The Market for Sculptures: an Adjacent Year Regression Index
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The Market for Sculptures: an Adjacent Year Regression Index
The Market for Sculptures: an Adjacent Year Regression Index Marilena Locatelli-Biey Department of Economics University of Torino - Italy E-mail: [email protected] Roberto Zanola Department of Public Policy and Public Choice - Polis Corso Borsalino, 50 – 15100 Alessandria - Italy E-mail: [email protected] ABSTRACT: This paper analyses the performance of an investment in sculptures during the period 1987-1995 by applying the hedonic price technique with time dummy variables to a sample of over 27,000 sales occured at auctions. The main finding is that the trend of the rate of return on an investment in sculptures is more stable than those associated to alternative forms of investment during the analysed period. JEL Classification Numbers: C5, Z1. Key Words: Auction; Hedonic Price; Sculpture; Return. 1 Introduction Sculptureis theartofproducinginthreedimensions representations ofnatural orimagined forms anditembraces avarietyofconstruction-techniques as well as a variety ofmaterials1 . T he most importantclassi…cation ofsculpture is basedon therawmaterialused, butitis alsoimportantthesize, thefunction, and theperiodoftheproduction. T he marketforsculptures has characteristics thatmake it di¤ erent from othermarkets forcollectibles. A lthough similarto the marketforpaintings, the marketforsculptures is smallerthan it, with about3-5 per-centoftotal collectiblessoldatauctions. A numberofreasons explainthis, suchas technical di¢culties and thehigh costs ofproduction as wellas thefactthatsculptures needappropriatespacestobeplacedorbecauseofthelowernumberofsculpture collectors than paintingcollectors [L ocatelli-B ieyand Z anola, 19 9 9 a]. T hepurposeofthis paperis toexaminetheinvestmentvalueofsculptures. A lthough there areanumberofstudies thathave investigated the investment valueofcollectibles, suchaspaintings[A nderson, 19 7 4;Stein, 19 7 7 ;B uelensand G insburgh, 19 9 3; de la B arre etal., 19 9 4;Chanel, 19 9 5; Chaneletal., 19 9 6 ; M ossetto and L azzaro, 19 9 6; A gnello and P ierce, 19 9 6; Candela and Scorcu, 19 9 7 ; R enneboogand V an H outte, 19 9 8 ; A gnelloand P ierce, 19 9 8 ;L ocatelliB iey and Z anola, 19 9 9 b] , prints [P esando, 19 9 3], violins [R oss and Z ondervan, 19 8 9 ], wine [N erlove, 19 9 5; Combis et al., 19 9 7 ], antique furniture [G raeser, 1T herawmaterialdepends ontheconstructiontechnique. H andmodellinguses terracotta, orrawmaterialthatallows toproduceglazed ceramics. Castingis an ancienttechniquewhich uses bronze. Carving is performed by usinga numberofdi¤ erentmaterials, such as marble, stone, wood, ivory, bone, and, more recently, plasterand resin. 1 19 9 3], photos [P ompe, 19 9 6], toourknowledgethis itis the…rsttimethatthe performanceofsculptures as …nancialassets is studied. T his studyapplies thehedonicpricetechnique2 withtimedummyvariables which allows priceindexes forsculptures and shadowvalues forcharacteristics to be simultaneously estimated. D ata are drawn from auctions hold during the period 19 8 7 -19 9 5, as compiled by M ayerInternationalA uction R ecord on CD -R om. T heremainderofthispaperisorganisedasfollows. Section2 brie‡youtlines the methodology of the hedonic technique. Section 3 de…nes the empirical speci…cation of the model. Section 4 describes the data set used, which is compiled from M ayerInternationalA uction R ecords on CD -R om. Section 5 summarises thebasic…ndings. Conclusions aredrawn in Section 6. 2 S ee G ordon (19 9 0);G riliches (19 9 0);and T riplett(19 9 0). 