# Paruolo PaoloEuropean Commission | ec · Joint Research Centre (JRC)

Paruolo Paolo

PhD

## About

110

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Introduction

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June 2013 - July 2015

## Publications

Publications (110)

This paper derives the analytic form of the multi-step ahead prediction density of a Gaussian GARCH(1,1) process with a possibly asymmetric news impact curve in the GJR class. These results can be applied when single-period returns are modeled as a GJR Gaussian GARCH(1,1) and interest lies in single-period returns at some future forecast horizon. T...

This Special Issue collects contributions related to the advances in the theory and practice of Econometrics induced by the research of Katarina Juselius and Søren Johansen, whom this Special Issue aims to celebrate [...]

This article was prepared for the Special Issue `Celebrated Econometricians: Katarina Juselius and Søren Johansen’ of Econometrics. It is based on material recorded on 30–31 October 2018 in Copenhagen. It explores Katarina Juselius’ research, and discusses inter alia the following issues: equilibrium; short and long-run behaviour; common trends; ad...

This article was prepared for the Special Issue "Celebrated Econometricians: Katarina Juselius and Søren Johansen" of Econometrics. It is based on material recorded on 30 October 2018 in Copenhagen. It explores Søren Johansen’s research, and discusses inter alia the following issues: estimation and inference for nonstationary time series of the I(1...

This paper discusses the notion of cointegrating space for linear processes integrated of any order. It first shows that the notions of (polynomial) cointegrating vectors and of root functions coincide. Second, it discusses how the cointegrating space can be defined (i) as a vector space of polynomial vectors over complex scalars, (ii) as a free mo...

This chapter summarises the role of EU actions in supporting healthcare policies in the EU Member States, both looking at implemented actions and describing current priorities for the future. It argues that these coordinated actions can be beneficial for EU Member States by helping them to avoid duplication of effort and to attain economies of scal...

Global sensitivity analysis is primarily used to investigate the effects of uncertainties in the input variables of physical models on the model output. This work investigates the use of global sensitivity analysis tools in the context of variable selection in regression models. Specifically, a global sensitivity measure is applied to a criterion o...

The spread of COVID-19 implied a large and fast increase of demand for intensive care services. To face this increase in demand, health care systems need to adapt their response by increasing hospital beds, intensive care unit (ICU) capacity and by (re-)deploying doctors and other personnel. This paper proposes a forecast approach based on the Vect...

Response management to the SARS-CoV-2 outbreak requires to answer several forecasting tasks. For hospital managers, a major one is to anticipate the likely needs of beds in intensive care in a given catchment area one or two weeks ahead, starting as early as possible in the evolution of the epidemic. This paper proposes to use a bivariate Error Cor...

This Chapter presents a set of quantitative modelling approaches, connected to various steps of the policy cycle, that aim at helping policy-makers and all social actors involved, by providing a scientific sound framework for a systematic, coherent and transparent analysis. Practical guidelines for structuring policy problems by using uncertainty a...

This paper investigates the effects of stricter job search-related conditions for Unemployment Insurance (UI) eligibility on the job search behaviour of claimants. Estimation makes use of exogenous variation introduced by the UK Jobseeker’s Allowance. A significant share of claimants is found to leave the register increasing search intensity as wel...

This chapter discusses the potential of systematic use of administrative microdata in policy research in Europe. It argues that their systematic and organised use can lead to substantial improvements in regulation and public investments, provided that some challenges are properly addressed.

Public organisations collect, supervise and keep track of extremely varied and extensive types of data. Modern technologies and better-organised civil lives have greatly facilitated the collection and custody of these data with a minute granularity and a scale previously unknown. This allows for a much more detailed and sound knowledge of economies...

A generalization of the Granger and the Johansen Representation Theorems valid for any (possibly fractional) order of integration is presented. This Representation Theorem is based on inversion results that characterize the order of the pole and the coefficients of the Laurent series representation of the inverse of a matrix function around a singu...

This paper derives the analytic form of the $h$-step ahead prediction density of a GARCH(1,1) process under Gaussian innovations, with a possibly asymmetric news impact curve. The analytic form of the density is novel and improves on current methods based on approximations and simulations. The explicit form of the density permits to compute tail pr...

Introduction
In the light of better and more detailed administrative databases, this open access book provides statistical tools for evaluating the effects of public policies advocated by governments and public institutions. Experts from academia, national statistics offices and various research centers present modern econometric methods for an eff...

