NEWDEVELOPMENTS IN DEVELOPMENTt

Modeling Technology Adoption in Developing Countries

By TIMOTHY BESLEY AND ANNE CASE*

Perhaps one of the main reasons for or a region must decide whether or not to studyingeconomic development is to under- adopt a particularagricultural technology. stand better how individuals are able to We are interested in understandingwhat make the transitionout of poverty.Technol- determines adoption of the technology ogy may be viewed as a means to this end. across space and time. We begin by review- Yet, while the developmentof higher-yield- ing three basic empirical approaches that ing varieties (HYV's) of many crops grown varyaccording to the type of data available. by poor farmershas enhanced this hope, it is essential to understand how new tech- I. EmpiricalApproaches to Analysisof nologies are adopted in practice if their TechnologyAdoption promise is to be fulfilled. In our collective understandingof technologyadoption, many A. Time-SeriesStudies questionsremain unanswered. For instance, to what extent are socially valuable tech- Much of what is known about the adop- nologies slow to realize their potential due tion of new technologies comes from time- to informationconstraints or to externalities series evidence. In these data, one observes that lead the privateand social value of new only an aggregatemeasure of adoption,such technologiesto diverge? as the percentageof farmersemploying the A prior step to answeringthese questions new technology at each date. The study of is to provide an adequate analysisof tech- hybrid corn in the by Zvi nology adoption decisions by poor farmers, Griliches (1957) is a classic study of this and the purpose of this paper is to review kind. In general, the aim is to capture the some possible empiricalmodels for studying shape of the time-series diffusion process, technology adoption. In so doing, we will and these studies tend to model the pattern belabor the issue of theoreticalconsistency. of adoption as a logistic-shapedfunction Can researchersensure that their empirical over time. Letting pi, denote the fractionof adoption models are consistentwith an un- adopters in region i at date t, one can derlyingchoice-based model? What are the estimate equationsof the form costs of such consistency,measured in terms of data needs and model complexity, and + what are the benefits, measuredin terms of (1) Pit f (Pit-1) ?it understandingthe microeconomicfounda- tions of adoption? While it may be possible to parameterize The typical scenario we investigate is as the function f( ) by regionalcharacteristics, follows. Each of M farmerswithin a village the main purpose in such studies is often to estimate the intertemporal component of the relationshipin (1). While disaggregating by region and investigating the effect of tDiscussants: TimothyBesley, PrincetonUniversity; Anne Case, PrincetonUniversity; Adam Jaffe,Harvard regional characteristics on adoption give University. some insight into what might drive adop- *Research Program in Development Studies, tion, this approachis limited in what it can WoodrowWilson School of Public and International Affairs,Bendheim Hall, PrincetonUniversity, Prince- ton NJ 08544. We are gratefulfor helpful discussions with tandAriel Pakes throughoutthis 1Ouraim here is not to surveythe existingtheoreti- project and for the financialsupport of the National cal and empirical literature. For that the reader is Science Foundation(SES-9121838). referredto GershonFeder et al. (1985). 