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A comment on competition and bidding behavior: some evidence from the rice market.


In testing agents' responses to increased competition in sealed-bid first price-rice auctions, Meyer [1988] makes two erroneous assumptions: (1) that agents know ex ante the number of bidders in the auction, and (2) that firms forecast resale prices with information unavailable at the time of the auction. These two misspecifications are identified and corrected. A probit model provides a forecast of market competition, and agents' bids are modeled as a function of expected competition and factors affecting the value of each rice lot. The bias toward zero in Meyer's estimated coefficient on market competition is reduced.


In an earlier article in this journal, Meyer [1988] presents empirical evidence on the effect of competition on agents' bids in sealed-bid first-price auctions. As Meyer recognizes, there are two opposing effects from increased competition: (1) a competitive reaction in which agents raise their bids toward their expected value of the object, and (2) a non-aggressive reaction in which they respond to the risk of the winner's curse by decreasing their bids. Using data from rice auctions, Meyer empirically tests which effect dominates.(1)

Section II discusses Meyer's model, its problems, and the corrections I introduce. Section III presents the empirical results.


Meyer's Model

As Meyer recognizes, three factors are of central importance in sealed-bid auctions for objects of uncertain value: an estimate of the object's value, the agent's uncertainty regarding this estimate, and the number of competing bidders. He proxies the value signal each agent receives with: (1) the expected resale price of the rice lot (EXPPRC) and (2) the quality of the rice sample relative to that of other samples (QUALITY). The agent's uncertainty regarding this signal is proxied by the absolute value of the difference between the actual and predicted resale price for the previous month (PRCUNC). His measure of market competition is the actual number of competing firms (NUMBID). The model he estimates, then, is (1) [bid.sub.x] = [Alpha] + [[Beta].sub.1](EXPPRC) + [[Beta].sub.2](QUALITY)

+ [[Beta].sub.3](PRCUNC) + [[Beta].sub.4](NUMBID) + [[Epsilon].sub.x] where [bid.sub.x] represents a mill's bid for a cwt (one hundred weight) of rice from lot x.


Expected Resale Price and Uncertainty. Meyer models monthly average resale price as a function of prices in the previous two periods.(3) The predicted value from this equation is defined as each mill's expectation of the resale price (EXPPRC). However, he also includes two dummy variables to account for world supply shocks that caused large price changes in September 1973 and August 1974. This specification implies mills perfectly forecast price only for those two months, while having an imperfect forecast for all other periods.

I correct this misspecification by excluding the dummy variables from the resale price equation. Akaike's final prediction error criterion was employed to determine the appropriate number of lags for the corrected model, and the price series was found to be reasonably explained with only the previous two periods' prices as exogenous variables.(4) Mills forecast each month's price using only information available at the time at which the expectation is formed. Hence, the resale price equation is recursively estimated to allow the coefficients to change as additional price information becomes available.(5)

Meyer defines PRCUNC, the agents' uncertainty about the value of the rice lot, as the absolute value of the OLS residuals, [Price.sub.t-1] minus [EXPPRC.sub.t-1]. However, when the dummy variables are excluded from the resale price equation, PRCUNC becomes very large in the shock periods, rather than zero as in Meyer's formulation. If Meyer's uncertainty measure is used after dropping the dummy variables, the coefficient on uncertainty will capture the price (shock) effect rather than agent uncertainty. To correct this problem, uncertainty is redefined as the recursive forecast variance from the revised resale price equation. Thus, the revised model assumes agents respond to changes in variance, rather than merely to any one period's forecast error.(6) Other Factors Affecting Bid Levels. To account for price variability that the monthly average resale price (EXPPRC) does not capture, I include additional variables affecting agents' estimates of a lot's value. First, EXPPRC may not account for price variability deriving from a lot's variety (e.g., white versus brown rice). Hence, three dummy variables are defined: VARIETY1, VARIETY2, VARIETY3; defined equal to one if the lot is "type" 1, 2, or 3, and equal to zero otherwise.(7) Second, to proxy for a mill's perception of the risk of the winner's curse, the VOLUME of the lot is included. Since the risk of the winner's curse is defined as the probability of winning times the expected payoff, and the expected payoff rises with larger volume lots, it is expected that mills decrease their bids as lot volume rises. Errors in Variables. As Meyer's [1988, 126] primary objective was to "determine the net effect of increased competition on the bid response of agents," the most crucial variable included is a measure of market competition. As he points out, since firms do not know ex ante the number of rivals that choose to participate in an auction, "the correct measure of competition is the expected number of bidding" firms.(8) However, Meyer assumes the actual number of bidders (NUMBID) is a good proxy for the expected number. It is likely that NUMBID consists of both a structural and a random component.(9) These are, respectively, the predicted number of bidders (PRED) and the difference between the actual and predicted number (ERROR). If the variable NUMBID is used in place of the more appropriate measure PRED, a standard errors-in-variables problem arises that causes Meyer's estimated coefficients for this key variable to be biased toward zero.(10)

Hausman [1978] shows how to test for the presence of this problem by examining the significance of the term ERROR in the bid level equations in which NUMBID is used as the measure of market competition. If ERROR is statistically significant, then NUMBID is correlated with [[Epsilon].sub.x] in equation (1) and should be replaced by an unbiased measure of market competition.

