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     

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.     

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 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.     

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.     

The missing link: using the NBER recession indicator to construct coincident and leading indices of economic activity

We use the information content in the decisions of the NBER Business Cycle Dating Committee to construct coincident and leading indices of economic activity for the United States. We identify the coincident index by assuming that the coincident variables have a common cycle with the unobserved state of the economy, and that the NBER business cycle dates signify the turning points in the unobserved state. This model allows us to estimate our coincident index as a linear combination of the coincident series. We compare the performance of our index with other currently popular coincident indices of economic activity.     

Processes with volatility-induced stationarity: an application for interest rates

In this paper we propose a refinement of the existing definition of volatility-induced stationarity that allows us to distinguish between processes with drift and diffusion induced stationarity and processes with pure volatility-induced stationarity. We also propose a classification of stationary processes with volatility-induced stationarity according to the volatility that is needed to inject stationarity. Processes with volatility-induced stationarity are potentially applicable to interest rate time-series since, as has been acknowledged, mean-reversion effects occur mainly in periods of high volatility. As such, we provide evidence that the logarithm of the Fed funds rate can be modelled as a local martingale with volatility-induced stationarity.     

Forecasting by factors,by variables,by both or neither?

We consider forecasting with factors, variables and both, modeling in-sample using Autometrics so all principal components and variables can be included jointly, while tackling multiple breaks by impulse-indicator saturation. A forecast-error taxonomy for factor models highlights the impacts of location shifts on forecast-error biases. Forecasting US GDP over 1-, 4- and 8-step horizons using the dataset from Stock and Watson (2009) updated to 2011:2 shows factor models are more useful for nowcasting or short-term forecasting, but their relative performance declines as the forecast horizon increases. Forecasts for GDP levels highlight the need for robust strategies, such as intercept corrections or differencing, when location shifts occur as in the recent financial crisis.     

Variable selection, estimation and inference for multi-period forecasting problems

This paper conducts a broad-based comparison of iterated and direct multi-period forecasting approaches applied to both univariate and multivariate models in the form of parsimonious factor-augmented vector autoregressions. To account for serial correlation in the residuals of the multi-period direct forecasting models we propose a new SURE-based estimation method and modified Akaike information criteria for model selection. Empirical analysis of the 170 variables studied by Marcellino, Stock and Watson (2006) shows that information in factors helps improve forecasting performance for most types of economic variables although it can also lead to larger biases. It also shows that SURE estimation and finite-sample modifications to the Akaike information criterion can improve the performance of the direct multi-period forecasts.     

Zum Problem der Saisonbereinigung ökonomischer Zeitreihen

Summary In this paper various aspects of seasonal adjustment of economic time series are discussed. Firstly, criteria relating to the adequacy of adjustment procedures based on spectral analysis of stationary stochastic processes are reviewed critically. In this context, some of the well-known adjustment procedures are critizised from a basic point of view: in general, they mostly lean heavily on the theory of stationary stochastic processes if a well-defined theoretical background can be detected at all. However, this very theory is of questionable value only in analyzing or adjusting especially economic time series since it implies a seasonal component of constant variance. Since no real seasonal component is of constant variance, adjustment procedures based on this theory have to be manipulated in various tricky ways so as to meet the fact of non-constancy of the variance. But this leads to a state of affairs which is unsatisfactory both from a practical and a theoretical point of view.The main purpose of the paper consists in the presentation of an adjustment procedure which avoids the defects mentioned above. It is formulated in terms of the theory of non-stationary stochastic processes where non-stationarity is defined suitably so as to allow a changing seasonal pattern of non-constant variance. Besides overcoming in this way the restrictive assumption of stationarity, the proposed procedure allows the estimation of the seasonal component directly, i. e. without estimating a smooth component in a first step. This is an important advantage of this procedure over the conventional procedures which is of a highly practical relevance. A practical example is given.     

Comparing Alternative Predictors Based on Large‐Panel Factor Models

This article compares the predictive ability of the factor models of Stock and Watson (2002a) and Forni, Hallin, Lippi and Reichlin (2005) using a ‘large’ panel of macroeconomic variables of the United States. We propose a nesting procedure of comparison that clarifies and partially overturns the results of similar exercises in the literature. Our main conclusion is that with the dataset at hand the two methods have a similar performance and produce highly collinear forecasts.     

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.     

Stability results for nonlinear error correction models

This paper studies analogs of Granger's representation theorem in the context of a general nonlinear vector autoregressive error correction model. The model allows for nonlinear autoregressive conditional heteroskedasticity and the conditional distribution involved can be a mixture distribution of a rather general type. Mixture models of this kind can be thought of as generalizations of threshold models and they have attracted attention in the recent time series and econometrics literature. The paper develops a useful transformation which shows how the nonlinear error correction model can be transformed to a nonlinear vector autoregressive model so that available results on the stationarity or nonstationarity of the latter can be used for the former. The most satisfactory results are obtained in a model in which a specific structural relation between the nonlinearity and equilibrium correction prevails. Without this structural relation only a lower bound for the number of long-run equilibrium relations can explicitly be determined because the exact number depends on properties of the first and second moments of a nonlinear stationary component of the process.     

