Panel index VAR models: Specification, Estimation, Testing and Leading Indicators

This paper proposes a method to conduct inference in panel VAR models with cross unit interdependencies and time variations in the coefficients. The approach can be used to obtain multi-unit forecasts and leading indicators and to conduct policy analysis in a multiunit setups. The framework of analysis is Bayesian and MCMC methods are used to estimate the posterior distribution of the features of interest. The model is reparametrized to resemble an observable index model and specification searches are discussed. As an example, we construct leading indicators for inflation and GDP growth in the Euro area using G-7 information.

Monetary policy misspecification in VAR models

We examine the effects of extracting monetary policy disturbances with semi-structural and structural VARs, using data generated bya limited participation model under partial accommodative and feedback rules. We find that, in general, misspecification is substantial: short run coefficients often have wrong signs; impulse responses and variance decompositions give misleadingrepresentations of the dynamics. Explanations for the results and suggestions for macroeconomic practice are provided.

Estimating multi-country VAR models

This paper describes a methodology to estimate the coefficients, to test specification hypothesesand to conduct policy exercises in multi-country VAR models with cross unit interdependencies, unit specific dynamics and time variations in the coefficients. The framework of analysis is Bayesian: a prior flexibly reduces the dimensionality of the model and puts structure on the time variations; MCMC methods are used to obtain posterior distributions; and marginal likelihoods to check the fit of various specifications. Impulse responses and conditional forecasts are obtained with the output of MCMC routine. The transmission of certain shocks across countries is analyzed.

Forecasting and turning point predictions in a Bayesian panel VAR model

We provide methods for forecasting variables and predicting turning points in panel Bayesian VARs. We specify a flexible model which accounts for both interdependencies in the cross section and time variations in the parameters. Posterior distributions for the parameters are obtained for a particular type of diffuse, for Minnesota-type and for hierarchical priors. Formulas for multistep, multiunit point and average forecasts are provided. An application to the problem of forecasting the growth rate of output and of predicting turning points in the G-7 illustrates the approach. A comparison with alternative forecasting methods is also provided.

Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing

Statistical tests in vector autoregressive (VAR) models are typically based on large-sample approximations, involving the use of asymptotic distributions or bootstrap techniques. After documenting that such methods can be very misleading even with fairly large samples, especially when the number of lags or the number of equations is not small, we propose a general simulation-based technique that allows one to control completely the level of tests in parametric VAR models. In particular, we show that maximized Monte Carlo tests [Dufour (2002)] can provide provably exact tests for such models, whether they are stationary or integrated. Applications to order selection and causality testing are considered as special cases. The technique developed is applied to quarterly and monthly VAR models of the U.S. economy, comprising income, money, interest rates and prices, over the period 1965-1996.

Bootstrap for panel data models with an application to the evaluation of public policies

