A laboratory investigation of alternative transfer pricing mechanisms

Accounting. Organizations and Society, Vol. 14, Nos. 1/2, pp. 41---64, 1989. Printed in Great Britain

0361-3682/89 $3.00+.00 Pergamon Press plc

A LABORATORY INVESTIGATION OF ALTERNATIVE TRANSFER PRICING MECHANISMS*

D O U G L A S V. D E J O N G a n d R O B E R T F O R S Y T H E

University o f l o w a J A E - O H KIM

Ohio State University and W I L F R E D C. U E C K E R

Rice University

Abstract In this study, we conduct a laboratory experiment to evaluate three alternative mechanisms for pricing transfers between a buyer and a seller. The three mechanisms are: ( 1 ) a direct negotiation mechanism with which either party suggests terms of trade that the other can accept or reject; (2) a traditional mechanism where the transfer price and quantity are determined by the intersection of the reported demand and supply schedules of the buyer and seller, respectively; and ( 3 ) the Ronen-McKinney mechanism which computes the transfer quantity in the same way as the traditional mechanism, but is designed to give different transfer prices to the buyer and seller in order to induce them to truthfully report their respective schedules. For all periods of the experiment, the direct negotiation mechanism is the least efficient of the three due to the high frequency of bargaining impasses. The efficiency of the traditional mechanism and the efficiency of the Ronen-McKinney mechanism are indistinguishable from one another. However, in the last four periods of the experiment where the data exhibit less volatility, the efficiencies of all three mechanisms are indistinguishable from each other. When truthful reporting is considered, the Ronen-McKinney mechanism had the least amount ofmisreporting followed by the traditional mechanism and then the direct negotiation mechanism.

A great deal of effort has been focused on designing mechanisms for the transfer pricing problem in a vertically integrated firm that decentralizes t h r o u g h p r o f i t c e n t e r s ( e . g . K a p l a n , 1 9 8 2 ; Ant h o n y et al., 1 9 8 4 ) . B e g i n n i n g i n t h e m i d 5 0 s (Dean, 1955) and continuing into the present ( e . g . S w i e r i n g a & W a t e r h o u s e , 1 9 8 2 ) , t h i s research has focused on the ability of alternative

transfer pricing mechanisms to satisfy two normative criteria. These criteria require that: ( 1 ) a m e c h a n i s m s h o u l d p r o v i d e i n c e n t i v e s f o r selfinterested managers to transfer a quantity which maximizes the firm's overall profit, and (2) the i n f o r m a t i o n t h a t is r e c e i v e d t h r o u g h t h e o p e r a tion of a mechanism should allow central management to evaluate the contribution of each

*We thank two anonymous referees and workshop participants at Case Western Reserve University, the University of Iowa, New York University, University of North Carolina and Texas A&M University for their comments and suggestions. An earlier version of this was also presented at the 1986 Behavioural Decision Research in Management Conference at Cornell University and the 1986 national meeting of the American Accounting Association. Funding for the experiment was provided by the Department of Accounting at the University of Iowa. Partial support for DeJong was provided by the summer grant program of the College of Business Administration at the University of Iowa; partial support for Forsythe was provided by NSF Grant SES-8607771. 41

42

DOUGLASV. DEJONGe¢ aL

profit center without sacrificing the autonomy of the centers. The techniques that have been employed in this research include formal economic analysis, mathematical p r o g r a m m i n g methods and behavioral approaches (Abdelkhalik & Lusk, 1974). Yet, to date, there has been no empirical evaluation of the performance of any of the proposed transfer pricing mechanisms. In this study, we report the results of a laboratory experiment which was designed to evaluate the performance of three alternative transfer pricing mechanisms. These mechanisms are applicable for pricing transfers b e t w e e n profit centers w h e n each manager's compensation scheme is based upon his center's profits. In this experiment, we restrict our attention to those situations w h e r e there is no external market for the c o m m o d i t y being transferred. The presence of such a market would require the simultaneous determination of the external market price and the transfer price. Since this is our first attempt at examining alternative transfer pricing mechanisms, w e have foregone this additional complexity and have concentrated solely on the mechanisms' performance in bilateral bargaining situations. Our laboratory experiment consists of an experimenter, whose actions vary with the transfer pricing mechanisms, and bargaining pairs, each pair consisting of a buyer and a seller. The transfer pricing mechanisms are then i m p l e m e n t e d in a manner such that the bargaining pairs engage in decision-making over a sequence of trading periods to determine a transfer price and quantity to be transferred. Since the e x p e r i m e n t e r never imposes price or quantity decisions, the a u t o n o m y of both the buyer and the seller is maintained. We use the data from the experiment to evaluate the efficiency and incentive compatability of each mechanism. Efficiency measures the ability of each mechanism to achieve an o u t c o m e which maximizes the combined profits of the buyer and seller, while incentive compatibility measures the accuracy

of the information reported by the buyer and seller. Since the mechanisms we consider all preserve divisional autonomy, the incentive compatibility measure indicates the reliability of the headquarter's assessment of each individual's profitability based upon the reported information. The first of the three alternative mechanisms permits direct negotiations between the buyer and the seller in that either party can suggest terms of trade that the other party may accept or reject. With this mechanism, the headquarters serves only as a conduit for the exchange of transfer price proposals b e t w e e n the two parties. If both parties behave non-strategically, they should agree to transfer the efficient quantity because this quantity maximizes their combined profits. However, critics have argued that this mechanism heightens conflict between the bargaining parties (Cyert & March, 1963). Furthermore, Coursey ( 1 9 8 2 ) has shown that impasse may b e c o m e a bargaining tool with direct negotiations. If similar results are observed in our environment, each bargaining pair's ability to maximize their c o m b i n e d profits will be impaired. Finally, Dopuch & Drake (1964) have suggested that with this mechanism, performance evaluation is based on the ability to negotiate rather than on performance itself. In turn, this should reduce the accuracy of the information reported by the buyer and the seller w h e n they engage in direct negotiation. The second mechanism is based upon the traditional view of transfer pricing (e.g. Hirsh. leifer, 1956), w h e r e each party announces their respective supply and demand schedules and the headquarters proposes a transfer price and quantity given by the intersection of the two reported schedules. This transfer pricing mechanism leads to an efficient transfer if b o t h parties truthfully reveal their information. However, with this mechanism, each party has an in. centive to misrepresent his private information at the expense of the other party's profit and

*Theonly empirical work to date consists of descriptive surveys of transfer pricing mechanismscurrently used by firms (e.g. Ecclcs, 1983).

ALTERNATIVETRANSFERPRICINGMECHANISMS c o m b i n e d profits. These misrepresentations will impair the incentive compatibility of the traditional mechanism which, in turn, should reduce its efficiency. The third mechanism, which was suggested by Ronen & McKinney (1970), has the important theoretical p r o p e r t y that it can lead to an equilibrium which is incentive compatible. As with the traditional mechanism, the buyer and seller report their demand and supply schedule to the headquarters which, in turn, proposes a transfer price and quantity. The proposed price and quantity with the Ronen-McKinney mechanism is, in general, different than that proposed with the traditional mechanism. In particular, while the traditional mechanism demonstrates what the optimal transfer price and quantity should be, it fails to suggest a way of implementing a p r o c e d u r e to accomplish this objective. By treating the buyer as a perfectly discriminating monopsonist, the seller as a perfectly discriminating monopolist and having the headquarters subsidize the buyer and seller, the Ronen-McKinney mechanism attempts to overc o m e this implementation problem. The difficulty with this mechanism is that while truthtelling leads to one equilibrium it is not the only equilibrium. We will discuss this difficulty in further depth in the next section. The theoretical properties of each of the three mechanisms have b e e n developed within the context of a single period model. Taken literally, this requires that the buyer and seller have only one opportunity to interact, w h e r e they each simultaneously report their private information as required by the mechanism and based on their reports, the mechanism determines a transfer price and quantity. After the transfer is made, the two parties c o m p u t e their respective profits and never interact again. As described earlier, our experimental environment does not correspond exactly to the above scenario since the b u y e r and seller interact repeatedly n both within and across trading periods. Thus, w e e m p l o y the "off the domain" approach which has b e e n used in m u c h of the recent experimental e c o n o m i c s literature (see Plott, 1982; Smith, 1982). With this

