How does Monetary Policy Respond to Exchange Rate Movements? New International Evidence*

This article analyzes how monetary policy has responded to exchange rate movements in six open economies, paying particular attention to the two‐way interaction between monetary policy and the exchange rate. We address this issue using a structural VAR model that is identified using a combination of sign and short‐term (zero) restrictions. Doing so we find that, while there is a instantaneous reaction in the exchange rate following a monetary policy shock in all countries, monetary policy responds significantly on impact to an exchange rate shock in only four of the six countries.     

Determinacy,indeterminacy and dynamic misspecification in linear rational expectations models

This paper proposes a testing strategy for the null hypothesis that a multivariate linear rational expectations (LRE) model may have a unique stable solution (determinacy) against the alternative of multiple stable solutions (indeterminacy). The testing problem is addressed by a misspecification-type approach in which the overidentifying restrictions test obtained from the estimation of the system of Euler equations of the LRE model through the generalized method of moments is combined with a likelihood-based test for the cross-equation restrictions that the model places on its reduced form solution under determinacy. The resulting test has no power against a particular class of indeterminate equilibria, hence the non rejection of the null hypothesis can not be interpreted conclusively as evidence of determinacy. On the other hand, this test (i) circumvents the nonstandard inferential problem generated by the presence of the auxiliary parameters that appear under indeterminacy and that are not identifiable under determinacy, (ii) does not involve inequality parametric restrictions and hence the use of nonstandard inference, (iii) is consistent against the dynamic misspecification of the LRE model, and (iv) is computationally simple. Monte Carlo simulations show that the suggested testing strategy delivers reasonable size coverage and power against dynamic misspecification in finite samples. An empirical illustration focuses on the determinacy/indeterminacy of a New Keynesian monetary business cycle model of the US economy.     

Bayesian Model Averaging and exchange rate forecasts

Exchange rate forecasting is hard and the seminal result of Meese and Rogoff [Meese, R., Rogoff, K., 1983. Empirical exchange rate models of the seventies: Do they fit out of sample? Journal of International Economics 14, 3–24] that the exchange rate is well approximated by a driftless random walk, at least for prediction purposes, still stands despite much effort at constructing other forecasting models. However, in several other macro and financial forecasting applications, researchers in recent years have considered methods for forecasting that effectively combine the information in a large number of time series. In this paper, I apply one such method for pooling forecasts from several different models, Bayesian Model Averaging, to the problem of pseudo out-of-sample exchange rate predictions. For most currency–horizon pairs, the Bayesian Model Averaging forecasts using a sufficiently high degree of shrinkage, give slightly smaller out-of-sample mean square prediction error than the random walk benchmark. The forecasts generated by this model averaging methodology are however very close to, but not identical to, those from the random walk forecast.     

Model-based asymptotic inference on the effect of infrequent large shocks on cointegrated variables

Quasi-maximum-likelihood (QML) estimation of a model combining cointegration in the conditional mean and rare large shocks (outliers) with a factor structure in the innovations is studied. The goal is not only to robustify inference on the conditional-mean parameters, but also to find regularities and conduct inference on the instantaneous and long-run effect of the large shocks. Given the cointegration rank and the factor order, χ²${\chi }^2$ asymptotic inference is obtained for the cointegration vectors, the short-run parameters, and the direction of each column of both the factor loading matrix and the matrix of long-run impacts of the large shocks. Large shocks, whose location is assumed unknown a priori, can be detected and classified consistently into the factor components.     

Testing and imposing Slutsky symmetry in nonparametric demand systems

Maximization of utility implies that consumer demand systems have a Slutsky matrix which is everywhere symmetric. However, previous non- and semi-parametric approaches to the estimation of consumer demand systems do not give estimators that are restricted to satisfy this condition, nor do they offer powerful tests of this restriction. We use nonparametric modeling to test and impose Slutsky symmetry in a system of expenditure share equations over prices and expenditure. In this context, Slutsky symmetry is a set of nonlinear cross-equation restrictions on levels and derivatives of consumer demand equations. The key insight is that due to the differing convergence rates of levels and derivatives and due to the fact that the symmetry restrictions are linear in derivatives, both the test and the symmetry restricted estimator behave asymptotically as if these restrictions were (locally) linear. We establish large and finite sample properties of our methods, and show that our test has advantages over the only other comparable test. All methods we propose are implemented with Canadian micro-data. We find that our nonparametric analysis yields statistically significantly and qualitatively different results from traditional parametric estimators and tests.     