Le but de cette thèse est d étendre la théorie du bootstrap aux modèles de données de panel. Les données de panel s obtiennent en observant plusieurs unités statistiques sur plusieurs périodes de temps. Leur double dimension individuelle et temporelle permet de contrôler l 'hétérogénéité non observable entre individus et entre les périodes de temps et donc de faire des études plus riches que les séries chronologiques ou les données en coupe instantanée. L 'avantage du bootstrap est de permettre d obtenir une inférence plus précise que celle avec la théorie asymptotique classique ou une inférence impossible en cas de paramètre de nuisance. La méthode consiste à tirer des échantillons aléatoires qui ressemblent le plus possible à l échantillon d analyse. L 'objet statitstique d intérêt est estimé sur chacun de ses échantillons aléatoires et on utilise l ensemble des valeurs estimées pour faire de l inférence. Il existe dans la littérature certaines application du bootstrap aux données de panels sans justi cation théorique rigoureuse ou sous de fortes hypothèses. Cette thèse propose une méthode de bootstrap plus appropriée aux données de panels. Les trois chapitres analysent sa validité et son application. Le premier chapitre postule un modèle simple avec un seul paramètre et s 'attaque aux propriétés théoriques de l estimateur de la moyenne. Nous montrons que le double rééchantillonnage que nous proposons et qui tient compte à la fois de la dimension individuelle et la dimension temporelle est valide avec ces modèles. Le rééchantillonnage seulement dans la dimension individuelle n est pas valide en présence d hétérogénéité temporelle. Le ré-échantillonnage dans la dimension temporelle n est pas valide en présence d'hétérogénéité individuelle. Le deuxième chapitre étend le précédent au modèle panel de régression. linéaire. Trois types de régresseurs sont considérés : les caractéristiques individuelles, les caractéristiques temporelles et les régresseurs qui évoluent dans le temps et par individu. En utilisant un modèle à erreurs composées doubles, l'estimateur des moindres carrés ordinaires et la méthode de bootstrap des résidus, on montre que le rééchantillonnage dans la seule dimension individuelle est valide pour l'inférence sur les coe¢ cients associés aux régresseurs qui changent uniquement par individu. Le rééchantillonnage dans la dimen- sion temporelle est valide seulement pour le sous vecteur des paramètres associés aux régresseurs qui évoluent uniquement dans le temps. Le double rééchantillonnage est quand à lui est valide pour faire de l inférence pour tout le vecteur des paramètres. Le troisième chapitre re-examine l exercice de l estimateur de différence en di¤érence de Bertrand, Duflo et Mullainathan (2004). Cet estimateur est couramment utilisé dans la littérature pour évaluer l impact de certaines poli- tiques publiques. L exercice empirique utilise des données de panel provenant du Current Population Survey sur le salaire des femmes dans les 50 états des Etats-Unis d Amérique de 1979 à 1999. Des variables de pseudo-interventions publiques au niveau des états sont générées et on s attend à ce que les tests arrivent à la conclusion qu il n y a pas d e¤et de ces politiques placebos sur le salaire des femmes. Bertrand, Du o et Mullainathan (2004) montre que la non-prise en compte de l hétérogénéité et de la dépendance temporelle entraîne d importantes distorsions de niveau de test lorsqu'on évalue l'impact de politiques publiques en utilisant des données de panel. Une des solutions préconisées est d utiliser la méthode de bootstrap. La méthode de double ré-échantillonnage développée dans cette thèse permet de corriger le problème de niveau de test et donc d'évaluer correctement l'impact des politiques publiques.

Forecasting accuracy and estimation uncertainty using VAR models with short- and long-term economic restrictions: a Monte-Carlo study

Using vector autoregressive (VAR) models and Monte-Carlo simulation methods we investigate the potential gains for forecasting accuracy and estimation uncertainty of two commonly used restrictions arising from economic relationships. The Örst reduces parameter space by imposing long-term restrictions on the behavior of economic variables as discussed by the literature on cointegration, and the second reduces parameter space by imposing short-term restrictions as discussed by the literature on serial-correlation common features (SCCF). Our simulations cover three important issues on model building, estimation, and forecasting. First, we examine the performance of standard and modiÖed information criteria in choosing lag length for cointegrated VARs with SCCF restrictions. Second, we provide a comparison of forecasting accuracy of Ötted VARs when only cointegration restrictions are imposed and when cointegration and SCCF restrictions are jointly imposed. Third, we propose a new estimation algorithm where short- and long-term restrictions interact to estimate the cointegrating and the cofeature spaces respectively. We have three basic results. First, ignoring SCCF restrictions has a high cost in terms of model selection, because standard information criteria chooses too frequently inconsistent models, with too small a lag length. Criteria selecting lag and rank simultaneously have a superior performance in this case. Second, this translates into a superior forecasting performance of the restricted VECM over the VECM, with important improvements in forecasting accuracy ñreaching more than 100% in extreme cases. Third, the new algorithm proposed here fares very well in terms of parameter estimation, even when we consider the estimation of long-term parameters, opening up the discussion of joint estimation of short- and long-term parameters in VAR models.

Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

We study the joint determination of the lag length, the dimension of the cointegrating space and the rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using model selection criteria. We consider model selection criteria which have data-dependent penalties for a lack of parsimony, as well as the traditional ones. We suggest a new procedure which is a hybrid of traditional criteria and criteria with data-dependant penalties. In order to compute the fit of each model, we propose an iterative procedure to compute the maximum likelihood estimates of parameters of a VAR model with short-run and long-run restrictions. Our Monte Carlo simulations measure the improvements in forecasting accuracy that can arise from the joint determination of lag-length and rank, relative to the commonly used procedure of selecting the lag-length only and then testing for cointegration.

Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

We study the joint determination of the lag length, the dimension of the cointegrating space and the rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using model selection criteria. We consider model selection criteria which have data-dependent penalties as well as the traditional ones. We suggest a new two-step model selection procedure which is a hybrid of traditional criteria and criteria with data-dependant penalties and we prove its consistency. Our Monte Carlo simulations measure the improvements in forecasting accuracy that can arise from the joint determination of lag-length and rank using our proposed procedure, relative to an unrestricted VAR or a cointegrated VAR estimated by the commonly used procedure of selecting the lag-length only and then testing for cointegration. Two empirical applications forecasting Brazilian inflation and U.S. macroeconomic aggregates growth rates respectively show the usefulness of the model-selection strategy proposed here. The gains in different measures of forecasting accuracy are substantial, especially for short horizons.

Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

We study the joint determination of the lag length, the dimension of the cointegrating space and the rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using model selection criteria. We consider model selection criteria which have data-dependent penalties as well as the traditional ones. We suggest a new two-step model selection procedure which is a hybrid of traditional criteria and criteria with data-dependant penalties and we prove its consistency. Our Monte Carlo simulations measure the improvements in forecasting accuracy that can arise from the joint determination of lag-length and rank using our proposed procedure, relative to an unrestricted VAR or a cointegrated VAR estimated by the commonly used procedure of selecting the lag-length only and then testing for cointegration. Two empirical applications forecasting Brazilian in ation and U.S. macroeconomic aggregates growth rates respectively show the usefulness of the model-selection strategy proposed here. The gains in di¤erent measures of forecasting accuracy are substantial, especially for short horizons.

Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

We study the joint determination of the lag length, the dimension of the cointegrating space and the rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using model selection criteria. We suggest a new two-step model selection procedure which is a hybrid of traditional criteria and criteria with data-dependant penalties and we prove its consistency. A Monte Carlo study explores the finite sample performance of this procedure and evaluates the forecasting accuracy of models selected by this procedure. Two empirical applications confirm the usefulness of the model selection procedure proposed here for forecasting.

Inflation and the variability of relative prices in the Caribbean: evidence from panel threshold models

