Testing Model Adequacy – A Metric Approach
50 Pages Posted: 26 Nov 2019
Date Written: November 13, 2019
The paper proposes a new method to assess model adequacy based on functionals with metric properties quantifying the deviation of the conditional expectation of a response variable Y from a suggested parametric non-linear model m(X). We derive the asymptotic distribution of a test statistic under linear and non-linear specifications, when the parameter estimator is asymptotically linear. We find that the power of the test in misspecified linear models is better or similar to some of the most commonly used alternatives in the literature. The metric properties uniquely position the proposed method to study the impact of three types of aggregation on the specification error – aggregation of observations across time, cross-sectional aggregation of variables, or aggregation of different models for the same variable. For example, neglected non-linearity in linear models is shown to be asymptotically negligible with a power-type rate of decay in the case of independent observations when data are aggregated across time. We provide an illustration from the field of finance with the capital asset pricing model (CAPM). The frequency of rejection of the linear specification of the CAPM can decline more than three times when the model is estimated with monthly rather than daily returns.
Keywords: model adequacy, non-linear models, model aggregation
JEL Classification: C50, C58, G12
Suggested Citation: Suggested Citation