Abstract
A number of recent papers have proposed a time-varying-coefficient (TVC) procedure that, in theory, yields consistent parameter estimates in the presence of measurement errors, omitted variables, incorrect functional forms, and simultaneity. The key element of the procedure is the selection of a set of driver variables. With an ideal driver set the procedure is both consistent and efficient. However, in practice it is not possible to know if a perfect driver set exists. We construct a number of Monte Carlo experiments to examine the performance of the methodology under (i) clearly-defined conditions and (ii) a range of model misspecifications. We also propose a new Bayesian search technique for the set of driver variables underlying the TVC methodology. Experiments are performed to allow for incorrectly specified functional form, omitted variables, measurement errors, unknown nonlinearity and endogeneity. In all cases except the last, the technique works well in reasonably small samples.
Highlights
A series of papers have proposed the use of time-varying coefficient (TVC) models to uncover the bias-free estimates of a set of model coefficients in the presence of omittedWe are grateful to Fredj Jawadi, and two referees for helpful comments on an earlier draft.variables, measurement error and an unknown true functional form.1 There have been a reasonably-large number of successful applications of the technique.2 it is difficult to establish the usefulness of a technique strictly through applications since we can never be certain of the accuracy of the results
This paper attempts to bridge the gap between the asymptotic theoretical results of the theoretical papers and the apparently good performance of the applied papers by constructing a set of Monte Carlo experiments to examine (1) how well the technique performs under clearlydefined conditions and (2) the limits on the technique’s ability to perform successfully under a broad range of model misspecifications
The technique being investigated here allows us, in principal, to decompose the TVCs into two components; we associate the first component with the true nonlinear structure, which we interpret as the derivative of the dependent variable with respect to each of the independent variables in the unknown, nonlinear, true function; we associate the second component with the biases emanating from misspecification, and which we remove from the TVC to give us our consistent estimates
Summary
A series of papers have proposed the use of time-varying coefficient (TVC) models to uncover the bias-free estimates of a set of model coefficients in the presence of omitted. The technique being investigated here allows us, in principal, to decompose the TVCs into two components; we associate the first component with the true nonlinear structure, which we interpret as the derivative of the dependent variable with respect to each of the independent variables in the unknown, nonlinear, true function; we associate the second component with the biases emanating from misspecification, and which we remove from the TVC to give us our consistent estimates. This technique offers an interesting way forward in dealing with model misspecification. An “Appendix” provides details on the computational methods used in the Monte Carlo simulations
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