University of Zurich
Department of Economics
Working Paper Series
ISSN 1664-7041 (print)
ISSN1664-705X(online)
Working Paper No. 43
How Do Informal Agreements and Renegotiation
Shape Contractual Reference Points?
Ernst Fehr, Oliver Hart and Christian Zehnder
October 2011
Electronic copy available at: http://ssrn.com/abstract=1997185
How Do Informal Agreements and Renegotiation Shape
Contractual Reference Points?
Ernst Fehr, Oliver Hart, and Christian Zehnder*
October 2011
Abstract
Previous experimental work provides encouraging support for some of
the central assumptions underlying Hart and Moore (2008)’s theory of
contractual reference points. However, existing studies ignore realistic
aspects of trading relationships such as informal agreements and ex
post renegotiation. We investigate the relevance of these features
experimentally. Our evidence indicates that the central behavioral
mechanism underlying the concept of contractual reference points is
robust to the presence of informal agreements and ex post
renegotiation. However, our data also reveal new behavioral features
that suggest refinements of the theory. In particular, we find that the
availability of informal agreements and ex post renegotiation changes
how trading parties evaluate ex post outcomes. Interestingly, the
availability of these additional options affects ex post evaluations even
in situations in which the parties do not use them.
*
Fehr: Department of Economics, University of Zurich, Blümlisalpstrasse 10, CH-8006 Zürich (e-mail:
ernst.fehr@econ.uzh.ch); Hart: Department of Economics, Harvard University, Littauer Center 220, 1805
Cambridge Street, Cambridge, MA02138 (e-mail: ohart@harvard.edu); Zehnder: Faculty of Business and
Economics, University of Lausanne, Quartier UNIL-Dorigny, Internef 612, CH-1015 Lausanne (e-mail:
christian.zehnder@unil.ch). We gratefully acknowledge financial support from the U.S. National Science
Foundation through the National Bureau for Economic Research and the Research Priority Program of the
University of Zurich on the "Foundations of Human Social Behavior". We would like to thank Heski Bar-Isaac,
Roland Benabou, Sylvain Chassang, Bob Gibbons, Wolfgang Pesendorfer, and Philipp Weinschenk for helpful
comments.
Electronic copy available at: http://ssrn.com/abstract=1997185
I. Introduction
A series of recent theory papers develops the idea that ex ante contracts may serve as
reference points for ex post trade (see Hart and Moore 2008, Hart 2009, Hart and Holmström
2010). The theoretical work not only helps us to understand the role of long-term contracts in
the absence of non-contractible investments, but also sheds light on the internal organization
of the firm, and provides a new perspective on authority and delegation. However, the theory
rests on strong behavioral assumptions that deviate from standard contract theory. While
initial tests provide encouraging support for the new approach (see Fehr, Hart, and Zehnder
2009, 2011), these experiments also have limitations. Most important, the experimental setups
ignore real-life aspects of trading relationships such as informal agreements and renegotiation.
As there are plausible reasons for these features to be important, we carry out new
experiments to investigate their relevance. Our evidence suggests that the central behavioral
mechanism underlying the concept of contractual reference points is robust to the possibility
of informal agreements and renegotiation, although new behavioral features emerge.
To clarify our contribution and embed it in the existing literature, it is helpful to start
with some background and motivation. While standard incomplete contract models (see
Grossman and Hart 1986 and Hart and Moore 1990) are useful for studying the determinants
of asset ownership and the boundaries of firms, they do not help much for understanding the
internal organization of larger firms. The reason is that these models are based on the
assumption that Coasian bargaining ensures ex post efficiency, so that it is hard to see why the
internal structure of firms should matter. To move towards more general and compelling
theories of contracts and organizational form, Hart and Moore (2008) depart from the existing
literature and drop the assumption that ex post trade is perfectly contractible. In addition, they
introduce the behavioral concept that ex ante contracts, negotiated under (relatively)
competitive conditions, shape parties’ entitlements regarding ex post trade. If a party does not
get what he feels entitled to he is aggrieved and provides perfunctory rather than consummate
performance, causing deadweight losses. These new assumptions deliver a trade-off between
rigid and flexible contracts and have significant organizational implications: among other
things, they can explain employment contracts, which fix wages in advance and leave
discretion to the employer over the task. Hart (2009) reintroduces asset ownership and shows
that the presence of contractual reference points can explain the use of indexation in contracts
and the role of payoff uncertainty in determining vertical integration. Hart and Holmström
(2010) apply the idea of contractual reference points to firm scope, authority and delegation.
1
While these results are promising, they are convincing only if the strong behavioral
assumptions on which they rely are empirically valid. Fehr et al. (2011, henceforth FHZ)
provide initial tests of the Hart-Moore theory. They set up a controlled laboratory experiment
based on the payoff uncertainty model in Hart and Moore (2008). In line with the prediction
of the model the experiments show that there is an important trade-off between contractual
rigidity and flexibility. Flexible contracts are useful because they allow the trading parties to
adjust the terms of the contract to the realized state of the world. However, flexibility causes
significant shading in ex post performance as parties seem to have misaligned reference
points. Contractual rigidity is helpful to overcome the shading problem, because a
competitively determined fixed price aligns ex ante expectations and avoids ex post
aggrievement. But rigid contracts suffer from the problem that their fixed terms prevent
mutually beneficial exchanges from occurring in some states of the world. These results are
reassuring for the theory, given that the different implications of rigid and flexible contracts
for ex post performance are the basis for most organizational implications derived from the
models.2 It is also noteworthy that the behavior observed in these experiments cannot be
explained either by traditional contract theory or by standard behavioral models.3
However, while the experimental results reported in FHZ are supportive of the theory
of contractual reference points, there are some limitations. Two important caveats are that the
experimental setup does not allow either for informal agreements or for ex post renegotiation.
Both these features are relevant in many real-life trading relationships and there are plausible
reasons why each of them might change how ex ante contracts affect ex post behavior.
To understand why informal agreements may matter, note that the Hart-Moore model
assumes that states of the world are ex post observable but not verifiable. This assumption is
standard in the incomplete contracts literature and implies that the parties cannot rely (at least
directly) on state-contingent contracts. However, ex post observability suggests that the
trading parties could reach informal, state-contingent agreements. The standard economic
approach deems such informal agreements irrelevant cheap-talk. However, if contracts
constitute reference points they may matter. Contractual reference points imply that ex post
performance depends on ex ante expectations. If the parties can use informal agreements to
2
Erlei and Reinhold (2011) replicate the experiment of FHZ. Although they find higher shading levels in both
types of contracts, they confirm the existence of the trade-off between contractual rigidity and flexibility.
3
In particular, existing theories of social preferences (Fehr and Schmidt 1999, Bolton and Axel Ockenfels 2000,
Rabin 1993, Charness and Rabin 2002, Dufwenberg and Kirchsteiger 2004, Falk and Fischbacher 2006) cannot
account for the observed trade-off between rigid and flexible contracts. See FHZ.
2
“manage” expectations, these agreements may have important consequences. Instead of
relying on rigid contracts, the trading parties could align reference points by combining
flexible contracts with informal agreements. Such enhanced flexible contracts would be
attractive as they would not only guarantee trade, but would also avoid inefficiencies caused
by aggrievement and shading. In this sense the presence of informal agreements might destroy
the trade-off between rigidity and flexibility. Hart and Moore (2008) abstract from informal
agreements, arguing that subjective interpretations of states and self-serving biases make it
unlikely that such agreements shape reference points. However, ultimately the role of
informal agreements remains an empirical question.
To see why ex post renegotiation might be important, suppose that a buyer and a seller
have agreed on a rigid ex ante contract. Ex post it turns out that the seller’s costs are higher
than the fixed price. Without renegotiation voluntary trade implies that the seller walks away
and realizes an outside option. In reality, however, it is unclear whether this is plausible. As
long as the buyer’s value is higher than the seller’s cost, what would prevent the parties from
renegotiating their contract and enjoying the gains from trade? Thus, the availability of
renegotiation would also seem to cast doubt on the trade-off between rigid and flexible
contracts: rigid contracts may achieve the best of both worlds by aligning expectations and
avoiding ex post inefficiency.
However, renegotiation raises a number of potential issues. First, even in the situation
described above it is not clear how profitable trade is after renegotiation. Although the
renegotiation is mutually beneficial, it reintroduces flexibility regarding the price choice and
may lead to misaligned expectations, aggrievement and shading. Second, renegotiation may
complicate situations in which trade would be feasible under the initial contract. A first
possibility is opportunistic renegotiation: a party may initiate renegotiation just to grab a
bigger share of the surplus. This may create bad feelings, shading, and significant
inefficiency. Another problem is that rigid contracts may no longer align reference points in
the first place. If renegotiation is always feasible, people may start to hope for outcomes
outside the contract. In this case performance may suffer from shading even if the parties
carry out the initially agreed upon contract.
In this paper we design new experiments that throw light on both informal agreements
and renegotiation. Our first experiment reveals that, although informal agreements have an
impact, they do not eliminate the trade-off between contractual rigidity and flexibility. If
buyers explicitly (by announcing low prices) or implicitly (by not making an announcement)
3
indicate that they are not willing to pay a high price, sellers are less aggrieved and less likely
to engage in shading in response to a low final price than in the baseline treatment where price
announcements are not feasible. However, shading is considerably higher if buyers choose
lower prices ex post than they announced ex ante. Thus buyers who attach an informal
message to a flexible contract are best off if they announce a low price and stick to it.
Somewhat surprisingly, we find that not making a price announcement at all is as good as
making a low price announcement. It seems that a flexible contract without a message is
evaluated differently by sellers depending on whether informal agreements are feasible or not:
sellers tend to interpret the lack of an explicit price announcement as an implicit message that
the buyer has no intention to pay a high price.
The overall lower shading in flexible contracts increases their attractiveness for buyers
relative to the baseline condition. However, the decrease in shading rates is only moderate and
not sufficient to eliminate the trade-off between contractual rigidity and flexibility. Even
when informal agreements are available, it is still true that lower prices trigger more shading
in flexible contracts than in rigid ones. As a result, buyers who choose rigid contracts realize
higher profits in the good state of the world than if they choose flexible contracts. This
advantage of rigid contracts is large enough to offset the disadvantage that rigid contracts do
not allow for trade in the bad state. The consequence is that on average flexible contracts are
no more profitable than rigid contracts.
We think that the finding that informal agreements do not eliminate the trade-off
between rigidity and flexibility is important, especially because the simplicity of our setup
(only two possible states, completely symmetric information) gives informal agreements a
very good chance to be effective. The effects of informal agreements are likely to be smaller
in more complicated situations.
Our findings contribute to the literature on pre-play communication. While it has been
well established that pre-play communication fosters cooperation (see, e.g., Sally 1995,
Ledyard 1995) and coordination (see, e.g., Crawford 1998), our data points out a very
different aspect: if market participants decide not to make use of available ex ante
communication opportunities, their ex post actions are evaluated differently than in a situation
in which communication has not been feasible. This resonates with earlier evidence indicating
that variations in the set of available but not chosen alternatives can importantly change how a
trading partner perceives a specific action (see e.g., Charness and Rabin 2002, Falk et al.
4
2003). Our findings suggest that these effects may apply not only to variations in the payoffrelevant action space, but also to modifications of non-binding communication opportunities.
Our second experiment investigates the effects of ex post renegotiation. We implement
a rather extreme form of renegotiation. We allow the buyer unilaterally to replace the existing
contract with a new one: since the seller has no veto, this is actually closer to what lawyers
call a “repudiation”. We consciously chose this particular form of renegotiation, because the
fact that contracts can be abandoned at no cost gives renegotiation the best chance to
minimize the behavioral impact of contracts. In this sense our treatment is a powerful stress
test for the relevance of contractual reference points. We find that renegotiation opportunities
do not imply that contractual reference points are irrelevant. Although renegotiation is always
feasible, the trading parties do not seem to hope for outcomes outside the contract when trade
is feasible within the contract. Specifically, if the buyer in a rigid contract decides to stick to
the agreed upon price in the good state, the shading rate remains the same as in the baseline
treatment. Sellers still seem to accept the competitively negotiated fixed price as a reference
point and do not feel entitled to an upward renegotiation of the price as long as the price
allows for trade. This is a strong finding. As the buyer can unilaterally change the contract in
this treatment, the contract choice is ultimately a framing decision without consequences for
feasible outcomes. Nevertheless, we find that contracts serve as salient reference points. This
makes it likely that contractual reference points also remain important in more realistic
situations, where renegotiation may be more difficult and/or costly.
