Censoring Due to Death, cont'd 

 John F. Friedman 

 The problem of "censoring by death" also surfaces up in a number of economic contexts.  For instance, firms that go bankrupt as a result of poor corporate policies will not appear in many datasets, making any analysis of the impact of other financial events biased upwards.  This problem has particularly plagued the literature on the impacts of corporate restructuring and leveraged buyouts (LBOs) of distressed firms.  Since these firms are at high risk of failure by nature of their inclusion in the study in the first place, such firms exit the sample at high frequency, and the benefits of restructuring and LBOs may be overstated. 

 One can theoretically correct for this problem by modeling the ways in which the sample selection occurs, but these approaches have performed poorly in many economic settings due to the sensitivity of the results to the parametric assumptions of the econometric model.  For instance, the "Heckman selection correction" - brought into Economics by Nobel laureate James Heckman in 1979 - models the death process as a first stage Probit based on observable characteristics.  By estimating this first stage, one can correct for the lost observations.  Bob LaLonde (1986) later tested this model by comparing the results from a job training study with random assignment to the results one would have gotten had one used Heckman's method on the treated group.  Though the selection correction performed better than many alternative methods, such as matching or differences-in-differences, the estimates were rather imprecise and confidence intervals mismeasured.  In this case, the problem is the joint assumption of normality and selection entirely on observables.  Though more flexible models have come into Economics in recent years - the Propensity Score, for instance – these too have proven sensitive to the particular model properties in many applications. 

 Though perhaps an old-fashioned solution, the studies in economics that best avoid this problem have simply endeavored to correct for the sample selection problem by collecting otherwise unavailable data on firm deaths in the sample.  These samples are often smaller, permitting less broad analysis, but effectively mitigate the selection by death problem.