Modelling multi‐period inflation uncertainty using a panel of density forecasts

This paper examines the determinants of inflation forecast uncertainty using a panel of density forecasts from the Survey of Professional Forecasters (SPF). Based on a dynamic heterogeneous panel data model, we find that the persistence in forecast uncertainty is much less than what the aggregate time series data would suggest. In addition, the strong link between past forecast errors and current forecast uncertainty, as often noted in the ARCH literature, is largely lost in a multi‐period context with varying forecast horizons. We propose a novel way of estimating ‘news’ and its variance using the Kullback‐Leibler information, and show that the latter is an important determinant of forecast uncertainty. Our evidence suggests a strong relationship of forecast uncertainty with level of inflation, but not with forecaster discord or with the volatility of a number of other macroeconomic indicators. Copyright © 2006 John Wiley & Sons, Ltd.     

Optimal forecasting with heterogeneous panels: A Monte Carlo study

We contrast the forecasting performance of alternative panel estimators, divided into three main groups: homogeneous, heterogeneous and shrinkage/Bayesian. Via a series of Monte Carlo simulations, the comparison is performed using different levels of heterogeneity and cross sectional dependence, alternative panel structures in terms of T and N and the specification of the dynamics of the error term. To assess the predictive performance, we use traditional measures of forecast accuracy (Theil’s U statistics, RMSE and MAE), the Diebold–Mariano test, and Pesaran and Timmerman’s statistic on the capability of forecasting turning points. The main finding of our analysis is that when the level of heterogeneity is high, shrinkage/Bayesian estimators are preferred, whilst when there is low or mild heterogeneity, homogeneous estimators have the best forecast accuracy.     

A Dynamic Panel Data Approach to the Forecasting of the GDP of German Länder

Abstract

In this paper, we make multi-step forecasts of the annual growth rates of the real GDP for each of the 16 German Länder simultaneously. We apply dynamic panel models accounting for spatial dependence between regional GDP. We find that both pooling and accounting for spatial effects help to improve the forecast performance substantially. We demonstrate that the effect of accounting for spatial dependence is more pronounced for longer forecasting horizons (the forecast accuracy gain is about 9% for a 1-year horizon and exceeds 40% for a 5-year horizon). We recommend incorporating a spatial dependence structure into regional forecasting models, especially when long-term forecasts are made.     

Forecasting macroeconomic time series: LASSO-based approaches and their forecast combinations with dynamic factor models

In a data-rich environment, forecasting economic variables amounts to extracting and organizing useful information from a large number of predictors. So far, the dynamic factor model and its variants have been the most successful models for such exercises. In this paper, we investigate a category of LASSO-based approaches and evaluate their predictive abilities for forecasting twenty important macroeconomic variables. These alternative models can handle hundreds of data series simultaneously, and extract useful information for forecasting. We also show, both analytically and empirically, that combing forecasts from LASSO-based models with those from dynamic factor models can reduce the mean square forecast error (MSFE) further. Our three main findings can be summarized as follows. First, for most of the variables under investigation, all of the LASSO-based models outperform dynamic factor models in the out-of-sample forecast evaluations. Second, by extracting information and formulating predictors at economically meaningful block levels, the new methods greatly enhance the interpretability of the models. Third, once forecasts from a LASSO-based approach are combined with those from a dynamic factor model by forecast combination techniques, the combined forecasts are significantly better than either dynamic factor model forecasts or the naïve random walk benchmark.     

A look into the factor model black box: Publication lags and the role of hard and soft data in forecasting GDP

We derive forecast weights and uncertainty measures for assessing the roles of individual series in a dynamic factor model (DFM) for forecasting the euro area GDP from monthly indicators. The use of the Kalman smoother allows us to deal with publication lags when calculating the above measures. We find that surveys and financial data contain important information for the GDP forecasts beyond the monthly real activity measures. However, this is discovered only if their more timely publication is taken into account properly. Differences in publication lags play a very important role and should be considered in forecast evaluation.     

