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.
This paper develops a consistent heteroskedasticity robust Lagrange Multiplier (LM) type specification test for semiparametric conditional mean models . Consistency is achieved by turning a conditional moment restriction into a growing number of unconditional moment restrictions using series methods. The proposed test statistic is straightforward to compute and is asymptotically standard normal under the null. Compared with the earlier literature on series-based specification tests in parametric models, I rely on the projection property of series estimators and derive a different normalization of the test statistic. Compared with the recent test in Gupta (2018), I use a different way of accounting for heteroskedasticity. I demonstrate using Monte Carlo studies that my test has superior finite sample performance compared with the existing tests . I apply the test to one of the semiparametric gasoline demand specifications from Yatchew and No (2001) and find no evidence against it.
A
heteroskedasticity robust
D
against nonparametric alternatives
R
test
proposed test statistic is straightforward to compute and
R
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
asymptotically standard normal under the null. Compared with the earlier literature on series-based specification tests in parametric models, I rely on the projection property
R
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
and derive a different normalization of the test statistic. Compared with the recent test in Gupta (2018), I use a different way of accounting for heteroskedasticity. I demonstrate using Monte Carlo studies that my test has superior
R
of the test
compared with the existing tests