This paper proposes a test of the null hypothesis of stationarity that is robust to the presence of fat-tailed errors. The test statistic is a modified version of the KPSS statistic, in which ranks substitute the original observations.... more
This paper proposes a test of the null hypothesis of stationarity that is robust to the presence of fat-tailed errors. The test statistic is a modified version of the KPSS statistic, in which ranks substitute the original observations. The rank KPSS statistic has the same limiting distribution as the standard KPSS statistic under the null and diverges under I(1) alternatives. It features good power both under thin-tailed and fat-tailed distributions and it turns out to be a valid alternative to the original KPSS and the recently proposed Index KPSS (de Jong et al. 2007).
The availability of scanner data from large-scale retailers makes the construction of a continuously updated system of price indexes over space and time for an important share of household consumption expenditures possible. However,... more
The availability of scanner data from large-scale retailers makes the construction of a continuously updated system of price indexes over space and time for an important share of household consumption expenditures possible. However, building a coherent (transitive) system of price indexes across space and time involves issues that are irrelevant for bilateral price indexes or multilateral price indexes only over space. Some of these issues were discussed by Hill (2004), but in my opinion the most important has been ignored. Indeed, it is very likely that the same commodity is differently priced across space, but in the long run the movements of its prices will be similar (stable) in space. So it is quite natural to ask price indexes for pairs of space situations not to diverge over time if the prices of each single commodity in the basket remain approximatively pairwise proportional in the two sites. In this work, we give a definition of the test of stability preservation, starting from the stochastic properties that panels of price time series seem to obey to. Then, many different approaches to the construction of the system of indexes are analysed in order to identify those that pass the test. The selected systems are applied both to simulated and to real-world data collected in four supermarkets located in the city of Milan for a time span of 24 months.
This paper analyses the interdependencies existing in wholesale electricity prices in six major European countries. The results of a robust multivariate long run dynamic analysis reveal the presence of four highly integrated central... more
This paper analyses the interdependencies existing in wholesale electricity prices in six major European countries. The results of a robust multivariate long run dynamic analysis reveal the presence of four highly integrated central European markets (France, Germany, the Netherlands and Austria). The trend shared by these four electricity markets appears to be common also to gas prices, but not to oil prices. The existence of a common long term dynamics among electricity prices and between electricity prices and gas prices can be explained by the similarity of the market design across Europe and by the same marginal generation technology. Since standard unit root and cointegration tests are not robust to the peculiar characteristics of electricity prices time series, we also develop a battery of robust inference procedures that should assure the reliability of our results.
The returns of many financial assets show significant skewness, but in the literature this issue is only marginally dealt with. Our conjecture is that this distributional asymmetry may be due to two different dynamics in positive and... more
The returns of many financial assets show significant skewness, but in the literature this issue is only marginally dealt with. Our conjecture is that this distributional asymmetry may be due to two different dynamics in positive and negative returns.
In this paper we propose a process that allows the simultaneous modelling of skewed conditional returns and different dynamics in their conditional second moments. The main stochastic properties of the model are analyzed and necessary and sufficient conditions for weak and strict stationarity are derived.
An application to the daily returns on the principal index of the London Stock Exchange supports our model when compared to other frequently used GARCH-type models, which are nested into ours.
In this paper we examine the bidding behaviour of firm competing in the Italian wholesale electricity market where generators submit hourly supply schedule to sell power. We describe the institutional characteristics of the Italian market... more
In this paper we examine the bidding behaviour of firm competing in the Italian wholesale electricity market where generators submit hourly supply schedule to sell power. We describe the institutional characteristics of the Italian market and derive generators' equilibrium bidding functions. We also discuss the main empirical strategies followed by the recent econometrical literature to obtain estimates of (unobservable) optimal bids. Then, we use individual bid data, quantity volumes and other control variables to compare actual bidding behaviour to theoretical benchmarks of profit maximization. We obtain estimates of generators' costs to be used in conjunction with hourly market equilibrium prices to derive some measures of the extent of market power in the Italian electricity sector and of its exploitation by firms.
In this paper we analyze a time series of daily average prices in the Italian electricity market, which started to operate as a Pool in April 2004. Our objective is to model the high degree of autocorrelation and the multiple... more
In this paper we analyze a time series of daily average prices in the Italian electricity market, which started to operate as a Pool in April 2004. Our objective is to model the high degree of autocorrelation and the multiple seasonalities in electricity prices. We use periodic time series models with GARCH disturbances and leptokurtic distributions and compare their performance with more classical ARMAGARCH processes. The within-year seasonal variation is modelled using the lowfrequency components of physical quantities, which are very regular throughout the sample. Our results reveal that much of the variability in the price series is explained by the interactions between deterministic multiple seasonalities. Periodic ARGARCH models seem to perform quite well in mimicking the features of the stochastic part of the price process.
Background The primary objective of this study was to make the first step in the modelling of pharmaceutical demand in Italy, by deriving a weighted capitation model to account for demographic differences among general practices. The... more
Background The primary objective of this study was to make the first step in the modelling of pharmaceutical demand in Italy, by deriving a weighted capitation model to account for demographic differences among general practices. The experimental model was called ASSET (Age/Sex Standardised Estimates of Treatment).
Methods and Major Findings Individual prescription costs and demographic data referred to 3,175,691 Italian subjects and were collected directly from three Regional Health Authorities over the 12-month period between October 2004 and September 2005. The mean annual prescription cost per individual was similar for males (196.13 euro) and females (195.12 euro). After 65 years of age, the mean prescribing costs for males were significantly higher than females. On average, costs for a 75-year-old subject would be 12 times the costs for a 25–34 year-old subject if male, 8 times if female. Subjects over 65 years of age (22% of total population) accounted for 56% of total prescribing costs. The weightings explained approximately 90% of the evolution of total prescribing costs, in spite of the pricing and reimbursement turbulences affecting Italy in the 2000–2005 period. The ASSET weightings were able to explain only about 25% of the variation in prescribing costs among individuals.
