Introduction
In , Hall notes that most statistical applications of the bootstrap to the calculation of confidence intervals use either ordinary bootstrap standard errors or the percentile method, both of which rely on point estimates obtained from the bootstrap samples. Those applications do not incorporate bootstrap refinements which can yield more accurate finite sample approximations through using the standard errors estimated from each bootstrap sample, as well as the point estimates from that sample. The same point applies to econometric applications (see for a brief survey). Of course, often there is little choice, simply because an analytic calculation of the standard errors is not feasible. However, the bootstrap is sometimes used specifically as a remedy for possible shortcomings in analytic standard errors. For example, [3-5] all calculate standard errors or confidence intervals by a particular bootstrap method, and compare their results to the analytic standard errors explicitly noting the problem of bias, but do not attempt any refinement of the bootstrap. One purpose of this paper is to compare a number of techniques, including several "refined" and "unrefined" bootstraps, on an econometric example, with the hope of stimulating the use of these techniques in other econometric contexts.
Our second purpose is specific to the example. A longstanding issue in quantitative economic history is whether, in 1929, the United States automobile market was tending to "saturation". Such saturation by itself could possibly have led to the subsequent sharp reduction in the demand for new automobiles and if similar conditions prevailed in other durable goods industries, this could have been a contributing factor in the onset of the Great Depression. In their pioneering study, Mercer and Morgan [6, hereafter MM] find evidence for saturation using regression estimates of the demand for automobiles. Using a framework similar but not identical to MM, George and Oksanen [7, hereafter GO] suggest that evidence from equations adjusted to compensate for parameter instability tends to support the hypothesis of no saturation.
However, despite the econometric nature of these investigations, neither study supplies formal statistical tests of the saturation hypothesis, relying instead on informal rules to evaluate