Working Paper No. 04-18

Fifty Years of Goodman's Identity: Its Implications for Regression-Based Inference
Jeffrey S. Zax
December 2004


This paper examines the implications of Goodman's Identity for estimation and inference in linear regression. Its empirical implementation requires the assumption of random coefficients or measurement error. Under the former, regression can be surprisingly potent but is typically misused. With one application of Goodman's Identity, regression can test the neighborhood model, aggregation bias and effects of covariates. Models with more than two groups are completely identified and yield more powerful tests. However, most implementations unwittingly impose the neighborhood model, weight incorrectly and offer meaningless R2 values as "validation". Moreover, regression is essentially useless for most models requiring two applications of Goodman's Identity, including those of voting with unknown group-specific turnout rates.