Retradng, producton, and asset market performance Steven D. Gjerstad, Davd Porter, Vernon L. Smth 1, and Abel Wnn Economc Scence Insttute, Argyros School of Busness and Economcs, Chapman Unversty, Orange, CA 92866 Contrbuted by Vernon Smth, August 31, 2015 (sent for revew June 8, 2015; revewed by Gunduz Cagnalp and Charles N. Noussar) Pror studes have shown that traders quckly converge to the prce quantty equlbrum n markets for goods that are mmedately consumed, but they produce speculatve prce bubbles n resalable asset markets. We present a stock-flow model of durable assets n whch the exstng stock of assets s subject to deprecaton and producers may produce addtonal unts of the asset. In our laboratory experments nexperenced consumers who can resell ther unts dsregard the consumpton value of the assets and compete vgorously wth producers, depressng prces and producton. Consumers who have frst partcpated n experments wthout resale learn to heed ther consumpton values and, when they are gven the opton to resell, trade at equlbrum prces. Reproducblty s therefore the most natural and most effectve treatment for suppresson of bubbles n asset market experments. durable assets stock-flow markets specalzaton of trade asset market bubbles Contrary to ratonal theory the frst asset market experments wth complete common nformaton on fundamental value exhbted unexpectedly strong tendences to yeld prce bubbles (1). The results, however, were soon extended (2, 3), ndependently replcated (4 8), and have qute mportant consequences for mproved understandng of the sources of nstablty n the economy (9 11). In contrast wth these robust asset market fndngs, earler experments had establshed that repeated trade across tme perods n statc supply and demand experments yelded effcent rapd convergence to ratonal compettve equlbrum outcomes under strctly prvate decentralzed nformaton (12). In the supply and demand experments, however, trades were for mmedate consumpton, as wth hamburgers and harcuts; as noted n ref. 13, tems could not be retraded and ndvduals knew n advance that they were specalzed as buyers or sellers and could not swtch roles dependng on prce as n asset markets. [These features also characterze nondurable goods and servces n the US natonal accounts and represent approxmately 75% of prvate product. Instablty n the US natonal accounts arses from the remanng 25% (11)]. Motvated by the glarng contrast n these two knds of markets, Dckhaut et al. (13) reformulated the tradtonal supply and demand envronment by explctly modelng two goods: cash as a means of payment and a commodty that had a heterogeneous end-of-perod dvdend consumpton yeld value. Ths formulaton exactly parallels the asset tradng envronment, except that cash and commodty endowments have only a oneperod lfe and dvdends are not common. Indvdual subjects receved dverse endowments, but n each of 10 perods a subject was endowed wth the same amounts of cash and commodty, thus nducng pure statc supply and demand condtons across 10 perods. Ths reformulated framework allowed the study of convergence n a 2 2 desgn, (retrade, no retrade) (low cash, hgh cash). Convergence was markedly slower n retrade vs. no retrade because traders who could retrade had dffculty learnng from market prces ther optmal role as buyers or sellers. Hgh cash exacerbated ths dffculty relatve to low cash, n lne wth prevous fndngs (14). Haruvy et al. (ref. 15, p. 7) observe that because durable goods can be retraded they carry an mplct opton value for resale at a hgher or lower prce dependng on ndvdual expectatons. [Harrson and Kreps (16) also demonstrated ths possblty n a theoretcal model.] A pershable good has only consumptve utlty value, f purchased, whereas a durable good wll yeld consumptve value f retaned, but a resale value f not. Thus, durable goods can nvolve a speculatve motve whereas nondurables cannot. It s ths speculatve motve that has drven prce bubbles n studes of asset markets. Prevous studes have modeled a durable asset whose lfe extends over the entre horzon of the experment; n those studes unlke house or automoble markets, for example no new unts were produced and exstng unts dd not deprecate durng the course of the experment. [However, Haruvy et al. (15) study a securtes market subject to external nterventons to repurchase exstng shares that reduce the asset stock, or ssue new shares that ncrease the stock.] In ths paper we model producers who at prvate unt cost may elect to sell newly produced unts that add to the exstng stock; also, we ntroduce an elementary replacement demand for asset unts: The exstng unts deprecate wth