Conclusions If mainly idiosyncratic prescribing by general practitioners causes the unexplained variations, the introduction of capitation-based budgets would gradually move practices with high prescribing costs towards the national average. It is also possible, though, that the unexplained individual variation in prescribing costs is the result of differences in the clinical characteristics or socio-economic conditions of practice populations. If this is the case, capitation-based budgets may lead to unfair distribution of resources. The ASSET age/sex weightings should be used as a guide, not as the ultimate determinant, for an equitable allocation of prescribing resources to regional authorities and general practices.
Duration dependent Markov-switching VAR (DDMS-VAR) models are time series models with data generating process consisting in a mixture of two VAR processes. The switching between the two VAR processes is governed by a two state Markov... more
Duration dependent Markov-switching VAR (DDMS-VAR) models are time series models with data generating process consisting in a mixture of two VAR processes. The switching between the two VAR processes is governed by a two state Markov chain with transition probabilities that depend on how long the chain has been in a state. In the present paper we analyze the second order properties of such models and propose a Markov chain Monte Carlo algorithm to carry out Bayesian inference on the model’s unknowns. Furthermore, a freeware software written by the author for the analysis of time series by means of DDMS-VAR models is illustrated. The methodology and the software are applied to the analysis of the U.S. business cycle.
A methodology based on the multivariate generalized Butterwoth filter for extracting the business cycles of the whole economy and of its productive sectors is developed. The method is then illustrated through an application to the Italian... more
A methodology based on the multivariate generalized Butterwoth filter for extracting the business cycles of the whole economy and of its productive sectors is developed. The method is then illustrated through an application to the Italian gross value added time series of the main economic sectors.
This paper analyses the interdependencies existing in wholesale European electricity prices. The results of a multivariate long run dynamic analysis of weekly median prices reveal the presence of a strong although not perfect integration... more
This paper analyses the interdependencies existing in wholesale European electricity prices. The results of a multivariate long run dynamic analysis of weekly median prices reveal the presence of a strong although not perfect integration among some neighboring markets considered in the sample and the existence of common long-term dynamics of electricity prices and gas prices but not oil prices. The existence of long-term dynamics among gas prices and electricity prices may prove to be important for long-term hedging operations to be conducted even in markets where there are no electricity derivatives.
A coincident business cycle indicator for the Milan area is built on the basis of a monthly industrial survey carried out by Assolombarda, the largest territorial entrepreneurial association in Italy. The indicator is extracted from three... more
A coincident business cycle indicator for the Milan area is built on the basis of a monthly industrial survey carried out by Assolombarda, the largest territorial entrepreneurial association in Italy. The indicator is extracted from three time series concerning the production level and the domestic and foreign order book as declared by some 250 Assolombarda associates. This indicator is potentially very valuable in itself, being the Milan area one of the most dynamic economic systems in Italy and Europe, but it becomes much more interesting when compared to the Italian business cycle as extracted from the Italian industrial production index. Indeed, notwithstanding the deep differences in the nature of the data, the indicator for Milan has an extremely high coherence with the Italian cycle and the former leads the latter by approximately 4-6 months. Furthermore there is a direct relation between the amplitude of the cycle and the leading time of the Milan indicator. The ability of the Milan indicator to predict in real time the turning points of the Italian business cycle is tested through a simple forecasting exercise.
We propose a rank-test of the null hypothesis of short memory stationarity possibly after linear detrending. For the level-stationarity hypothesis, the test statistic we propose is a modified version of the popular KPSS statistic, in... more
We propose a rank-test of the null hypothesis of short memory stationarity possibly after linear detrending. For the level-stationarity hypothesis, the test statistic we propose is a modified version of the popular KPSS statistic, in which ranks substitute the original observations. We prove that the rank KPSS statistic shares the same limiting distribution as the standard KPSS statistic under the null and diverges under I(1) alternatives. For the trend-stationarity hypothesis, we apply the same rank KPSS statistic to the residual of a Theil-Sen regression on a linear trend. We derive the asymptotic distribution of the Theil-Sen estimator under short memory errors and prove that the Theil-Sen detrended rank KPSS statistic shares the same weak limit as the least-squares detrended KPSS. We study the asymptotic relative efficiency of our test compared to the KPSS and prove that it may have unbounded efficiency gains under fat-tailed distributions compensated by very moderate efficiency losses under thin-tailed distributions. For this and other reasons discussed in the body of the article our rank KPSS test turns out to be an irresistible competitor of the KPSS for most real-world economic and financial applications. The weak convergence results and asymptotic representations proved in this article may have an interest on their own, as they extend to ranks analogous results widely used in unit-root econometrics.
In this paper we consider an oligopolistic market in which one firm can be monopolist on her residual demand function and derive implications on the shape of her profit function, which we show may not be concave in price. We propose a... more
In this paper we consider an oligopolistic market in which one firm can be monopolist on her residual demand function and derive implications on the shape of her profit function, which we show may not be concave in price. We propose a simple price-capping rule that induce the pivotal operator to compete for quantity instead of taking advantage of her monopoly. Then, we analyze the bidding behaviour of the dominant electricity producer oper- ating in the Italian wholesale power market (IPEX). This firm is vertically integrated and in many instances she acts as a monopolist on the residual demand. We find that, contrary to expectations, this pivotal firm refrains to exploit totally her unilateral market power and, therefore, bids at levels well below the cap. We discuss such a behaviour and derive implications for the setting of the price cap.
