Alternative ways of conducting inference and measurement for long-horizon forecasting are explored with an application to dividend yields as predictors of stock returns. Monte Carlo analysis indicates that the L. Hansen and R. Hodrick (1980) procedure is biased at long horizons, but the alternatives perform better. These include an estimator derived under the null hypothesis as in M. Richardson and T. Smith (1991), a reformulation of the regression as in N. Jegadeesh (1990), and a vector autoregression (VAR) as in J. Campbell and R. Shiller (1988), S. Kandel and R. Stambaugh (1988), and J. Campbell (1991). The statistical properties of long-horizon statistics generated from the VAR indicate interesting patterns in expected stock returns. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

Alternative ways of conducting inference and measurement for long-horizon forecasting are explored with an application to dividend yields as predictors of stock returns. Monte Carlo analysis indicates that the Hansen and Hodrick (1980) procedure is biased at long horizons, but the alternatives perform better. These include an estimator derived under the null hypothesis as in Richardson and Smith (1991), a reformulation of the regression as in Jegadeesh (1990), and a vector autoregression (VAR) as in Campbell and Shiller (1988), Kandel and Stambaugh (1988), and Campbell (1991). The statistical properties of long-horizon statistics generated from the VAR indicate interesting patterns in expected stock returns.

[Alternative ways of conducting inference and measurement for long-horizon forecasting are explored with an application to dividend yields as predictors of stock returns. Monte Carlo analysis indicates that the Hansen and Hodrick (1980) procedure is biased at long horizons, but the alternatives perform better. These include an estimator derived under the null hypothesis as in Richardson and Smith (1991), a reformulation of the regression as in Jegadeesh (1990), and a vector autoregression (VAR) as in Campbell and Shiller (1988), Kandel and Stambaugh (1988), and Campbell (1991). The statistical properties of long-horizon statistics generated from the VAR indicate interesting patterns in expected stock returns.]

This paper examines recent theoretical and empirical analyses that may help us understand and eventually model the observed movements of foreign exchange rates and stock prices. Whether these prices are rational, efficient, and hence not excessively volatile is, of course, a joint hypothesis. The question in the title can never be answered in the abstract. We must always compare actual volatility to the volatility implied by a benchmark model.

Investigations of the basic risk-return trade-off for the market return typically use maximum likelihood estimation (MLE) with a monthly or quarterly horizon and data sampled to match the horizon even though daily data are available. We develop an overlapping data inference methodology for such models that uses all of the data while maintaining the monthly or quarterly forecasting period. Our approach recognizes that the first order conditions of MLE can be used as orthogonality conditions of the generalized method of moments (GMM). While parameter estimates from the different non-overlapping monthly samples that start on different days vary substantively, a formal test does not reject parameter equality and constrained estimation of the risk-return trade-off produces a statistically significant value of 3.35 in post-1955 data.

This paper first characterizes the predictable components in excess rates of returns on major equity and foreign-exchange markets using lagged excess returns, dividend yields, and forward premiums as instruments. Vector autoregressions demonstrate one-step-ahead predictability and facilitate calculations of implied long-horizon statistics, such as variance ratios. Estimation of latent variable models then subjects the vector autoregressions to constraints derived from dynamic asset pricing theories. Examination of volatility bounds on intertemporal marginal rates of substitution provides summary statistics that quantify the challenge facing dynamic asset pricing models.

Evidence of excess volatilities of asset prices compared with those of market fundamentals is often attributed to speculative bubbles. This study demonstrates that bubbles could in theory lead to excess volatility, but it shows that certain variance bounds tests preclude bubbles as an explanation. The evidence ought to be attributed to model misspecification or inappropriate statistical tests. One important misspecification occurs if a researcher incorrectly specifies the time series properties of market fundamentals. A bubble‐free example economy characterized by a potential switch in government policies produces asset prices that would appear, to an unwary researcher, to contain bubbles.

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