The Equity Premium and the Risk Free Rate: Matching the Moments

Abstract

This paper investigates the ability of a representative agent model with time separable utility to explain the mean vector and the covariance matrix of the risk free interest rate and the return to leveraged equity in the stock market. The paper generalizes the standard calibration methodology by accounting for the uncertainty in both the sample moments to be explained and the estimated parameters to which the model is calibrated. We develop a testing framework to evaluate the model's ability to match the moments of the data.We study two forms of the model, both of which treat leverage in a manner consistent with the data. In the first, dividends explicitly represent the flow that accrues to the owner of the equity, and they are discounted by the marginal rate of intertemporal substitution defined over consumption. The second form of the model introduces bonds and treats equities as the residual claim to the total endowment stream. We find that the first moments of the data can be matched for a wide range of preference parameter values. But for both models the implied first and second moments taken together are always statistically significantly different from the data at standard levels. This last result contrasts sharply with other recent treatments of leverage in the literature.

Regime Shifts in a Dynamic Term Structure Model of U.S. Treasury Bond Yields

“…There is an extensive empirical literature on bond yields (particularly short-term rates) that suggests that "switching regime" models describe the historical interest rate data better than single-regime models (see, for example, Cecchetti, Lam, and Mark [1993], Gray [1996], Garcia and Perron [1996], and Ang and Bekaert [2002a]). 1 In spite of this evidence, largely for reasons of tractability, most of the empirical literature on DTSMs has continued to focus on single-regime models (see Dai and Singleton [2003] for a survey).…”

House Price Dynamics: Fundamentals and Expectations

“…The solution (13) presents similarities with the bubble component solution (6). But while both solutions introduce persistence in the model with respect to the fundamental solution only the intrinsic bubble model allows for mean reversion of the price-dividend ratio.…”

“…6 We use a Lucas tree type model 7 with a risky asset to obtain a fundamental value for the house price and price-dividend ratio (p t =d t ). We think of the dividend as rent, the stream of consumption and services that is derived from owning 8 (and renting out) a house; we will use the terms dividends and rents interchangeably.…”

The role of simulation methods in Macroeconomics

“…However, even without measurement errors, Sargent (1987) shows that correlations and cross-correlations can contain more information on a given model than sample averages, so that it is important to test the model by confronting the data in many dimensions, using a wide variety of statistics from the multivariate distribution of the variables of interest. 7 Pagan (1994), Canova (1994) and Canova and Ortega (1996), take a more general view. For Canova (1994), calibrating is the full process which starts with the de…nition of the question to be analyzed, selecting a theoretical model, assigning parameter values, generating time series, characterizing its properties, and comfronting them with the similar characteristics in a real economy (empirical regularities), and it may even include economic policy analysis.…”

“…From a purely technical point of view, calibrating a model consists in associating numerical values to its parameters 7 , so that a given numerical solution method can be used to generate time series sample realizations for its variables. Since it associates numerical values to parameters, there is some sense in which calibration is similar to estimation.…”