Evidence suggests the calibration of hypothetical and actual behavior is good-specific. We examine whether clustering commodities into mutual categories can reduce the burden. While we reject a common calibration across sets of commodities, a sport-specific calibration function cannot be rejected.Valuation, Calibration, Clusters

J. Shogren

John A. List

M. Margolis

English

Research Papers in Economics

Economics Letters 60 (1998) 263–268
Hypothetical–actual bid calibration of a multigood auction
ab c , * John A. List , Michael Margolis , Jason F. Shogren
a
Department of Economics, University of Central Florida, Orlando, FL 32765, USA
bEconomics Department, Libbey Forum, Bates College,4 4Mountain Ave., Lewiston, ME 04240-6241, USA
cDepartment of Economics and Finance, University of Wyoming, Laramie, WY 82071-3985, USA
Received 7 January 1997; received in revised form 24 April 1998; accepted 28 April 1998
Abstract
Evidence suggests the calibration of hypothetical and actual behavior is good-speciﬁc. We examine whether clustering
commodities into mutual categories can reduce the burden. While we reject a common calibration across sets of
commodities, a sport-speciﬁc calibration function cannot be rejected. Ó 1998 Elsevier Science S.A.
Keywords: Valuation; Calibration; Clusters
JEL classiﬁcation: C9; Q0
1. Introduction
A nagging question in the nonmarket valuation literature is whether hypothetical bids send
systematic but upwardly biased signals of underlying preferences for goods with intangible qualities
(see Diamond and Hausman, 1994, and the cites therein). If so, researchers may be able to correct the
bias of some goods by conducting nonhypothetical lab auctions, and then calibrating hypothetical and
1 actual bidding behavior. The results from some initial in-sample calibration experiments have been
discouraging—evidence suggests the in-sample calibration function is commodity- and context-
speciﬁc, implying that each hypothetical study would need its own lab auction to calibrate behavior
2 (see, e.g., Fox et al., 1998 and List and Shogren, 1998).
*Corresponding author. Tel.: 11-307-766-5430; Fax: 11-307-766-5090; E-mail: jramses@uwyo.edu
1The National Oceanic and Atmospheric Administration’s proposed rules for natural resource damage assessment suggest a
default calibration factor of two (NOAA, 1994). This deﬂator serves as an ad hoc placeholder until researchers develop an
empirically based alternative. A key item on the research agenda is the nature of calibration for large-scale public goods. If
calibration is infeasible because the researcher is unable to construct an experiment that would auction the good in the lab,
then more information is needed on how calibration works for private goods and whether these functions are transferable to
public goods.
2Diamond and Hausman (1994) note that the calibration factors implied by several studies vary from 1.5 to 10. Since these
studies vary widely in method, they do not indicate that surveys administered according to a consistent protocol will fail to
reveal consistent calibration. Fox et al. (1998), whose experimental results suggest that even with the same treatment,
calibration factors may vary between commodities, poses a more serious caveat to calibration.
0165-1765/98/$19.00 Ó 1998 Elsevier Science S.A. All rights reserved.
PII: S0165-1765(98)00117-7264 J.A. List et al. / Economics Letters 60 (1998) 263–268
The evidence has only been suggestive, however, since previous experiments have not been
structured to test the hypothesis that goods share the same calibration function. This note presents
such a test and explores whether clustering goods into common categories can reduce the burden of
calibration. Using data from a ﬁeld auction that elicited both hypothetical and actual bids for ﬁve
baseball and ﬁve football sportscards, we reject the hypothesis that a common calibration function
exists for all cards. This suggests that hypothetical bias varies signiﬁcantly across commodities, even
under identical experimental treatment. Our results, however, leave open the possibility that goods
might be clustered on some objective basis. This ﬁnding provides some support for the supposition
that each hypothetical study will not need a unique lab auction to calibrate bidding behavior.
2. Data
We use data from a ﬁeld experiment at a 1995 Denver trading card show (List and Shogren, 1998).
Sports trading cards are a useful object to explore calibration because they are familiar and
