A Note on the Structural Stability of the Joint Distribution of Income and Wealth

This paper analyzes the change over time in the distribution of households' income and financial wealth in Great Britain. Empirical analysis based on the British Family Resources Survey data from the period 1996-2001 examines whether the sequence of these distribution is structurally stable in the sense related to Malinvaud (1993). In order to do this, we look for the local time-invariance of a distribution derived after applying simple transformations like scaling or standardizing to the original distribution. In our study we make use of adaptive bandwidth univariate and bivariate kernel density estimation to identify the changes in shapes of the aforementioned distributions and to perform a nonparametric density time-invariance test as proposed by Li (1996). Our main result is that accounting only for the changes in the vector of means of the original distribution is not sufficient to obtain the desired local time-invariance. In fact, this can be achieved by accounting for changes in the vector of means and dispersion parameters of the original distribution.