Parametric estimation of hidden stochastic model by contrast minimization and deconvolution

We study a new parametric approach for particular hidden stochastic models. This method is based on contrast minimization and deconvolution and can be applied, for example, for ecological and financial state space models. After proving consistency and asymptotic normality of the estimation leading to asymptotic confidence intervals, we provide a thorough numerical study, which compares most of the classical methods that are used in practice (Quasi-Maximum Likelihood estimator, Simulated Expectation Maximization Likelihood estimator and Bayesian estimators) to estimate the Stochastic Volatility model. We prove that our estimator clearly outperforms the Maximum Likelihood Estimator in term of computing time, but also most of the other methods. We also show that this contrast method is the most robust with respect to non Gaussianity of the error and also does not need any tuning parameter.     

EXCHANGE RATE TARGET ZONES: A SURVEY OF THE LITERATURE

This work selectively reviews the literature on exchange rate target zones and their theoretical and empirical methodologies and examines whether they can be used to clarify to what extent this type of exchange rate regime could contribute to greater exchange rate stability. We discuss the main contributions of the first and second generations of exchange rate target zone models. In an attempt to reconcile the poor empirical performance of the Krugman model with the reality of exchange rate target zone regimes, this line of research integrates target zones with alternative underlying economic models, such as imperfect credibility, intra‐marginal interventions and sticky price models. It was thus possible to understand the correlations observed between the exchange rate, its fundamentals determinants and the interest rate differential, and to explain the fact that the statistical distribution of the exchange rate is hump shaped rather than U shaped. This implies that the initial emphasis of target zone models on nonlinearities, ‘honeymoon effect’, ‘smooth pasting’ and marginal interventions has vanished. Exchange rate target zones are better described as similar to managed floating regimes with intra‐marginal interventions, with some marginal interventions when the exchange rate reaches the edges of the floating band.     

An EMS target zone model in discrete time

The discrete time analogue of the continuous time Krugman target zone model is developed in order to capture the typical volatility clusters and fat-tailed distributed innovations of exchange rates. It is shown that under these more general stochastic conditions the S-shaped relation between exchange rate and fundamentals is preserved, but is less pronounced. The model is tested for its S-shape and stochastic properties. Two clearly distinct sets of EMS currencies are detected on the basis of the curvature features. One-step-ahead realignment probabilities are used as an alternative evaluation method. © 1998 John Wiley & Sons, Ltd.     

Bayesian semiparametric estimation of discrete duration models: an application of the dirichlet process prior

This paper proposes a Bayesian estimator for a discrete time duration model which incorporates a non‐parametric specification of the unobserved heterogeneity distribution, through the use of a Dirichlet process prior. This estimator offers distinct advantages over the Nonparametric Maximum Likelihood estimator of this model. First, it allows for exact finite sample inference. Second, it is easily estimated and mixed with flexible specifications of the baseline hazard. An application of the model to employment duration data from the Canadian province of New Brunswick is provided. Copyright © 2001 John Wiley & Sons, Ltd.     

A Jump-diffusion Model for Exchange Rates in a Target Zone

We propose a simple jump-diffusion model for an exchange rate target zone. The model captures most stylized facts from the existing target zone models while remaining analytically tractable. The model is based on a modified two-limit version of the C OX , I NGERSOLL and R OSS (1985) model. In the model the exchange rate is kept within the band because the variance decreases as the exchange rate approaches the upper or lower limits of the band. We also consider an extension of the model with parity adjustments, which are modeled as Poisson jumps. Estimation of the model is by GMM based on conditional moments. We derive prices of currency options in our model, assuming that realignment jump risk is idiosyncratic. Throughout, we apply the theory to EMS exchange rate data. We show that, after the EMS crisis of 1993, currencies remain in an implicit target zone which is narrower than the officially announced target zones.     

The LIML estimator has finite moments!

The Limited Information Maximum Likelihood estimator of the vector of coefficients of a structural equation in a simultaneous equation model is the vector that defines the linear combination maximizing the effect variance relative to the error variance. If this “eigenvector” solution is normalized by setting a designated coefficient equal to 1, the second-order moment of the estimator may be unbounded. However, the second-order moment is finite if the normalization sets the sample error variance of the linear combination equal to 1.     

Problems with the estimation of moving average processes

As a consequence of the well-known underidentification of the moving average model unless the parameter space is restricted, Maximum Likelihood and other estimators possess properties which can pose problems for estimation when a root of the process is close to the unit circle. The behaviour of the estimators is studied both through the analytic properties of their criterion functions and by Monte Carlo simulation. Conclusions about the choice of estimator are drawn, in particular regarding the treatment of the pre-sample residuals.     

