Tests of misspecification or other defects in microeconometric models are usually numerical and based on an average over the sample. In this paper, it is shown that certain types of misspecification can be concealed by averaging, and a framework is developed which allows the specification to be checked in the near neighbourhood of each sample point, rather than for the sample as a whole. The framework involves the application of a scatter-plot smoothing technique to a pair of auxiliary variables derived from the estimated model. Using the sampling distribution of the location of the smooth under correct specification, a rejection rule based on the location of the realized smooth is established. Thus the smooth itself is used as a test statistic. A natural application of the procedure is to tests of equi-dispersion in count data models, and we find that it is particularly useful in the case in which a sample contains elements of both under- and over-dispersion, since it is in this case that numerical tests based on averaging are most likely to lack power. Two specific applications, one on takeover bids and the other on worker absenteeism, are used to illustrate the procedure.