deliverable, but still have some intangible qualities beyond a standard market good. Using a
simultaneous sealed-bid, second-price auction (Vickrey, 1961; Melton et al., 1996), the ﬁeld
experiment followed a four-step experimental design: (1) inspection of the good(s), (2) hypothetical
bid(s), (3) actual bid(s), and (4) debrieﬁng. Ninety-three attendees followed this four step format and
ﬁrst submitted a set of hypothetical bids, and then a set of actual bids for 10 trading cards—ﬁve
3 baseball and ﬁve football. The hypothetical and actual auctions were identical except for the
4 understanding that the actual bids were binding. Table 1 presents the summary statistics for the
hypothetical and actual bids for the 10 cards. Results from a Wilcoxon matched-pairs signed-ranks test
rejects equality of the distributions of hypothetical and actual bids at the 1% level for each card (card
1: z 527.71; card 2: z 527.76; card 3: z 527.67; card 4: z 527.44; card 5: z 527.4; card 6:
z 526.9; card 7: z 526.89; card 8: z 526.48; card 1: z 526.77; card 10: z 526.31). Hence,
the distribution of hypothetical bids lies to the right of the distribution of actual bids, a pattern
5 consistent with some earlier valuation exercises (e.g., Neill et al., 1994).
3. Results and discussion
Given that the hypothetical–actual bid wedge persists, we consider whether a common calibration
function exists for all cards, two clustered functions exist for baseball and football cards, or if a
unique function is needed for each card. Since each subject submitted 10 bid pairs, one for each card,
we estimated models allowing ﬁxed or random effects to control for unobserved characteristics of
3 Table 1-column 1 shows the contents of the bundles.
4See List and Shogren (1998) for a more complete discussion of the experimental design.
5As an aside, consider the default calibration scheme suggested in NOAA (1994), m 5a 1am; where m and m are the A 0 1H A H
mean actual and hypothetical bids, and the a are parameters which are constant across commodities. NOAA suggested that i
a 50.0 and a 50.5 until evidence proves otherwise. Our estimated equation is m 520.092 10.291m (N 5 01 A (0.442) H(0.12)
10), where the terms in parenthesis are standard errors. Thus we cannot reject either of the NOAA default values.J.A. List et al. / Economics Letters 60 (1998) 263–268 265
Table 1
a Descriptive statistics
Card Actual bids Hypothetical bids
Mean Std. Dev. Median Mean Std. Dev. Median
Cal Ripken 26.40 52.207 0 91.71 102.668 40
1982 TT
Cal Ripken 11.76 18.318 0 40.32 30.599 35
1982 Topps
Cal Ripken 7.85 11.604 0 29.03 20.354 25
1982 Donruss
1982 TT w/o 5.80 10.303 0 21.96 19.299 20
Cal Ripken
Billy Ripken 4.88 8.578 0 22.34 23.186 15
1982 Fleer
Troy Aikman 0.82 1.170 0 3.32 2.662 4
1989
Troy Aikman 10.85 16.674 0 29.81 32.489 20
1989 TT
Troy Aikman 0.93 1.576 0 3.12 2.978 2
1989 Proset
1989 TT w/o 1.20 1.9267 0 4.29 4.231 3
Aikman
Michael Irvin 0.90 1.399 0 2.87 2.736 3
1989 Topps
aSample includes actual and hypothetical bids from 93 participants. Each participant ﬁrst submitted a hypothetical bid for
each card and proceeded to place an actual bid for each card.
each subject. For brevity, we present results from only one of these models—the maximum likelihood
6 estimator of the standard random effects. Column 1 of Table 2 shows results from the equation:
10 10
A 5Ob D 1OwHD1m 1« ,( 1 ) ij j j j ij j i ij
j51 j51
th th where A and H represent the actual and hypothetical bid of the i bidder for the j card, D is a ij ij j
th dummy variable for card j, m |N(0, s ) is the random disturbance characterizing the i bidder, and i m
e |N(0, s ) is the bid-speciﬁc error term. ij e
First, we test the restriction that all ten cards can be pooled into a single common calibration
function (column 2 of Table 2):
A 5a 1wH 1m 1« .( 2 ) ij ij i ij
2 We reject this restriction at the 1% level (LR tests: x 529.13; 18 d.f.). Rejection of the common
6 2 A Hausman (1978) test failed to reject the orthogonality assumption (x 53.46; 19 d.f.), thus we do not report the less
efﬁcient ﬁxed effects estimates. Nevertheless, results from the ﬁxed effects model are qualitatively identical to those in Table
2. Note also that the bids are truncated. We do not present random effects Tobit estimates since the Tobit random effects
likelihood function appears to be highly nonconcave with the present data. Furthermore, the Tobit procedure is inconsistent
