Alvaro Escribano

• Ph.D in Economics, 1986 UCSD
• Managing Director at University Carlos III de Madrid

Score-driven filters are updated by the scaled gradient of the log-likelihood (LL). The gradient is with respect to a dynamic parameter and the scaling parameter is 1, or the information quantity or its square root in the literature. The information quantity is minus the expected value of the Hessian of the LL with respect to a dynamic parameter, i...

Since the influential works of Friedman and Schwartz (1963, 1982) and Hendry and Ericsson (1991), on the monetary history of the United States of America and the United Kingdom from 1876 to 1975, there has been a great concern in the literature about the instability of money demand functions. This concern together with the results of the New Keynes...

We introduce the quasi-vector autoregressive fractionally integrated (QVAR-FI) model. We apply QVAR-FI to climate data and introduce the fractionally integrated score-driven ice-age model. We use global sea ice volume, atmospheric carbon dioxide (CO 2) concentration, and Antarctic land surface temperature data from 798,000 to 1,000 years ago. We co...

The literature on sea ice predictions uses a variety of general circulation models (GCMs), which suggest diverse predictions of the date of ice-free or almost ice-free oceans, and focus mainly on the Arctic. GCMs are not sensitive enough to tipping points in the Atlantic meridional overturning circulation (AMOC), and they underestimate the sensitiv...

Climate variables are known to be subject to abrupt changes when some threshold levels are surpassed. We use data for the last 798,000 years on global ice volume (Ice t), atmospheric carbon dioxide level (CO 2), and Antarctic land surface temperature (Temp t) to model and measure those long-run nonlinear climate effects. The climate variables have...

We contribute to the literature on empirical macroeconomic models with time-varying conditional moments, by introducing a heteroskedastic score-driven model with Student's t-distributed innovations, named the heteroskedastic score-driven t-QVAR (quasi-vector autoregressive) model. The t-QVAR model is a robust nonlinear extension of the VARMA (VAR m...

We contribute to the literature on empirical macroeconomic models with time-varying conditional moments, by introducing a heteroskedastic score-driven model with Student's t-distributed innovations, named the heteroskedastic score-driven t-QVAR (quasi-vector autoregressive) model. The t-QVAR model is a robust nonlinear extension of the VARMA (VAR m...

Climate variables are known to be subject to abrupt changes when some threshold levels are surpassed. We use data for the last 798,000 years on global ice volume, atmospheric carbon dioxide level (CO2), and Antarctic land surface temperature to model and measure those long-run nonlinear climate effects. The climate variables have very long and asym...

We suggest a new value-at-risk (VaR) framework using EGARCH (exponential generalized autoregressive conditional heteroskedasticity) models with score-driven expected return, scale, and shape filters. We use the EGB2 (exponential generalized beta of the second kind), NIG (normal-inverse Gaussian), and Skew-Gen-t (skewed generalized-t) distributions,...

We present the Beta-t-QVAR (quasi-vector autoregression) model for the joint modelling of score-driven location plus scale of strictly stationary and ergodic variables. Beta-t-QVAR is an extension of Beta-t-EGARCH (exponential generalized autoregressive conditional heteroscedasticity) and Beta-t-EGARCH-M (Beta-t-EGARCH-in-mean). We prove the asympt...

Climate variables are known to be subject to abrupt changes when some threshold levels are surpassed. We use data for the last 798,000 years on global ice volume (Ice), atmospheric carbon dioxide level (CO2), and Antarctic land surface temperature (Temp) to model and measure those long-run nonlinear climate effects. The climate variables have very...

We present the Beta-t-QVAR (quasi-vector autoregression) model for the joint modelling of score-driven location plus scale of strictly stationary and ergodic variables. Beta-t-QVAR is an extension of Beta-t-EGARCH (exponential generalized autoregressive conditional heteroscedasticity) and Beta-t-EGARCH-M (Beta-t-EGARCH-in-mean). We prove the asympt...

We extend a recent climate-econometric model that we call benchmark ice-age model, by using score-driven filters of conditional mean and variance which generalize the updating mechanism of the benchmark model. For the period of the last 798 thousand years, we use the climate variables global ice volume (Ice t), atmospheric carbon dioxide level (CO...

