A Consistent Heteroskedasticity‐Robust LM‐Type Specification Test for Semiparametric Models
Abstract
ABSTRACT This article develops a heteroskedasticity‐robust Lagrange Multiplier‐type specification test for semiparametric regression models. The test is able to detect a wide class of deviations from the null hypothesis. The test statistic is based on the estimates from the restricted semiparametric model, can be computed in a regression‐based way, and is asymptotically standard normal under the null. I apply the test to Environmental Engel Curves and find that while the relationship between income and emissions may be quadratic, its shape changes with other variables in the model. Monte Carlo studies suggest that my test controls size well, has good power, and is fairly robust to the tuning parameter choice.
Fields of Study & Subjects
Statistical Methods and Inference
Monetary Policy and Economic Impact
Global trade and economics
Publication details
- Journal / source
- Journal of Applied Econometrics
- Volume
- 41
- Issue
- 3
- Pages
- 240–252
- Publication date
- 10 January 2026
- Language
- EN