There is a growing interest in voluntary programmes for climate change mitigation, including greenhouse gas (GHG) emission reduction commitments. This paper gauges evidence on the support of citizens for climate change mitigation programmes at the local level, analysing voting behaviour. A quasi-experimental set-up is offered by the EU Covenant of...

This paper derives a generalization of the Granger-Johansen Representation Theorem valid for $H$-valued autoregressive (AR) processes, where $H$ is an infinite dimensional separable Hilbert space, under the assumption that 1 is an eigenvalue of finite type of the AR operator function and that no other non-zero eigenvalue lies within or on the unit...

This paper provides some test cases, called circuits, for the evaluation of Gaussian likelihood maximization algorithms of the cointegrated vector autoregressive model. Both I(1) and I(2) models are considered. The performance of algorithms is compared first in terms of effectiveness, defined as the ability to find the overall maximum. The next ste...

Composite indicators are very popular tools for assessing and ranking countries and institutions in terms of environmental performance, sustainability, and other complex concepts that are not directly measurable. Because of the stakes that come with the media attention of these tools, a word of caution is warranted. One common misconception relates...

Likelihood ratio tests of over-identifying restrictions on the common trends loading matrices in I(2) VAR systems are discussed. It is shown how hypotheses on the common trends loading matrices can be translated into hypotheses on the cointegration parameters. Algorithms for (constrained) maximum likelihood estimation are presented, and asymptotic...

Multidimensional measures (often termed composite indicators) are popular tools in the public discourse for assessing the performance of countries on human development, perceived corruption, innovation, competitiveness, or other complex phenomena. These measures combine a set of variables using an aggregation formula, which is often a weighted arit...

This paper discusses identification of systems of simultaneous cointegrating equations with integrated variables of order two or higher, under constraints on the cointegration parameters. Rank and order conditions for identification are provided for general linear constraints, covering both cross-equation and equation-by-equation restrictions.

Multi-dimensional measures (often termed composite indicators) are popular tools in the public discourse for assessing the performance of countries on human development, perceived corruption, innovation, competitiveness, or other complex phenomena. These measures combine a set of variables using an aggregation formula, which is often a weighted ari...

This paper proposes a recursive procedure, called the extended local rank factorization (elrf), that characterizes the order of the pole and the coefficients of the Laurent series representation of the inverse of a regular analytic matrix function around a given point. The ELRF consists in performing a finite sequence of rank factorizations of matr...

Composite indicators are aggregations of measurable variables (indicators) that aim to quantify underlying concepts that are not directly observable, such as competitiveness, freedom of press or climate hazards. Composite indicators, otherwise referred to as performance indices, are employed for many purposes, including policy monitoring. Sensitivi...

In many multivariate volatility models, the number of parameters increases faster than the cross-section dimension, hence creating a curse of dimensionality problem. This paper discusses specification and identification of structured parameterizations based on weight matrices induced by economic proximity. It is shown that structured specifications...

Standard solution methods of DSGE models do not necessarily deliver minimal state space forms. When the ABCD form is non-minimal, the conditions in the literature are not necessary for the existence of a VAR representation of the observables. In this paper we present necessary and sufficient conditions that are valid in general, and hence can be ap...

This paper investigates variable-selection procedures in regression that make
use of global sensitivity analysis. The approach is combined with existing
algorithms and it is applied to the time series regression designs proposed by
Hoover and Perez. A comparison of an algorithm employing global sensitivity
analysis and the (optimized) algorithm of...

This paper discusses identification of systems of simultaneous cointegrating equations with integrated variables of order two. Rank and order conditions for identification are provided for general linear restrictions, as well as for equation-by-equation constraints. As expected, the application of the rank conditions to triangular forms and other p...

This paper investigates possible structural changes induced by the Euro on the relations among wages, prices and unemployment for the five major European economies. The dynamic adjustment and the level relations are found to be different across subperiods as well as across countries. During the European Economic and Monetary Union (EMU) period, the...

A statistical bias correction technique is applied to twelve high-resolution climate change simulations of temperature and precipitation over Europe, under the SRES A1B scenario, produced for the EU project ENSEMBLES. The bias correction technique is based on a transfer function, estimated on current climate, which affects the whole Probability Dis...

This paper shows that the poor man's invertibility condition in Fernandez-Villaverde et al. (2007) is, in general, sufficient but not necessary for fundamentalness; that is, a violation of this condition does not necessarily imply the impossibility of recovering the structural shocks of a DSGE via a VAR. The permanent income model in Fernandez-Vill...