We present the Beta-t-QVAR (quasi-vector autoregression) model for the joint modelling of score-driven location plus scale of strictly stationary and ergodic variables. Beta-t-QVAR is an extension of Beta-t-EGARCH (exponential generalized autoregressive conditional heteroscedasticity) and Beta-t-EGARCH-M (Beta-t-EGARCH-in-mean). We prove the asympt...

We suggest a new value-at-risk (VaR) framework using EGARCH (exponential generalized autoregressive conditional heteroskedasticity) models with score-driven expected return, scale, and shape filters. We use the EGB2 (exponential generalized beta of the second kind), NIG (normal-inverse Gaussian), and Skew-Gen-t (skewed generalized-t) distributions,...

Score-driven models applied to finance and economics have attracted significant attention in the last decade. In this paper, we apply those models to climate data. We study the robustness of a recent climate econometric model, named ice-age model, and we extend that model by using score-driven filters in the measurement and transition equations. Th...

Score-driven models applied to finance and economics have attracted significant attention in the last decade. In this paper, we apply those models to climate data. We study the robustness of a recent climate econometric model, named ice-age model, and we extend that model by using score-driven filters in the measurement and transition equations. Th...

Spectrum auctions have recently experienced increased sophistication in the allocation of multi-band frequencies, with efficiency issues becoming much more complex in such scenarios. This empirical analysis seeks to identify the drivers of auction prices associated with 4G and 5G technologies in seven European countries during the period 2008–2019....

Gaussian-ABCD representations of dynamic stochastic general equilibrium (DSGE) models are extended to score-driven $t$-ABCD representations using the multivariate $t$-distribution. For $t$-ABCD, not only the variance of variables but also their transition equations are score-driven. Asymptotic properties of the maximum likelihood (ML) estimator are...

One of the most successful forecasting machine learning (ML) procedures is random forest (RF). In this paper, we propose a new mixed RF approach for modeling departures from linearity that helps identify (i) explanatory variables with nonlinear impacts, (ii) threshold values, and (iii) the closest parametric approximation. The methodology is applie...

The seed of this special section was the workshop celebrated at FUNCAS in Madrid in February 2019 “30 Years of Cointegration and Dynamic Factor Models Forecasting and its Future with Big Data”. In this editorial, we describe the main contributions of the 13 papers published within the special section towards forecasting in the context of non- stati...

Emerging countries are increasingly concerned with improving their competitiveness and productivity. This Element develops a robust econometric methodology, based on controlling for usual unobservable effects at the firm or plant level. By robust empirical results in total factor productivity (TFP), we mean estimating investment climate (IC) elasti...

Nonlinear co-integration is studied for score-driven models, by using a new multivariate dynamic conditional score (DCS) / generalized autoregressive score (GAS) model. The model is named t-QVARMA (quasi-vector autoregressive moving average model), which is a location model for the multivariate t-distribution. In t-QVARMA, I(0) and co-integrated I(...

A new class of multivariate nonlinear quasi-vector autoregressive (QVAR) models is introduced. It is a Markov switching score-driven model with stochastic seasonality for the multivariate t-distribution (MS-Seasonal-t-QVAR). As an extension, we allow for the possibility of having common-trends and nonlinear co-integration. Score-driven nonlinear up...

In this paper, we introduce Beta-t-QVAR (quasi-vector autoregression) for the joint modelling of score-driven location and scale. Asymptotic theory of the maximum likelihood (ML) estimator is presented, and sufficient conditions of consistency and asymptotic normality of ML are proven. For the joint score-driven modelling of risk premium and volati...

In this paper, we introduce Beta-t-QVAR (quasi-vector autoregression) for the joint modelling of score-driven location and scale. Asymptotic theory of the maximum likelihood (ML) estimator is presented, and sufficient conditions of consistency and asymptotic normality of ML are proven. For the joint score-driven modelling of risk premium and volati...

For policy decisions, capturing seasonal effects in impulse responses is important for the correct specification of dynamic models that measure interaction effects for policy-relevant macroeconomic variables. In this paper a new multivariate method is suggested, which uses the score-driven quasi-vector autoregressive (QVAR) model, to capture season...

Supplementary Material for the manuscript entitled "Co-integration with score-driven models: an application to US real GDP growth, US inflation rate, and effective federal funds rate"

For policy decisions, capturing seasonal effects in impulse responses is important for the correct specification of dynamic models that measure interaction effects for policy-relevant macroeconomic variables. In this paper a new multivariate method is suggested, which uses the score-driven quasi-vector autoregressive (QVAR) model, to capture season...