43

approach, one inquires about the ability of existing models to predict behavior in an environm e n t that has s o m e subjectively determined, interesting properties. Even in situations w h e r e one or m o r e assumptions are clearly violated, it is not u n c o m m o n for a model to accurately capture the observed behavior. In the next section, the experimental design is outlined, along with a description of the laboratory e x p e r i m e n t used to analyze the three alternative solutions to the transfer pricing problem. This section also includes the predictions of the three transfer pricing mechanisms. In the Results section, w e present s u m m a r y measures of the e x p e r i m e n t and provide a discussion and interpretation of them. A s u m m a r y and s o m e suggestions for future research are given in the final section. THE LABORATORY EXPERIMENT Each mechanism was tested on nine separate bargaining pairs; thus, the e x p e r i m e n t consisted of twenty-seven bargaining pairs, all of w h o m w e r e student volunteers of the University of Iowa. The e x p e r i m e n t was conducted in nine separate sessions with each session consisting of three bargaining pairs. The same mechanism was imposed on all three pairs in each session. Participants w e r e randomly designated as either buyers or sellers. To maintain anonymity, buyers arrived about 10 minutes before sellers and w e r e seated in a separate r o o m from sellers. The buyers w e r e also excused ahead of the sellers. When all participants had arrived, the instructions (which are r e p r o d u c e d in the appendix) w e r e read separately in each r o o m and questions w e r e answered. Participants w e r e then asked to c o m p l e t e a set of practice calculations (also r e p r o d u c e d in the appendix) which was designed to verify that they understood the trading procedures, the information available in the exp e r i m e n t and their profit calculations. Value for the units being traded was established by application of induced value theory (Smith, 1976). Specifically, the c o m m o d i t y being transferred was given value by the rules governing the transfer and the marginal cost and

44

DOUGLASV. DEJONGet aL

marginal r e v e n u e s c h e d u l e s g i v e n b y the seller a n d buyer, respectively. In o u r e x p e r i m e n t , each b u y e r was g i v e n a marginal r e v e n u e s c h e d u l e w h i c h was his private information. This s c h e d u l e c o n t a i n e d the a m o u n t the experim e n t e r w o u l d pay h i m for each of the u n i t s p u r c h a s e d from the seller d u r i n g a trading period. T h e difference b e t w e e n each unit's r e v e n u e a n d its p u r c h a s e p r i c e is the b u y e r ' s profit w h i c h was his to keep. C o r r e s p o n d i n g l y , each seller's private i n f o r m a t i o n was his marginal cost schedule, i.e. the a m o u n t the seller m u s t pay to the e x p e r i m e n t e r for each of the units sold to the b u y e r d u r i n g a trading period. A seller's profit, w h i c h was his to keep, ks the differe n c e b e t w e e n each u n i t ' s selling p r i c e and its COSt.

J3.06

Figure 1 p r e s e n t s the p a r a m e t e r values that w e r e used by each b a r g a i n i n g pair in the experim e n t . From this figure, it c a n b e s e e n that the optimal q u a n t i t y to be transferred is six o r s e v e n units s i n c e the c o m b i n e d profits of the b u y e r a n d seller, $1.92, are m a x i m i z e d at this quanity. Further, the transfer p r i c e associated w i t h this q u a n t i t y is $2.80. 2 Each b a r g a i n i n g pair p a r t i c i p a t e d in t e n decis i o n - m a k i n g periods. After the first period, each successive p e r i o d was a strict r e p l i c a t i o n of previous p e r i o d s in the sense that the same transfer p r i c i n g m e c h a n i s m was e m p l o y e d a n d each b u y e r ' s ( s e l l e r ' s ) marginal r e v e n u e ( c o s t ) s c h e d u l e was the same. At the c o n c l u s i o n of these t e n periods, each p a r t i c i p a n t c u m u l a t e d his profits from all trading p e r i o d s a n d was paid

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QuanLiLy Fig. !. Parameter values.[ ] buyer's profit which is $0.96,[ ] seger's profit which is $0.96,[ ] + [ ] combinedprofits of buyer and seller which equal $1.92. "Note, however, that with a transfer price of $2.80, both the buyer and the seller earn zero profits on trading the 7th unit. Since traders should be indifferent towards exchanging this unit, we are unable to provide a precise prediction about whether or not this unit will be transferred. One approach to overcoming this difficultywould be to adopt the procedure of Plott & Smith (1978) who paid participants a 5¢ commission on each unit that they traded. However, they prevented traders from shifting their schedules by this amount by prohibiting buyers (sellers) from reporting more (less) than their marginal revenue (cost) schedule. We are reluctant to use this technique here since, as will be seen below, some of the more interesting equilibria in the Ronen-McKinneymechanism occur when buyers (sellers) overreport (underreport) their private valuation schedules. Consequently, the optimal quantity under each mechanism is 6 or 7 units.

ALTERNATIVETRANSFERPRICINGMECHANISMS this amount in cash. Payments ranged from about $8.00 to $19.00. The treatment variable in the experiment is the transfer pricing mechanism. A mechanism, however, is simply a rule which specifies a transfer price and quantity given the information reported by the buyer and seller. To implement such a rule or mechanism, a process must be specified which defines h o w information is transferred, h o w agreement is reached, and h o w payoffs are made. While there are conceivably many such processes, we chose one particular process in which each transfer pricing mechanism was imbedded. The process we chose was c o n d u c t e d as a three stage iterative procedure where: ( 1 ) each participant sent a private message to the experimenter; ( 2 ) the experimenter calculated proposed transfer prices and quantities and sent this message to both parties; and ( 3 ) the buyer and seller either accepted or rejected the proposal. If both accepted the proposal, an agreement was reached and each participant c o m p u t e d his profits for the period based on this agreement. If either rejected the agreement, the participants repeated the above procedure. If the 10-minute time limit was exceeded before an agreement was reached, each subject earned zero profits for that period.

The direct negotiation m e c h a n i s m With direct negotiations, the buyer's message consisted of a bid indicating h o w much he was willing to pay the seller for 1 unit, 2 units, etc., up to and including 10 units. The seller's message consisted of an offer indicating the price required to sell 1 unit, 2 units, etc., up to and including 10 units. The experimenter simply transferred the buyer's proposal to the seller and vice versa. There could be only one proposal from either the buyer or seller outstanding at any point in time and the party receiving the proposal had to either accept or reject it. An

45

agreement occurred when one party accepted one of the price and quantity combinations the other party had proposed. If both parties behave non.strategically, they should transfer the efficient quantity since this quantity maximizes their combined profits. Further, if they split these profits equally, the transfer price will be $2.80, the efficient transfer price for the parameter values in Fig. 1. However, each party may have an incentive to behave strategically. This occurs whenever one of the parties believes that he can manipulate the outc o m e to earn larger profiits. For instance, a seller has an incentive to sell less than the efficient quantity if he believes that he will receive a price which will increase his profits.

The traditional m e c h a n i s m With the traditional mechanism, both the buyer and seller provided schedules to the experimenter. The schedule reported by the buyer (seller) indicated h o w much he was willing to pay for (required to sell) 1 unit, 2 units, etc., on up to and including 10 units. The experimenter then proposed a transfer price and quantity. This proposed price and quantity was determined by the intersection of the two reported schedules. Either the buyer or seller could veto the proposal. 3 If both accepted the proposal, a binding agreement was mad e based upon the proposal. If both parties truthfully report their respective schedule, an efficient transfer should occur. However, each party has an incentive to misreport in this environment. To see this, reexamine the parameter values in Fig. 1. If the buyer truthfully reports his marginal revenue schedule then, relative to reporting truthfully, the seller can increase his profits by reporting the marginal cost of his first four units truthfully and reporting that his marginal cost for the fifth and all additional units is $2.90 each. The traditional mechanism would then transfer five units

-~Sinceindividuals could only trade an integer-valuednumber of units, there is sometimes a range of prices at which the quantity demanded and supplied are equal with the traditional mechanism.That is, a bid submitted by the buyer for the last unit transacted may exceed the offersubmitted by the seller to sell that unit. When this occurred, the averageof these prices was proposed as the transfer price. Sinceboth the buyer and seller could veto such a proposal, this rule should have no effecton the outcomes.

46

DOUGLASV. DEJONG et aL

and set a transfer price of $2.90. Such a reporting strategy would increase the seller's profits from $0.96 to $1.40. However, the buyer's profits would decrease from $0.96 to $0.40 and combined profits would also be reduced from $1.92 to $1.80. Similarly, it can be shown that when the seller reports truthfully, the buyer has an incentive to understate his marginal revenue information.

+ APbDB - PsPbDC = AOB. For the parameter values used in the experiment, the transfer price for the seller and buyer is $2.96 and $2.64, respectively, when the quantity is 6 units ( $2.94 and $2.66, respectively, when the quantity is 7 units). This implies a profit of $1.92 for the buyer and $1.92 for the seller; consequently, the subsidy is also $1.92.