平滑转换自回归模型的平稳性问题研究

根据时间序列宽平稳的定义,本文认为,平滑转换自回归模型的序列不是宽平稳序列,利用ADF统计量检验其平稳性是没有意义的;其次,依据马尔科夫链的遍历性,我们认为,STAR模型的序列是严平稳序列,且通过对模型系数的联合取值的限制保证了模型的平稳性。以一阶对数平滑转换自回归模型为例,其平稳的条件是,β与r符号相反,且|β+r|<1,β可以等于1,也可以绝对值小于1。     

Purchasing power parity as a long-run relation

Dickey–Fuller and Stock–Watson tests of purchasing power parity (PPP) as a long-run proposition are provided within the cointegration framework proposed by Granger. Since different countries use different weights to construct price indices, the traditional constraint that the coefficients on the price indices should be unity in the log-linear PPP relation is relaxed. The absence of a general PPP relation cannot be rejected. At most, a PPP relation is indicated in five out of fifteen country pairs that are examined. Even if a long-run PPP relation exists, it is not found to be useful in predicting future nominal exchange rates, which is consistent with efficient speculative markets.     

Dynamic factor model with infinite‐dimensional factor space: Forecasting

The paper compares the pseudo real‐time forecasting performance of three dynamic factor models: (i) the standard principal component model introduced by Stock and Watson in 2002; (ii) the model based on generalized principal components, introduced by Forni, Hallin, Lippi, and Reichlin in 2005; (iii) the model recently proposed by Forni, Hallin, Lippi, and Zaffaroni in 2015. We employ a large monthly dataset of macroeconomic and financial time series for the US economy, which includes the Great Moderation, the Great Recession and the subsequent recovery (an update of the so‐called Stock and Watson dataset). Using a rolling window for estimation and prediction, we find that model (iii) significantly outperforms models (i) and (ii) in the Great Moderation period for both industrial production and inflation, and that model (iii) is also the best method for inflation over the full sample. However, model (iii) is outperformed by models (ii) and (i) over the full sample for industrial production.     

HAZARDS IN IMPLEMENTING A MONETARY CONDITIONS INDEX

Some recent studies have suggested constructing a Monetary Conditions Index (or MCI) to serve as an indicator of monetary policy stance. The central banks of Canada, Sweden and Norway all construct an MCI and (to varying degrees) use it in conducting monetary policy. Empirically, an MCI is calculated as the weighted sum of changes in a short-term interest rate and the exchange rate relative to values in a baseline year. The weights aim to reflect these variables’ effects on longer-term focuses of policy — economic activity and inflation. This paper derives analytical and empirical properties of MCIs in an attempt to ascertain their usefulness in monetary policy. An MCI assumes an underlying model relating economic activity and inflation to the variables in the MCI. Several issues arise for that model, including its empirical constancy, cointegration, exogeneity, dynamics and potential omitted variables. Because of its structure, the model is unlikely to be constant or to have strongly exogenous variables, yet constancy and exogeneity are critical for the usefulness of an MCI. Empirical analyses of Canadian, Swedish and Norwegian MCIs confirm such difficulties. Thus, the value of an MCI for conduct of economic policy is in doubt.     

Spurious Regression and Trending Variables*

This paper analyses the asymptotic and finite‐sample implications of different types of non‐stationary behaviour among the dependent and explanatory variables in a linear spurious regression model. We study cases when the non‐stationarity in the dependent and explanatory variables is deterministic as well as stochastic. In particular, we derive the order in probability of the t‐statistic in a spurious regression equation under a variety of empirically relevant data generation processes, and show that the spurious regression phenomenon is present in all cases when both dependent and explanatory variables behave in a non‐stationary way. Simulation experiments confirm our asymptotic results.     

The Flexible Fourier Form and Local Generalised Least Squares De‐trended Unit Root Tests*

In two recent papers Enders and Lee (2009) and Becker, Enders and Lee (2006) provide Lagrange multiplier and ordinary least squares de‐trended unit root tests, and stationarity tests, respectively, which incorporate a Fourier approximation element in the deterministic component. Such an approach can prove useful in providing robustness against a variety of breaks in the deterministic trend function of unknown form and number. In this article, we generalize the unit root testing procedure based on local generalized least squares (GLS) de‐trending proposed by Elliott, Rothenberg and Stock (1996) to allow for a Fourier approximation to the unknown deterministic component in the same way. We show that the resulting unit root tests possess good finite sample size and power properties and the test statistics have stable non‐standard distributions, despite the curious result that their limiting null distributions exhibit asymptotic rank deficiency.     

Modelling Inflation Volatility

This paper discusses estimation of US inflation volatility using time‐varying parameter models, in particular whether it should be modelled as a stationary or random walk stochastic process. Specifying inflation volatility as an unbounded process, as implied by the random walk, conflicts with priors beliefs, yet a stationary process cannot capture the low‐frequency behaviour commonly observed in estimates of volatility. We therefore propose an alternative model with a change‐point process in the volatility that allows for switches between stationary models to capture changes in the level and dynamics over the past 40 years. To accommodate the stationarity restriction, we develop a new representation that is equivalent to our model but is computationally more efficient. All models produce effectively identical estimates of volatility, but the change‐point model provides more information on the level and persistence of volatility and the probabilities of changes. For example, we find a few well‐defined switches in the volatility process and, interestingly, these switches line up well with economic slowdowns or changes of the Federal Reserve Chair. Moreover, a decomposition of inflation shocks into permanent and transitory components shows that a spike in volatility in the late 2000s was entirely on the transitory side and characterized by a rise above its long‐run mean level during a period of higher persistence. Copyright © 2015 John Wiley & Sons, Ltd.