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Abstract:
Cubic splines have long been used to extract the discount, yield, and forward rate curves from coupon bond data. McCulloch used regression splines to estimate the discount function, and, more recently, Fisher, Nychka, and Zervos used smoothed splines, with the roughness penalty selected by generalized cross-validation, to estimate the forward rate curve. I propose using a smoothed spline but with a roughness penalty that can vary across maturities, to estimate the forward rate curve. This method is tested against the methods of McCulloch and Fisher, Nychka, and Zervos using monthly bond data from 1970 through 1995.

Abstract:
Prior research documents unusually high returns on the last trading day of the month and over the next three consecutive trading days. This phenomenon is known as the turn-of-the-month (TOTM) effect. According to Siegel (1998), why these anomalies occur is not well understood, and whether they will continue to be significant in the future is an open question. In this paper, we examine the S&P 500 futures contract for evidence that turn-of-the-month effects have continued. Transaction costs are low for index futures, and the absence of short-sale restrictions makes index futures an attractive venue for testing the continuation of market anomalies because of the low cost of arbitrage. We find that TOTM effects for S&P 500 futures disappear after 1990, and this result carries over to the S&P 500 spot market. We conjecture that a change in the preference of individual investors over time from making direct to making indirect stock purchases through mutual funds is related to the disappearance of the TOTM effect for more recent return data. In this paper, we argue that turn-of-the-month return patterns for both spot and futures prices are dynamic and related to market microstructure and therefore subject to change without notice. Financial economists should be careful when making out-of-sample inferences from observed in-sample return regularities.

Disappearing turn-of-the-month effect, S&P 500 futures, market efficiency

Abstract:
This paper develops a new and easily implementable necessary and sufficient condition for the exact identification of a Markov-switching structural vector autoregression (SVAR) model. The theorem applies to models with both linear and some nonlinear restrictions on the structural parameters. We also derive efficient MCMC algorithms to implement sign and long-run restrictions in Markov-switching SVARs. Using our methods, four well-known identification schemes are used to study whether monetary policy has changed in the euro area since the introduction of the European Monetary Union. We find that models restricted to only time-varying shock variances dominate the other models. We find a persistent post-1993 regime that is associated with low volatility of shocks to output, prices, and interest rates. Finally, the output effects of monetary policy shocks are small and uncertain across regimes and models. These results are robust to the four identification schemes studied in this paper.

Markov switching, regime changes, volatility, identification

Abstract:
Many economic applications call for simultaneous equations VAR modeling. We show that the existing importance sampler can be prohibitively inefficient for this type of models. We develop a Gibbs simulator that works for both simultaneous and recursive VAR models with a much broader range of linear restrictions than those in the existing literature. We show that the required computation is of an SUR type, and thus our method can be implemented cheaply even for large systems of multiple equations.

Abstract:
The issue of normalization arises whenever two different values for a vector of unknown parameters imply the identical economic model. A normalization does not just imply a rule for selecting which point, among equivalent ones, to call the maximum likelihood estimator (MLE). It also governs the topography of the set of points that go into a small-sample confidence interval associated with that MLE. A poor normalization can lead to multimodal distributions, disjoint confidence intervals, and very misleading characterizations of the true statistical uncertainty. This paper introduces the identification principle as a framework upon which a normalization should be imposed, according to which the boundaries of the allowable parameter space should correspond to loci along which the model is locally unidentified. The authors illustrate these issues with examples taken from mixture models, structural VARs, and cointegration.

Normalization, mixture distributions, vector autoregressions, cointegration, regime switching, numerical Bayesian methods, small sample distributions, weak identification

Abstract:
This paper proposes a methodology for assessing the joint performance of multivariate forecasts of economic variables. The methodology is illustrated by comparing the rankings of forecasters by the Wall Street Journal with the authors' alternative rankings. The results show that the methodology can provide useful insights as to the certainty of forecasts as well as the extent to which various forecasts are similar or different.

Wall Street Journal, joint forecast, probability, ranking, correlation, variance, multivariate assessment

Abstract:
When impulse responses in dynamic multivariate models such as identified VARs are given economic interpretations, it is important that reliable statistical inferences be provided. Before probability assessments are provided, however, the model must be normalized. Contrary to the conventional wisdom, this paper argues that normalization, a rule of reversing signs of coefficients in equations in a particular way, could considerably affect the shape of the likelihood and thus probability bands for impulse responses. A new concept called ML distance normalization is introduced to avoid distorting the shape of the likelihood. Moreover, this paper develops a Monte Carlo simulation technique for implementing ML distance normalization.