Forecasting banking crises with dynamic panel probit models

Banking crises are rare events, but when they occur, their consequences are often dramatic. The aim of this paper is to contribute to the toolkit of early warning models that is available to policy makers by exploring the dynamics and exuberances embedded in a panel dataset that covers 22 European countries over four decades (from 1970Q1 to 2012Q4). The in- and out-of-sample forecast performances of several (dynamic) probit models are evaluated, with the objective of developing common vulnerability indicators with early warning properties. The results obtained show that adding dynamic components and exuberance indicators to the models improves the performances of early warning models significantly.     

Individual effects and dynamics in count data models

In this paper we examine the panel data estimation of dynamic models for count data that include correlated fixed effects and predetermined variables. Use of a linear feedback model is proposed. A quasi-differenced GMM estimator is consistent for the parameters in the dynamic model, but when series are highly persistent, there is a problem of weak instrument bias. An estimator is proposed that utilises pre-sample information of the dependent count variable, which is shown in Monte Carlo simulations to possess desirable small sample properties. The models and estimators are applied to data on US patents and R&D expenditure.     

Forecasting economic time series using score-driven dynamic models with mixed-data sampling

We introduce a mixed-frequency score-driven dynamic model for multiple time series where the score contributions from high-frequency variables are transformed by means of a mixed-data sampling weighting scheme. The resulting dynamic model delivers a flexible and easy-to-implement framework for the forecasting of low-frequency time series variables through the use of timely information from high-frequency variables. We verify the in-sample and out-of-sample performances of the model in an empirical study on the forecasting of U.S. headline inflation and GDP growth. In particular, we forecast monthly headline inflation using daily oil prices and quarterly GDP growth using a measure of financial risk. The forecasting results and other findings are promising. Our proposed score-driven dynamic model with mixed-data sampling weighting outperforms competing models in terms of both point and density forecasts.     

Bias in dynamic panel estimation with fixed effects,incidental trends and cross section dependence

Explicit asymptotic bias formulae are given for dynamic panel regression estimators as the cross section sample size N→∞$N\to \infty$. The results extend earlier work by Nickell [1981. Biases in dynamic models with fixed effects. Econometrica 49, 1417–1426] and later authors in several directions that are relevant for practical work, including models with unit roots, deterministic trends, predetermined and exogenous regressors, and errors that may be cross sectionally dependent. The asymptotic bias is found to be so large when incidental linear trends are fitted and the time series sample size is small that it changes the sign of the autoregressive coefficient. Another finding of interest is that, when there is cross section error dependence, the probability limit of the dynamic panel regression estimator is a random variable rather than a constant, which helps to explain the substantial variability observed in dynamic panel estimates when there is cross section dependence even in situations where N is very large. Some proposals for bias correction are suggested and finite sample performance is analyzed in simulations.     

Forecast revisions of Mexican inflation and GDP growth

We analyze the forecasts of inflation and GDP growth contained in the Banco de México’s Survey of Professional Forecasters for the period 1995–2009. The forecasts are for the current and the following year, and comprise an unbalanced three-dimensional panel with multiple individual forecasters, target years, and forecast horizons. The fixed-event nature of the forecasts enables us to examine their efficiency by looking at the revision process. The panel structure allows us to control for aggregate shocks and to construct a measure of the news that impacted expectations in the period under study. We find that respondents anchor to their initial forecasts, updating their revisions smoothly as they receive more information. In addition, they do not seem to use publicly-known information in an efficient manner. These inefficiencies suggest clear areas of opportunity for improving the accuracy of the forecasts, for instance by taking into account the positive autocorrelation found in forecast revisions.     

