This paper develops a consistent Lagrange Multiplier (LM) type specification test for semiparametric conditional mean models against nonparametric alternatives. Consistency is achieved by turning a conditional moment restriction into a growing number of unconditional moment restrictions using series methods. The test is simple to implement, because it requires estimating only the restricted semiparametric model and because the asymptotic distribution of the test statistic is pivotal. The use of series methods in estimation of the null semiparamertic model allows me to account for the estimation variance and obtain refined asymptotic results. The testdemonstrates good size and power properties in simulations . I apply the test to one of the semiparametric gasoline demand specifications from Yatchew and No (2001) and find no evidence against it.
This paper develops a consistent Lagrange Multiplier (LM) type specification test for semiparametric conditional mean models against nonparametric alternatives. Consistency is achieved by turning a conditional moment restriction into a growing number of unconditional moment restrictions using series methods. The test is simple to implement, because it requires estimating only the restricted semiparametric model and because the asymptotic distribution of the test statistic is pivotal. The projection interpretation of series estimators allows me to derive a degrees of freedom correction. This correction allows me to account for the estimation variance and develop refined asymptotic results. It also substantially improves the finite sample performance of the test . I apply the test to one of the semiparametric gasoline demand specifications from Yatchew and No (2001) and find no evidence against it.
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use of series methods in estimation of the null semiparamertic model
projection interpretation of series estimators allows me to derive a degrees of freedom correction. This correction
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obtain
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The testdemonstrates good size and power properties in simulations
It also substantially improves the finite sample performance of the test