A Coincident Index,Common Factors,and Monthly Real GDP*

The Stock–Watson coincident index and its subsequent extensions assume a static linear one‐factor model for the component indicators. This restrictive assumption is unnecessary if one defines a coincident index as an estimate of monthly real gross domestic products (GDP). This paper estimates Gaussian vector autoregression (VAR) and factor models for latent monthly real GDP and other coincident indicators using the observable mixed‐frequency series. For maximum likelihood estimation of a VAR model, the expectation‐maximization (EM) algorithm helps in finding a good starting value for a quasi‐Newton method. The smoothed estimate of latent monthly real GDP is a natural extension of the Stock–Watson coincident index.     

Discussion of “Nowcasting US GDP: The role of ISM Business Surveys”

This paper discusses the contribution of Lahiri and Monokroussos, published in the current issue of this journal, where they investigate the nowcasting power of ISM Business Surveys for real US GDP. The second part of this note includes some empirical considerations on nowcasting quarterly real GDP by using the monthly PMI index for Switzerland. The results indicate that the Swiss PMI is not leading GDP growth; rather, it is coincident, and its nowcasting power is quite good. The signs of the fitted values mostly correspond to the sign of the actual GDP growth, and the important turning points are identified accurately by the model. This also holds true during the recent crisis.     

Extracting Nonlinear Signals from Several Economic Indicators

We develop a twofold analysis of how the information provided by several economic indicators can be used in Markov switching dynamic factor models to identify the business cycle turning points. First, we compare the performance of a fully nonlinear multivariate specification (one‐step approach) with the ‘shortcut’ of using a linear factor model to obtain a coincident indicator, which is then used to compute the Markov switching probabilities (two‐step approach). Second, we examine the role of increasing the number of indicators. Our results suggest that one step is generally preferred to two steps, especially in the vicinity of turning points, although its gains diminish as the quality of the indicators increases. Additionally, we also obtain decreasing returns of adding more indicators with similar signal‐to‐noise ratios. Using the four constituent series of the Stock–Watson coincident index, we illustrate these results for US data. Copyright © 2014 John Wiley & Sons, Ltd.     

Forecasting the New York State economy: The coincident and leading indicators approach

Currently there are no reliable summary indicators of the economic and fiscal condition of states and localities. This deficiency has hampered the efforts of policy makers at the sub-national level to monitor changes in the economic environment and predict how those changes will impact the fiscal health of governments. This paper attempts to fill this analytical vacuum by providing summary indicators of economic and fiscal health for New York State. The models developed are based on the single-index methodology developed by Stock and Watson [(1991). A probability model of the coincident economic indicators. In K. Lahiri and G. H. Moore (eds.), Leading economic indicators: new approaches and forecasting records (pp. 63–85). New York: Cambridge University Press]. This approach allows us to date New York business cycles and compare local cyclical behavior with the nation as a whole. We develop a leading index of economic indicators which predicts future movements in the coincident indicator. The Stock and Watson approach is used to create a fiscal indicator which acts as a summary indicator of revenue performance for New York. In addition, we explore the ability of our economic indicator series to predict future changes in state revenues. We find that changes in the leading indicator series have significant predictive power in forecasting changes in our revenue index.     

Weekly economic activity: Measurement and informational content

We construct a composite index to measure the real activity of the Swiss economy on a weekly frequency. The index is based on a novel high-frequency data set capturing economic activity across distinct dimensions over a long time horizon. We propose a six-step procedure for extracting precise business cycle signals from the raw data. By means of a real-time evaluation, we highlight the importance of our proposed adjustment procedure: (i) our weekly index significantly outperforms a comparable index without adjusted input variables; and (ii) the weekly index outperforms established monthly indicators in nowcasting GDP growth. These insights should help improve other recently developed high-frequency indicators.     