The R o n e n - M c K i n n e y m e c h a n i s m

Trading procedures in this mechanism are exactly the same as the procedures for the traditional mechanism except for the determination of the transfer price. As before, the proposed quantity to be traded is the amount which equates the reported marginal cost to the reported marginal revenue. However, the proposed transfer price which the buyer must pay is the seller's reported average cost for providing that quantity. The proposed transfer price the seller receives is the buyer's reported average revenue from receiving that quantity. 4 To illustrate h o w this mechanism operates, let the linesMC* andAC* in Fig. 2 represent the seller's true marginal cost and average cost, respectively, and let the lines MR* and AR* represent the buyer's true marginal revenue and average revenue, respectively. The efficient quantity to be transferred is Q* since combined profits, A O B are maximized at this quantity. If the buyer and seller report their true marginal cost and revenue information, the seller's transfer price is Ps and the buyer's transfer price is Pb and the quantity Q* is transferred. The profit to the seller is OPsCB, the profit to the buyer isAPtyDB and the subsidy is PsP~DC. Furthermore, since OPb E -E B D and APsF = F B C (because, by construction, the total amount paid by the buyer equals the seller's reported total cost, OP~DQ* = OBQ*, and the total amount received by the seller equals the buyer's reported total revenue, OPsCQ* = OABQ* ), combined profits are OPsCB

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Fig. 2. Ronen-McKinneytransfer pricing mechanism.OPsCB, seller's profit;APt,DB, buyer's profit; PsPt,LKT,subsidy;AOB, combined profits where OPsCB+ APbDB - P,PbDC --- AOB. With this mechanism, truthful reporting is a Nash equilibrium strategy for both the buyer and seller. To illustrate this, suppose the seller reports his true marginal cost schedule to the experimenter. This reported information then becomes the buyer's marginal cost s c h e d u l e . Since the seller's reported marginal cost equals the buyer's marginal revenue at Q*, the buyer's most preferred transfer quantity is Q*. Since the schedule reported by the buyer only affects the quantity he will receive from the seller, the

4Moreover, the Ronen-McKinneymechanism maintains the autonomyof the buyer and seller because either the buyer, the seller or both can select the quantity to be transferred without having that decision monitored by the headquarters. In our experiment, the experimenter proposed both a quantity to be transferred and a separate transfer price for the buyer and seller, respectively.Since either the buyer or seller could veto anyproposal, this procedure also maintained their autonomy.

ALTERNATI~'ETRANSFERPRICINGMECHANISMS buyer will report information such that the headquarters will propose Q*. Hence, the buyer can do no better than report his true marginal revenue information. Correspondingly, the seller's true marginal cost information is his best report given the buyer sends his true marginal revenue information. With this reported information, the headquarters will propose Q*, Ps and Pb and both parties should accept this proposal. Thus, an incentive-compatible Nash equilibrium exists with the Ronen-McKinney mechanism. Unfortunately, while truthful reporting is a Nash equilibrium, it is not the only equilibrium that exists with the Ronen-McKinney mechanism (Groves & Loeb, 1974). Alternative Nash equilibria result whenever each party's reported schedule intersects the other party's true schedule at the same quantity. Of particular interest is the equilibrium where the combined profits of the buyer and seller are the largest. In this case, the equilibrium strategies are for the seller to understate his marginal cost as $O.00 for all 10 units and for the buyer to overstate his marginal revenue as $3.00 for all 10 units, s Based on this information, the headquarters will propose that ten units be transferred where the proposed transfer price for the seller is $3.00 and the proposed transfer price for the buyer is $0.00. Profits of the buyer and seller are $28.58 and $2.58, respectively, which are greater than their respective profits at the incentive-compatible Nash equilibrium. Thus, this equilibrium leaves both parties better off than at the truthful equilibrium and it seems plausible that both parties would discover this method for exploiting the mechanism to their mutual advantage.

RESULTS Figures 3, 4 and 5 present the data from the experiment for the direct negotiation, traditional and Ronen-McKinney mechanisms, respectively. Figures 3 and 4 are organized into two

47

panels with the first panel displaying the time series of transfer quantities and the second panel displaying the time series of transfer prices for each of the nine bargaining pairs. A dot in the NA row of the quantity and price panels indicates a failure of the bargaining pair to reach an agreement in that period. Figure 5 is organized the same way as Figs 3 and 4, with the exception that the second panel has two transfer prices in each period: the one the seller receives, s, and the one the buyer pays, b. Our analysis of the data proceeds in two parts: first, we examine the profitability of the decisions reached under each mechanism; second, we evaluate the ability of each mechanism to provide incentives for eliciting truthful reporting. In dealing with the data, we are confronted with some open problems which arise in experimental work where the cost of conducting experiments places a significant constraint on the number of observations. As is obvious from the figures, there is a high degree of serial correlation in the decisions made by each bargaining pair. While this is suggestive of a learning process, a convergence process or both, we are without a theory about such processes and thus are unable to account for their effect. Consequently, we must provide the usual caveat that the statistical tests reported below should be regarded more as descriptive measures than as classical hypothesis tests. It is also known that experimental markets tend to converge rather than attain equilibrium immediately. Further, many static economic models of market behaviour are known to be accurate only after a series of repeated trials in a stationary environment (Plott, 1982; Smith, 1982). However, no convention has been established for the number of replications that are required for the data to approach equilibrium levels. Due to this, we conduct each of our analyses using all the data from the experiment and also using only the data from the last four periods. For the measures examined, the data

SForthe laboratoryenvironment we examined, these particular values arise since we restricted the buyer from reporting a marginal revenue of more than $3.00 and the seller from reporting a negative marginalcost. This was done in order to limit the maximum possible payout that participants would earn in the event they found this alternative Nash equilibrium.

48

DOUGLAS V. DEJONG et aZ Bargaining I

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from the last four periods are of particular interest because these data exhibit less volatility and relative to the early periods, seem to h a v e " s e t t l e d d o w n " . 6 Finally, a f t e r w e i n t r o d u c e e a c h of these measures, the evidence on the dec r e a s e d v o l a t i l i t y o f e a c h m e a s u r e is g i v e n .

Arejoint profit-maximizing decisions achieved?

To determine whether the decisions made by

the bargaining pairs maximized their joint profit, w e constructed an efficiency measure for each p o s s i b l e t r a n s a c t i o n . E f f i c i e n c y is d e f i n e d ratio of combined profits realized by the and seller to their maximum combined attainable in equilibrium. We examine

as t h e buyer profits these

efficiencies and contrast them by mechanism to identify significant differences b e t w e e n the mechanisms' performance. We c o n c l u d e by examining the transfer quantities to identify the source of any inefficiencies. The maximum joint profit attainable in equilibrium is $1.92 (see Fig. 1). The realized joint profit of the buyer and seller could exceed this maximum with the Ronen-McKinney mechanism due to the subsidy paid to the buyer and seller. To compensate for this potential difficulty, the subsidy paid to the buyer and seller was not included in this calculation. Net of the subsidy, realized joint profit for the RonenMcKinney mechanism can not exceed $1.927 The average efficiencies for the three

°When analyzing the last four periods, it should be emphasized that each bargaining pair had collected more information in the first six periods than was available from just six buy and sell offers. On average, each pair initiated five buy and sell offers per period. Thus, each pair had considered on average 30 buy and sell offers by the end of period 6. 7An alternative way to view this calculation is that it is the maximum joint profit of the buyer, seller and the headquarters. This is also $1.92 because the headquarters' losses equal the subsidy paid to the buyer and seller.

ALTERNATIVE TRANSFER PRICING MECHANISMS

49

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t

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mechanisms are presented in the upper lefthand panel o f Table 1. These means w e r e calculated for all periods and the last four periods. For all periods, the average efficiencies for the direct negotiation, traditional and Ronen-McKinney mechanism, respectively, are significantly less than 1.0 using a one-tailed t-test. 8 When the m e a n s w e r e compared across mechanisms, the Ronen-McKinney mechanism had the highest efficiency. The traditional mechanism was s e c o n d and the direct negotiation mechanism was third. To determine the significance of these differences across the mechanisms, w e conducted an analysis of variance (ANOVA) with a repeated measure design .° The results, pre-

s e n t e d in t h e l o w e r left-hand p a n e l o f T a b l e 1, ind i c a t e that at least o n e o f t h e m e c h a n i s m s is dist i n c t f r o m t h e o t h e r t w o , s i n c e t h e m a i n effect, m e c h a n i s m , is statistically significant. F u r t h e r , w h e n e a c h p a i r o f m e c h a n i s m s is individually c o n t r a s t e d , t h e efficiency o f t h e d i r e c t negotiat i o n m e c h a n i s m differs significantly f r o m t h e eff i c i e n c y o f b o t h t h e t r a d i t i o n a l and RonenM c K i n n e y m e c h a n i s m s . T h e r e is n o significant difference between the latter two mechanisms. T h e r e a r e t w o p o s s i b l e s o u r c e s for t h e signific a n t d i f f e r e n c e in efficiencies b e t w e e n t h e direct negotiation mechanism and the other two m e c h a n i s m s . First, w i t h t h e d i r e c t n e g o t i a t i o n m e c h a n i s m , t h e r e c o u l d b e m o r e p e r i o d s in

