In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

A finite sample correction for the variance of linear efficient two-step GMM estimators

Weak instruments arise when the instruments in linear instrumental variables (IV) regression are weakly correlated with the included endogenous variables. In generalized method of moments (GMM), more generally, weak instruments correspond to weak identification of some or all of the unknown parameters. Weak identification leads to GMM statistics with nonnormal distributions, even in large samples, so that conventional IV or GMM inferences are misleading. Fortunately, various procedures are now available for detecting and handling weak instruments in the linear IV model and, to a lesser degree, in nonlinear GMM.

A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments

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We model dividend and consumption growth rates as containing a small long-run predictable component and economic uncertainty (i.e., growth rate volatility) as being time-varying. The magnitudes of the predictable variation and changing volatility in growth rates, as in the data, are quite small. These growth rate dynamics, for which we provide empirical support, in conjunction with plausible parameter configurations of the Epstein and Zin (1989) preferences can explain key observed asset markets phenomena. In particular, we show that the model can justify the observed equity premium, the low risk free rate, and the ex-post volatilities of the market return, real risk free rate, and the price-dividend ratio. As in the data, the model also implies that dividend yields predict returns and that market return volatility is stochastic. The main economic insight we capture is that news about growth rates significantly alter agent's perceptions regarding long run expected growth rates and growth rate uncertainty--in equilibrium, this leads to a large equity risk premium, low risk free interest rate, and large market volatility.

Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles

We model consumption and dividend growth rates as containing (1) a small longrun predictable component, and (2) fluctuating economic uncertainty (consumption volatility). These dynamics, for which we provide empirical support, in conjunction with Epstein and Zin’s (1989) preferences, can explain key asset markets phenomena. In our economy, financial markets dislike economic uncertainty and better long-run growth prospects raise equity prices. The model can justify the equity premium, the risk-free rate, and the volatility of the market return, risk-free rate, and the price‐ dividend ratio. As in the data, dividend yields predict returns and the volatility of returns is time-varying.

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We investigate the small-sample properties of three alternative generalized method of moments (GMM) estimators of asset-pricing models. The estimators that we consider include ones in which the weighting matrix is iterated to convergence and ones in which the weighting matrix is changed with each choice of the parameters. Particular attention is devoted to assessing the performance of the asymptotic theory for making inferences based directly on the deterioration of GMM criterion functions.

Finite sample properties of some alternative GMM estimators

Is individual labor income more risky in recessions? This is a difficult question to answer because existing panel data sets are so short. To address this problem, we develop a generalized method of moments estimator that conditions on the macroeconomic history that each member of the panel has experienced. Variation in the cross‐sectional variance between households with differing macroeconomic histories allows us to incorporate business cycle information dating back to 1930, even though our data do not begin until 1968. We implement this estimator using household‐level labor earnings data from the Panel Study of Income Dynamics. We estimate that idiosyncratic risk is (i) highly persistent, with an annual autocorrelation coefficient of 0.95, and (ii) strongly countercyclical, with a conditional standard deviation that increases by 75 percent (from 0.12 to 0.21) as the macroeconomy moves from peak to trough.

https://www.jstor.org/stable/10.1086/383105

Cyclical Dynamics in Idiosyncratic Labor Market Risk

A striking feature of U.S. data on income and consumption is that inequality increases with age. Using both panel data and an equilibrium life cycle model, we argue that this is informative for understanding the importance and the characteristics of idiosyncratic labor market risk. We find that uncertainty distributed throughout the working years accounts for 40 percent of life time uncertainty, with the remainder being realized prior to entering the labor market. We estimate that the shocks received over the life cycle contain a highly persistent component, with an autocorrelation coefficient between 0.98 and unity. The joint behavior of earnings and consumption inequality, interpreted using our model, adds to the body of evidence suggesting that labor market risks are imperfectly pooled and that a precautionary motive is an important aspect of U.S. savings behavior. The restrictions imposed by general equilibrium theory play an important role in arriving at each of these conclusions.

Amir Yaron

Papers

Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles

Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles

Finite sample properties of some alternative GMM estimators

Cyclical Dynamics in Idiosyncratic Labor Market Risk

Consumption and Risk Sharing Over the Life Cycle