One of the most interesting issues in economics is the study of industrial dynamics and evolution. Firm size distributions are central when analyzing market structures. The intimate relationship between the firm growth process and the emanating market structures demands attention to firm size distributions and firm growth rate distributions. The stochastic firm growth approach builds on the firm growth rates being normally distributed and size being determined by a first order autoregressive process leaving the size distribution log-normal. The paper analyses these distributional pattern in an impirical context questioning the foundation of the stochastic growth approach. In a cross section analysis of four industries it is shown that neither the foundation nor the outcome of the stochastic firm growth process is empirical regularities. By testing growth rates and log(Size) for normality, reviewing their moments and looking at the plotted data an alternative interpretation is put forward. This interpretation mainly gives reference to industrial evolution, limited effect of heterogeneity on growth rates and the level of disaggregation.

Recently there has been a renewed interest in the study of firm size distributions and firm growth rate distributions. The stochastic firm growth approach builds on the assumption that firm growth rates are independent identically distributed and size is determined by a first order autoregressive process leaving the size distribution log-normal. This paper analyzes these distributional patterns in an empirical context questioning the foundation of the stochastic growth approach. In a cross section analysis of four industries using Danish data it is shown that the foundation for and the outcome of the stochastic firm growth process as it has so far been conceived are empirically far-fetched. In particular significant deviations from normality are found with respect to third and fourth moments.

We analyze three sets of income data: the US Panel Study of Income Dynamics (PSID), the British Household Panel Survey (BHPS), and the German Socio-Economic Panel (GSOEP). It is shown that the empirical income distribution is consistent with a two-parameter lognormal function for the low-middle income group (97%–99 % of the population), and with a Pareto or power law function for the high income group (1%–3 % of the population). This mixture of two qualitatively different analytical distributions seems stable over the years covered by our data sets, although their parameters significantly change in time. It is also found that the probability density of income growth rates almost has the form of an exponential function. Key words: Personal income, lognormal distribution, Pareto’s law, income growth rate