This paper uses Vector Autoregressions that allow for nonstationarity and cointegration to investigate the dynamic relation between income and emissions in the period 1970-2008, for all world countries. We consider three emissions compounds, namely CO2, SO2 and a composite global warming index (GWP100). These emissions include energy-related activi...

This paper analyzes the relation between the local rank-structure of a regular analytic matrix function and the one of its inverse function. The local rank factorization (lrf) of a matrix function is introduced, which characterizes extended canonical systems of root functions and the local Smith form. An interpretation of the local rank factorizati...

The transmission mechanisms of monetary policy have been at the centre of a vast debate in the last decade and it is currently receiving increasing attention because of Stage III of European Monetary Union (EMU). It is common knowledge that focusing on a closed economy, standard transmission channels include an aggregate demand channel and an expec...

A statistical bias correction technique is applied to a set of high-resolution climate change simulations for Europe from 11 state-of-the-art regional climate models (RCMs) from the project ENSEMBLES. Modeled and observed daily values of mean, minimum and maximum temperature and total precipitation are used to construct transfer functions for the p...

This paper presents necessary and sufficient conditions for the existence of common cyclical features in Vector Auto Regressive (VAR) processes integrated of order 0, 1, 2, where the common cyclical features correspond to common serial correlation (CS), commonality in the final equations (CE) and co-dependence (CD). The results are based on local r...

Composite indicators aggregate a set of variables using weights which are
understood to reflect the variables' importance in the index. In this paper we
propose to measure the importance of a given variable within existing composite
indicators via Karl Pearson's `correlation ratio'; we call this measure `main
effect'. Because socio-economic variabl...

The `local rank factorization' (lrf) of a regular matrix polynomial at an eigenvalue consists of a sequence of matrix rank factorizations of a certain function of its coecients; the lrf delivers the local Smith form and extended canonical systems of root functions that correspond to the eigenvalue. In this paper it is shown that by performing the l...

This paper discusses summary measures for the speed of adjustment in possibly cointegrated Vector Autoregressive Processes (VAR). In particular we propose long-run half-lives, based on interim and total multipliers. We discuss their relation with Granger-noncausality and other types of half-life, which are shown to convey different information, exc...

This paper discusses likelihood-ratio (LR) tests on the cointegrating (CI) rank which consider any possible dimension of the CI rank under the alternative. The trace test and lambda-max test are obtained as special cases. Limit quantiles for all the tests in the class are derived. It is found that any of these tests can be used to construct an esti...

This paper proposes structured parametrizations for multivariate volatility models, which use spatial weight matrices induced by economic proximity. These structured specifications aim at solving the curse of dimensionality problem, which limits feasibility of model-estimation to small cross-sections for unstructured models. Structured parametrizat...

In many multivariate volatility models, the number of parameters increases faster than the cross-section dimension, hence creating a curse of dimensionality problem. This paper discusses specification and identification of structured parameterizations based on weight matrices induced by economic proximity. It is shown that structured specifications...

Ways of improving the efficiency of Monte-Carlo (MC) techniques are studied for dynamic models. Such models cause the conventional Antithetic Variate (AV) technique to fail, and will be proved to reduce the benefit from using Control Variates with nearly nonstationary series. This paper suggests modifications of the two conventional variance reduct...

This paper compares the finite sample performance of alternative tests for rank-dficiency of a submatrix of the cointegrating matrix. The paper focuses on the (implementation of the) likelihood ratio test proposed in Paruolo (2007, Oxford Bulletin of Economics and Statistics), and compares its finite sample performance with the ones of alternative...

This paper analyzes common cycles in I(2) vector autoregressive (VAR) systems. We consider different choices of stationary variables extracted from a VAR, including deviations from equilibria. This extension is based on the equilibrium dynamics representation of the system, introduced in this paper. Inference on the number of common features is add...

This paper proposes a likelihood ratio test for rank deficiency of a submatrix of the cointegrating matrix. Special cases of the test include the one of invalid normalization in systems of cointegrating equations, the feasibility of permanent-transitory decompositions and of subhypotheses related to neutrality and long-run Granger noncausality. The...

This paper applies a new spatial approach for the specfication of multivariate GARCH models, called Spatial Effects in ARCH, SEARCH. We consider spatial dependence associated with industrial sectors and capitalization size. This parametrization extends current feasible specifications for large scale GARCH models, keeping the numbers of parameters l...

This paper addresses the problem of measuring the speed of adjustment of exchange rates and relative prices to purchasing power parity (PPP), in the multivariate context of Vector Autoregressive Processes (VAR). We consider the speed of adjustment of one variable y in response to another variable x, where x, y belong to the VAR. We propose a multiv...

