Calibration algorithm for spatial partial equilibrium models with conjectural variations

TL;DR

This paper introduces a calibration algorithm for spatial partial equilibrium models with conjectural variations that handles user-imposed parameter bounds and ensures realistic market behavior, demonstrated on European gas market data.

Contribution

The proposed algorithm allows simultaneous calibration of supplier sales and parameters within bounds, improving model realism and flexibility.

Findings

Calibration completed in under one minute on European gas data.

Algorithm effectively manages bounds on market power parameters.

Iterative adjustment aligns model outputs with reference data.

Abstract

When calibrating spatial partial equilibrium models with conjectural variations, some modelers fit the suppliers' sales to the available data in addition to total consumption and price levels. While this certainly enhances the quality of the calibration, it makes it difficult to accommodate user-imposed bounds on the model parameters such as restricting the market power parameters to the interval [0,1], which is a common requirement in conjectural variations approaches. We propose an algorithm to calibrate the suppliers' sales and simultaneously deal with user-defined bounds on parameters. To this end, we fix the suppliers' sales at reference values and obtain the marginal costs for each supplier and market. We then limit the market power parameters to the interval [0,1], and calculate intervals of anchor prices and price elasticities that reproduce the reference supplier sales in the state of equilibrium. If these intervals do not contain the reference price elasticities and prices, we face a mismatch between reality and the model mechanics. We resolve this by altering the reference sales for the critical suppliers, and iterate. Thereby, the user controls whether price elasticities and anchor prices should be close to their reference values, or the suppliers' sales. The algorithm is tested on data from the European gas market, and required less than one minute to identify calibrated parameters. Our algorithm is widely applicable, since it is based on mild (and common) underlying assumptions and can be configured to suit a specific purpose thanks to the inclusion of user-defined bounds on all relevant parameters.