396 VOL. 83 NO. 2 NEWDEVELOPMENTS IN DEVELOPMENT 397 say about the underlyingdynamic process at Some cross-sectionalsurveys contain in- work. formation, based on recall, about when a farmer adopted a technology. Under some B. Cross-Sectional Studies circumstances,recall data may provide a means for dealingwith the above problems. There are also many studies of technol- If, for example, the dynamicstructure was ogy adoption that use cross-sectionaldata. well representedby ifit = 8xtx, we can aug- Such data are broadly of two kinds. First, ment equation (2) above. Creatingfor each there are studies that take a snapshotof M farmera set of discrete choice observations, farmers'technology use at some date. The dit, equal to 1 if farmer i was using the gain to farmeri of using the new technology technologyat time t, t E [1, ...., r], and zero is typicallyparameterized as yxi + ui, where otherwise,we estimate a probit: are farm and farmer characteristicsand xi (3) ui is an independentlyand identically dis- Prob{dit=1} It is tributed farm specific ex ante shock. = 4((yxi + pT+ 8[TX xi])/ou). often assumed that these shocks are nor- mallydistributed, and the model is then run where T is a set of ir - 1 year indicators and as a probit, so that Tx xi are interactionterms that allow the influenceof field and farm characteristicsto (2) Prob{adoptionby farmeri} change over the diffusion process. While = more flexible than (2), this structureis also (4yxi /au) extremelylimiting. It is necessary to main- where 4(Q) is the distributionfunction of tain the assumption that influential farm the standardnormal. The intention of this and farmervariables xi do not change over line of research is often to measure the time. In general, this seems unreasonable impact of xi on adoption decisions. since farmer wealth and credit-worthiness However,this model is problematicif, as are apt both to influence and to be influ- the time-series analysis suggests, there is enced by adoption choices taken. If these some dynamicstructure to the adoption de- data are availableonly at the time when the cision. The cross section provides only a survey was done, their use in (3) will bias snapshot;at that point, the technologymay the parameters of interest. It also seems be incompletelydiffused throughthe popu- unlikely that the dynamicsof adoption can lation. This confoundsthe interpretationof be well captured by allowing time-varying the coefficients in (2). For example, there coefficients on variables whose values are may be a time-dependent element in the assumed to be constant over time. Thus, adoption decision, so that the expected while one might be able to do better by profits are yx1 +it, where if= having informationabout the year in which Dt-1, xit)+ it, where Dt-1 is a history of the technologywas adopted, there are still the new technology'suse up to period t -1. problems.2 There are many possible interpretationsof qIit,including (i) a farmer's knowledge about C. Panel-Data Studies the new technologyor (ii) evolvingcosts of adoption,which vary with credit availability. If panel data detailing farm and farmer Either way, it may depend upon farm and characteristics and the adoption choices farmer characteristicsat time t. In these cases, hit will bias the parameter estimates of y. Thus, upon completion of the adop- 2There are other possible ways of using recall data. tion process, cross-sectionalstudies of this For example, the researcher may wish to stratify the kind may be able to provideinsight into the sample into individuals who always used the technology farm and farmer characteristicsassociated during the recall period, those who adopted during the period, and those who never used it. Predicting with ultimatelyaccepting the new technol- adopters in such circumstances may be interesting, but ogy. However,these data are of limited use is still subject to the criticism that the xi's may be in exploringthe adoptionprocess itself. endogenous. 398 AEA PAPERS AND PROCEEDINGS MAY 1993

