Nonparametric Estimation of Time-VaryingCharacteristics of Intertemporal Asset Pricing Models

Macroeconomic asset pricing literature is concerned with many puzzling aspects in the financial market. Most prominent are the equity premium puzzle, the risk–free rate puzzle, and the volatility puzzle. Moreover, the literature has come to different conclusions regarding the movement of the risk–to–reward measure over the business cycle. It has been shown that one can improve on those puzzles by the introduction of habit formation, see Campbell and Cochrane (1999), or Boldrin, Christiano and Fisher (1997, 2001). This paper is concerned less with the solution of the above puzzles, but rather with the time variation of the financial measures. Following the above literature we focus on a time varying Sharpe ratio. Campbell and Cochrane (1999) obtain a Sharpe–ratio moving counter–cyclically with respect to the business cycle for an exchange economy. Yet, Lettau and Ludvigson (2003) have pointed out that the risk–return trade/off changes over time with a standard deviation considerably exceeding that suggested by Campbell and Cochrane (1999). In this contribution we demonstrate that the model with habit formation is able to match the observed standard deviation of the Sharpe ratio, since the variables regarding production exhibit a larger standard deviation than consumption, and (ii) the restrictive assumptions associated with the log–linear solution of Campbell and Cochrane are relaxed. We solve and estimate the model based on the solution technique of Den Haan and Marcet (1990). In our estimation approach we are able to use full structural information and, consequently, Monte Carlo simulations show that our estimations are less biased and more effcient than the widely applied GMM procedure. Based on quarterly U.S. data we estimate the structural parameters of the model and investigate its Sharpe ratio for preferences with habit persistence. We find indication that the model is able to capture the time variation of the Sharpe ratio, i.e. its standard deviation. We obtain a negative relation betwe