In addition, we find that the possibility of renegotiation increases the attractiveness of
rigid contracts in the bad state. In this situation renegotiation allows the buyers to transform a
rigid contract into a flexible one that permits them to increase the price to cover the seller’s
cost. While these mutually beneficial renegotiations of a rigid contract trigger some shading
activities on the seller side (probably as a consequence of the misaligned entitlements caused
by the newly introduced flexibility), the gains from trade are still substantial. Thus, overall,
buyers who choose rigid contracts manage to realize significantly higher profits in the
presence of renegotiation opportunities than in their absence.
However, renegotiation is problematic to the extent that buyers behave
opportunistically, i.e., they breach the contract to lower the price and grab a larger share of the
surplus. In this case most of the affected sellers seem to be aggrieved and there is a large and
significant increase in shading. It seems that most buyers anticipate the sellers’ reaction and
therefore opportunistic renegotiation occurs almost exclusively in the rare situations where the
5
competitive ex ante process yielded unfavorable terms for the buyer. Our finding that
opportunistic renegotiation triggers inefficient shading has important implications for the
hold-up literature. While the leading formal models ignore the possibility that renegotiation
may trigger counterproductive reactions (see, e.g., Grossman and Hart 1986 and Hart and
Moore 1990), recent theoretical work suggests that taking into account the psychological
aspects of renegotiation may have important implications. In particular, Hart (2009) shows
that such a behavioral model allows us to identify payoff uncertainty as a driving force of
organizational form, a result which resonates well with empirical findings on vertical
integration (see Lafontaine and Slade 2007, for a review).
Interestingly, and perhaps surprisingly, the availability of renegotiation also seems to
have an impact on sellers’ evaluations of outcomes in flexible contracts. While higher shading
rates still imply that buyers’ profits are significantly lower in non-renegotiated flexible
contracts than in non-renegotiated rigid contracts in the good state, this difference is
significantly smaller in the renegotiation treatment than in the baseline condition.
Renegotiation opportunities seem to render the choice of inequitable terms in nonrenegotiated contracts more acceptable, i.e., as long as the buyer adheres to the contract,
sellers are less likely to engage in shading when the buyer picks a low price as compared to
the baseline condition. While this behavior may be partly attributable to our assumption that
buyers can unilaterally change the contract (i.e., no veto for sellers), it also reinforces the view
that available but not chosen alternatives shape perceptions. The lower shading rates also
imply that flexible contracts are more attractive for buyers when renegotiation is available.
However, if buyers renegotiate optimally (i.e., no opportunistic renegotiations), rigid contracts
still yield higher overall profits for buyers than flexible contracts.
To summarize, both our experiments provide further evidence that contractual
reference points shape performance in relationships governed by incomplete contracts. In
addition, our evidence suggests interesting refinements regarding the theory. We find that the
trading parties’ evaluation of the ex post outcome is influenced by informal agreements and
ex post renegotiation and that the availability of these additional options affects ex post
evaluations even in situation in which the parties do not use them.
The remainder of the paper is organized as follows: In Section II, we describe the
design of our experiment and provide details of procedures. Section III contains the
behavioral predictions. We present and discuss our results in Section IV. Section V concludes.
6
II. Experimental Design
We present the market setup and the parameters in Section II.A. Section II.B describes the
interaction of buyers and sellers in the experiment. The details of the different experimental
conditions that we investigate are provided in Section II.C. We describe the laboratory
procedures in Section II.D.
II.A.
Market Setup and Parameters
Each experimental session has an equal number of buyers and sellers. In every period of the
experiment buyers and sellers have the possibility to trade a product. Since each seller can sell
up to two units, but every buyer can buy at most one unit of the product per period, the supply
of the product is twice as large as the demand. Thus, sellers face competition for buyers.
When a buyer purchases a unit of the product from a seller, his payoff is equal to his valuation
for the product v minus the price p. The payoff of the seller is defined as the difference
between the price p and the production cost c. The buyer’s valuation for the product depends
only on the seller’s ex post quality choice q. The seller’s production cost, in contrast, also
depends on the realized state of the world . There are two states of nature: a good state ( =
g), in which the seller’s production costs are low, and a bad state ( = b), in which the
production costs are high. The good state occurs with probability wg = 0.8.
The payoffs of buyers and sellers can be summarized as follows:
Buyer’s payoff: B = v(q) – p.
Seller’s payoff: S = p – c(q, ).
When trade occurs sellers can choose between two quality levels: normal quality (q = qn) or
low quality (q = ql). The production costs for low quality are slightly higher than the
production costs for normal quality: c(ql, ) > c(qn, ). This reflects the idea that sellers can
minimize costs if they simply provide the product desired by the buyer. However, they can
sabotage output (at a small cost) if they want to.4 For each unit of the product which a seller
cannot sell – either because he did not manage to conclude a contract with a buyer or because
4
The quality choice of the seller in our experiment is similar to costly punishment technologies that have been
used in many other cooperation experiments (see, e.g., Fehr and Gaechter (2000) for a typical example).
However, it is important to notice that our experiment differs from the typical gift exchange experiments (see,
e.g., Fehr et al. (2009) for a review of this literature). In gift-exchange games the pecuniary incentive for workers
(i.e., sellers) is to provide the minimal effort (i.e., quality) level, whereas in our paper the normal quality level
maximizes seller earnings.
7
his contract does not allow for a mutually beneficial trade – he realizes an outside option xS =
10. When a buyer is unable to trade, he also realizes an outside option xB = 10. Table 1
summarizes the cost and value parameters of the experiment:
In the experiment sellers and buyers interact in groups of four (two buyers and two sellers).
To minimize the role of reputational considerations, these groups are randomly reconstituted
at the beginning of every period. Thus, our protocol induces a series of one-shot interactions.
II.B.
Interaction of Buyers and Sellers Within a Period of the Experiment
In the following we describe the different steps which characterize the interaction of buyers
and sellers in all our treatments. Particularities of the different experimental condition are
discussed in the next section:
Random formation of interaction groups:
At the beginning of every period a computerized random device defines the interaction
groups consisting of two buyers and two sellers.
Phase 1: Ex ante contracting:
Step 1: Buyers’ contract choice
Each transaction begins with the buyer’s choice of a contract type (t). The buyer has to
decide whether he wants to offer a rigid contract (t = r) or a flexible contract (t = f). Rigid
contracts already define a fixed transaction price pr ex ante. Flexible contracts, in contrast,
specify only a price range [pl, pu] from which the price can be chosen ex post. It is
important to note that the buyer can choose only the type of contract, but not the terms.
The terms (i.e., the fixed price or the price range, respectively) are determined in a
competitive auction among the sellers.
Step 2: Sellers’ contract auction
After both buyers in an interaction group have chosen their type of contract, the two
contracts are auctioned off to the sellers. The sequence of the auctions is randomly
determined within each group. If a rigid contract is auctioned off the auction directly
determines the fixed price pr [c(ql,g) + xS, 75] = [35, 75].5 In a flexible contract the
5
The minimum of 35 for the fixed price ensures that the seller cannot make losses relative to his outside option
in the good state even if he provides low quality. This feature guarantees that sellers do not refrain from
8
auction determines the lower bound of the price range pl [35, 75]. The upper bound of
the price range is exogenously fixed and equal to the buyer’s valuation of the product
when the seller provides normal quality: pu = v(qh) = 140. Thus, in both cases the auction
starts off at 35 and then increases by one unit every half second. Each of the two sellers
has a button that allows him to accept the contract at any time during the auction. Thus,
the first seller who is willing to accept the displayed fixed price or the displayed lower
bound respectively gets the contract. The seller who loses the auction and does not get the
contract directly realizes the outside option xS.
Determination of the state of the world:
After the contract auctions the computer randomly determines the state of the world for
each contract independently. The state is common knowledge to the trading parties.
Phase 2: Ex post trading:
Step 3: Buyers’ choice of contract terms
Once the state has been revealed, the buyer determines the final terms of the contract.
How much flexibility he has in doing this depends on the experimental condition and the
ex ante chosen contract. To initiate a mutually beneficial trade the buyer needs to be able
to pick a price that covers the seller’s cost. The flexible contract always allows for such a
choice, but the fixed price contract does not: in the bad state the fixed price of a rigid
contract is lower than the seller’s cost (pr [c(ql,g) + xS, 75] < c(qn,g) = 80 < c(ql,g) = 85).
In the latter case trade is feasible only if the buyer can renegotiate the contract
(renegotiation is permitted in only one of our experimental conditions). If the buyer
cannot or does not want to renegotiate the contract, trade does not occur and both trading
parties realize their outside options. If the contract allows for trade the buyer either pays
the fixed price (rigid contract) or picks a price out of the available price range (flexible
contract, or if a contract has been renegotiated).6
choosing low quality, just because they want to avoid losses (loss aversion). The maximum of 75 for the fixed
price ensures that the price is always below the seller’s cost in the bad state of the world. This guarantees that
trade is infeasible within rigid contracts if the bad state is realized. However, in the experiment the competitive
forces in the auction were strong enough so that the maximum was never binding.
6
In the bad state the buyer has to ensure that the price is such that the seller cannot make losses, i.e., he must
choose a price p [c(ql,b) + xS, v(qh)] = [95, 140]. Again we do not allow prices to be such that the seller can
make losses by choosing low quality, since we want to avoid the possibility that people refrain from shading
because of loss aversion (see also Footnote 5).
9
Step 4: The seller’s quality choice
Sellers observe the price choice of their buyer and then determine their quality. The sellers
always have the choice between normal (qn) and low (ql) quality. Remember that choosing
low instead of normal quality increases the seller’s cost by 5 units irrespective of the
contract type and realized state of the world (see Table 1).
Payoffs and Market Information:
When all decisions have been made, profits are calculated and displayed on subjects’
screens. In addition, to their profit information buyers also get some aggregated
information about the market outcome.7
Subsequently. a new period begins and the participants are randomly reassigned to a new
interaction group.
II.C.
Experimental Treatments
In the following we describe our two main treatment conditions. For completeness we also
provide the details of the baseline condition of FHZ, because we later use this condition as a
benchmark for our results.
The Informal Agreement Condition (IA):
In the informal agreement condition buyers who choose a flexible contract in Step 1 can
decide whether they want to combine the contract with a message of the following form:
“If costs are low, I plan to pay a price of pA(g). If costs are high, I plan to pay a price
of pA(b).”
The price announcements are in no way binding for the buyer, i.e., the message does not
affect the range of actual prices available to the buyer ex post. The buyer can always pick
prices which are higher or lower than the announced price if the competitively determined
price range of the contract allows for this. All market participants are informed about the
presence of the message opportunity in flexible contracts in the instructions of the experiment,
i.e., the availability of messages is common knowledge in the experiment.
7
The buyers are informed about average payoffs in rigid and flexible contracts of all buyers in all previous
periods. In addition, they also learn how many buyers have chosen rigid and flexible contracts in the current
period. The aim of the provision of this information is to make learning easier for buyers. Since our setup allows
for many possible constellations (two contract types, two states of nature, two quality levels, many prices),
learning from individual experience is rather difficult.
10
In the informal agreement condition renegotiation of contracts is not permitted.
Accordingly, rigid contracts allow for trade only if the good state of the world is realized. In
the bad state trading parties with a rigid contract have to realize their outside option.
The Renegotiation Condition (RG):
In the renegotiation condition, there are no informal agreements. However, buyers always
have the possibility to renegotiate the contract ex post (see Step 3 above). If a buyer decides
to renegotiate the contract, the original contract is no longer of relevance and the buyer can
choose any price that satisfies p [c(ql, ) + xs, 140]. The seller cannot veto the buyer’s
decision to renegotiate the terms.8 Renegotiation is available for rigid and flexible contracts in
both states of the world, i.e., the buyer can always decide whether he wants to stick to the
competitively concluded ex ante contract and accept the imposed restrictions (i.e., the fixed
price in rigid contracts and the lower bound of the price range in flexible contracts,
respectively) or whether he wants to abandon the contract and pick his price without
restrictions.
It is useful to distinguish three types of renegotiation which may occur in this
condition. First, the buyer may renegotiate a rigid contract in the bad state of the world. This
allows for a price increase and makes trade feasible. As both parties benefit (at least weakly)
from such a renegotiation, we call this a “mutually beneficial renegotiation”. Second, the
buyer may renegotiate a contract in the good state of the world in order to decrease the price
to a level below the ex ante agreed upon fixed price or lower bound of the price range,
respectively. We call this an “opportunistic renegotiation”, because the buyer intends to
increase his own profit at the expense of the seller. Finally, there is also the possibility that a
buyer voluntarily increases the fixed price of a rigid contract in the good state of the world.
As this is a costly attempt to increase the seller’s profit we call this an “altruistic
renegotiation”.
The Baseline Condition of FHZ (BL)
In the baseline condition of FHZ neither informal agreements nor ex post renegotiation are
available.
8
We discuss this feature of the experiment in detail in section III.C.
11
II.D.