Abstract:
In 1994 the FOMC began to release statements after each meeting. This paper investigates whether the public's views about the current path of the economy and of future policy have been affected by changes in the Federal Reserve's communications policy as reflected in private sector's forecasts of future economic conditions and policy moves. In particular, has the ability of private agents to predict where the economy is going improved since 1994? If so, on which dimensions has the ability to forecast improved? We find evidence that the individuals' forecasts have been more synchronized since 1994, implying the possible effects of the FOMC's transparency. On the other hand, we find little evidence that the common forecast errors, which are the driving force of overall forecast errors, have become smaller since 1994.

Transparency, common errors, idiosyncratic errors

Abstract:
The inference for hidden Markov chain models in which the structure is a multiple-equation macroeconomic model raises a number of difficulties that are not as likely to appear in smaller models. One is likely to want to allow for many states in the Markov chain without allowing the number of free parameters in the transition matrix to grow as the square of the number of states but also without losing a convenient form for the posterior distribution of the transition matrix. Calculation of marginal data densities for assessing model fit is often difficult in high-dimensional models and seems particularly difficult in these models. This paper gives a detailed explanation of methods we have found to work to overcome these difficulties. It also makes suggestions for maximizing posterior density and initiating Markov chain Monte Carlo simulations that provide some robustness against the complex shape of the likelihood in these models. These difficulties and remedies are likely to be useful generally for Bayesian inference in large time-series models. The paper includes some discussion of model specification issues that apply particularly to structural vector autoregressions with a Markov-switching structure.

volatility, coefficient changes, discontinuous shifts, Lucas critique, independent Markov processes

Abstract:
Causal analysis in multiple equation models often revolves around the evaluation of the effects of an exogenous shift in a structural equation. When taking into account the uncertainty implied by the shape of the likelihood, we argue that how normalization is implemented matters for inferential conclusions around the maximum likelihood (ML) estimates of such effects. We develop a general method that eliminates the distortion of finite-sample inferences about these ML estimates after normalization. We show that our likelihood-preserving normalization always maintains coherent economic interpretations while an arbitrary implementation of normalization can lead to ill-determined inferential results.

Bayesian methods, causal analysis, supply and demand, simultaneity, likelihood shape, equilibrium effects

Abstract:
This paper studies a New Keynesian model in which monetary policy may switch between regimes. We derive sufficient conditions for indeterminacy that are easy to implement and we show that the necessary and sufficient condition for determinacy, provided by Davig and Leeper, is necessary but not sufficient. More importantly, we use a two-regime model to show that indeterminacy in a passive regime may spill over to an active regime no matter how active the latter regime is. As a result, a passive monetary policy is more damaging than has been previously thought. Our results imply that the propagation of shocks in an active regime, such as that of the Federal Reserve in the post-1982 period, may be substantially affected by the possibility of a return to a passive regime of the kind that was followed in the 1960s and 1970s.

active and passive regimes, indeterminacy, cross-regime spillovers, conditioning, expectations formation, inflation hawk, inflation dove

Abstract:
Structural vector autoregressions (SVARs) are widely used for policy analysis and to provide stylized facts for dynamic general equilibrium models. Yet there have been no workable rank conditions to ascertain whether an SVAR is globally identified. When identifying restrictions such as long-run restrictions are imposed on impulse responses, there have been no efficient algorithms for small-sample estimation and inference. To fill these important gaps in the literature, this paper makes four contributions. First, we establish general rank conditions for global identification of both overidentified and exactly identified models. Second, we show that these conditions can be checked as a simple matrix-filling exercise and that they apply to a wide class of identifying restrictions, including linear and certain nonlinear restrictions. Third, we establish a very simple rank condition for exactly identified models that amounts to a straightforward counting exercise. Fourth, we develop a number of efficient algorithms for small-sample estimation and inference.

linear and nonlinear restrictions, global identification, almost everywhere, rank conditions, orthogonal rotation, transformation, simultaneity