2 2 M ethodology T heapproachusedtoestimateapriceindexforsculptures is thehedonicprice technique as developed in similar studies analysing the investment value of collectibles. T hehedonicapproach involves theestimateofthe implicitprices toeachcharacteristicincludedintheequationbyallowingtocontrolforpossible non-temporaldeterminants ofpricevariations. A setofj-characteristics, xjkt, withj = 1 ;:::n;areidenti…edforaregression ofthepriceofthesculpturek, withk= 1 ;:::;m, soldinyeart, witht= 1 ;:::;T ; on its j-characteristics, such that: lnpkt = ¯ 0 + TX ¡1 ¯ tzt + t=1 Xn ° jxjkt + "kt (1) j=1 wherelnpkt is thelogarithm ofthepriceofsculptures soldinyeart;zt is a dummyequalto1 when asaleoccurs in yeart, 0 otherwise;¯ 0 ;¯ t and ° j are coe¢cients tobe estimated, where ° j is the implicitprice; "kt is the random P errorterm, with "s N (0 ; k-I . T) T wo observations are necessary. First, an implicit assumption in (1) is thatthesocialvaluationofsculpturecharacteristics does notchangeovertime given the shortness ofthe analysed period. Secondly, the modelis speci…ed in semi-logtransformations in ordertohandle the severe skewness in auction prices. T ransformingthe dependentvariable, enables us touse ordinary least squares estimators withouthavingtoworryaboutthesensitivityoftheresults toskewness. B asedonhedonicregressionequation(1), anumberofpriceindexes canbe computed3. In this studyweadopttheadjacentyearregressions index, which implicitlyweights each observation equally[B erndtetal., 19 9 5] . 3In this respect, we are only considering sculptures as …nancialassets, withoutany refer- 3 B y subtractingfrom the logarithm ofthe auction price the implicitprices given tospeci…c characteristics, the characteristic-free price ofsculpture kin yeartis equalto: Xn zkt = lnpkt ¡ ° jxjkt (2) j=1 G iventhefunctionalform ofequation(1), theannualreturnona‘standardised sculpture’[B uelens and G insburg, 19 9 3]maybewritten as: ¯t = 1 X zkt mt (3) Settingthepriceindexattimetequalto1 , thepriceindexattimet+ 1 is given byexponentiatingthecoe¢cientassociated tothetimedummyvariable from adjacentyearregressions. D e…neI t thepriceindexattimet, theadjacent yearregression indexis: I t+ 1 = I t (1 + ³) b̄ b̄ where» is equaltoe( t+ 1 ¡ t)¡1 : (4) ence to their psychic returns [B aumol, 19 8 6; Frey and Eichnberger, 19 9 5; S antagata, 19 9 8 ; Czujack, 19 9 7 ] . 4 3 FunctionalForm T hehedonicregressionframeworktakes intoaccountthee¤ ectofheterogeneity on prices by controlling fora numberofdi¤ erences in characteristics among sculptures. T hedependentvariableis thelogarithm ofsaleprice, de‡ated and reduced by 15% to correctfortransaction fees charged by auction houses to sellers. T heindependentvariables areclassi…ed as follows: ²P roduction A vailabledatadonotallowustodistinguishbetweendi¤ erent schools. H owever, as suggested bysomeauctionexperts contacted byus, threedi¤ erentperiods ofproductionmaybeidenti…ed: old, forsculptures produced before 18 00; mod, forsculptures produced between 1801 and 19 30;and cont, forsculptures produced after19 31. ²N ationality U sing the frequency with which the sculptors’ nationalities appearin the data set, the following dummy variables are introduced: France, natf;U sa, natus;G ermany, natd;Italy, natit;andG reatB ritain, natgb: ²Size T hereis nostandard measureofsizeduethevarietyofconstruction techniques4. In what follows, foreach observation we use the highest dimension value(width, length, thickness), size, as aproxyforvolume. ²M edia A setofdummy variables is used: bronze, bro, and marble, mar, are the traditional raw materials used, expecially for old and modern sculptures, whileresin and plaster, res, are used in contemporary sculptures. Finally, giventhehighnumberofsculpturesofthis kind, alsoivory, ivo, and terra-cotta, ter, areconsidered. 