Mixed Frequency Data in a Multiproduct (S, s) Pricing Model

Øivind Anti Nilsen


In order to obtain meaningful results from models of sticky prices, it is crucial to have high frequency (such as monthly) data on prices. If explanatory variables, such as wage costs, are observed at all, these are typically on a lower frequency (yearly) and prices are therefore, often, aggregated to that same low frequency. In this paper, we propose a mixed-frequency stochastic (S, s)-model, which exploits the relatively high frequencies of prices in combination with plant- and product-specific components both in the price-, costs- and threshold-equations.

The model is formulated as a non-linear state space model and is estimated by means of the R-package ‘TMB’, see Kristensen et al. (2016). The estimation procedure allows us to formulate the model as if the explanatory variables are observed at the same frequency as the prices, enhancing computational efficiency. The results, based on merged survey- and register-data, document economies of scope in price adjustment within the plant together with a great share of plant-, product- and season-specific heterogeneity. However, the overall findings align with existing literature. Finally, time-aggregation blurs the intermittency in price changes.

As urbanization increases, municipalities across the world have become aware of the negative impacts of road-based transportation, which include traffic congestion and air pollution. As a result, several cities have introduced tolling schemes to discourage vehicles from entering the inner city. However, little research has been done to examine the impact of tolling schemes on the routing of commercial fleets, especially on the resulting costs and emissions. In this study, we investigate a vehicle routing problem considering different congestion charge schemes for several city types. We design comprehensive computational experiments to investigate whether different types of tolling schemes work in the way municipalities expect and what factors affect the performance of the congestion charge schemes. We compare the impact on a company’s total costs, fuel usage (which drives emissions), and delivery tour plans. Our experimental results demonstrate that some congestion pricing schemes may even increase the emi