This paper presents new identifiability conditions for the Cox proportional hazard model for duration data when unobserved person specific variables are present. We compare our conditions with those presented by Elbers and Ridder. We also present identifiability conditions for a rich class of parametric hazard models without regressor variables.

James J. Heckman, Thomas E. Macurdy; A Life Cycle Model of Female Labour Supply, The Review of Economic Studies, Volume 47, Issue 1, 1 January 1980, Pages 47–74

This paper develops the method of matching as an econometric evaluation estimator. A rigorous distribution theory for kernel-based matching is presented. The method of matching is extended to more general conditions than the ones assumed in the statistical literature on the topic. We focus on the method of propensity score matching and show that it is not necessarily better, in the sense of reducing the variance of the resulting estimator, to use the propensity score method even if propensity score is known. We extend the statistical literature on the propensity score by considering the case when it is estimated both parametrically and nonparametrically. We examine the benefits of separability and exclusion restrictions in improving the efficiency of the estimator. Our methods also apply to the econometric selection bias estimator.

This paper considers whether it is possible to devise a nonexperimental procedure for evaluating a prototypical job training programme. Using rich nonexperimental data, we examine the performance of a two-stage evaluation methodology that (a) estimates the probability that a person participates in a programme and (b) uses the estimated probability in extensions of the classical method of matching. We decompose the conventional measure of programme evaluation bias into several components and find that bias due to selection on unobservables, commonly called selection bias in econometrics, is empirically less important than other components, although it is still a sizeable fraction of the estimated programme impact. Matching methods applied to comparison groups located in the same labour markets as participants and administered the same questionnaire eliminate much of the bias as conventionally measured, but the remaining bias is a considerable fraction of experimentally-determined programme impact estimates. We test and reject the identifying assumptions that justify the classical method of matching. We present a nonparametric conditional difference-in-differences extension of the method of matching that is consistent with the classical index-sufficient sample selection model and is not rejected by our tests of identifying assumptions. This estimator is effective in eliminating bias, especially when it is due to temporally-invariant omitted variables.

The conventional approach to social programme evaluation focuses on estimating mean impacts of programmes. Yet many interesting questions regarding the political economy of programmes, the distribution of programme benefits and the option values conferred on programme participants require knowledge of the distribution of impacts, or features of it. This paper presents evidence that heterogeneity in response to programmes is empirically important and that classical probability inequalities are not very informative in producing estimates or bounds on the distribution of programme impacts. We explore two methods for supplementing the information in these inequalities based on assumptions about participant decision-making processes and about the strength in dependence between outcomes in the participation and non-participation states. Dependence is produced as a consequence of rational choice by participants. We test for stochastic rationality among programme participants and present and implement methods for estimating the option values of social programmes.