4Forinstance, there are sculptures in the round, which can be viewed from any direction, as wellas incised relief, in which the lines are cutintoa ‡atsurface. 5 ²Salerooms and Cities of Sale Sotheby’s, soth, and Christie’s, chr; are knowntobetheleadingauctionhouses inthis kindoftransactions. T heir overallperformances di¤ eronly slightly. T hemostimportantsculptures auction’ markets are N ew Y ork, ny, L ondon, lon, and P aris, par. A furthercity is introduced, R ome and M ilan, rom, given the importance oftheItalian marketforarts. ²M asterpieces Inordertotakeintoaccountthemostvaluedsculptors, fol- lowingP esando(19 9 3), dummyvariables proxythemasterpieceportfolio ofthe top 20 percentofsculptures by prices, top20 , as wellas the inexpensiveportfolio, low20 ;theremainderis assignedtothemiddlemarket, mid20 . ²P eriod: a setofdummies, d, is introduced foreach yearbetween 19 8 7 and19 9 5. Formally, ourspeci…cation is given by: lnp = ¯ 0 + ¯ 1 old+ ¯ 2 mod+ ¯ 3 natf + ¯ 4 natus+ ¯ 5 natd+ ¯ 6 natit+ ¯ 7natgb+ ¯ 8 size+ ¯ 9 bro+ ¯ 1 0 mar+ ¯ 1 1 res+ ¯ 1 2 pla+ ¯ 1 3 ter+ ¯ 1 4 ivo+ ¯ 1 5 soth+ ¯ 1 6 chr+ ¯ 1 7ny + ¯ 1 8 lon+ ¯ 1 9 par+ ¯ 20 rom + 30 X ¯ 21 top20 + ¯ 22 low20 + ¯ jdj + " (5) j=23 6 4 D ata T he data used in this paperare drawn from auctions hold duringthe period oftime 19 8 7 -19 9 5. T he source ofthis data is the 19 9 5 edition ofthe M ayer InternationalA uction R ecords (M IA R ) onCD -R om, which contains records of 27 119 sculptures soldattheworld’s majorauctions5 . Foreachsculptureinthe dataset, anumberofinformations areprovided. P rices aregross ofthebuyers’ and sellers’ transaction fees paid to auction houses and are recorded in four di¤ erentcurrencies. N oinformations is providedontheoriginofthesculptures andexhibitions ofthesculptures. Forthesakeofsimplicity, weassumethatall sales occurattheend ofeach period. A llsculptures arepriced in U S. dollars, de‡ated by using the U S. consumerprice index (19 9 0 = 100)6 toremove the generaltrend ofin‡ation. P rices are 15% less to correctfortransaction fees chargedbyauctionhouses tosellers, butas inmoststudies, wedonottakeinto accountstorageand insurancecosts. Summarystatistics ofthesamplearedisplayed in T able1. [T A B L E 1] 5 Even ifauction records alone donotre‡ecttheentire market- since auction houses have little incentive to sell out of fashion sculptures and, besides, ‘bought in’ works may in‡ate prices [G oetzmann, 19 9 3]- it is not clear whether prices are biased upwards ordownwards [A gnelloand P ierce, 19 9 8 ]. 6S ource: T he FedaralR eserve B ank. 7 5 R esults FollowingB erndtetal. (19 9 5), sinceheteroscedasticity may be present, standarderrors andvariance-covariancematrices ofthecoe¢cients havebeencomputed byusingtheW hite(19 80) heteroscedasticity-robustprocedure. T able2 displays themainresults obtained inthehedonicregression. [T A B L E 2] In almostallcases the coe¢cients aresigni…cantly di¤ erentfrom zeroat5 percentoreven at1 percentprobability level. T he coe¢cients associated to each kind ofindependentvariablecan beused toranksculptures accordingto thepriceofa‘normalised’sculpture, thatis, theprice ofasculpturewhen all theothervariables areassumed tobeatastandard level. Sculptures producedbefore18 00 arethemostpro…tableduetothescarcity ofoldestsculptures, whilethoseproducedafter19 30 performsworsethansculptures producedbetween1801 and19 30. A s tonationality, theG erman, theEnglish and the Italian sculptors secure the highestprices. P rices are increasing in size, as in thecaseofpaintings [B uelens and G insburg, 19 9 3;Chaneletal., 19 9 6 ;A gnelloandP ierce, 19 9 6;CandelaandScorcu, 19 9 7 ;R enneboogandV an H outte, 19 9 8 ;A gnelloand P ierce, 19 9 8 ] . T