the standard normal density relationship: evaluatedat zNA. It is clear that expression (12) is positive. Thus, an increase in pesticide (13) R(m PHI) = C(m PHI) · E(PHI) · D costs increases the thresholdpest population where R is health risk, C is contamination size above which it is optimal to apply pesti- (or deposited pesticide residue), E is expo- cides, thereby confirming that pesticide use is sure, and D is the dose–response parameter. decreasing in the cost of pesticides. Note that since the dose–response parameter It is also interesting to examine how simply maps exposure to illness, it is affected changes in the marketability standard affect by physiology andnot policy choices. the incentives for pesticide use and worker In this paper, we will largely confine our- health levels. Given some fixedprice of selves to the problem of protecting harvest output, relaxing the marketability standard worker health. It is straightforwardto apply would clearly reduce the amount of pesticide the basic framework to other target popu- use. However, it is unlikely that output price lations including pesticide applicators, irriga- wouldremain fixedif the number of insects tion workers, andfarmers themselves. There present at harvest were increased. A full are numerous policies designed to improve understanding of how product quality stan- farmworker health, including posting and dards affect pesticide use therefore requires training regulations, protective clothing, and specification of a hedonic demand function. It protective equipment regulations (Sunding seems clear, however, that the effect of prod- andZivin). As mentionedearlier, in this uct quality on price wouldreinforce the pure paper we limit attention to two policies: the effect of the marketability standard on pes- pre-harvest interval andpesticidetaxation. ticide use. Lowering the net price received Pesticide taxation is designed to change by farmers for the crop further reduces the the marginal incentives to use a toxic sub- incentive to use pesticides. Consumers suffer stance. To the extent that this regulation pro- in this case, however, since they value product vides a marginal disincentive to use the toxic quality anda reducedpriceof output simply material (through higher costs), use is dimin- reflects their diminished marginal valuation ishedandworkplace injuries are reduced.In of the crop output. terms of the risk factors outlinedin (14), taxation reduces pesticide use but leaves exposure unaffected. The pre-harvest interval reg- The Health Risk Generation Process ulation, by contrast, is primarily designed as an exposure regulation. As the PHI is length- In order to assess the effectiveness of pes- ened, pesticides in the field have more time to ticide regulation, we must first define the decay, ultimately reducing farmworker expo- health risk generation process. The magni- sure. However, our earlier economic analy- tude of health risk in a population of workers sis shows that PHI regulation also alters the Sunding and Zivin Pesticide Use and Farmworker Health 533 incentives for pesticide use by changing pes- of measurement error (e.g., under-reporting ticide productivity. Thus, in terms of equation of injury) andmisspecification of the underly- (14), PHI regulation affects both contamina- ing econometric model. Third, it is impossible tion andexposure. The net effect of these to use an econometric model to examine impacts will be discussed in detail in a later the effects of changing PHI if there are no section. observedchanges in this regulation in the The approach taken in this paper is pred- sample. In order to avoid these problems, icatedon basic toxicology andis consistent but most importantly to help builda bridge with risk assessment methods currently in between economics andthe rest of the risk use in the UnitedStates andother coun- regulation community, we adopt the toxicol- tries. That is, the health effects of pesticide ogy approach to modeling health impacts of use are supposedto result from the prod- pesticide use. uct of total pesticide use, worker exposure to the pesticide, and a dose–response, or toxic- Deposited Residue ity, parameter extrapolatedfrom controlled, replicable animal studies. There is some liter- In the context of pesticide application, it is ature on pesticides and worker health in this sensible to treat contamination as deposited journal that takes a different approach. For residue, defined as the amount of pesticide example, Antle andPingali developan econo- present per unit of plant surface area at metric model of pesticide