a constant probablty, ndependent of age and prce. Hence, there s a net addton (or loss) of asset unts n the market dependng on whether producton s greater than or less than the deprecaton rate. We set the stage for expermental studes of asset market tradng characterzed by dynamc stock-flow trajectores over tme wth the stock determned endogenously. [Abstract general stock-flow models were ntroduced by Clower (17) for captal asset prcng and Smth (18) for the theory of the frm.] In our new experments we fnd that resale nhbts prce dscovery, whch n turn dstorts producton and retards effcency. However, whereas resale has generated prce bubbles n asset markets wthout producton, n our asset markets resale suppresses prces well below equlbrum. Ths s because many consumers fal to specalze as buyers, and nstead compete wth producers as sellers. When we rerun the resale experments wth subjects who are experenced as specalzed buyers and sellers n the no-resale treatment prces and producton converge to equlbrum and effcency mproves. Reproducblty s therefore the most natural and most effectve treatment Sgnfcance We conduct the frst expermental study to our knowledge of producton and trade n a stock-flow market for durable assets. When nexperenced consumers are allowed to resell assets they compete wth producers and depress prces, dsruptng producton and causng neffcency. Consumers wth experence specalzng as buyers compete less vgorously, whch allows prces and producton to converge to equlbrum. Author contrbutons: S.D.G., D.P., and V.L.S. desgned research; A.W. performed research; S.D.G., D.P., and V.L.S. contrbuted new reagents/analytc tools; A.W. analyzed data; and S.D.G., D.P., V.L.S., and A.W. wrote the paper. Revewers: G.C., Unversty of Pttsburgh; and C.N.N., Tlburg Unversty. The authors declare no conflct of nterest. Freely avalable onlne through the PNAS open access opton. 1 To whom correspondence should be addressed. Emal: vsmth@chapman.edu. ECONOMIC SCIENCES www.pnas.org/cg/do/10.1073/pnas.1517038112 PNAS November 24, 2015 vol. 112 no. 47 14557 14562
for suppresson of bubbles n asset market experments. [Hong et al. (19) develop a theoretcal model n whch release of locked up shares can suppress a prce bubble followng an ntal publc offerng.] Theoretcal Model Our model of a reproducble durable asset has several key elements. Frst, asset unts provde use value to ther owners, whch we refer to as dvdends. Dvdends represent the stream of servces to an owner occupyng hs home or the rental stream to a landlord. The asset yelds a dvdend but also has some persstence. Deprecaton s a common feature of durable assets, ncludng resdental, commercal, and ndustral structures. We assume that an asset unt deprecates wth probablty μ, ndependent of ts age. (As a result of ths dealzaton unts are homogeneous.) If μ > 0 then the dvdends receved from an asset unt have a fnte expected value, whch we assume represents ts value to a consumer. Indvdual demand s functonally determned from the unt values to a consumer, and market demand s the aggregaton of the ndvdual demands. Theoretcally, prce at any tme s determned from the condton that the market demand s equal to the supply, whch s the current stock of unts avalable. Supplers can proftably sell newly produced unts f ther cost s below the market prce. The total produced less the loss from deprecated unts s the ncrement to the stock of asset unts n the subsequent perod. These elements consttute the model, formally descrbed below. Asset Lfe. We assume that at tmes t = 1, 2, 3,... an asset unt deprecates wth probablty μ. The probablty that a unt deprecates s ndependent for each unt. In partcular, t does not depend upon the tme perod a unt was produced. Dvdends. We assume that consumer receves a dvdend d ðjþ ðtþ for the j th unt that owns n perod t. In our experments unt j yelds a constant dvdend n each perod that t s owned by consumer, so we suppress the tme varable and denote the dvdend by d ðjþ. An asset purchased or held at tme t pays a dvdend at tme t wth certanty, but mmedately after the dvdend s pad t deprecates wth probablty μ. The probablty that the asset unt pays a dvdend n perod t + 1s1 μ, so ts expected value n the next tme perod s ð1 μþd ðjþ. The probablty that the asset unt lasts from perod t untl at least perod t + k sð1 μþ k, so at tme t the expected value of the dvdends from the asset unt n perod t + k s ð1 μþ k d ðjþ. The expected value of the asset unt servces from perod t onward s V ðjþ ðtþ = X ð1 μþ k d ðjþ k=0. = d ðjþ μ. [1] Because the value of unt j for consumer does not depend on the tme when t s purchased, we wrte