Impact of some parameters on investments in oligopolistic electricity markets

Abstract

It is seldom the case that one has the opportunity to compare investments as projected by a long-term multi-period model to what is eventually realized in practice. Further, although sensitivity analysis is of common use in any optimization setting, the impact of some parameters on strategic investments is not yet fully assessed in the context of the deregulated electricity industry. Starting with a benchmark model of the Finnish industry, we precisely explore the impact on equilibrium investments of varying such parameters as direct- and cross-price elasticities, length of the planning horizon and the depreciation rate of capacity. We run the model with different parameter values and compare the predicted equilibrium with what companies have actually done. The model is a stochastic dynamic game involving three players and played over a ten-year period.

Our results show the depreciation rate and the planning horizon have a notable effect on investment levels, whereas price elasticities seem to play a lesser role. Although the model’s results are rather well aligned to total industry investments, it diverges from individual levels. This may be due to the cost parameter used and/or to the open-loop information structure adopted in the computations. In any event, these results should be of methodological and practical interest to scholars and practitioners involved in strategic investment in the electricity industry.

Introduction

Investment decisions in electricity generation capacity have received considerable attention during the last fifty years or so. Till the recent wave of deregulation, the methodological framework to deal with the generation expansion problem (GEP) was optimization (see e.g., Masse and Gilbrat, 1957, Bloom, 1982, Borison et al., 1984, Mo et al., 1991, Hobbs, 1995). This approach was natural given the mandate assigned to the vertically integrated and regulated utility, namely, serving its protected market at the lowest possible cost. Deregulation brought an overnight paradigm change. The new context involves few generators competing for profits and grants strategic values to capacity (see e.g., Newbery, 2000, Stoft, 2002 for descriptions of deregulated electricity markets, and Ventosa et al., 2005 for an overview of decision-support models used in electricity market modelling). More specifically, the GEP is now viewed as a multi-player profit-maximization problem, with its solution derived as an equilibrium of a noncooperative game (Nanduri and Das (2008)).

When setting a model to deal with the capacity expansion problem in an oligopolistic context, one has to make some assumptions related to the structure of the model (e.g., stochastic or deterministic, static or dynamic, number of market segments), the mode of play and the equilibrium concept, the functional forms of production and investment costs and demand functions, as well as assumptions regarding the numerical values of some key parameters. The objective of this paper is to assess the impact on investment prescriptions of some of these choices (assumptions), namely, (i) the depreciation rate of physical capacity (zero vs. positive rate); (ii) the values of short- and long-term price elasticities; (iii) the planning horizon; and (iv) the number and relationship between market segments. Whereas the first three items are akin to sensitivity analysis, the last point involves somehow a change in the model.

To assess the impact of such changes in an empirical setting, we adopt as a starting point the stochastic and dynamic model of the Finnish electricity provided in Pineau and Murto (2003). The rationale for choosing this model is twofold. First, we have access to all modeling and estimation details as well as forecasted investments, and, second, we have the actual realizations, i.e., the investments made by the companies in Finland during the relevant period of time, that is from 1996 to 2006. Therefore, we can interestingly compare the predicted equilibrium investment levels provided by two models (the benchmark and one of its variation) to realizations. Our methodology can be seen as an experimental design with the items (i)–(iv) above being the manipulated factors and the level of investment being the dependent variable. Ultimately, our objective is to assess the robustness of some of the modeling choices involved in the generation expansion capacity model. Although we compare our results to realizations, our goal is not to replicate past investment decisions, but to assess how some modeling choices influence these results.

The rest of the paper is organized as follows. In Section 2, we present a brief description of the electricity industry context, followed by a review of the literature on GEP (Section 3). In Section 4, we introduce the stochastic dynamic model for GEP in general terms. A short description of the model developed by Pineau and Murto is provided in Section 5, with details on its calibration and on implemented modifications. We present our results in Section 6, and conclude in Section 7.