[335] A CAUTIONARY NOTE ON THE USE OF TWO-STAGE LEAST SQUARES

David Knoke for providing useful comments on an earlier draft of this paper. I am solely responsible for any errors that remain. SOCIOLOGICAL METHODS & RESEARCH, Vol. 5 No. 3, February 1977 A computational error in the application of multiple regression computer programs to two-stage least squares estimation of the standardized coefficients for nonrecursive models leads to the understatement of the relative size of reciprocal effects. Furthermore, an error in the computation of the disturb-ance variance invalidates significance tests for the metric coefficients. The sources of the errors are derived and an example is presented. The example reveals that not only do the incorrectly computed standardized coefficients underestimate reciprocal effects, they also may lead to specious conclusions regarding group differences in the relative impact of causal variables. although one-step methods for the computation of two-stage least squares (2SLS) estimates of the param-eters of nonrecursive structural equation models have been. known for some time (e.g., Goldberger, 1964), most package programs, e.g., SPSS (Nie et al., 1975), do not include one-step routines. Consequently, most researchers applying 2SLS to nonrecursive models employ ordinary least squares (OLS) in two steps. In this note, I show how applying OLS packages to that two-step procedure can lead to incorrect estimates of (a) the standardized coefficients for endogenous variables, (b) the disturbance variances, (c) the standard errors of metric coeffi-cients, and (d) significance tests. An example that demonstrates the consequences of the miscalculations for causal inference is also presented