hemostexpensivemediais marbleduetothehigh costofproduction, as wellas technicaldi¢culties in producing sculptures by using this media. B y contrast, othermediadisplaynegativecoe¢cients, even ifbronzeand resin are notstatisticallysigni…cant. P rices recorded atSotheby’s are higherthan those atChristie’s, and N ew Y ork is the city where prices ofsculptures are the highest. B y generalising P esando’s analysis ofthe marketforprints, a possible reason forthis is due to N ewY ork’s capacity toattracthigh quality sculptures because the bidder 8 audienceis trulyinternational. Finally, masterpieces perform betterthanmiddlemarketartists;bycontrast, inexpensiveportfolioworks perform worsethan middlemarketportfolio. T he set of dummy variables introduced for each year between 19 8 8 and 19 9 5 is used in equation (4) to build the adjacentyearregressions index for sculptures, which is reproduced in T able3. [T A B L E 3] A marketshockcharacterises theperiod19 8 7 -19 9 5 coveredbythedata-set, since after a boom period until 19 9 0, the market for collectibles registers a non-boom period from 19 9 1 to19 9 4. T he rate ofreturn ofan investmenton sculptures seems tofollowthe trend ofthe rate ofreturn on paintings during thesameperiodoftime[CandelaandScorcu, 19 9 7 ;L ocatelli-B ieyandZ anola, 19 9 9 b]. R atesofreturnarepositiveuntil19 9 0, followedbyanegativetrendfrom 19 9 1 to19 9 4, with apositivesign in 19 9 5, butstilllowerthan thepriceindex 19 8 7 . H owever, the trend ofthe performance ofan investmentin sculptures is lower than those associated to alternative forms of investment. Figure 1 compares the de‡ated index for sculptures with the de‡ated indexes of real returns on U S stocks, U S 30 yeargovernmentbonds and gold. [ FIG U R E 1] D uringtheboom periodinvestments insculptures earnedlowerrealreturns than U S stocks, U S 30 yeargovernmentbonds, and gold, forms ofinvestment characterised byacomparabledegreeofrisk. H owever, startingfrom 19 9 1, returnsonsculpturesdecrease, butatalowerratethanotherkindsofinvestment. T his resultmay be due tothe characteristics ofthe marketforsculptures, as illustrated in Section 1. In fact, the demand forthis kind ofcollectibles is expectedtoberatherinelastic, sothatthereturns onsculptures arenotsomuch a¤ ected byboom and non-boom periods. 9 6 Conclusions T his paperanalyses therateofreturnonsculptures, akindofcollectibleabout which very little is known. A lthough the market for sculptures only represents about3-5 percentoftotalcollectibles sold atauctions, good investment opportunities may exist. In ordertoaddress this question, the adjacentyear regressions index forsculptures, sold atauctions duringtheperiod 19 8 7 -19 9 5, has been computed byusingan hedonicpricetechnique. O urresults canbesummarised as follows. T herateofreturnonsculptures seemstofollowthetrendofothercollectiblesduringtheanalysedperiod, suchas paintings [Candelaand Scorcu, 19 9 7 ;L ocatelli-B ieyand Z anola, 19 9 9 b]. H owever, thetrendoftheperformanceofaninvestmentinsculpturesislowerduring theanalysed period, duetotheinelasticity ofthedemand which characterises this market. A numberofissues remain forfurtherresearch. Following similarstudies which applythehedonictechniquetoestimatereturns on paintings, itmaybe interestingtoanalyse the production ofa restricted numberoffamous sculptures. T his allows us bothtoisolatefactors thatin‡uenceprices and tocollect additionaldata towhatis listed in published data sets [Czujack, 19 9 7 ] . Furthermore, inthis studyweonlyfocuseonthereturns onsculptures as …nancial assets. H owever, anumberofauthors [B aumol, 19 86;Frey and Eichenberger, 19 9 5;Santagata, 19 9 8;Czujack, 19 9 7 ]highlightthatvisualarts arealsocharacterised by aesthetic returns, an analysis of which may represent a future developmentofthis paper. A cknowledgments T heauthorsaregratefulfor…nancialsupportfrom CN R program oncultural 10 goods. T his paperhas bene…ted from comments by G .B rosio, M .Ferreroand W .Santagata. 