THESE RECENT MODELS REPRESENT A METHODOLOGICAL ADVANCE OVER PREVIOUS EMPIRICAL RESEARCH ON CRIMINAL BEHAVIOR BECAUSE THEY CAN ISOLATE DETERRENT EFFECTS AND INTERACTIONS BETWEEN CRIMINAL BEHAVIOR AND THE CRIMINAL JUSTICE SYSTEM. NEVERTHELESS, BOTH THEIR METHODOLOGY AND THEIR EMPIRICAL FINDINGS HAVE BEEN CHALLENGED BY CRITICS. THE MICROTHEORETIC FRAMEWORK THE MODELS USE HAS PERMITTED USE OF SOCIOECONOMIC AND DETERRENT MEASURES IN CRIME RATE EQUATIONS, EMPHASIZED THE NEED FOR SIMULTANEOUS EQUATION METHODS, AND GENERATED FUNCTIONAL FORMS WHICH INCLUDE BOTH PROBABILITY OF PUNISHMENT AND SEVERITY OF PUNISHMENT AS COMPONENTS OF DETERRENCE. SIX EMPIRICAL STUDIES IN THE U.S., CANADA, AND THE UNITED KINGDOM ILLUSTRATE THE USE OF AGGREGATIVE CROSS-SECTIONAL DATA TO ESTIMATE CRIME RELATIONSHIPS. AMONG THE MAIN METHODOLOGICAL PROBLEMS FOUND IN THESE STUDIES ARE MEASUREMENT ERROR AND IDENTIFICATION PROBLEMS. THESE PROBLEMS ARE NOT, HOWEVER, MORE SERIOUS THAN THOSE FOUND IN OTHER AREAS OF APPLIED ECONOMETRICS. THE GENERAL FINDING THAT PUNISHMENT DETERS CRIME HOLDS ACROSS BOTH GEOGRAPHIC REGIONS AND STATISTICAL TECHNIQUES, EXCEPT IN THE CASE OF CAPITAL PUNISHMENT, FOR WHICH A SIGNIFICANT DETERRENT EFFECT IS NOT USUALLY FOUND. NEVERTHELESS, BEFORE RESULTS CAN BE USED WITH CONFIDENCE, ADDITIONAL RESEARCH IS NEEDED TO RESOLVE MANY ECONOMETRIC AND MEASUREMENT PROBLEMS. FIGURES, FOOTNOTES, AND A BIBLIOGRAPHY ARE INCLUDED. FOR THE TOTAL VOLUME OF WHICH THIS STUDY IS A PART, SEE NCJ 61013. (CFW)