The analysis used a set of two-wave panel data collected from 130 cities in the United States for an earlier study by Michael Victor. The analysis sought to determine whether police spending reduces violent crime rates and whether police spending rises in response to crime. The data on police spending and violent crime rates came from 1960 and 1962. Nine variables controlled for sociodemographic and political influences on crime rates and police spending. Two-wave models in which only cross-lagged or only cross-instantaneous effects were estimated yielded fairly similar results because crime rates and police spending were each highly stable over the 2 years of the panel. The third model assumed that change in one variable influenced change in the other variable and that the initial values of the predictor variable did not influence change in the dependent variable. This model reproduced the observed correlations among the variables perfectly, but yielded parameter estimates which were very different from the earlier models. The fourth model contained unconstrained lagged and contemporaneous effects and yielded parameter estimates which were quite different from those of the earlier three models. Thus, parameter estimates can be sensitive to the specification of a model. Unless close attention is given to the specification and interpretation of panel models, the estimates obtained in empirical research may mean something very different from what the investigator supposes. Detailed descriptions of the models, one table, notes, and a list of 14 references are included.