Determinacy in the Linear Model: Gauss to Bose and Koopmans

Gauss showed that least squares fails to produce a unique solution only when the problem is indeterminate. This note considers his argument and the notion of indeterminacy underlying it. It also relates the argument to twentieth-century discussions of estimability and identifiability.     

商业银行不良贷款的宏观经济影响因素分析

商业银行不良贷款总额一直在高位徘徊,成为制约中国商业银行发展的重要因素之一.通过收集2004年1季度～2009年1季度的最新数据,运用相关分析、共线性诊断、主成分回归分析等方法建立模型,探讨宏观经济因素对商业银行不良贷款的影响和贡献率.由实证结论发现:宏观经济因素与不良贷款余额负相关;社会消费品零售总额、进出口总额对降低商业银行不良贷款的贡献度最大,每增加1%会导致不良贷款平均降低0.0249%和0.0248%;宏观经济因素对降低不良贷款有正向促进作用,因此,在操作层面上可通过扩大内需、改善商业银行的外部信用环境等措施间接降低商业银行的不良贷款.     

Business performance of airports: Non-aviation revenues and their determinants

Management of non-core commercial activities has become a key issue amongst the leverages for improving modern airport industry. Today airports have increased dramatically their dependence on non-aeronautical revenues, which on average account for half of all revenues with this share being highly heterogeneous across regions and airports. Using a dataset of German airports, this paper discusses the improvement of commercial revenues by exploring its determinants. Previous contributions assessed the impact of a selected set of variables non-aviation revenues. Such approach was mainly the effect of multicollinearity, as the majority of relevant variables are strongly correlated to the size of the structures. We address this issue by using ridge regression and partial least squares. Results suggest the potential conflict of non-aviation revenues per passenger and per square meter with the need to expand the number of passengers.     

Standardization of Variables and Collinearity Diagnostic in Ridge Regression

Ridge estimation (RE) is an alternative method to ordinary least squares when there exists a collinearity problem in a linear regression model. The variance inflator factor (VIF) is applied to test if the problem exists in the original model and is also necessary after applying the ridge estimate to check if the chosen value for parameter k has mitigated the collinearity problem. This paper shows that the application of the original data when working with the ridge estimate leads to non‐monotone VIF values. García et al. (2014) showed some problems with the traditional VIF used in RE. We propose an augmented VIF, VIF_R(j,k), associated with RE, which is obtained by standardizing the data before augmenting the model. The VIF_R(j,k) will coincide with the VIF associated with the ordinary least squares estimator when k = 0. The augmented VIF has the very desirable properties of being continuous, monotone in the ridge parameter and higher than one.     

Sampling error and the joint estimation of imputation credit value and cash dividend value

The value of imputation credits can only be estimated jointly with the value of cash dividends. We show that random variation across samples leads to estimates of credit value that move in the opposite direction to estimates of cash value. Derivative prices suggest a value for credits of 0.01 to 0.20 (0.01 to 0.07 if cash is worth 0.94, and 0.13 to 0.20 if cash is worth 0.87). Ex-dividend prices suggest a value for credits of 0.23 to 0.46 (0.23 to 0.36 if cash is worth 0.85, and 0.33 to 0.46 if cash is worth 0.75).