The Incremental Predictive Information Associated with Using Theoretical New Keynesian DSGE Models vs. Simple Linear Econometric Models*

In this paper we construct output gap and inflation predictions using a variety of dynamic stochastic general equilibrium (DSGE) sticky price models. Predictive density accuracy tests related to the test discussed in Corradi and Swanson [Journal of Econometrics (2005a), forthcoming] as well as predictive accuracy tests due to Diebold and Mariano [Journal of Business and Economic Statistics (1995) , Vol. 13, pp. 253–263]; and West [Econometrica (1996) , Vol. 64, pp. 1067–1084] are used to compare the alternative models. A number of simple time‐series prediction models (such as autoregressive and vector autoregressive (VAR) models) are additionally used as strawman models. Given that DSGE model restrictions are routinely nested within VAR models, the addition of our strawman models allows us to indirectly assess the usefulness of imposing theoretical restrictions implied by DSGE models on unrestricted econometric models. With respect to predictive density evaluation, our results suggest that the standard sticky price model discussed in Calvo [Journal of Monetary Economics (1983), Vol. XII, pp. 383–398] is not outperformed by the same model augmented either with information or indexation, when used to predict the output gap. On the other hand, there are clear gains to using the more recent models when predicting inflation. Results based on mean square forecast error analysis are less clear‐cut, although the standard sticky price model fares best at our longest forecast horizon of 3 years, it performs relatively poorly at shorter horizons. When the strawman time‐series models are added to the picture, we find that the DSGE models still fare very well, often outperforming our forecast competitions, suggesting that theoretical macroeconomic restrictions yield useful additional information for forming macroeconomic forecasts.     

On forecasting cointegrated seasonal time series

We analyze periodic and seasonal cointegration models for bivariate quarterly observed time series in an empirical forecasting study. We include both single equation and multiple equation methods for those two classes of models. A VAR model in first differences, with and without cointegration restrictions, and a VAR model in annual differences are also included in the analysis, where they serve as benchmark models. Our empirical results indicate that the VAR model in first differences without cointegration is best if one-step ahead forecasts are considered. For longer forecast horizons however, the VAR model in annual differences is better. When comparing periodic versus seasonal cointegration models, we find that the seasonal cointegration models tend to yield better forecasts. Finally, there is no clear indication that multiple equations methods improve on single equation methods.     

Permanent-transitory Decomposition in Var Models With Cointegration and Common Cycles

In this paper we derive permanent-transitory decompositions of non-stationary multiple times series generated by (r)nite order Gaussian VAR(p) models with both cointegration and serial correlation common features. We extend existing analyses to the two classes of reduced rank structures discussed in Hecq, Palm and Urbain (1998). Using the corresponding state space representation of cointegrated VAR models in vector error correction form we show how decomposition can be obtained even in the case where the number of common feature and cointegration vectors are not equal to the number of variables. As empirical analysis of US business fluctuations shows the practical relevance of the approach we propose.     

Bayesian point estimation of the cointegration space

A neglected aspect of the otherwise fairly well developed Bayesian analysis of cointegration is point estimation of the cointegration space. It is pointed out here that, due to the well known non-identification of the cointegration vectors, the parameter space is not Euclidean and the loss functions underlying the conventional Bayes estimators are therefore questionable. We present a Bayes estimator of the cointegration space which takes the curved geometry of the parameter space into account. This estimate has the interpretation of being the posterior mean cointegration space and is invariant to the order of the time series, a property not shared with many of the Bayes estimators in the cointegration literature. An overall measure of cointegration space uncertainty is also proposed. Australian interest rate data are used for illustration. A small simulation study shows that the new Bayes estimator compares favorably to the maximum likelihood estimator.     

A new look at the relationship between time-series and structural econometric models

This paper examines the relationship between dynamic structural econometric models (SEM) and time series (TS) models. It extends the work of others by suggesting a reconciliation of SEM and TS models based on classical linear parameter restrictions in regression models rather than on time series methods. The paper demonstrates that in a number of common economic contexts there exist sets of plausible restrictions on the stochastic properties of the disturbances and on the dynamic adjustment processes in a SEM such that familiar structural models take on the form of univariate TS models. Consequently, it is argued that TS models should not be arbitrarily dismissed as being devoid of economic content.     

Low-frequency robust cointegration testing

Standard inference in cointegrating models is fragile because it relies on an assumption of an I(1)$I\left(1\right)$ model for the common stochastic trends, which may not accurately describe the data’s persistence. This paper considers low-frequency tests about cointegrating vectors under a range of restrictions on the common stochastic trends. We quantify how much power can potentially be gained by exploiting correct restrictions, as well as the magnitude of size distortions if such restrictions are imposed erroneously. A simple test motivated by the analysis in Wright (2000) is developed and shown to be approximately optimal for inference about a single cointegrating vector in the unrestricted stochastic trend model.     

