Empirical methods in the analysis of collusion

Abstract

Regression methods are commonly used in competition lawsuits for, e.g., determining overcharges in price-fixing cases. Technical evaluations of these methods’ pros and cons are not necessarily intuitive. Appraisals that are based on case studies are descriptive but need not be universally valid. This paper opens up the black box called econometrics for competition cases. This is done by complementing theoretical arguments with estimation results. These results are obtained for data that is generated by a simulation-model of a collusive industry. Using such data leaves little room for debate about the quality of these methods because estimates of, e.g., overcharges can be compared to their true underlying values. This analysis provides arguments for demonstrating that thoroughly conducted econometric analyses yield better results than simple techniques such as before-and-after comparisons.

Appendix 1: Generating a collusive industry

The dataset that is used in the above regressions is generated by running the simulation model with the parameter values given in Table 5. Except for the number of cartelists m, these parameter values are randomly determined from uniform distributions within the bounds provided by Table 5.

Table 5 Parameter values

Choosing n ∈ [7,15] is reasonable because, first, all firms would join the cartel with probability 1 if the number of firms was too small. Second, the time for calculating the participation-equilibrium rises exponentially in the number of firms and, thus, would be undesirably long for n > 15. From the viewpoint of economic theory, the size of ν is irrelevant as it only affects the size of prices and quantities but does not have an impact on the ratio of profit-measures. Using μ _upper  = 100 as an upper bound is reasonable as it suffices to produce rather homogeneous goods. Choosing a ₁ ∈ [0.05, 1.0] is reasonable because values below 0.05 would indicate that marginal costs are quite negligible. The production of such firms may be supposed to rather generate fixed costs that, however, are beyond the scope of this model. Choosing a ₄ ∈ [0.05, 0.15] gives economically meaningful yet not unrealistically large cost shocks. Drawing P from the wide interval [0.05, 0.4] reflects our lack of knowledge about the effectiveness of competition authorities. This is because one knows the number of discovered cartels but can hardly determine the number of undiscovered ones. The interval encloses the 15–20% detection probability that some studies suggest. Choosing r ∈ [0.05, 0.25] suggests that firms’ discount rate is somewhere between the return of government bonds and some (ambitious) firms’ target value of their return on equity. The number of cartelists m is determined endogenously as the mixed-strategy Nash-equilibrium of the cartel-formation game.