Although researchers have discovered a negative and often statistically significant association between crime rates and sanction measures, recent analyses have questioned these findings on the assumption that crimes and sanctions simultaneously influence each other. This paper reviews the rationales underlying this viewpoint, such as the hypothesis that society is willing to deliver only a limited amount of punishment, and then addresses its inherent problems in identifying the crime function. Simultaneous estimation procedures are detailed, along with restrictions that some researchers have used to identify the crime function. The difficulties of finding variables that influence sanctions but have no direct effect on crime are discussed, beginning with an analysis of simple models in which a single crime type and sanction type are simultaneously related. Criminal justice expenditures, prison cell utilization, and lagged sanctions are tested as restrictions, but all fail to identify the crime function. Also considered are the more complex but more realistic models in which a single crime type is simultaneously related to multiple sanction types and multiple crime types and a single sanction type are simultaneously related. These approaches also encounter problems that are fatal to valid identification. In conclusion, analyses using aggregate nonexperimental data must have a time series component, and estimation procedures must account for the possibility of serial correlation in the stochastic components of the specifications. A technical note on lagged models and 19 references are appended. See also NCJ 44669.