Measuring underlying economic activity

Recently, interest in the methodology of constructing coincident economic indicators has been revived by the work of Stock and Watson (1989b). 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 apply the Stock and Watson approach to the UK where the observed indicator variables are those that make up the Central Statistical Office (CSO) coincident indicator. The time series properties of the indicator variables are examined and three of the five variables are first difference stationary and are cointegrated, the remaining two are stationary in levels. We then construct two alternative measures of economic activity, each of which deals with the different orders of stationarity of the variables. The first uses the levels of the observed component variables that allows for the cointegrating relationship. The second imposes stationarity on the I(1) variables before the estimation by taking first differences. The levels index is viewed as the preferred specification as it allows for the long-run relationships between the variables and has a superior statistical fit. ©1996 John Wiley & Sons, Ltd.     

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.     

A new coincident index of business cycles based on monthly and quarterly series

Popular monthly coincident indices of business cycles, e.g. the composite index and the Stock–Watson coincident index, have two shortcomings. First, they ignore information contained in quarterly indicators such as real GDP. Second, they lack economic interpretation; hence the heights of peaks and the depths of troughs depend on the choice of an index. This paper extends the Stock–Watson coincident index by applying maximum likelihood factor analysis to a mixed‐frequency series of quarterly real GDP and monthly coincident business cycle indicators. The resulting index is related to latent monthly real GDP. Copyright © 2002 John Wiley & Sons, Ltd.     

A Reduced Rank Regression Approach to Coincident and Leading Indexes Building*

This paper proposes a reduced rank regression framework for constructing a coincident index (CI) and a leading index (LI). Based on a formal definition that requires that the first differences of the LI are the best linear predictor of the first differences of the CI, it is shown that the notion of polynomial serial correlation common features can be used to build these composite variables. Concepts and methods are illustrated by an empirical investigation of the US business cycle indicators.     

Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment*

We introduce a general class of periodic unobserved component (UC) time series models with stochastic trend and seasonal components and with a novel periodic stochastic cycle component. The general state space formulation of the periodic model allows for exact maximum likelihood estimation, signal extraction and forecasting. The consequences for model‐based seasonal adjustment are discussed. The new periodic model is applied to postwar monthly US unemployment series from which we identify a significant periodic stochastic cycle. A detailed periodic analysis is presented including a comparison between the performances of periodic and non‐periodic UC models.     

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.     

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     

Sectoral Survey‐based Confidence Indicators for Europe*

We analyse a novel dataset of Business and Consumer Surveys, using dynamic factor techniques, to produce composite coincident indices (CCIs) at the sectoral level for the European countries and for Europe. Surveys are timely available, not subject to revision, and fully comparable across countries. Moreover, the substantial discrepancies in activity at the sectoral level justify the interest in sectoral disaggregation. Compared with the confidence indicators produced by the European Commission we show that factor‐based CCIs, using survey answers at a more disaggregate level, produce higher correlation with the reference series for the majority of sectors and countries.     

Modelling Regime‐Specific Stock Price Volatility*

Single‐state generalized autoregressive conditional heteroscedasticity (GARCH) models identify only one mechanism governing the response of volatility to market shocks, and the conditional higher moments are constant, unless modelled explicitly. So they neither capture state‐dependent behaviour of volatility nor explain why the equity index skew persists into long‐dated options. Markov switching (MS) GARCH models specify several volatility states with endogenous conditional skewness and kurtosis; of these the simplest to estimate is normal mixture (NM) GARCH, which has constant state probabilities. We introduce a state‐dependent leverage effect to NM‐GARCH and thereby explain the observed characteristics of equity index returns and implied volatility skews, without resorting to time‐varying volatility risk premia. An empirical study on European equity indices identifies two‐state asymmetric NM‐GARCH as the best fit of the 15 models considered. During stable markets volatility behaviour is broadly similar across all indices, but the crash probability and the behaviour of returns and volatility during a crash depends on the index. The volatility mean‐reversion and leverage effects during crash markets are quite different from those in the stable regime.     

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.     

Identification of Slowdowns and Accelerations for the Euro Area Economy*

Business cycle analyses have proved to be helpful to practitioners in assessing current economic conditions and anticipating upcoming fluctuations. In this article, we focus on the acceleration cycle in the euro area, namely the peaks and troughs of the growth rate which delimit the slowdown and acceleration phases of the economy. Our aim is twofold: first, we put forward a reference turning point chronology of this cycle on a monthly basis, based on gross domestic product and industrial production indices. We consider both euro area aggregate level and country‐specific cycles for the six main countries of the zone. Second, we come up with a new turning point indicator, based on business surveys carefully watched by central banks and short‐term analysts, to follow in real‐time the fluctuations of the acceleration cycle.     