s W h e n r e p o r t i n g t h e r e s u l t s o f s t a t l s t i c a l tests, w e w i l l a d o p t t h e c o n v e n t i o n o f r e f e r r i n g t o a d i f f e r e n c e as b e i n g statistically significant ff t h e test has a p v a l u e o f 0.05 o r less. I f p is g r e a t e r t h a n O.O5 b u t less t h a n o r e q u a l to O. 1O, t h e difference w i l l b e c a l l e d m a r g i n a l l y significant. All o t h e r d i f f e r e n c e s w i l l b e said to b e n o t significant. S i n c e p values for all o f t h e test results are also r e p o r t e d , t h e r e a d e r s h o u l d h a v e n o difficulty in i n t e r p r e t i n g o u r results. ~{/hile ANOVA w i t h a r e p e a t e d m e a s u r e d e s i g n a l l o w s for a u t o c o r r e l a t i o n , this c o r r e l a t i o n is a s s u m e d t o b e c o n s t a n t ( s e e W i n • r , 1971, c h a p t e r 7). Since w e are u n a b l e to c l a i m that this t e c h n i q u e w i l l b e c o m p l e t e l y c o r r e c t for t h e a u t o c o r r e l a t i o n in t h e data w e e x a m i n e , w e m u s t c o n t i n u e to p r o v i d e a c a v e a t a b o u t i n t e r p r e t i n g any of o u r tests as classical h y p o t h e s i s tests.

50

DOUGLASV. DEJONGe t aL Bargaining pair I

2

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7

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Fig. 5. Ronen-McKinneytransfer pricing mechanism,a~price received by seller; b, price paid by buyer;~) price received by seller equals price paid by buyer;NAno agreement. which no agreements were reached. Efficiency is zero in such periods. Second, the agreements that are reached could be less efficient with the direct negotiation mechanism. To evaluate these two possible explanations, we analyzed the number of agreements and the efficiencies of actual agreements. The number of agreements reached with each mechanism and the average efficiencies of these agreements are given in Table 1 in the upper center and upper right-hand panels, respectively. Using a one-tailed t-test, the average efficiencies for all agreements are significantly less than 1.0 for all three mechanisms. However, when considering these averages there is no apparent difference across the three mechanisms. On the other hand, there is a striking difference in the number of agreements reached between the direct negotiation mechanism and the other two mechanisms. This, in turn suggests why the direct negotiation

mechanism attains significantly less efficient all•cations than the other mechanisms; there are fewer agreements with the direct negotiation mechanism. We also tested for differences in these measures across mechanisms using an ANOVA. The results of the ANOVA which analyzes the number of agreements is presented in the lower center panel of Table 1. The main effect, mechanism, is statistically significant and the contrasts indicate that this significance is due to the direct negotiation mechanism being different from the both traditional and Ronen-McKinhey mechanisms. The traditional and RonenMcKinney mechanisms do not differ from each other. In the lower right.hand panel of Table 1, we present the results from the ANOVA which analyzes the efficiencies for actual agreements. We found no significant differences between mechanisms. We analyzed the average efliciencies for the

ALTERNATIVE TRANSFER PRICING MECHANISMS

51

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eq

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c.

~. ~.

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eq

52

DOUGLASV. DEJONG e t aL

N

u'~ •

°

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i~

7~ ~: ~ .-~

~i~ 0 o

i~ .b-

ALTERNATIVE TRANSFER PRICING MECHANISMS

last f o u r

periods o f

experiment a n d

the

found

that all three mechanisms continue to perform at l e s s t h a n 1 0 0 % e f f i c i e n c y ( s e e last f o u r p e r i o d s

under the efficiency c o l u m n in Table 1 ). While the Ronen-McKinney mechanism continues to give the highest efficiency and the direct negotiation m e c h a n i s m c o n t i n u e s t o y i e l d t h e l o w e s t , t h e A N O V A r e s u l t s f o r t h e last f o u r p e r i o d s indic a t e that n o n e of the mechanisms are statistically d i s t i n c t f r o m t h e o t h e r m e c h a n i s m s . Similarly, t h e m a i n e f f e c t , M e c h a n i s m , is n o t s t a t i s t i c a l l y s i g n i f i c a n t in e i t h e r t h e A N O V A w h i c h a n a l y z e s

the efliciencies of the agreements or the A N O V A which examines the number t h e last f o u r p e r i o d s .

of agreements

in

Quantity

For all of the measures presented in Table 1, the data from the last four periods s e e m to have settled down. To see this, examine the significance of the time period in each ANOVA. In all cases, the main effect, Time, is statistically significant w h e n all data are used. On the other hand, w h e n the analysis is c o n d u c t e d on the last four periods of data, neither the main effect, Time, nor the interaction effect, Mechanism* Time, are statistically significant, t° The time series of the average transfer quantities and prices for agreements presented in Fig, 6 reinforces the conclusion that there is considerably less volatility in the last four periods. Since efficiency depends directly upon the transfer quan-

~,ronsferred Ronen - McKi nney_

Traditional.

Direct. neqot.iot.ion 8-

8

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Tronsfer Direct. negotio~.ion

I

IIII

Period

Period

Period

price

Traditional.

Ronen-

McKinney '"

3.O0

3.00

3.00

2.96

2.96

2.96 . . . . . . . . . . . . . . . . . . . .

2.92

2.92

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2.88

2.88

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2.84

2.84

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2.72

2.72

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2.68

2.68

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2.60

2.60

2.80

2.56

2.56

I I

I I 2 3

I 4

I 5

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Period

I 7

I I 8 9

I I0

2.76

I

b

b

b

b

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b

b

b

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I 7

t 1 I 8 9 10

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Period

Fig. 6. Mean quantities and prices for agreements, b, buyer's transfer price; s, seller's transfer price. t°Since there is a relatively small number of observations in the last four periods, this lack of significance could be due to the low power of the test. To evaluate the ability of this test to detect significance, w e also conducted A-NOVAsfor all performance measures using the data from the first four periods. Either the main effect (Time), the interaction effect (Mechanism" Time) or both are statistically significant in all of these ANOVAs. Thus, relative to the first four periods, these results demonstrate that the data in the last four periods are less volatile.

54

DOUGLASV. DEJONG et aL

tit'y, this figure also g r a p h i c a l l y d e m o n s t r a t e s t h e i n c r e a s e d stability o f this m e a s u r e t o w a r d s the conclusion of the experiment. Finally, t h e t i m e series o f transfer quantities in Figs 3, 4, a n d 5 d e m o n s t r a t e that the inefficiencies are a result o f a less than o p t i m a l q u a n t i t y being transferred.l ~ T h e s e inefficiencies o c c u r r e d w h e n e v e r sellers o v e r r e p o r t e d their marginal c o s t s o r b u y e r s u n d e r r e p o r t e d t h e i r marginal r e v e n u e s o r both. F o r example~ w h e n sellers o v e r r e p o r t t h e i r cost, t h e marginal c o s t s c h e d u l e shifts u p a n d to t h e left o f t h e t r u e marginal c o s t s c h e d u l e in Fig. 1. C o r r e s p o n d i n g l y , w h e n b u y e r s u n d e r r e p o r t t h e i r r e v e n u e s , the marginal r e v e n u e s c h e d u l e shifts d o w n and to t h e left o f t h e t r u e marginal r e v e n u e s c h e d u l e in Fig. 1. Thus, t h e "new" marginal c o s t and r e v e n u e s c h e d u l e s i n t e r s e c t to t h e left o f t h e optimal quantity. T h e q u a n t i t y t r a n s f e r r e d is t h e n less than t h e o p t i m a l q u a n t i t y o f 6 o r 7 units. W e n e x t e x a m i n e t h e results o f this m i s r e p o r t i n g b y mechanism.

