Defining Relevant Product Markets for Pharmaceuticals

To identify the relevant product markets for Swedish pharmaceuticals, a spatial econometrics approach is employed. First, we calculate Moran’s Is for different market definitions and then we use a spatial Durbin model to determine the effect of price changes on quantity sold off own and competing products. As expected, the results show that competition is strongest between close substitutes; however, the relevant product markets for Swedish pharmaceuticals extend beyond close substitutes down to products included in the same class on the four-digit level of the Anatomic Therapeutic Chemical system as defined by the World Health Organization. The spatial regression model further indicates that increases in the price of a product significantly lower the quantity sold of that product and in the same time increase the quantity sold of competing products. For close substitutes (products belonging to the same class on the seven-digit level of the Anatomic Therapeutic Chemical system), as well as for products that, without being close substitutes, belong to the same therapeutic/pharmacological/chemical subgroup (the same class on the five-digit level of the Anatomic Therapeutic Chemical system), a significant change towards increased competition is also visible after 1 July 2009 when the latest policy changes with regards to pharmaceuticals have been implemented in Sweden.

Short Communication: A compelling argument for the gravity p-median model

The p-median model is used to locate P facilities to serve a geographically distributed population. Conventionally, it is assumed that the population always travels to the nearest facility. Drezner and Drezner (2006, 2007) provide three arguments on why this assumption might be incorrect, and they introduce the extended the gravity p-median model to relax the assumption. We favour the gravity p-median model, but we note that in an applied setting, Drezner and Drezner’s arguments are incomplete. In this communication, we point at the existence of a fourth compelling argument for the gravity p-median model.

Fitting spatial models in the R package: hglm

We present a new version of the hglm package for fittinghierarchical generalized linear models (HGLM) with spatially correlated random effects. A CAR family for conditional autoregressive random effects was implemented. Eigen decomposition of the matrix describing the spatial structure (e.g. the neighborhood matrix) was used to transform the CAR random effectsinto an independent, but heteroscedastic, gaussian random effect. A linear predictor is fitted for the random effect variance to estimate the parameters in the CAR model.This gives a computationally efficient algorithm for moderately sized problems (e.g. n<5000).

Spatial modeling of data with excessive zeros applied to reindeer pellet-group counts

We analyze a real data set pertaining to reindeer fecal pellet-group counts obtained from a survey conducted in a forest area in northern Sweden. In the data set, over 70% of counts are zeros, and there is high spatial correlation. We use conditionally autoregressive random effects for modeling of spatial correlation in a Poisson generalized linear mixed model (GLMM), quasi-Poisson hierarchical generalized linear model (HGLM), zero-inflated Poisson (ZIP), and hurdle models. The quasi-Poisson HGLM allows for both under- and overdispersion with excessive zeros, while the ZIP and hurdle models allow only for overdispersion. In analyzing the real data set, we see that the quasi-Poisson HGLMs can perform better than the other commonly used models, for example, ordinary Poisson HGLMs, spatial ZIP, and spatial hurdle models, and that the underdispersed Poisson HGLMs with spatial correlation fit the reindeer data best. We develop R codes for fitting these models using a unified algorithm for the HGLMs. Spatial count response with an extremely high proportion of zeros, and underdispersion can be successfully modeled using the quasi-Poisson HGLM with spatial random effects.