Subjects, Payments and Procedures
All subjects were students of the University of Zurich or the Swiss Federal Institute of
Technology Zurich (ETH). Economists and psychologists were excluded from the subject
pool. We used the recruitment system ORSEE (Greiner 2004). Each subject participated in
only one session. Subjects were randomly subdivided into two groups before the start of the
experiment; some were assigned the role of buyers and others the role of sellers. The subjects’
roles remained fixed for the whole session. All interactions were anonymous, i.e., the subjects
did not know the personal identities of their trading partners.
To make sure that subjects fully understood the procedures and the payoff
consequences of the available actions, each subject had to read a detailed set of instructions
before the session started. Participants then had to answer several questions about the feasible
actions and the payoff consequences of different actions. We started a session only after all
subjects had correctly answered all questions. The exchange rate between experimental
currency units (“points”) and real money was 15 Points = 1 Swiss Franc (~US $ 1, in
November and December 2010).
In order to make the sellers familiar with the auction procedure we implemented two
trial auctions – one with a rigid contract and one with a flexible contract – before we started
the actual experiment. In the trial phase each seller had his own auction, i.e., they did not
compete with another seller and no money could be earned.
The experiment was programmed and conducted with z-Tree (Fischbacher 2007). We
conducted 5 sessions of the informal agreement condition, and 5 sessions of the renegotiation
condition. We had 28 subjects (14 buyers and 14 sellers) in 5 of our 10 sessions and – owing
to no-shows – 24 subjects (12 buyers and 12 sellers) in 4 sessions, and 20 subjects (10 buyers
and 10 sellers) in 1 session. This yields a total number of 256 participants in the experiment.
A session lasted approximately two hours and subjects earned on average about 50 Swiss
Francs (including a show-up fee of 10 Swiss Francs).
III. Behavioral Predictions
In this section we derive a set of hypotheses for our experiment. In section III.A we present
the predictions that result from the assumption that people are purely self-interested moneymaximizers. While we do not believe that the self-interest hypothesis is an accurate
description of our participants’ behavior, we still feel that these predictions are a useful
12
benchmark, not least because much of the theoretical literature on incomplete contracts is
based on models that assume pure self-interest. In section III.B we discuss how the presence
of contractual reference points affects the predictions for our experiment. As there are always
different ways to design a particular experiment we use section III.C to discuss some features
of our design and their role for the interpretation of the results.
III.A. Predictions under Pure Self-Interest
The prediction of the self-interest model is straightforward. Buyers anticipate that selfish
sellers are never willing to engage in costly shading and therefore offer the lowest price
permitted by the contract. Competition in the contract auctions implies that the fixed price in
rigid contracts and the lower bound in flexible contracts are at the competitive level, i.e. pr =
35 and pl = 35.9 This implies that rigid and flexible contracts yield the same profit for buyers
in the good state of the world (B = v(qn) – p = 140 – 35 = 105). In the bad state payoffs
depend on whether renegotiation is available. If the buyer can renegotiate the contract, both
contracts yield the same profit for the buyer (B = v(qn) – p = 140 – 95 = 45) and the buyer is
indifferent between the two. If renegotiation is not possible, the rigid contract results in the
outside option (B = xB = 10) and therefore the buyer strictly prefers the flexible contract.
Whether or not informal agreements are available does not affect the predictions.
We summarize the prediction of the standard economic model as the
Standard Hypothesis:
a) Market forces imply that the fixed price in rigid contracts and the lower bound of the
price range in flexible contracts end up at the competitive level, i.e., pr = pl =35.
b) Sellers never choose low quality irrespective of the contract type and price level.
Buyers always choose the lowest price available in flexible contracts.
c) In the absence of renegotiation opportunities buyers’ profits are higher in flexible
contracts than in rigid contracts. Therefore, buyers prefer flexible contracts.
d) The presence of informal agreements does not affect outcomes.
9
Remember: Since p = 35 corresponds to p = c(ql,g) + xS and the seller must offer at least p = c(ql,b) + xS = 95 in
the bad state of the world, a seller can never be worse off if he accepts a contract than if he accepts his outside
option.
13
e) When ex post renegotiation is possible, both types of contracts yield identical payoffs
and buyers are indifferent between them (if they choose the rigid contract, they always
renegotiate the price from pr = 35 to p = 95 if the bad state is realized).
III.B. Predictions if Contracts are Reference Points
In this section we discuss how the Hart-Moore notion that competitively negotiated ex ante
contracts provide reference points for ex post trade affects the predictions for each of our
experimental conditions. In FHZ we provide a slightly modified version of the Hart-Moore
model and derive the following prediction for the baseline treatment: While contractual
reference points do not affect the prediction that the contract auctions yield competitive
outcomes (pr = pl =35), they change the consequences of the buyers’ contract choice. Of
particular importance is the fact that flexible contracts may induce sellers to hope for high
prices.10 If a buyer picks a price which is below the seller’s reference price, the seller may be
aggrieved and engage in shading. As sellers may have heterogeneous reference points the
frequency of shading is predicted to be decreasing in price. Thus, depending on the
distribution of sellers’ reference prices it can be optimal for the buyer either to increase the
price to avoid shading or to accept the risk of getting low quality. Rigid contracts should
avoid the shading problem, because they pin down the price from the outset and thereby fix
expectations. Thus, if the shading problem in flexible contracts is severe enough, rigid
contracts may be more profitable for buyers, even though they prevent the parties from
trading in the bad state of the world.
Next we discuss the predictions for our new experimental conditions in the light of
contractual reference points. We begin with the informal agreements condition. In FHZ we
assume that the reference price is a function of the type of contract (t) and the state (): pR(t,
). A rigid contract allows for only one price so that the reference price is equal to the fixed
price: pR(r, ) = pr. In flexible contracts we assume that the reference price can be any price
permitted by the contract (i.e., we allow for heterogeneity in sellers’ reference points): pR(f, )
10
Hart and Moore (2008) assume that each party compares the ex post outcome to the most favorable outcome
permitted by the contract. In FHZ we extend the model to allow for the case where parties may have
heterogeneous reference points, i.e., we take into account that some traders may feel entitled to an outcome other
than the most favorable outcome. We show that the predictions of such an extended model remain very similar to
those of the original model.
14
[pl, pu]. The role of the reference point for the seller’s utility is illustrated by the following
equation:
uS = S – max[(pR(t, ) – p), 0] I(q),
where 0 and I(q) is an indicator function, which is unity if q = qn and zero otherwise. The
second term captures the psychic costs of aggrievement, which become relevant if the realized
price p is smaller than the seller’s reference price pR. The parameter measures the intensity
of the seller’s aggrievement if he feels shortchanged. The indicator function I(q) captures the
idea that a seller can completely offset his aggrievement if he shades on performance and
thereby hurts the buyer by lowering his valuation for the delivered product. This formulation
implies that a seller engages in shading if the price is below the threshold price defined as:
pT() = pR(f, ) – [c(ql, ) – c(qn, ) / ].
We can now take up the idea that the trading parties may have the possibility to “manage” the
reference point in flexible contracts using informal agreements. To this end let pA() be an
informal (i.e., non-enforceable), state-contingent price announcement of the buyer. In our
experiment the price announcement is either a set of two prices (pA() = {pA(g), pA(b)}) or the
empty set (pA() = ). In accordance with the idea of managing expectations, we define the
reference price in a flexible contract when informal agreements are available as follows:
pR(f, , pA()) = pA() + (1 – ) pR(f, , ), where [0, 1].
This means we assume that the seller’s reference price in the presence of informal agreements
is a weighted average of the buyer’s price announcement pA() and the seller’s reference price
that he would have had in the absence of a price announcement. The weighting parameter
determines the importance of the price announcement for the reference price. If is equal to
one, this means that the buyer can fully control the seller’s reference point by informally
announcing a state-contingent price. If is equal to zero, this means that the buyer’s price
announcement is completely irrelevant, i.e., the seller feels entitled to the same price as in the
absence of a price announcement.
If is strictly positive, low price announcements reduce the reference price and
thereby the threshold price that ensures high quality (pR(f, )/ pA() = pT()/ pA() < 0).
We would therefore expect that buyers try to manage their seller’s reference points by
announcing low prices. Specifically, profit-maximization implies that buyers who choose a
15
flexible contract should combine the contract with a price announcement that informs the
seller that the buyer always plans to pay the lowest price possible:
pA() = {pA(g) = c(ql,g) + xs = 35, pA(b) = c(ql,b) + xS = 95}.
Such a price announcement shifts the distribution of sellers’ threshold prices to the left and
therewith maximizes the profitability of flexible contracts. If is equal to one, the optimal
price announcement above would allow the buyer to pay the competitive price while
completely avoiding shading in flexible contracts. If this is the case, the availability of
informal agreements would imply that buyers would strictly prefer the flexible contract,
because a flexible contract would not only generate the same profit as a rigid one in the good
state, but it would also make (shading-free) trade feasible in the bad state. However, if is
sufficiently small, the positive impact of low price announcements on the profitability of
flexible contracts may be small and rigid contracts may remain more attractive than flexible
ones.
We now turn to the role of renegotiation in our setup. Let {–1, 0, 1} be the buyer’s
renegotiation decision, where equal to zero signifies the absence of renegotiation, equal to
minus one stands for opportunistic renegotiation, and equal to one captures mutually
beneficial or altruistic renegotiation. The availability of renegotiation raises two important
questions regarding contractual reference points. The first one is: do contracts remain
reference points even when renegotiation is always feasible? And the second question is: how
is the reference point determined once renegotiation has been initiated?
We first consider the question of whether contracts remain reference points in the
presence of renegotiation. This question is of great interest for the cases where the parties
decide to stick to the ex ante agreed upon contract, i.e., it is important to determine the seller’s
reference point if the buyer decides not to renegotiate the contract. Basically, there are two
interesting possibilities. One possibility is that the parties continue to hope for their preferred
outcome within the limits of the contract, i.e., the contract remains the reference point even
though renegotiation would have been possible. In this case the definition of reference prices
is not affected by the presence of renegotiation opportunities: pR(r, , = 0) = pR(r, ) = pr
and pR(f, , = 0) = pR(f, ) [pl, pu]. The argument for this possibility would be that sellers
explicitly agree to the contract in the competitive bargaining process and therefore it is not
unreasonable to assume that the contract is a focal point and defines their expectations.
16
The alternative view would be that contracts completely lose their meaning in the
presence of renegotiation opportunities and parties simply hope for their preferred outcome
within the set of all feasible outcomes (including ones that can be reached only if the contract
is renegotiated). This would actually imply that the reference prices are independent of both
the contract type and the renegotiation decision: pR() [c(ql,g) + xs, v(qn)]. As a
consequence, the buyer’s contract choice would no longer make any difference for ex post
performance. Which of these two views is realistic can be determined only by the data.
We now turn to the definition of the reference point after renegotiation. It is obvious
that this question is important only if contracts continue to shape reference points when
renegotiation is not initiated (otherwise the parties just hope for their preferred outcome
pR(); see above). One possible view is that renegotiation simply turns the existing contract
(be it a flexible or a rigid contract) into a completely flexible contract with price range p
[c(ql,g) + xs, v(qn)]. Accordingly, the reference point after renegotiation would be pR(t, , ≠
0) = pR(f, ) [c(ql,g) + xs, v(qn)]. We think that this view is a plausible one when it comes to
mutually beneficial or altruistic renegotiation ( = 1). In our setup mutually beneficial
renegotiation occurs when the buyer renegotiates a rigid contract in order to be able to
increase the price in the bad state of the world. In this case the situation is indeed very similar
to the situation in a flexible contract: both renegotiated rigid contracts and flexible contracts
allow for prices p [c(ql,b) + xS, v(qn)] and there is no obvious reason why the seller should
respond differently in the two situations. The situation is similar if the buyer decides to
initiate an altruistic renegotiation (i.e., the buyer renegotiates a rigid contract in the good state
of the world and increases the price to a level above the ex ante agreed upon fixed price).11
However, we do not think that this view is accurate when it comes to opportunistic
renegotiation ( = –1). In our experiment opportunistic renegotiation can occur in two
situations: i) if a buyer renegotiates a rigid contract in the good state of the world and picks a
price below the competitively determined fixed price, and ii) if a buyer renegotiates a flexible
contract in the good state of the world and picks a price below the competitively determined
11
One might argue that altruistic renegotiations should always be perceived as generous, because the buyer
renegotiates the contract and increases the price although this lower his own payoff. However, if the sellers'
aggrievement level is shaped by a self-serving bias, the sellers may still be disappointed if the buyer does not
increase the price as much as they would have liked.
