# A THEORETICAL AND EMPIRICAL ANALYSIS OF THE DURATION OF UNEMPLOYMENT

#### Abstract

Recent considerations of the duration of unemployment have analyzed this concept within the framework of a steady state economy with constant flows into unemployment. These studies concentrate on deriving estimates of duration consistent with the steady-state level of unemployment; namely, the total length of time an individual entering unemployment can expect to remain in that state before leaving. Termed the expected completed spell duration of an entering cohort, these studies explicitly or implicitly characterize the unemployed in terms of having constant probabilities of remaining unemployed over the length of their spells. A major focus of these analyses is the fact that the estimates of unemployment duration provided by the Bureau of Labor Statistics (BLS) only provide information on the average age of spells currently in existence. Since BLS data does not estimate the total time unemployed of individuals, the published duration measures may be biased relative to the expected completed spell duration for entering cohorts. The identification and measurement of bias in BLS duration data has been a chief issue of concern. A pathbreaking study by Salant utilized renewal theory to estimate these biases. His estimation technique required the assumption of steady state inflows into unemployment and as well a distribution of constant unemployment remaining probability patterns across the pool of the unemployed. Salant derives a theoretical relationship between the BLS type measure of duration and the expected completed spell duration of entering cohorts. This relationship has served as the cornerstone for numerous other studies of duration in the literature; including studies which attribute greater relative importance to another steady--state duration measure--the expected completed spell duration of the currently unemployed. This dissertation seeks to construct estimates of duration which are consistent with theory but do not require the restrictive assumptions presently used for estimation. In particular, we seek duration measures which do not restrict the behavior of individual probability patterns to being constant. As well, using presently unpublished BLS survey data we seek to construct duration estimates sensitive to the non-steady state nature of inflows into unemployment. By constructing such statistic we are able to analyze many of the testable implications arising from the current literature on the duration of unemployment. Included in this analyses are tests of the implications derived from assuming constant probability patterns of remaining unemployed for individuals and the appropriateness of using Salant's steady-state relationship between the duration of entering cohorts and the currently unemployed. To facilitate this analysis we develop the concept of duration in a rigorous mathematical framework. Subtler themes develop as a result of this effort. In particular, we evaluate the effects of the discrete monthly basis for BLS surveys on the theoretical and empirical analysis of duration. As well, we formalize in this mathematical setting certain duration measures previously intuited in the literature, such as the expected completed spell of ending cohorts and of the currently unemployed.

#### Degree

Ph.D.

#### Subject Area

Economics

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