Harrison and List:Field Experiments 1019 for predicting the p opulation response.25 All The reason is simple to understand.It is as the bons the behavioral r much easier to predict the behavior of a 26- of students to be the year-old when one has a model that is based on the behavior of people whose ages range cither or, from 21 to 79 than it is to estimate the tested by samping nonstude behavior of a 69-vear-old based on the nts as well dents behavioral model from a sample whose ages course e,it is always better to be fore range from 19 to 27 ng on th basi an What is the relevance of these methods for rather than an extrapolation.and that is lem one has with stu the c dent sam d in some enience sample in the HLar The lessor s that a ned fr (1994).They estimated a statistical mod el o uld b a statist subject response using a sample of college students and also estimated a statistica 6 ith implic arge population model of subject response using field sub th son an￥ jects drawn from a wide range of churches in as yet the same urban area Each were conven representativeness nt ora ience samples.The only difference is that respon conditi on th character the church sample exhibited a much wider s for evalu ating the ext conclusions about students apply to a broader population ranged from 21 to 79:in the student san How could this method ever lead to inte esting results?The answer depends on the church context.Consider a situation in which the estimated behavioral mode int olatio behavioral model showed that age was an used and dict important determinant of behavior consider P In th re further a situation in which the sample used pre to estimate the model had an average age that tima mode was not representative of the population as a in the sense whole.In this case,it is perfectly ossible tha wer naving extremely vanance nses of the student sar ple could be ugh no such in For example. rod in of thi dom happens to have thus far,the uled o ter ofr We ude the that of the aised b alid the d no able to be ed by simple exte vide mor of the me perime ers cu eteioeoe und n for this to ren would extensions genera sam experimental metl ds obtained with studen the of the unde ing way in 6 Further prob ms arise if one allows unob ion researc (the propos al to served individual effects to play a role.In ossible correlation between the two questions). some statistical settings it is possible to allow This content downle a20g2016o61s4UTC
Harrison and List: Field Experiments for predicting the population response.25 All that is needed is for the behavioral respons- es of students to be the same as the behav- ioral responses of nonstudents. This can either be assumed a priori or, better yet, tested by sampling nonstudents as well as students. Of course, it is always better to be fore- casting on the basis of an interpolation rather than an extrapolation, and that is the most important problem one has with stu- dent samples. This issue is discussed in some detail by Blackburn, Harrison, and Rutstrom (1994). They estimated a statistical model of subject response using a sample of college students and also estimated a statistical model of subject response using field sub- jects drawn from a wide range of churches in the same urban area. Each were conven- ience samples. The only difference is that the church sample exhibited a much wider variability in their socio-demographic char- acteristics. In the church sample, ages ranged from 21 to 79; in the student sample, ages ranged from 19 to 27. When predicting behavior of students based on the church- estimated behavioral model, interpolation was used and the predictions were extreme- ly accurate. In the reverse direction, howev- er, when predicting church behavior from the student-estimated behavioral model, the predictions were disastrous in the sense of having extremely wide forecast variances.26 25 For example, assume a population of 50 percent men and 50 percent women, but where a sample drawn at ran- dom happens to have 60 percent men. If responses differ according to sex, predicting the population is simply a mat- ter of reweighting the survey responses. 26 On the other hand, reporting large variances may be the most accurate reflection of the wide range of valua- tions held by this sample. We should not always assume that distributions with smaller variances provide more accurate reflections of the underlying population just because they have little dispersion; for this to be true, many auxiliary assumptions about randomness of the sam- pling process must be assumed, not to mention issues about the stationarity of the underlying population process. This stationarity is often assumed away in contin- gent valuation research (e.g., the proposal to use double- bounded dichotomous choice formats without allowing for possible correlation between the two questions). The reason is simple to understand. It is much easier to predict the behavior of a 26- year-old when one has a model that is based on the behavior of people whose