V ðjþ = d ðjþ =μ. We also assume that d ðjþ d ðj+1þ for all j because a consumer wll put the frst unt purchased to ts most valuable use. Demand and Asset Stock. If consumers have the per-perod dvdends and average lfetme dvdends shown n Table 1 then P = D 1 (Q) = 235 2.5 * Q s a lnear approxmaton to the market nverse demand functon. In ths case Q = D(P) = 94 0.4 * P s a lnear approxmaton to the market demand. The theoretcal market prce s determned from the demand and the stock of asset unts. Fg. 1 shows an example market demand D(P) = 94 0.4 * P and a stock of X(0) = 22 asset unts. The equlbrum prce n ths market s determned from X(0) = D(P*) so P* = 180. All of these elements are shown n Fg. 1, Left. Producers Costs and Market Supply. In our experment μ = 0.2 so that on average 20% of the asset stock deprecates n tme t. Wth the costs shown n Table 1, the market nverse supply functon s approxmated by P = S 1 (Q) = 15 * Q + 15, so market supply s approxmated by Q = S(P) = P/15 1. Wth the shortrun equlbrum prce of P* = 180 producers wll add Q* = 11 unts to the market. Because μ = 0.2, 4.4 unts can be expected to deprecate. Hence, 6.6 unts are added to the stock of assets, as shown n Fg. 1, Rght. Steady State. Producton and deprecaton at tme t determnes the asset stock at tme t + 1. Ths results n a new short-run equlbrum prce, producton and deprecaton at t + 1, determnng the asset stock at t + 2. The process reaches a steady state f t exsts that s characterzed by the condtons XðtÞ = DðP p Þ and SðP p Þ = μxðtþ. That s, the prce s set where demand ntersects the stock of asset unts and at ths prce producton replaces the unts that deprecate. Gven the parameters n Table 1 and a deprecaton rate of 20%, the steady state occurs wth an asset stock of 40 unts. The resultng prce of 135 would elct 8 unts of producton, exactly offsettng the 20% deprecaton of the 40 unts of stock. Table 1. Induced values and costs for consumers and producers Type 1 producers Type 2 producers Type 1 consumers Type 2 consumers Unt Producton cost Producton cost Dvdend per perod Average lfetme dvdend Dvdend per perod Average lfetme dvdend 1 30 60 46 230 44 220 2 120 90 42 210 40 200 3 150 180 38 190 36 180 4 240 210 34 170 32 160 5 30 150 28 140 6 26 130 24 120 7 22 110 20 100 8 18 90 16 80 9 0 0 0 0 In our experments each consumer had a carryng capacty of nne unts; each producer could produce up to four unts per perod. The probablty of deteroraton after a gven perod was 0.2, so a unt had an expected lfetme of fve perods. 14558 www.pnas.org/cg/do/10.1073/pnas.1517038112 Gjerstad et al.
Fg. 1. Unt stocks and flows from a sample envronment. If we assume that n tme perod 0 the ntal stock s 22 unts, the equlbrum prce n that perod wll be P 0 * = 180. Ths prce elcts 11 unts of producton, and 20% of the ntal stock deterorates. The resultng ncrement to the stock s 6.6 unts, whch s shown by the short dashed lnes (Rght). The process s terated; n the lmt the process reaches a steady state wth a stock of 40 unts. The prce of 135 elcts 8 unts of producton, whch s exactly offset by 20% deprecaton of the 40 unts of stock. Experment Desgn We tested our durable goods model under two treatment condtons, both of whch used a double aucton to medate trade. In the baselne treatment (BL) we suppressed the asset unts opton rsk by requrng unts that were purchased n the BL to be held untl they deprecated. In the resale treatment (RS) we allowed consumers to freely resell ther unts to one another. Producers were not allowed to purchase unts n ether treatment; speculaton could occur only among consumers. In our RS treatment the resale opton rsk hndered prces from convergng to equlbrum and degraded market effcency. We then conducted addtonal sessons under the RS condton usng partcpants wth pror experence n the BL. We refer to these sessons as resale wth experence (RSX). Experment Parameters. The laboratory experments mplement the dscrete approxmated supply and demand functons shown n Table 1. Our approxmatons preserve the long-run equlbrum prce, stock, and flow predctons descrbed above. We allocated holdng values and producton costs among eght consumers and four producers. Induced costs and values were descrbed n terms of experment currency unts (ECUs). (The exchange rate for ECUs to dollars was 75 to 1 for consumers and 50 to 1 for producers.) All experment sessons lasted 16 perods, each consstng of a producton phase followed by a tradng phase. The producers had 30 s to decde how many unts to produce, wth a maxmum of four unts each. Producers who dd not fnalze ther producton decson wthn the tme lmt produced no unts for