use and farmer the time of application. Depositedresidueis health to measure the impacts of pesticide determined in part by the amount of pes- use on health levels andthe impact of health ticide application, which is in turn affected on farm productivity in two regions of the by the marginal productivity of the pesticide. Philippines. They demonstrate that pesticide Depositedresidue(or contamination, C)is use has a deleterious effect on farmer health the product of the share of acres treated with andthat productivityis increasing in the the pesticide (RS), the amount of the chem- level of farmer health, implying that there ical usedper acre treated( a) anda crop- may well be social gains from reducing pes- specific coefficient (v) that converts per-acre ticide use in this case study.4 The economet- application into deposited residue. Formally, ric approach taken in their paper is a type C(m PHI) = RS(m PHI) · a · v. of epidemiological analysis that characterizes Recall from the discussion on profit- the ex post statistical relation between health maximizing pesticide application that a levels andvarious environmental factors. farmer will apply the pesticide if the num- We adopt the toxicology approach in this ber of insects exceeds some threshold level. paper for several reasons. First, toxicology Denote the probability density of the initial methods are used by the U.S. EPA and insect population across fields in a defined state agencies to set pesticide regulations. region as f(x). The regional share of acres on Indeed, many of the basic parameters used which the pesticide is used, RS, is the prob- in our case study are taken directly from the ability that the initial insect population on a risk assessments performedby the State of given plot will exceedthe thresholdpopula- California prior to registration of the pes- tion X . Formally, then, ticide that is the subject of our case study. c Clearly, if economic concepts are to be used ∞ (14) RS(m PHI) = f(X) dX to influence risk regulation, it is impera- tive that economists use similar methods and X(mPHI) data as the rest of the regulatory community. This coefficient measures the probability that Second, the epidemiological approach to risk a randomlyselectedacre will be treatedwith regulation, while interesting from an econo- the pesticide. metric point of view, is out of favor with reg- The coefficients a and v are exogenous, and ulators for some validreasons. Toxicological are invariant with respect to the length of analysis is basedon laboratory experiments the pre-harvest interval. The amount of pes- andcan thus be confirmedor deniedina sys- ticide applied per acre, a, is specifiedon the tematic way. Epidemiological analysis is non- product label, typically in terms of pounds of replicable andsubject to the usual problems active ingredient per acre. The coefficient v maps pounds of chemical per acre into micro- grams per square centimeter of surface area. 4 Other papers in this vein include Antle and Capalbo; Crissman, Cole, andCarpio; andPingali, Marquez, andPalis; as This coefficient reflects the fact that only a well as the volume edited by Warborton, Pingali, and Palis. fraction of all applied pesticides ends up as 534 August 2000 Amer. J. Agr. Econ. deposited foliar residue that harvest workers A marginal increase in the pesticide tax can contact (Zweig, Leffingwell, andPopen- unambiguously reduces the number of poi- dorf),andis heavily influencedby plant shape sonings; deposited residue is reduced while andsize. exposure is unaffected. The marginal impact of lengthening the PHI is less certain theoret- Exposure ically since deposited residue may increase, although exposure must decrease. In any case, Harvest worker exposure to the pesticide is it is necessary to compute the effects of the given as PHI on both contamination andexposure to develop a true measure of health impacts. (15) E(PHI) = q · e−kPHI Before proceeding, it is important to point out that most of the parameters of (16) where k is a residue decay parameter and q will, in reality, only be known with some is an exposure coefficient. Exposure is mea- error, even though our analysis treats all suredin units of square centimeters of plant these factors as known. Given the relatively surface area per kilogram of body weight undeveloped state of the interval regula- per day. The decay parameter converts units tion literature andthe fact that we wish to of deposited residue at the time of applica- emphasize how PHIs alter economic incen- tion into units of pesticide residue at har- tives for pesticide