Bayesian inference in a time varying cointegration model

There are both theoretical and empirical reasons for believing that the parameters of macroeconomic models may vary over time. However, work with time-varying parameter models has largely involved vector autoregressions (VARs), ignoring cointegration. This is despite the fact that cointegration plays an important role in informing macroeconomists on a range of issues. In this paper, we develop a new time varying parameter model which permits cointegration. We use a specification which allows for the cointegrating space to evolve over time in a manner comparable to the random walk variation used with TVP–VARs. The properties of our approach are investigated before developing a method of posterior simulation. We use our methods in an empirical investigation involving the Fisher effect.     

Cointegration Testing in Panels with Common Factors*

Panel unit‐root and no‐cointegration tests that rely on cross‐sectional independence of the panel unit experience severe size distortions when this assumption is violated, as has, for example, been shown by Banerjee, Marcellino and Osbat [Econometrics Journal (2004), Vol. 7, pp. 322–340; Empirical Economics (2005), Vol. 30, pp. 77–91] via Monte Carlo simulations. Several studies have recently addressed this issue for panel unit‐root tests using a common factor structure to model the cross‐sectional dependence, but not much work has been done yet for panel no‐cointegration tests. This paper proposes a model for panel no‐cointegration using an unobserved common factor structure, following the study by Bai and Ng [Econometrica (2004), Vol. 72, pp. 1127–1177] for panel unit roots. We distinguish two important cases: (i) the case when the non‐stationarity in the data is driven by a reduced number of common stochastic trends, and (ii) the case where we have common and idiosyncratic stochastic trends present in the data. We discuss the homogeneity restrictions on the cointegrating vectors resulting from the presence of common factor cointegration. Furthermore, we study the asymptotic behaviour of some existing residual‐based panel no‐cointegration tests, as suggested by Kao [Journal of Econometrics (1999), Vol. 90, pp. 1–44] and Pedroni [Econometric Theory (2004a), Vol. 20, pp. 597–625]. Under the data‐generating processes (DGP) used, the test statistics are no longer asymptotically normal, and convergence occurs at rate T rather than as for independent panels. We then examine the possibilities of testing for various forms of no‐cointegration by extracting the common factors and individual components from the observed data directly and then testing for no‐cointegration using residual‐based panel tests applied to the defactored data.     

Stochastic trends and economic fluctuations in a small open economy

In this paper we describe how restricted vector autoregressions can be employed to examine the sources of macroeconomic fluctuations. We show how cointegration restrictions can be used to identify a VAR system with common stochastic trends subject to transitory and permanent changes in average growth, and how we may investigate the system's responses to permanent shocks, i.e. to innovations to the trends. Theoretical cointegration vectors are derived from a small open economy growth model for terms of trade, real GDP, real consumption, and real investments. Applying these methods to Swedish annual data (1875–1986) we find that permanent real (supply) shocks account for most of the fluctuations in GDP, even in the short run.     

Stochastic search variable selection in vector error correction models with an application to a model of the UK macroeconomy

This paper develops methods for stochastic search variable selection (currently popular with regression and vector autoregressive models) for vector error correction models where there are many possible restrictions on the cointegration space. We show how this allows the researcher to begin with a single unrestricted model and either do model selection or model averaging in an automatic and computationally efficient manner. We apply our methods to a large UK macroeconomic model. Copyright © 2011 John Wiley & Sons, Ltd.     

Bayesian prediction with cointegrated vector autoregressions

A complete procedure for calculating the joint predictive distribution of future observations based on the cointegrated vector autoregression is presented. The large degree of uncertainty in the choice of cointegration vectors is incorporated into the analysis via the prior distribution. This prior has the effect of weighing the predictive distributions based on the models with different cointegration vectors into an overall predictive distribution. The ideas of Litterman [Mimeo, Massachusetts Institute of Technology, 1980] are adopted for the prior on the short run dynamics of the process resulting in a prior which only depends on a few hyperparameters. A straightforward numerical evaluation of the predictive distribution based on Gibbs sampling is proposed. The prediction procedure is applied to a seven-variable system with a focus on forecasting Swedish inflation.     

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.     

Inference in Cointegrating Models: UK M1 Revisited

The paper addresses the practical determination of cointegration rank. This is difficult for many reasons: deterministic terms play a crucial role in limiting distributions, and systems may not be formulated to ensure similarity to nuisance parameters; finite-sample critical values may differ from asymptotic equivalents; dummy variables alter critical values, often greatly; multiple cointegration vectors must be identified to allow inference; the data may be I(2) rather than I(1), altering distributions; and conditioning must be done with care. These issues are illustrated by an empirical application of multivariate cointegration analysis to a small model of narrow money, prices, output and interest rates in the UK.     

