Green shoots and double dips in the euro area: A real time measure

In order to perform real-time business cycle inferences and forecasts of GDP growth rates in the euro area, we use an extension of the Markov-switching dynamic factor models that accounts for the features of the day-to-day monitoring of economic developments, such as ragged edges, mixed frequencies and data revisions. We provide examples that show the nonlinear nature of the relationships between data revisions, point forecasts and forecast uncertainty. Based on our empirical results, we think that the real-time probabilities of recession inferred from the model are an appropriate statistic for capturing what the press call green shoots, and for monitoring double-dip recessions.     

Calling recessions in real time

This paper surveys efforts to automate the dating of business cycle turning points. Doing this on a real time, out-of-sample basis is a bigger challenge than many academics might assume, due to factors such as data revisions and changes in economic relationships over time. The paper stresses the value of both simulated real-time analysis — looking at what the inference of a proposed model would have been using data as they were actually released at the time — and actual real-time analysis, in which a researcher stakes his or her reputation on publicly using the model to generate out-of-sample, real-time predictions. The immediate publication capabilities of the internet make the latter a realistic option for researchers today, and many are taking advantage of it. The paper reviews a number of approaches to dating business cycle turning points and emphasizes the fundamental trade-off between parsimony — trying to keep the model as simple and robust as possible — and making full use of the available information. Different approaches have different advantages, and the paper concludes that there may be gains from combining the best features of several different approaches.     

Optimal policy in Markov-switching rational expectations models

In this paper we consider the optimal quadratic control problem of Markov-switching linear rational expectation models. These models are general and flexible tools for modelling not only regime but also model or parameter uncertainty. We show, first, how to find the solution of a Markov-switching linear rational expectation model. Based on this solution we then show how to apply dynamic programming to find the optimal time-consistent policy and the resulting Nash-Stackelberg equilibrium. Suitable modifications of the algorithm allow to deal with the (non-RE) case in which the policymaker and the private sector hold different beliefs or probabilities over regime change. We also show how the optimisation procedure can be employed to obtain the optimal policy under commitment. As an illustration we compute the optimal policy in a small open economy subject to stochastic structural breaks in some of its key parameters.     

What do interest rates reveal about the functioning of real business cycle models?

This paper begins by documenting the extent to which the predictions of standard Real Business Cycle (RBC) models are incompatible with observed movements in real interest rates. The main finding of the paper is that extending the baseline model to include habit persistence in consumption and adjustment costs to capital significantly improves the model's empirical performance. In our evaluation of the model's performance, we take special care of estimating and testing predictions of the model using both moments drawn directly from the data and moments calculated after identifying shocks to the stochastic trend.     

Tapping the supercomputer under your desk: Solving dynamic equilibrium models with graphics processors

This paper shows how to build algorithms that use graphics processing units (GPUs) installed in most modern computers to solve dynamic equilibrium models in economics. In particular, we rely on the compute unified device architecture (CUDA) of NVIDIA GPUs. We illustrate the power of the approach by solving a simple real business cycle model with value function iteration. We document improvements in speed of around 200 times and suggest that even further gains are likely.     

Predicting benchmarked US state employment data in real time

US payroll employment data come from a survey and are subject to revisions. While revisions are generally small at the national level, they can be large enough at the state level to alter assessments of current economic conditions. Users must therefore exercise caution in interpreting state employment data until they are “benchmarked” against administrative data 5–16 months after the reference period. This article develops a state-space model that predicts benchmarked state employment data in real time. The model has two distinct features: (1) an explicit model of the data revision process and (2) a dynamic factor model that incorporates real-time information from other state-level labor market indicators. We find that the model reduces the average size of benchmark revisions by about 11 percent. When we optimally average the model’s predictions with those of existing models, the model reduces the average size of the revisions by about 14 percent.     

