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SPECIFICATION TEST FOR MISSING FUNCTIONAL DATA

Published online by Cambridge University Press:  21 May 2012

Federico A. Bugni
Federico A. Bugni*
Affiliation:
Duke University
*
*Address correspondence to Federico A. Bugni, Department of Economics, Duke University, 213 Social Sciences (Box 90097), Durham, NC 27708, USA; e-mail: federico.bugni@duke.edu.
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Abstract

Economic data are frequently generated by stochastic processes that can be modeled as realizations of random functions (functional data). This paper adapts the specification test for functional data developed by Bugni, Hall, Horowitz, and Neumann (2009, Econometrics Journal12, S1–S18) 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) even under the presence of significant amounts of missing data. The procedure is illustrated by testing whether the Burdett–Mortensen labor market model is the correct framework for wage paths constructed from the National Longitudinal Survery of Youth, 1979 survey.

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Type
Articles
Information
Econometric Theory , Volume 28 , Issue 5 , October 2012 , pp. 959 - 1002
Copyright
Copyright © Cambridge University Press 2012

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