Consider a nonseparable model Y=R(X,U) where Y and X are observed, while U is unobserved and conditionally independent of X. This paper provides the first nonparametric test of whether R takes the form of a transformation model, meaning that Y is monotonic in the sum of a function of X plus a function of U. Transformation models of this form are commonly assumed in economics, including, e.g., standard specifications of duration models and hedonic pricing models. Our test statistic is asymptotically normal under local alternatives and consistent against nonparametric alternatives. Monte Carlo experiments show that our test performs well in finite samples. We apply our results to test for specifications of generalized accelerated failure-time (GAFT) models of the duration of strikes and of marriages.
additivity, control variable, endogenous variable, monotonicity, nonparametric nonseparable model, hazard model, specification test, transformation model, unobserved heterogeneity
Econometrics | Economics
LEWBEL, Arthur; LU, Xun; and SU, Liangjun.
Specification Testing for Transformation Models. (2014). 1-35. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/1489
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