Maximum likelihood estimation for dynamic factor models with missing data

This paper concerns estimating parameters in a high-dimensional dynamic factor model by the method of maximum likelihood. To accommodate missing data in the analysis, we propose a new model representation for the dynamic factor model. It allows the Kalman filter and related smoothing methods to evaluate the likelihood function and to produce optimal factor estimates in a computationally efficient way when missing data is present. The implementation details of our methods for signal extraction and maximum likelihood estimation are discussed. The computational gains of the new devices are presented based on simulated data sets with varying numbers of missing entries.     

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.     

Kernel-weighted GMM estimators for linear time series models

This paper analyzes the higher-order asymptotic properties of generalized method of moments (GMM) estimators for linear time series models using many lags as instruments. A data-dependent moment selection method based on minimizing the approximate mean squared error is developed. In addition, a new version of the GMM estimator based on kernel-weighted moment conditions is proposed. It is shown that kernel-weighted GMM estimators can reduce the asymptotic bias compared to standard GMM estimators. Kernel weighting also helps to simplify the problem of selecting the optimal number of instruments. A feasible procedure similar to optimal bandwidth selection is proposed for the kernel-weighted GMM estimator.     

Consistent estimation of a general nonparametric regression function in time series

We propose an estimator of the conditional distribution of X_t|X_t−1,X_t−2,…, and the corresponding regression function , where the conditioning set is of infinite order. We establish consistency of our estimator under stationarity and ergodicity conditions plus a mild smoothness condition.     

Methods for inference in large multiple-equation Markov-switching models

Inference for multiple-equation Markov-chain models raises a number of difficulties that are unlikely to appear in smaller models. Our framework allows for many regimes in the transition matrix, without letting the number of free parameters grow as the square as the number of regimes, but also without losing a convenient form for the posterior distribution. Calculation of marginal data densities is difficult in these high-dimensional models. This paper gives methods to overcome these difficulties, and explains why existing methods are unreliable. It makes suggestions for maximizing posterior density and initiating MCMC simulations that provide robustness against the complex likelihood shape.     

The second-order bias and mean squared error of estimators in time-series models

We develop analytical results on the second-order bias and mean squared error of estimators in time-series models. These results provide a unified approach to developing the properties of a large class of estimators in linear and nonlinear time-series models and they are valid for both normal and nonnormal samples of observations, and where the regressors are stochastic. The estimators included are the generalized method of moments, maximum likelihood, least squares, and other extremum estimators. Our general results are applied to four time-series models. We investigate the effects of nonnormality on the second-order bias results for two of these models, while for all four models, the second-order bias and mean squared error results are given under normality. Numerical results for some of these models are also presented.     

Incorporating vintage differences and forecasts into Markov switching models

This paper incorporates vintage differences and forecasts into the Markov switching models described by Hamilton (1994). The vintage differences and forecasts induce parameter breaks close to the end of the sample, too close for standard maximum likelihood techniques to produce precise parameter estimates. A supplementary procedure estimates the statistical properties of the end-of-sample observations that behave differently from the rest, allowing inferred probabilities to reflect the breaks. Empirical results using real-time data show that these techniques improve the ability of a Markov switching model based on GDP and GDI to recognize the start of the 2001 recession.     

Consistent factor estimation in dynamic factor models with structural instability

This paper considers the estimation of approximate dynamic factor models when there is temporal instability in the factor loadings. We characterize the type and magnitude of instabilities under which the principal components estimator of the factors is consistent and find that these instabilities can be larger than earlier theoretical calculations suggest. We also discuss implications of our results for the robustness of regressions based on the estimated factors and of estimates of the number of factors in the presence of parameter instability. Simulations calibrated to an empirical application indicate that instability in the factor loadings has a limited impact on estimation of the factor space and diffusion index forecasting, whereas estimation of the number of factors is more substantially affected.     