ages range from 21 to 79 than it is to estimate the behavior of a 69-year-old based on the behavioral model from a sample whose ages range from 19 to 27. What is the relevance of these methods for the original criticism of experimental proce- dures? Think of the experimental subjects as the convenience sample in the HL approach. The lessons that are learned from this stu- dent sample could be embodied in a statisti- cal model of their behavior, with implications drawn for a larger target population. Although this approach rests on an assump- tion that is as yet untested, concerning the representativeness of student behavioral responses conditional on their characteris- tics, it does provide a simple basis for evalu- ating the extent to which conclusions about students apply to a broader population. How could this method ever lead to inter- esting results? The answer depends on the context. Consider a situation in which the behavioral model showed that age was an important determinant of behavior. Consider further a situation in which the sample used to estimate the model had an average age that was not representative of the population as a whole. In this case, it is perfectly possible that the responses of the student sample could be quite different than the predicted responses of the population. Although no such instances have appeared in the applications of this method thus far, they should not be ruled out. We conclude, therefore, that many of the concerns raised by this criticism, while valid, are able to be addressed by simple exten- sions of the methods that experimenters cur- rently use. Moreover, these extensions would increase the general relevance of experimental methods obtained with student convenience samples. Further problems arise if one allows unob- served individual effects to play a role. In some statistical settings it is possible to allow 1019 This content downloaded from 218.106.182.180 on Sat, 11 Jun 2016 06:18:54 UTC All use subject to http://about.jstor.org/terms
1020 Journal of Economic Literature,Vol.XLII (December 2004) for those effects by means of"fixed effect"o e implication i But to col an ttery measures o mon in the e tool. dividual characterist all some sta kit of expe economists,do no tis deeper problem.The interna But even h ere we car validity of a randomized design is maximize only easily condition on observable charac. when one knows that the samples in each teristics. and additional identifying assump treatment are identical.This happy extreme tions will be needed to allow for correlated leads many to infer that matching subjects differences in unobservables on a finite set of characteristics must be bet 4.4 Precursors ter in terms of interal validity than not matching them on any characteristics. Several experimenters have used artefac But partial matching can be worse than tual field experiments;that is,they have no matching.The most important example deliberately sought out subjects in the of this is due to James Heckman and Pete wild,"or brought subjects from the "wild' Siegelman (1993)and Heckman 1998 into labs.It is notable that this effort ha who critique paired-audit tests of discrimi nation.In these experiments.two applicants mental omics and that it has for a iob are matched in terr ms o recently beco such as age nd educati stein and differ in only ected charact and Slovic(1973)replicated their tic. mel as ption ut etting experiment: e ture pr casino in s in Las V (p. 17 co dir tion c the bias" mente w a prof ona r,an and ere n from th floor of t Heck P 110)illustra casino the experim Bovs and girls s of th age are in a high me may have een relatively forbiddin jump competition, and jump the (it include a PDP. computer,a DEC height on a CRT.and a kevboard).the goa was to iden variance in their jumping technique,for any tify gamblers in their natural habitat bject pool of 44 did include seven kno dealers who worked in las vegas.and the like better jumpers:if the bar is set very dealer's impression was that the game high then the bovs will look like bette attracted a higher proportion of profession iumpers The implications for numerous al and educated persona than the usual (lab and field)experimental studies of the casino clientele"(18) effect of gender.that do not control for Kagel.Battalio. nd lames Walker (1979 other characteristics shoud be apparent. provide a remarkable,early examination of This metaphor also serves to mind us many of the issues we raise.They were that what laboratory xperimenters think of cerned with "volunteer ,artifacts”in lab asa“standard populat on' need not be a eriments,ranging fror m the characteristic ulation Altho ough tha volunteers ha to the issue of san om diff pu a untry ma hav d rough the cally in 0 stics such intelligence an This content downl