Includes bibliography

VAR models and methods for monetary and health economics

Negli ultimi anni i modelli VAR sono diventati il principale strumento econometrico per verificare se può esistere una relazione tra le variabili e per valutare gli effetti delle politiche economiche. Questa tesi studia tre diversi approcci di identificazione a partire dai modelli VAR in forma ridotta (tra cui periodo di campionamento, set di variabili endogene, termini deterministici). Usiamo nel caso di modelli VAR il test di Causalità di Granger per verificare la capacità di una variabile di prevedere un altra, nel caso di cointegrazione usiamo modelli VECM per stimare congiuntamente i coefficienti di lungo periodo ed i coefficienti di breve periodo e nel caso di piccoli set di dati e problemi di overfitting usiamo modelli VAR bayesiani con funzioni di risposta di impulso e decomposizione della varianza, per analizzare l'effetto degli shock sulle variabili macroeconomiche. A tale scopo, gli studi empirici sono effettuati utilizzando serie storiche di dati specifici e formulando diverse ipotesi. Sono stati utilizzati tre modelli VAR: in primis per studiare le decisioni di politica monetaria e discriminare tra le varie teorie post-keynesiane sulla politica monetaria ed in particolare sulla cosiddetta "regola di solvibilità" (Brancaccio e Fontana 2013, 2015) e regola del GDP nominale in Area Euro (paper 1); secondo per estendere l'evidenza dell'ipotesi di endogeneità della moneta valutando gli effetti della cartolarizzazione delle banche sul meccanismo di trasmissione della politica monetaria negli Stati Uniti (paper 2); terzo per valutare gli effetti dell'invecchiamento sulla spesa sanitaria in Italia in termini di implicazioni di politiche economiche (paper 3). La tesi è introdotta dal capitolo 1 in cui si delinea il contesto, la motivazione e lo scopo di questa ricerca, mentre la struttura e la sintesi, così come i principali risultati, sono descritti nei rimanenti capitoli. Nel capitolo 2 sono esaminati, utilizzando un modello VAR in differenze prime con dati trimestrali della zona Euro, se le decisioni in materia di politica monetaria possono essere interpretate in termini di una "regola di politica monetaria", con specifico riferimento alla cosiddetta "nominal GDP targeting rule" (McCallum 1988 Hall e Mankiw 1994; Woodford 2012). I risultati evidenziano una relazione causale che va dallo scostamento tra i tassi di crescita del PIL nominale e PIL obiettivo alle variazioni dei tassi di interesse di mercato a tre mesi. La stessa analisi non sembra confermare l'esistenza di una relazione causale significativa inversa dalla variazione del tasso di interesse di mercato allo scostamento tra i tassi di crescita del PIL nominale e PIL obiettivo. Risultati simili sono stati ottenuti sostituendo il tasso di interesse di mercato con il tasso di interesse di rifinanziamento della BCE. Questa conferma di una sola delle due direzioni di causalità non supporta un'interpretazione della politica monetaria basata sulla nominal GDP targeting rule e dà adito a dubbi in termini più generali per l'applicabilità della regola di Taylor e tutte le regole convenzionali della politica monetaria per il caso in questione. I risultati appaiono invece essere più in linea con altri approcci possibili, come quelli basati su alcune analisi post-keynesiane e marxiste della teoria monetaria e più in particolare la cosiddetta "regola di solvibilità" (Brancaccio e Fontana 2013, 2015). Queste linee di ricerca contestano la tesi semplicistica che l'ambito della politica monetaria consiste nella stabilizzazione dell'inflazione, del PIL reale o del reddito nominale intorno ad un livello "naturale equilibrio". Piuttosto, essi suggeriscono che le banche centrali in realtà seguono uno scopo più complesso, che è il regolamento del sistema finanziario, con particolare riferimento ai rapporti tra creditori e debitori e la relativa solvibilità delle unità economiche. Il capitolo 3 analizza l’offerta di prestiti considerando l’endogeneità della moneta derivante dall'attività di cartolarizzazione delle banche nel corso del periodo 1999-2012. Anche se gran parte della letteratura indaga sulla endogenità dell'offerta di moneta, questo approccio è stato adottato raramente per indagare la endogeneità della moneta nel breve e lungo termine con uno studio degli Stati Uniti durante le due crisi principali: scoppio della bolla dot-com (1998-1999) e la crisi dei mutui sub-prime (2008-2009). In particolare, si considerano gli effetti dell'innovazione finanziaria sul canale dei prestiti utilizzando la serie dei prestiti aggiustata per la cartolarizzazione al fine di verificare se il sistema bancario americano è stimolato a ricercare fonti più economiche di finanziamento come la cartolarizzazione, in caso di politica monetaria restrittiva (Altunbas et al., 2009). L'analisi si basa sull'aggregato monetario M1 ed M2. Utilizzando modelli VECM, esaminiamo una relazione di lungo periodo tra le variabili in livello e valutiamo gli effetti dell’offerta di moneta analizzando quanto la politica monetaria influisce sulle deviazioni di breve periodo dalla relazione di lungo periodo. I risultati mostrano che la cartolarizzazione influenza l'impatto dei prestiti su M1 ed M2. Ciò implica che l'offerta di moneta è endogena confermando l'approccio strutturalista ed evidenziando che gli agenti economici sono motivati ad aumentare la cartolarizzazione per una preventiva copertura contro shock di politica monetaria. Il capitolo 4 indaga il rapporto tra spesa pro capite sanitaria, PIL pro capite, indice di vecchiaia ed aspettativa di vita in Italia nel periodo 1990-2013, utilizzando i modelli VAR bayesiani e dati annuali estratti dalla banca dati OCSE ed Eurostat. Le funzioni di risposta d'impulso e la scomposizione della varianza evidenziano una relazione positiva: dal PIL pro capite alla spesa pro capite sanitaria, dalla speranza di vita alla spesa sanitaria, e dall'indice di invecchiamento alla spesa pro capite sanitaria. L'impatto dell'invecchiamento sulla spesa sanitaria è più significativo rispetto alle altre variabili. Nel complesso, i nostri risultati suggeriscono che le disabilità strettamente connesse all'invecchiamento possono essere il driver principale della spesa sanitaria nel breve-medio periodo. Una buona gestione della sanità contribuisce a migliorare il benessere del paziente, senza aumentare la spesa sanitaria totale. Tuttavia, le politiche che migliorano lo stato di salute delle persone anziane potrebbe essere necessarie per una più bassa domanda pro capite dei servizi sanitari e sociali.

