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Abstract:
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In recent years there has been an increase in the number of quantitative studies examining the consequences of individual-level socioeconomic mobility. Nearly all of these studies in sociology and demography have used Sobel’s (1981, 1985) diagonal reference model (DRM). In this paper we examine the mathematical properties of the Sobel model. Using Sobel’s fertility data we first show that, under plausible values of the mobility effects, the DRM generates results that implicitly force the mobility linear effect to nearly zero. Next, we outline the bias formulas for the DRM’s estimated mobility effects. Both mathematically and using simulations, we demonstrate that the DRM’s estimated mobility effects are sensitive to the size and sign of the origin and destination effects, often in ways that are likely non-intuitive to applied researchers. Lastly, using the counterfactual framework, we discuss how the DRM requires extremely strong assumptions for causal identification, which are impossible to test using a randomized controlled trial. We conclude with a caution to researchers interested in using the DRM to estimate the individual-level consequences of social mobility.
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