Thursday, October 27, 2011
A Note on “Modeling the Birth and Death of Cartels with An Application to Evaluating Competition Policy” by Harrington and Chang (2009)
Posted by D. Daniel Sokol
Jun Zhou (University of Bonn) provides A Note on “Modeling the Birth and Death of Cartels with An Application to Evaluating Competition Policy” by Harrington and Chang (2009).
ABSTRACT: In the December 2009 issue of the Journal of European Economic Association, Harrington and Chang presented a model of dynamic cartel formation and dissolution where an industry of firms interact repeatedly over an infinite time horizon. Absent antitrust intervention, there is a “marginal industry” in which firms are indifferent between collusion and competing because the short-run gain of cheating for each firm equals its long-run benefit from colluding. An efficacious antitrust innovation works its effect by increasing a firm’s short-run benefit from cheating to a level that exceeds its long-run gains from colluding. In this way, the policy-innovation moves the “marginal type” from a population of sustainable, longer-lived cartels to a population of unstable, shorter-lived ones. The model generates intuitive predictions that can be used to assess the efficacy of antitrust innovations (such as the leniency program): The impact of an efficacious policy on the duration of discovered cartels is time-dependent. In particular, following an antitrust innovation that increases probability of detection, the marginal cartels immediately break up and the ensuing cartel discovery comes from a population of longer-lasting cartels. Because of such a sample selection effect, the average duration of discovered cartels increases in the short-run. That is, the short-run distribution of cartel duration dominates the steady-state pre-innovation distribution in the sense of first order stochastic dominance (FOSD) (Theorem 7 of Harrington and Chang); in the long run, the duration decreases due to the enhanced overall deterrence. That is, the post-innovation steady-state distribution of cartel duration dominates the short-run one in the sense of FOSD (Theorem 8 of Harrington and Chang). These theoretical predictions can be tested empirically but not direct ways. This is because the estimation of the cartel duration from discovered cartels must consider the censoring of duration for cartels ending due to antitrust interventions (Levenstein and Suslow (forthcoming)). For such cartels, we can only infer that collusion would have exceeded the observed cartel duration at the time of the cartel’s dissolution. In this note, I provide two stronger theorems than Theorems 7 and 8 in Harrington and Chang. My results can be directly corroborated in a empirical model of survival analysis— a by now standard approach to the analysis of cartel durations.2 They relate to the probability that a cartel survives for t periods conditional on the event that the cartel survives for at least t periods, i.e., the dissolution hazard of discovered cartels.
I show within Harrington and Chang’s framework that (1) in the short-run an after an antitrust innovation that raises the probability of detection, the distribution of cartel duration shifts and dominates, in the sense of hazard rate dominance (HRD), the pre-innovation distribution; and that (2) in the long run after the innovation, the distribution readjusts and dominates the short-run distribution in the sense of HRD.