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W hite (19 8 0), A heteroskedasticity-consisten covariance matrix estimator and adirecttestforheretoskedasticity, Econometrica, 48 , 8 17 -8 38. 14 Table 1: Descriptive Statistics Variable poddc old mod cont natf natus natd natit natgb size bro mar res ivo ter soth chr ny lon par rom low20 mid20 top20 d87 d88 d89 d90 d91 d92 d93 d94 d95 Number of obs. = 27119 Mean 26595.1300 0.0278 0.4879 0.4751 0.3249 0.1610 0.0857 0.0806 0.0643 288.1932 0.5535 0.0503 0.0023 0.0417 0.0256 0.2458 0.2074 0.2622 0.1743 0.1738 0.0217 0.2002 0.6001 0.1997 0.0611 0.0784 0.0918 0.0999 0.0757 0.1748 0.1238 0.1515 0.1430 Std. Dev. Min 125903.6 0.1645 0.4999 0.4994 0.4683 0.3676 0.2799 0.2722 0.2453 375.4276 0.4971 0.2186 0.0481 0.1998 0.15780 0.4306 0.4055 0.4398 0.3794 0.3789 0.1456 0.4001 0.4899 0.3998 0.2396 0.2687 0.2888 0.2999 0.2646 0.3798 0.3293 0.3585 0.3501 15 Max 4.0716 0 0 0 0 0 0 0 0 3.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7200002 1 1 1 1 1 1 1 1 7924 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Table 2: Hedonic Price Equation Variables Robust Coefficent old mod natf natus natd natit natgb size bro mar res ivo ter soth chr ny lon par rom top20 low20 d88 d89 d90 d91 d92 d93 d94 d95 constant Number of obs. R2 0.1105 -0.0817 0.0499 0.0912 0.1260 0.1134 0.1151 0.0002 -0.0094 0.0405 -0.0348 -0.0543 -0.0556 0.1064 0.0703 0.2282 0.1028 0.0497 0.1221 2.3530 -1.6582 -0.0420 0.0597 0.0723 -0.0891 -0.1027 -0.1191 -0.1776 -0.1328 8.4277 27119 0.79 F 3967.58 Standard Error 0.0296 0.0100 0.0121 0.0153 0.0162 0.0199 0.0215 0.0000 0.0107 0.0220 0.0817 0.0229 0.0268 0.0178 0.0194 0.0196 0.0187 0.0122 0.0321 0.0129 0.0091 0.0260 0.0253 0.0246 0.0247 0.0222 0.0227 0.0225 0.0225 0.0214 0,95% Confidence Interval 0.0525 0.1684 -0.1013 -0.0622 0.0261 0.0736 0.0612 0.1212 0.0942 0.1578 0.0744 0.1524 0.0730 0.1572 0.0002 0.0002 -0.0305 0.0116 -0.0026 0.0835 -0.1937 0.1265 -0.0993 -0.0094 -0.1082 -0.0030 0.0714 0.1413 0.0323 0.1083 0.1899 0.2666 0.0662 0.1394 0.0258 0.0736 0.0593 0.1849 2.3275 2.3781 -1.6760 -1.6403 -0.0929 0.0090 0.0100 0.1093 0.0241 0.1205 -0.1376 -0.0406 -0.1462 -0.0593 -0.1635 -0.0746 -0.2218 -0.1335 -0.1769 -0.0887 8.3858 8.4696 16 Table 3. Price indexes Gold* Dow Jones* 100.00 100.00 Year 1987 US 30Y bonds* Sculptures 100.00 100.00 1988 87.46 90.61 101.11 95.89 1989 79.69 110.42 111.74 106.15 1990 76.94 117.86 108.03 107.50 1991 74.53 128.76 112.75 91.47 1992 69.85 144.45 116.70 90.24 1993 79.55 154.99 129.84 88.77 1994 79.25 166.88 113.89 83.73 1995 79.95 197.44 133.57 87.56 * a Source: Torino Finanza. Figure 1. Comparison between different deflated price indexes 200,00 175,00 150,00 125,00 100,00 75,00 50,00 25,00 0,00 1987 1988 1989 Sculptures 1990 Gold 1991 1992 D.J. Stocks 17 1993 U.S. 30Y Bonds 1994 1995 Working Papers The full text of the working papers is downloadable at http://polis.unipmn.it/ * Economics Series **Political Theory Series 2000 n. 15* Marilena Locatelli-Biey and Roberto Zanola, The Market for Sculptures: An Adjacent Year Regression Index 2000 n. 14* Daniele Bondonio, Metodi per la valutazione degli aiuti alle imprese con specifico target territoriale 2000 n. 13* Roberto Zanola, Public goods versus publicly provided private goods in a two-class economy 2000 n. 12** Gabriella Silvestrini, Il concetto di <<governo della legge>> nella tradizione repubblicana. 