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The matching problem (and inventories) in private negotiation.


by Menkhaus, Dale J.^Phillips, Owen R.^Bastian, Christopher T.^ Gittings, Lance B.

Menkhaus, D.J., O.R. Phillips, A.F.M. Johnston, and A.V. Yakunina. 2003. "Price Discovery in Private Negotiation Trading with Forward and Spot Deliveries." Review of Agricultural Economics 25:89-107.

Noussair, C.N., C.R. Plott, and R.O. Riezman. 1995. "An Experimental Investigation of the Patterns of International Trade." American Economic Review 85:462-91.

Parks, R.W. 1967. "Efficient Estimation of a System of Regression Equations When Disturbances Are Both Serially and Contemporaneously Correlated." Journal of the American Statistical Association 62:500-09.

Phillips, O.R., D.J. Menkhaus, and J.L. Krogmeier. 2001. "Laboratory Behavior in Spot and Forward Markets." Experimental Economics 4:243-56.

Sexton, R.J., and M. Zhang. 1996. "A Model of Price Determination for Fresh Produce with Application to California Iceberg Lettuce." American Journal of Agricultural Economics 78:924-34.

Ward, C.E. 2005. "Beef Packers' Captive Supplies: An Upward Trend? A Pricing Edge?" Choices 20:167-71.

(1) Supplementary Appendix A (Menkhaus et al. 2007) provides more detail of inventory loss risk when sellers produce in advance of sale.

(2) Additional description of matching risk is contained in supplementary Appendix A (Menkhaus et al. 2007).

(3) Hong and Plott (1982) conducted experiments where trading occurred via negotiation by telephone with chosen trading partners. They found that as the number of matching opportunities increased in bilateral trading, prices approached the predicted competitive equilibrium and quantities traded were slightly higher than the competitive level. Private negotiation with many bargaining rounds resembles the matching rich double auction when there is no advance production. The double auction is "matching rich" in that when a bid or offer is announced, it is immediately available to all agents in the market. As a result, market participants have no difficulty finding a trading partner.

(4) This is a version of Akerlof's (1970) lemons problem. In our case, units held late in the production cycle are the "poorer" quality and these units drive down the price of units sold earlier in the cycle.

(5) There is some empirical evidence that directly suggests this type of control. For example, the price effects of advance production in the case of California iceberg lettuce are reported by Sexton and Zhang (1996). They document a decline in spot lettuce prices related to greater advance production. Their model allows for imperfect competition among buyers. From this, they estimate the loss in seller bargaining power due to a larger sunk lettuce harvest. Sexton and Zhang argue the buyers have an advantage "when the sellers' asset is sunk and highly perishable" (p. 932).

(6) On the rare occasion, it was necessary to ask individuals who happened to be in the vicinity of the experiment location, whether or not they had participated in a previous experiment, to fill in for a no show. Otherwise, new recruits were used for each replication of each treatment. Individual influences were minimized by averaging the data across individuals and replications in the analysis.

(7) For completeness, the estimated [[GAMMA].sub.j] (the starting level coefficients) and estimated starting levels are presented in supplementary Appendix B (Menkhaus et al. 2007) for the trade and price equations for each base category.

(8) The Parks method of estimation requires an equal number of observations in the times series (trading periods) of each cross section (treatment). There are twenty observations for each of the four test treatments (3M, 5M, 2B5M, and 2S5M) and another twenty observations for the base treatment for a total of a hundred observations for each equation in each of the three base categories (competitive, Cournot, or monopsony).

(9) We estimated the convergence models (trades and prices) for the Cournot solution for two sellers. This model did not perform as well as the competitive and monopsony models.

Dale J. Menkhaus is professor in the Department of Agricultural and Applied Economics. Owen R. Phillips is professor in the Department of Economics and Finance. Christopher T. Bastian is assistant professor, and Lance B. Gittings is former graduate assistant in the Department of Agricultural and Applied Economics. Menkhaus, Phillips, and Bastian are at the University of Wyoming.