Relevant works from the literature on crude oil market use structural vector autoregressive (SVAR) models with several lags to approximate the true model for the variables change in global crude oil production, global real economic activity and log real crude oil prices. Those variables involve seasonality, co-integration, structural changes, and o...

In this paper, the benefits of statistical inference of score-driven state-space models are incorporated into the inference of dynamic stochastic general equilibrium (DSGE) models. We focus on DSGE models, for which a Gaussian ABCD representation exists. Precision of statistical estimation is improved, by using a score-driven multivariate t-distrib...

The main objective of this article is to analyse the different sources of asymmetric price transmissions in the fuel market for France, Germany and Spain. During the last decades, the EU has carried out several common energy policies to achieve more efficient and competitive markets. However, given the specific characteristics of each country, the...

In this paper, new Seasonal-QVAR (quasi-vector autoregressive) and Markov switching (MS) Seasonal-QVAR (MS-Seasonal-QVAR) models are introduced. Seasonal-QVAR is an outlier-robust score-driven state space model, which is an alternative to classical multivariate Gaussian models (e.g. basic structural model; Seasonal-VARMA). Conditions of the maximum...

Co-integration and common trends are studied for time series variables, by introducing the new t-QVARMA (quasi-vector autoregressive moving average) model. t-QVARMA is an outlier-robust nonlinear score-driven model for the multivariate t-distribution. In t-QVARMA, the I(0) and I(1) components of the variables are separated in a way that is similar...

Dynamic conditional score (DCS) models with time-varying shape parameters provide a flexible method for volatility measurement. The new models are estimated by using the maximum likelihood (ML) method, conditions of consistency and asymptotic normality of ML are presented, and Monte Carlo simulation experiments are used to study the precision of ML...

We introduce new dynamic conditional score (DCS) volatility models with dynamic scale and shape parameters for the effective measurement of volatility. In the new models, we use the EGB2 (exponential generalized beta of the second kind), NIG (normal-inverse Gaussian) and Skew-Gent (skewed generalized-t) probability distributions. Those distribution...

Electricity prices are characterised by strong autoregressive persistence, periodicity (e.g. intraday, day-of-the week and month-of-the-year effects), large spikes or jumps, GARCH and – as evidenced by recent findings – periodic volatility. We propose a multivariate model of volatility that decomposes volatility multiplicatively into a non-stationa...

Over the last decades a transition from a state-own monopoly to a private business took place in the Spanish fuel sector. To figure out whether downstream prices react differently to upstream price increases than to price decreases, alternative dynamic nonlinear and asymmetric error correction models are applied to weekly price data. This paper ana...

This article introduces a new Cramer-Von Misses (CVM) cointegration test robust to nonlinearities. We characterize nonlinear cointegration in terms of a nonlinear moving-average filter (high pass filter) of a matrix based on permutation matrices on the discrepancy of empirical distributions. A Cramer-Von Misses (CVM) test statistic is proposed for...

A critique that has been directed towards the log-GARCH model is that its log-volatility specification does not exist in the presence of zero returns. A common ‘remedy’ is to replace the zeros with a small (in the absolute sense) non-zero value. However, this renders estimation asymptotically biased if the true return is equal to zero with probabil...

Research is a key determinant of health improvement. However, there is little empirical evidence showing how the research conducted in hospitals affects healthcare outcomes. To address this issue, we used panel data of 189 Spanish public hospitals over the period 1996–2009 to estimate the causal effect of both clinical and basic research on hospita...

In this paper, we propose the use of Dynamic Conditional Score (DCS) count panel data models. We compare the statistical performance of the static model with different dynamic models: finite distributed lag, exponential feedback and different DCS models. For DCS, we consider random walk or quasi-autoregressive dynamics. We use panel data for a larg...

We propose a new class of dynamic patent count panel data models that is based on dynamic conditional score (DCS) models. We estimate multiplicative and additive DCS models, MDCS and ADCS respectively, with quasi-ARMA (QARMA) dynamics, and compare them with the �nite distributed lag, exponential feedback and linear feedback models. We use a large p...

A general framework for the estimation and inference in univariate and multivariate Generalised log-ARCH-X (i.e. log-GARCH-X) models when the conditional density is unknown is proposed. The framework employs (V)ARMA-X representations and relies on a bias-adjustment in the log-volatility intercept. The bias is induced by (V)ARMA estimators, but the...