under virtually any relaxation of the underlying stochastic assumptions (Amemiya, 1985).266 J.A. List et al. / Economics Letters 60 (1998) 263–268
Table 2
a,b Maximum likelihood random effects estimates
Variable (1) (2) (3)
Ten groups General Sport-speciﬁc
Constant 27.78 21.27 23.04
(1.783) (0.758) (0.923)
D2 4.95
(2.635)
D3 6.01
(2.727)
D4 7.42
(2.510)
D5 7.40
(2.392)
D6 8.45 2.82
(2.610) (0.928)
D7 7.86
(2.375)
D8 8.51
(2.463)
D9 8.27
(2.44)
D10 8.35
(2.466)
Hypo 0.37 0.34 0.35
(0.013) (0.009) (0.010)
HypoD2 20.01
(0.043)
HypoD3 20.04
(0.064)
HypoD4 20.09
(0.067)
HypoD5 20.14
(0.056)
HypoD6 20.33 0.01
(0.483) (0.033)
HypoD7 20.01
(0.041)
HypoD8 20.31
(0.433)
HypoD9 20.21
(0.305)
HypoD10 20.26
(0.470)
LL 23672.74 23687.31 23681.05
ab Dependent variable is actual bid. Standard errors in parentheses.J.A. List et al. / Economics Letters 60 (1998) 263–268 267
calibration function null implies that hypothetical bias is not systematically identical across baseball
and football cards. This is potentially damaging to the idea that calibration functions can be readily
and costlessly transferred across goods (Blackburn et al., 1994). If a common calibration function
eludes football and baseball cards—relatively similar goods—how conﬁdent can one be that a
common function would exist across a broader spectrum of goods?
Second, we consider whether clustering the cards into good-speciﬁc groups can reduce the burden
on calibration. Instead of ten calibration functions, we test the restriction that the ten cards can be
pooled into two sport-speciﬁc clusters, baseball and football cards, such that two calibration functions
exist (column 3 of Table 2):
51 05 1 0
A 5bOD 1fOD 1wOHD1rOHD1m 1« .( 3 ) ij j j ij j ij j i ij
j51 j56 j51 j56
2 This looser restriction cannot be rejected at any conventional signiﬁcance level (x 516.62; 16 d.f.).
Rejection of the pooling null (Eq. (2)), but nonrejection of the quasi-pooling null (Eq. (3)), could be
due to many reasons, but one intuitive explanation is that many collectors trade baseball cards more
7 intensely and view baseball cards as more central to their collection. Therefore, many collectors may
view baseball and football cards as distinct commodities. In any case, the evidence so far leaves open
the possibility that similar commodities have similar calibration functions.
Overall, the evidence suggests that some measurable correlation exists between intentions and
actual behavior. This measurable correlation appears to be commodity- and context-speciﬁc. Although
one size does not necessarily ﬁt all, a potentially proﬁtable research direction is to identify goods with
tangible parameters that can be clustered into common calibration functions. Perhaps these calibration
clusters can replace the need for actual auctions, but we are a long way from that day. Future
in-sample calibration experiments involving goods further out on the continuum of intangibility may
get us closer to a systematic understanding of why and to what degree hypothetical bids diverge from
real commitments.
4. Concluding remarks
When the tanker Exxon Valdez ran aground on Bligh Reef in March 1989, it reinvigorated the
debate about the usefulness of hypothetical valuation exercises. The persistent fear that hypothetical
bids send systematically upwardly biased signals of real preferences triggered a search for an ex post
calibration function to deﬂate these bids. Using data from a ﬁeld experiment, we ﬁnd that an
interchangeable calibration function did not exist for a set of sports trading cards, but that one
common calibration function might exist if the cards are clustered into their respective sports. The
ability to cluster goods provides some optimism that each survey might not need its own lab auction
to calibrate hypothetical intentions with real economic commitments. More research exploring the
robustness of our ﬁndings would be most useful.
7 TM TM TM According to representatives from Scoreboard Inc., Fleer/Skybox Inc., and Pinnacle Inc., baseball cards make up
an estimated 65–80 percent of the sportscard market, suggesting collectors are more familiar with baseball cards or view
baseball cards as more central to their collection or both.268 J.A. List et al. / Economics Letters 60 (1998) 263–268
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Hypothetical-Actual Bid Calibration of a Multi-Good Auction

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Hypothetical-Actual Bid Calibration of a Multi-Good Auction

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