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.     

Inferring Policy Objectives from Economic Outcomes*

Estimated policy rules are reduced‐form equations that are silent on many important policy questions. However, a structural understanding of monetary policy can be obtained by estimating a policymaker's objective function. The paper derives conditions under which the parameters in a policymaker's policy objective function can be identified and estimated. We apply these conditions to a New Keynesian sticky‐price model of the US economy. The results show that the implicit inflation target and the relative weight placed on interest rate smoothing both declined when Paul Volcker was appointed Federal Reserve chairman.     

New Methods for Forecasting Inflation,Applied to the US*

Models for the 12‐month‐ahead US rate of inflation, measured by the chain‐weighted consumer expenditure deflator, are estimated for 1974–98 and subsequent pseudo out‐of‐sample forecasting performance is examined. Alternative forecasting approaches for different information sets are compared with benchmark univariate autoregressive models, and substantial out‐performance is demonstrated including against Stock and Watson's unobserved components‐stochastic volatility model. Three key ingredients to the out‐performance are: including equilibrium correction component terms in relative prices; introducing nonlinearities to proxy state‐dependence in the inflation process and replacing the information criterion, commonly used in VARs to select lag length, with a ‘parsimonious longer lags’ parameterization. Forecast pooling or averaging also improves forecast performance.     

Testing Steady‐State Restrictions of Linear Rational Expectations Models when Data are Highly Persistent*

Steady‐state restrictions are commonly imposed on highly persistent variables to achieve stationarity prior to confronting rational expectations models with data. However, the resulting steady‐state deviations are often surprisingly persistent indicating that some aspects of the underlying theory may be empirically problematic. This paper discusses how to formulate steady‐state restrictions in rational expectations models with latent forcing variables and test their validity using cointegration techniques. The approach is illustrated by testing steady‐state restrictions for alternative specifications of the New Keynesian model and shown to be able to discriminate between different assumptions on the sources of the permanent shocks.     

Monetary Policy in the Greenspan Era: A Time Series Analysis of Rules vs. Discretion*

Relationships between the Federal funds rate, unemployment, inflation and the long‐term bond rate are investigated with cointegration techniques. We find a stable long‐term relationship between the Federal funds rate, unemployment and the bond rate. This relationship is interpretable as a policy target because deviations are corrected via the Federal funds rate. Deviations of the actual Federal funds rate from the estimated target give simple indications of discretionary monetary policy, and the larger deviations relate to special episodes outside the current information set. A more traditional Taylor‐type target, where inflation appears instead of the bond rate, does not seem congruent with the data.     

General‐to‐Specific Model Selection Procedures for Structural Vector Autoregressions*

Structural vector autoregressive (SVAR) models have emerged as a dominant research strategy in empirical macroeconomics, but suffer from the large number of parameters employed and the resulting estimation uncertainty associated with their impulse responses. In this paper, we propose general‐to‐specific (Gets) model selection procedures to overcome these limitations. It is shown that single‐equation procedures are generally efficient for the reduction of recursive SVAR models. The small‐sample properties of the proposed reduction procedure (as implemented using PcGets) are evaluated in a realistic Monte Carlo experiment. The impulse responses generated by the selected SVAR are found to be more precise and accurate than those of the unrestricted VAR. The proposed reduction strategy is then applied to the US monetary system considered by Christiano, Eichenbaum and Evans (Review of Economics and Statistics, Vol. 78, pp. 16–34, 1996) . The results are consistent with the Monte Carlo and question the validity of the impulse responses generated by the full system.     

Automated Model Selection in Finance: General‐to‐Specific Modelling of the Mean and Volatility Specifications*

General‐to‐Specific (GETS) modelling has witnessed major advances thanks to the automation of multi‐path GETS specification search. However, the estimation complexity associated with financial models constitutes an obstacle to automated multi‐path GETS modelling in finance. Making use of a recent result we provide and study simple but general and flexible methods that automate financial multi‐path GETS modelling. Starting from a general model where the mean specification can contain autoregressive terms and explanatory variables, and where the exponential volatility specification can include log‐ARCH terms, asymmetry terms, volatility proxies and other explanatory variables, the algorithm we propose returns parsimonious mean and volatility specifications.     

Identification of Slowdowns and Accelerations for the Euro Area Economy*

Business cycle analyses have proved to be helpful to practitioners in assessing current economic conditions and anticipating upcoming fluctuations. In this article, we focus on the acceleration cycle in the euro area, namely the peaks and troughs of the growth rate which delimit the slowdown and acceleration phases of the economy. Our aim is twofold: first, we put forward a reference turning point chronology of this cycle on a monthly basis, based on gross domestic product and industrial production indices. We consider both euro area aggregate level and country‐specific cycles for the six main countries of the zone. Second, we come up with a new turning point indicator, based on business surveys carefully watched by central banks and short‐term analysts, to follow in real‐time the fluctuations of the acceleration cycle.     

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.     

Money‐output Causality Revisited – A Bayesian Logistic Smooth Transition VECM Perspective*

This article proposes a Bayesian approach to examining money‐output causality within the context of a logistic smooth transition vector error correction model. Our empirical results provide substantial evidence that the postwar US money‐output relationship is nonlinear, with regime changes mainly governed by the output growth and price levels. Furthermore, we obtain strong support for nonlinear Granger causality from money to output, although there is also some evidence for models indicating that money is not Granger causal or long‐run causal to output.     