use, our treatment seems vest time, reflecting the fact that PHIs are reasonable. In other applications, however, primarily designed to give pesticides time to it will be important to account for this “cool down” before they are encountered by parameter uncertainty. At least two economic harvest workers. The decay parameter is a studies have identified methods for deal- function of the type of pesticide applied, and ing with this problem when making envi- may also be influencedby weather conditions ronmental health regulations (Lichtenberg such as humidity, temperature, and rainfall andZilberman; Lichtenberg, Zilberman, and (Popendorf and Leffingwell). Bogen). As these papers indicate, parameter The coefficient q in equation (15) simply uncertainty will influence policy choices if the denotes the amount of plant surface area regulator is risk averse or if the risk factors that a worker contacts while on the job. The are covariant (as may be the case if a number type of job performedby the worker influ- of them are affectedby weather). ences this coefficient. For example, harvest workers have more exposure to plant sur- faces than installers of irrigation equipment. Case Study: Mevinphos Application in The coefficient q is also heavily influencedby California’s Salinas Valley workplace safety measures such as manda- tory protective clothing (Sunding and Zivin). This section presents an application of the For the sake of clarity, it is wise to review conceptual model to a specific case of worker the units in which contamination andexpo- protection regulation: farm worker poison- sure are measured.Contamination is expressed ing from the pesticide mevinphos used on in terms of µg/cm2, exposure is measuredas leaf lettuce in California’s Salinas Valley, a cm2/kg/day. Thus, the product of contamina- prime vegetable-producing region located on tion andexposure has units of µg/kg/day. This the central coast of the state. Mevinphos (2- measure conforms to the toxicological notion carbomethoxy-1-methylvinyl dimethyl phos- of an average daily dose, which is standard phate) is an organophosphate insecticide in the scientific literature. The dose–response usedon a variety of crops, mainly vegetables. parameter, denoted D in equation (14), maps In California, mevinphos is appliedprimar- average daily dose into numbers of acute poi- ily to headlettuce, leaf lettuce, cauliflower, soning cases. The dose–response relationship broccoli, andcelery. Mevinphos is a foliar is fundamental to modern toxicology, and insecticide used primarily to control aphids, although it is also effective against mites, dose–response parameters are readily avail- grasshoppers, cutworms, leafhopper caterpil- able for most pesticides. lars, andother insects. The pesticidalactivity Written in full, the health risk equation is of mevinphos is due to its inhibition of acetyl- as follows: cholinesterase activity.5 (16) R(m PHI) = RS(m PHI) · a · v · q · e−kPHI · D 5 Cholinesterases are a family of enzymes foundthroughout the body that hydrolyze choline esters. In the nervous sys- Sunding and Zivin Pesticide Use and Farmworker Health 535

There are numerous reportedcases of or that worker poisoning involving mevinphos, most X − X resulting from acute exposure. Indeed, mev- t+1 t (17) = α + σεt inphos is responsible for more acute ill- Xt ness than any other insecticide currently This expression implies that the percentage in use (California Environmental Protection change in the aphidpopulation is equal to Agency 1996). The principal symptoms of an average growth rate plus a variance term, mevinphos poisoning are nausea, diarrhea, vomiting, pinpoint pupils, tremors, and, in andthat the estimates of α and σ are sim- extreme cases, paralysis. Mevinphos is not ply the sample mean andstandarddeviation. known to be carcinogenic andis not believed Utilizing the fact that the mean andstandard to cause reproductive or developmental tox- deviation of average daily June temperatures icity. In California, there were 548 reported in the Salinas Valley are 58.98 and10.38 cases of acute mevinphos poisoning involv- (National Oceanic andAtmospheric Admin- ing farm workers from 1982 to 1991. There istration), it follows that α = 01199 and were sixty-eight cases involving one or more σ = 01152. days of hospitalization and 201 cases involv- In order to describe the mevinphos appli- ing one or more lost sick days during this cation decision, it is also necessary to gather period(O’Malley). some information on leaf lettuce produc- We now turn to a description of the data tion in the