Likelihood diagnostics and Bayesian analysis of a micro-economic disequilibrium model for retail services
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In this paper we apply Maximum Likelihood and Bayesian methods to explain differences in floorspace productivity among retail establishments in the grocery trade. The model we develop is a switching model where sales are either supply-determined or demand-determined. Under excess supply the model allows for so-called ‘trading-down’, i.e., an increase in the share of selling area, and, thereby, a decrease in service level. To estimate our model we employ a cross-section of observations on individual shops. We present maximum likelihood results, and also study the shape of the likelihood surface by means of Monte Carlo numerical integration methods. With a uniform prior we obtain marginal posterior density functions both of the parameters of interest and of the average probability of the excess supply regime in the sample. The average probability of excess supply is 0.23, with a standard deviation of 0.06. This shows that, according to our estimates, excess demand is the rule and excess supply the exception in the sample that we analyse.
- density function
- likelihood function
- density functions