Funding support was provided by the U.S. Department of Agriculture under Agreement No. 00-35400-9126 and the Lowham Research Endowment. Any opinions, findings, conclusions, or recommendations expressed in this work are those of the authors and do not necessarily reflect the views of the funding agencies. Helpful comments from anonymous reviewers and Editor Paul V. Preckel are gratefully acknowledged. Any remaining errors are the authors'. Table 1. Experiment Design--Private Negotiation Trading with Advance Production, Buyer and Seller Numbers and Alternative Buyer/Seller Matches Treatment No. of No. of No. of Designation

Buyers Sellers Matches 1 4 4 5 5M 2 4 4 3 3M 3 2 4 5 2B5M 4 4 2 5 2S5M Table 2. Unit Buyer Redemption Values and Seller Costs (Tokens) Used in the Experiments

Redemption Cost

Value for for Unit Buyers Sellers 1 130 30 2 120 40 3 110 50 4 100 60 5 90 70 6 80 80 7 70 90 8 60 100 Table 3. Asymptote Coefficients (Standard Errors) and [Convergence Levels]--for Trades and Prices--Competitive, Cournot, and Monopsony Bases by Treatment Treatment Competitive Competitive Cournot Asymptotes Trades Prices Trades Predicted base 20 80 19.56 5M -2.72 * (a) -2.36 * (a) -2.26 * (a)

(0.29) (0.77) (0.29)

[17.28] [77.64] [17.30] 3M -5.39 * (b) -7.06 * (b) -4.95 * (b)

(0.20) (0.72) (0.20)

[14.61] [72.94] [14.61] 2B5M -7.26 * (c) -17.58 * (c) -6.82 * (c)

(0.16) (0.80) (0.16)

[12.74] [62.42] [12.74] 2S5M -6.77 * (c) -0.96 (a) -6.33 * (c)

(0.18) (1.24) (0.18)

[13.23] [79.04] [13.23] [R.sup.2] 0.99 0.99 0.99 Treatment Cournot Monopsony Monopsony Asymptotes Prices Trades Prices Predicted base 86.11 16 60 5M -8.62 * (a) 1.29 * (a) 17.50 * (a)

(0.77) (0.29) (0.77)

[77.49] [17.29] [77.50] 3M -13.24 * (b) -1.40 * (b) 12.87 * (b)

(0.00) (0.20) (0.72)

[72.87] [14.60] [72.87] 2B5M -23.82 * (c) -3.27 * (c) 2.30 * (c)

(0.80) (0.16) (0.80)

[62.29] [12.73] [62.30] 2S5M -7.41 * (a) -2.77 * (c) 18.71 * (a)

(1.24) (0.18) (1.24)

[78.70] [13.23] [78.71] [R.sup.2] 0.99 0.99 0.99 Note: Single asterisk (*) denotes estimated convergence level significantly different from the base value, [alpha] = 0.01. Note: (a, b, c, d)--same letter indicates no significant difference between estimated convergence levels in the respective equations. Different letters indicate a significant difference between estimated asymptotes, [alpha] = 0.01. Table 4. Average Percentage of Trades and Average Prices for Each Bargaining Round by Treatment--Periods 16-20

Round 1 Round 2 Round 3 Round 4 Round 5

Treatment 5M % trades 37.90 22.85 20.60 7.74 10.91 Ave. price 78.48 80.50 80.36 77.56 66.33

Treatment 3M % trades 38.45 35.55 26.01 -- -- Ave. price 76.65 74.68 70.45 -- --

Treatment 2B5M % trades 31.09 28.28 18.00 14.13 8.50 Ave. price 65.39 64.64 65.57 63.29 58.70

Treatment 2S5M % trades 26.75 24.68 16.94 16.50 15.13 Ave. price 80.85 80.30 84.78 79.55 67.33 Table 5. Summary of Selected Laboratory Results Reviewed and Presented in This Article No. of No. of Trading Advance Resulting Buyers Sellers Institution (a) Production Quantity (b) Many Many CEM No [Q.sup.comp] 4 4 DA(PMK) * No [Q.sup.comp] 4 4 DA(PMK) Yes [Q.sup.comp] 4 4 EA(MPB) Yes [less than or

equal to]


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