Salinas Valley. Estimates of out- used to quantify the model in the case study. put price andper acre yieldsare based First consider parameters of the stochastic on averages calculatedfrom eight years of process describing the evolution of the insect data presented in the Monterey County Agri- population. In the theoretical discussion of cultural Commissioner’s Reports (1989–96). the previous section, it was assumedthat Mean yieldis 791.12 cartons per acre and the insect population level (aphids in our mean farm gate price is $6.71 per carton. case study) followed a GBM process. This Pre–harvest production costs (excluding the assumption is especially appropriate for the cost of mevinphos application) are taken case study chosen here. Recall that the GBM from University of California Extension crop process is tantamount to assuming normally budgets and are set at $1,590.09 per acre. distributed population growth. Ruggle and Contractedharvesting costs are $3.50 per Gutierrez show that the green peach aphid carton (University of California Cooperative growth rate is linear in average daily temper- Extension). These cost figures imply a net ature, andis given by the formula: price of $1.20 per carton of lettuce. The cost of mevinphos application is $50 per acre % daily growth (Chaney). Total acreage of leaf lettuce in =−5348 + 111 the Salinas Valley is set at 19,000 (Monterey ∗ average daily temperature. County Agricultural Commissioner). Lastly, the quantification of the application Further, average daily temperature is nor- decision in equation (5) requires specifica- mally distributed. Combining these two relation of status quo policy parameters. In par- tionships, it follows that the percentage ticular, it is necessary to know current pre- growth rate of the aphidpopulation is nor- harvest interval regulation andmarketability mally distributed in the case study situation, standards for leaf lettuce. Initially, the pesti- just as assumedby the GBM framework. cide tax is set at zero, so the cost of applica- To findthe parameters of equation (2), it tion is simply its market price. The state pre- is helpful to rearrange this expression. This harvest interval for mevinphos usedon leaf difference equation implies that lettuce is presently seven days (California Environmental Protection Agency 1994). A Xt+1 − Xt = αXt + σXtεt carton of lettuce (composedof twenty-four heads) is deemed unacceptable if more than three heads contain insect defects, where an tem, acetylcholinesterase (AChE) is involvedin the termina- insect defect is defined as any head contain- tion of impulses across nerve synapses including neuromuscular junctions by rapidly hydrolyzing the neural transmitter acetyl- ing five or more aphids (Chaney). Thus, we choline. Inhibition of AChE results in overstimulation followed set the government marketability standard at by depression or paralysis of the cholinergic nerves throughout the central andperipheral nervous systems (California Environ- fifteen aphids per carton, or 11,866.80 aphids mental Protection Agency 1994). per acre. 536 August 2000 Amer. J. Agr. Econ.

Given this basic biological andeconomic To address aggregate mevinphos appli- information, it is possible to determine an cation under some configuration of policy individual farmer’s application decision con- parameters, it is necessary to know the occur- ditionedonan initial aphidpopulation [see rence of aphids across fields in the Sali- equation (5)]. Recall that for an individ- nas Valley. As part of a pest management ual farmer, this decision is a discrete choice: study, the University of California Coopera- apply the pesticide or not given the ini- tive Extension office in Salinas has been col- tial aphidpopulation. Using equation (5) lecting data on aphid populations on com- andretaining the assumption that µ = 0 mercially farmedleaf lettuce plots in the (Chaney), the critical initial aphidpopulation region. We obtaineddataon aphidpopula- is 614.85 per acre; that is, a farmer will apply tion levels from ninety plots farmedusing standard (i.e., non-IPM) methods observed mevinphos if he observes an aphidpopula- prior to June harvest. The aphidpopulation tion above this level. Table 1 summarizes the level per acre is normally distributed with exogenous parameters underlying the case a mean of 1,265.79 anda standarddevia- study, as well as the endogenous values of the tion of 965.17. Given a PHI of seven days, it critical aphidpopulation, the share of fields follows that the probability that a randomly treatedwith mevinphos, andthe number of