Patrick Bajari's thesis, "The First Price Auction with Asymmetric Bidders: Theory and Applications" uses new methods in economic theory and Markov Chain Monte Carlo to tackle an old problem: developing an econometric model of competitive bidding. Understanding competitive bidding is a question of considerable practical importance. Worldwide, the construction industry is a 3.2 trillion dollar market (Engineering New-Record, 11/30/98) where a large percentage of contracts are awarded by some form of competitive bidding. The particular market considered in his research was bidding by construction firms in Minneapolis, Minnesota for contracts to repair and build highways. The methodology, however, could be applied to study bidding in other procurements. The research addressed three questions. First, what is the (unobserved to the econometrician) cost structure of each firm in the market. Second, what is the posterior probability that the market is competitive or collusive. Third, what are the econometrician's posterior beliefs about bidding if different rules were used in awarding the contracts.

Bayesian methods are well suited to study these problems. After considerable research into the cost structure of the market, the author was able to develop restrictions on the space of parameter values in the firm's cost structures. The prior had compact support, that is, some parameter values were given zero prior probability (a trivial example is that trucking costs should not be negative and can be bounded above by using market prices for rental rates on trucking). Also, the support of the likelihood function depends on model parameters, greatly complicating the study of the asymptotic properties of maximum likelihood estimation. This poses no particular difficulty for Bayesian methods, however.

Economic theory is used to construct the likelihood function used in this research. Equilibrium models of strategic bidding generate a probability density for the bids that firms submit, condition on the model parameters (which characterized the firm's cost structures). The economic theory of equilibrium imposes two assumptions: first, firms have correct beliefs about the probability distribution of bids for all other firms and second, firms maximize expected profit.

In this research, a panel data set of bidding by 21 firms for 52 contracts was constructed. Data on project specific variables that enter a firm's cost (for instance, the distance of each firm from the project) was also collected. For a fixed set of parameter values, the equilibrium was computed for each bid in each project. The likelihood function is then the product of the probability density function evaluated at each bid in each project.

Conditional upon the observed bids and project specific cost variables, the posterior distribution of model parameters was simulated by using a Metropolis-Hastings algorithm. Several models were considered: a model of competition, a model of collusive bidding, and models with unobserved, project specific heterogeneity. Using the simulation output, it was straightforward to compute marginalized likelihoods for each model. Bayes factors were used to decide between the non-nested models in this research. The preferred specification was a model of competition with unobserved, project specific heterogeneity.

Using the posterior simulator, the econometrician's posterior beliefs about functions of the model parameters can be explored. The posterior distribution of firm's markups implied that the market was highly competitive. The posterior mean was between 1 and 7 percent for most projects. Bayes factors overwhelming favored the competitive specifications over the collusive specifications. Prior robustness analysis was conducted to study the sensitivity of these conclusions to the prior and in the class of priors with the same compact support, the results were not terribly sensitive.

A last question this research studies was to compare alternative rules for awarding the contract. The standard rule in bidding for government contracts is to award the contract to the lowest responsible bidder and the lowest bid. An alternative mechanism discussed among economists, with highly attractive theoretical properties, is a second price auction. Here, the firm with the lowest bid is still awarded the contract, but is paid the amount of the second lowest bid. For each construction project, the econometrician's posterior expectation of the cost to the government under both rules was computed. This research found that the second price auction results in a lower expected cost to the government, saving, on average, between 2 and 5 percent. Readers interested in reading this research can find it on the author's web page. .
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