Sequentially testing polynomial model hypotheses using power transforms of regressors

Abstract

We provide a methodology for testing a polynomial model hypothesis by generalizing the approach and results of Baek, Cho, and Phillips (2015; BCP) which test for neglected nonlinearity using power transforms of regressors against arbitrary nonlinearity. We use the BCP quasi-likelihood ratio test and deal with the new multifold identification problem that arises under the null of the polynomial model. The approach leads to convenient asymptotic theory for inference, has omnibus power against general nonlinear alternatives, and allows estimation of an unknown polynomial degree in a model by way of sequential testing, a technique that is useful in the application of sieve approximations. Simulations show good performance in the sequential test procedure in both identifying and estimating unknown polynomial order. The approach, which can be used empirically to test for misspecification, is applied to a Mincer (1958, 1974) equation using data from Card (1995) and Bierens and Ginther (2001). The results confirm that the standard Mincer log earnings equation is readily shown to be misspecified. The applications consider different data sets and examine the impact of nonlinear effects of experience and schooling on earnings, allowing for flexibility in the respective polynomial representations.

Weakσ-convergence: Theory and applications

“…Model M3: ( = ) For brevity, we consider only the case = . Simulation results for other cases are available online 11 . As in Model M1, we consider two cases depending on the value of a : Table 1 reports size and power of the one-sided convergence test in model M1 with settings = 1=3 and L = int(T ) in the long run variance calculation.…”

Multidimensional skills and the returns to schooling: Evidence from an interactive fixed‐effects approach and a linked survey‐administrative data set

“…Supporting Information Appendix D.1 shows that our empirical findings are robust to the inclusion of quadratic schooling and/or quartic age variables (Cho & Phillips, ; Murphy & Welch, ) for all specifications described above, while Appendix D.2 shows the results to be robust to an alternative interpretation of the factor structure in terms of time‐varying returns to observable, time‐invariant individual‐specific characteristics. We have also estimated specifications 1 and 3 with demographic controls including race, Hispanic status, foreign born status, marital status, state of residence during the SIPP survey and birth year.…”

Boosting: Why You Can Use the Hp Filter

“…According to Theorem 2, the boosted HP filter can asymptotically remove any finite‐order polynomial drift, whereas the HP filter can only handle a polynomial drift up to the third order. Higher order time polynomials are known to be useful in modeling the nonlinear growth of both macroeconomic and microeconomic time series and as sieve approximations to more general nonlinear trend functions (Baek et al., 2015; Cho and Phillips, 2018). We are therefore interested in the capability of the boosting mechanism to enable the HP filter to capture these general deterministic trend elements in addition to stochastic trends.…”