Specification Test for Missing Functional Data

Economic data are frequently generated by stochastic processes that can be modeled as realizations of random functions (functional data). This paper adapts the speci cation test for functional data developed by Bugni, Hall, Horowitz and Neumann to the presence of missing observations. By using a worst case scenario approach, our method is able to extract the information available in the observed portion of the data while being agnostic about the nature of the missing observations. The presence of missing data implies that our test will not only result in the rejection or lack of rejection of the null hypothesis, but it may also be inconclusive. Under the null hypothesis, our specification test will reject the null hypothesis with a probability that, in the limit, does not exceed the significance level of the test. Moreover, the power of the test converges to one whenever the distribution of the observations conveys that the null hypothesis is false. Monte Carlo evidence shows that the test may produce informative results (either rejection or lack of rejection of the null hypothesis) in relevant economic models. The procedure is illustrated by testing whether the Burdett-Mortensen labor market model is the correct framework for wage paths constructed from the NLSY79 survey.