In this article, dynamic interactions among stock return, Research and Development (R&D) investment, patent applications and patent propensity of firms are studied. Patent innovation leader and follower firms are identified with respect to their quality-adjusted knowledge stock. Significant and positive dynamic spillover effects are obtained in a p...

This paper provides evidence on the effect of recessions and expansions on the productivity growth rate of productivity leaders and followers. We use data of a representative sample of the Spanish manufacturing sector for the period 1991 and 2005. These data allow us to estimate firm level productivity for a relatively long period of time and provi...

In recent years, research policy stakeholders have emphasized their interest in the societal returns of research. The goal of this study is to assess the impact of research activities on Spanish hospitals clinical outcomes. To do so, we use a panel data set of Spanish hospitals, and we consider two fixed effects models, one for medical and the othe...

General-to-Specific (GETS) modelling has witnessed major advances over the last decade thanks to the automation of multi-path GETS specification search. However, several scholars have argued that the estimation complexity associ-ated with financial models constitutes an obstacle to multi-path GETS mod-elling in finance. Making use of a recent resul...

Developing countries are increasingly concerned about improving country competitiveness and productivity, as they face the increasing pressures of globalization and attempt to improve economic growth and reduce poverty. Among such countries, Investment Climate surveys (ICs) at the firm level, have become the standard way for the World Bank to ident...

This paper studies the dynamic interactions and the spillovers that exist among patent application intensity, secret innovation intensity and stock returns of a well-defined technological cluster of firms. We study the differential behavior when there is an Innovation Leader (IL) and the rest of the firms are Innovation Followers (IFs). The leader...

This article analyses the evolution of electricity prices in deregulated markets. We present a general class of models that simultaneously takes into account several factors: seasonality, mean reversion, GARCH behaviour and time-dependent jumps. The models are applied to daily equilibrium spot prices of eight electricity markets. Eight different ne...

During the past two decades, innovations protected by patents have played a key role in business strategies. This fact enhanced studies of the determinants of patents and the impact of patents on innovation and competitive advantage. Sustaining competitive advantages is as important as creating them. Patents help sustaining competitive advantages b...

The Investment Climate surveys (ICSs) are valuable instruments which improve our understanding of the economic, social, political and institutional factors determining economic growth, particularly in emerging and transition economies. However, at the same time, they have to overcome some difficult issues related with the quality of the information...

Exponential models of autoregressive conditional heteroscedasticity (ARCH) are attractive in empirical analysis because they guarantee the non-negativity of volatility, and because they enable richer autoregressive dynamics. However, the currently available models exhibit stability only for a limited number of conditional densities, and the availab...

Investment Climate surveys (ICs) are a recent instrument used by the World Bank to identify key obstacles to country competitiveness and to guide policy reforms and government interventions in developing countries. In this paper, panel data from four ICs of four South East Asian (SEA) countries namely, Indonesia, Malaysia, The Philippines, and Thai...

In this paper, we argue that those firms with higher levels of absorptive capacity can manage external knowledge flows more efficiently, and stimulate innovative outcomes. We test this contention with a sample of 2265 Spanish firms, drawn from the Community Innovation Surveys (CIS) for 2000 and 2002, produced by the Spanish National Statistics Inst...

In this paper, we present a Bayesian analysis of exponential power mixture models in the presence of a covariate. Considering Gibbs sampling with MetropolisHastings algorithms, we obtain Monte Carlo estimates for the posterior quantities of interest.

Spain has recently experienced more than a decade of price stability and economic growth however now is showing one of the most significant slowdowns in economic activity of the EU economies. There is a general consensus that this slowdown in economic activity is particularly important in Spain due to the low level and low rates of growth experienc...

Most empirical studies show strong detrimental evidence that regulatory, and administrative, barriers to entry have on productivity and on firm growth. In this paper we evaluate and measure the total factor productivity (TFP) impacts of having; low quality physical infrastructures (electricity, telecommunications, transport, customs, etc.) and bad...

Alternative common factor representations for cointegrated vectors are studied. This is done by embedding them into the dynamic factor model proposed by Peña and Box (Identifying a simplifying structure in time series. J. Am. Statist. Assoc. 82 (1987), 836–43). It is shown that dynamic factor models produce as a particular case the alternative comm...

