Partial Identification of State Dependence

Many empirical questions in economics require the answer to some form of the following question: To what extent do past outcomes causally a�ect current and future out- comes? Such a causal e�ect is commonly referred to as state dependence. State dependence can arise in (e.g.) employment processes if past unemployment has a causal e�ect on cur- rent or future unemployment through signalling processes in hiring (\stigma" or \scarring" e�ects). Other economic applications abound (see proposal). It is di�cult to identify state dependence with observational panel data. The funda- mental problem is that the e�ect of past outcomes will confound with temporally persistent unobservable heterogeneity across agents. For example, observing in a panel that previously unemployed agents are less likely to be employed could be due to scarring e�ects, but it could also result if unemployed agents are less likely to be employed due to other unobservable factors such as preferences or productivity. This problem of distinguishing state dependence from persistent unobservable hetero- geneity in economic panel data traces back to the work of Heckman (1978, 1981). To date, the vast majority of solutions to this problem use variants of highly-parameterized dynamic binary choice models. A number of objections can be raised against these models, in par- ticular that they depend on choosing arbitrary and typically unjusti�able functional forms for the distribution(s) of unobserved heterogeneity. It is widely recognized by empirical researchers that such arbitrary functional form restrictions are unattractive for answering questions about causality, however there exist relatively few nonparametric alternatives for the particular problem of identifying state dependence in observational panel data. The goal of this proposal is to develop and apply transparent nonparametric approaches for identifying state dependence from unobserved heterogeneity. Owing to the di�culty of point identifying state dependence, the proposed methods use partial identi�cation tech- niques. In particular, I propose a new dynamic potential outcomes (DPO) model, study its properties, and apply it to questions of state dependence in employment outcomes.