The matching problem (and inventories) in private negotiation.

Observations generated over several time periods may be serially correlated and heteroscedastic. Data also may be contemporaneously correlated between cross-sections due to the same unit values/costs being used by subjects across alternative treatments. The Parks (1967) method was used to estimate equation (1). The use of the Parks method allowed us to take account of the unique statistical problems resulting from the panel data sets that consist of time series observations on each of the several cross-sectional units generated in our experiments, along with base category predictions. (8)

Quantities Traded

The 5M treatment exhibits the greatest number of units traded, slightly more than seventeen units and consistently above the monopsony level, followed by the 3M treatment; see figure 2. Treatments in which the buyers or sellers are consolidated consistently show the fewest units traded. As discussed later, trades in these two treatments converge to levels that are not significantly different but are statistically different from the 3M and 5M treatments (table 3). Quantities traded in all treatments are below the predicted competitive and Cournot levels, and each treatment, as shown in figure 2, generally reflects a pattern with small variations across the trading periods.

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Estimated convergence levels for trades in all treatments are low, relative to base values. They are significantly less than the predicted competitive and Cournot quantities in all treatments, and are generally below the monopsony prediction, except in the 5M treatment, which converges to a quantity slightly greater than the monopsony level (table 3). The estimated convergence levels for trades for the 5M and 3M treatments, between which the effects of limited matching can be isolated, are about 17.30 and 14.60, respectively, and are significantly different. This is a simple, but important, observation. Less access between the bargaining agents when there is advance production decreases production and the quantity traded. In this particular instance, a 40% decrease in matches resulted in a 15% decrease in trades; this occurred with no change in the basic supply and demand conditions. Lower production/trades also reflect the perceived higher costs associated with the risk of inventory loss.

The greatest differences from the base trade levels are for the 2B5M and 2S5M treatments, with estimated convergence levels of about 12.70 and 13.20 units, respectively. These levels are not significantly different from each other but are significantly lower than 5M and 3M treatment levels, and are significantly below the monopsony level of sixteen units. This result reflects the impact of fewer matches for sellers or buyers resulting from concentrated markets on either the buyer side or seller side. Buyers and sellers appear equally capable of exploiting bargaining power due to their relatively small number. Limited access in a bargaining environment that arises through increased concentration can have a substantial impact on trades. Taking the market from four to two sellers or four to two buyers (each with five matches) reduces estimated convergence quantities from 17.28 to levels near 13 units. This represents about a 24% decrease in trades. Based on the relative magnitudes of the estimated differences from the respective predicted levels, the monopsony model predicts trades in all treatments more accurately than the competitive or Cournot models. The differences from the monopsony equilibrium level of sixteen units are all significant, however.

The highest fractions of all trades occur in the first and second bargaining rounds as reported in table 4. Trading periods sixteen to twenty are used for illustration. Subjects have the most experience in these trading periods. This pattern of trades indicates the desire by buyers and especially sellers to avoid later mismatches. The lack of transactions late in a trading period arises from an absence of viable bargains. About 81% of all trades are executed in the first three rounds of the 5M treatment. When the number of buyers is reduced (2B5M), 77.83% of trades occur in the first three rounds, as compared to 68.71% when the number of sellers is reduced (2S5M). The market containing two sellers has 15.34% of the trades occurring in the fifth round, which is the highest among the treatments with five matches. This last result suggests that risk from holding inventory is not as severe for sellers when they are relatively concentrated. Sellers do not produce additional units and are more patient in this environment (table 3). The two sellers are in a position to exercise monopoly power facilitated by the limited access to them.

At the end of a trading period any unsold inventories (charged at the unit costs) become a sunk cost to sellers. These losses and the potential for losses put pressure on sellers to accept lower prices in the current period and produce less in future periods. An analysis of unsold inventory for periods sixteen through twenty reveal an average of unsold inventory of 0.07 units per period for the 5M treatment, 0.66 units for the 3M treatment, 1.73 units for the 2BSM treatment, and 0.17 units for the 2S5M treatment (see figure 3). The highest level of loss occurs when there are just two buyers with the next highest average number of unsold units occurring during the 3M treatment. It is possible that buyers in the 2B5M treatment were establishing a reputation early on for letting inventory "spoil"--opportunistic behavior resulting in the classic hold-up problem. These unsold inventory numbers reflect levels of matching risk faced by sellers. It was greatest when either the number of bargaining rounds or number of buyers was reduced. Comparing the average units lost between the early and later trading periods generally suggests more units were lost in early periods than later. Experience did matter in these bargaining treatments (table insert--figure 3).

Prices

Figure 4 summarizes average transaction prices for each treatment. Most noticeable is that prices in the buyer concentrated treatment (2B5M) are much lower than prices in other treatments, and exhibit convergence levels significantly lower than in other treatments (table 3). Toward the end of the experimental session prices in the 2B5M treatment are around sixty-five tokens, while in the other treatments they are in the range of seventy-five to eighty tokens. The concentration of buyers brings a substantial reduction in negotiated prices. Noteworthy is that prices are consistently lower in the 3M treatment relative to the 5M treatment, with convergence levels statistically different. A general reduction in the number of matches reduces trade prices. Hence both quantities and prices fall in going from the 5M to 3M environment. Generally higher prices are observed in the 5M and 2S5M market environment, and prices in these two treatments tend toward, or vary about, the competitive equilibrium level of eighty tokens. Quantities sold in the 2S5M are lower, so the total market surplus will be lower.

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The estimated convergence price increases by 4.70 tokens when the number of bargaining rounds increases from three to five (3M to 5M treatment) per trading period and moves to within 2.36 tokens of the competitive equilibrium price of eighty tokens (table 3). Price tends toward the competitive level as the matching problem decreases for both buyers and sellers. The risk of inventory loss also diminishes with more matches, as gleaned from the table insert in figure 3. Thus, the overall convergence patterns show that by going from three to five matches, trades and prices increase. Trades rise from 14.61 to 17.28 units (an 18% increase) and prices rise 6.4%, from 72.94 to 77.64 tokens.

Prices are most depressed in the 2B5M treatment, exhibiting an estimated convergence level of just over sixty-two tokens, the statistically lowest among all treatments and near the monopsony level of sixty tokens. Few expected matches for sellers put buyers in an advantageous bargaining position in private negotiation trading with advance production. Compared to the 5M treatment, prices in the 2B5M treatment fall by over fifteen tokens (or about 20%) per unit sold. This decline will boost the earnings of buyers, and perhaps is the strongest indicator of monopsony power among the bargaining treatments.

Prices in other treatments (5M, 3M, and 2S5M) converge closer to the competitive prediction than to either Cournot or monopsony predictions. Price differences are significantly lower than the competitive norm, however, in the 5M and 3M treatments. We conclude that the Cournot model is not a good predictor of trades and prices where there is bilateral bargaining for price in the market environment created in this study, relative to the competitive and monopsony models. (9)