that perod. Producers nventores carred over, so that f a unt went unsold n the perod n whch t was produced t could be sold n a subsequent perod. Unts n nventory dd not deprecate. At the outset of the experment every producer was endowed wth startng captal of 520 ECUs, allowng each to produce up to three unts. Funds for addtonal producton had to be earned by sellng unts. The 520 ECUs were reclamed from a producer s earnngs at the end of the sesson. The duraton of the tradng phase vared by perod. For the frst fve perods subjects had 3 mn to execute ther trades. As subjects ganed experence wth the tradng process the duraton was reduced to 2.5 mn for perods 6 10 and reduced agan to 2 mn thereafter. We descrbed a unt s consumpton value to the consumers as a dvdend that t would pay them at the end of each perod untl t deprecated (or was sold n the RS and RSX). Every asset unt had probablty μ = 0.2 of deteroratng per perod and dd not deprecate untl after t had earned ts dvdend for the perod. (Unts deprecated ndependently; more or less than 20% of unts could deprecate n a perod.) Consequently, all unts had an expected lfetme of fve perods and the expected earnngs from holdng a unt was fve tmes ts dvdend per perod. We descrbed these expected earnngs to the consumers as a unt s average lfetme dvdend (ALD). Rsk-neutral consumers wth no speculatve motve should not be wllng to pay any more than the ALD for an asset unt. (In the resale treatments, they should not be wllng to accept less than the ALD for a unt.) Unts that had not deprecated by the end of perod 16 contnued to pay dvdends through a number of perods that contnued untl all unts had deprecated. Ths ensured that a unt s ALD dd not dmnsh n the last few perods of the experment. Durng these smulatons, producton and trade dd not occur. The only actvty was the payment of dvdends and the usual probablstc decay of asset unts. The consumers receved an ncome of 400 ECUs per perod, whch they could use to buy unts. In our model agents splt consumpton between the durable asset and a composte commodty; they do not carry cash holdngs across tme perods. We mplemented ths n the experments by sequesterng all dvdends, unspent ncome, and cash earned from resale (n the RS and RSX) at the close of the tradng phase. The sequestered amount was added to a consumer s total earnngs, whch was vsble on her computer screen. We subtracted 6,000 ECUs that s, ther cash ncome for 15 of the 16 tradng perods from ther total earnngs at the end of the experment. Ths ensured that the majorty of earnngs came from actvty n the asset market rather than from passvely collectng ncome. The producers cost schedules are presented n the second and thrd columns of Table 1. The four producers were splt evenly nto two types. Type 1 producers had a cost advantage on ther frst and thrd unts, whereas type 2 s had a cost advantage on ther second and fourth unts. The ffth and seventh columns of Table 1 contan the consumers value schedules. The eght consumers were also splt evenly nto two types. Type 1 consumers dvdends were 2 ECUs Table 2. Results of random effects regresson models of consumers share of sales and percent of resales that were surplus-enhancng Independent varable Consumers sales share, coeffcent (SE) % Effcent resale, coeffcent (SE) Constant 0.840*** (0.030) 0.535*** (0.033) RSX 0.280*** (0.054) 0.113 (0.076) Perod 0.021*** (0.002) 0.007* (0.003) RSX perod 0.001 (0.004) 0.005 (0.006) Observatons 208 207 Wald χ 2 180.09 33.97 R 2 0.5911 0.1434 Sgnfcant at 10%, *5%, **1%, or ***0.1%. ECONOMIC SCIENCES Gjerstad et al. PNAS November 24, 2015 vol. 112 no. 47 14559
Table 3. Results of random effects regresson models of prce devaton from the short-run equlbrum, producton devaton from the optmal response, producton effcency, and trade effcency Independent varable Prce devaton, coeffcent (SE) Producton, coeffcent (SE) Producton effcency, coeffcent (SE) Trade effcency, coeffcent (SE) Global effcency, coeffcent (SE) Constant 27.40* (11.09) 9.13*** (0.44) 0.846*** (0.027) 0.787*** (0.048) 0.667*** (0.049) RS 71.99*** (15.68) 3.24*** (0.63) 0.060 (0.038) 0.155* (0.068) 0.091 (0.069) RSX 37.07 (19.99) 2.50** (1.07) 0.116* (0.048) 0.019 (0.086) 0.074 (0.088) Perod 0.008*** (0.001) 0.005 (0.004) 0.011** (0.004) RS perod 0.017*** (0.002) 0.012* (0.006) 0.22*** (0.005) RSX perod 0.007** (0.002) 0.003 (0.008) 0.009 (0.007) Log(perod) 22.64*** (5.49) 0.88** (0.32) RS log(perod) 8.04 (7.77) 0.57 (0.45) RSX log(perod) 23.21* (9.90) 1.77** (1.23) No. of observatons 352 352 330 330 330 Wald χ 2 80.20 89.12 96.35 47.25 56.22 R 2 0.5311 0.5544 0.3296 0.2532 0.3470 Sgnfcant