In this paper we explore the usefulness of induced-order statistics in the characterization of integrated series and of cointegration relationships. We propose a non-parametric test statistic for testing the null hypothesis of two independent random walks against wide cointegrating alternatives including monotonic nonlinearities and certain types o...

ABSTRACT : This paper looks at how well Finland performs in high growth entrepreneurship and uses data from the Global Entrepreneurship monitor to benchmark Finland against other European countries. It is found that Finland’s prevalence rate of high growth entrepreneurial activity lags significantly behind most of its European and all of its Scandi...

The choice of an appropriate social rate of discount is critical in the decision-making process on public investments. In this paper we review the literature on social discounting, and address in particular a recently growing field of related research, that is, individual time preferences. We argue that an explicit consideration and analysis of the...

This paper is devoted to presenting wider characterizations of memory and cointegration in time series, in terms of information-theoretic statistics such as the entropy and the mutual information between pairs of variables. We suggest a nonparametric and nonlinear methodology for data analysis and for testing the hypotheses of long memory and the e...

In this article we propose a record counting cointegration (RCC) test that is robust to nonlinearities and certain types of structural breaks. The RCC test is based on the synchronicity property of the jumps (new records) of cointegrated series, counting the number of jumps that simultaneously occur in both series. We obtain the rate of convergence...

Since the seminal paper by Dickey and Fuller in 1979, unit-root tests have conditioned the standard approaches to analysing time series with strong serial dependence in mean behaviour, the focus being placed on the detection of eventual unit roots in an autoregressive model fitted to the series. In this paper, we propose a completely different meth...

The aim of the paper is the analysis of ECM (Error Correction Model) bootstrap cointegration tests under structural breaks. Classical ECM tests depend on some nuisance parameters, which is an undesirable feature for empirical applications. This problem is overcome by using the bootstrap ECM test, which shows good size and power properties when ther...

Conventional Dickey-Fuller tests have very low power in the presence of structural breaks. Critical values are very sensitive to: the type of break, the timing and size of the break. Therefore, correct critical values are usually obtained by adding dummy variables to the Dickey-Fuller regression. From the empirical point of view almost any result f...

This paper proposes a new approach to jointly model the trading process and the revisions of market quotes. This method accommodates asymmetries in the dynamics of ask and bid quotes after trade-related shock. The empirical specification is a vector error correction (VEC) model for ask and bid quotes, with the spread as the co-integrating vector, a...

Desde la apertura a la competencia del Sector de las Telecomunicaciones en España a finales de 1997, el volumen de tráfico se ha incrementado significativamente, especialmente en las llamadas con origen o terminación en la red móvil. Sin embargo, desde el año 2003 el tráfico ha comenzado a disminuir debido a las fuertes reducciones en los precios f...

This paper has benefited from the support of the Spanish DGICYT project #PB98-0030 and the European Project on VPM-Improving Human Research Potential, HPRN-CT-2002-00232. The authors are grateful for the comments received from an anonymous referee and from Mikel Tapia, Ignacio Pe�a, Winfried Pohlmeier and the attendants to the Econometrics Research...

Developing countries are increasingly concerned about improving country competitiveness and productivity as they face the increasing pressures of globalization and attempt to improve economic growth and reduce poverty. Among such countries, investment climate assessments (ICA) have become a standard instrument for identifying key obstacles to count...

The main goal of this paper is to analyze the behavior of the ECM non-cointegration test when there are additive outliers in the time series under different co-breaking situations. We show that the critical values of the usual ECM test are not robust to the presence of transitory shocks and we suggest a procedure based on signal extraction to bypas...

Since the seminal paper by Dickey and Fuller in 1979, unit-root tests have conditioned the standard approaches to analyse time series with strong serial dependence, the focus being placed in the detection of eventual unit roots in an autorregresive model fitted to the series. In this paper we propose a completely different method to test for the ty...

Variations in overall liquidity can be measured by simultaneous changes in both immediacy costs and depth. Liquidity changes, however, are ambiguous whenever both liquidity dimensions do not reinforce each other. In this paper, ambiguity is characterized using an instantaneous time-varying elasticity concept. Several bi-dimensional liquidity measur...

This paper explores single-equation nonlinear error correction (NEC) models with linear and nonlinear cointegrated variables. Within the class of semiparametric NEC models, we use smoothing splines. Within the class of parametric models, we discuss the interesting properties of cubic polynomial NEC models and we show how they can be used to identif...

