An evaluation of the effectiveness of Value-at-Risk (VaR) models for Australian banks under Basel III

This study compares Value-at-Risk (VaR) measures for Australian banks over a period that includes the Global Financial Crisis (GFC) to determine whether the methodology and parameter selection are important for capital adequacy holdings that will ultimately support a bank in a crisis period. VaR methodology promoted under Basel II was largely criticised during the GFC for its failure to capture downside risk. However, results from this study indicate that 1-year parametric and historical models produce better measures of VaR than models with longer time frames. VaR estimates produced using Monte Carlo simulations show a high percentage of violations but with lower average magnitude of a violation when they occur. VaR estimates produced by the ARMA GARCH model also show a relatively high percentage of violations, however, the average magnitude of a violation is quite low. Our findings support the design of the revised Basel II VaR methodology which has also been adopted under Basel III.

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.

Optimal lag-length choice in stable and unstable VAR models under situations of homoscedasticity and ARCH

The performance of different information criteria - namely Akaike, corrected Akaike (AICC), Schwarz-Bayesian (SBC), and Hannan-Quinn - is investigated so as to choose the optimal lag length in stable and unstable vector autoregressive (VAR) models both when autoregressive conditional heteroscedasticity (ARCH) is present and when it is not. The investigation covers both large and small sample sizes. The Monte Carlo simulation results show that SBC has relatively better performance in lag-choice accuracy in many situations. It is also generally the least sensitive to ARCH regardless of stability or instability of the VAR model, especially in large sample sizes. These appealing properties of SBC make it the optimal criterion for choosing lag length in many situations, especially in the case of financial data, which are usually characterized by occasional periods of high volatility. SBC also has the best forecasting abilities in the majority of situations in which we vary sample size, stability, variance structure (ARCH or not), and forecast horizon (one period or five). frequently, AICC also has good lag-choosing and forecasting properties. However, when ARCH is present, the five-period forecast performance of all criteria in all situations worsens.

Is there a unit root in the inflation rate? New evidence from panel data models with multiple structural breaks

In this article, we examine whether or not the inflation rate for 17 OECD countries can be modelled as a stationary process. We find that (1) conventional univariate unit root tests without any structural breaks generally reveal that the inflation rate contains a unit root; (2) the KPSS univariate test with multiple structural breaks reveals that for 10 out of 17 countries inflation is stationary; and (3) the KPSS panel unit root test reveals strong evidence for stationarity of the inflation rate for panels consisting of countries which were declared nonstationary by univariate tests.

Are OECD stock prices characterized by a random walk? Evidence from sequential trend break and panel data models

This paper examines whether stock prices for a sample of 22 OECD countries can be best represented as mean reversion or random walk processes. A sequential trend break test proposed by Zivot and Andrews is implemented, which has the advantage that it can take account of a structural break in the series, as well as panel data unit root tests proposed by Im et al., which exploits the extra power in the panel properties of the data. Results provide strong support for the random walk hypothesis.

Is there really a unit root in the inflation rate? More evidence from panel data models

Time series unit root evidence suggests that inflation is nonstationary. By contrast, when using more powerful panel unit root tests, Culver and Papell (1997) find that inflation is stationary. In this article, we test the robustness of this result by applying a battery of recent panel unit root tests. The results suggest that the stationarity of inflation holds even after controlling for cross-sectional dependence and structural change.

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.