at 10%, *5%, **1%, or ***0.1%. hgher than type 2 s for all unts except for unt 9, whch was worth 0 to both types. The nnth unt allowed for the possblty of purely speculatve purchases n the RS and RSX. In the frst perod we endowed half of the consumers (two of each type) wth seven unts and the other half wth sx unts. Ths generated an ntal asset stock of 52 unts, 12 more than the long-run equlbrum. Consequently, the short-run equlbrum prces were predcted to ncrease as the excess unts deprecated. Ths allows us to test the ablty of traders to track the short-run equlbrum and acheve the long-run steady state. Increasng prces n the early rounds also presented the possblty of nducng a speculatve prce bubble n the RS and RSX by encouragng consumers to expect the prces to contnue to rse. Methods. The subjects nteracted va computers separated by prvacy dvders. They frst read through nteractve nstructons on ther screens explanng the rules of the experment and ther user nterface. After completng the nstructons the subjects partcpated n a sngle practce perod that dd not affect ther earnngs or unt holdngs durng the actual experment. We conducted nne sessons of both the BL and RS treatments, and four sessons of the RSX. The subject sample conssted of 264 undergraduate and graduate students from Chapman Unversty who were recruted at random from a database of 2,000. Asde from the RSX no subjects partcpated n more than one sesson. In addton to earnngs based on ther decsons we pad subjects $7 for attendng the BL and RS sessons and $15 for attendng the RSX. (The hgher RSX attendance payment was to encourage partcpaton due to the smaller pool of potental partcpants.) The average decson-based earnngs were $27.81 n the BL, $23.02 n the RS, and $26.35 n the RSX. Results We examne dfferences n resale between the RS and RSX treatments, as well as the performance of all treatments on convergence to the equlbrum prce and producton levels, and effcency. We analyze the data wth a set of random effects regresson models. For resale the dependent varables are a treatment dummy for the RSX, a tme trend varable, and an nteracton of the tme trend and treatment dummy (Table 2). For prces, producton, and effcency the dependent varables are treatment dummes for the RS and RSX, a tme trend varable, and nteractons of the tme trend wth each treatment dummy (Table 3). The prce and producton data showed nonlnear convergence, so the regresson models for these data use the log of the perod for the tme trend. Trader performance changed wth experence and the estmated tme trends are often dfferent across treatments, so we calculated the model estmates for each treatment n each perod and used Wald tests to compare these estmates across treatments and/or to theoretcal predctons. We report the results of these tests where approprate. Result 1. There was less resale n RSX than RS, and resale n the RSX ncreased effcency more frequently. Resale could enhance welfare by reallocatng unts from consumpton values below the market clearng prce to values above t. We analyze consumer resale wth two metrcs: the percent of all trades n a perod n whch a consumer was the seller (.e., consumers sales share) and the percent of resale n a perod n whch the buyng consumer valued the unt more hghly than the sellng consumer (.e., effcent resale rate). Our regresson model demonstrates that consumers n the RS faled to optmally specalze as buyers, nstead competng as sellers wth the producers. The estmated constant ndcates that at the start of the RS treatment consumers were the sellers n 84% of all trades (P < 0.001). Consumers who were experenced n the BL were more specalzed as buyers. The RSX dummy ndcates that the consumers sales share was 28 percentage ponts lower at the start of RSX than n the RS (P < 0.001). The man tme trend estmate s 0.021 (P < 0.001), ndcatng that consumers became more specalzed over tme n the RS. However, experence had the same effect n the RSX. The tme trend nteracton term s statstcally nsgnfcant (P = 0.509). Resale was more effcent when the consumers were experenced. Our regresson model estmates that the ntal rate of effcent resale n the RS was 53.5%. Ths s not sgnfcantly Fg. 2. Average devaton of prce from the short-run equlbrum by treatment., BL;, RS;, RSX. 14560 www.pnas.org/cg/do/10.1073/pnas.1517038112 Gjerstad et al.