2000 n. 11** Silvano Belligni, Magistrati e politici nella crisi italiana. Democrazia dei guardiani e neopopulismo 2000 n. 10* Rosella Levaggi and Roberto Zanola, The Flypaper Effect: Evidence from the Italian National Health System 1999 n. 9* Mario Ferrero, A model of the political enterprise 1999 n. 8* Claudia Canegallo, Funzionamento del mercato del lavoro in presenza di informazione asimmetrica 1999 n. 7** Silvano Belligni, Corruzione, malcostume amministrativo e strategie etiche. Il ruolo dei codici. 1999 n. 6* Carla Marchese and Fabio Privileggi, Taxpayers Attitudes Towaer Risk and Amnesty Partecipation: Economic Analysis and Evidence for the Italian Case. 1999 n. 5* Luigi Montrucchio and Fabio Privileggi, On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type 1999 n. 4** Guido Ortona, A weighted-voting electoral system that performs quite well. 1999 n. 3* Mario Poma, Benefici economici e ambientali dei diritti di inquinamento: il caso della riduzione dell’acido cromico dai reflui industriali. 1999 n. 2* Guido Ortona, Una politica di emergenza contro la disoccupazione semplice, efficace equasi efficiente. 1998 n. 1* Fabio Privileggi, Carla Marchese and Alberto Cassone, Risk Attitudes and the Shift of Liability from the Principal to the Agent 18 Department of Public Policy and Public Choice “Polis” The Department develops and encourages research in fields such as: • theory of individual and collective choice; • economic approaches to political systems; • theory of public policy; • public policy analysis (with reference to environment, health care, work, family, culture, etc.); • experiments in economics and the social sciences; • quantitative methods applied to economics and the social sciences; • game theory; • studies on social attitudes and preferences; • political philosophy and political theory; • history of political thought. The Department has regular members and off-site collaborators from other private or public organizations. 19 Instructions to Authors Please ensure that the final version of your manuscript conforms to the requirements listed below: The manuscript should be typewritten single-faced and double-spaced with wide margins. Include an abstract of no more than 100 words. Classify your article according to the Journal of Economic Literature classification system. Keep footnotes to a minimum and number them consecutively throughout the manuscript with superscript Arabic numerals. Acknowledgements and information on grants received can be given in a first footnote (indicated by an asterisk, not included in the consecutive numbering). Ensure that references to publications appearing in the text are given as follows: COASE (1992a; 1992b, ch. 4) has also criticized this bias.... and “...the market has an even more shadowy role than the firm” (COASE 1988, 7). List the complete references alphabetically as follows: 20 Periodicals: KLEIN, B. (1980), “Transaction Cost Determinants of ‘Unfair’ Contractual Arrangements,” American Economic Review, 70(2), 356-362. KLEIN, B., R. G. CRAWFORD and A. A. ALCHIAN (1978), “Vertical Integration, Appropriable Rents, and the Competitive Contracting Process,” Journal of Law and Economics, 21(2), 297-326. Monographs: NELSON, R. R. and S. G. WINTER (1982), An Evolutionary Theory of Economic Change, 2nd ed., Harvard University Press: Cambridge, MA. Contributions to collective works: STIGLITZ, J. E. (1989), “Imperfect Information in the Product Market,” pp. 769-847, in R. SCHMALENSEE and R. D. WILLIG (eds.), Handbook of Industrial Organization, Vol. I, North Holland: Amsterdam-London-New York-Tokyo. Working papers: WILLIAMSON, O. E. (1993), “Redistribution and Efficiency: The Remediableness Standard,” Working paper, Center for the Study of Law and Society, University of California, Berkeley. 21