Price Wars and Collusion in the Spanish Electricity Market

We analyze the time-series of prices in the Spanish electricity market by means of a time varying-transition-probability Markov switching model. Accounting for changes in demand and cost conditions (which re°ect changes in input costs, capacity avail- ability and hydro power), we show that the time-series of prices is characterized by two signi¯cantly di®erent price levels. Based on a Green and Porter (1984)'s type of model that introduces several institutional details, we construct trigger variables that a®ect the likelihood of starting a price war. By interpreting the signs of the triggers, we are able to infer some of the properties of the collusive strategy that ¯rms might have followed. We obtain more empirical support to Green and Porter's model than previous studies

The Fall in British Electricity Prices: Market Rules, Market Structure, or Both?

In this paper we investigate the factors contributing to the fall in the Lerner Index (price-cost margin) in the British electricity market during the 90s. A first stage of our analysis models the number of breaks in the Lerner Index and their dating as unknowns. Our results suggest the existence of one structural break in the time series of the Lerner Index. The break point interval includes the go-live of the New Electricity Trading Arrangements (NETA), but also several other (but not all) regulatory interventions. In a second stage, we construct a general regression model for the Lerner index as a function of the regulatory interventions within the estimated break point interval, the Herfindahl- Hirschman Index (HHI), and the demand-capacity ratio. The results show that both the HHI and the demand-capacity ratio are strongly significant for explaining the fall in the Lerner Index. NETA is also significant, even when the Lerner Index is corrected for the influence of the HHI and the demand-capacity ratio.Electricity Markets, Regulatory Reform, Structural Breaks

Price Wars and Collusion in the Spanish Electricity Market

\We analyze the time-series of prices in the Spanish electricity market by means of a time varying-transition-probability Markov switching model. Accounting for changes in demand and cost conditions (which reflect changes in input costs, capacity availability and hydro power), we show that the time-series of prices is characterized by two significantly different price levels. Based on a Green and Porter (1984)'s type of model that introduces several institutional details, we construct trigger variables that affect the likelihood of starting a price war. By interpreting the signs of the triggers, we are able to infer some of the properties of the collusive strategy that firms might have followed. We obtain more empirical support to Green and Porter's model than previous studies. REVISED: January 2004Electricity Markets, Collusion, Markov Switching

Price Wars and Collusion in the Spanish Electricity Market

We analyze the pattern of pool prices in the Spanish electricity market during 1998 by means of a Time Varying Transition Probabilities Markov switching model. Our purpose is two­fold: firstly, to identify and date the drops in prices that cannot be accounted for by supply nor demand conditions; and secondly, under the assumption that these correspond with reversions to non­cooperative behaviour, to identify the trigger variables upon which a collusive equilibrium could be based upon. Our results confirm the hypothesis that two distinct price levels characterize the time series of pool prices, and point to the conclusion that price wars are induced by changes in the major generators' market shares. In turn, this shows that firms' pricing behaviour is highly influenced by the way in which the so­called Competition Transition Charges (CTCs) are computed.Electricity Markets, Tacit Collusion, Markov Switching

Classical and Modern Business Cycle Measurement: The European Case

This paper intends to harmonize two different approaches to the analysis of the business cycle and in doing so it retrieves the stylized facts of the business cycle in Europe. We start with the “classical” approach proposed in Burns and Mitchell (1946) of dating and analyzing the business cycle; we then adopt the “modern” alternative: the Markov-switching vector autoregression (MS-VAR). The model's regime probabilities provide an optimal statistical inference of the turning point of the European business cycle. For assessing the capacity of the parametric approach to generate the stylized facts of the classical cycle in Europe, the stylized facts of the original data are compared to those of simulated data. The MS-VAR model is shown to be a good candidate for use as an statistical instrument to improve the understanding of the business cycle.International business cycles, European Union, Markov Switching, Structural breaks, Time series analysis.

Optimal portfolio choice in real terms : measuring the bene ts of TIPS.

In this paper, we solve an optimal portfolio choice problem to measure the bene ts of Treasury In ation Indexed Securities (TIPS) to investors concerned with maximizing real wealth. We show how the introduction of a real riskless asset completes the investor asset space, by contrasting optimal portfolio allocations with and without such assets. We use historical data to quantify gains from availability of TIPS in the presence of other asset classes such as equities, commodities, and real estate. We draw a distinction between buy-and-hold long-term investors for whom TIPS fully displace nominal riskfree assets and short-term investors for whom TIPS improve the investment opportunity set of real returns. Finally, we show how gains from TIPS are tempered by availability of alternative assets that covary with in ation, such as gold and real estatePortfolio choice in real terms; Treasury inflaction Indexed Securities (TIPS); Buy-and-hold long-term investors; Money illusion;

Emergence of a phonological bias in ChatGPT

Current large language models, such as OpenAI's ChatGPT, have captured the public's attention because how remarkable they are in the use of language. Here, I demonstrate that ChatGPT displays phonological biases that are a hallmark of human language processing. More concretely, just like humans, ChatGPT has a consonant bias. That is, the chatbot has a tendency to use consonants over vowels to identify words. This is observed across languages that differ in their relative distribution of consonants and vowels such as English and Spanish. Despite the differences in how current artificial intelligence language models are trained to process linguistic stimuli and how human infants acquire language, such training seems to be enough for the emergence of a phonological bias in ChatGPTComment: 15 pages, 1 figure, corrected typ

Definition of the invariant and the relationship with the compounds numbers. Generalisation of the Euler theorem

The purpose of this article is to introduce the concept of invariance and its properties. These properties can be used to check the primality of a number. Combining these properties with the Euler theorem, it is possible to generalize this theorem for all the values of $a^{\varphi(m)}$ where $0 < a < m {\pmod {m}}$ independently if a is co prime or not with m. As $a^{\varphi(m)+1} \equiv a$ if $m = a \cdot b$ and $GCD(a, b) = 1$. As the following steps, a new hypothesis is formulated regarding the substitution of the Totien function for an equivalent function that explains the Carmichael numbers. Keywords: Prime Numbers, Compound Numbers, Primality test, Euler theore