Journal of Economic Literature, Vol. XLII (December 2004) for those effects by means of"fixed effect" or "random effects" analyses. But these stan- dard devices, now quite common in the tool- kit of experimental economists, do not address a deeper problem. The internal validity of a randomized design is maximized when one knows that the samples in each treatment are identical. This happy extreme leads many to infer that matching subjects on a finite set of characteristics must be bet- ter in terms of internal validity than not matching them on any characteristics. But partial matching can be worse than no matching. The most important example of this is due to James Heckman and Peter Siegelman (1993) and Heckman (1998), who critique paired-audit tests of discrimi- nation. In these experiments, two applicants for a job are matched in terms of certain observables, such as age, sex, and education, and differ in only one protected characteris- tic, such as race. However, unless some extremely strong assumptions about how characteristics map into wages are made, there will be a predetermined bias in out- comes. The direction of the bias "depends," and one cannot say much more. A metaphor from Heckman (1998, p. 110) illustrates: Boys and girls of the same age are in a high- jump competition, and jump the same height on average. But boys have a higher variance in their jumping technique, for any number of reasons. If the bar is set very low relative to the mean, then the girls will look like better jumpers; if the bar is set very high then the boys will look like better jumpers. The implications for numerous (lab and field) experimental studies of the effect of gender, that do not control for other characteristics, should be apparent. This metaphor also serves to remind us that what laboratory experimenters think of as a "standard population" need not be a homogeneous population. Although stu- dents from different campuses in a given country may have roughly the same age, they can differ dramatically in influential characteristics such as intelligence and beauty. Again, the immediate implication is to collect a standard battery of measures of individual characteristics to allow some sta- tistical comparisons of conditional treatment effects to be drawn.27 But even here we can only easily condition on observable charac- teristics, and additional identifying assump- tions will be needed to allow for correlated differences in unobservables. 4.4 Precursors Several experimenters have used artefac- tual field experiments; that is, they have deliberately sought out subjects in the "wild," or brought subjects from the "wild" into labs. It is notable that this effort has occurred from the earliest days of experi- mental economics, and that it has only recently become common. Lichtenstein and Slovic (1973) replicated their earlier experiments on "preference reversals" in "... a nonlaboratory real-play setting unique to the experimental litera- ture on decision processes-a casino in downtown Las Vegas" (p. 17). The experi- menter was a professional dealer, and the subjects were drawn from the floor of the casino. Although the experimental equip- ment may have been relatively forbidding (it included a PDP-7 computer, a DEC-339 CRT, and a keyboard), the goal was to iden- tify gamblers in their natural habitat. The subject pool of 44 did include seven known dealers who worked in Las Vegas, and the "... dealer's impression was that the game attracted a higher proportion of profession- al and educated persona than the usual casino clientele" (p. 18). Kagel, Battalio, and James Walker (1979) provide a remarkable, early examination of many of the issues we raise. They were con- cerned with "volunteer artifacts" in lab experiments, ranging from the characteristics that volunteers have to the issue of sample 27 George Lowenstein (1999) offers a similar criticism of the popular practice in experimental economics of not conditioning on any observable characteristics or random- izing to treatment from the same population. 1020 This content downloaded from 218.106.182.180 on Sat, 11 Jun 2016 06:18:54 UTC All use subject to http://about.jstor.org/terms
Harrison and List:Field Experiments 1021 selection bias.28 They conducted a field reason for trade in this environment.30 The nining electricity demand maj pi ical result is the large r mber of o rved ce bubbles of th nse to cha prices weekly feed back on can id to have had some rmat They a erg also tion ample i ned a comp e pop e f usin eck for any biases in the volunteer were just ent suby cts,Smi Such and ms(1988)recruited nstudent sub (1980,1981 jects for one experiment.As they put it,one ts eliciting mea es of risk aver is not worthy because of its sion from farmers in rural India.Apart from use of professional and business people from the policy interest of studying agents in the Tucson community,as subjects. This one stated goal of market belies any notion that our results are was to an artifact of student subjects,and that busi assess risk attitudes for choices in which the nessmen who'run the real world'would income from the experimental task was a quickly learn to have rational expectations substantial fraction of the wealth or annual This is