We investigate the estimation of dynamic models of criminal activity, when there is significant under-recording of crime. We give a theoretical analysis and use simulation techniques to investigate the resulting biases in conventional regression estimates. We find the biases to be of little practical significance. We develop and apply a new simulated maximum likelihood procedure that estimates simultaneously the measurement error and crime processes, using extraneous survey data. This also confirms that measurement error biases are small. Our estimation results for data from England and Wales imply a significant response of crime to both the economic and the enforcement environment.