Beyond the Diagonal Reference Model: Critiques and New Directions

Ethan Fosse , Harvard University
Fabian T. Pfeffer, University of Michigan

There has recently been an increase in the number of quantitative studies examining the consequences of individual-level socioeconomic mobility. Nearly all of these studies have used Sobel’s (1981; 1985) diagonal reference model. Here, we critically examine the properties of the model, and show mathematically and via simulation that, under plausible values of mobility effects, it tends to generate results that implicitly force the mobility linear effect to zero. As such, the model has little advantage over Duncan’s square additive model, which has been abandoned for similar reasons. We conclude with a caution to researchers interested in using the diagonal reference model. The resulting estimated mobility effects are, in part, an artifact of the model and should be interpreted judiciously. In general, when using the technique researchers should decompose the mobility parameters using orthogonal projection, which will reveal the potentially strong assumptions underlying the model.

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 Presented in Session 165. Mathematical Demography