Resumen
Using hazard analysis procedures, this study undertakes a longitudinal examination of Israeli Nonprofit Organizations? (NPOs?) financial vulnerability arising from governmental funding instability. Funding instability is characterized by time-at-risk, which measures the level of financial instability faced by an NPO and reflects the different funding situations it encounters. The vulnerability is expressed by the hazard rate (HR), which measures the speed at which NPOs? close at a given point in time. The probability of an NPO failure is then estimated. The improvements presented in the current work are concerned with the methods of estimation of time at risk, which is a key variable in the hazard analysis, and testing a robustness of the method. The generalized time-at-risk, which measures the ?level of instability? more consistently reflecting different situations encountered by a NPO, is introduced. The definition of generalized time-at-risk contains arbitrary coefficients whose values the current study determines using some optimization procedure. The optimization incorporates the idea of testing a possibility of using the results for predicting financial vulnerability by dividing the set of 2660 NPOs into two approximately equivalent samples. The coefficients in the time-at-risk definition are optimized by minimizing the average distance between the HR?time-at-risk curves based on these two samples.