An input–output model of exchange-rate pass-through

The impact of the exchange rate on price formation is often debated through a mechanism called the exchange-rate pass-through. Studies of the pass-through generally rely on econometric analysis implemented on time series data. This study examines pass-through to the domestic price level through an input–output model. The proposed model is implemented on a sample of countries, and a number of different variables connected to the pass-through are examined. A comparison across countries and sectors highlights the importance of the construction sector in price formation. National income is negatively related to the pass-through. A high dependence on intermediate imports implies higher pass-through. Price level volatility and pass-through are positively related; whereas a country’s monetary policy stance has no apparent effect. The effect of exchange-rate volatility is unclear; it is negative for the real effective exchange rate, the connection is very weak in the case of the nominal exchange rate.     

The core-periphery model: A note on the existence and uniqueness of short-run equilibrium

We consider the core-periphery model [P. Krugman, Increasing returns and economic geography, Journal of Political Economy 199 (1) (1991) 483–499]. The nature and stability of the possible steady states of the model have been made progressively precise; [M. Fujita, P. Krugman, A. Venables, The Spatial Economy. Cities, Regions and International Trade, MIT Press, Cambridge, 1999; R. Baldwin, R. Forslid, Ph. Martin, G. Ottaviano, F. Robert-Nicoud, Economic Geography and Public Policy, Princeton Univ. Press, 2003]. In that model as well as in all the new economic geography models that have been derived from it, the short-run (instantaneous) equilibrium is implicitly determined by the current labor distribution across regions. The numerical computations used so far to determine the short-run equilibrium, tend to suggest its existence. In this paper, an existence and uniqueness proof of short-run equilibrium is provided.     

The conditional autoregressive Wishart model for multivariate stock market volatility

We propose a Conditional Autoregressive Wishart (CAW) model for the analysis of realized covariance matrices of asset returns. Our model assumes an autoregressive moving average structure for the scale matrix of the Wishart distribution. It accounts for positive definiteness of covariance matrices without imposing parametric restrictions, and can be estimated by Maximum Likelihood. We also propose extensions of the CAW model obtained by including a Mixed Data Sampling (MIDAS) component and Heterogeneous Autoregressive (HAR) dynamics for long-run fluctuations. The CAW models are applied to realized variances and covariances for five New York Stock Exchange stocks.     

Bootstrap refinements for QML estimators of the GARCH(1,1) parameters

This paper reconsiders a block bootstrap procedure for Quasi Maximum Likelihood estimation of GARCH models, based on the resampling of the likelihood function, as proposed by Gonçalves and White [2004. Maximum likelihood and the bootstrap for nonlinear dynamic models. Journal of Econometrics 119, 199–219]. First, we provide necessary conditions and sufficient conditions, in terms of moments of the innovation process, for the existence of the Edgeworth expansion of the GARCH(1,1) estimator, up to the k$k$-th term. Second, we provide sufficient conditions for higher order refinements for equally tailed and symmetric test statistics. In particular, the bootstrap estimator based on resampling the likelihood has the same higher order improvements in terms of error in the rejection probabilities as those in Andrews [2002. Higher-order improvements of a computationally attractive k$k$-step bootstrap for extremum estimators. Econometrica 70, 119–162].     

Do terror attacks affect the dollar-pound exchange rate? A nonparametric causality-in-quantiles analysis

While much significant research has been done to study the effects of terror attacks on stock markets, less is known about the response of exchange rates to terror attacks. We suggest a non-parametric causality-in-quantiles test to study whether (relative) terror attacks affect exchange-rate returns and volatility. Using data on the dollar-pound exchange rate to illustrate the test, we show that terror attacks mainly affect the lower and upper quantiles of the conditional distribution of exchange-rate returns, while misspecified (due to nonlinearity and structural breaks) linear Granger causality test show no evidence of predictability. Terror attacks also affect almost all quantiles of the conditional distribution of exchange-rate volatility (except the extreme upper-end), with the significance of the effect being particularly strong for the lower quantiles. The importance of terror attacks is shown to hold also under an alternative measure of volatility and for an important emerging-market exchange rate as well.     

Variations in exchange rates and inflation in 82 countries: an empirical investigation

In this paper, we examine the hypothesis that nominal exchange-rate variability can have a positive and significant effect on the variability of inflation, when the statistical relationship between the variability of inflation and its mean rate is estimated for the 1973Q2–1998Q1 period. The analysis employs cross-country data for 82 countries over the current floating exchange-rate era. It employs the instrumental variable estimator, so as to obtain consistent estimates and the Newey–West estimator to account for non-spherical residuals. The empirical evidence supports the hypothesis.     

