There is a growing body of evidence that traditional asymptotically efficient momentbased estimators for the linear structural model may have large biases for the relatively small sample sizes usually encountered in applied economic research (see, e.g., Newey and Smith, 2000). Furthermore, instrumental variables that are utilized in the context of a set of moment-orthogonality conditions may be only weakly correlated with the endogenous variables in the model and consequently the parameters of the structural model are only poorly or weakly identified. In these situations it is generally recognized that, for both traditional and nontraditional estimators, bias and variability problems may arise and that large sample normal approximations provide a poor basis for finite sample performance (see, e.g., Nelson and Startz, 1990; Maddala and Jeong, 1992; Bound et al., 1995; Stock and Wright, 2000). Given these general problem areas the focus of this chapter is on semiparametric estimation and inference relative to the response parameters for a linear structural statistical model. Using Monte Carlo sampling procedures and a range of underlying data-sampling processes, we provide finite sample comparisons of the two-stage least squares (2SLS) and the empirical likelihood (EL) estimator for recovering the unknown parameters of the linear structural statistical model.