Fg. 3. Producton levels by treatment. In the steady-state equlbrum eght unts are produced., BL;, RS;, RSX. hgher than 50%, the rate we would expect f consumers n the RS resold ther unts at random (Wald test, P = 0.357). The estmated coeffcent of the RSX dummy s postve and ndcates an ntal effcent resale rate of 64.8%. Ths estmate s only margnally sgnfcant compared wth the RS (P = 0.061), but experenced consumers outperformed random resale. A Wald test rejects the null hypothess that the sum of the constant term and the RSX dummy equals 50% (P = 0.003). Moreover, resale became less effcent over tme n the RS, whereas t remaned constant n the RSX. The estmated man tme trend ndcates that effcent resale fell by 0.7 percentage ponts per perod n the RS (P = 0.046). In contrast, a Wald test cannot reject the null hypothess that the sum of the man tme trend and ts nteracton wth the RSX dummy s sgnfcantly dfferent from zero (P = 0.747). Our statstcal analyss gves us strong confdence that consumers were more focused on the consumpton value of ther unts n the RSX than n the RS and consequently captured more gans from exchange. Ths affected prce and producton convergence, as well as effcency, as we demonstrate n the three remanng results. Result 2. Prcesconvergedtotheshort-runequlbrumntheBL and RSX but dverged from t n the RS. The short-run equlbrum prces and producton levels are temporally nterdependent because a prce (quantty) devaton from equlbrum n perod t alters the quantty (prce) equlbrum n perod t + 1. Consequently, for each perod of each sesson we calculate δp t = P t P p t,wherep t s the observed average prce and P p t s the short-run equlbrum prce. The average δp t s plotted by perod for each treatment n Fg. 2. Traders n the BL acheved the short-run equlbrum prces early n the sesson and contnued to do so throughout the sesson. In our regresson model for prce devatons the estmated constant term ndcates that prces were 27.4 ECUs above equlbrum n the frst perod (P = 0.013), and the estmated coeffcent for the tme trend s negatve and statstcally sgnfcant (P < 0.001). Wald tests reject the null hypothess that δp t = 0 for perods 1 and 2 (P 0.05) but cannot reject t for the remanng 14 perods (P > 0.1 n all cases). Smlarly, experence n the BL traned consumers to trade at short-run equlbrum prces despte the opton to resell ther unts. A Wald test cannot reject the null hypothess that the constant and RSXdummysumtozero(P = 0.561) and the estmated RSX tme trend nteracton s of approxmately equal magntude to the man tme trend varable, but of opposte sgn (β = 23.21, P = 0.019). Wald tests cannot reject the null hypothess that δp t = 0nthe RSX n any perod (P > 0.5 n all cases). The most strkng pattern n the data s the persstence of low prces n RS. The estmated coeffcent of the RS treatment dummy s negatve and of substantally greater magntude than the constant term (β = 71.99, P < 0.001), ndcatng that prces were almost 45 ECUs below the short-run equlbrum n perod 1. These prces tended to dverge further from equlbrum over tme. The sum of the man tme trend varable and the RS tme trend nteracton s negatve. Ths result s precsely the opposte of what has been observed n prevous studes of asset markets wthout producton, n whch speculatve purchases contrbuted to the formaton of prce bubbles. In the current study nexperenced consumers used ther resale opton to compete wth the producers, pushng prces well below fundamental value. [Producers made fewer unts n response to low prces, but on average consumer earnngs were hgher n the RS ($29.21) compared wth the BL ($24.15). Producer s earnngs were consderably lower n the RS ($10.63) than n the BL ($35.13).] Result 3. Producton converged to the steady state n the BL and RSX but dverged n the RS (Fg. 3). In the BL average producton of new asset unts was wthn one unt of the steady-state level of eght n all perods except perod 1. Ths was true even n early perods when the short-run equlbrum producton was below eght because unts were tradng somewhat above ther short-run equlbrum prce. The constant term n our producton regresson model estmates that producers produced 9.13 unts n the frst perod of the BL (P < 0.001). Statstcally ths s sgnfcantly greater than the steady state (Wald test, P = 0.011), but the estmated tme trend s negatve and statstcally sgnfcant (β = 0.88, P = 0.005), ndcatng convergence over tme. Wald tests reject the null hypothess that producton was at the steady state level of eght unts at the 5% level for perods 1 and 2, and at the 10% level for perod 3 (P = 0.058). In all remanng perods the tests are not statstcally sgnfcant. In RSX where prces were close to the short-run equlbrum n every perod producton started slghtly below the steady state and converged to t as prces ncreased. The RSX dummy s negatve and statstcally sgnfcant (β = 2.50, P = 0.002). The RSX nteracton wth the tme trend s