Is the information reported accurate? W e a d d r e s s this issue b y e x a m i n i n g e a c h b u y e r ' s and e a c h seller's r e p o r t e d s c h e d u l e for all m e c h a n i s m s for all a g r e e m e n t s a n d agreem e n t s in t h e last four periods, t2 W e c o m p u t e d t h e average a b s o l u t e d e v i a t i o n o f t h e i r r e p o r t e d marginal r e v e n u e a n d marginal c o s t f r o m t h e i r t r u e marginal r e v e n u e and marginal c o s t for t h e first 7 units o n t h e i r schedules. T h e tests w e r e c o n d u c t e d using t h e s e first 7 units. W e have chos e n to d o this for t w o reasons. First, s i n c e each b u y e r ' s a n d e a c h seller's s c h e d u l e d i d n o t

c h a n g e f r o m o n e p e r i o d to t h e n e x t , it a p p e a r s that t h e y s o o n l e a r n e d that t h e last 3 units w e r e e x t r a m a r g i n a l and p a i d little a t t e n t i o n to t h e a m o u n t s t h e y r e p o r t e d for t h e s e units. ( R e c a l l that m o r e than s e v e n units w e r e t r a n s f e r r e d o n l y o n c e . ) S e c o n d , if t h e h e a d q u a r t e r s w e r e to assess t h e p r o f i t a b i l i t y o f t h e b u y e r a n d seller, it w o u l d o n l y r e q u i r e t h e i n f o r m a t i o n r e p o r t e d o n inframarginal a n d marginal units. H o w e v e r , w e also c o n d u c t e d all o f o u r tests using all 10 units a n d w e will use f o o t n o t e s to r e p o r t w h e n t h e results using all 10 units differ q u a l i t a t i v e l y from t h o s e using t h e first 7 u n i t s ) 3 T a b l e 2 p r e s e n t s o u r analysis o f truthful reporting. The means of the absolute deviations from t r u e marginal c o s t a n d m a r g i n a l r e v e n u e for t h e t h r e e m e c h a n i s m s a r e all significantly g r e a t e r than z e r o for all a g r e e m e n t s a n d for a g r e e m e n t s in t h e last four p e r i o d s . C o m p a r i n g across m e c h a n i s m s , the Ronen-McKinney mechanism had the smallest average absolute deviation while the direct negotiation m e c h a n i s m h a d t h e largest a v e r a g e deviation. This r a n k i n g s t a y e d t h e s a m e r e g a r d l e s s o f w h e t h e r all a g r e e m e n t s o r a g r e e m e n t s in t h e last four p e r i o d s w e r e used. W e again c o n d u c t e d an ANOVA w i t h a r e p e a t e d m e a s u r e d e s i g n to d e t e r m i n e t h e significance o f t h e s e differences, using all a g r e e m e n t s a n d using a g r e e m e n t s in t h e last four p e r i o d s . T h e results a r e p r e s e n t e d in t h e l o w e r p a n e l o f T a b l e 2. Since t h e m a i n effect, M e c h a n i s m , is statistically significant, w e t h e n c o n t r a s t e d t h e m e c h a n i s m s against o n e a n o t h e r . T h e results o f this analysis, w h i c h a r e also rep o r t e d in T a b l e 2, s u g g e s t that in all p a i r w i s e

t ~There is only one instance when a quantity greater than the e~cient level was transferred. This occurred in the first period of the third bargaining pair with the direct negotiation mechanism. '2For the traditional and Ronen-McKinneey mechanisms, these were the schedules that led to the proposed contract which both parties accepted. For the direct negotiation mechanism, however, the schedule that led to the agreement was used along with the one that immediatelypreceded it (i.e. the one previously reported by the other party). t~Occasionally, market participants grossly misstated their true information. So that these few observations would not significantly skew the measures reported here, we censored our data by eliminating any entry where buyers misreported their marginal revenue by more than $1.00 or where sellers misreported their marginal cost by more than $1.00. For all agreements, this procedure deleted 47 observations with the direct negotiation mechanism, one observation with the traditional mechanism, and none of the observations with the Ronen-McKirmey mechanism. When using only the data for the agreements in the last four periods, this procedure deleted 20 observations from the direct negotiation mechanism and no observations from either the traditional or Ronen-MeKinney mechanism. It should be kept in mind that this evidence is consistent with the direct negotiation mechanism leading to the most misreporting.

ALTERNATIVE TRANSFER PRICING MECHANISMS

55

TABLE 2. Truthful reporting Mean (p-value)° Absolute deviation from true information All Agreements in agreements last four periods

Mechanism Direct negotiation

$0.203

$0.176

(0.001 )

(O.OOt)

Traditional

O. 142 ( 0.001 )

O. 124 (0.001 )

Ronen-McKinney

0.099 (0.001)

0.090 (0.001)

Source

ANOVA results All agreements dr. F p

Agreements in last four periods ~f. F p

Between subject pairs Mechanism Error ( b e t w e e n ) t

2 24

18.76

0.001

2 24

16.58

0.001

Within subject pairs, Time Time* Mechanism Error (Time* between)§

2 4 48

16.23 4.19

0.001 0.005

1 2 24

0.09 0.04

0.76 0.96

1 2

0.68 0.27

0.42 0.77

1 2

0.58 0.56

0.45 0.58

24 1 2 24

42.14 5.53

0.001 0.01

24 1 12 24

55.48 7.67

0.001 0.003

Contrastll Direct negotiation vs traditional

1

16.42

0.001

1

14.67

0.061

Direct negotiation vs Ronen-MeKinney

1

36.17

0.001

1

31.91

0.001

Traditional vs Ronen-McKinney

1

3.91

0.06

1

3.36

Buyer-Seller Buyer-Seller* Mechanism Error ( Buyer-Seller *between)§ Unit Unit *Mechanism Error (Unit *between)§

0.08

* The absolute deviation is calculated by taking t h e absolute value of the difference b e t w e e n reported marginal revenue or cost and true marginal revenue or cost. The first 7 units from the schedules are used in the absolute deviation calculations. For all agreements ( a g r e e m e n t s in last four periods) there were 68 ( 4 8 ) observations with the direct negotiation m e c h a n i s m w h e r e subjects did not report a revenue or cost number. There were no ( n o ) s u c h observations with t h e traditional m e c h a n i s m and 1 ( n o s u c h ) observation with the Ronen-McKinney mechanism. T h e p value indicates the level of significance for a one-tailed t-test that the absolute deviation is greater than zero. t For the F value to follow an F distribution, the sources o f variation m u s t be h o m o g e n o u s . A check o n this assumption using the F ~ test indicates this assumption is satisfied (see Winer, 1971, pp. 5 2 0 - 5 2 1 ).

(continued)

56

DOUGLAS V. DEJONG et aL TABLE 2. Truthful repotting (continued) , Because of the design, there are e m p t y cells with the Time and Unit variables w h e n time is 1-10 and units are 1-7. Thus, Time is defined in terms of 3 s e g m e n t s (periods 1-4, 5-7, 8 - 1 0 ) for all agreements and 2 segments (periods 7-8, 9 - 1 0 ) for agreements in the last periods. Unit is defined in terms of 2 segments (units 1-4, 5 - 7 ) for both all agreements and agreements in the last four periods. § See W i n e r ( 1971, p.540) t'or a description o f this design and the construction of the error terms. IIThe between subject pairs error term is used in this analysis.

comparisons, each mechanism is statistically distinct from the other, although the distinction between traditional and Ronen-McKinney mechanisms is marginal. This holds for all agreements and for agreements in the last four periods, t4 Further, the truthful reporting measures seems to have "settled down" by the end of the experiment. The main effect, Time, and the interaction effect, Mechanism* Time, are both statistically significant when all data are used, while neither effect remains significant when the last four periods of data are considered, t5 The ANOVAs also show that there is no distinction between buyer reporting and seller reporting nor do the reporting patterns of buyers and sellers differ by mechanism. In particular, the buyer-seller main effect and interaction (Buyer-Seller * Mechanism) effect are not statistically significant for all agreements or for agreements in the last four periods. However, the truthful reporting measure varied across units and the pattern of the variation across units also differed by mechanism, i.e. the unit main effect and interaction effect (Unit * Mechanism) are statistically significant for all agreements and agreements in the last four periods. Figure 7 presents the reporting patterns for the three mechanisms for all 10 units. As illustrated in the figure, the means of absolute deviation differ by

unit for each of the mechanisms and the pattern of the means differ across mechanisms. =6 It can also be seen from the figure that the RonenMcKinney mechanism has the smallest absolute deviation from true information for the first 7 units. 0.26 -o o

0.26-

I

0.22 ~

0.20

--

0.18

--

0.14 ~ 0.12 ~

I

2

2

0 . 1 6 ~o

I

0.24 --

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2 3

t

2

2

3

0.1o~

0.08 0.06 ~

3

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2

3

I

i

I

1

I

I

I

I

I

I

2

4

5

6

7

8

9

I0

Unit.

Fig. 7. Truthful reporting by unit. "The m e a n absolute deviation is calculated by taking the mean of the absolute values of the differences between relc~orted and true marginal revenue and marginal cost by unit for each of the three mechanisms. 1, direct negotiation; 2, traditional; 3, Ronen-McKinney; (~) traditional and Ronen-McKinney have same mean values.

While there is little difference between buyer and seller reporting strategies in terms of absolute deviation, this measure does not provide any information about the systematic tendencies

t*When reporting is evaluated using all 10 units, the results are qualitatively the same except the difference between the traditional and Ronen-McKinney mechanisms is no longer statistically significant both for all agreements and for agreements in the last four periods. t~I'his is reinforced by the result that both effects are statistically significant w h e n the first four periods of data are used in the ANOVA. re'An ANOVA with the same design as that described in Table 2 was run using only the units which were most frequently transferred (i.e. units 4, 5, 6 and 7). The results o f the ANOVA were qualitatively the same as the results of the ANOVA presented in Table 2.

