Identifying the Hand of the Past: Distinguishing State Dependence from Heterogeneity

A basic problem in social science is to ascertain the importance of initial endowments on subsequent outcomes of a dynamic process. Interest in this topic centers on two distinct issues: (a) Do initial endowments have a temporally persistent effect on outcomes (i.e., is there "heterogeneity")?; (b) Are the effects of initial endowments attenuated or accentuated by subsequent experiences of the process being studied or by related processes (i.e., is there "state dependence")? These two questions show up in a variety of contexts. 1) The importance of family background on a person's subsequent education and earnings is a hotly debated topic. Do market or nonmarket mechanisms reinforce or diminish initial endowments? 2) The incidence of criminal activity is concentrated among a small population of repeated offenders. Are certain persons "prone" to criminality, or does crime breed crime? 3) Are persons who experience unemployment more likely to experience future unemployment due to loss of work experience or market stigma? 4) Does early entry into an industry confer an advantage of incumbency, or does it merely proxy the basic managerial and innovative ability of early entrants? Many formal models of state-dependent processes or processes with persistent effects of initial conditions have been formulated. Invariance of steady states to initial endowments was viewed as a desirable feature of an economic model in the 1960's and 1970's. Path-dependent synergism and nonergodicity are fashionable features of models today. Is the choice between models with long-run dependence on initial conditions and those without solely a matter of intellectual esthetics? Can data discriminate between these two classes of models? How many economically extraneous statistical "regularity conditions" have to be imposed in order to distinguish between these models? How many and what kind of maintained assumptions are required in order to let the data speak on these important questions? In this paper I focus on one nonergodic model that receives much attention in the literature-the model of "duration dependence" and "heterogeneity" discussed by Herbert Silcock (1954) and also examined by Tony Lancaster (1979), Chris Elbers and Geert Ridder (1982), myself and Burton Singer (1984), and myself and Bo Honore (1989).