Model Selection, Estimation, and Marginal Effects for Markets in Equilibrium and Disequilibrium

Abstract

I examine an equilibrium and four prevalent disequilibrium model specifications under joint-normally distributed shocks and propose a statistical method for assessing whether a market is in an equilibrium state. I derive the marginal effects on the shortage probabilities and illustrate how one can interpret them. I provide analytic expressions for the gradients of all the models and the Hessians of the equilibrium and two of the disequilibrium models. Lastly, I use simulations to illustrate the performance of the models concerning, firstly, their estimation accuracy and, secondly, the computational gains of using gradient-based likelihood optimization methods.

Keywords: disequilibrium, marginal effects, model selection, maximum likelihood, Markov switching

JEL Classification: C01, C18, C34, C52, D50, D45