Abstract: This article proposes a coefficient constancy test in semi-varying coe¢ cient models, which only needs to estimate the restricted coefficients under the null hypothesis. The test statistic resembles the union-intersection test after ordering the data according to the varying coefficients' explanatory variable. This statistic depends on a trimming parameter that can be chosen by the data-driven calibration method we propose. A bootstrap test is justified under fairly general regularity conditions. Under more restrictive assumptions, the critical values can be tabulated, and trimming is unnecessary. The proposed test can be applied to specification testing of partial effects in the direction of non(semi)-parametric alternatives. The finite sample performance is studied by means of Monte Carlo experiments, and a real data application for modelling education returns.

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