Interest Yields, Credit Ratings, and Economic Characteristics of State Bonds: Reply
回应Cranford和Stover对作者1984年论文的批评，指出直接使用普通最小二乘法估计方程会因多重共线性导致经济变量被错误识别为不显著，而作者提出的方法能避免此问题。
In commenting on our 1984 paper, Cranford and Stover (C-S) raise three objections. First, in terms of credit rating, they claim that our procedure gives no new information since same information can be obtained by applying OLS directly to equation (2).' l Second, they claim that 'sthe additional information on the economic/demographic variables can be obtained simply by estimating the reduced-form equation (5).ss Third, they claim our model unduly burdensome relative to their procedure. This last claim is apparently based on the assertion that the C-S procedure somehow involves estimating fewer equations than ours. All three claims are incorrect. First, because credit ratings depend on economic variables, the direct application of OLS to equation (2) encounters a multicollinearity problem. (This C-S appear to agree with.) While multicollinearity does not bias the estimated coefElcients, it does increase their standard errors, and thus reduces the t-statistics associated with the economic variables. As a result, the economic variables which are signiElcant in explaining interest yields may be incorrectly identified as insigniElcant. This possible misidentification problem was addressed in footnote 1 of our paper (p. 347). It was also numerically confirmed by a comparison of Table 1 and Table 4 of our paper. This problem is further apparent in the p-values of equations (2) and (4) in C-S. While economic variables Zl, Z4, and Zs are statistically signiElcant in theirequation (4) which is the procedure we suggested they are not signiElcant in equation (2) at any conventional level. Thus, the direct estimation of equation (2) would incorrectly label signiElcant variables as insigniElcant. The problems with the estimation of the reduced equation (5) are more serious. First, when equation (5) is estimated, the error term is no longer just pure noise.ss Rather, it is (ag + e), and hence a function of credit ratings. Therefore, (5) is a