This paper discusses the Monte Carlo (MC) design of Gaussian Vector Au- toregressive processes (VAR) for the evalutation of invariant statistics. We focus on the case of cointegrated (CI) I(1) processes, linear and invertible trans- formations and CI rank likelihood ratio (LR) tests. It is found that all VAR of order 1 can be reduced to a system of...

In this paper we discuss sensitivity of forecasts with respect to the information set considered in prediction; a sensitivity measure called impact factor, IF, is defined. This notion is specialized to the case of VAR processes integrated of order 0, 1 and 2. For stationary VARs this measure corresponds to the sum of the impulse response coefficien...

Let * be any basis of col( ) and * be any basis of col( ); we note col( ) = col( * ), col( ) = col( * ) so no distinction is made between and * , and * in the following discussion.

This paper proposes a new approach for the specification of multivariate GARCH models for data sets with a potentially large cross-section dimension. The approach exploits the spatial dependence structure associated with asset characteristics, like industrial sectors and capitalization size. We use the acronym SEARCH for this model, short for Spati...

This note discusses the (dis-)similarities between automated inference and computer-aided decisions, at the interface of econometrics and economics. It is argued that computer-aided decisions are best suited for scientific communication. For the future, the topic of learning is singled out as one of the most promising areas of integration of econom...

We generate observable expectations about fiscal variables through laboratory experiments using real world data from several European countries as stimuli. We compare a VAR model of expectations for data that is presented in a fiscal frame with one for neutrally presented data. We test the validity of the setup and find that participants understand...

In establishing the Problems and Solutions (P S) series of Econometric Theory, the primary objective was pedagogical to provide an intellectual resource for students, instructors, and researchers through the publication of student exercises and research-level problems in econometrics. Over the past 20 years, the P S series has successfully served t...

This problem discusses an I(2) model in the VAR(1) case. The I(2) representation theorem of Johansen (1992) (JRT) holds also for VAR(1) processes. The I(2) model for VAR(k) processes has been discussed for k 2 in Johansen (1996, Ch. 9; 1997). We here discuss a parametrization for the I(2) case of VAR(1) that differs from the VAR(k) model.

This paper discusses common cycles in I(1) vector autoregressive (VAR) systems, both for the first di¤erences of the process and for deviations from equilibrium. This extension is based on the equilibrium dynamics representation of I(1) systems, which is presented in this paper. Inference on the number of common features is addressed via reduced ra...

We generate observable expectations about fiscal variables through laboratory experiments using real world data from several European countries as stimuli.We estimate an econometric model of individual expectations for fiscal policy, which nests various theories of expectations-forming and encompasses both micro- and macro- economic lines of resear...

This paper presents cointegration tests in the integration indices (II) in cointegrated (CI) vector autoregressive processes (VAR). The statistical analysis is performed under the assumption that some variables are weakly exogenous with respect to the (multi-)cointegration parameters, a condition that corresponds to no integral and proportional fee...

This paper provides evidence on price markup and inflation dynamics in Italy over the period 1970-1998. We investigate the price mark-up on imported and labor costs and its relation to inflation, using cointegration techniques. It is found that, despite different policy regimes across decades, the relation between the markup and inflation is remark...

This paper discusses serial correlation common features, CF, and integration of order 2, I(2), in VAR systems. The interplay of the CF restrictions and the I(2) conditions is discussed both for full VAR systems and for conditional systems with no levels and difference feedback, NF. Several notions of CF are introduced for I(2) systems; some of thes...

This paper derives standard errors for Monte Carlo (MC) estimators of (relative) power of tests when the critical values under the null have also been estimated. This situation is common, for example, in unit root and cointegration (CI) tests. The associated issue of MC design is discussed. The results are illustrated on likelihood-based tests for...

This paper provides asymptotic standard errors for the moving average (MA) impact matrix for the second differences of a vector autoregressive (VAR) process integrated of order 2, I(2). Standard errors of the row space of the MA impact matrix are also provided; bases of this row space define the common I(2) trends linear combinations. These standar...

The paper by Kiefer, Vogelsang and Bunzel (2000), KVB henceforth, provides an interesting unconventional application of functional limit theory to a conventional problem. In this note, we point out that the limiting distribution of the t^{∗} test proposed by KVB turns out to be equivalent to the asymptotic distribution of one of the statistics anal...

This paper considers likelihood ratio (LR) cointegration rank tests in vector autoregressive models (VAR); the local power of the most widely used LR "trace" test is compared with the LR "lamda max" test. It is found that neither test uniformly dominates the other one. Moreover it is shown that the asymptotic properties of the estimator of the coin...

