This scholarly paper assesses biases due to measurement errors in structural equation models of the intergenerational transmission of socioeconomic status by estimating unobserved variable models with data from the remeasurement program of the 1973 Occupational Changes in Generation-II survey. It is noted that reports of social background and achievement variables by nonblack males are subject to strictly random errors, while reports of black males appear subject to significant nonrandom errors. When measurement errors are ignored for nonblacks, occupational returns to schooling are underestimated by about 15%, the effects of some background variables are underestimated by as much as 22%, and variation in socioeconomic achievements not attributable to education or social origins by as much as 27%. Biases appear to be substantially greater for nonblacks. Consequently ignoring measurement error exaggerates racial differences in returns to schooling and occupational inequality not attributable to social origins. (Author/AM)