Postel-Vinay and Robin's (2002) sequential auction model is extended to allow for aggregate productivity shocks. Workers exhibit permanent differences in ability while firms are identical. Negative aggregate productivity shocks induce job destruction by driving the surplus of matches with low ability workers to negative values. Endogenous job destruction coupled with worker heterogeneity thus provides a mechanism for amplifying productivity shocks that offers an original solution to the unemployment volatility puzzle (Shimer (2005)). Moreover, positive or negative shocks may lead employers and employees to renegotiate low wages up and high wages down when agents' individual surpluses become negative. The model delivers rich business cycle dynamics of wage distributions and explains why both low wages and high wages are more procyclical than wages in the middle of the distribution.

In this paper, we document whether and how much the equalizing force of earnings mobility has changed in France in the 1990's. For this purpose, we use a representative three-year panel, the French Labour Force Survey. We develop a model of earnings dynamics that combines a flexible specification of marginal earnings distributions (to fit the large cross-sectional dimension of the data) with a tight parametric representation of the dynamics (adapted to the short time-series dimension). Log earnings are modelled as the sum of a deterministic component, an individual fixed effect and a transitory component which is assumed first-order Markov. The transition probability of the transitory component is modelled as a one-parameter Plackett copula. We estimate this model using a sequential expectation-maximization algorithm. We exploit the estimated model to study employment/earnings inequality in France over the 1990–2002 period. We show that, in phase with business-cycle fluctuations (a recession in 1993 and two peaks in 1990 and 2000), earnings mobility decreases when cross-section inequality and unemployment risk increase. We simulate individual earnings trajectories and compute present values of lifetime earnings for various horizons. Inequality presents a hump-shaped evolution over the period, with a 9% increase between 1990 and 1995 and a decrease afterwards. Accounting for unemployment yields an increase of 11%. Moreover, this increase is persistent, as it translates into a 12% increase in the variance of log present values. The ratio of inequality in present values to inequality in one-year earnings, a natural measure of immobility or of the persistence of inequality, remains remarkably constant over the business cycle.

In this paper we study the evolution of lifetime labour income inequality by constructing present value life cycle measures that incorporate both earnings and employment risk. We find that, even though lifetime income inequality is 40% less than earnings inequality, the total increase in lifetime income inequality over the past 20 years is the same as earnings inequality. While the total increase is the same, the pathways there differ with earnings inequality experiencing a steady increase and lifetime income inequality increasing in spurts particularly in the latter half of the 1990s. Finally, we find the changes in lifetime income inequality are primarily driven by changes in earnings mobility and changes in the earnings distribution itself, changes in employment risk and the composition of the sample, such as the shift toward attaining more education and the ageing population, do not play a large role.