Consistent estimation of asset pricing models using generalized spectral estimator

This paper essentially extends the generalized spectral estimation of Berkowitz (2001) to provide a consistent generalized spectral estimator (GSE), considering all the information available, possibly with in…nite dimensions, based upon Escanciano (2006). Our estimator can entertain the strengths of the Berkowitz-GSE over the standard GMM. In contrast, more importantly, the newly proposed estimator has consistency which the Berkowitz-GSE is de…cient in, overcoming Domínguez and Lobato’s (2004) critique on the identi…ability of the GMM approach. Furthermore, our estimator is more general, based upon fairly relaxed assumptions for its asymptotic behaviors, than the Berkowitz-GSE. Finally, as an empirical application, using the proposed estimation strategy, we estimate the standard consumption-based asset pricing model in Hansen and Singleton (1982) to investigate the possibility that the equity premium puzzle may be due to underidenti…cation of risk aversion parameters. JEL Classi…cation: C13; C22 Keywords: Identi…cation; Conditional moment; Spectral analysis Department of Economics, 105 Wylie Hall, 100 S. Woodlawn, Bloomington, IN 47405, U.S.A.; [email protected]. I would like to thank my advisor, Professor Juan Carlos Escanciano for many helpful comments and suggestions. All errors are mine. 1 Introduction Since introduced by Hansen (1982), the generalized method of moments (GMM) has been widely used to estimate conditional moment restrictions implied by economic theories. Among a variety of the advantages, GMM has immediately gained popularity in econometrics mainly because no distributional assumptions are needed. For instance, as micro-founded macroeconomics becomes standard in the decade, a great number of literature in …nance and macroeconomics has employed the GMM approach to estimate a speci…c type of conditional moment restrictions called the Euler equations, which characterize the agents’ decisionmaking resulting from the utility maximization; for illustration, see Hansen and Singleton (1982), Harvey (1991), and Gali and Gertler (1999). Although most applications of GMM are based upon the time domain approach, Berkowitz’s (2001) work is remarkable in the sense that he proposes a frequency domain version of GMM, named generalized spectral estimator (GSE).1 In estimating parameters of interest, both approaches convert conditional moment restrictions into unconditional moments, whereas subsequent procedures would be entirely di¤erent across the two approaches. To clarify this point, suppose we derive arbitrary conditional moment restrictions from the theory as follows: E[h(Yt; 0)jXt] = 0 a:s: for a unique value 0 2 , where R (1) Then, to apply the standard GMM or GSE appoach, econometricians take into account unconditional moments as their moment conditions: E[h(Yt; 0)g(Xt)] = 0 a:s: for any given g( ) (2) Given the population condition (2), the standard estimation strategy in the literature is …rmly based upon the assumption that 0 is globally identi…ed, arbitrarily selecting a …nite number of unconditional moments out of in…nite candidates of g(Xt), and then minimizing a sample analogue of the objective function to yield GMM-type estimators. However, Domínguez and Lobato (2004) point out that the key assumption in the GMM literature may be seriously ‡awed and thus give rises to nontrivial problems in terms of consistency because the unconditional moments utilize fairly limited information on the data generating process, 1In his earlier working paper version, Berkowitz (1996) named the proposed methodology as Spectral GMM. However, Chacko and Viceira (2003) also use the term to denote their estimation strategy for continuous-time stochastic models based upon the characteristic function. In order to avoid confusion, we do not use the term Spectral GMM in this paper.