The behavior of speculative prices and the consistency of economic models

Modern financial economic theory suggest that changes in speculative prices should follow simple ‘fair game’ processes in an informationally efficient capital market. The observation that changes in speculative prices follow simple time series processes both supports this theoretical proposition and suggest restrictions on the transfer functions of structural econometric models in which speculative prices appear as output variables. The simplicity of the time series processes for observed changes in speculative prices are shown to impose strong restrictions on potential equilibrium models of asset pricing, informational disequilibrium models of financial markets, and many monetary and macroeconomic models as well.     

The price-wage inflationary spiral in Poland

In this paper the problem of price-wage relationship modelling in the case of a mixed economy is addressed. The empirical investigation was based on Polish annual data for the period of a centrally planned system (1964–1989) and on quarterly data for the period of transition towards a market economy (1990.1–1990.3). The traditional approach proved to be inappropriate because of the variables' nonstationarity. Identification of long-run behaviour was attempted by applying the two-step Engle-Granger's, or alternatively, Johansen's maximum likelihood (ML) procedures. The ML estimator provided better estimates of cointegration vectors and, even more important, allowed as many as three to be found.The main conclusion which can be drawn from the empirical findings is that three variables: price index, average wages and labour productivity, form a multi-dimensional equilibrium space. This property of the described phenomena needs to be taken into serious account when building macroeconometric models explaining the behaviour of the Polish economy.The existence of these three cointegration vectors is troublesome because of unusual problems of interpretation. However, if it is not as a result of misspecification and/or small sample bias, it proves that much remains to be learned about the price-wage mechanisms functioning in economies having a mixed character.     

Seasonal cointegration and cross-equation restrictions on a forward-looking buffer stock model of money demand

The present study derives a set of cross-equation restrictions imposed on a forward-looking buffer stock model of money demand. Since typically data are seasonally unadjusted for many countries, a seasonal difference rather than the conventional first difference is employed here to compute the growth rate. This seemingly innocuous change in the computation of the growth rate nevertheless makes the multi-period forward-looking money demand equilibrium model substantially different from previous studies. In addition, the related cointegration analysis and implied cross-equation restrictions are also considerably changed. The existence of up to three seasonal unit roots derived from a seasonal difference supports the need for seasonal cointegration, suggesting a new test for the forward-looking equilibrium model. An application of testing such derived cross-equation restrictions to the equilibrium model is illustrated through use of macroeconomic data on Taiwan.     

Cointegration Testing in Single Error-Correction Equations in the Presence of Linear Time Trends

Banerjee, Dolado and Mestre (J. Time Ser. Anal. 19 (1998) 267−283)introduce an error-correction test for the null hypothesis of no cointegration. The present paper supplements their work. They provide critical values forregressions with and without detrending. Here it is shown that the latter arenot appropriate if the series display linear trends. This does not mean thatdetrending is required. Correct percentiles are suggested for the case thatseries follow linear time trends but tests are based on regressions withoutdetrending. They are readily available from the literature.     

THEORETICAL AND PRACTICAL ARGUMENTS FOR MODELING LABOR SUPPLY AS A CHOICE AMONG LATENT JOBS

Models of labor supply derived from stochastic utility representations and discretized sets of feasible hours of work have gained popularity because they are more practical than the standard approaches based on marginal calculus. In this paper we argue that practicality is not the only feature that can be addressed by means of stochastic choice theory. This theory also offers a powerful framework for developing a more realistic model for labor supply choices, founded on individuals having preferences over jobs and facing restrictions on the choice of jobs and hours of work. We discuss and clarify how this modeling framework deviates from both the conventional discrete approach [Van Soest, A. ( 1995 ) Structural models of family labor supply. A discrete choice approach. Journal of Human Resources 30: 63–88), as well as the standard textbook approach based on marginal calculus (Hausman, J.A. ( 1992 ) The econometrics of nonlinear budget sets. Econometrica 53: 1255–1282]. We furthermore discuss how the model based on job choice can be applied to simulate effects of alternative restrictions on hours of work.     

A fractional cointegration analysis of Fisher hypothesis: evidence from Turkey

This paper examines the validity of Fisher hypothesis in Turkey over the period from 1990:01 through 2010:03 by using cointegration and fractional cointegration approaches. The findings from Engle and Granger cointegration test indicate that inflation and nominal interest rate series are cointegrated. Since the conventional cointegration tests do not provide strong evidence on the long run relationship, we also use fractional cointegration definition suggested by Cheung and Lai (J Bus Econ Stat 11:103–112, 1993) which requires only a mean reverting (d < 1) relationship between the series. The results from fractional cointegration tests based on GPH and Robinson methods show that inflation and nominal interest rate series are fractionally cointegrated. These findings support the validity of the Fisher hypothesis in Turkey.