Factor MIDAS for Nowcasting and Forecasting with Ragged‐Edge Data: A Model Comparison for German GDP*

In this article, we merge two strands from the recent econometric literature. First, factor models based on large sets of macroeconomic variables for forecasting, which have generally proven useful for forecasting. However, there is some disagreement in the literature as to the appropriate method. Second, forecast methods based on mixed‐frequency data sampling (MIDAS). This regression technique can take into account unbalanced datasets that emerge from publication lags of high‐ and low‐frequency indicators, a problem practitioner have to cope with in real time. In this article, we introduce Factor MIDAS, an approach for nowcasting and forecasting low‐frequency variables like gross domestic product (GDP) exploiting information in a large set of higher‐frequency indicators. We consider three alternative MIDAS approaches (basic, smoothed and unrestricted) that provide harmonized projection methods that allow for a comparison of the alternative factor estimation methods with respect to nowcasting and forecasting. Common to all the factor estimation methods employed here is that they can handle unbalanced datasets, as typically faced in real‐time forecast applications owing to publication lags. In particular, we focus on variants of static and dynamic principal components as well as Kalman filter estimates in state‐space factor models. As an empirical illustration of the technique, we use a large monthly dataset of the German economy to nowcast and forecast quarterly GDP growth. We find that the factor estimation methods do not differ substantially, whereas the most parsimonious MIDAS projection performs best overall. Finally, quarterly models are in general outperformed by the Factor MIDAS models, which confirms the usefulness of the mixed‐frequency techniques that can exploit timely information from business cycle indicators.     

Factor models for large and incomplete data sets with unknown group structure

Most economic applications rely on a large number of time series, which typically have a remarkable clustering structure and they are available over different spans. To handle these databases, we combined the expectation–maximization (EM) algorithm outlined by Stock and Watson (JBES, 2002) and the estimation algorithm for large factor models with an unknown number of group structures and unknown membership described by Ando and Bai (JAE, 2016; JASA, 2017) . Several Monte Carlo experiments demonstrated the good performance of the proposed method at determining the correct number of clusters, providing the appropriate number of group-specific factors, identifying error-free group membership, and obtaining accurate estimates of unobserved missing data. In addition, we found that our proposed method performed substantially better than the standard EM algorithm when the data had a grouped factor structure. Using the Federal Reserve Economic Data FRED-QD, our method detected two distinct groups of macroeconomic indicators comprising the real activity indicators and nominal indicators. Thus, we demonstrated the usefulness of our group-specific factor model for studies of business cycle chronology and for forecasting purposes.     

Short-term forecasting of GDP with a DSGE model augmented by monthly indicators

DSGE models are useful tools for evaluating the impact of policy changes, but their use for (short-term) forecasting is still in its infancy. Besides theory-based restrictions, the timeliness of data is an important issue. Since DSGE models are based on quarterly data, they suffer from the publication lag of quarterly national accounts. In this paper we present a framework for the short-term forecasting of GDP based on a medium-scale DSGE model for a small open economy within a currency area. We utilize the information available in monthly indicators based on the approach proposed by Giannone et al. (2009). Using Austrian data, we find that the forecasting performance of the DSGE model can be improved considerably by incorporating monthly indicators, while still maintaining the story-telling capability of the model.     

Forecast Overview

The national accounts reported quarterly GDP growth of 0.4% in Q3, up from the preliminary estimate of 0.3%. This continued the run of volatile quarterly readings, with output having contracted 0.2% in Q2. And a series of soft monthly GDP readings, along with some very poor business survey results, suggest that GDP is likely to have flatlined in Q4. This would result in GDP growth of 1.3% for 2019 as a whole, in line with the 2018 outturn which was the weakest since the financial crisis.     

Forecast combination for U.S. recessions with real-time data

This paper proposes the use of forecast combination to improve predictive accuracy in forecasting the U.S. business cycle index, as published by the Business Cycle Dating Committee of the NBER. It focuses on one-step ahead out-of-sample monthly forecast utilising the well-established coincident indicators and yield curve models, allowing for dynamics and real-time data revisions. Forecast combinations use log-score and quadratic-score based weights, which change over time. This paper finds that forecast accuracy improves when combining the probability forecasts of both the coincident indicators model and the yield curve model, compared to each model's own forecasting performance.     