This paper explores single-equation nonlinear error correction (NEC) models with linear and nonlinear cointegrated variables. Within the class of semiparametric NEC models, we use smoothing splines. Within the class of parametric models, we discuss the interesting properties of cubic polynomial NEC models and we show how they can be used to identif...

This paper studies the role that trading activity plays in the price discovery process of a NYSE-listed stock. We measure the expected information content of each trade by estimating its permanent price impact. It depends on observable trade features and market conditions. We also estimate the time required for quotes to incorporate all the informa...

This paper explores single-equation nonlinear error correction (NEC) models with linear and nonlinear cointegrated variables. Within the class of semiparametric NEC models, we use smoothing splines. Within the class of parametric models, we discuss the interesting properties of cubic polynomial NEC models and we show how they can be used to identif...

Las sociedades avanzadas han ido generando cada vez nuevos tipos de demandas; los clientes necesitan decidir cu�ndo, c�mo y d�nde utilizar, enviar y recibir informaci�n y mercanc�as de forma r�pida. Estos hechos han llevado a liberalizar recientemente los servicios postales en muchos pa�ses para poder atender esas nuevas necesidades de servicios. U...

El sector de las telecomunicaciones es uno de los que est�n avanzando m�s r�pidamente hacia un mercado liberalizado, si lo comparamos con otros como el el�ctrico, gas, transporte, servicio postal, etc�tera. Las telecomunicaciones son fundamentales para fomentar el crecimiento del producto interior bruto y conseguir reducciones en costes y mejoras d...

In this paper we focus on cycles and trends of some macroeconomic and housing market variables representative of the French economy. In a first part, we empirically show that cycles in the housing sector, measured by housing prices, housing starts, building permits, sales or residential investment, are strongly correlated to GDP cycles with a lead...

In this paper we focus on cycles and trends of some macroeconomic and housing market variables representative of the French economy. In a first part, we empirically show that cycles in the housing sector, measured by housing prices, housing starts, building permits, sales or residential investment, are strongly correlated to GDP cycles with a lead...

In this paper we propose an alternative characterization of the central notion of cointegration, exploiting the relationship between the autocovariance and the cross-covariance functions of the series. This characterization leads us to propose a new estimator of the cointegrating parameter based on the instrumental variables (IV) methodology. The i...

Juan Urrutia ha sido profesor de economía en las Universidades del País Vasco y Carlos III de Madrid. Su impulso a la investigación en el área de economía ha tenido un impacto decisivo en estas dos universidades. En este documento se recogen los textos de las intervenciones que se realizaron en un acto de homenaje a Juan Urrutia que se celebró el 1...

El sector de las telecomunicaciones ha experimentado un importante cambio estructural durante los �ltimos cuatro a�os, tanto en los aspectos regulatorios como de mercado. La raz�n, sin duda, est� en el cambio tecnol�gico y de mentalidad que ha permitido la liberalizaci�n y globalizaci�n de los mercados. En este art�culo se da una visi�n panor�mica...

This paper investigates the intraday price volatility process in four Australian wholesale electricity markets; namely New South Wales, Queensland, South Australia and Victoria. The data set consists of half-hourly electricity prices and demand volumes over the period January 1, 2002 to June 1, 2003. A range of processes including GARCH, RiskMetric...

A new LM specification procedure to choose between Logistic and Exponential Smooth Transition Autoregressive (STAR) models is introduced. The new decision rule has better properties than those previously available in the literature when the model is ESTAR and similar properties when the model is LSTAR. A simple natural extension of the usual LM-tes...

The relationship between cointegration and error correction models (EC) is well characterized in a linear context, but the extension to the nonlinear context is still a challenge. Few extensions of the linear framework have been done in the context of nonlinear error correction (NEC) or asymmetric and time varying error correction models. In this p...

En este trabajo se revisan de forma intuitiva y gráfica los aspectos fundamentales del funcionamiento de los cuatro tipos de mercados más importantes: competencia perfecta, monopolio, competencia monopolística y oligopolio. Se realiza un análisis detallado de las justificaciones económicas de la discriminación de precios y sus efectos sobre el bien...

It is well known that unit root tests and non-cointegration tests depend on the deterministic elements like: constants, trends, breaks, outliers, segmented trends, etc., that are present under the null hypothesis and maybe also under the alternative hypothesis. This is a serious inconvenience for empirical work since one could arbitrarily influence...