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This paper develops a consistent heteroskedasticity robust LagrangeMultiplier (LM) type specification test for semiparametric conditional meanmodels. Consistency is achieved by turning a conditional moment restrictioninto a growing number of unconditional moment restrictions using seriesmethods. The proposed test statistic is straightforward to compute and isasymptotically standard normal under the null. Compared with the earlierliterature on series-based specification tests in parametric models, I rely onthe projection property of series estimators and derive a differentnormalization of the test statistic. Compared with the recent test in Gupta(2018), I use a different way of accounting for heteroskedasticity. Idemonstrate using Monte Carlo studies that my test has superior finite sampleperformance compared with the existing tests. I apply the test to one of thesemiparametric gasoline demand specifications from Yatchew and No (2001) andfind no evidence against it.

A Consistent Heteroskedasticity Robust LM Type Specification Test for Semiparametric Models