Recent studies emphasize the role of the network structure of production input interlinkages for a wide range of economic outcomes including shock propagation and the emergence of aggregate fluctuations. In most of these studies the input-output architecture is fixed and exogenously given and relatively little work has considered its evolution and the underlying mechanism of network formation. Here we provide evidence on the evolution of production input interlinkages on the most granular level of economic activity, building on a diverse set of more than 80,000 companies sampled across nearly all industries of the Japanese economy. We review the main empirical properties of the Japanese production network level and and that these features are remarkably stable over time. To estimate the mechanism of supplier selection inducing this stability, we employ a stochastic actor-oriented model that sidesteps the econometric problem of mutual dependencies inherent to networked environments. Building on this approach, we find that topological features of the network such as the geodesic distance between the firms and their current number of relationships are a main driver of network dynamics in subsequent periods, and are quantitatively more important than selection based on productivity.