Individual labor earnings observed in worker panel data have complex, highly persistent dynamics. We investigate the capacity of a structural job search model with i.i.d. productivity shocks to replicate salient properties of these dynamics, such as the covariance structure of earnings, the evolution of individual earnings mean and variance with the duration of uninterrupted employment, or the distribution of year-to-year earnings changes. Specifically, we show within an otherwise standard job search model how the combined assumptions of on-the-job search and wage renegotiation by mutual consent act as a quantitatively plausible "internal propagation mechanism" of i.i.d. productivity shocks into persistent wage shocks. The model suggests that wage dynamics should be thought of as the outcome of a specific acceptance/rejection scheme of i.i.d. productivity shocks. This offers an alternative to the conventional linear ARMA-type approach to modelling earnings dynamics. Structural estimation of our model on a 12-year panel of highly educated British workers shows that our simple framework produces a dynamic earnings structure which is remarkably consistent with the data.