17
lower bound of the price range.12 Since the buyer intentionally lowers the seller’s profit,
opportunistic renegotiation itself may be an important source of aggrievement on the seller
side. If the sellers see opportunistic renegotiation of the contract as a hostile act, it is likely
that the same deviation from their reference point produces much more aggrievement than in
a comparable situation in a flexible contract. To capture this aspect we assume that the
intensity of the seller’s aggrievement is a function of the renegotiation decision ():
(0) = (1) < (–1).13
As a higher intensity of the seller’s aggrievement implies a shift of the distribution of
threshold prices to the right (pT()/ > 0), we expect to see a particularly high shading rate
after opportunistic renegotiation.
Finally, we summarize all these considerations in the
Reference Point Hypothesis:
a) Market forces imply that the fixed price in rigid contracts and the lower bound of the
price range in flexible contracts end up at the competitive level, i.e., pr = pl =35.
b) In rigid contracts there is no shading irrespective of the price when renegotiation is not
possible. In flexible contracts heterogeneity in seller entitlements implies that the
shading rate is decreasing in the price. Depending on the distribution of sellers’
reference prices buyers may choose higher prices to lower the shading rate or pay low
prices and accept a certain amount of shading.
c) Buyers’ profits in flexible contracts are lower than predicted by the standard model. If
the impact of the reference dependent preferences is strong, rigid contracts may be
more profitable for buyers, even if renegotiation is not feasible and trade occurs only
in the good state.
d) Informal agreements may help buyers to manage sellers’ reference points in flexible
contracts. If low price announcements reduce the shading frequency, buyers should
12
It is important to mention that neither of these situations can occur in competitive equilibrium. If the fixed
price or the lower bound of the price range is at the competitive level, the buyer cannot lower the price after
renegotiation. However, since we expect that auction outcomes will often deviate from the competitive level
(although they usually converge to the competitive level over time, see FHZ for details on the baseline
condition), it is useful to consider these situations anyway.
13
This formulation resonates with Hart (2009)'s notion that (opportunistic) renegotiation turns a friendly
relationship into a hostile one. See also Hoppe and Schmitz (2011) for related experimental evidence.
18
announce that they plan to pay the lowest price possible. Whether buyers prefer rigid
or flexible contracts depends on the base level of shading and on how much informal
agreements reduce shading in flexible contracts.
e) The consequences of the availability of renegotiation depend on how renegotiation
opportunities affect reference points. If contracts continue to provide reference points
in the presence of renegotiation opportunities, the following three results should be
observed: i) Buyers renegotiate rigid contracts if the bad state of the world is realized.
After such a mutually beneficial renegotiation, prices and the shading rate will be
similar to the ones in flexible contracts. ii) If buyers opportunistically renegotiate
contracts in the good state of the world, this will trigger a lot of shading. Accordingly,
only few buyers should engage in opportunistic renegotiation. iii) If buyers do not
renegotiate contracts in the good state, the same difference between rigid and flexible
contracts as in the absence of renegotiation should be realized. In particular, sellers
should not shade even if prices are low in rigid contracts (i.e., sellers do not hope for
outcomes outside the contract). However, if contracts no longer serve as reference
points, any difference between rigid and flexible contracts should disappear and the
parties should behave always as if the contract was completely flexible.
III.C. Discussion of Design Features
Our experiment modifies the baseline design of FHZ in two important ways.14 We first
discuss the informal agreement condition of our experiment. While Hart and Moore (2008)
admit that the idea of managing reference points through informal agreements has some force,
they argue that the presence of asymmetric information in combination with self-serving
biases may limit the impact of such agreements considerably. The reason is that each party
may be able to convince himself that the state is favorable to him, so that there are still
14
FHZ provide a detailed discussion of several important aspects of the baseline game. As our new experiments
share some of these design features, we briefly summarize the three most important points here: i) We exclude
lump sum transfers and consider only contracts in which the buyer chooses the ex post price. This greatly
simplifies the experiment as it allows us to study the trade-off between rigidity and flexibility in a setup in which
the buyer’s value is certain and only sellers can shade. ii) Contrary to the Hart-Moore model where parties are
assumed to be indifferent between perfunctory and consummate performance, we implement costly shading. We
do this to rule out equilibrium shading under standard economic assumptions in our setup. However, as shading
costs are small relative to the damage imposed on the buyer, the setup is still in the spirit of the Hart-Moore
model. iii) The relative attractiveness of rigid and flexible contracts depends on the probabilities with which the
two states of the world occur. We pick a high probability for the good state, so that the rigid contract is
potentially attractive if the Hart-Moore forces are at work.
19
conflicting entitlements that trigger shading. It is important to remember that there is no
asymmetric information at all in our experimental setup. Both parties are fully informed about
the cost level of the seller as soon as the computerized random device has determined the
state. Accordingly, it is hard to see how self-serving biases in the interpretation of the state
can play any role in the experiment. In addition, our setup is very simple, in the sense that
there is no uncertainty about buyer values and only two possible realizations of seller costs.
This makes state-contingent informal agreements easily feasible, because it is sufficient to
determine a price for each of the two cost levels. We think it is therefore fair to say that we
implement an environment in which informal agreements have a very good chance to have
large effects. So, if we find that the impact of informal agreements is weak in this situation, it
is likely that their effect is even weaker in more realistic situations where the number of
possible states is much larger and various sources of asymmetric information may give rise to
conflicting expectations.
Second, we would like to discuss some aspects of our renegotiation condition. We are
aware of the fact that we study an extreme form of renegotiation. In fact, in our experiment
the buyer always has the chance to ignore the contract completely and to come up with a new
suggestion at zero cost. Since the seller has no veto right this is in fact more a repudiation than
a renegotiation. The design of this treatment implies that there is no longer any formal
difference between rigid and flexible contracts. Since the range of feasible prices is identical
after the initiation of renegotiation of any contract (p [c(ql,) + xs, v(qn)]), renegotiated
contracts allow for exactly the same set of outcomes irrespective of whether the original
contract was rigid or flexible. In other words, the buyer’s contract choice is essentially just
framing. We do not think that this setup is realistic. It is easy to think of reasons why the
renegotiation of contracts may be costly in reality. However, we consciously chose this
particular form of renegotiation, because it provides a powerful stress test for the relevance of
contractual reference points. If we find that the ex ante contract still shapes ex post behavior
even though the contract can be abandoned at no cost, then this is a strong result. The easier a
contract is to overturn, the less likely it is that it serves as a reference point. In this sense any
findings that we identify in this treatment can be seen as lower bound estimate of the
importance of contractual reference points when renegotiation of contracts is costly.
Furthermore, we suppose that sellers are forced to trade with the buyer even if the
buyer has not respected the contract and has initiated renegotiation. However, it is important
to realize that the seller can never be worse off by trading than by realizing his outside
20
option.15 Had sellers had the opportunity to walk away after renegotiation, this would have
provided them with another, more powerful punishment device (in addition to shading). This
would have severely complicated clean comparison of outcomes without and with
renegotiation, without generating much additional insight.
One limitation of our design is that it allows only the buyer to initiate renegotiation.
We think that it would also be interesting to study situations in which two-sided renegotiation
is possible. However, in order to make such a treatment interesting, we would require that the
buyer has ways to harm the seller by shading on performance, and also that the buyer’s value
is uncertain. It is obvious that two-sided shading and uncertainty about values and costs would
considerably complicate the strategic considerations in the experiment. We leave this
interesting extension for future work.
IV. Results
In this part of the paper we present and discuss our results. First, we examine the outcomes in
the informal agreement treatment. In Section IV.A we present an analysis of outcomes in rigid
and flexible contracts at the aggregate level and we investigate how the availability of
informal agreements changes outcomes in both types of contracts relative to the baseline
condition. Section IV.B completes the results on informal agreements by showing in detail
how non-binding, state-contingent price announcements affect seller performance in flexible
contracts. Second we study the effects of renegotiation. In Section IV.C we analyze whether
ex ante contracts still affect ex post trade when renegotiation is available but not initiated.
This is important in order to determine whether contracts remain reference points. In addition,
we also provide a comparison to the baseline treatment. Section IV.D completes the analysis
by discussing the detailed effects of mutually beneficial and opportunistic renegotiations on
ex post outcomes in rigid and flexible contracts.
IV.A. Informal Agreements: Comparison of Rigid and Flexible Contracts
In this section we compare rigid and flexible contracts at the aggregate level and investigate
how the availability of informal agreements affects the trade-off between the two. Columns
(1) to (4) of Table 2 summarize the results in rigid and flexible contracts. The table indicates
average prices, relative frequencies of shading, auction outcomes, and profits of buyers and
15
As the price always satisfies p ≥ c(ql, ) + xs, the seller's payoff is never lower than the outside option xS.
21
sellers. We first consider the outcomes of the contract auctions. The table indicates that both
fixed prices in rigid contracts, and lower bounds of price ranges in flexible contracts are
slightly above the predicted competitive level of 35 (Fixed price: 39.8 / Lower Bound: 38.7).
However, if we consider the development over the periods of the experiment, we observe that
prices actually converge to the competitive level. While the first 5 periods yield average
auction outcomes of 44.1 (rigid contracts) and 44.4 (flexible contracts), the corresponding
values in the final 5 periods are 36.4 (rigid contracts) and 35.1 (flexible contracts). This
negative time trend is statistically significant.16 However, the auction outcomes are not
statistically different between contract types.17 This implies that, in principle, the price range
in flexible contracts would have allowed buyers to choose the same prices as in rigid contracts
when the good state of the world has been realized. If buyers successfully use informal
agreements to manage sellers’ reference points, we would therefore expect that prices and
shading rates are identical across contracts in the good state of the world. The table shows that
this is not what happens: we find that, on average, buyers with flexible contracts pay
substantially higher prices (47.8) than buyers who have chosen rigid contracts (39.8). Column
(1) of Table 3 investigates the statistical significance of this result. We regress prices in the
good state of the world on an indicator variable which is unity if the buyer has picked a
flexible contract. The regression reveals that the price in flexible contracts is significantly
higher (p-value = 0.037, OLS estimation, standard errors clustered at the session level).18
Interestingly, the higher prices in the flexible contract are not sufficient to prevent the sellers
from engaging in shading activities. While the shading rate is only about 5 percent in rigid
contracts, it amounts to 13 percent in flexible contracts. Columns (2) and (3) of Table 3 reveal
that this difference is significant irrespective of whether we control for the difference in prices
or not (p-value < 0.001 in both columns, Probit estimation (marginal effects reported),
standard errors clustered at the session level).19 The estimation in column (3) also reveals that
higher prices reduce the shading rate significantly (p = 0.033). Additional estimations in
which we regress the shading dummy on prices for each contract type separately (not included
16
OLS regressions of auction outcomes on period reveal significantly negative time trends for both types of
contracts (p-value < 0.01, standard errors clustered at the session level).
17
An OLS regression of auction outcomes on a dummy for flexible contracts yields no significant effect (p-value
= 0.276, standard errors clustered at the session level). A non-parametric signed-rank test with session averages
as observations yields the same result (p-value = 0.312, two-sided).
18
A non-parametric signed-rank test with session averages as observations yields p-value = 0.031 (one-sided).
19
A non-parametric signed-rank test with session averages as observations yields p-value = 0.031 (one-sided).
22
in the table) reveal that this effect is entirely driven by flexible contracts (p-value = 0.072). In
rigid contracts prices do not significantly affect the quality choice of sellers (p-value = 0.237).
Table 2 also shows the impact of the lower prices and shading rates in rigid contracts
on buyer profits. In the good state of the world buyers who have chosen a rigid contract
realize an average payoff of about 98, while buyers with flexible contracts get, on average,
only about 87. Column (4) of Table 3 confirms that this difference is significant (p-value =
0.027, OLS estimation, standard errors adjusted for clustering at the session level).20 As rigid
contracts do not allow for trade when the seller’s costs are high, the higher profits of buyers
with rigid contracts in the good state are obviously counterbalanced by lower profits in the
bad state. Although flexible contracts also exhibit a considerable shading rate in the bad state
(sellers engage in shading in 21 percent of the cases), trade is still much more attractive
(average buyer profit = 33.9) than the low outside option in case of no trade (outside option =
10). However, it is interesting to notice that the difference in buyer profits in the good state of
the world is large enough to offset the disadvantage that rigid contracts do not allow for trade
in the bad state: overall buyer profits are slightly higher in rigid contracts (78.2) than in
flexible contracts (76.9) (see Table 2), but the difference is not statistically significant (pvalue = 0.759, see column (5) of Table 3).21
Overall, these results demonstrate that the availability of informal agreements does not
eliminate the trade-off between contractual flexibility and rigidity. Even if state-contingent
price announcements are available to the buyer, rigid contracts still have the advantage that
lower prices and lower shading rates generate higher profits when the good state of the world
has been realized. This advantage is large enough, so that flexible contracts do not lead to
higher overall profits, even though they allow for profitable trade in both states of the world.
