Threshold models have a wide variety of applications in economics. Direct applications include models of separating and multiple equilibria. Other applications include empirical sample splitting when the sample split is based on a continuously-distributed variable such as firm size. In addition, threshold models may be used as a parsimonious strategy for nonparametric function estimation. For example, the threshold autoregressive model (TAR) is popular in the nonlinear time series literature. Threshold models also emerge as special cases of more complex statistical frameworks, such as mixture models, switching models, Markov switching models, and smooth transition threshold models. It may be important to understand the statistical properties of threshold models as a preliminary step in the development of statistical tools to handle these more complicated structures. Despite the large number of potential applications, the statistical theory of threshold estimation is undeveloped. It is known that threshold estimates are super-consistent, but a distribution theory useful for testing and inference has yet to be provided. This paper develops a statistical theory for threshold estimation in the regression context. We allow for either cross-section or time series observations. Least squares estimation of the regression parameters is considered. An asymptotic distribution theory for the regression estimates (the threshold and the regression slopes) is developed. It is found that the distribution of the threshold estimate is nonstandard. A method to construct asymptotic confidence intervals is developed by inverting the likelihood ratio statistic. It is shown that this yields asymptotically conservative confidence regions. Monte Carlo simulations are presented to assess the accuracy of the asymptotic approximations. The empirical relevance of the theory is illustrated through an application to the multiple equilibria growth model of Durlauf and Johnson (1995).

This study examines the behavior of spreads paid in firm underwritten seasoned common stock offerings and straight bond offerings. Estimates indicate that up to 85% of the spread is variable cost and that the marginal spread is rising. Further, offerings that are likely to require greater underwriting services encounter higher marginal spreads. These findings are consistent with there being a family of U-shaped spreads, with lower quality offerings priced on higher spreads, unlike the economies of scale view of spreads. They agree with the views that underwriters provide valuable services and that the marginal cost of external finance is rising.

Journal Article Are There Economies of Scale in Underwriting Fees? Evidence of Rising External Financing Costs Get access Oya Altınkılıç, Oya Altınkılıç Virginia Tech Search for other works by this author on: Oxford Academic Google Scholar Robert S. Hansen Robert S. Hansen Virginia Tech Address correspondence to Robert S. Hansen, Department of Finance, Pamplin College of Business, Virginia Tech, Blacksburg, VA 24061, or e-mail: [email protected]. Search for other works by this author on: Oxford Academic Google Scholar The Review of Financial Studies, Volume 13, Issue 1, January 2000, Pages 191–218, https://doi.org/10.1093/rfs/13.1.191 Published: 15 June 2015