Measuring Bias and Uncertainty in Ideal Point Estimates Via the Parametric Bootstrap

Abstract

Over the last 15 years a large amount of scholarship in legislative politics has used NOMINATE or other similar methods to construct measures of legislators' ideolog-ical locations. These measures are then used in subsequent analyses. Recent work in political methodology has focused on the pitfalls of using such estimates as vari-ables in subsequent analysis without explicitly accounting for their uncertainty and possible bias (Herron and Shotts, 2003). This presents a problem for those employing NOMINATE scores because estimates of their unconditional sampling uncertainty or bias have until now been unavailable. In this paper, we present a method of form-ing unconditional standard error estimates and bias estimates for NOMINATE scores using the parametric bootstrap. Standard errors are estimated for the 90th Senate in two dimensions. Standard errors of ýrst dimension placements are in the 0.03 to 0.08 range. The results are compared to those obtained using the MCMC estimator of Clinton, Jackman, and Rivers (2002). We also show how the bootstrap can be used to construct standard errors and conýdence intervals for auxiliary quantities of interest such as ranks and the location of the median Senator.