Next we compare the results of our informal agreement treatment (IA) to the results of
the baseline condition (BL) in FHZ. As the only difference between these two setups is that
buyers in the informal agreement treatment have access to state-contingent price
announcements in flexible contracts, this comparison is informative. It will reveal how the
availability of the informal agreements affects the trade-off between rigidity and flexibility
relative to a situation in which informal agreements cannot play a role. A contrast of columns
20
21
A non-parametric signed-rank test with session averages as observations yields p-value = 0.031 (one-sided).
A non-parametric signed-rank test with session averages as observations yields p-value = 0.313 (one-sided).
23
(1) to (4) with columns (5) to (8) of Table 2 allows us to compare prices, shading rates,
auction outcomes, and buyer and seller profits across treatments and contracts.
With regard to rigid contracts the table shows that outcomes remain virtually
unaffected by the availability of informal state-contingent contracts. In the good state average
prices (IA: 39.8 / BL: 40.7) and shading rates (IA: 0.05 / BL: 0.06) are very similar and not
statistically different from each other.22 In the bad state trade remains infeasible in both
treatments. As prices and shading frequencies are not affected, there are also no substantial
differences in market participants’ profits. Overall, buyers succeed in making average profits
of 78.2 (IA) and 77.9 (BL), while sellers end up with average profits of 17.4 (IA) and 18.1
(BL). Neither difference is statistically significant.23
In flexible contracts, in contrast, the availability of informal state-contingent contracts
has an impact on outcomes. While price levels are not (or are at most marginally)
significantly different across treatments in both states of the world (Good state: IA: 47.8, BL:
51.1 / Bad state: IA: 97.9, BL 98.4)24, shading rates in flexible contracts decrease when
buyers have the possibility to combine flexible contracts with non-binding state-contingent
price announcements (Good state: IA: 0.12, BL: 0.25 / Bad state: IA: 0.21, BL 0.30).
However, only the effect in the good state is of statistical significance.25 As a consequence of
the lower shading frequencies, flexible contracts yield higher buyer profits in the informal
agreement treatment than in the baseline treatment in both states of the world (Good state: IA:
87.3, BL: 79.9 / Bad state: IA: 33.9, BL 29.7 / Overall: IA 76.9, BL: 68.9). The increase in the
good state and the overall increase in buyer profits are statistically significant.26 Accordingly,
22
Regressions of price and shading on a treatment dummy for the baseline condition yield insignificant effects
(Price: p-value = 0.409 (OLS) / Shading: p-value = 0.574 (Probit), standard errors adjusted for clustering at the
session level in both regressions). Non-parametric rank-sum tests with session averages as observations yield pvalue = 0.421 (prices, two-sided) and p-value = 0.548 (shading, two-sided). In both treatments prices in rigid
contracts converge to the competitive level over time. OLS regressions of price on period reveal significantly
negative time trends in both treatments (p-value < 0.01). In the final period average prices are equal to 36.5 (IA)
and 36.0 (BL), respectively. The shading rates, in contrast, do not exhibit significant time trends.
23
Buyers: p-value = 0.887 / Sellers: p-value = 0.381, OLS estimations, standard errors adjusted for clustering at
the session level. Non-parametric rank-sum tests with session averages as observations yield p-value = 0.421
(buyers, two-sided) and p-value = 0.421 (sellers, two-sided).
24
Good state: p-value = 0.196 / Bad state: p-value = 0.610, OLS estimations, standard errors adjusted for
clustering at the session level. Non-parametric rank-sum tests with session averages as observations yield pvalue = 0.075 (good state, one-sided) and p-value = 0.421 (bad state, one-sided).
25
Good state: p-value = 0.006 / Bad state: p-value = 0.253, Probit estimations, standard errors adjusted for
clustering at the session level. Non-parametric rank-sum tests with session averages as observations yield pvalue = 0.016 (good state, one-sided) and p-value = 0.210 (bad state, one-sided).
26
Good state: p-value = 0.044 / Bad state: p-value = 0.224 / Overall: p-value = 0.021, OLS estimations, standard
errors adjusted for clustering at the session level. Non-parametric rank-sum tests with session averages as
24
it is not surprising that buyers are less likely to choose the rigid contract in the informal
agreement treatment (28 percent) than in the baseline treatment (50 percent, see FHZ for more
details).27 As shading has only small monetary consequences for sellers (the cost difference
between normal and low quality is merely 5 points), the lower shading rates do not have a
statistically significant impact on seller profits (IA: 25.1 / BL: 27.2).28
We find these results interesting. Although the availability of informal agreements
does not eliminate the trade-off between rigid and flexible contracts, their presence increases
the attractiveness of flexible contracts by lowering the shading rate. To understand how
exactly informal agreements affect performance in flexible contracts, we will now turn to a
detailed analysis of how buyers use state-contingent price announcements and how they
influence sellers’ quality choice.
IV.B. Informal Agreements: Effects of Non-Binding State-Contingent Price Announcements
In this section we examine to what extent and in what way buyers make use of informal statecontingent contracts and how these contracts affect seller performance. Figure 1 sheds some
light on the use of informal agreements by buyers. The labels on the horizontal axis categorize
the different types of flexible contracts that we observe in the experiment. While “No” stands
for flexible contracts in which the buyer has decided not to make a price announcement, the
remaining categories indicate the level of the price announcement in those contracts where the
buyer has attached an informal agreement (e.g., “40” means that the buyer has announced a
price in the range [35, 40], “50” stands for an announcement in the range [41,50] etc.). The
bars represent the relative frequencies of price announcements in the corresponding range.
Cases in which the informal agreement has been violated by the buyer (i.e., observations with
actual prices that are lower than the price announcement of the buyer) are displayed in light
grey, while cases in which informal agreements have been honored (i.e., observations with
actual prices that are equal to or higher than the price announcement of the buyer) are
displayed in dark grey. The dots represent averages of ex post prices paid by buyers for each
type of flexible contract.
observations yield p-value = 0.075 (good state, one-sided), p-value = 0.210 (bad state, one-sided), and p-value =
0.016 (overall, one-sided).
27
This difference is significant: p-value < 0.001, Probit regression of an indicator variable for rigid contracts on
a treatment dummy for the baseline condition, standard errors adjusted for clustering at the session level.
28
p-value = 0.340, OLS estimations, standard errors adjusted for clustering at the session level. A nonparametric rank-sum test with session averages as observations yields p-value = 0.210 (one-sided).
25
The figure shows that the use of informal state-contingent contracts is not very intense.
More than 50 percent of the buyers who choose flexible contracts do not attach a price
announcement at all.29 One might suspect that the low overall use of informal agreements is a
consequence of a learning process in which buyers learn to use informal agreements only over
time. This does not seem to be the case. Regressing an indicator variable for using informal
agreements on period yields an insignificant coefficient close to zero (p-value = 0.445, Probit
estimation, standard errors clustered at the session level). Furthermore, among those buyers
who attach a price announcement to a flexible contract only relatively few make very low
price announcements. Among the price announcements for the good state of the world only
about 34 percent turn out to be in the range between 35 and 40, while the majority is higher
(about 32 percent of the announcements are in the range between 41 and 50, the remaining 34
percent are higher than 50). Price announcements for the bad state, in contrast, are more likely
to be low. About 74 percent of the announcements are in the range between 95 and 100 and
only about 11 percent of the announcements are higher than 110. In addition, only about 25
percent of buyers who attach informal agreements make low price announcements for both
states (i.e., between 35 and 40 for the good state and between 95 and 100 in the bad state).
Figure 1 also shows that buyers who make high price announcements are more likely
to pay high prices. This is true for both states of the world (Spearman’s Rho for the relation
between prices and price announcements is 0.33 in the good state and 0.53 in the bad state).
However, average prices exceed price announcements only as long as price announcements
are relatively low. When price announcements are high, average prices are below price
announcements and buyers are therefore more likely to violate their informal agreement with
the seller (see the increasing trend in the light grey bars in Figure 1). Regressions of an
indicator variable for violation of an informal agreement on the level of the price
announcement confirm that this effect is statistically significant in both states of the world
(Good state: p-value = 0.014 / Bad state: p < 0.001, Probit estimations, standard errors
clustered at the session level).
Next we explore how sellers react to informal agreements. The hypothesis that
informal state-contingent contracts allow buyers to manage sellers’ expectations suggests that
buyers might be able to reduce seller aggrievement and shading if they announce explicitly
29
For the figure we have separated observations by the ex post realized state of the world. If we consider ex ante
decisions of buyers for all contracts, we observe that 53 percent of the buyers who choose a flexible contract do
not make use of the possibility to attach a state-contingent price announcement.
26
that they plan to pay low prices. The idea is that sellers who agree to such a contract know
what to expect and do not feel aggrieved if the buyer sticks to his announcement. The first
column of Table 4 makes a first step to investigate the relevance of this hypothesis in our data
set. The column reports a regression of an indicator variable for shading on prices and price
announcements in the good state of the world. The regression includes only observations in
which the buyer has attached a price announcement to a flexible contract. The significantly
positive coefficient of price announcements confirms that when controlling for the final price
a lower price announcement significantly reduces the probability that the seller engages in
shading (p-value = 0.007, Probit estimation (marginal effects reported), standard errors
clustered at the session level). In addition, the coefficient of the price has a negative sign
indicating that sellers are less likely to engage in shading when buyers pay higher prices.
However, the price effect is not statistically significant (p-value = 0.273). Column (2)
performs the same analysis for the bad state of the world. The results are similar: again the
coefficient of the price has a negative sign, while price announcements have a positive sign.
However, this time the price effects are statistically significant (p-value = 0.007), while the
effects of price announcements are not (p-value = 0.218).
While the regressions of columns (1) and (2) of Table 4 are a useful starting point, we
find it important to dig a bit deeper. In particular, since we know that buyers who announce
higher prices are more likely to renege on their announcement (see Figure 1), it is interesting
to examine the role of violations of informal agreements for quality choices of sellers. A
simple comparison of shading rates in flexible contracts with informal agreements reveals that
in the good state the shading rate is about 0.09 in contracts in which the buyer complies with
his price announcement and about 0.25 in contracts in which the buyer violates the informal
agreement. In the bad state the corresponding numbers are 0.11 and 0.48. In columns (3) and
(4) of Table 4 we assess the statistical significance of these differences. To this end we regress
the shading dummy on prices and an indicator variable which is unity in case of underbidding
of a price announcement. As in columns (1) and (2) the regressions include only observations
in which a price announcement was attached to a flexible contract. Column (3) investigates
the good state of the world, while column (4) contains the analysis for the bad state. Both
regressions confirm that the increase in the shading rate is statistically significant (Good state:
p-value = 0.005, Bad state: p-value 0.028, Probit estimations (marginal effects reported),
standard errors clustered at the session level). These findings support the interpretation that
price announcements play a role for seller reference points. The same ex post price is
27
substantially more likely to trigger shading activities on the seller side if the buyer has
previously announced that he intends to pay a price above the finally chosen price. It seems
that the availability of informal state-contingent contracts induces many sellers to concentrate
on whether the buyer delivers on his promises when they assess the fairness of an outcome. If
they feel that the buyer does not live up to his promise, they feel aggrieved and engage in
shading.
In light of the finding that price announcements seem to constitute promises which
play an important role for reference points, it is now useful to compare seller behavior in
flexible contracts with and without informal agreements. In particular, it is interesting to see
how sellers respond to the lack of an explicit price announcement in flexible contracts in an
environment in which all market participants know that each buyer who chooses a flexible
contract always has the possibility to make an announcement. Columns (5) and (6) of Table 4
are helpful to address this question. In these regressions we include observations from all
flexible contracts (with and without informal agreements). We regress an indicator variable
for shading on an indicator variable which is unity if the buyer made a low price
announcement in both states (i.e., price announcement ≤ 40 in the good state, and a price
announcement ≤ 100 in the bad state) and an indicator variable which is unity if the buyer
made a high announcement (i.e., price announcement > 40 in the good state, or price
announcement > 100 in the bad state). These regressions show that when controlling for the
price level flexible contracts with low price announcements do not lead to different shading
levels than flexible contracts without price announcements. The coefficient in column (5)
which identifies the effect for the good state is essentially zero and not significant (p-value =
0.963, Probit estimation (marginal effects reported), standard errors clustered at the session
level), while the effect for the bad state in column (6) is insignificantly positive (p-value =
0.706). This result is compatible with the following interpretation: sellers do not expect
buyers who refrain from making explicit price announcements to pay higher prices than the
ones who explicitly say that they plan to pay low prices. In this sense sellers seem to interpret
the lack of an explicit price announcement as an implicit message that the buyer has no
intention to pay a high price.30 Not surprisingly and in line with our previous analysis we see
30
The finding that sellers seem to interpret the absence of an informal agreement as a signal that the buyer plans
to pay a low price may partly be driven by our experimental procedures. In order to clarify the procedures of the
decision making process for the participants our written instructions explain the presence of the opportunity to
attach informal agreements to flexible contracts in great detail. In this sense, the availability of these agreements
is very salient for the participants. As a consequence, the absence of an informal agreement may be interpreted
28
again that flexible contracts with high price announcements (which often lead to violations of
informal agreement) lead to substantially higher shading rates in both states of the world.