Abstract:
This paper is about the properties of Markov-switching rational expectations (MSRE) models. We present a simple monetary policy model that switches between two regimes with known transition probabilities. The first regime, treated in isolation, has a unique determinate rational expectations equilibrium, and the second contains a set of indeterminate sunspot equilibria. We show that the Markov switching model, which randomizes between these two regimes, may contain a continuum of indeterminate equilibria. We provide examples of stationary sunspot equilibria and bounded sunspot equilibria, which exist even when the MSRE model satisfies a generalized Taylor principle. Our result suggests that it may be more difficult to rule out nonfundamental equilibria in MRSE models than in the single-regime case where the Taylor principle is known to guarantee local uniqueness.

policy rule, inflation, serial dependence, multiple equilibria, regime switching

Abstract:
Davig and Leeper (2007) have proposed a condition they call the generalized Taylor principle to rule out indeterminate equilibria in a version of the New Keynesian model, where the parameters of the policy rule follow a Markov-switching process. We show that although their condition rules out a subset of indeterminate equilibria, it does not establish uniqueness of the fundamental equilibrium. We discuss the differences between indeterminate fundamental equilibria included by Davig and Leeper's condition and fundamental equilibria that their condition misses.

bounded solutions, multiple fundamental equilibria, historical dependence

Abstract:
We develop a new method for computing minimal state variable solutions (MSV) to Markov-switching rational expectations models. We provide an algorithm to compute an MSV solution and show how to test a given solution for uniqueness and boundedness. We construct an example that is calibrated to U.S. data and show that the MSV solution in our example is unique. This solution can potentially explain in three different ways the observed reduction in the variance of inflation and the interest rate after 1980: The policy rule might have changed, the variance of the fundamental shocks might have fallen, or the private sector equations might have been different across regimes. We compare these three explanations for the change in variance and show that any one of them can potentially account for the facts. Our paper provides the necessary tools for a future empirical study of this issue.

regime switching, volatility, rational expectations

Abstract:
This paper is about the properties of Markov switching rational expectations (MSRE) models. We present a simple monetary policy model that switches between two regimes with known transition probabilities. The first regime, treated in isolation, has a unique determinate rational expectations equilibrium and the second contains a set of indeterminate sunspot equilibria. We show that the Markov switching model, which randomizes between these two regimes, may contain a continuum of indeterminate equilibria. We provide examples of stationary sunspot equilibria and bounded sunspot equilibria which exist even when the MSRE model satisfies a 'generalized Taylor principle'. Our result suggests that it may be more difficult to rule out non-fundamental equilibria in MRSE models than in the single regime case where the Taylor principle is known to guarantee local uniqueness.

Indeterminacy, regime switching, Taylor Principle

Abstract:
This paper is about the properties of Markov switching rational expectations (MSRE) models. We present a simple monetary policy model that switches between two regimes with known transition probabilities. The first regime, treated in isolation, has a unique determinate rational expectations equilibrium and the second contains a set of indeterminate sunspot equilibria. We show that the Markov switching model, which randomizes between these two regimes, may contain a continuum of indeterminate equilibria. We provide examples of stationary sunspot equilibria and bounded sunspot equilibria which exist even when the MSRE model satisfies a `generalized Taylor principle`. Our result suggests that it may be more difficult to rule out non-fundamental equilibria in MRSE models than in the single regime case where the Taylor principle is known to guarantee local uniqueness.

Abstract:
We develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forward-looking Markov-switching rational expectations models and we develop an algorithm to check these conditions in practice. We use three examples, based on the new-Keynesian model of monetary policy, to illustrate our technique. Our work connects applied econometric models of Markov-switching with forward looking rational expectations models and allows an applied researcher to construct the likelihood function for models in this class over a parameter space that includes a determinate region and an indeterminate region.

Abstract:
This paper studies a New-Keynesian model in which monetary policy may switch between regimes. We derive sufficient conditions for indeterminacy that are easy to implement and we show that the necessary and sufficient condition for determinacy, provided by Davig and Leeper, is necessary but not sufficient. More importantly, we use a two-regime model to show that indeterminacy in a passive regime may spill over to an active regime, no matter how active the latter regime is. As a result, a passive monetary policy is more damaging than has been previously thought. Our results imply that the propagation of shocks in an active regime, such as that of the Federal Reserve in the post-1982 period, may be substantially affected by the possibility of a return to a passive regime of the kind that was followed in the 1960s and 1970s.