This paper considers the asymptotic analysis of the likelihood ratio (LR), cointegration (CI) rank test in vector autoregressive
models (VAR) when some CI vectors are known and fixed. It is shown that the limit law is free of nuisance parameters. In the
case of LR tests against the alternative of completely unrestricted CI space, the limit law can...

The asymptotic distributions of cointegration tests are approximated using the Gamma distribution. The tests considered are for the I(1), the conditional I(1), as well as the I(2) model. Formulae for the parameters of the Gamma distributions are derived from response surfaces. The resulting approximation is flexible, easy to implement and more accu...

This paper derives the distribution of the two-stage estimator of cointegrating parameters in I(2) systems, abbreviated 2SI2, under several assumptions regarding the drift of the process. The asymptotic distribution is compared with that of the maximum likelihood (ML) estimator derived by S. Johansen [Scand. J. Stat. 24, No. 4, 433-462 (1997; Zbl 0...

This paper defines parametric conditions under which a subset of variables is weakly exogenous with respect to the (multi)-cointegration parameters in I(2) VAR systems. The weak exogeneity conditions can be interpreted in terms of common trends, corresponding to the cumulation of the errors from the marginal equations into the I(2) trends, or in te...

Two likelihood-ratio tests of the hypothesis of integration of order 1 in Gaussian circular vector autoregressive models (CAR)
are derived. The tests have non-standard limit distributions which can be expressed as functionals of Brownian motion. Inference
on the unit roots can be decomposed and addressed in independent subsystems with 1 or 2 compon...

The US economy is arguably following an unsustainable trajectory. The main indicators of this are a large current account deficit, a large federal budget deficit and trend-wise increasing costs of Social Security and Medicare. In this chapter, we will discuss these observations and to what extent the financial and economic crisis may have changed t...

Summary A correction of the proof of Theorem 5.1 is given. All the statements of the Theorem and the Tables associated with it are
unaffected by the correction.

Standard Errors for the Long-Run Variance Matrix - Volume 13 Issue 2 - Paolo Paruolo

This paper addresses the problem of inference on the moving average impact matrix and on its row and column spaces in cointegrated 1(1) VAR processes. The choice of bases (i.e., the identification) of these spaces, which is of interest in the definition of the common trend structure of the system, is discussed. Maximum likelihood estimators and the...

This paper addresses the problem of inference on the moving average impact matrix and on its row and column spaces in cointegrated I(1) VAR processes. The choice of bases (i.e., the identification) of these spaces, which is of interest in the definition of the common trend structure of the system, is discussed. Maximum likelihood estimators and the...

Both the Arbitrage Pricing Theory (APT) and the Capital Asset Pricing Model (CAPM) place restrictions of the cross sectional variation of conditional expectations of asset returns and of macro-indicators. The authors show that these restrictions imposed on the reference statistical models lead to special cases of the reduced rank regression model....

The distribution of a unit norm basis of the orthogonal complement of a bidimensional Gaussian vector. The present note shows the distribution of a unit norm basis of the orthogonal complement of a two-dimensional Gaussian random vector. It also shows that the same distribution can be obtained in the more general case of an elliptic distribution.

Corruption in the public sector erodes tax compliance and leads to higher tax evasion. Moreover, corrupt public officials abuse their public power to extort bribes from the private agents. In both types of interaction with the public sector, the private agents are bound to face uncertainty with respect to their disposable incomes. To analyse effect...

This paper discussed the role of the drift in vector autoregressive processes allowing for integrated components up to order
2. It is shown how the drift can generate linear and quadratic deterministic trends. A two-stage statistical analysis of the
system in the presence of quadratic trends is proposed. The analysis of the system allows to define...

The observation of a high degree of time dependence in macro-economic time series is the starting point of much of the recent empirical macroeconomics. This dependence is translated into a strong persistence of the impulses imparted to time series. Indeed, it appears (2) that many time series can be adequately represented as non stationary stochast...

Exxon Mobil and ConocoPhillips stock price has been predicted using the difference between core and headline CPI in the United States. Linear trends in the CPI difference allow accurate prediction of the prices at a five to ten-year horizon.

Through an appropriate statistical method the correlation between the rate of occurrence of geomagnetic reversals and the mean sea level according to the best available data is analyzed. A highly negative significant correlation (significance level < 0.01) is found only with long-term sea-level variations that follow by about 6–9 m.y. the non-stati...