the only experiment we conducted income of the subject.The method he devel that closed on a mean price higher than in all oped has been used recently in conventional previous trading periods"(p.1130-31).The laboratory settings with student subjects by reference at the end is to the observation Charles Holt and Susan Laury (2002) that the price bubble did not burst as the Burns (1985)conducted induced-value finite horizon of the eriment wa market experiments with floor traders from roachi wool markets,to compare with the behav ior of student subjects in such settings.The e unlike the bubbl see if the heuristics ved ed subje traders Alth natural field setting affe ected their beha ough th xperienced th hot of the She did find that thei auctio 1 a powerful experin motiv ating effe e there is no pre nen relevant for this s type o asse ernon Smith,G.L Sucha Arlingto arg series of ex with stude in an "asse t bubble eriment.In the experiments they report,nine to welve dt see the ected divi traders with experience in the doubl -auc players premium tion institution traded a number of fifteen or thirty period assets with the same com Thi mon value distribution of dividends.If all tually lead to subjects are risk neutral and have common price expectations,then there would be no bubbles.and sho ddressed n the it s in which t ort-lived twice experienced in asset market trading. xperienced,or there is some with it. This content downle a20g2016o61s4UTC org/term
Harrison and List: Field Experiments selection bias.28 They conducted a field experiment in the homes of the volunteer subjects, examining electricity demand in response to changes in prices, weekly feed- back on usage, and energy conservation information. They also examined a compar- ison sample drawn from the same popula- tion, to check for any biases in the volunteer sample. Binswanger (1980, 1981) conducted experiments eliciting measures of risk aver- sion from farmers in rural India. Apart from the policy interest of studying agents in developing countries, one stated goal of using artefactual field experiments was to assess risk attitudes for choices in which the income from the experimental task was a substantial fraction of the wealth or annual income of the subject. The method he devel- oped has been used recently in conventional laboratory settings with student subjects by Charles Holt and Susan Laury (2002). Burns (1985) conducted induced-value market experiments with floor traders from wool markets, to compare with the behav- ior of student subjects in such settings. The goal was to see if the heuristics and deci- sion rules these traders evolved in their natural field setting affected their behavior. She did find that their natural field rivalry had a powerful motivating effect on their behavior. Vernon Smith, G. L. Suchanek, and Arlington Williams (1988) conducted a large series of experiments with student subjects in an "asset bubble" experiment. In the 22 experiments they report, nine to twelve traders with experience in the double-auc- tion institution traded a number of fifteen or thirty period assets with the same com- mon value distribution of dividends. If all subjects are risk neutral and have common price expectations, then there would be no 28 They also have a discussion of the role that these pos- sible biases play in social psychology experiments, and how they have been addressed in the literature. And either inexperienced, once experienced, or twice experienced in asset market trading. reason for trade in this environment.30 The major empirical result is the large number of observed price bubbles: fourteen of the 22 experiments can be said to have had some price bubble. In an effort to address the criticism that bubbles were just a manifestation of using student subjects, Smith, Suchanek, and Williams (1988) recruited nonstudent sub- jects for one experiment. As they put it, one experiment "... is noteworthy because of its use of professional and business people from the Tucson community, as subjects. This market belies any notion that our results are an artifact of student subjects, and that busi- nessmen who 'run the real world' would quickly learn to have rational expectations. This is the only experiment we conducted that closed on a mean price higher than in all previous trading periods" (p. 1130-31). The reference at the end is to the observation that the price bubble did not burst as the finite horizon of the experiment was approaching. Another notable feature of this price bubble is that it was accompanied by heavy volume, unlike the price bubbles observed with experienced subjects.31 Although these subjects were not students, they were inexperienced in the use of the double auction experiments. Moreover, there is no presumption that their field expe- rience was relevant for this type of asset market. 