selectedfieldwill be treatedwith mevinphos harvest worker poisonings. is Pr(X ≥ 61485) = 07512, or 75.12%. This figure corresponds closely to the actual application rate of 74.57% of leaf lettuce acres in the Salinas Valley (California Environmental Table 1. Key Parameters of the Case Study Protection Agency 1998). Exogenous Value We now turn to the parameters of the health risk generation process. Consider first P: net price 120 the deposited residue or contamination com- ($/carton) Y: yield 79112 ponent of the process. Depositedresidue (cartons/acre) is the product of the application share, m: pesticide cost 50 the amount of active ingredient applied ($/acre) per acre, andthe foliar residuecoefficient. α: intrinsic growthrate 01199 The approvedrate of mevinphos application σ: variance of growthrate 01152 statedon the label is 0.25 poundsper acre. XG : quality threshold 1186680 Field studies by Spencer et al. demonstrate (aphids/acre) that mevinphos application on leaf lettuce PHI 7 at the prescribedrate results in an initial (days) deposited foliar residue of 0.066 µg/cm2. Mean aphids/acre 126580 As discussedearlier, exposure is basedon S.D. aphids/acre 96717 a · v: deposited residue 00660 values of q and k, andthe length of time µ(g/cm2) between application andexposure. In theory, q: exposure coefficient 136300 the decay parameter k can be affectedby (cm2/kg) weather conditions such as rainfall and tem- k: residue decay 00720 perature (Spear et al., Nigg et al.). However, (µg/cm2/day) Spencer et al. have demonstrated that for Bodyweight 70 many vegetable crops produced under vary- (kg) ing weather conditions in California, includ- Crew size 60 ing leaf lettuce in the Salinas Valley, the mev- (people) inphos decay coefficient is in fact constant at Time to harvest an acre 8 k = 0072 µg/cm2/day. (hours/crew) The exposure parameter q is a function Acres 19000 6 D: dose–response 385E-05 of some crop-specific dosing coefficient that 6 This coefficient varies by task andalso accordingto protec- Endogenous Value tive clothing andequipment regulations. Typically, this dosing X: application threshold 61485 coefficient is broken down into a transfer component and an absorption component. Transfer components are often expressed (aphids/acre) as a clothing penetration measure or as an inhalation uptake, RS: share of acres treated 07512 depending on the route of contact, and vary by type of cloth- R: poisonings 179176 ing andequipment (see for example Fong, Brodberg, andFong; Maddy et al.; Brodberg and Sanborn). Absorption coefficients (cases) are generally extrapolated from toxicological studies conducted Sunding and Zivin Pesticide Use and Farmworker Health 537

Table 2. Marginal Impacts of Policy Reforms Policy Change dm dPHI Marginal Change in: Application threshold dX 897 × E-4 −011 Application share dRS −170 × E-4 002 Contamination dC −112 × E-5 139 × E-3 Exposure dE 0 −059 Poisonings dR −406 × E-3 −079 Expected proﬁt dEπ −14273 −145 × E6

Lost expected proﬁt per poisoning averted dE/dR 351 × E6 184 × E6

relates the amount of active ingredient con- Interestingly, this number corresponds closely tactedto an hourly doseof poison, as well as to the reportednumber of mevinphos poi- certain worker characteristics, including the sonings (17.78 cases) resulting from leaf let- duration of contact and worker body weight. tuce harvest work.7 Thus, both the application We assume that a workday consists of one share (75.12%) andthe number of poisonings eight-hour shift andthat each worker has (17.91) predicted by the model correspond a body weight of 70 kg. Further, Formoli, closely to actual observations (74.57% and Thongsinthusak, andSanborn estimate the 17.78 cases, respectively). crop-specific dosing coefficient for mevinphos Table 2 presents the results of the marginal use in leaf lettuce to be 119.28 cm2/hr. This impact analysis basedon the parameters per- figure is basedon the assumption that har- taining to the leaf lettuce case study. The sec- vest workers wear the standard uniform of ondcolumn denotesthe marginal change in long-leggedpants, long-sleevedshirts, gloves, the thresholdnumber of aphidsabove which anda hat. Thus, the exposure parameter q the farmer will apply mevinphos. As indi- for an individual harvester is 13.63 cm2/kg. catedby expression (11), this thresholddrops Recognizing that a sixty-person crew can har- as PHI increases. Consequently, as shown in vest one acre of leaf lettuce in one eight-hour the thirdcolumn, the fraction of growers workday (University of California Coopera- applying mevinphos increases by 