While this effect is highly significant in the good state (p-value = 0.005), it is not significant
in the bad state (p-value = 0.371).
Finally, Figure 2 and Table 5 allow us to compare outcomes in flexible contracts with
and without informal agreements, as well as in rigid contracts. Figure 2 displays shading
frequencies (grey bars), average prices (dots), average lower bounds (solid lines), and average
price announcements (dotted lines) for rigid contracts, flexible contracts without informal
agreements (NoIA), flexible contracts with low price announcements (LowIA), and flexible
contracts with high price announcements (HighIA). Table 5 provides the corresponding
numbers and adds a comparison of auction outcomes and buyer and seller profits across all
different kinds of observed contracts. The figure and the table show that when viewed from
the buyer perspective rigid contracts dominate all kinds of flexible contracts in the good state
of the world. Prices (39.8) and the shading rate (0.05) are lowest, so that buyer profits are
highest (98.2). Regressions of buyer profits on indicator variables for the different kinds of
flexible contracts (NoIA, LowIA, and HighIA) reveal that in the good state buyer profits in
rigid contracts are significantly higher than buyer profits in all kinds of flexible contracts
(NoIA: 90.1, p-value = 0.045, HighIA: 81.9, p-value = 0.007, LowIA: 91.2, p-value = 0.071,
OLS estimations, standard errors clustered at the session level).31 In the bad state, in contrast,
rigid contracts do not allow for trade (average buyer profit = outside option = 10) and
therefore flexible contracts are always more profitable for buyers (NoIA: 35.9, LowIA: 37.1,
HighIA: 21.2). However, the advantage of rigid contracts in the good state is large enough to
offset the disadvantage in the bad state, i.e., overall (across both states) buyer profits in rigid
contracts (78.2) are not significantly different from buyer profits in any type of flexible
contract (NoIA: 79.1, p-value = 0.824, LowIA: 81.6, p-value = 0.469, HighIA: 71.9, p-value =
0.199, OLS estimations, standard errors clustered at the session level).32
To summarize, it seems that the availability of informal state-contingent contracts
changes how sellers assess the fairness of outcomes. If buyers explicitly (by announcing low
somewhat differently in the experiment than in a situation outside of the lab in which the availability of such
agreements would be less obvious.
31
Non parametric signed-rank tests using session averages as observations yield p-value = 0.031 (NoIA, onesided), p-value = 0.063 (LowIA, one-sided), and p-value = 0.031 (HighIA, one-sided).
32
Non parametric signed-rank tests using session averages as observations yield p-value = 0.406 (NoIA, onesided), p-value = 0.500 (LowIA, one-sided), and p-value = 0.156 (HighIA, one-sided).
29
prices) or implicitly (by not making an announcement) indicate that they are not willing to
pay a high price, sellers are less aggrieved and less likely to engage in shading in response to
a low final price than in the baseline treatment where price announcements are not feasible. A
possible interpretation of this behavior is that the opportunity to conclude informal
agreements induces sellers not only to concentrate on the price level, but also to take into
account whether the buyer made a “promise”. It seems that sellers are somewhat more likely
to perceive a given price as acceptable if it is in accordance with the buyer’s ex ante stated
announcement. But if sellers feel that the buyer did not deliver on his promise, they feel
shortchanged and engage in shading. The overall somewhat lower shading in flexible
contracts increases their attractiveness for buyers relative to the baseline condition. As a
consequence, buyers are less likely to choose rigid contracts when informal agreements are
available. However, it is important to emphasize that the decrease in shading rates in flexible
contracts is only moderate and not sufficient to eliminate the trade-off between contractual
rigidity and flexibility. Even when informal agreements are available, it is still true that lower
prices trigger more shading in flexible contracts than in rigid ones. As a result, buyers who
choose rigid contracts realize higher profits in the good state of the world than buyer who
choose flexible contracts. The advantage of rigid contracts in the good state is large enough to
offset the disadvantage that rigid contracts do not allow for trade in the bad state. The
consequence is that on average rigid contracts are as profitable as flexible contracts.
IV.C. Renegotiation: Effects of Ex ante Contracts When Renegotiation is Not Initiated
We now turn to the analysis of our renegotiation treatment. The discussion of the possible
behavioral effects of renegotiation in Section III.B has revealed that one of the central
questions in the context of contractual reference points is whether contracts still shape
expectations and entitlements even if the trading parties know that renegotiation is always
feasible. To shed light on this question we start the analysis of our renegotiation condition by
investigating the outcomes in non-renegotiated rigid and flexible contracts. If the availability
of renegotiation eliminates contractual reference points, we would expect that the buyer’s ex
ante contract choice becomes irrelevant and that the seller’s quality choice is solely
determined by the ex post realized price. However, if contracts continue to serve as reference
points when renegotiation is feasible, rigid and flexible contracts should lead to different ex
post outcomes in non-renegotiated contracts. In particular, we would expect to see that in the
good state of the world rigid contracts are more attractive for buyers as they allow them to
obtain normal quality at lower prices than in flexible contracts.
30
Columns (1) to (4) of Table 6 summarize the results in non-renegotiated rigid and
flexible contracts in the renegotiation treatment. The table indicates average prices, relative
frequencies of shading, auction outcomes, and profits of buyers and sellers. As in our other
treatments we find that in both types of contracts the auction outcomes are slightly above the
competitive prediction of 35 on average (Fixed price: 39.8 / Lower Bound: 38.7), but they
converge to the competitive level over time.33 In line with the hypothesis that contracts also
shape reference points when renegotiation is available we find that in the good state of the
world prices and shading rates are higher in flexible contracts (42.2 / 0.09) than in rigid
contracts (38.5 / 0.04). As a consequence, buyers make higher profits in rigid contracts (99.8)
than in flexible contracts (94.4). Table 7 reports regressions that assess the statistical
significance of these results. In column (1) we regress prices in the good state on an indicator
variable which is unity if the buyer has chosen a rigid contract. The regression reveals that the
price difference is significant (p-value = 0.016, OLS estimation, standard errors clustered at
the session level).34 Columns (2) and (3) show that the difference in shading rates across types
of contracts is not statistically significant (not controlled for prices: p-value = 0.239 /
controlled for prices: p-value = 0.250, Probit estimations, marginal effects reported, standard
errors clustered at the session level).35 Column (4), however, confirms that the difference in
buyer profits is significant (p = 0.049, OLS estimation, standard errors clustered at the session
level).36 Table 6 also reports outcomes for the bad state of the world. While non-renegotiated
rigid contracts do not allow for trade and yield the outside option of 10, flexible contracts
exhibit an average price of 96.1 and a shading rate of 11 percent, so that buyer profits amount
to 39.4. This higher profit in the bad state offsets the disadvantage of flexible contracts in the
good state, so that rigid and flexible contracts yield very similar expected overall profits for
buyers (Rigid: 81.8 / Flexible: 79.4).37 Sellers who succeed in accepting flexible contracts
33
While the first 5 periods yield average auction outcomes of 43.1 (rigid contracts) and 41.6 (flexible contracts),
the corresponding values in the final 5 periods are 36.2 (rigid contracts) and 35.9 (flexible contracts). These
negative time trends are statistically significant. OLS regressions of auction outcomes on period reveal
significantly negative time trends for both types of contracts (p-value < 0.01, standard errors clustered at the
session level).
34
A non-parametric signed-rank test with session averages as observations yields p-value = 0.031 (one-sided).
35
A non-parametric signed-rank test with session averages as observations yields p-value = 0.156 (one-sided).
36
A non-parametric signed-rank test with session averages as observations yields p-value = 0.063 (one-sided).
37
It does not make sense to compare observed overall profits. The reason is that renegotiation is not equally
likely in the good and the bad state, so that the empirical weights of observations are distorted. The numbers for
overall profits reported in Table 6 are therefore weighted averages of profits in the good and the bad state of the
world.
31
realize higher profits (20.5) than sellers who obtain rigid contracts (26.5), because they
benefit from higher prices in the good state and trade opportunities in the bad state.
Our comparison of non-renegotiated rigid and flexible contracts illustrates that rigid
and flexible ex ante contracts also have different implications for ex post behavior even if all
market participants are aware that renegotiation is always feasible. This is interesting because
it suggests that the availability of renegotiation does not eliminate contractual reference
points. However, in order to get a more complete understanding of how the presence of
renegotiation opportunities affects trade in non-renegotiated contracts, it is also insightful to
compare these outcomes to the outcomes of the baseline treatment of FHZ, where the trading
parties do not have the possibility to renegotiate contracts. This is what we do next.
A comparison of columns (1) and (2) with columns (5) and (6) in Table 7 shows that
outcomes in non-renegotiated rigid contracts in the renegotiation treatment and outcomes in
rigid contracts of the baseline treatment are quite similar. In both treatments buyers get away
with low prices and low shading rates in the good state of the world. In fact, if anything, we
observe that lower prices (RG: 38.5 / BL: 40.7) and lower shading rates (RG: 0.04 / BL: 0.06)
lead to even higher buyer profits in the renegotiation treatment than in the baseline
condition.38 This reinforces our interpretation that the presence of renegotiation opportunities
does not induce sellers to hope for outcomes outside the contract. Even though sellers know
that the buyer can renegotiate the contract and increase the price at no cost, they do not seem
to expect him to do that and there is only very little shading if the buyer decides to stick to the
contract.
In flexible contracts, however, the availability of renegotiation affects outcomes
considerably. Comparing columns (3) and (4) to columns (7) and (8) in Table 7 allows us to
contrast outcomes in non-renegotiated flexible contracts in the renegotiation treatment with
outcomes in flexible contracts in the baseline treatment. In the good state we observe that
prices (RG: 42.2 / BL: 51.1) and shading rates (RG: 0.09 / BL: 0.25) in the renegotiation
treatment are substantially lower, so that buyer profits (RG: 94.4 / BL: 79.9) are much higher.
38
Regressions of prices (OLS), shading (Probit), and buyer profits (OLS) on a treatment dummy show that the
differences in prices and profits are significant, while the difference in shading is not (Price: p-value = 0.067 /
Shading: p-value = 0.349 / Buyer profits: p-value = 0.007, standard errors clustered at the session level). The
difference in shading remains insignificant if we control for the price level in the corresponding regression (pvalue = 0.426). Non-parametric rank-sum tests using session averages as observations yield p-value = 0.056
(prices, two-sided), p-value = 0.690 (shading, two-sided), and p-value = 0.016(buyer profits, two-sided).
32
All these differences are highly significant.39 The effects in the bad state are very similar.
Also here prices (RG: 96.1.2 / BL: 98.4) and shading rates (RG: 0.11 / BL: 0.30) are lower in
the renegotiation condition, and profits of buyers increase considerably (RG: 39.4 / BL: 29.7).
Again all differences are significant.40 These differences suggest that the availability of
renegotiation affects sellers’ perception of outcomes in non-renegotiated flexible contracts. It
seems that sellers are more willing to accept low prices in flexible contracts if they know that
the seller also has the possibility to renegotiate the contract. The fact that the price plays a less
significant role for sellers’ shading decision is further supported by the fact that higher prices
no longer reduce shading significantly (see the insignificant coefficient of price in column (3)
of Table 7). A possible explanation for this effect is that the presence of the renegotiation
possibility shifts part of the sellers’ focus away from prices to the renegotiation decision itself,
i.e., there may be sellers who find all outcomes acceptable as long as the buyer does not take
advantage of his possibility to renegotiate the contract in opportunistic ways.41 We will
further look into this possibility when we investigate the consequences of renegotiation
decisions in the following section.
To summarize, the data from non-renegotiated contracts suggest that rigid and flexible
contracts still have different implications for ex post performance in the presence of
renegotiation. In particular, it is still true that buyers who have picked a rigid contract realize
higher profits in the good state of the world because they can, on average, pay lower prices
without lowering quality. This implies that sellers apparently do not hope for outcomes which
would be feasible only if the buyer renegotiated the contract. We think that this is a strong
result. In this treatment the buyer’s contract choice has ultimately no consequence for the
39
Regressions of prices (OLS), shading (Probit), and buyer profits (OLS) on a treatment dummy show that the
all differences are highly significant (Price: p-value < 0.001 / Shading: p-value < 0.001 / Buyer profits: p-value <
0.001, standard errors clustered at the session level). The difference in shading is, of course, also significant if
we control for the price level in the corresponding regression (p-value < 0.001). Non-parametric rank-sum tests
using session averages as observations yield p-value = 0.008 (prices, two-sided), p-value = 0.008 (shading, twosided), and p-value = 0.008 (buyer profits, two-sided).