made at each point in time are available, namic choice as being governedby a recur- then a number of the criticismsraised for sive problem: time-series and cross-sectionaldata can be met. Here, for example, the researchercan (5) Vti(kit allow for householdeffects and state-depen- dence. Thus, consider a model in which the = + underlyingdynamic component is well rep- Max{rrjt(djt,ki) E[V/ 1(ki+1)lkki,dt]} resented by where VO(k) is farmer i's value function at time t, n-it(d ,,kt) is some current payoff, (4) it =,I H dit- + at + Ai+ uit. and 8 reflects the discount rate. Several i C N(i) different interpretationsof the state vari- able are possible: (1981) offers an excellent survey of methods for handling such mod- (a) Credit availability.-The variable k' may els, where Ai is either a randomor a fixed represent current assets that are avail- effect. able to pay for implementationof the However, the availabilityof panel data new technology. forces researchers to think harder about (b) Learning.-The variable k' may repre- reasonable dynamic specificationsfor dis- sent the stock of knowledge about the crete choice. For, while there is a rich set of new technology which evolves through empirical models available for panel data, time. there is a real question about how these (c) An Irreversible Investment.-The vari- relate to the underlyingchoice problemthat able k' equals 1 if the investmentwas individuals face. For policy analysis, the ever undertakenpreviously and 0 other- abilityto returnto the underlyingmicroeco- wise. nomic foundations of adoption is impera- tive. This will lead us, in Section II, to think In any of these cases, current choices once again about theory. have future consequences,and any current decisionsought to weigh these. In designing II. DynamicChoice an econometric specification for studying technologyadoption, we would formulatea So far, we have said very little about the model whose likelihood function comprised dynamicchoices that generate the data. In this section, we do this in order to reap- (6) Prob{dit= 1} praise what empiricalmethods might be ap- propriate.We discuss two scenarios,distin- - Prob{ditE argmax A E {O,1}0) } guished by their allowance for externalities ( Ics between farmers'choices. where A. Dynamic Choices WithoutExternalities A =1Tt(9w, k') + E[VtF+1(k+1)jkt, wJ. Let the dynamicprocess drivingadoption be characterizedby a vector of state vari- The parameters to be estimated would ables kt = (kl,..., km) and let their transi- depend upon the exact structureof the un- tion function be k'+1 - h(k, d; eit), where derlying choice problem, which we could ? is an independentlyand identicallydis- specify by giving functional form to the tributed shock experienced by farmer i at Markovtransition kernel describingthe evo- time t. We can write the probability of lution of k'. To our knowledge, specifying observingany value of the state variable in and estimatingmodels of this kind have not the future as a first-orderMarkov process: been attemptedin the literatureon agricul- F(k't+1Ik',dit). We can then consider dy- tural technologyadoption, although there is VOL. 83 NO. 2 NEWDEVELOPMENTS IN DEVELOPMENT 399 now a considerable literature focused on by using it. We believe that such exter- estimatinginvestment decisions in this way. nalities are potentially important in Two key contributions are Ariel Pakes's agriculturaltechnology adoption. This (1986) option-valuemodel of the decision to has long been recognizedby ruralsoci- invest in or renew a patent and John Rust's ologists (see e.g., Everett Rogers [1983] (1987) model of bus engine replacement. for a review). Surveys of the literature can be found in Pakes (1993) and Rust (1993). The canonical decision problem to be It is clear from (6) that panel-datamodels solved in a model with externalitiesinvolves estimable using equation (5) are not neces- conditioning one individual'sbehavior on sarily good representationsof optimal dy- that of others. To model this, suppose that namic choices. The main problem is that the state variablesfor individuali evolve in optimal choices are forward-looking, and a way that depends upon d-it, the choices we need to find some way of specifyingthe made by farmersother than i. The interde- fiutureof some action when specifying the pendent decision-makingthat ensues is po- model. The models discussed in (5) above tentially quite complicated. Moreover, a use only lagged values of variables to do strategy for farmer i, sit, can potentially this. depend upon all current and past behavior as well as current and past values of the B. Dynamic Choices with Externalities state variables. A common simplification, first suggested in Eric Maskin and Jean Externalitiesmay play an importantrole Tirole (1988), and used in empiricalwork by in technology-adoptiondecisions. The liter- Pakes and Paul McGuire(1991) and Besley atures cites a number of relevant sources, and Case (1992), is to confine strategies to including:3 depend only upon the vector of current state variables, denoted by kt. Strategies (i) Network Externalities.-Adopters care that comprise a Nash equilibriumat each abouthow manyother individualsadopt date are then referredto as Markovperfect. because there is some public-goodele- The optimaldecision for farmeri condition- ment to the technology.In agriculture, ing in d_it is then characterizedby the the most common form of externalities recursion arises in the need to build a marketing infrastructurefor a new crop. (7) Jti(k;Vt t dit) = max{7rit(dit, k) (ii) Market Power Extemalities.-Adopters d~~~~~~~it with market power will care about adoption by others if adopting early +SE(Vt+ l( k+ 1)Ikti, dit, d _-it})) implies some advantage in market power. We do not know of examplesin whereIVI'7(kt) AV(k; s-it(kt)), so that the agriculturewhere this is important. equilibrium value function now depends (iii) Learning Externalities.-Farmers may upon the whole vector of state variables.4 care about others' adoptiondecisions if Studyingproblems like (7), even as a pure early adopters teach late adopters something. For example, if a technol- ogy is of uncertain profitability,some potential adopters may wait until they 4We use the followingshorthand notation: observewhether others have fared well s_it(kt) [s(k,),...si-,,(k.1