2%. Thus, tive Extension), we can calculate total worker increasing PHI increases contamination by 2 exposure per acre. As mentionedearlier the 1.39 × E-3 µg/cm , as shown in the fourth pre-harvest interval for mevinphos usedon column. lettuce in Monterey County is seven days. A marginal increase in the pesticide tax The dose–response relationship D is a bio- has the opposite effect on contamination. The logical relationship that maps the amount of secondcolumn of Table 2 shows the marginal toxin taken up by an individual (i.e., the prod- impact of increasing the per acre cost of uct of contamination andexposure, or aver- mevinphos on the application threshold. As age daily dose) into a manifestation of clini- predictedbyequation (12), this thresholdis cal symptoms requiring at least one lost day increasing in the tax, which implies that RS of work. Typically, this relationship is deter- is decreasing in the tax. The fourth column minedby extrapolating from animal models of the table shows the effect of an increase by adjusting for differences in body mass. Fol- in the tax on deposited residue. Increasing −5 the tax marginally reduces contamination by lowing O’Malley, we set D at 385 × 10 . 2 It is now possible to calculate the number 1.12 × E-5 µg/cm . of poisonings predicted by the model. Muti- The exposure parameter is affectedonly plying the contamination parameter by the by the PHI. As discussed above, this effect is exposure parameter andthe dose–response unambiguous since increasing the PHI gives parameter, it follows that the predicted num- the pesticide time to decay, which reduces ber of poisonings is 17.91 in the base case. 7 This latter figure is derived by multiplying the total number of reportedmevinphos poisonings (201) by the share of mevinphos on laboratory animals, are specific to neither clothing nor equip- appliedto leaf lettuce in the Salinas Valley (8.85%) (California ment, andvary by route of exposure. Environmental Protection Agency 1998). 538 August 2000 Amer. J. Agr. Econ. worker injury per unit of pesticide applica- Similar analysis yields an expression for tion. Table 2 indicates that the marginal effect the marginal change in profit as PHI andthe of PHI on per acre exposure is equal to -0.59 marketability standard increase. Taking the µg/kg/day. derivative of (19) with respect to PHI, we Next, we calculate the marginal impact of have the policy changes on the number of poi- ∂E X ∂D sonings. These calculations are given in the =− PY NA f(X) dX sixth column of Table 2. The marginal effect ∂PHI 0 ∂PHI ∞ of the PHI on worker health is especially ∂DA interesting in this case study since we have − PY f(X) dX ∂PHI exactly the type of situation in which increas- X ing PHI can harm workers: namely, increasing making use of Leibniz’ Rule andthe defini- the PHI increases the incentives to use mev- tion of X. This derivative can be expressed as inphos. The empirical analysis shows, how- X ever, that the drop in exposure outweighs the ∂E ∂zNA (20) = P Y ϕ(zNA) f(X) dX increase in contamination for the parameters ∂PHI 0 ∂PHI of this case study, and as a result the number ∞ of mevinphos poisonings drops by 0.79 cases + P Y ϕ(zA) X in response to a unit increase in the PHI. ∂z As expected, the pesticide tax also reduces × A f(X) dX < 0 the number of poisonings; Table 2 indicates ∂PHI that this marginal change is small (4.06 × E- Table 2 shows the marginal change in 3 cases). This latter result follows from the grower profit andalso the change in profit small impact of the tax on deposited residue per poisoning averted. Increasing the PHI (which follows from the modest marginal has a significant impact on profit since the impact of a per acre tax on the percentage of probability of crop damage increases for all growers using the pesticide). growers using mevinphos. The pesticide tax It is of interest to evaluate the change in has a much smaller impact on profit since grower profit resulting from each of these it does not affect expected crop damage at marginal reforms since understanding how the margin. It is most interesting to consider profit changes allows a comparison of policies the profit impact per poisoning avoided. The in terms of lost profit per poisoning averted. PHI is nearly twice as efficient as the pes- Expectedprofit per acre is given as ticide tax by this measure, despite the fact that lengthening the PHI increases aggregate X mevinphos use. Increasing the PHI reduces (18) E = PY 1 − DNA f(X)dX 0 grower profit by $1.84 million per poisoning

