Playing by the rules? Agreement between predicted and observed binary choices

Empirical economics frequently involves testing whether the predictions of a theoretical model are realized under controlled conditions. This paper proposes a new method for assessing whether binary (‘Yes’/‘No’) observations ranging over a continuous covariate exhibit a discrete change which is consistent with an underlying theoretical model. An application using observations from a controlled laboratory environment illustrates the method, however, the methodology can be used for testing for a discrete change in any binary outcome variable which occurs over a continuous covariate such as medical practice guidelines, firm entry and exit decisions, labour market decisions and many others. The observations are optimally smoothed using a nonparametric approach which is demonstrated to be superior, judged by four common criteria for such settings. Next, using the smoothed observations, two novel methods for assessment of a step pattern are proposed. Finally, nonparametric bootstrapped confidence intervals are used to evaluate the match of the pattern of the observed responses to that predicted by the theoretical model. The key methodological contributions are the two innovative methods proposed for assessing the step pattern. The promise of this approach is illustrated in an application to a controlled experimental lab data set, while the methods are easily extendable to many other settings. Further, the results generated can be easily communicated to diverse audiences.