The predicted number of bidders in each auction is estimated from a separate probit model for each firm's participation decision. The dependent variable, [Y.sub.ij], is a dummy variable that equals one if mill j submits a bid in auction i and equals zero otherwise. The parameter estimates from this model yield the predicted probability that each mill j submits a bid in auction i, F([Z.sub.ij][[Tau].sub.j]), where F is the standard normal cumulative density and Z is a vector of variables affecting a mill's participation decision.(11) The predicted number of bidders in each auction i (PRED) is defined as [PRED.sub.i] = [[Sigma].sub.j]F([z.sub.ij][[Tau].sub.j]). Each mill k expects to face PRED minus F([Z.sub.ik][[Tau].sub.k]) rivals, defined as EXP[N]. The random component of NUMBID (ERROR) is estimated as the difference between the actual and predicted number of bidders in each auction.(12)

Given estimates of PRED, EXP[N], and ERROR, I then conduct a Hausman test for measurement error in NUMBID in Meyer's bid level equations (1).


Hausman Test

The results of this test are reported in the last row of Table I. In three of the seven bid equations ERROR is statistically significant. An F-test of the null hypothesis that the coefficient on ERROR equals zero across the seven equations is rejected at the .0137 level.(13)

Reestimation of Bid Equations

The bid equations (1) are reestimated by replacing NUMBID, the actual number of bidders, with each mill's expecation of its number of rivals, EXP[N]. The results are presented in Table I.

The estimated coefficients on EXP[N] are positive and significant. An F-test that EXP[N] equals zero across the seven equations is rejected at the .0001 level.(14) Hence, as in Meyer, the null that the competitive effect dominates in the rice market cannot be rejected. With each additional bidder, Meyer finds mills increase their bids $0.38-0.58/cwt. The corrected model reveals an increase of $1.95-7.25/cwt from an additional expected bidder. As such, the results strongly support the expectation of a downward bias in Meyer's model. Note also that an F-test that the coefficients on EXP[N] are the same across firms is rejected at the .0616 level.(15) This indicates that while all seven firms react competitively to more bidders, they do so in different magnitudes.

A comparison of the remaining coefficients supports the results above. Meyer finds mills decrease their bids $0.22-0.67/cwt when the lot is second crop (lower quality), while the revised model reveals a decrease of $1.14-2.29/cwt. With each $1.00 increase in the expected resale price, Meyer finds mills increase their bids $0.43-0.51/cwt, while the revised model reveals an increase of $0.17-0.62/cwt. In response to a $1.00 absolute error in last period's forecast price, Meyer finds mills decrease their bids $0.38-1.01/cwt. The revised model reveals mills 2, 6, and 7 decrease their bids $0.74-8.04/cwt from an increase in the forecast variance.(16) Examining the estimated coefficients on lot volume reveals that a one (cwt) increase in lot size causes mills to decrease their bids $0.01-0.07/cwt. Last, the estimated coefficients on the rice variety dummies merely allow mills' intercepts to differ to account for their differing technologies.


Using Meyer's data, this paper corrects three problems in Meyer's econometric model. First, the misspecification of his resale price equation is corrected, and a more commonly used measure of uncertainty is employed. Second, additional variables that affect firms' bid levels independent from the expected resale price are successfully incorporated into the model. Third, a predicted measure of market competition is employed to test and correct an errors-in-variables problem. As expected, the finding that the competitive effect dominates is strengthened when the misspecification is identified and corrected. [Tabular Data Omitted]

