Spillover Bias in Multigenerational Income Regressions

Abstract

Intergenerational persistence estimates are susceptible to several well-documented biases arising from income measurement, and it has become standard practice to construct income measures to mitigate these. However, remaining bias can lead to a spurious grandparent coefficient estimate in multigenerational regressions, a recent focus of the mobility literature. We show with theory and simulations that even using a 30-year income average can result in a small positive spurious grandfather coefficient estimate. We further propose an IV approach, showing that it is not susceptible to this spillover bias in simplified settings and that it can provide bounds on the parameters in a more general scenario. With administrative data from Norway, we reveal a positive spillover bias in the grandfather coefficient estimates, and the combined evidence from our OLS and IV approaches suggest the preferred small positive OLS estimate could still be upward biased.

Intergenerational Mobility in American History: Accounting for Race and Measurement Error

“…Rather than using the classical measurement error formula, one could instead use instrumental variables to estimate the IGE. This method instruments one father observation with another one under the assumption that the transitory components are not correlated across observations (Altonji andDunn, 1991, Modalsli andVosters, 2019). If one takes this approach and instruments the 1910 father observation with the 1920 father observation, then the estimated IGE is 0.82close to the 0.84 estimate under classical measurement error.…”

“…Given classical measurement error, eliminating noise leads to a "true" father-son elasticity of 0.84, which is 2.3 times higher than the baseline estimate of 0.37. An alternative fix for measurement error is to instrument one father observation with a second (Altonji and Dunn, 1991;Modalsli and Vosters, 2019), which yields a similar IGE estimate of 0.82. If one iterates the 0.82 coefficient across generations, then initial gaps take ten generations to converge to about 15 percenteight generations or about 200 years longer than the estimate with one father observation and white families of 0.37.…”

Intergenerational Mobility in Income and Consumption: Evidence from Indonesia

“…To address the measurement error, I adopt the approach of using different measures of the same variable (in this case parental income) as an instrument for annual parental income. It is standard in the literature to use another measure of the same variable to address measurement error/attenuation bias in the OLS estimates (Aizer et al, 2018;Altonji & Dunn, 1991;Angrist & Krueger, 2001;Mani et al, 2012;Modalsli & Vosters, 2019;Ward, 2021). Therefore, I now use parental income from 1993 as an instrument for parental income from 1997, assuming the measurement error in 1993 is uncorrelated with the measurement error in 1997.…”

Intergenerational Mobility in American History: Accounting for Race and Measurement Error

“…Rather than using the classical measurement error formula, one could instead use instrumental variables to estimate the father-son association. This method instruments one father observation with another one under the assumption that the transitory components are not correlated across observations (Altonji andDunn 1991, Modalsli andVosters 2019)…”

“…Assuming classical measurement error, eliminating noise leads to "true" father-son associations that are 33 to 50 percent higher than when using one father observation. An alternative fix for measurement error is to instrument one father observation with a second, which leads to similar estimates (Altonji and Dunn 1991;Modalsli and Vosters 2019). Updated estimates suggest that up to 74 percent of the gaps across white fathers persisted to the next generation, which changes our understanding of generational inequality in the past.…”