ALTERNATIVETRANSFERPRICINGMECHANISMS of buyers or sellers to underreport vs o v e r r e p o r t their true marginal revenue or marginal cost. To assess overreporting and underreporting, w e used the reported schedules to c o m p u t e each buyer's (seller's) average ratio of reported mar. ginai revenue (marginal cost) to true marginal revenue (marginal cost) for the first 7 units on the schedule. A ratio greater than one indicates overstatement on average and a ratio less than one indicates understatement on average. A ratio of o n e indicates that players reported truthfully on average. The means of the ratios for all buyers are 0.924 0.960 and 0.959 for all agreements for the direct negotiation, traditional and Ronen-McKinney mechanisms, respectively. For agreements in the last four periods, the means of the ratios are 0.942, 0.966 and 0.960, respectively. For all sellers, the means of the ratios for all agreements are 1.065, 1.055 and 1.023 for the direct negotiation, traditional and Ronen-McKinney mechanisms, respectively. For agreements in the last four periods for all sellers, the means of the ratios are 1.062, 1.050 and 1.014, respectively.17 For each mechanism, the b u y e r ratio is less than one and the seller ratio is greater than one and these differences from one are statistically significant using a two-tailed t-test (,p-values are 0.01 or less). Thus, buyers tend to underreport and sellers tend to overreport. These results are consistent with the observation that, on average, the transferred quantity was less than the optimal quantity. They also demonstrate that there is no apparent tendency toward any of the alternative equilibria with the Ronen-McKinney mechanism w h e r e buyers overreport and sellers underreport, even though both parties' profits can increase if they adopt these strategies.

CONCLUDING REMARKS The surprising result of this laboratory experim e n t is h o w similar the transfer pricing mechanisms are with respect to performance, in

57

particular the traditional and Ronen-McKinney mechanisms. When all periods of the experim e n t are considered, the direct negotiation mechanism is significantly less efficient than the other two mechanisms ( d u e to a lower n u m b e r of agreements). However, the efficiencies of the traditional and Ronen-McKinney mechanisms are indistinguishable. In the last four periods of the experiment, the efficiencies of all three mechanisms are indistinguishable. While there is less misreporting with the Ronen-McKinney mechanism, the amount of misreporting in the traditional mechanism is not very different from the Ronen-McKinney mechanism. For example, if the means of the absolute deviation from true information for agreements in the last four periods are used, the amount of misreporting under the traditional mechanism is only 3.4¢ greater than the amount of misreporting under the Ronen-McKinney mechanism. When all 10 units are considered, the traditional and Ronen-McKinney mechanisms are statistically indistinguishable. On the other hand, the amount of misreporting for the first 7 units under the direct negotiation mechanism is 8.6¢ greater than the amount of misreporting under the Ronen-McKinney mechanism even after w e censored 20 observations w h e r e the amount of misreporting e x c e e d e d $1.00. Similar conclusions are reached w h e n comparing the direct negotiation and Ronen-McKinney mechanisms using all 10 units. Thus, the above results suggest that the incentive compatibility issue may not be a critical one, at least in the environments considered here. However, this does not imply that the literature on incentive compatibility is the result of misplaced emphasis. Indeed, none of the mechanisms examined here possesses a unique equilibrium which is incentive compatible; we also did not measure the performance of these mechanisms directly on their domain. Instead, w e view o u r results as a n initial attempt to collect and evaluate empirical evidence about the p e r f o r m a n c e of alternative transfer pricing

7The relative rankingsamong the mechanismsby buyers and by sellers stay the same when all 10 units are used in the calculations.

58

DOUGLASV. DEJONG et aL

m e c h a n i s m s in an i n t e r e s t i n g e n v i r o n m e n t w h e r e t h e m o d e l s s h o u l d have s o m e p r e d i c t i v e ability. T h e fact that a m e c h a n i s m , such as t h e traditional one considered here, performs well in this e n v i r o n m e n t s h o u l d n o t b e c o n s i d e r e d startling. T h e e x p e r i m e n t a l e v i d e n c e a b o u t t h e p e r f o r m a n c e o f p u b l i c g o o d m e c h a n i s m s is r e p l e t e w i t h e x a m p l e s in w h i c h a m e c h a n i s m w i t h t h e o r e t i c a l l y u n d e s i r a b l e p r o p e r t i e s exhib i t e d s u p e r i o r p e r f o r m a n c e (see, for e x a m p l e , F e r e j o h n et aL, 1982; Smith, 1977). Finally, w e h a v e d e m o n s t r a t e d that l a b o r a t o r y e x p e r i m e n t a t i o n p r o v i d e s a d i r e c t m e a n s for evaluating issues in transfer pricing. H o w e v e r , evaluating the performance of three alternative m e c h a n i s m s r e p r e s e n t s o n l y an initial step. Specifically, in its m o s t e l e m e n t a r y form, a transfer

p r i c i n g e n v i r o n m e n t consists o f a b u y e r a n d seller w h o bargain o v e r t h e p r i c e a n d units to b e exc h a n g e d and w h o a r e i n c o m p l e t e l y i n f o r m e d a b o u t e a c h o t h e r ' s v a l u a t i o n s a n d costs, r e s p e c tively. Thus, t h e transfer p r i c i n g p r o b l e m s h a r e s many of the characteristics of a noncooperative b a r g a i n i n g p r o c e s s in w h i c h t h e r e is i n c o m p l e t e i n f o r m a t i o n ( C r a m t o n , 1984; Sobel & Takahashi, 1983). Using r e c e n t a d v a n c e s in b a r g a i n i n g t h e o r y , e x i s t i n g transfer p r i c i n g m o d e l s c o u l d b e r e f o r m u l a t e d to e x p l i c i t l y i n c o r p o r a t e i n c o m p l e t e information. A w e l l - c o n t r o l l e d i n c o m p l e t e i n f o r m a t i o n transfer p r i c i n g e x p e r i m e n t c o u l d t h e n b e c o n d u c t e d to e x p l o r e t h e r e l a t i o n s h i p b e t w e e n efficiency a n d different i n f o r m a t i o n conditions.

BIBLIOGRAPHY Abdel-ldaalik,A. R. & Lusk, E., Transfer Pricing - - a Synthesis, Accounting Review (1974) pp. 8-23. Anthony, R. N., Dearden,J. & Bedford, N. M.,Management Con trolSyston$, (Homewood, IL:Irwin, 1984). Coursey, D., Bilateral Bargaining, Pareto Optimality, and the Frequency of Impasse,Journal of Eco~omic Behavtor and Organization (1982) pp. 243--260. Cramton, P. C., Bargaining with Incomplete Information: an Infinite-Horizon Model with Two-Sided Uncertainty, Review of Economic Studies (1984) pp. 579-593. Cyert, R. & March, J.,A Behavioral Theory oftheFirm (Englewood Cliffs,NJ: Prentice-Hall, 1963). Dean, J., Decentralization and Into-Company Pricing, Harvard Business Review ( 1955) pp. 65--74. Dopuch, N. & Drake, D., Accounting Implications of a Mathematical Programming Approach to the Transfer Pricing Problemdournal of Accounting Research ( 1964 ) pp. 10-24. Eccles, IL G., Control with Fairness in Transfer Pricing, Harvard Business Review (1983 ) pp. 149-- 161. Ferejohn, J. A., Forsythe, IL,NolI, IL G. & Palfrey,T. R.,An Experimental Examination of Auction Mechanisms for Discrete Public Goods, in Research in Experimental Economics, vol. 2 (Greenwich, CT: JAI Press, 1982). Groves, T. & Loeb, M., Reflections on Social Costs and Benefits and the Transfer Pricing Problem,Journal ofPubltc Economics (1976) pp. 353-359. Hirshleffer, J., On the Economics of Transfer Pricing,Journal of Business (1956) pp. 72--84. Kaplan, IL S.,AdvancedManagerialAccounting (Englewood Cliffs,NJ: Prentice-Hall, 1982). Plott, C. R., Industrial Organization Theory and Experimental EconomicsJournal of EconomtcLiterature (1982) pp. 1485--1527. Plott, C. IL & Smith, V. L, An Experimental Examination of Two Exchange Institutions, Review of Economic$ Studies (1978) pp. 133-153. Ronen, J. & McKinney III, G., Transfer Pricing for Divisional Autonomy,Journal of Accounting Research (1970) pp. 99-112. Smith, V. L, Experimental Economics: Induced Value Theory, American Economic Review (1976) pp. 274-- 279. Smith, V. L, The Principle of Unanimity and Voluntary Consent in Social Choice, Journal of Political Economy (1977) pp. 1125--1139. Smith, V. L, Microeconomics Systems as an Experimental Science, American Economic Review ( 1982 ) pp. 923-955. Sobel, J. & Takahashi, I., A Multistage Model of Bargaining, Review of Economic Studies (1983) pp. 411426.

