xthtaylor fits panel-data random-effects models in which some of the covariates are correlated with the unobserved individual-level random effect. The estimators, originally proposed by Hausman & Taylor (1981) and Amemiya & MaCurdy (1986), are based on instrumental variables. By default, xthtaylor uses the Hausman-Taylor estimator. When the amacurdy option is specified, xthtaylor uses the Amemiya-MaCurdy estimator.
Although the estimators implemented in xthtaylor and xtivreg (see [XT] xtivreg) use the method of instrumental variables, each command is designed for different problems.
The estimators implemented in xtivregassume that a subset of the explanatory variables in the model are correlated with the idiosyncratic error e[i,t]. In contrast, the Hausman-Taylor and Amemiya-MaCurdy estimators that are implemented in xthtaylorassume that some of the explanatory variables are correlated with the individual-level random effects, u[i], but that none of the explanatory variables are correlated with the idiosyncratic error e[i,t].