Life-cycle variation in the association between current and lifetime earnings

All of our analyses tell the same story: contrary to the textbook errors-in-variables model usually assumed in applied research, the slope coefficient in the regression of log current earnings on log annual earnings varies systematically over the life cycle and is not generally equal to one. We can illustrate the usefulness of our results by applying them to the intergenerational mobility regression in which sons' log of lifetime earnings is the dependent variable and fathers' log of lifetime earnings is the explanatory variable. As summarized in Solon (1999), most recent research in that literature has devoted considerable attention to the right-side measurement error from using short-run proxies for fathers' lifetime earnings. Our estimates of 0, shown in Figures 2 and 3 confirm the literature's presumption that right-side measurement error causes an attenuation inconsistency in OLS estimation of the intergenerational elasticity.12 The literature, however, has given much less attention to the left-side measurement error from using short-run proxies for sons' lifetime earnings. Presumably, this neglect reflects an assumption by researchers that, in accordance with the textbook errors-in-variables model, left-side measurement error is innocuous for consistency. All our estimates of λt suggest that assumption would be fairly well founded if sons' earnings were measured between the early thirties and mid-forties. Many intergenerational mobility studies, however, have measured sons' earnings at earlier ages, and this has substantially affected the findings. Reville (1995), for example, estimates intergenerational elasticities of about 0.25 when he measures the sons' earnings in their twenties, but his estimates start approaching 0.5 when he observes the sons well into their thirties. This is just the pattern one should expect from the trajectories of λt, in Figures 2 and 3. An important implication is that many estimates of the intergenerational earnings elasticity have been subject to substantial attenuation inconsistency from left-side measurement error, in addition to the well-known inconsistency from right-side measurement error. Of course, interpreting evidence on intergenerational earnings mobility is just one example of how our results might be applied. We advise readers, however, to exercise due caution in importing our estimates of λt, and θt, to other earnings data. We already have mentioned issues of comparability between administrative and survey data. Furthermore, the life-cycle trajectories for our U.S. cohort born 1931-1933 may differ from those for other cohorts and other countries. In addition, as emphasized in Solon (1992), sample selection criteria that affect the sample's dispersion in earnings also affect the measurement error properties of current earnings as proxies for lifetime earnings. Nevertheless, taking account of our evidence on departures from the textbook errors-in-variables model should enable better-informed analyses of estimation biases in a wide variety of research that uses current earnings variables as proxies for long-run earnings.