(1)These auctions, which transfer ownership from farmer to mill, took place in Matagorda County, Texas, between 1970 and 1975. (2)The problems addressed focus on three of the four independent variables in equation (1). The fourth, QUALITY, is retained to control for the fact that firms are willing to pay more for a lot of higher quality regardless of its expected average resale price due to cost differences in processing. QUALITY equals zero if the auctioned lot is from the first crop harvested during the rice season and equals one if the lot is second crop. Second crop rice is of lower quality since it has lower mill yield and a higher level of impurities. (3)The average time lag between mills purchasing the rough rice and selling the milled product is approximately one month. Hence, time is indexed in months. This equation models the monthly average resale price for U.S. Number 2 Long-Grain F.O.B. See Meyer [1988, 127]. Meyer's equation (1) and Table II were replicated with price data starting in December 1969. Meyer assumes firms do not know the average price until the end of each month. Hence, for all auctions occurring in month t, [Price.sub.t] is not known to the mills. (4)Akaike's final prediction error (fpe) criterion is discussed in McMillan and Fackler [1984]. Note that while the price series has a unit root (e.g., the coefficient on [Price.sub.t-1] is not significantly different from zero if no other lags are included), tests reveal it is not a random walk (e.g., there remains serial correlation in the error term). The fpe criterion suggests the estimated model is reasonable in terms of its predictive power ([R.sup.2] = 0.97). Hence, it is assumed that additional information mills might use in forecasting price would not provide a significant improvement in the model. (5)The resale price equation is recursively estimated by adding an observation and then deleting an earlier observation. This is done so the variance will not change merely due to changes in the sample size. Note that the sample size is kept at fourteen for each estimation. (6)The forecast variance is a natural measure of uncertainty. Engle [1982], for example, uses an estimate of the forecast variance to proxy for inflation uncertainty. (7)The rice variety dummies are included in the bid level rather than the resale price equation since variety-specific resale prices are unavailable (e.g., varieties vary across all auctions occurring in any one month while the prices vary only by month). (8)See Meyer [1988, 126] footnote 6. In footnote 11, he states that he was unable to obtain data on the variables that determined the set of rice lots for which each mill chose to submit a bid. Hence, his attempts to model and obtain each firm's expectation of the number of bidders in each auction were unsuccessful. (9)This specification error is succinctly described in Johnston [1984]. Also see Hausman [1978]. (10)Johnston [1984, 428-435] and Kennedy [1985, 113, 119-120]. (11)The exogenous variables in the probit models are as follows: Mills' risk aversion in their participation decision is proxied by PRCUNC. Mills' ability to process large volumes of rice (storage capacity) is proxied by the volume of each auctioned lot, VOLUME. Hence, lot volume (in cwt) accounts for differences in firm size. While their identities are proprietary, some mills have national distribution while others are only regional. To proxy for the differing types and qualities of rice a mill might seek to purchase, QUALITY and the VARIETY dummies are included. Some mills' processing includes par boiling (breaking down and then reconstituting the raw rice), while others do not. Lower quality rice raises costs in this process, and certain varieties are better suited to this milling technique. (12)Due to space constraints, the probit results are not presented here. Briefly, the results are as follows: For mills 4, 5, and 6, as rice quality goes down mills are less likely to submit a bid, while mills 3 and 7, due to their differing processing technologies, are more likely to bid for lots of lower quality; PRCUNC reveals relative risk aversion and indicates that mills are less likely to participate as the forecast variance rises; as the volume of the lot rises, with the exception of mills 3 and 7, mills are more likely to participate, reflecting the increased market value of the lot and suggesting mills bid only when they have available storage space. (13)The calculated F-statistic, with 7/5774 degrees of freedom, is 2.52. (14)The calculated F-statistic, with 7/5781 degrees of freedom, is 6.37. (15)The calculated F-statistic, with 7/5781 degrees of freedom, is 2.00. (16)Meyer's uncertainty measure, if employed in the corrected model, has a positive and significant sign in the bid equations. This change in sign results directly from excluding the dummy variables from the resale price equation. In fact, if the supply shock dummies are included in the resale price equation and the corrected model is reestimated, the sign on PRCUNC becomes negative and significant. Hence, Meyer's estimated coefficients on PRCUNC result directly from his inclusion of the two dummy variables in the resale price equation, and capture the large price changes in the two shock periods, rather than capturing agent uncertainty. Therefore, the results support the expectation that the forecast variance is a superior measure of agent uncertainty.


Engle, R. F. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United

Kingdom Inflation." Econometrica, July 1982, 987-1007. Hausman, J. A. "Specification Tests in Econometrics." Econometrica, November 1978, 1251-71. Johnston, J. Econometric Methods, 3rd ed. New York: McGraw-Hill, 1984. Kennedy, Peter. A Guide to Econometrics, 2nd ed. Cambridge: MIT Press, 1985. McMillan, Douglas W. and James S. Fackler. "Monetary vs. Credit Aggregates: An Evaluation of

Monetary Policy Targets." Southern Economic Journal, January 1984, 711-83. Meyer, Donald J. "Competition and Bidding Behavior: Some Evidence from the Rice Market." Economic

Inquiry, January 1988, 123-32.

PHILLIP A. BEUTEL, National Economic Research Associates, Inc., White Plains, New York. I thank Bill Even, George Davis, Winn Fields, Bryce Kanago, and two anonymous referees for useful comments. Any errors are my own.
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Author:Beutel, Phillip A.
Publication:Economic Inquiry
Date:Apr 1, 1991
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