Errors-in-variables jump regression using local clustering.

Errors-in-variables (EIV) regression is widely used in econometric models. The statistical analysis becomes challenging when the regression function is discontinuous and the distribution of measurement error is unknown. In the literature, most existing jump regression methods either assume that there is no measurement error involved or require that jumps are explicitly detected before the regression function can be estimated. In some applications, however, the ultimate goal is to estimate the regression function and to preserve the jumps in the process of estimation. In this paper, we are concerned with reconstructing jump regression curve from data that involve measurement error. We propose a direct jump-preserving method that does not explicitly detect jumps. The challenge of restoring jump structure masked by measurement error is handled by local clustering. Theoretical analysis shows that the proposed curve estimator is statistically consistent. A numerical comparison with an existing jump regression method highlights its jump-preserving property. Finally, we demonstrate our method by an application to a health tax policy study in Australia.

A quantile regression approach to panel data analysis of health-care expenditure in Organisation for Economic Co-operation and Development countries.

This paper investigates the variation in the effects of various determinants on the per capita health-care expenditure. A total of 28 Organisation for Economic Co-operation and Development countries are studied over the period 1990-2012, employing an instrumental variable quantile regression method for a dynamic panel model with fixed effects. The results show that the determinants of per capita health-care expenditure growth, involving the growth of lagged health spending, of per capita gross domestic product (GDP), of physician density, of elderly population, of life expectancy, of urbanization, and of female labor force participation, do vary with the conditional distribution of the health-care expenditure growth, while the changing patterns are dissimilar. Moreover, we show that Baumol's model of "unbalanced growth" has a significantly positive effect on per capita health spending growth, and its effect is quite stable over the entire distribution. However, the correlation between the components (wage growth and labor productivity growth) of the "Baumol variable" and health expenditure growth is more varied. As a comparison, only the growth of lagged health spending, per capita GDP, and the Baumol variable (or its components) are found related to health spending growth in conditional mean regressions. The prediction results were also quite different between the quantile regression dynamic panel instrumental variable models and linear panel data models. More attention needs to be paid to the varying influence of determinants in health expenditure study.