A Unified Theory of Consistent Estimation for Parametric Models

Abstract

Ve present a general theory of consistent estimation for possibly misspecified parametric models based on recent results of Domowitz and White [17].This theory extends the iinification of Burguete, Gallant and Souza [12] by allowing for heterogeneous, time dependent data and d3mamic models. The theory is applied to yield consistency results for quasi-maximum likelihood and method of moments estimators. Of particular interest is a new generalized rank condition for identifiability. SEP 3 19851 .

Quasi-maximum likelihood estimation of volatility with high frequency data

“…In addition, Bates and White (1985) extend the theory to general quasi-M-estimators, by introducing discrepancy functions. Now, we add more randomness to the misspecification theory, which enables our applications to stochastic volatility models, where the parameter of interest itself is random.…”

“…In these articles, the framework of misspecified estimation has been built and its close connection with Kullback-Leibler Information Criterion (KLIC) (see Kullbacks and Leibler (1951)) has been illustrated. Since these seminal works, Domowitz and White (1982) and Bates and White (1985) have extended the consistency results of the QMLE with i.i.d. models to various cases including dependent observations, Quasi-GMM-estimators, and Quasi-M-estimators.…”

The Impact of Foreign Equity Ownership on Emerging Market Share Price Volatility

“…Under very general conditions, it can be shown that σ -2 jT -1/T ΣS j t r 0 with probability one. A similar formulation of asymptotically valid moment conditions appears in the theoretical treatment of Bates and White (1985), for example. Equations (A7) are consistent with the theoretical model structure, as long as almost surely, for example, which holds as long as 1/T Σω t z t -1/T Σω -T z t r 0 base-level variances (and their averages) are …”

Optimal comparison of misspecified moment restriction models under a chosen measure of fit

“…Although it is beyond the scope of this paper, we suggest two directions to relax this assumption. First, Assumption 1(b) may be generalized by using the notion of ''identifiably unique parameters'' in Domowitz and White (1982, Definition 2.1), which are not required to converge to a limit (see also Bates and White (1985) for a detailed discussion on consistency). Second, a recent paper by Shi (2009) proposed the notion of ''pseudo-true sets'' 10 In MATLAB, fmincon allows nonlinear constraints.…”