Fitting dynamic factor models to non-stationary time series

Factor modelling of a large time series panel has widely proven useful to reduce its cross-sectional dimensionality. This is done by explaining common co-movements in the panel through the existence of a small number of common components, up to some idiosyncratic behaviour of each individual series. To capture serial correlation in the common components, a dynamic structure is used as in traditional (uni- or multivariate) time series analysis of second order structure, i.e. allowing for infinite-length filtering of the factors via dynamic loadings. In this paper, motivated from economic data observed over long time periods which show smooth transitions over time in their covariance structure, we allow the dynamic structure of the factor model to be non-stationary over time by proposing a deterministic time variation of its loadings. In this respect we generalize the existing recent work on static factor models with time-varying loadings as well as the classical, i.e. stationary, dynamic approximate factor model. Motivated from the stationary case, we estimate the common components of our dynamic factor model by the eigenvectors of a consistent estimator of the now time-varying spectral density matrix of the underlying data-generating process. This can be seen as a time-varying principal components approach in the frequency domain. We derive consistency of this estimator in a “double-asymptotic” framework of both cross-section and time dimension tending to infinity. The performance of the estimators is illustrated by a simulation study and an application to a macroeconomic data set.     

Does inequality help in forecasting equity premium in a panel of G7 countries?

This paper investigates whether the post-tax and transfer growth rate in the Gini index can help in forecasting the equity premium in the G7 countries (Canada, France, Germany, Italy, Japan, United Kingdom (UK), and United States (US)). To this end, we use a panel data-based predictive framework, which controls for heterogeneity, cross-sectional dependence, persistence and endogeneity. When we analyze the annual out-of-sample period of 1990–2011, given an in-sample period of 1967–1989, our results show that: (a) Time series based predictive regression models fail to beat the benchmark of historical average, except for Italy; and, (b) the panel data models beat the benchmark in a statistically significant fashion for all the seven countries. Further, our results highlight the importance of pooling information when trying to forecast excess stock returns based on a measure of inequality.     

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.     

Bootstrap unit root tests in panels with cross-sectional dependency

We apply bootstrap methodology to unit root tests for dependent panels with N cross-sectional units and T time series observations. More specifically, we let each panel be driven by a general linear process which may be different across cross-sectional units, and approximate it by a finite order autoregressive integrated process of order increasing with T. As we allow the dependency among the innovations generating the individual series, we construct our unit root tests from the estimation of the system of the entire N cross-sectional units. The limit distributions of the tests are derived by passing T to infinity, with N fixed. We then apply bootstrap method to the approximated autoregressions to obtain critical values for the panel unit root tests, and establish the asymptotic validity of such bootstrap panel unit root tests under general conditions. The proposed bootstrap tests are indeed quite general covering a wide class of panel models. They in particular allow for very general dynamic structures which may vary across individual units, and more importantly for the presence of arbitrary cross-sectional dependency. The finite sample performance of the bootstrap tests is examined via simulations, and compared to that of commonly used panel unit root tests. We find that our bootstrap tests perform relatively well, especially when N is small.     

Forecasting macroeconomic variables using collapsed dynamic factor analysis

We explore a new approach to the forecasting of macroeconomic variables based on a dynamic factor state space analysis. Key economic variables are modeled jointly with principal components from a large time series panel of macroeconomic indicators using a multivariate unobserved components time series model. When the key economic variables are observed at a low frequency and the panel of macroeconomic variables is at a high frequency, we can use our approach for both nowcasting and forecasting purposes. Given a dynamic factor model as the data generation process, we provide Monte Carlo evidence of the finite-sample justification of our parsimonious and feasible approach. We also provide empirical evidence for a US macroeconomic dataset. The unbalanced panel contains quarterly and monthly variables. The forecasting accuracy is measured against a set of benchmark models. We conclude that our dynamic factor state space analysis can lead to higher levels of forecasting precision when the panel size and time series dimensions are moderate.     