ALTERNATIVE TRANSFER PRICING MECHANISMS

59

Swieringa, It. J. & Waterhouse, J. H., Organizational Views of Transfer Pricing, Accounting Organizations and Society (1982) pp. 149-165. Winer, B. J., Statistical Principles in Experimental Design ( N e w York: McGraw-Hill, 1971 ).

APPENDIX

General instructions This is an experiment in the economics of decision-malting. The instructions are simple and if you follow them carefully and make good decisions, you can earn a considerable amount of money which will be paid to you in cash at the end of the experiment. In this experiment you will be either a buyer or a seller. Your identification number at the top of this page tells you whether you are a buyer or a seller. Buying and selling will take place over a sequence of trading periods. All the rules described below apply equally to each trading period. In the instructions that follow, the value of any decisions you might make is described along with specific rules for trading and record-keeping.

Specific instructions to buyers During each trading period you are free to purchase up to ten units from the seller, in your folder you will find a packet containing the Buyer's Resale Value and Profit Schedule. The information provided in this schedule is for your private use. Do not reveal this information to anyone. On the Buyer's Resale Value and Profit Schedule you will find a column labelled "Resale Value." The entries in this column tell you the amount the experimenter will pay you for each unit that you purchase from the seller in a trading period. Although you will have a separate schedule for each trading period, your resale values will never change from one trading period to the next. Consider the sample Resale Value and Profit Schedule below:

Unit (1) 1 2 3

Resale Value ( $ ) (2)

Price per Unit (3)

Profit per Unit (4)--(2)-(3)

300 200 100 Total profits for the period

This schedule tells you that if you purchase 1 unit, your resale value for that unit you purchase is $300. If you purchase a second unit, your resale value on that unit is $200. During a trading period, you will have to come to an agreement with the seller over the n u m b e r of units you will purchase and the price you will pay for each unit. The specific trading rules which you must use to come to an agreement will be described later in these instructions. Once an agreement is reached, you should go to column ( 3 ) of your Resale Value and Profit Schedule and record the price per unit that you have agreed to pay for units on each row corresponding to each unit you have agreed to purchase. Your profit on each unit you have purchased can then be determined by subtracting the price per unit you have agreed to pay from your resale value for each unit you have agreed to purchase. This is done by subtracting the entries in column ( 3 ) from the amounts given in column ( 2 ) for each unit you have purchased, and by recording this difference in column (4). Your total profit for the trading period is determined by adding up your profit per unit on each unit you have purchased and recording this amount on the last r o w of your Resale Value and Profit Schedule. Refer once again to your sample Resale Value and Profit schedule above. Suppose you agree to buy 2 units from the seller for $100 each. You should first record this price on the first two rows of column ( 3 ) corresponding to the two units you have purchased. Your profit on the first unit you have purchased is (300 100 ----) $200 and your profit on the second unit you have purchased is (200 - 100 = ) $100. These amounts should be recorded on the first two rows of column (4). To determine your profit for the trading period, add these amounts to obtain (200 + 100 = ) $300, and record this in the space provided at the bottom of the schedule. When correctly filled out, your sample Resale Value and Profit Schedule should look like the following:

60

DOUGLAS V. DEJONG et aL

Unit (1) 1 2 3

Resale Value ( $ ) (2) 300 200 100 Total profits for the period

Price per Unit ( $ ) (3~

Profit p e r Unit ( $ ) (4)=(2)--(3)

100 100

200 100 300

Obviously these figures are illustrative only and should not be a s s u m e d to apply in the actual experiment. At the end of each trading period, record your total profit for t h e period on your profit sheet provided in your folder. At the end of the experiment, add up your total profit from each trading period. The experim e n t e r will pay you this a m o u n t in cash. Specific in*tructtons to sellers During each trading period you are free to sell up to ten units to the buyer. However, the units that you sell are not free. You must pay a production cost for units which you sell. In your folder you will find a packet containing the Seller's Production Cost and Profit Schedule. The information provided in this schedule is for your private use. Do not reveal this information to anyone. O n the Seller's Production Cost and Profit Schedule you will find a c o l u m n labelled "Production Cost." The entries in this c o l u m n tell you the production cost you must pay for each unit you will sell in a trading period. Although you will have a separate schedule for each trading period, your production costs will never change from one trading period to the next. Consider t h e sample Production Cost and Profit Schedule below:

Unit (1)

Price per Unit (2)

Production Cost ( $ ) (3)

Profit per Unit (4)=(2)-(3)

3O 80 150

1

2 3 Total profits for the period

This schedule tells you that if you sell 1 unit, your cost for that unit you sell is $30. If you sell a s e c o n d unit, the cost of selling that unit is $80. During a trading period, you will have to c o m e to an agreement with the buyer over the n u m b e r of units you will sell and the price you will receive for each unit. The specific trading rules which you m u s t use to c o m e to an agreement will be described later in these instructions. O n c e an agreement is reached, you should go to column ( 2 ) of your Production Cost and Profit Schedule and record the price per unit you have agreed to sell. Your profit on each unit you have sold can then be determined by subtracting your production cost for that unit you have agreed to sell from the price per unit you have agreed to receive. This is done by subtracting the a m o u n t s given in c o l u m n ( 3 ) from the entries in c o l u m n ( 2 ) for each unit you have sold, and by recording this difference in c o l u m n (4). Your total profit for the trading period is determined by adding up your profit per unit for each unit you have sold and recording this a m o u n t on the last row of your Production Cost and Profit Schedule. Refer once again to your sample Production Cost and Profit Schedule above. Suppose you agree to sell two units to the buyer for $100 each. You should first record this price o n the first two rows of c o l u m n ( 2 ) corresponding to the two units you have sold. Your profit on the fast unit you have sold is ( 100 - 30 = ) $70 and your profit on the second unit you have sold is (100 - 80 = ) $20. These a m o u n t s should be recorded on the first two rows of c o l u m n (4). To d e t e r m i n e your profit for the trading period, add these a m o u n t s to obtain ( 7 0 + 20 = ) $90, and record this in the space provided at the b o t t o m of the schedule. W h e n correctly filled out, your sample Production Cost and Profit Schedule should look like the following:

ALTERNATIVE TRANSFER PRICING MECHANISMS

Unit (1)

Resale Value($) (2)

Price per Unit($) (3)

100 100

3O 80 150

1 2 3

Total profits for the period

61 Profit per Unit($) (4)=(2)-(3) 70 20

90

Obviously these figures are illustrative only and should not be assumed to apply in the actual experiment. At the end of each period, record your total profit for the period on your profit sheet provided in our folder. At the end of the experiment, add up your total profit from each trading period. The experimenter will pay you this amount in cash. Trading rules ~ direct negotiation

During each trading period, you are free to send messages to the other party with w h o m you are negotiating In your folder you will find an ample supply of Offer Forms. If you are a buyer, you should write in the price per unit you are willing to pay for each given n u m b e r of units on this form. For example, if you write in 50 next to 3 units, this means you are willing to buy 3 units at a price per unit of $50 for a total of (3 x 50 -- ) $150. You should write in all your purchase offers for ten units. If you are a seller, you should write in the price per unit you require to sell each given number of units on this form. For example, if you write in 1OO next to 6 units, this means you are willing to sell 6 units at a price per unit of $1OO for a total o f ( 6 × IOO = ) $600. You should write in all your sales offers for 10 units. When you finish recording these amounts, hand this form to the experimenter and he will deliver it to the other pary with w h o m you are negotiating. If you wish to accept an offer that has been made to you by the other party, circle the number of units you wish to transact. If you are a buyer and you accept a seller's offer, you must pay the seller the price per unit that the seller has recorded next to the number of units you have decided to purchase. If you are a seller and you accept a buyer's offer, the buyer will pay you the price per unit that the buyer has recorded next to the number of units you have decided to sell. When an offer has been accepted, an agreement has been reached and the trading period is over. You should then compute your total profit for that trading period and record it on your profit sheet. Trading rules m traditional

During each trading period, you should send your offers to the experimenter. In your folder you will find an ample supply of Offer Schedule Forms. If you are a buyer, you should write in the price per uftit you are willing to pay for each given number of units on this form. For example, if you write in 50 next to 3 units, this means you are willing to buy 3 units at a price per unit of $50 for a total o f ( 3 x 50 = ) $150. You should write in all your purchase offers for ten units. If you are a seller, you should write in the price per unit you require to sell each given number of units on this form. For example, if you write in 1OO next to 6 units, this means you are willing to sell 6 units at a price per unit of $1OO for a total o f ( 6 x 1OO = ) $(300. You should write in all your sales offers for 10 units. When you finish recording these amounts, hand this form to the experimenter. After both the buyer and the seller have submitted their forms, the experimenter will return your offer form to you with a suggested number of units to be transacted and the suggested price per unit you will pay ffyou are a buyer or the suggested price per unit you will receive if you are a seller. The experimenter will suggest a number of units to be transacted and a price per unit that you will pay or receive for these units as follows: ( 1 ) The suggested number of units to be transacted is the largest n u m b e r of units for which the price the seller requires to sell these units is not greater than the price the buyer is willing to pay for these units. ( 2 ) The suggested price the buyer is asked to pay to the seller for these units will be determined by averaging the price the seller requires to sell these units and the price the buyer is willing to pay to purchase these units. The suggested selling price that is offered to the seller by the experimenter is the same as the suggested buying price that is offered to the buyer. To see h o w this will work, suppose the buyer gives the experimenter the following purchase offer schedule which specifies the price per unit that the buyer is willing to pay for a given number of units. Also suppose that the seller gives the experimenter the following sales offer schedule which specifies the price per unit that the seller requires to sell a given number of units.