Model uncertainty and policy evaluation: Some theory and empirics

This paper explores ways to integrate model uncertainty into policy evaluation. We describe a general framework that includes both model averaging methods as well as some measures that describe whether policies and their consequences are model dependent. These general ideas are then applied to assess simple monetary policy rules for some standard New Keynesian specifications. We conclude that the original Taylor rule has good robustness properties, but may reasonably be challenged in overall quality with respect to stabilization by alternative simple rules, even when these rules employ parameters that are set without accounting for model uncertainty.     

VARs,common factors and the empirical validation of equilibrium business cycle models

Equilibrium business cycle models have typically less shocks than variables. As pointed out by Altug (1989) International Economic Review 30 (4) 889–920 and Sargent (1989) The Journal of Political Economy 97 (2) 251–287, if variables are measured with error, this characteristic implies that the model solution for measured variables has a factor structure. This paper compares estimation performance for the impulse response coefficients based on a VAR approximation to this class of models and an estimation method that explicitly takes into account the restrictions implied by the factor structure. Bias and mean-squared error for both factor- and VAR-based estimates of impulse response functions are quantified using, as data-generating process, a calibrated standard equilibrium business cycle model. We show that, at short horizons, VAR estimates of impulse response functions are less accurate than factor estimates while the two methods perform similarly at medium and long run horizons.     

The New Keynesian Model and the Euro Area Business Cycle*

This paper describes a New Keynesian model incorporating transactions‐facilitating money and a time‐to‐build constraint into endogenous capital accumulation. The calibrated New Keynesian model performs almost as well as the estimated vector autoregressive model in replicating Euro area cyclical correlations between key variables such as output and inflation, although it fares less well in predicting the procyclical dynamics of nominal interest rates. The presence of a time‐to‐build requirement in the model helps to improve its fit to Euro area data, whereas the role of transactions‐facilitating money is much less important. Impulse–response functions and a decomposition of variance complete the analysis.     

How Stable is the Forecasting Performance of the Yield Curve for Output Growth?*

We provide an extensive evaluation of the predictive performance of the US yield curve for US gross domestic product growth by using new tests for forecast breakdown, in addition to a variety of in‐sample and out‐of‐sample evaluation procedures. Empirical research over the past decades has uncovered a strong predictive relationship between the yield curve and output growth, whose stability has recently been questioned. We document the existence of a forecast breakdown during the Burns–Miller and Volker monetary policy regimes, whereas during the early part of the Greenspan era the yield curve emerged as a more reliable model to predict future economic activity.     

Combining Forecasts from Nested Models*

Motivated by the common finding that linear autoregressive models often forecast better than models that incorporate additional information, this paper presents analytical, Monte Carlo and empirical evidence on the effectiveness of combining forecasts from nested models. In our analytics, the unrestricted model is true, but a subset of the coefficients is treated as being local‐to‐zero. This approach captures the practical reality that the predictive content of variables of interest is often low. We derive mean square error‐minimizing weights for combining the restricted and unrestricted forecasts. Monte Carlo and empirical analyses verify the practical effectiveness of our combination approach.     

How useful are no-arbitrage restrictions for forecasting the term structure of interest rates?

We develop a general framework for analyzing the usefulness of imposing parameter restrictions on a forecasting model. We propose a measure of the usefulness of the restrictions that depends on the forecaster’s loss function and that could be time varying. We show how to conduct inference about this measure. The application of our methodology to analyzing the usefulness of no-arbitrage restrictions for forecasting the term structure of interest rates reveals that: (1) the restrictions have become less useful over time; (2) when using a statistical measure of accuracy, the restrictions are a useful way to reduce parameter estimation uncertainty, but are dominated by restrictions that do the same without using any theory; (3) when using an economic measure of accuracy, the no-arbitrage restrictions are no longer dominated by atheoretical restrictions, but for this to be true it is important that the restrictions incorporate a time-varying risk premium.     

Analysing I(2) Systems by Transformed Vector Autoregressions*

We characterize the restrictions imposed by the minimal I(2)‐to‐I(1) transformation that underlies much applied work, e.g. on money demand relationships or open‐economy pricing relationships. The relationship between the parameters of the original I(2) vector autoregression, including the coefficients of polynomially cointegrating relationships, and the transformed I(1) model is characterized. We discuss estimation of the transformed model subject to restrictions as well as the more commonly used approach of unrestricted reduced rank regression. Only a minor loss of efficiency is incurred by ignoring the restrictions in the empirical example and a simulation study. A properly transformed vector autoregression thus provides a practical and effective means for inference on the parameters of the I(2) model.     

Estimation with overidentifying inequality moment conditions

This paper derives limit distributions of empirical likelihood estimators for models in which inequality moment conditions provide overidentifying information. We show that the use of this information leads to a reduction of the asymptotic mean-squared estimation error and propose asymptotically uniformly valid tests and confidence sets for the parameters of interest. While inequality moment conditions arise in many important economic models, we use a dynamic macroeconomic model as a data generating process and illustrate our methods with instrumental variable estimators of monetary policy rules. The results obtained in this paper extend to conventional GMM estimators.     

Are Weekly Inflation Forecasts Informative?*

Are weekly inflation forecasts informative? Although several central banks review and discuss monetary policy issues on a bi‐weekly basis, there have been no attempts by analysts to construct systematic estimates of core inflation that supports such a decision‐making schedule. The timeliness of news releases are recognized to be an important information source in real‐time estimation. We incorporate real‐time information from macroeconomic releases and revisions into our weekly updates of monthly Swiss core inflation using a common factor procedure. The weekly estimates for Swiss core inflation show that it is worthwhile to update the forecast at least twice a month.     

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.