30 There are only two reasons players may want to trade in this market. First, if players differ in their risk attitudes then we might see the asset trading below expected divi- dend value (since more-risk-averse players will pay less- risk-averse players a premium over expected dividend value to take their assets). Second, if subjects have diverse price expectations, we can expect trade to occur because of expected capital gains. This second reason for trading (diverse price expectations) can actually lead to contract prices above expected dividend value, provided some sub- ject believes that there are other subjects who believe the price will go even higher. 31 Harrison (1992b) reviews the detailed experimental evidence on bubbles, and shows that very few significant bubbles occur with subjects who are experienced in asset market experiments in which there is a short-lived asset, such as those under study. A bubble is significant only if there is some nontrivial volume associated with it. 1021 This content downloaded from 218.106.182.180 on Sat, 11 Jun 2016 06:18:54 UTC All use subject to http://about.jstor.org/terms
1022 Journal of Economic Literature,Vol.XLII(December 2004) Artefactual field have tasks ma ol sub lab. Th ts provide sup augh and port for t notion rbaugh e,an Harbaugh. experience does appear tocarry over toom Timothy Berry (2001) parable settings,at least with respect to Krause,and Lise Vesterlund(2002)explore these types of auctions other-regarding preferences,indivic ua This experimental design emphasizes the rationality,and risk attitudes among children identification of a naturally occurring setting in school environments. in which one can control for experience in Joseph Henrich(2000)and Henrich and the way that it is accumulated in the field Richard McElreath (2002),and Henrich et Experienced traders gain experience ove al.(2001,2004)have even taken artefactual time by observing and surviving a relatively field experiments to the true“wilds”ofa wide range of trading circumstances.In number of peasant societies.emploving the some settings this might be proxied by the procedures of cultural anthropology to manner in which expe rienced or s recruit and instruct subjects and conduct rienced subjects are defined in the lab.but it artefactual field exne nents.Their focus emains on estion whether standard was on the ultimatum bargaining game and reliably capture the full measures of risk aversion extent of the field counte art ofe This is not a criticism of exp experiments iust their do ain of a 5.Framed Field Experiments draw is that 5.1 The Nature of the Information Subjects should be Alreadu Hav the evide nner's curse by rich set of the fed dictio 6 cont salien find ional sports-carc experiments s not predi common-va iction theo fall prey to th they point to a more fundamental need to only consider the field context of experiments winners curse Onl uper-ex before drawing general conclusions.It is not subjects,wh are in fact recruited on the the case that abstract.context-free experi basis of not having lost money in previou ments provide more general findings if the experiments,avoid it regularly.This would context itself is relevant to the seem to suggest that experience is a suffi of subiects cient condition for an individual bidder to expect such context-free experiments to be avoid the winner's curse.Harrison and list unusually tough tests of economic theory (2003)show that this implication is support- since there is no control for the context that ed when one considers a natural setting in subjects might themselces impose on the which it is relatively easy to identify traders abstract experimental task. that are more or less experienced at the task The main result is that if one wants to In their experiments the experie of suh conclusions about the validity of theor iects is either tied to the cor modity.the val in the field,then one r attention uation task,and the use of auction ns(in the riad of w which field ents with s ports c ards) or sim We belie that se of auctio (in the lab al lab conventio nts with induced values). In assigne defined in This content downl
Journal of Economic Literature, Vol. XLII (December 2004) Artefactual field experiments have also made use of children and high school sub- jects. For example, William Harbaugh and Kate Krause (2000), Harbaugh, Krause, and Timothy Berry (2001), and Harbaugh, Krause, and Lise Vesterlund (2002) explore other-regarding preferences, individual rationality, and risk attitudes among children in school environments. Joseph Henrich (2000) and Henrich and Richard McElreath (2002), and Henrich et al. (2001, 2004) have even taken artefactual field experiments to the true "wilds" of a number of peasant societies, employing the procedures of cultural anthropology to recruit and instruct subjects and conduct artefactual field experiments. Their focus was on the ultimatum bargaining game and measures of risk aversion. 