The asymmetry of judgemental confidence intervals in time series forecasting

In forecasting a time series, one may be asked to communicate the likely distribution of the future actual value, often expressed as a confidence interval. Whilst the accuracy (calibration) of these intervals has dominated most studies to date, this paper is concerned with other possible characteristics of the intervals. It reports a study in which the prevalence and determinants of the symmetry of judgemental confidence intervals in time series forecasting was examined. Most prior work has assumed that this interval is symmetrically placed around the forecast. However, this study shows that people generally estimate asymmetric confidence intervals where the forecast is not the midpoint of the estimated interval. Many of these intervals are grossly asymmetric. Results indicate that the placement of the forecast in relation to the last actual value of a time series is a major determinant of the direction and size of the asymmetry.     

Testing for structural breaks in dynamic factor models

In this paper we investigate the consequences of structural breaks in the factor loadings for the specification and estimation of factor models based on principal components and suggest procedures for testing for structural breaks. It is shown that structural breaks severely inflate the number of factors identified by the usual information criteria. The hypothesis of a structural break is tested by using LR, LM and Wald statistics. The LM test (which performs best in our Monte Carlo simulations) is generalized to test for structural breaks in factor models where the break date is unknown and the common factors and idiosyncratic components are serially correlated. The proposed test procedures are applied to datasets from the US and the euro area.     

Bias in dynamic panel models under time series misspecification

We consider within-group estimation of higher-order autoregressive panel models with exogenous regressors and fixed effects, where the lag order is possibly misspecified. Even when disregarding the misspecification bias, the fixed-effect bias formula is quite different from the correctly specified case though its asymptotic order remains the same under the stationarity. We suggest bias reduction methods under the possible time series misspecification.     

Sensitivity to autocorrelation in judgmental time series forecasting

How well can people use autocorrelation information when making judgmental forecasts? In Experiment 1, participants forecast from 12 series in which the autocorrelation varied within subjects. The participants showed a sensitivity to the degree of autocorrelation. However, their forecasts indicated that they implicitly assumed positive autocorrelation in uncorrelated time series. Experiments 2 and 2a used a one-shot single-trial between-subjects design and obtained similar results. Experiment 3 investigated the way in which the between-trials context influenced forecasting. The results showed that forecasts are affected by the characteristics of previous series, as well as those of the series from which forecasts are to be made. Our findings can be accommodated within an adaptive approach. Forecasters base their initial expectations of series characteristics on their past experience and modify these expectations in a pseudo-Bayesian manner on the basis of their analysis of those characteristics in the series to be forecast.     

Bootstrap prediction intervals for SETAR models

This paper considers four methods for obtaining bootstrap prediction intervals (BPIs) for the self-exciting threshold autoregressive (SETAR) model. Method 1 ignores the sampling variability of the threshold parameter estimator. Method 2 corrects the finite sample biases of the autoregressive coefficient estimators before constructing BPIs. Method 3 takes into account the sampling variability of both the autoregressive coefficient estimators and the threshold parameter estimator. Method 4 resamples the residuals in each regime separately. A Monte Carlo experiment shows that (1) accounting for the sampling variability of the threshold parameter estimator is necessary, despite its super-consistency; (2) correcting the small-sample biases of the autoregressive parameter estimators improves the small-sample properties of bootstrap prediction intervals under certain circumstances; and (3) the two-sample bootstrap can improve the long-term forecasts when the error terms are regime-dependent.     

Testing neoclassical convergence in regional incomes and earnings

The time-series properties of per capita income and per capita earnings in the regions of the United States are tested for consistency with the neoclassical growth model's prediction of convergence. We find evidence for per capita income convergence for U.S. regions during the 1929–1990 period after allowing for a trend break in 1946. These findings support the neoclassical model's prediction of convergence. The evidence for per capita earnings convergence is, however, less conclusive. Shocks to per capita earnings are found to be more persistent than shocks to per capita income. This implies that the regional distribution of transfer payments tends to smooth the effects of deviation on relative regional per capita earnings and reinforce trends in per capita income convergence.