40
Regressions of prices (OLS), shading (Probit), and buyer profits (OLS) on a treatment dummy show that the
all differences are significant (Price: p-value = 0.015 / Shading: p-value < 0.041 / Buyer profits: p-value < 0.014,
standard errors clustered at the session level). The difference in shading is even more significant if we control for
the price level in the corresponding regression (p-value < 0.002). Non-parametric rank-sum tests using session
averages as observations yield p-value = 0.095 (prices, two-sided), p-value = 0.158 (shading, two-sided), and pvalue = 0.056(buyer profits, two-sided).
41
The effect that sellers seem to focus away from prices to the renegotiation decision itself may be more
accentuated in our laboratory setting than in real-world contexts. The reason is that the possibility of
renegotiation is very salient in the experiment. The written instructions to the experiment explain the
renegotiation opportunity and its consequences for the feasible outcomes in much detail. In many real-world
settings the possibility of renegotiation may not be as prominent in trading parties’ mind and they may therefore
concentrate more on the realized outcome within the bounds of the contract.
33
feasible outcomes (the buyer can always renegotiate for free and pick any price p [c(ql,) +
xs, v(qn)]). This implies that our design essentially turns the buyer’s contract choice into a
framing decision. Nevertheless, the contract still serves as a salient reference point. This
makes it likely that contractual reference points have also important implications in more
realistic situations, in which renegotiation of contracts is typically much more difficult and/or
costly.
IV.D. Renegotiation: Effects of Renegotiation on Ex post Performance
In this section we analyze the impact of renegotiation decisions on ex post performance. We
start with mutually beneficial renegotiations. In Section III.B we put forward the hypothesis
that mutually beneficial renegotiations (i.e., if the buyer renegotiated a rigid contract to make
trade feasible in the bad state of the world) turn rigid contracts into completely flexible
contracts. If this is true we should observe the same outcomes in renegotiated rigid contracts
and flexible contracts in the bad state of the world.
Figure 3 and Table 8 summarize outcomes in non-renegotiated and renegotiated rigid
and flexible contracts across both states of nature. Figure 3 displays shading frequencies (grey
bars), average prices (dots), and average lower bounds (solid lines). Table 8 provides the
corresponding numbers and adds information about auction outcomes and buyer and seller
profits for all different kinds of observed contracts. The figure and the table show that in the
bad state the average price (97.3), the shading rate (0.10), and average buyer profits (38.8) in
renegotiated rigid contracts are very similar to the corresponding values in flexible contracts
(96.1 / 0.11 / 39.4). The regression analysis in Table 9 confirms that neither of these
differences is statistically significant (Prices: p-value = 0.139 (OLS), Shading: p-value =
0.814 (Probit), Buyer profits: p-value = 0.871 (OLS), standard errors clustered at the session
level).42 These observations suggest that mutually beneficial renegotiations do not have
important psychological implications on their own. It rather seems that they just turn a rigid
contract into a flexible one and trigger the corresponding behavior on the seller side. It is
obvious that this makes mutually beneficial renegotiation a very attractive option for buyers
who have chosen rigid contracts. The realized buyer profit in trades permitted by renegotiated
rigid contracts (38.8) is much higher than the outside option of 10 that the buyer realizes if he
42
Non-parametric signed-rank tests with session averages as observations yield p-value = 0.625 (prices, twosided), p-value = 0.438 (shading, two-sided), p-value = 0.438 (buyer profits, two-sided).
34
doesn’t renegotiate the contract. Accordingly, it is not a big surprise that the vast majority of
rigid contracts (78 percent) are renegotiated when it turns out that the state of the world is
bad.
We now turn to opportunistic renegotiation. In Section III.B we hypothesize that
opportunistic renegotiation may be seen as a hostile act. In contrast to the mutually beneficial
renegotiations that we have discussed above, opportunistic renegotiations are never necessary
to avoid inefficiency, i.e., their only purpose is that they allow the buyer to grab a bigger share
of the gains from trade. Our hypothesis implies that a given outcome should lead to more
shading if the outcome came about by an opportunistic renegotiation than if the outcome has
been realized within the bounds of an existing contract. Figure 3 and Table 8 provide support
for this view. In both types of contracts opportunistic renegotiations in the good state of the
world yield low prices (Rigid: 37.5 / Flexible: 37:3), very high shading rates (Rigid: 0.50 /
Flexible: 0.45), and rather low profits (Rigid: 82.5 / Flexible: 84.7). Table 10 investigates the
statistical significance of these effects. In column (1) we use the data from rigid contracts and
regress an indicator variable for shading on an indicator variable for opportunistic
renegotiation, while controlling for the price level.43 Column (2) reports the same regression
for flexible contracts. Both regressions show that shading rates for a given price are
significantly higher if the price is the result of an opportunistic renegotiation than if the price
has been determined within the bound of an existing contract (p-value < 0.001 for both
contract types, standard errors clustered at the session level). These findings reinforce our
earlier interpretation that the sellers put considerable weight on the buyer’s renegotiation
decision when they evaluate the fairness or acceptability of ex post outcomes.
In columns (3) and (4) we compare buyer profits in non-renegotiated and
opportunistically renegotiated contracts, while controlling for the final price. We find that
buyer profits are significantly lower if the price has been determined by opportunistic
renegotiation than if the price has been realized within the bounds of an ex-ante determined
contract. In rigid contracts opportunistic renegotiation reduces buyer profits by about 18
points, in flexible contracts the reduction amounts to about 14 points (Rigid: p-value = 0.058 /
Flexible: p-value < 0.001, OLS estimation, standard errors clustered at the session level).
43
The regression contains only observations in which there was either no renegotiation or an opportunistic
renegotiation, i.e., we exclude observations in which buyers initiated renegotiation in the good state to increase
the price voluntarily ("altruistic" renegotiations).
35
However, it seems that most buyers are aware of the negative consequences of
opportunistic renegotiation. Overall, only about 5 percent of the rigid contracts and about 7
percent of the flexible contracts in which the good state has been realized are subject to
opportunistic renegotiation (see also Table 8). Moreover, Figure 3 shows that contracts are
more likely to be opportunistically renegotiated if auction outcomes (i.e., fixed prices or lower
bounds of the price range) are high. A simple regression of an indicator variable for
opportunistic renegotiation on the auction outcome confirms that there is a significantly
positive impact of a higher auction outcome on the probability of opportunistic
renegotiation.44 This makes sense as high auction outcomes imply that sticking to the contract
results in a low buyer profit.
Finally, we also observe “altruistic” renegotiations in a small number of rigid contracts
(about 5 percent of the cases in which the good state has been realized in a rigid contract, see
Table 8). By “altruistic” renegotiation we mean cases in which the buyer renegotiated the
contract and increased the price although the good state had been realized and trade would
have been possible at the fixed price defined in the contract. Not surprisingly, the affected
sellers seem to perceive these choices as generous and do not engage in shading.
Summarizing, our renegotiation treatment produces the following results: The
presence of renegotiation opportunities does not seem to eliminate the role of contracts as
reference points. In non-renegotiated contracts in the good state of the world, we still see that
rigidity has the advantage that buyers make high profits as they get high quality at lower
prices. This suggests that sellers still accept the competitively negotiated fixed prices as a
reference point and do not hope for higher profits that would be obtainable only by
renegotiation. However, although contracts seem to remain reference points, our evidence
also suggests that the availability of renegotiation changes how the trading parties evaluate ex
post outcomes. In particular, we observe that sellers are more willing to accept low prices in
flexible contracts if renegotiation is feasible. There appears to be a shift in the sellers’ focus
away from the price choice within the contract to the renegotiation decision itself. This
interpretation is further reinforced by the fact that opportunistic renegotiations trigger a strong
increase in sellers’ shading rates. Finally, we find that mutually beneficial renegotiations are
relatively unproblematic. If a rigid contract does not allow for trade because the price is lower
44
Probit estimation, standard errors adjusted for clustering at the session level: p-value < 0.001. The effects
remains significant if the regression is performed for each type of contract separately.
36
than the seller’s cost, the buyer can renegotiate the price upwards. While the newly introduced
flexibility in the ex post price choice leads to some shading, the profits from trade are still
much higher than the outside option.
V. Conclusions
In this paper we show experimentally that the central behavioral mechanism underlying the
concept of behavioral reference points is robust to the availability of informal agreements and
ex post renegotiation. Our first experiment reveals that the availability of informal, statecontingent messages affects sellers’ ex post evaluations of outcomes in flexible contracts. If
buyers explicitly or implicitly (by not sending a message) indicate that they are not willing to
pay a high price in a flexible contract, sellers are less aggrieved and less likely to engage in
shading in response to a low final price than in the baseline treatment where price
announcements are not feasible. However, the reduction in shading rates is not sufficient to
eliminate the trade-off between rigid and flexible contracts. As we deliberately designed the
experiment in a way that gives informal agreements a good chance to have an effect, we
interpret these findings as strong evidence that informal, state-contingent agreements are not
sufficient to avoid the shading problem caused by misaligned expectations in flexible
contracts.
Our second experiment suggests that the feasibility of ex post renegotiation does not
imply that contractual reference points become irrelevant. As long as the contract permits
trade in the realized state of the world parties seem to accept the contract as a reference point
and do not hope for unilaterally better outcomes that could be achieved only through
renegotiation. However, as in our first experiment we again observe that the broader action
space changes how ex post outcomes are evaluated. It seems that the presence of the
renegotiation opportunity renders the choice of inequitable terms in non-renegotiated
contracts more acceptable, i.e., as long as the contract is honored the parties are less likely to
engage in shading even if the realized outcome is not very favorable to them. The
interpretation that the renegotiation decision itself plays an important role for the evaluation
of an outcome is further reinforced by the finding that opportunistic renegotiation triggers a
large increase in the shading rate.
Taken together, the two experiments reported in this paper provide further evidence in
line with the idea that contractual reference points importantly shape performance in trading
relationships governed by incomplete contracts. We think that the insight that the main
37
underlying mechanisms of the theory are robust to realistic features like informal agreements
and renegotiation helps to clarify the range of applicability of the theory. In addition, we find
it interesting that our evidence also suggests refinements regarding the theory. The
observation that the trading parties’ evaluation of the ex post outcome depends not only on the
terms of the ex ante contract and the ex post realized state of the world but also on the
availability of other features such as informal agreements and renegotiation (even if these
features are eventually not used) indicates that the ex post evaluation of outcomes is a more
nuanced process than the current version of the theory assumes.
One important limitation of our paper is that opportunistic renegotiation is not very
tempting in our setup. As the competitive auction implies that buyers typically have the
opportunity to pay a low price within the bounds of the contract, buyers usually cannot gain
much from opportunistic renegotiation. In this sense our current experiment may present a too
positive view of renegotiation. Our finding that opportunistic renegotiation triggers severe
levels of shading suggests that renegotiation may actually lead to much larger problems in a
setup in which opportunistic renegotiation is very attractive for one of the parties. We leave
this interesting possibility for future work.
38
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40
Figure 1 (Informal Agreements): Price Announcements and Actual Prices
Good State
Bad State
0.60
90
0.60
150
0.50
80
0.50
140
0.40
70
0.40
130
0.30
60
0.30
120
0.20
50
0.20
110
0.10
40
0.10
100
0.00
30
0.00
90
No 40 50 60 70 80+
Price Announcements
Rel. Freq. of PA (l)
No 100 110 120 130 140
Price Announcements
Violation of IA
Average Price (r)
Notes: The labels of the horizontal axis categorize informal agreements. “No” indicates that the buyer has not
made a price announcements. The numbers describe ranges of price announcements (e.g., “40” means 35-40,
“50” means 41-50 etc., and “80+” means 71 or higher). The bars represent relative frequencies of price
announcements in the corresponding range (left axis). Observations for which the actual price is smaller than the
announced price (violation of informal agreements) are displayed in light gray. Averages of actual prices per
range of price announcements are represented as dots (right axis).
41
Figure 2 (Informal Agreements): Shading Behavior in Rigid and Flexible Contracts
0.35
140
0.30
120
0.25
100
0.20
80
0.15
60
0.10
40
0.05
20
0.00
0
NoPA
Rigid
NoPA
LowPA
Flexible
Good State
HighPA
NoPA
Rel. Frequency of Shading (r)
Lower Bound (l)
LowPA HighPA
Flexible
Bad State
Price (l)
Price Announcement (l)
Notes: “NoPA” stands for “no price announcement”. “LowPA” represents contracts, in which the buyer
announced a low price (i.e., price announcement ≤ 40 in the good state, or price announcement ≤ 100 in the bad
state). “HighPA” contains contracts, in which the buyer announced a high price (i.e., price announcement > 40 in
the good state, or price announcement > 100 in the bad state). The bars represent relative shading frequencies
(left axis). The solid lines display the average lower bound of the price range, dotted lines show average price
announcements and dots represent average actual prices (right axis).
