Our paper presents new estimates of matching functions on partial labor markets. We used extensive data, ranging from 1982 to 2003, which results in new insights, extending the knowledge obtained by former empirical studies. We also used the extended time series data to validate model assumptions, like stationarity, statistically. It is shown that some of these assumptions do not hold if recent data is included. We discuss potential consequences and modifications, resulting from these findings. Subsequently, we use a sophisticated pooled mean group panel model to provide more detailed insights into matching processes in the concerning partial labor markets. This approach allows for a more general perspective and furthermore, parameters can be estimated asymptotically efficient via maximum likelihood. The results obtained suggest movements to stable matching processes, positive elasticities of overall matching and decreasing returns to scale. The economical implications of these findings are discussed and compared with the results of other recent studies.