Do U.S. and Colombian macro factors improve the forecasting ability of unrestricted VAR models of the local term structure of interest rate?

Este estudio empírico compara la capacidad de los modelos Vectores auto-regresivos (VAR) sin restricciones para predecir la estructura temporal de las tasas de interés en Colombia -- Se comparan modelos VAR simples con modelos VAR aumentados con factores macroeconómicos y financieros colombianos y estadounidenses -- Encontramos que la inclusión de la información de los precios del petróleo, el riesgo de crédito de Colombia y un indicador internacional de la aversión al riesgo mejora la capacidad de predicción fuera de la muestra de los modelos VAR sin restricciones para vencimientos de corto plazo con frecuencia mensual -- Para vencimientos de mediano y largo plazo los modelos sin variables macroeconómicas presentan mejores pronósticos sugiriendo que las curvas de rendimiento de mediano y largo plazo ya incluyen toda la información significativa para pronosticarlos -- Este hallazgo tiene implicaciones importantes para los administradores de portafolios, participantes del mercado y responsables de las políticas

A DYNAMIC FRAMEWORK FOR THE RELATIONS BETWEEN FOREIGN EXCHANGE RATES, SAVINGS AND INVESTMENTS

The Meese-Rogoff forecasting puzzle states that foreign exchange (FX) rates are unpredictable. Since one country’s macroeconomic conditions could affect the price of its national currency, we study the dynamic relations between the FX rates and some macroeconomic accounts. Our research tests whether the predictability of the FX rates could be improved through the advanced econometrics. Improving the predictability of the FX rates has important implications for various groups including investors, business entities and the government. The present thesis examines the dynamic relations between the FX rates, savings and investments for a sample of 25 countries from the Organization for Economic Cooperation and Development. We apply quarterly data of FX rates, macroeconomic indices and accounts including the savings and the investments over three decades. Through preliminary Augmented Dickey-Fuller unit root tests and Johansen cointegration tests, we found that the savings rate and the investment rate are cointegrated with the vector (1,-1). This result is consistent with many previous studies on the savings-investment relations and therefore confirms the validity of the Feldstein-Horioka puzzle. Because of the special cointegrating relation between the savings rate and investment rate, we introduce the savings-investment rate differential (SID). Investigating each country through a vector autoregression (VAR) model, we observe extremely insignificant coefficient estimates of the historical SIDs upon the present FX rates. We also report similar findings through the panel VAR approach. We thus conclude that the historical SIDs are useless in forecasting the FX rate. Nonetheless, the coefficients of the past FX rates upon the current SIDs for both the country-specific and the panel VAR models are statistically significant. Therefore, we conclude that the historical FX rates can conversely predict the SID to some degree. Specifically, depreciation in the domestic currency would cause the increase in the SID.