Bounds for exact moments of estimators in the errors-in-variables model and simultaneous equations

An application of approximate finite sample results to parameter estimation in a linear errors‐in‐variables model

“…These bounds are simple to calculate. Further FRIEDMANN (1990) showed that aT the ratioof the exact relative bias to the asymptotic relative bias is an e increasing function of K. Table 1 illustrates how aT and the bounds a$ and a; depend on the sample size T and the noise-to-signal ratio K. The last row in Table 1 gives the absolute value of the asymptotic relative bias e for the given values of K. We calculated UT by using an iterative algorithm (see MIITAG, 1987, p. 112-114). By T + 00 both aT and the bounds converge to the absolute asymptotic relative LS bias e which only depends on K. The behaviour of aT and the corresponding bounds for increasing T can be grasped immediately by using a graphical representation as given by figure 1 for K=0.10 and K=0.30.…”

“…With respect to the sample size MIITAG (1987) proposed to correct the LS estimator by removing the exact bias instead of the asymptotic bias. The resultant corrected least squares estimator (CLS) can be considerably simplified using a finite sample approximation by FRIEDMANN (1990) for the bias. The theoretical forms of the CLS estimators all depend on an unknown parameter value.…”