John J. Spitzer

Small-Sample Properties of Nonlinear Least Squares and Maximum Likelihood Estimators in the Context of Autocorrelated Errors

Abstract Rao and Griliches (1969) compared several methods of parameter estimation in models having autocorrelated errors. They concluded that nonlinear least squares estimators were not superior to two-stage linear estimators. This study partially replicates the Rao and Griliches Monte Carlo simulation and, in addition, examines the maximum likelihood estimator as a possible competitor. The simulation results are not consistent with those of Rao and Griliches; the small-sample efficiency of nonlinear and maximum likelihood estimators appears to be consistently high and thus reverses some of Rao and Grilichess conclusions.

A Fast and Efficient Algorithm for the Estimation of Parameters in Models with the Box-and-Cox Transformation

Abstract A modified Newton algorithm for the estimation of parameters in models containing the Box-Cox transformation is presented. It is shown that the usual maximum likelihood estimator for the k linear parameters and the m power transformation parameters may be specified as an m-parameter nonlinear least squares estimator. Several models containing Box-Cox transformations are estimated and the speed and efficiency of the modified algorithm compared with three other gradient estimation techniques. The modified Newton algorithm obtains the same parameter estimates, but two to four times faster.

The fallacy of cookie cutter asset allocation: some evidence from “New York’s College Savings Program”

Abstract In this paper, we establish why “prefabricated” asset allocation schemes mandated by some education savings programs might be suboptimal. Then, using the New York’s College Savings Program as an example, we simulate and then compare end of period wealth accumulated in both a tax preferred but regimented asset allocation plan, and in a nontax protected plan. We find, first, that the longer the child participates in the plan, the greater the benefit. Second, participants in higher tax brackets derive greater benefits; adherence to prespecified asset allocation for low tax bracket investors often results in return loss that overshadows the tax benefit.

Optimizing Retirement Savings

In this article, the authors compare five retirement saving choices, namely, the employer match plan (like the SIMPLE or 401-k), the traditional IRA, the Roth IRA, a tax-deferred annuity, and a simple savings plan with no tax benefits. They show that employer match plans are usually but not always the most beneficial alternative for maximizing post-retirement income. They argue that, for certain combinations of pre- and post-retirement tax rates, the Roth IRA can be shown to be superior to all other choices, including the employer match plans. While circumstances under which the Roth is shown to be superior to an employer match plan are uncommon, the fact that this can occur at all is contrary to conventional wisdom.