postve, statstcally sgnfcant, and roughly twce the magntude of the man tme trend (β = 1.77, P = 0.002), ndcatng convergence to the steady state from below. Wald tests reject the null hypothess that producton was eght unts at the 5% level for perod 1 and at 10% for perods 2 and 3 (P = 0.059 and P = 0.089, respectvely). Perod 1 producton was smlar n the RS to the other two treatments, but as prces perssted below ther short-run equlbrum levels the producers responded wth lower levels of output. Producton fell below four unts on average by perod 4 and perssted near ths level for the remanng 12 perods. Our regresson model estmates that producers n the RS produced 3.23 fewer unts n the frst perod than producers n the BL (P < 0.001). The estmated nteracton of RS wth the tme trend s negatve but not statstcally sgnfcant (β = 0.57, P = 0.205). Thus, our model confrms that producton fell over tme n the Fg. 4. Average global effcency by treatment., BL;, RS;, RSX. ECONOMIC SCIENCES Gjerstad et al. PNAS November 24, 2015 vol. 112 no. 47 14561
RS, but not at a faster rate than n the BL. However, producton never reached the steady state n the RS. Wald tests strongly reject the null hypothess that producton was equal to eght unts for all perods of the RS (P < 0.001 n each case). Result 4. There was substantal uncaptured surplus n all treatments, but effcency was lowest n the RS. We constructed a measure of global effcency for each perod, defned as the surplus traders captured durng the perod dvded by the maxmum surplus that could have been captured f all unts had been traded to ther hghest valued uses and producers produced only those unts that could be proftably sold. We also decomposed our global effcency measure nto producton effcency and trade effcency. Producton effcency s the surplus producers made achevable n the perod through ther producton decsons dvded by the maxmum surplus. Trade effcency s the surplus that was captured n the perod dvded by the surplus that producers had made achevable. These addtonal measures allow us to pnpont the major source(s) of neffcency at the global level. (In all effcency calculatons we subtracted the dle surplus the surplus that traders would have captured f there had been no producton or trade n the perod from both the numerator and denomnator. Ths allows us to measure only the surplus that was generated by the traders decsons. In some sessons effcency was negatve n perod 1 because traders decsons destroyed surplus relatve to dong nothng.) The average global effcency by perod n each treatment s dsplayed n Fg. 4. In all treatments average effcency was negatve n perod 1. Ths was because producers had no prce sgnal from a prevous perod to gude ther decsons and generally overproduced. Moreover, the consumers unsatsfed carryng capactes were of low value n perod 1 because of ther large ntal endowments. There was a large jump n effcency n perod 2, whch was sustaned across the remanng perods. Thus, we omt perod 1 data from our statstcal analyss. Global effcency was smlar n all treatments n the ntal perods, but from perod 5 on t was substantally lower n the RS than n the BL and RSX. Between perods 5 and 16 average global effcencywas44.9%ntherscomparedwth73.4%nthebl and 74.9% n the RSX. Our regresson model estmates that global effcency was 66.7% at the begnnng of the BL (P < 0.001) and ncreased by 1.1 percentage ponts per perod (P = 0.003). The RS dummy varable s not statstcally sgnfcant (P = 0.189), but ts nteracton wth the tme trend ndcates a loss of 2.2 percentage ponts per perod relatve to the BL (P < 0.001). Wald tests ndcate that global effcency was hgher n the BL than the RS wth at least 95% confdence n perods 2 16. Nether the RSX dummy nor ts nteracton wth the tme trend s statstcally sgnfcant. Wald tests cannot reject the equalty of global effcency for any perod between the BL and RSX. Lttle of the global neffcency was due to producers. After the frst perod average producton effcency was 91.5% n the BL, 82.6% n the RS, and 96.9% n the RSX. Our regresson model estmates that producton effcency started at 84.6% n the BL (P < 0.001) and ncreased by 0.7 percentage ponts per perod (P < 0.001). The RS dummy varable n our regresson model of producton effcency s not statstcally sgnfcant (P = 0.116) but ts nteracton term ndcates that producton effcency fell by 1.7 percentage ponts relatve to the BL (P < 0.001). Ths decrease was drven by the fact that producers had unts that cost less than ther value to the consumers, but they could not be produced at a proft due to the below-equlbrum prces n the RS. Experence substantally mproved producton effcency. The