The effect of explanatory variables on income: A tool that allows a closer look at the differences in income

Investigation of the effect of covariates on income typically relies on regression models with a transformed income. An underlying assumption is that the exact income is available. However, in surveys reported income is often available in income brackets only. For such grouped data one can use ordered regression models, which in their simplest form with a linear predictor work in a similar way as regression models for exact income. They yield an overall measure of the effect of covariates but fail to detect the specific structure of the effects of single covariates. A model is proposed that allows a closer look at the effect of single covariates, showing in more detail how the income is determined by explanatory variables. The model exploits the potential of sequential regression models, which are extended to allow for varying coefficients. The model is not harder to use than classical regression models but is much more informative. The method is illustrated by using data from the German Socio-Economic Panel Study and the United States Census Bureau.