62

DOUGLAS V. DEJONG e t aL Number of Units

Buyer's Purchase Offer Schedule ( $ )

S~ller's Sales Offer Schedule ( $ )

1 2 3 4 5 6 7 8 9 10

600 590 570 56O 545 530 510 500 480 460

500 5 lO 520 53O 54O 55O 560 570 580 590

With this information, the experimenter will suggest that 5 units be transacted since this is the largest number of units for which the price the seller requires to sell is not greater than the price the buyer is willing to pay. The suggested price the buyer will be asked to pay to the seller for these units and the seller will be offered to sell these units is the average of the price the seller requires to sell five units (i.e. 540) and the price the buyer is willing to pay for five units (i.e. 545). Thus, the suggested price per unit to both parties will be (540 + 545)/2 = 542.5. Obviously these figures are illustrative only and should not be assumed to apply in the actual experiment. After the experimenter gives you the suggested number of units to be transacted and the suggested price per unit you must pay or receive, you must indicate your decision of whether to accept or reject the suggessted n u m b e r of units and the suggested price per unit. To do this, check the space marked ~Accept" or "Reject" on the form the experimenter gives you, and hand it back to him. if both parties agree to the suggested number of units to be transacted and the suggested price per unit, the trading period is over. You should then compute your profit for that period and record it on your profit sheet. If either you or the other party does not agree with the suggested number of units and the suggested price per unit, you will be asked to send another schedule of prices to the experimenter and the above procedure will be repeated. Trading rules - - R o n e n . M c K i n n e y

During each trading period, you should send your offers to the experimenter. In your folder you will find an ample supply of OfferSchedule Forms. If you are a buyer, you should write in the price per unit you are willing to pay for each given number of units on this form. For example, if you write in 50 next to 3 units, this means you are wiBing to buy 3 units at a price per unit of $50 for a total o f ( 3 x 50 = ) $150. You should write in all your purchase offers for ten units. If you are a seller, you should write in the price per unit you require, to sell each given number of units on this form. For example, if you write in 100 next to 6 units, this means you are willing to sell 6 units at a price per unit of $ IOO for a total o f ( 6 x 100 = ) $600. You should write in all your sales offers for ten units. When you finish recording these amounts, hand this form to the experimenter. After both the buyer and the seller have submitted their forms, the experimenter will return your offer form to you with a suggested n u m b e r of units to be transacted and the suggested price per unit you will receive if you are a seller. The experimenter will suggest a number of units to be transacted and a price per unit that you will pay or receive for these units as follows: ( 1 ) The suggested n u m b e r of units to be transacted is the largest number of units for which the price the seller requires to sell these units is not greater than the price the buyer is willing to pay for these units. ( 2 ) The suggested price the buyer is asked to pay to the seller for these units will be determined by averaging all of the prices that the seller requires to sell all units up to and including the suggested number of units. ( 3 ) The suggested price the seller will be offered to sell these units will be determined by averaging all of the prices that the buyer is willing to pay for all units up to and including the suggested number of units. To see h o w this will work, suppose the buyer gives the experimenter the following purchase offer schedule which specifies the price per unit that the buyer is willing to pay for each given n u m b e r of units. Also suppose that the seller gives the experimenter the following sales offer schedule which specifies the price per unit that the seller requires to sell each given n u m b e r of units.

ALTERNATIVE TRANSFER PRICING MECHANISMS

63

Number of Units

Buyer's Purchase Offer Schedule ( $ )

Seller's Sales Offer Schedule ( $ )

1 2 3 4 5 6 7 8 9 10

600 590 570 56O 545 530 510 500 480 460

5OO 510 520 53O 540 550 560 570 580 590

With this information, the experimenter will suggest that 5 units be transacted since this is the largest number of units for which the price the seller requires to sell is not greater than the price the buyer is willing to pay. The suggested price the buyer will be asked to pay for these five units is the average of the prices the seller requires to sell 1, 2, 3, 4, and 5 units. That is. the buyer will be asked to pay a price o f ( 500 + 510 + 520 + 530 + 540)/5 = 520 per unit. Note that the price the buyer is asked to pay does not depend on the purchase offer schedule which the buyer has submitted. The suggested price the seller will be offered for selling these five units is the average of the prices the buyer is willing to pay for 1, 2, 3, 4 and 5 units. That is, the seller will be offered a price o f ( 6 0 0 + 590 + 570 + 560 + 545)/5 = 573 per unit. Note that the price the seller is offered does not depend on the sales offer schedule which the seller has submitted. Obviously these figures are illustrative only and should not be assumed to apply in the actual experiment. After the experimenter gives you the suggested n u m b e r of units to be transacted and the suggested price per unit you must pay or receive, you must indicate your decision of whether to accept or reject the suggested number of units and the suggested price per unit. To do this, check the space marked "Accept" or "Reject" on the form the experimenter gives you, and hand it back to him. If both parties agree to the suggested number of units to be transacted and the suggested price per unit, the trading period is over. You should then compute your profit for that period and record it on your profit sheet. If either you or the other party does not agree with the suggested n u m b e r of units and the suggested price per unit, you will be asked to send another schedule of prices to the experimenter and the above procedure will be repeated.

Final remarks Each trading period will last for IO minutes. However, the time spent by the experimenter will not be counted. If you fail to come to an agreement in that time, your total profit for that period will be zero. There will be many trading periods and there are likely to be many cases of disagreement, but you are free to keep trying, and as a buyer or a seller you are free to make as much profit as you can. Are there any questions?

Practice calculations f o r buyer (seller) 1. Does the seller ( b u y e r ) know your resale value (production cost) schedule? Yes _ _ 2. Suppose you have the following Resale Value and Profit (Production Cost) Schedule:

Unit (1)

Resale Value(S) (2)

1 2 3 4 5 6

500 450 4OO 35O 3OO 25O

Priceper Unit(S) (3)

Production CostperUnit($) (3a) 200 250 3OO 35O 4OO 45O

No

Profit per Unit($) 4 = 2- 3(4=3-3a)

64

DOUGLAS V. DEJONG e t a t If you can purchase (sell) units at a price of 375, what is the largest n u m b e r o f units you can purchase without incurring a negative profit or any unit purchased (sold)? ~ units. 3. Suppose the experimenter receives the following schedule from the seller and schedule ( 1 ) from you:

Units

Seller's Schedule

Buyer's Schedule(l)

Buyer's Schedule(2)

l 2 3 4 5 6 7 8 9 10

100 150 200 250 300 350 400 450 500 55O

360 300 240 185 160 135 110 85 6O 35

350 280 210 150 100 70 50 35 25 2O

How m a n y units will the experimenter suggest that you should purchase from the seller? " units. What suggested price per unit will the experimenter propose to you? $ _ _ per unit. What suggested price per unit will the experimenter propose to t h e seller? $ _ _ per unit. 4. Suppose instead that you submitted schedule (2). Answer the same questions. 3a. ( T o sellers) Suppose the e x p e r i m e n t e r received the following schedule from the buyer and schedule ( 1 ) from you:

Units

Seller's Schedule(l)

Seller's Schedule(2)

Buyer's Schedule

1 2 3 4 5 6 7 8 9 10

100 150 200 250 300 350 400 45O 50O 550

170 200 230 280 340 410 490 58O 68O 790

360 300 240 185 160 135 110 85 6O 35

How many units will the experimenter suggest that you should sell to the buyer? $ _ _ units. What suggested price p e r unit will the experimenter propose to you? $ per unit. What suggested price per unit will the experimenter propose to the buyer? $ _ _ per unit. 4a. ( T o sellers) Suppose instead that you submitted schedule (2). Answer the same questions. 5. Compare your answers to question 3 (3a) and question 4 ( 4 a ) and circle the correct answer in the following statements. The n u m b e r of units I can purchase (sell) is higher, the same, lower in question 3 than in question 4. The price per unit I have to pay (will receive ) is higher, the same, lower in question 3 than in question 4. The price p e r unit the seller ( b u y e r ) will receive (pay) is higher, the same, lower in question 3 than in question 4.