Estimation And Testing For Moment Condition Models With Parameter Instability

The traditional moment condition models assume that structural parameters are time-invariant over the entire sample period.However,various economic factors such as time-varying market conditions,technological innovations,market fluctuations,and behavioral changes in rational economic agents may change during the entire sample period.However,the size,duration,and individuals’ characters may lead to abrupt breaks or smooth structural changes while modeling.Therefore,this study investigates the moment condition models with both abrupt break and smooth structural changes.First,this study investigates the fixed-smoothing asymptotics of the GMM estimator based on the moment condition models with an unknown abrupt break,and examines the fixed-smoothing asymptotics that includes the asymptotically equivalent and the limiting distributions of the supremum-type structural change test statistics under the null hypothesis that there is no structural changes in the model and the alternative hypothesis that there is an unknown jump in the model.This study provides a unifying framework for the kernelbased HAC variance estimators with fixed truncation parameter and the orthogonal series HAC variance estimators with fixed-amount basis functions to investigate the fixe-smoothing asymptotics of GMM estimator and the supremum-type tests for the moment conditional model existing an unknown abrupt break.This paper finds that the asymptotically equivalent and the limiting distributions of GMM estimators based on fixed-smoothing weighting matrices are pivotal,and the limiting distribution is mixed normal.For the supremum-type structural change test statistics,their limiting distributions are asymptotically pivotal in the fixed-bandwidth framework,and the asymptotically equivalent and limiting distributions of these test statistics are related to the degree of overidentification of the parameters.When the moment condition model is just-identified and the change point is known,the statistic will asymptotically converge to an F distribution,while the limiting distribution of the statistic will converge to a nonstandard distribution function when the change point is unknown.For the case of orthogonal series HAC variance estimation,the test statistics of just-identified model with a known break will converge to a mixed chi-square distribution as the sample size increases.Secondly,this study considers the moment condition models with structural changes,and establishes the large sample property of the LGMM estimator.We show that the LGMM estimator is consistent and biased asymptotically normal,and the bias disappears with the increase of the sample size,but the convergence rate of bias in the boundary and interior regions are different.Therefore,in order to solve the "boundary effect" of LGMM,this paper uses the reflection method to construct "pseudo data" to correct the boundary bias of LGMM,and then eliminate the estimated "boundary effect".In addition,to detect the smooth structural changes in the time-varying moment condition models,this paper proposes a test statistic based on the sample moment function,which can detect both the smooth structural changes and the multiple or single abrupt breaks in the models.We show that the smooth structural change test statistic asymptotically converges to a normal distribution under the null hypothesis that there is no structural changes in the moment condition models,and the structural change test statistic has better power under the alternative hypothesis.In order to improve the poor performance of the GMM under small samples,this paper develops a new block bootstrap method.This bootstrap takes into account the dependence of the data.The Monte Carlo simulation experiments show that the test statistic proposed in this paper has better finite sample performance than the supremum-type test statistics that is designed to detect the jump change of the parameters.Thirdly,this study examines the large-sample properties of the Local Generalized Mothed of Moments estimator of the misspecified time-varying moment condition models,and investigates the asymptotic behavior under different weighting matrices.We find that the LGMM estimator is consistent among the four weight matrices considered,but the LGMM estimator is an unbiased estimation of the “pseudo-true parameters” when the weighting matrix is the inverse of the decentralized time-varying HAC variance estimator parameter.In order to detect the structural changes in the misspecified moment condition models,this paper proposes a new test based on the distance between the time-varying LGMM estimator and the time-invariant traditional GMM estimator.This paper finds that,except for the case of the non-centralized timevarying HAC weighting matrix,the asymptotic distributions of the test statistic based on other three weighting matrices are normal,but their asymptotic variances are different.Finally,this study investigates the investors’ risk aversion behavior in Chinese and the U.S.financial markets using the proposed LGMM approach.Specifically,based on the Recursive Expected Utility function proposed by Epstein and Zin(1989)[1],this paper examines the time-varying risk aversion,time preference and intertemporal marginal substitution of investors in China and the United States finance markets.The empirical findings show that investors’ risk aversion,time preference factor and intertemporal marginal substitution vary over time,whether it is in the Chinese or the U.S.markets.Finally,this study has important theoretical and application significance.