∞ averted, while the pesticide tax lowers grower + [PY(1 − DA) − m] X profit by $3.51 million per case. The basic rea- f(X) dX son for this disparity in our case study is the sensitivity of exposure to changes in the PHI. Taking the derivative with respect to the pesticide cost per acre, we have ∂E ∞ Conclusions =− f(X) dX ∂m 0 This paper presents an explicit model of ∂X +PY 1 − D X f(X) insect population dynamics and employs it to NA ∂m measure pesticide productivity, derive profit- maximizing pesticide application levels, and −[PY(1 − D (X)) − m] A assess the impact of regulations intended to ∂X reduce worker pesticide poisonings. A main × f(X) ∂m result of our conceptual analysis is that pre- harvest interval regulation affects both con- Using the definition of the critical insect pop- tamination andexposure, perhaps in opposite ulation, it follows that marginal lost profit per directions. Pesticide taxation unambiguously acre is given by reduces the incidence of poisoning. ∂E Regulators typically set pre-harvest inter- (19) =−[1 − F(X) ] ∂m vals to separate farmworkers from health Sunding and Zivin Pesticide Use and Farmworker Health 539 hazards by increasing the time between pes- Brodberg, R., and J. Sanborn. “Compilation ticide application and exposure. The intent of Clothing Penetration Values: Har- of increasing this interval is to allow more vesters.” Sacramento CA: California Envi- time for the pesticide to decay. Our paper ronmental Protection Agency, HS-1652, shows that increasing the pre-harvest inter- 1996. val may increase the incentive for pesticide California Environmental Protection Agency. Cal- use, thereby resulting in reduced exposure ifornia Pesticide Illness Surveillance Program but increasedcontamination. The impact of Overview. Department of Pesticide Regula- PHI regulation on pesticide use levels should tion, Sacramento CA, 1996. be factoredin to regulatory impact analyses . Draft Mevinphos Risk Characterization Doc- rather than assuming that contamination is ument. Department of Pesticide Regulation, constant, as is typically the case. Sacramento CA, 1994. It is important for economists to pay . 1996 Pesticide Use Report. Department of attention to insect population dynamics Pesticide Regulation, Sacramento CA, 1998. when assessing pesticide productivity and the Chaney, B. Farm Advisor, Monterey County, CA. impact of pesticide regulations, particularly Personal communication, September 1997. Crissman, C., D. Cole, andF. Carpio. “Pesticide regulations like the PHI that alter the timing Use andFarm Worker Health in Ecuado- of pesticide use. Without these dynamics, the rian Potato Production.” Amer. J. Agr. Econ. pesticide use decision can only be motivated 76(August 1994):593–97. by the prevailing conditions at the time of Crump, K., andR. Howe. “The Multi-Stage Model application, andmisses an important dimen- with a Time-Dependent Dose Pattern: Appli- sion of the pesticide problem. Our hope is cations to Carcinogenic Risk Assessment.” that more economists will work with ento- Risk Anal. 4, no. 3(1984):163–76. mologists andother specialists to create even Fong, H., Brodberg, R., and B. Fong. “Mea- more elaborate andaccurate modelsof insect suring Dislodgeable Propargite Residue on population growth anddevelopsolidmicro- Field-GrownRoses andPenetratedCloth- foundations for the economics of pesticide ing Residues.” Sacramento CA: California regulation. Department of FoodandAgriculture, HS- Future work shouldalso focus on the 1549, 1990. multiplicity of regulatory instruments and Formoli, T.A., T. Thongsinthusak, andJ. Sanborn. how these can be combinedmost effec- “Estimation of Exposure of Persons in Cal- tively to reduce the adverse public health ifornia to Pesticide Products that Con- consequences of pesticide use. There are tain Mevinphos.” Sacramento CA: California many more potential interventions than the Environmental Protection Agency, HS-1653, three considered here; training, posting, label- 1993. ing, andprotective equipment regulations Hubbell, B.J., andG.A. Carlson. “Effects of Insec- are only a few examples. Given the likely ticide Attributes Within-Season Insecticide decreasing marginal benefits of each regula- Product and Rate Choices: The Case of U.S. tion, it seems likely that a combination of Apple Growers.” Amer. J. Agr. Econ. 80(May instruments will be optimal in many cases. 1998):382–96. Krewski, D., andJ. Van Ryzin. “Dose Response Models for Quantal Response Toxicity Data.” [Received May 1998; Statistics and Related Topics. E. Salah, ed., pp. accepted October 1999.] 201–31. 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