42
Figure 3 (Renegotiation): Shading Behavior in Rigid and Flexible Contracts
0.60
120
0.50
100
0.40
80
0.30
60
0.20
40
0.10
20
0.00
0
NoR
AltR
OppR
NoR
Rigid
OppR
Flexible
Good State
MuBR
NoR
Rigid
Flexible
Bad State
Relative Frequency of Shading (l)
Fixed Price (l)
Average Price (r)
Lower Bound (r)
Notes: “NoR” stands for contracts that have not been renegotiated. “AltR” represents cases of “altruistic”
renegotiations, i.e., rigid contracts in which the buyer has increased the price although the good state has been
realized. “OppR” contains contracts in which the buyer has initiated opportunistic renegotiation to lower the
price below the fixed price in rigid contracts or below the lower bound of the price range in flexible contracts.
“MuBR” stands for mutually beneficial renegotiations. These are rigid contracts in which the buyer has
increased the price to make trade feasible after the bad state has been realized. The bars represent relative
shading frequencies (left axis). The solid lines display the average fixed price in rigid contracts, dashed lines
show average lower bounds in flexible contracts and dots represent average actual prices (right axis).
43
Table 1: Experimental Parameters
State of nature
Seller's quality
Good [Prob(s = g) = 0.8]
n
Bad [Prob(s = b) = 0.2]
l
n
l
normal (q = q )
low (q = q )
normal (q = q )
low (q = q )
Seller's costs
20
25
80
85
Buyer's valuations
140
100
140
100
Notes: The table summarizes the main parameters of the experiment. Buyers’ valuations for the product and
sellers’ production costs are displayed for both states of nature and both quality levels available to the seller.
44
Table 2 (Informal Agreements / Baseline): Comparison of Contracts
Informal Agreement
Contract
Rigid
Baseline
Flexible
Rigid
Flexible
State
Good
Bad
Good
Bad
Good
Bad
Good
Bad
Average Price
39.8
-
47.8
97.9
40.7
-
51.1
98.4
Rel. Freq. of Shading
0.05
-
0.13
0.21
0.06
-
0.25
0.30
Av. Auction Outcomce
Average Profit Buyer
38.7
39.8
98.2
10.0
87.3
76.9
78.2
Average Profit Seller
19.5
10.0
27.2
201
16.8
25.1
17.4
Number of Observations
33.9
59
539
131
40.7
96.8
10.0
77.9
20.4
10.0
18.1
398
111
40.2
79.9
29.7
68.9
29.8
16.9
27.2
407
104
Notes: The table summarizes the outcomes for rigid and flexible contracts in both states of nature. “Average
Price” is the average of the trading price and “Relative Frequency of Shading” measures how often the seller has
chosen the low quality. For rigid contracts this information is available only for the good state, because trade
does not occur in the bad state. “Average Auction Outcome” is the average of the fixed price in case of rigid
contracts and the lower bound of the price range in case of flexible contracts. “Average Profit Buyer (Seller)”
measures the average payoff of buyers (sellers) for each (state and) contract. In rigid contracts the payoffs in the
bad state of the world are the outside options of the market participants.
45
Table 3 (Informal Agreements): Trade-off Between Contractual Rigidity and Flexibility
Dependent Variable
State
Flexible contract
Price
Good
OLS
(1)
Shading
Good
Probit
(2)
Shading
Good
Probit
(3)
Profit
Good
OLS
(4)
Profit
Good&Bad
OLS
(5)
7.993**
(2.608)
0.073***
(0.018)
0.082***
(0.025)
-0.002**
(0.001)
-10.901**
(3.198)
-1.326
(4.033)
98.239***
(0.877)
78.215***
(2.231)
740
930
0.086
0.000
Price
Constant
Observation
R2
39.771***
(0.664)
740
740
740
0.090
Notes: “Flexible contract” is an indicator variable which is unity if the contract is of the flexible type and
zero otherwise. Columns (1), (4) and (5) report coefficients of OLS estimations. Columns (2) and (3) report
marginal effects based on Probit estimations. Since observations within sessions may be dependent all
reported standard errors are adjusted for clustering at the session level. *** p<0.01, ** p<0.05, * p<0.1.
46
Table 4 (Informal Agreements): Effects of Informal Agreements
Dep. Variable
State
Shading
Good
Probit
(1)
Shading
Bad
Probit
(2)
Shading
Good
Probit
(3)
Shading
Bad
Probit
(4)
Shading
Good
Probit
(5)
Shading
Bad
Probit
(6)
Price
-0.004
(0.003)
0.003***
(0.001)
-0.027***
(0.008)
0.008
(0.007)
-0.001
(0.003)
-0.017**
(0.010)
-0.004*
(0.002)
-0.017***
(0.008)
0.131***
(0.077)
0.382**
(0.216)
0.002
(0.033)
0.069***
(0.033)
0.019
(0.046)
0.127
(0.150)
539
131
Price Announc.
Violation of IA
Low PA
High PA
Observation
256
59
256
59
Notes: “Violation of IA” is an indicator variable which is unity if the buyer picks a final price which is below
his price announcement. “Low PA” is an indicator variable which is unity if the buyer announced low prices
for both states (i.e., price announcement ≤ 40 in the good state, and price announcement ≤ 100 in the bad
state). “High PA” is an indicator variable which is unity if the buyer announced a high price for at least one
state (i.e., price announcement > 40 in the good state, or price announcement > 100 in the bad state). All
columns report marginal effects based on Probit estimations. Since observations within sessions may be
dependent, all reported standard errors are adjusted for clustering at the session level. *** p<0.01, ** p<0.05,
* p<0.1.
47
Table 5 (Informal Agreements): Prices, Shading, and Buyer Profits Across Contracts
Contract
Rigid
Flexible
NoPA
LowPA
HighPA
State
Good
Bad
Good
Bad
Good
Bad
Good
Bad
Average Price
39.8
-
45.7
96.8
44.5
97.9
52.0
99.5
Rel. Freq. of Shading
0.05
-
0.11
0.18
0.11
0.14
0.15
0.27
Av. Auction Outcome
Average Profit Buyer
39.8
98.2
39.1
10.0
90.1
78.2
Average Profit Seller
19.5
201
35.9
91.2
79.1
10.0
25.1
59
283
38.4
36.4
81.6
15.9
24.0
23.3
17.4
Number of Observations
38.6
66
29.8
71.9
17.1
22.8
72
81.9
31.3
18.2
28.8
14
190
45
Notes: “NoPA” stands for “no price announcement”. “LowPA” represents contracts, in which the buyer
announced low prices for both states (i.e., price ≤ 40 in the good state, and price ≤ 100 in the bad state).
“HighPA” contains contracts, in which the buyer announced a high price for at least one state (i.e., price > 40 in
the good state, or price > 100 in the bad state). For descriptions of the variables please see the notes of Table 2.
48
Table 6 (Renegotiation / Baseline): Comparison of Non-Renegotiated Contracts
Renegotiation
Contract
Rigid
Baseline
Flexible
Rigid
Flexible
State
Good
Bad
Good
Bad
Good
Bad
Good
Bad
Average Price
38.5
-
42.2
96.1
40.7
-
51.1
98.4
Rel. Freq. of Shading
0.04
-
0.09
0.11
0.06
-
0.25
0.30
Av. Auction Outcomce
Average Profit Buyer
(weighted average)
Average Profit Seller
(weighted average)
Number of Observations
37.3
38.6
99.8
10.0
94.4
10.0
21.7
16.6
282
39.4
83.4
81.8
18.3
40.7
418
10.0
79.4
15.5
20.5
20
96.8
20.4
10.0
18.3
79
398
111
40.2
79.9
29.7
69.9
29.8
16.9
27.2
407
104
Notes: See the notes of Table 2 for a detailed description of all variables. Since renegotiation is not equally
likely in the good and the bad state, we do not compare observed overall profits (the empirical weights are
distorted). Instead we provide weighted averages of profits in the good and the bad state of the world (using the
theoretical probabilities for the realization of each state).
49
Table 7 (Renegotiation): Comparison of Non-Renegotiated Rigid and Flexible Contracts
Dependent Variable
State
Flexible contract
Price
Good
OLS
(1)
Shading
Good
Probit
(2)
Shading
Good
Probit
(3)
Profit
Good
OLS
(4)
3.642**
(0.909)
0.043
(0.038)
0.045
(0.040)
-0.001
(0.001)
-5.398**
(1.925)
Price
Constant
Observation
R2
38.521***
(0.634)
710
99.777***
(0.618)
710
0.048
710
710
0.041
Notes: “Flexible contract” is an indicator variable which is unity if the contract is of the flexible type and
zero otherwise. Columns (1) and (4) report coefficients of OLS estimations. Columns (2) and (3) report
marginal effects based on Probit estimations. Since observations within sessions may be dependent all
reported standard errors are adjusted for clustering at the session level. *** p<0.01, ** p<0.05, * p<0.1.
50
Table 8 (Renegotiation): Effects of Renegotiation on Prices, Shading, and Buyer Profits
Rigid
Contract
Flexible
Good
State
Bad
Good
Bad
Renegotion
No
Alt
Opp
No
MuB
No
Opp
No
Average Price
38.5
55.3
37.5
-
97.3
42.2
37.3
96.1
Rel. Freq. of Shading
0.04
0.00
0.50
-
0.10
0.09
0.45
0.11
Auction Outcome
38.5
38.4
46.8
39.5
38.9
37.2
51.3
37.9
Average Profit Buyer
99.8
84.7
82.5
10.0
38.8
94.4
84.7
39.4
Opt. Profit Buyer
Average Profit Seller
87.6
18.3
35.3
Prof. Seller if Buyer opt.
Number of Observations
15.0
83.4
10.0
16.9
21.7
18.0
282
15
16
15.0
15.5
20.5
20
63
428
31
105
Notes: “No” stands for contracts that have not been renegotiated. “Alt” represents contracts in which the buyer
has initiated “altruistic” renegotiation in order to increase the fixed price of a rigid contract although the good
state has been realized. “Opp” contains contracts in which the buyer has initiated an opportunistic renegotiation
to lower the price below the fixed price in rigid contracts or below the lower bound of the price range in flexible
contracts. “MuB” stands for mutually beneficial renegotiations. These are rigid contracts in which the buyer has
increased the price to make trade feasible after the bad state has been realized. “Optimal Profit Buyer” is the
expected profit of a buyer who chooses a specific contract type and behaves optimally in each state (based on
observed profits). “Profit Seller if Buyer optimizes” is the expected profit of sellers if the buyer behaves
optimally in each state.
51
Table 9 (Renegotiation): Effects of Mutually Beneficial Renegotiations
Dependent Variable
State
Flexible contract
Price
Bad
OLS
(1)
Shading
Bad
Probit
(2)
Shading
Bad
Probit
(3)
Profit
Bad
OLS
(4)
-1.273
(0.692)
0.019
(0.079)
0.000
(0.080)
-0.015*
(0.013)
0.511
(2.956)
Price
Constant
Observation
R2
97.349***
(0.835)
168
38.841***
(3.512)
168
0.039
168
168
0.000
Notes: “Flexible contract” is an indicator variable which is unity if the contract is of the flexible type and
zero otherwise. Columns (1) and (4) report coefficients of OLS estimations. Columns (2) and (3) report
marginal effects based on Probit estimations. Since observations within sessions may be dependent all
reported standard errors are adjusted for clustering at the session level. *** p<0.01, ** p<0.05, * p<0.1.
52
Table 10 (Renegotiation): Effects of Opportunistic Renegotiations
Dep. Variable
State
Contract
Shading
Good
Rigid
Probit
(1)
Shading
Good
Flexible
Probit
(2)
Profit
Good
Rigid
OLS
(3)
Profit
Good
Flexible
OLS
(4)
Price
-0.002
(0.002)
0.469***
(0.168)
-0.002
(0.002)
0.350***
(0.029)
-1.114***
(0.119)
-18.414*
(7.010)
-0.951***
(0.057)
-14.368***
(1.031)
142.679***
(4.093)
134.488***
(2.793)
298
459
0.415
0.342
Opp. Reneg.
Auction Outc.
Constant
Observations
2
R
298
459
Notes: “Opportunistic Renegotiation” is an indicator variable which is unity if the buyer has initiated
renegotiation in the good state of the world to either lower the price to a level below the fixed price of a rigid
contract or the lower bound of the price range in a flexible contract. Columns (1) and (2) report marginal
effects based on Probit estimations. Columns (3) and (4) report coefficients of OLS estimations. Since
observations within sessions may be dependent, all reported standard errors are adjusted for clustering at the
session level. *** p<0.01, ** p<0.05, * p<0.1.
53