The Discontinuous Nature of Kriging Interpolation for Digital Terrain Modeling

Kriging is a widely employed method for interpolating and estimating elevations from digital elevation data. Its place of prominence is due to its elegant theoretical foundation and its convenient practical implementation. From an interpolation point of view, kriging is equivalent to a thin-plate spline and is one species among the many in the genus of weighted inverse distance methods, albeit with attractive properties. However, from a statistical point of view, kriging is a best linear unbiased estimator and, consequently, has a place of distinction among all spatial estimators because any other linear estimator that performs as well as kriging (in the least squares sense) must be equivalent to kriging, assuming that the parameters of the semivariogram are known. Therefore, kriging is often held to be the gold standard of digital terrain model elevation estimation. However, I prove that, when used with local support, kriging creates discontinuous digital terrain models, which is to say, surfaces with “rips” and “tears” throughout them. This result is general; it is true for ordinary kriging, kriging with a trend, and other forms. A U.S. Geological Survey (USGS) digital elevation model was analyzed to characterize the distribution of the discontinuities. I show that the magnitude of the discontinuity does not depend on surface gradient but is strongly dependent on the size of the kriging neighborhood.

Corporate Tax Avoidance and High Powered Incentives

This paper analyzes the links between corporate tax avoidance, the growth of highpowered incentives for managers, and the structure of corporate governance. We develop and test a simple model that highlights the role of complementarities between tax sheltering and managerial diversion in determining how high-powered incentives influence tax sheltering decisions. The model generates the testable hypothesis that firm governance characteristics determine how incentive compensation changes sheltering decisions. In order to test the model, we construct an empirical measure of corporate tax avoidance - the component of the book-tax gap not attributable to accounting accruals - and investigate the link between this measure of tax avoidance and incentive compensation. We find that, for the full sample of firms, increases in incentive compensation tend to reduce the level of tax sheltering, suggesting a complementary relationship between diversion and sheltering. As predicted by the model, the relationship between incentive compensation and tax sheltering is a function of a firm.s corporate governance. Our results may help explain the growing cross-sectional variation among firms in their levels of tax avoidance, the .undersheltering puzzle,. and why large book-tax gaps are associated with subsequent negative abnormal returns.