Discussion Paper Abstracts

Some Key Global Adjustment Scenarios and Their Effects on Major Developing Country Regions Forecasting Inflation from the Term Structure: A Cointegration Approach An International CAPM for Bonds and Equities Fiscal and Monetary Policy Under EMU: Credible inflation targets or unpleasant monetary arithmetic? Capital-Skill Complementarity and Relative Employment in West German Manufacturing Estimating Long-run Relationships from Dynamic Heterogeneous Panels Measuring and Forecasting Underlying Economic Activity Discussion Paper No.18–92 Recently, interest in the methodology of constructing coincident economic indicators has been revived by the work of Stock and Watson (1988,1991). They adopt the framework of the state space form and Kalman filter in which to construct an optimal estimate of an unobserved component. This is interpreted as corresponding to underlying economic activity derived from a set of observed indicator variables. In this paper we suggest a modification to the Stock and Watson approach which allows for cointegration between some of the variables. We also discuss the general relationship between cointegration and the appropriate specification of stochastic trend models. The technique is applied to the UK where the observed indicator variables used are those which make up the CSO coincident indicator, therefore constructing alternative measures of economic activity. Two of the calculated series are forecast using a systems VAR with error correction terms, where the VAR consists of the CSO longer leading indicator component variables plus a term structure variable. The derived forecasts represent an alternative longer leading economic indicator. Price and Quantity Responses to Cost and Demand Shocks     

Nowcasting China’s GDP Using a Bayesian Approach

Real time nowcasting is an assessment of current-quarter GDP from timely released economic and financial series before the GDP figure is disseminated. Providing a reliable current quarter nowcast in real time based on the most recently released economic and financial monthly data is crucial for central banks to make policy decisions and longer-term forecasting exercises. In this study, we use dynamic factor models to bridge monthly information with quarterly GDP and achieve reduction in the dimensionality of the monthly data. We develop a Bayesian approach to provide a way to deal with the unbalanced features of the dataset and to estimate latent common factors. We demonstrate the validity of our approach through simulation studies, and explore the applicability of our approach through an empirical study in nowcasting the China’s GDP using 117 monthly data series of several categories in the Chinese market. The simulation studies and empirical study indicate that our Bayesian approach may be a viable option for nowcasting the China’s GDP.     

A comparison of monthly global indicators for forecasting growth

This paper evaluates the predictive content of a set of alternative monthly indicators of global economic activity for nowcasting and forecasting quarterly world real GDP growth using mixed-frequency models. It shows that a recently proposed indicator that covers multiple dimensions of the global economy consistently produces substantial improvements in forecasting accuracy, while other monthly measures have more mixed success. Specifically, the best-performing model yields impressive gains with MSPE reductions of up to 34% at short horizons and up to 13% at long horizons relative to an autoregressive benchmark. The global economic conditions indicator also contains valuable information for assessing the current and future state of the economy for a set of individual countries and groups of countries. This indicator is used to track the evolution of the nowcasts for the U.S., the OECD area, and the world economy during the COVID-19 pandemic and the main factors that drive the nowcasts are quantified.     

A comparison of mixed frequency approaches for nowcasting Euro area macroeconomic aggregates

In this paper, we focus on the different methods which have been proposed in the literature to date for dealing with mixed-frequency and ragged-edge datasets: bridge equations, mixed-data sampling (MIDAS), and mixed-frequency VAR (MF-VAR) models. We discuss their performances for nowcasting the quarterly growth rate of the Euro area GDP and its components, using a very large set of monthly indicators. We investigate the behaviors of single indicator models, forecast combinations and factor models, in a pseudo real-time framework. MIDAS with an AR component performs quite well, and outperforms MF-VAR at most horizons. Bridge equations perform well overall. Forecast pooling is superior to most of the single indicator models overall. Pooling information using factor models gives even better results. The best results are obtained for the components for which more economically related monthly indicators are available. Nowcasts of GDP components can then be combined to obtain nowcasts for the total GDP growth.     

Sparse structures with LASSO through principal components: Forecasting GDP components in the short-run

This paper examines the use of sparse methods to forecast the real (in the chain-linked volume sense) expenditure components of the US and EU GDP in the short-run sooner than national statistics institutions officially release the data. We estimate current-quarter nowcasts, along with one- and two-quarter forecasts, by bridging quarterly data with available monthly information announced with a much smaller delay. We solve the high-dimensionality problem of monthly datasets by assuming sparse structures of leading indicators capable of adequately explaining the dynamics of the analyzed data. For variable selection and estimation of the forecasts, we use LASSO together with its recent modifications. We propose an adjustment that combines LASSO cases with principal components analysis to improve the forecasting performance. We evaluated the forecasting performance by conducting pseudo-real-time experiments for gross fixed capital formation, private consumption, imports, and exports over a sample from 2005–2019, compared with benchmark ARMA and factor models. The main results suggest that sparse methods can outperform the benchmarks and identify reasonable subsets of explanatory variables. The proposed combination of LASSO and principal components further improves the forecast accuracy.     

