The purpose here is to assess empirically the quasi-supply side model of the firm developed in the paper by Ashton et al. (2004) by testing the prediction of the model that the evolution of a firm's debt to equity ratio will be compatible with a non-linear (target adjustment) process whose underlying probability density function possesses no convergent moments. Using a thirty-two-year history of the debt to equity ratio for each of ninety ‘mature’ United Kingdom firms, a non-parametric estimation procedure shows that the debt to equity ratio evolves in terms of a process which is largely consistent with the predictions of this model. In particular, the evolution of the debt to equity ratio is compatible with a ‘long (fat) tailed’ density function with no convergent moments. This has the important implication, supported by our empirical analysis, that the linear dynamic models which characterize empirical work in this area will be mis-specified and will return inconsistent and temporally unstable estimates of the target adjustment process as a consequence.