Separating Information Maximum Likelihood estimation of the integrated volatility and covariance with micro-market noise

For estimating the integrated volatility and covariance by using high frequency financial data, we propose the Separating Information Maximum Likelihood (SIML) method when there are possibly micro-market noises. The resulting estimator, which is represented as a specific quadratic form of returns, is simple and their properties have been investigated by [Kunitomo and Sato, 2008a], [Kunitomo and Sato, 2008b], [Kunitomo and Sato, 2010], [Kunitomo and Sato, 2011]. We show that the SIML estimator has reasonable asymptotic properties; it is consistent and it has the asymptotic normality when the sample size is large and the integrated volatility is deterministic under general conditions including some non-Gaussian and volatility models. Based on simulations, we find that the SIML estimator has reasonable finite sample properties and it would be useful for practice. The SIML estimator has the asymptotic robustness properties in the sense it is consistent when the noise terms are weakly dependent and they are endogenously correlated with the efficient market price process. We illustrate the use of SIML by analyzing Nikkei-225 futures, which are the derivatives of the major stock index in Japan.     

Efficient estimation of probit models with correlated errors

Maximum Likelihood (ML) estimation of probit models with correlated errors typically requires high-dimensional truncated integration. Prominent examples of such models are multinomial probit models and binomial panel probit models with serially correlated errors. In this paper we propose to use a generic procedure known as Efficient Importance Sampling (EIS) for the evaluation of likelihood functions for probit models with correlated errors. Our proposed EIS algorithm covers the standard GHK probability simulator as a special case. We perform a set of Monte Carlo experiments in order to illustrate the relative performance of both procedures for the estimation of a multinomial multiperiod probit model. Our results indicate substantial numerical efficiency gains for ML estimates based on the GHK–EIS procedure relative to those obtained by using the GHK procedure.     

Non-causality in bivariate binary time series

In this paper we develop a dynamic discrete-time bivariate probit model, in which the conditions for Granger non-causality can be represented and tested. The conditions for simultaneous independence are also worked out. The model is extended in order to allow for covariates, representing individual as well as time heterogeneity. The proposed model can be estimated by Maximum Likelihood. Granger non-causality and simultaneous independence can be tested by Likelihood Ratio or Wald tests. A specialized version of the model, aimed at testing Granger non-causality with bivariate discrete-time survival data is also discussed. The proposed tests are illustrated in two empirical applications.     

Exchange rate target zone models: a Bayesian evaluation

This paper develops a Bayesian approach to estimating exchange rate target zone models and rational expectations models in general. It also introduces a simultaneous-equation target zone model that incorporates stochastic realignment risk. Using FF/DM and IL/DM exchange rate data, we find that the signing of the 1987 Basle–Nyborg Agreement reduces both the magnitude and the likelihood of a central parity realignment, while the lagged exchange rate deviation from its central parity increases them. Furthermore, the interest rate policies and the monetary conditions of the participating countries signal a forthcoming realignment. In general, we are unable to improve upon a simple random walk model in out-of-sample exchange rate prediction by introducing target zone models. Copyright © 1999 John Wiley & Sons, Ltd.     

Structural VAR Estimation with Exogeneity Restrictions

ABSTRACT Exogenous variables arise quite naturally in macroeconomic models of small open economies. In these models overidentification is also a common feature. In the presence of exogeneity restrictions and overidentification the usual two-steps approach to the estimation of structural VAR's is not equivalent to Maximum Likelihood (ML). We propose a simple modification of that usual approach which produces ML estimators.     

Are precious metals a hedge against exchange-rate movements? An empirical exploration using bayesian additive regression trees

We use Bayesian additive regression trees to reexamine whether investments in precious metals are a hedge against exchange-rate movements. We quantify the relative importance of several major exchange rates, and we study how the marginal effects differ across times of appreciations/depreciations and across times of small/large exchange-rate fluctuations. Results show that investments in gold and silver are strong hedges against depreciations of major exchange rates. The hedging properties of palladium and platinum are mainly confined to the Australian dollar and Canadian dollar. We also study whether precious metals investments are a safe-haven in times of large exchange-rate movements.     

Agglomeration under forward-looking expectations: Potentials and global stability

This paper considers a class of migration dynamics with forward-looking agents in a multi-country solvable variant of the core–periphery model of Krugman [Krugman, P., 1991. Increasing returns and economic geography. Journal of Political Economy 99, 483–499]. We find that, under a symmetric externality assumption, our static model admits a potential function, which allows us to identify a stationary state that is uniquely absorbing and globally accessible under the perfect foresight dynamics whenever the degree of friction in relocation decisions is sufficiently small. In particular, when trade barriers are low enough, full agglomeration in the country with the highest barrier is the unique stable state for small frictions. New aspects in trade and tax policy that arise due to forward-looking behavior are discussed.