Si+it( k,+ ),.* *smt( kM)]. 3Forreview of the theoreticalliterature, see Jennifer Reinganum(1990). We are not aware of an empirical Even though current payoffs depend only on k,, the literaturewhich has investigatedthese issues in indus- value function depends upon the whole vector kt, trial organization. becauseindividual j's (j # i) strategydepends upon kt'. 400 AEA PAPERS AND PROCEEDINGS MAY 1993 computationalventure, is quite demanding. (see, e.g., MorrisH. De Groot, 1970 p. 167.) Consequently,few studies have exploreddy- This is the source of the externality,since namic models of equilibriumbehavior in updatingdepends upon the total numberof any context, including agriculturaltechnol- plots sown. ogy adoption.The next section presentsone As shown in Besley and Case (1992), approachto solvingsuch a problem. equation(8) can be used to characterizethe Markovtransition kernel for this problem. III. Examples: Learning from the Behavior It is normal and depends upon the vari- of Others ances W, ok2,,). That paper also shows how the parameters W, o,2) might be identified We focus here on how one might build a from farmer-level data. Finally, the esti- dynamic multiagent model of learning in mated parametervalues are used to simu- the adoption of a new technology.The first late dynamicchoices as suggested in equa- exampleis based on Besley and Case (1992), tion (7). Each simulation gives an equilib- to which the reader is referred for a full rium set of predicted choices dit. Each set developmentand empiricalimplementation of such simulationsis, however,conditioned of the model. In that study, we apply the on a set of starting values. To find these model to the diffusionof a new cotton seed values, we take advantageof a technique, in a south Indianvillage. first suggested by Pakes (1986) and devel- In a world of learning,we interpret k' as oped in Pakes and David Pollard(1989), of the state of farmer i's knowledgeabout the computing the pseudo-likelihood function new technologyat time t. Our first simplifi- from simulatedruns from the model. There cation is to suppose that knowledge is a remain a numberof issues to be dealt with, public good so that kt = kt for all i. Sup- such as the treatmentof multiple equilibria. pose that each farmer has one field and is The data may suggest appropriate refine- deciding whether or not to sow this with a ment strategies;research in this area is still new seed. Each farmer observes the yields unfolding. other farmersobtain on their land. Knowl- A different approach to learning and edge evolves with the realization of yields technology adoption has recently been put from past planting decisions. We parame- forwardby Glenn Ellison and Drew Fuden- terize the model so that kt is the expected berg (1991), who suggest some rules of gain from the new technology.The planting thumbto captureadopters' behavior in situ- decision at time t by farmer i is based on ations in which individualsmay learn from expected gains 7* = k + vit, where vit is a each other's past experience but do not random shock not observed by the re- solve the kinds of dynamic optimization searcher.The realized gain in profits using problemsgiven by (7). Given the complexity the new seed, 7its differsfrom the expected of the calculations required in structural gain by a shock Eit, assumedto be normally dynamicmodels, this direction of research distributedwith mean zero and variancea. is appealing. But is such an approachuse- Then the prior distributionof k, the change ful? One way of appraisingthis would be by in profitabilityattributable to the new seed, fitting such models to the data and compar- is normal with mean kt 1 and variance ing them with other possibilitiesavailable to Ok,2t-1 and we have the following standard the researcher, such as structuralmodels. Bayesian updating formula for normal dis- To illustrate how this might be done, con- tributions:if mt farmers sow to the new sider Ellison and Fudenberg's(1991) sim- seed at time t, plest rule for time-seriesdata: (1- a)pit-l + a (8) kt+1 = kt + Ok, t (9) Pi,= t(l with probabilityq