5. Framed Field Experiments 5.1 The Nature of the Information Subjects Already Have Auction theory provides a rich set of pre- dictions concerning bidders' behavior. One particularly salient finding in a plethora of laboratory experiments that is not predicted in first-price common-value auction theory is that bidders commonly fall prey to the winner's curse. Only "super-experienced" subjects, who are in fact recruited on the basis of not having lost money in previous experiments, avoid it regularly. This would seem to suggest that experience is a suffi- cient condition for an individual bidder to avoid the winner's curse. Harrison and List (2003) show that this implication is support- ed when one considers a natural setting in which it is relatively easy to identify traders that are more or less experienced at the task. In their experiments the experience of sub- jects is either tied to the commodity, the val- uation task, and the use of auctions (in the field experiments with sports cards), or sim- ply to the use of auctions (in the laboratory experiments with induced values). In all tasks, experience is generated in the field and not the lab. These results provide sup- port for the notion that context-specific experience does appear to carry over to com- parable settings, at least with respect to these types of auctions. This experimental design emphasizes the identification of a naturally occurring setting in which one can control for experience in the way that it is accumulated in the field. Experienced traders gain experience over time by observing and surviving a relatively wide range of trading circumstances. In some settings this might be proxied by the manner in which experienced or super-expe- rienced subjects are defined in the lab, but it remains on open question whether standard lab settings can reliably capture the full extent of the field counterpart of experience. This is not a criticism of lab experiments, just their domain of applicability. The methodological lesson we draw is that one should be careful not to generalize from the evidence of a winner's curse by student subjects that have no experience at all with the field context. These results do not imply that every field context has experienced sub- jects, such as professional sports-card deal- ers, that avoid the winner's curse. Instead, they point to a more fundamental need to consider the field context of experiments before drawing general conclusions. It is not the case that abstract, context-free experi- ments provide more general findings if the context itself is relevant to the performance of subjects. In fact, one would generally expect such context-free experiments to be unusually tough tests of economic theory, since there is no controlfor the context that subjects might themselves impose on the abstract experimental task. The main result is that if one wants to draw conclusions about the validity of theory in the field, then one must pay attention to the myriad of ways in which field context can affect behavior. We believe that convention- al lab experiments, in which roles are exoge- nously assigned and defined in an abstract 1022 This content downloaded from 218.106.182.180 on Sat, 11 Jun 2016 06:18:54 UTC All use subject to http://about.jstor.org/terms
Harrison and List:Field Experiments 1023 manner,cannot ubiquitously provide reliable rather than abstract commodities,is not insights into field behavior.One might be unique to the field,nor does one have to able to modify the lab experimental design to eschew experimenter-induced valuations in mimic those field contexts more reliably.and the field.But the use of real goods does have that would make for a more robust applica consequences that apply to both lab and tion of the experimental method in gen field experiments.32 Consider as an example.the effect of Abstraction Requires Abstracting.One "insiders'” on the market simple the To r of Hanoi known as the "winner's curs For define an insider nation than othe If insiders er market who has bete Snd H simon 1974 andJ.R.Hays m200 (Tanga ting exper rma This leads orm of the game,as to t gen mark do ins and in Judea Pear rl(1984,p.28),is shown in 's curs Second,does th figure I presence he top picture shows the initial state,in curse for the market which r are by Harrison and the goal state in the bottom picture.The naturally occurring settings in which the fac constraints are that only one disk may be tors that are at the heart of the theory are moved at a time.and no disk may ever lie identifiable and arise endogenously, and under a bigger disk.The objective is to reach then to impose the remaining controls need the goal state in the least number of moves ed to implement a clean experiment.In othe The“trick”to solving the Tower of Hanoi is words,rather than impose all controls exoge to use backwards induction:visualize the nously on a convenience sample of colle final,goal state and use the constraints to fig ure out what the penultimate state mus have looked like(viz.,the tiny disk on the top naturally.where it can be identified easily and then add the necessary controls.To test e their methodological hypotheses,they also from that ultimate state implement a fully co trolled labor the cons ts (viz the experi t with ts dra from the 3 in the ould have to b pobelow their findings We discuss someo lation. or peg 2 the sr 5.2 The Nature of the Commodity th clea der for the third largest disko Many field experim ents involve real.phys ff peg 3,one of peg on pe have to ical com odities and the values that subje be cl d,so th est should be on place on them in th eir daily lives.This is dis top of the second smal est disk) tinct from the traditional focus in experi Observation of students in Montessori mental economics on experimenter-induced classrooms makes it clear how they (eventu valuations on an abstract commodity,often ally)solve the puzzle.when confronted with referred to as"tickets"just to emphasize the lack of any field referent that might suggest 32e.日 Ronald Harstad,and Rutstrom (2004 a valuation.The use of real commodities, for a general treatment. This content downlo
Harrison and List: Field Experiments manner, cannot ubiquitously provide reliable insights into field behavior. One might be able to modify the lab experimental design to mimic those field contexts more reliably, and that would make for a more robust applica- tion of the experimental method in general. Consider, as an example, the effect of "insiders" on the market phenomenon known as the "winner's curse." For now we define an insider as anyone who has better information than other market participants. If insiders are present in a market, then one might expect that the prevailing prices in the market will reflect their better information. This leads to two general questions about market performance. First, do insiders fall prey to the winner's curse? Second, does the presence of insiders mitigate the winner's curse for the market as a whole? The approach adopted by Harrison and List (2003) is to undertake experiments in naturally occurring settings in which thefac- tors that are at the heart of the theory are identifiable and arise endogenously, and then to impose the remaining controls need- ed to implement a clean experiment. In other words, rather than impose all controls exoge- nously on a convenience sample of college students, they find a population in the field in which one of the factors of interest arises naturally, where it can be identified easily, and then add the necessary controls. To test their methodological hypotheses, they also implement a fully controlled laboratory experiment with subjects drawn from the same field population. We discuss some of their findings below. 5.2 The Nature of the Commodity Many field experiments involve real, phys- ical commodities and the values that subjects place on them in their daily lives. This is dis- tinct from the traditional focus in experi- mental economics on experimenter-induced valuations on an abstract commodity, often referred to as "tickets" just to emphasize the lack of any field referent that might suggest a valuation. The use of real commodities, rather than abstract commodities, is not unique to the field, nor does one have to eschew experimenter-induced valuations in the field. But the use of real goods does have consequences that apply to both lab and field experiments.32 Abstraction Requires Abstracting. One simple example is the Tower of Hanoi game, which has been extensively studied by cognitive psychologists (e.g., J. R. Hayes and H. A. Simon 1974) and more recently by economists (Tanga McDaniel and Rutstr6m 2001) in some fascinating experi- ments. The physical form of the game, as found in all serious Montessori classrooms and in Judea Pearl (1984, p. 28), is shown in figure 1. The top picture shows the initial state, in which n disks are on peg 1. The goal is to move all of the disks to peg 3, as shown in the goal state in the bottom picture. The constraints are that only one disk may be moved at a time, and no disk may ever lie under a bigger disk. The objective is to reach the goal state in the least number of moves. The "trick" to solving the Tower of Hanoi is to use backwards induction: visualize the final, goal state and use the constraints to fig- ure out what the penultimate state must have looked like (viz., the tiny disk on the top of peg 3 in the goal state would have to be on peg 1 or peg 2 by itself). Then work back from that penultimate state, again respecting the constraints (viz., the second smallest disk on peg 3 in the goal state would have to be on whichever of peg 1 or peg 2 the smallest disk is not on). One more step in reverse and the essential logic should be clear (viz., in order for the third largest disk on peg 3 to be off peg 3, one of peg 1 or peg 2 will have to be cleared, so the smallest disk should be on top of the second-smallest disk). Observation of students in Montessori classrooms makes it clear how they (eventu- ally) solve the puzzle, when confronted with 32 See Harrison, Ronald Harstad, and Rutstrom (2004) for a general treatment. 1023 This content downloaded from 218.106.182.180 on Sat, 11 Jun 2016 06:18:54 UTC All use subject to http://about.jstor.org/terms