A long-run Pure Variance Common Features model for the common volatilities of the Dow Jones

In this paper, a new model to analyze the comovements in the volatilities of a portfolio is proposed. The Pure Variance Common Features model is a factor model for the conditional variances of a portfolio of assets, designed to isolate a small number of variance features that drive all assets’ volatilities. It decomposes the conditional variance into a short-run idiosyncratic component (a low-order ARCH process) and a long-run component (the variance factors). An empirical example provides evidence that models with very few variance features perform well in capturing the long-run common volatilities of the equity components of the Dow Jones.     

Exact local Whittle estimation of fractionally cointegrated systems

Semiparametric estimation of a bivariate fractionally cointegrated system is considered. We propose a two-step procedure that accommodates both (asymptotically) stationary (δ<1/2)$(\delta <1/2)$ and nonstationary (δ≥1/2)$(\delta \ge 1/2)$ stochastic trend and/or equilibrium error. A tapered version of the local Whittle estimator of Robinson (2008) is used as the first-stage estimator, and the second-stage estimator employs the exact local Whittle approach of Shimotsu and Phillips (2005). The consistency and asymptotic distribution of the two-step estimator are derived. The estimator of the memory parameters has the same Gaussian asymptotic distribution in both the stationary and the nonstationary case. The convergence rate and the asymptotic distribution of the estimator of the cointegrating vector are affected by the difference between the memory parameters. Further, the estimator has a Gaussian asymptotic distribution when the difference between the memory parameters is less than 1/2.     

Model Selection for Monetary Policy Analysis: How Important is Empirical Validity?*

We investigate the economic significance of trading off empirical validity of models against other desirable model properties. Our investigation is based on three alternative econometric systems of the supply side, in a model that can be used to discuss optimal monetary policy in Norway. Our results caution against compromising empirical validity when selecting a model for policy analysis. We also find large costs from basing policies on the robust model, or on a suite of models, even when it contains the valid model. This confirms an important role for econometric modelling and evaluation in model choice for policy analysis.     

A characterization of vector autoregressive processes with common cyclical features

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 rank factorizations of the reversed AR polynomial around the poles of its inverse. All processes with CS structures are found to present also CE structures and vice versa. The presence of CD structures, instead, implies the presence of both CS and CE structures, but not vice versa. Characterizations of the CS, CE, CD linear combinations are given in terms of linear subspaces defined in the local rank factorizations.     

Cointegration,long-run structural modelling and weak exogeneity: Two models of the UK economy

Cointegration ideas as introduced by Granger in 1981 are commonly embodied in empirical macroeconomic modelling through the vector error correction model (VECM). It has become common practice in these models to treat some variables as weakly exogenous, resulting in conditional VECMs. This paper studies the consequences of different approaches to weak exogeneity for the dynamic properties of such models, in the context of two models of the UK economy, one a national-economy model, the other the UK submodel of a global model. Impulse response and common trend analyses are shown to be sensitive to these assumptions and other specification choices.     

Inference on impulse response functions in structural VAR models

Skepticism toward traditional identifying assumptions based on exclusion restrictions has led to a surge in the use of structural VAR models in which structural shocks are identified by restricting the sign of the responses of selected macroeconomic aggregates to these shocks. Researchers commonly report the vector of pointwise posterior medians of the impulse responses as a measure of central tendency of the estimated response functions, along with pointwise 68% posterior error bands. It can be shown that this approach cannot be used to characterize the central tendency of the structural impulse response functions. We propose an alternative method of summarizing the evidence from sign-identified VAR models designed to enhance their practical usefulness. Our objective is to characterize the most likely admissible model(s) within the set of structural VAR models that satisfy the sign restrictions. We show how the set of most likely structural response functions can be computed from the posterior mode of the joint distribution of admissible models both in the fully identified and in the partially identified case, and we propose a highest-posterior density credible set that characterizes the joint uncertainty about this set. Our approach can also be used to resolve the long-standing problem of how to conduct joint inference on sets of structural impulse response functions in exactly identified VAR models. We illustrate the differences between our approach and the traditional approach for the analysis of the effects of monetary policy shocks and of the effects of oil demand and oil supply shocks.