4 The estimation procedure 39
Chapter 4 The estimation procedure This chapter addresses the estimation of the MRW parameters using an itera- ted generalized method of moments (GMM) approach. The originality of this estimation procedure consists in a new moments configuration which improves the performance of the GMM estimation in finite samples. Moreover, we in- troduce an effective initialization method for the variance parameter using a preliminary estimate. 4.1 The iterated GMM estimation Let us denote with index 0 the unknown MRW parameters λ20, ln (T0) and ln (σ0), which we want to estimate from a time series Z (k) , k ∈ N of length N . Accordingly θ0 = ( λ20 ln (T0) ln (σ0) )′ will identify the unknown parameter vector. This is assumed to lie in a given set Θ ⊂ [0, 0.5)×R2.1 The GMM estimator θ̂N is the value of θ, which minimizes the deviation of the sample moments from their theoretical counterparts with respect to the quadratic norm: θ̂N = argmin θ∈Θ QN (θ) (4.1) with QN (θ) = ( 1 N N∑ k=1 f (Z (k) , θ)′ ) WN ( 1 N N∑ k=1 f (Z (k) , θ) ) . (4.2) 1 Without loss of generality we will choose Θ compact for the purpose of empirical ap- plications. 40 Chapter 4. The estimation procedure In this connection, the weighting matrix WN is positive semi-definite and is assumed to converge in probability to a positive definite matrix of constants W . The function f captures the moments employed in the estimation (Greene 2003, pp. 536-538). In this study we employ the moment conditions (3.5), (3.6) and (3.7) with lags...
You are not authenticated to view the full text of this chapter or article.
This site requires a subscription or purchase to access the full text of books or journals.
Do you have any questions? Contact us.Or login to access all content.