regresson model estmates that producton effcency was ntally 11.6 percentage ponts hgher n the RSX relatve to the BL (P = 0.017) and that t ncreased by 0.8 percentage ponts per perod faster than the BL (P = 0.003). Trade effcency was lower than producton effcency n all treatments. The average trade effcency after perod 1 was 76.3% n the BL, 56.8% n the RS, and 78.5% n the RSX. Our regresson model estmates that trade effcency was 78.7% throughout the BL, because the estmated constant s 0.787 (P < 0.001) and the man tme trend s not statstcally sgnfcant (P = 0.218). Resale reduced trade effcency among nexperenced traders but not those experenced n the BL. The model estmates that trade effcency started 15.5 percentage ponts lower n the RS than the BL (P = 0.022) and decreased by 1.2 percentage ponts per perod relatve to the BL s tme trend (P = 0.038). Conversely, the estmated coeffcents for the RSX dummy and ts tme trend nteracton are both statstcally nsgnfcant (P 0.67 n both cases). Ths comports wth our fndngs n result 1 that consumers resold less actvely n the RSX than n the RS, and ther resales were more lkely to generate gans from trade. Concluson We present and test a stock-flow model of durable goods wth endogenous producton dstnct from standard asset market experments wth an exogenous supply of assets. We fnd that the opton to resell unts dstracts nexperenced consumers from the consumpton value of unts. However, rather than generatng speculatve prce bubbles they compete wth producers, dampenng prces, whch results n reduced producton and a concomtant loss of effcency. However, consumers who have come to understand ther role through experence wthout resale mantan a stronger focus on consumpton, leadng to equlbrum prces and producton. Resale alone although destablzng does not generate prce bubbles. Over the past quarter century, numerous real estate prce bubbles have occurred around the world, wth serous economc consequences (10, 11). Our desgn wth reproducble assets suggests that these markets should be stable unless other factors such as credt, cash nfusons, and lmtatons on producton dsrupt market equlbraton. Our experment desgn provdes a framework for tests of these factors. 1. Smth VL, Suchanek GL, Wllams AW (1988) Bubbles, crashes and endogenous expectatons n expermental spot asset markets. Econometrca 56(5):1119 1151. 2. Van Boenng MV, Wllams AW, LaMaster S (1993) Prce bubbles and crashes n expermental call markets. Econ Lett 41(2):179 185. 3. Porter DP, Smth VL (1994) Stock market bubbles n the laboratory. Appl Math Fnance 1(2):111 128. 4. Noussar C, Robn S, Ruffeux B (2001) Prce bubbles n laboratory asset markets wth constant fundamental values J. Exp Econ 4(1):87 105. 5. Le V, Noussar CN, Plott CR (2004) Non-speculatve bubbles n expermental asset markets: Lack of common knowledge of ratonalty vs. actual rratonalty. Econometrca 69(4):831 859. 6. Dufwenberg M, Lndqvst T, Moore E (2005) Bubbles and experence: An experment. Am Econ Rev 95(5):1731 1737. 7. Noussar CN (2006) Futures markets and bubble formaton n expermental asset markets. Pac Econ Rev 11(2):167 184. 8. De Martno B, O Doherty JP, Ray D, Bossaerts P, Camerer C (2013) In the mnd of the market: Theory of mnd bases value computaton durng fnancal bubbles. Neuron 79(6):1222 1231. 9. Akerlof G, Shller R (2009) Anmal Sprts (Prnceton Unv Press, Prnceton). 10. Renhart C, Rogoff K (2009) The aftermath of fnancal crses. Am Econ Rev 99(2):466 472. 11. Gjerstad S, Smth V (2014) Rethnkng Housng Bubbles (Cambrdge Unv Press, Cambrdge, UK). 12. Smth VL (1962) An expermental study of compettve market behavor. J Polt Econ 70(2):111 137. 13. Dckhaut J, Ln S, Porter D, Smth V (2012) Commodty durablty, trader specalzaton, and market performance. Proc Natl Acad Sc USA 109(5):1425 1430. 14. Cagnalp G, Porter D, Smth V (1998) Intal cash/asset rato and asset prces: An expermental study. Proc Natl Acad Sc USA 95(2):756 761. 15. Haruvy E, Noussar CN, Powell OR (2012) The mpact of asset repurchases and ssues n an expermental market. CentER Dscusson Paper, Vol. 2012-092 (Dept of Economcs, Tlburg Unv, Tlburg, The Netherlands). 16. Harrson JM, Kreps DM (1978) Speculatve nvestor behavor n a stock market wth heterogeneous expectatons. Quarterly Journal of Economcs 92(2):323 336. 17. Clower RW (1954) An nvestgaton nto the dynamcs of nvestment. Am Econ Rev 44(1):64 81. 18. Smth VL (1961) Investment and Producton (Harvard Unv Press, Cambrdge, MA). 19. Hong H, Schenkman J, Xong W (2006) Asset float and speculatve bubbles. Journal of Fnance LXI(3):1073 1117. 14562 www.pnas.org/cg/do/10.1073/pnas.1517038112 Gjerstad et al.