x d -t(it-Tit) with probability1- q. VOL. 83 NO. 2 NEWDEVELOPMENTS IN DEVELOPMENT 401

The parameter a represents the inertia in model that does not correspondto an un- the population. Only a fraction a of the derlyingdecision process.To get the best of populationconsiders switchingtechnologies both worlds, one might try to combine both each period. The parameter q represents types of modeling on any given data set. the probabilitythat the new technology is Statisticalmodels may suggestwhat is worth better than the old one. The likelihood modeling structurally.The latter is then a function for the model in (9) for a sample good way of developing theoretical models (Pill,... ,Pi), given some initial pio, is that are better tailored to the data under consideration, thereby encouraging re- ( 10) Y (Pil, .. *, PiT IAo ) searchersto think more carefullyabout the underlyingprocess generatingthe data. T H Prob{pj,Ipj,i-) REFERENCES T = 1

T Besley, Timothy and Case, Anne, "Taking Learning Seriously: A Diffusion Model = 7 {(a-)PiT-+aq}. T = 1 for HYV Cotton," unpublished manu- script, Princeton University, 1992. It is, in principle,possible to find the values Deaton,Angus, "Data and Econometric Tools of (a,q) that maximize (10) for some data for Development ," in Jere set. Computationally,there are certainlyad- Berhman and T. N. Srinivasan, eds., vantages in using rule-of-thumb models. Handbook of Development Economics, There are limits, however, in the use of Vol. III, Amsterdam: North-Holland, such models, especially for policy analysis. 1993 (forthcoming). If learning is important,then even socially De Groot,Morris H., Optimal Statistical Deci- optimal paths would have gradualdiffusion sions, New York: McGraw-Hill, 1970. of a technology. One would ideally like to Ellison, Glenn and Fudenberg,Drew, "Rules of compare the private and socially optimal Thumb in Social Learning," unpublished situations, and rules-of-thumbmodels pro- manuscript, Massachusetts Institute of vide little help in this respect. Technology, 1991. Feder, Gershon, Just, Richard E. and Zilber- IV. Conclusions man, David, "Adoption of Agricultural In- novations in Developing Countries: A One of the key decisions in modeling Survey," Economic Development and Cul- technologyadoption concerns the extent to tural Change, January 1985, 33, 255-98. which empiricalestimation is consistentwith Griliches,Zvi, "Hybrid Corn: An Exploration an underlyingtheoretical model of optimiz- in the Economics of Technological ing behavior. If the adoption decision is Change," , October 1957, motivatedby models of the form (5) or (7), 25, 501-22. researchersmay face a dilemma;it appears Heckman,James, "Statistical Models for Dis- that the data and computationcosts of re- crete Panel Data," in Charles Manski and search are rather high. Some researchers Daniel McFadden, eds., StructuralAnaly- find structuralmodels unconvincing,noting sis for Discrete Data with Econometric Ap- the lack of specification tests or well- plications, Cambridge, MA: MIT Press, defined null hypotheses to test the model 1981, pp. 114-78. against. Of course, this critique is not con- Maskin, Eric and Tirole, Jean, "A Theory of fined to dynamicstructural approaches, and Dynamic Oligopoly I: Overview and Angus Deaton (1992) broadens it to other Quantity Competition with Large Fixed studies in developmenteconomics. Costs," Econometrica, May 1988, 56, At the other extreme, some models pay 549-70. only lip service to the underlyingtheory. It Pakes, Ariel, "Patents as Options: Some Esti- is often difficultto interpret results from a mates of the Value of Holding European 402 AEA PAPERS AND PROCEEDINGS MAY1993

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