Forecasting the US term structure of interest rates using a macroeconomic smooth dynamic factor model

We extend the class of dynamic factor yield curve models in order to include macroeconomic factors. Our work benefits from recent developments in the dynamic factor literature related to the extraction of the common factors from a large panel of macroeconomic series and the estimation of the parameters in the model. We include these factors in a dynamic factor model for the yield curve, in which we model the salient structure of the yield curve by imposing smoothness restrictions on the yield factor loadings via cubic spline functions. We carry out a likelihood-based analysis in which we jointly consider a factor model for the yield curve, a factor model for the macroeconomic series, and their dynamic interactions with the latent dynamic factors. We illustrate the methodology by forecasting the U.S. term structure of interest rates. For this empirical study, we use a monthly time series panel of unsmoothed Fama–Bliss zero yields for treasuries of different maturities between 1970 and 2009, which we combine with a macro panel of 110 series over the same sample period. We show that the relationship between the macroeconomic factors and the yield curve data has an intuitive interpretation, and that there is interdependence between the yield and macroeconomic factors. Finally, we perform an extensive out-of-sample forecasting study. Our main conclusion is that macroeconomic variables can lead to more accurate yield curve forecasts.     

Policy intervention and forecasting: An application to minimum wages

This paper examines the forecasting implications of incorporating policy effects into the structure of unconditional time series models. The forecasting model is applied to the Puerto Rican experience with minimum wages from 1953 to 1982. The empirical results suggest that significant disemployment and unemployment followed the imposition of economy-wide minimum wages in 1974. The growth of employment suffered and the aggregate unemployment rate reached an unprecedented level. Multivariate time-series models for the employment-population ratio and the unemployment rate capture these effects well. They also forecast more accurately than unvariate and intervention models over the ex post period, 1983–1984. It is argued that models that combine subject matter-specific structure within a dynamic time-series framework greatly help to satisfy demands for theoretical consistency and forecast accuracy. Multivariate time-series models play an important complementary role in the structural modelling of economic policy analysis. This is particularly so when limitations of either data or theory preclude complete specification of structural equations.     

Maximum Likelihood Estimation in Panels with Incidental Trends

It is shown that the maximum likelihood estimator of a local to unity parameter can be consistently estimated with panel data when the cross-section observations are independent. Consistency applies when there are no deterministic trends or when there is a homogeneous deterministic trend in the panel model. When there are heterogeneous deterministic trends the panel MLE of the local to unity parameter is inconsistent. This outcome provides a new instance of inconsistent ML estimation in dynamic panels, and, unlike earlier results of this type, applies when both T →∞ and N →∞.     

A test of cross section dependence for a linear dynamic panel model with regressors

This paper proposes a new testing procedure for detecting error cross section dependence after estimating a linear dynamic panel data model with regressors using the generalised method of moments (GMM). The test is valid when the cross-sectional dimension of the panel is large relative to the time series dimension. Importantly, our approach allows one to examine whether any error cross section dependence remains after including time dummies (or after transforming the data in terms of deviations from time-specific averages), which will be the case under heterogeneous error cross section dependence. Finite sample simulation-based results suggest that our tests perform well, particularly the version based on the [Blundell, R., Bond, S., 1998. Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics 87, 115–143] system GMM estimator. In addition, it is shown that the system GMM estimator, based only on partial instruments consisting of the regressors, can be a reliable alternative to the standard GMM estimators under heterogeneous error cross section dependence. The proposed tests are applied to employment equations using UK firm data and the results show little evidence of heterogeneous error cross section dependence.     

Forecasting correlated time series with exponential smoothing models

This paper presents the Bayesian analysis of a general multivariate exponential smoothing model that allows us to forecast time series jointly, subject to correlated random disturbances. The general multivariate model, which can be formulated as a seemingly unrelated regression model, includes the previously studied homogeneous multivariate Holt-Winters’ model as a special case when all of the univariate series share a common structure. MCMC simulation techniques are required in order to approach the non-analytically tractable posterior distribution of the model parameters. The predictive distribution is then estimated using Monte Carlo integration. A Bayesian model selection criterion is introduced into the forecasting scheme for selecting the most adequate multivariate model for describing the behaviour of the time series under study. The forecasting performance of this procedure is tested using some real examples.