The Beveridge–Nelson decomposition in retrospect and prospect

Beveridge and Nelson [Beveridge, Stephen, Nelson, Charles R., 1981. A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the ‘business cycle’. Journal of Monetary Economics 7, 151–174] proposed that the long-run forecast is a measure of trend for time series such as GDP that do not follow a deterministic path in the long run. They showed that if the series is stationary in first differences, then the estimated trend is a random walk with drift that accounts for growth, and the cycle is stationary. In contrast to linear de-trending, the smoother of Hodrick and Prescott (1981) and Hodrick and Prescott [Hodrick, Robert, Prescott, Edward C., 1997. Post-war US business cycles: An empirical investigation. Journal of Money Credit and Banking 29 (1), 1–16] and the unobserved components model of Harvey, [Harvey, A.C., 1985. Trends and cycles in macroeconomic time series. Journal of Business and Economic Statistics 3, 216–227]. Watson [Watson, Mark W., 1986. Univariate detrending methods with stochastic trends Journal of Monetary Economics 18, 49–75] and Clark [Clark, Peter K., 1987. The cyclical component of US economic activity. The Quarterly Journal of Economics 102 (4), 797–814], the BN decomposition attributes most variation in GDP to trend shocks while the cycles are short and brief. Since each is an estimate of the transitory part of GDP that will die out, it seems natural to compare cycle measures by their ability to forecast future growth. The results presented here suggest that cycle measures contain little if any information beyond the short-term momentum captured by BN.     

Monitoring recessions: A Bayesian sequential quickest detection method

Monitoring business cycles faces two potentially conflicting objectives: accuracy and timeliness. To strike a balance between these dual objectives, we propose a Bayesian sequential quickest detection method to identify turning points in real time with a sequential stopping time as a solution. Using four monthly indexes of real economic activity in the United States, we evaluated the method’s real-time ability to date the past five recessions. The proposed method identified similar turning-point dates as the National Bureau of Economic Research (NBER), with no false alarms, but on average, it dated peaks four months faster and troughs 10 months faster relative to the NBER announcement. The timeliness of our method is also notable compared to the dynamic factor Markov-switching model: the average lead time was about five months when dating peaks and two months when dating troughs.     

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.     

STATE DEPENDENCE AND HETEROGENEITY IN HEALTH USING A BIAS‐CORRECTED FIXED‐EFFECTS ESTIMATOR

This paper estimates a dynamic ordered probit model of self‐assessed health with two fixed effects: one in the linear index equation and one in the cut‐points. This robustly controls for heterogeneity in unobserved health status and in reporting behavior, although we cannot separate both sources of heterogeneity. We find important state dependence effects, and small but significant effects of income and other socioeconomic variables. Having dynamics and flexibly accounting for unobserved heterogeneity matters for those estimates. We also contribute to the bias correction literature in nonlinear panel models by comparing and applying two of the existing proposals to our model. Copyright © 2012 John Wiley & Sons, Ltd.     

Indirect estimation of large conditionally heteroskedastic factor models,with an application to the Dow 30 stocks

We derive indirect estimators of conditionally heteroskedastic factor models in which the volatilities of common and idiosyncratic factors depend on their past unobserved values by calibrating the score of a Kalman-filter approximation with inequality constraints on the auxiliary model parameters. We also propose alternative indirect estimators for large-scale models, and explain how to apply our procedures to many other dynamic latent variable models. We analyse the small sample behaviour of our indirect estimators and several likelihood-based procedures through an extensive Monte Carlo experiment with empirically realistic designs. Finally, we apply our procedures to weekly returns on the Dow 30 stocks.     

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.     

Improved recession dating using stock market volatility

We offer an improved dating of U.S. business cycle turning points both retrospectively and in real time. This improvement is made possible by augmenting existing Markov-switching dynamic factor models with additional information on the stock return volatility. The model improves the prediction of the state of the economy using fully revised data significantly. Real-time identification can be made noticeably earlier than the NBER announcements, beating both the peak and trough announcements for recent recessions by several months.     

Dating Business Cycles: A Methodological Contribution with an Application to the Euro Area

This paper proposes a dating algorithm based on an appropriately defined Markov chain that enforces alternation of peaks and troughs, and duration constraints concerning the phases and the full cycle. The algorithm, which implements Harding and Pagan's non‐parametric dating methodology, allows an assessment of the uncertainty of the estimated turning points caused by filtering and can be used to construct indices of business cycle diffusion, aiming at assessing how widespread are cyclical movements throughout the economy. Its adaptation to the notion of a deviation cycle and the imposition of depth constraints are also discussed. We illustrate the algorithm with reference to the issue of dating the euro‐area business cycle and analysing its characteristics, both from the classical and the growth cycle perspectives.     

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.