The paper develops a model of retirement based on the option value of continuing to work.Continuing to work maintains the option of retiring on more advantageous terms later.The model is used to estimate the effects on retirement of firm pension plan provisions.Typical defined benefit pension plans in the United States provide very substantial incentives to remain with the firm until some age, often the early retirement age, and then a strong incentive to leave the firm thereafter.(This may be a major reason for the rapidly declining labor force participation rates of older workers in the United States.)The model fits firm retirement data very well; it captures very closely the sharp discontinuous jumps in retirement rates at specific ages.The model is used to simulate the effect on retirement of potential changes in pension plan provisions.Increasing the age of early retirement from 55 to 60, for example, would reduce firm departure rates between ages 50 and 59 by almost forty percent.

In the general structural equation model only the direction of the vector of coefficients of the endogenous variables is determined.The traditional normalization rule defines the coefficients that are of interest but should not be embodied in the estimation procedure: we show that the properties of the traditionally defined ordinary least squares and two stage least squares estimators are distorted by their dependence on the normalization rule.Symmetrically normalized analogues of these estimators are defined and are shown to have essentially similar properties to those of the limited information maximum likelihood estimator.

This paper considers estimation and hypothesis testing in linear time series when some or all of the variables have (possibly multiple) unit roots. The motivating example is a vector autoregression with some unit roots in the companion matrix, which might include polynomials in time as regressors. Parameters that can be written as coefficients on mean zero, nonintegrated regressors have jointly normal asymptotic distribution, converging at the rate of T(superscript "one-half") In general, the other coefficients (including the coefficient on polynomials in time), and associated t and F test statistics, have nonstandard asymptotic distributions.

EMPIRICAL STUDIES OF TWO SIDED MATCHING have so far concentrated on markets in which certain kinds of market failures were addressed by resorting to centralized, deterministic matching procedures. Loosely speaking, the results of these studies are that those centralized procedures which achieved stable outcomes resolved the market failures, while those markets organized through procedures that yielded unstable outcomes continued to fail.2 So the market failures seem to be associated with instability of the outcomes. But many entry-level labor markets and other two-sided matching situations don't employ centralized matching procedures, and yet aren't observed to experience such failures. So we can conjecture that at least some of these markets may reach stable outcomes by means of decentralized decision making. And decentralized decision making in complex environments presumably introduces some randomness into what matchings are achieved. However, as far as we are aware, no nondeterministic models leading to stable outcomes have yet been studied. The present paper demonstrates that, starting from an arbitrary matching, the process of allowing randomly chosen blocking pairs to match will converge to a stable matching with probability one. (This resolves an open question raised by Knuth (1976), who showed that such a process may cycle.) Furthermore, every stable matching can arise