Economist have recently begun to consider the questions raised by the ecological concept of resilience - a measure of the degree to which a system can be perturbed before it switches from one stability domain to another. At a theoretical level, it has been argued that the loss of resilience in an ecological-economic system involves a change in its long-run productive potential, but no consideration has yet been given to the empirical investigation of this. This paper discusses an econometric approach to the problem, using the example of semi-arid rangelands. The long-run productive potential of the system is regarded as an unobserved state variable, change in which is irreversible or at least only slowly reversible. It is estimated by applying the extended (nonlinear) Kalman filter. The paper illustrates the approach using data from Botswana for the period 1965-1993. The maximum likelihood estimates of the parameters associated with the loss of resilience mechanism are non-zero. They indicate a small loss of resilience event at the end of the long drought in the 1980s. However, these parameters are very imprecisely estimated and are therefore statistically insignificant. We find that the sensitivity of the system to exogenous shocks varies with fluctuations in both economic and non-economic parameters. Contratry to what is usually thought to be the case, the sensitivity of the system to exogenous shocks is only weakly affected by variations in offtake prices, but is very strongly affected by variations in the cost of herd maintenance. This suggests that offtake prices may be a weak tool for controlling the size of cattle stocks and preventing a loss of resilience. On the other hand, taxes on cattle stocks or grazing fees may be very effective.