Forecasting US output growth using leading indicators: an appraisal using MIDAS models

We evaluate the predictive power of leading indicators for output growth at horizons up to 1 year. We use the MIDAS regression approach as this allows us to combine multiple individual leading indicators in a parsimonious way and to directly exploit the information content of the monthly series to predict quarterly output growth. When we use real‐time vintage data, the indicators are found to have significant predictive ability, and this is further enhanced by the use of monthly data on the quarter at the time the forecast is made. Copyright © 2009 John Wiley & Sons, Ltd.     

Monthly forecasting of GDP with mixed-frequency multivariate singular spectrum analysis

The literature on mixed-frequency models is relatively recent and has found applications across economics and finance. The standard application in economics considers the use of (usually) monthly variables (e.g. industrial production) for predicting/fitting quarterly variables (e.g. real GDP). This paper proposes a multivariate singular spectrum analysis (MSSA) based method for mixed-frequency interpolation and forecasting, which can be used for any mixed-frequency combination. The novelty of the proposed approach rests on the grounds of simplicity within the MSSA framework. We present our method using a combination of monthly and quarterly series and apply MSSA decomposition and reconstruction to obtain monthly estimates and forecasts for the quarterly series. Our empirical application shows that the suggested approach works well, as it offers forecasting improvements on a dataset of eleven developed countries over the last 50 years. The implications for mixed-frequency modelling and forecasting, and useful extensions of this method, are also discussed.     

MIDAS vs. mixed-frequency VAR: Nowcasting GDP in the euro area

This paper compares the mixed-data sampling (MIDAS) and mixed-frequency VAR (MF-VAR) approaches to model specification in the presence of mixed-frequency data, e.g. monthly and quarterly series. MIDAS leads to parsimonious models which are based on exponential lag polynomials for the coefficients, whereas MF-VAR does not restrict the dynamics and can therefore suffer from the curse of dimensionality. However, if the restrictions imposed by MIDAS are too stringent, the MF-VAR can perform better. Hence, it is difficult to rank MIDAS and MF-VAR a priori, and their relative rankings are better evaluated empirically. In this paper, we compare their performances in a case which is relevant for policy making, namely nowcasting and forecasting quarterly GDP growth in the euro area on a monthly basis, using a set of about 20 monthly indicators. It turns out that the two approaches are more complements than substitutes, since MIDAS tends to perform better for horizons up to four to five months, whereas MF-VAR performs better for longer horizons, up to nine months.     

Estimation of Common Factors under Cross‐Sectional and Temporal Aggregation Constraints

The paper estimates a large‐scale mixed‐frequency dynamic factor model for the euro area, using monthly series along with gross domestic product (GDP) and its main components, obtained from the quarterly national accounts (NA). The latter define broad measures of real economic activity (such as GDP and its decomposition by expenditure type and by branch of activity) that we are willing to include in the factor model, in order to improve its coverage of the economy and thus the representativeness of the factors. The main problem with their inclusion is not one of model consistency, but rather of data availability and timeliness, as the NA series are quarterly and are available with a large publication lag. Our model is a traditional dynamic factor model formulated at the monthly frequency in terms of the stationary representation of the variables, which however becomes nonlinear when the observational constraints are taken into account. These are of two kinds: nonlinear temporal aggregation constraints, due to the fact that the model is formulated in terms of the unobserved monthly logarithmic changes, but we observe only the sum of the monthly levels within a quarter, and nonlinear cross‐sectional constraints, since GDP and its main components are linked by the NA identities, but the series are expressed in chained volumes. The paper provides an exact treatment of the observational constraints and proposes iterative algorithms for estimating the parameters of the factor model and for signal extraction, thereby producing nowcasts of monthly GDP and its main components, as well as measures of their reliability.